Subgroups — C₂×C₃×C₃⋊D₃×AGL(1,ℤ/8) #72269002

Order 3456.

11512 conjugacy classes of subgroups.

The subgroup lattice has 1544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃³×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#64158	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#64141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₃⋊D₃×AGL(1,ℤ/8)	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#64123	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×SD₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#64120	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×D₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#64117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×M₁₆×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×D₃×AGL(1,ℤ/8)	—	3	4	no	maximal
14	C₂×C₃⋊D₃×AGL(1,ℤ/8)	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂⁴×C₃×C₃⋊D₃	—	2	1	no	—
16	C₂×C₃³×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×#638	—	2	1	no	—
19	C₃×#41×C₃⋊D₃	—	2	4	no	—
20	C₃×#41×C₃⋊D₃	C₂²	1	8	yes	complemented
21	C₂×C₃×#3832	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×Q₈×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#3830	—	2	1	no	—
24	C₂×C₃×#3830	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×D₄×C₃⋊D₃	—	2	1	no	—
26	C₂×C₃×D₄×C₃⋊D₃	—	2	1	no	—
27	C₂×C₃×D₄×C₃⋊D₃	—	2	4	no	—
28	C₂×C₃×D₄×C₃⋊D₃	—	2	1	no	—
29	C₂×C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	—
30	C₂×C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	complemented
31	C₂×C₃×D₄×C₃⋊D₃	C₂²	1	8	yes	complemented
32	C₂×C₃×D₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#3828	—	2	1	no	—
34	C₂×C₃×#3828	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₃×C₄×C₃⋊D₃	—	2	1	no	—
37	C₂²×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
38	C₃³×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
39	C₂×C₃³×SD₁₆	C₂²	1	2	yes	complemented
40	C₂×C₃³×D₈	C₂²	1	2	yes	complemented
41	C₂×C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₃×#64158	C₂²	1	8	yes	complemented
43	C₂×C₃×#3755	C₂²	1	2	yes	complemented
44	C₂×C₃×#3754	C₂²	1	2	yes	complemented
45	C₃×#64141	C₂²	1	8	yes	complemented
46	C₂×C₃×#3753	C₂²	1	2	yes	complemented
47	C₂×C₃×#3753	C₂²	1	2	yes	complemented
48	C₂×C₃×#3748	C₂²	1	1	yes	characteristic, complemented
49	C₃×#64123	C₂²	1	16	yes	complemented
50	C₃×SD₁₆×C₃⋊D₃	C₂²	1	16	yes	complemented
51	C₃×#64120	C₂²	1	16	yes	complemented
52	C₃×D₈×C₃⋊D₃	C₂²	1	16	yes	complemented
53	C₃×#64117	C₂²	1	8	yes	complemented
54	C₃×M₁₆×C₃⋊D₃	C₂²	1	8	yes	complemented
55	C₂×C₃×#3745	C₂²	1	2	yes	complemented
56	C₂×C₃×#3744	C₂²	1	2	yes	complemented
57	C₂×C₃×#3743	C₂²	1	2	yes	complemented
58	C₂×C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	complemented
59	C₂×#41×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃×#41	—	3	4	no	—
62	C₂²×C₃×D₃×D₄	—	3	4	no	—
63	C₂×C₃²×AGL(1,ℤ/8)	—	2	4	no	—
64	C₂×C₃²×AGL(1,ℤ/8)	D₃	1	4	yes	complemented
65	C₂×C₃²×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#64158	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#64141	C₂×C₃	1	1	yes	characteristic, complemented
68	C₃⋊D₃×AGL(1,ℤ/8)	C₂×C₃	1	16	yes	direct product factor
69	C₂×#64123	C₂×C₃	1	2	yes	complemented
70	C₂×SD₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
71	C₂×#64120	C₂×C₃	1	2	yes	complemented
72	C₂×D₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
73	C₂×#64117	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×M₁₆×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₃×#949	—	3	4	no	—
76	C₂×C₃×#932	—	3	4	no	—
77	C₃×D₃×AGL(1,ℤ/8)	—	3	64	no	—
78	C₂×C₃×#914	—	3	8	no	—
79	C₂×C₃×D₃×SD₁₆	—	3	8	no	—
80	C₂×C₃×#911	—	3	8	no	—
81	C₂×C₃×D₃×D₈	—	3	8	no	—
82	C₂×C₃×#908	—	3	4	no	—
83	C₂×C₃×D₃×M₁₆	—	3	4	no	—
84	C₂⁴×C₃³	—	2	1	no	—
85	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
86	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
87	C₂³×C₃×C₃⋊D₃	—	2	2	no	—
88	C₂³×C₃×C₃⋊D₃	—	2	2	no	—
89	C₂³×C₃×C₃⋊D₃	—	2	8	no	—
90	C₂³×C₃×C₃⋊D₃	—	4	8	no	—
91	C₂³×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
92	C₃³×#41	—	2	2	no	—
93	C₃³×#41	C₂³	1	4	yes	complemented
94	C₂×C₃³×Q₈	C₂³	1	1	yes	characteristic, complemented
95	C₂×C₃³×D₄	—	2	1	no	—
96	C₂×C₃³×D₄	—	2	1	no	—
97	C₂×C₃³×D₄	—	2	2	no	—
98	C₂×C₃³×D₄	C₂³	1	2	yes	—
99	C₂×C₃³×D₄	C₂³	1	4	yes	complemented
100	C₂×C₃³×D₄	C₂³	1	1	yes	characteristic, complemented
101	C₂²×C₃³×C₄	—	2	1	no	—
102	C₂²×C₃³×C₄	C₂³	1	1	yes	characteristic
103	C₂×C₃×#638	—	2	1	no	—
104	C₂×C₃×#638	—	2	1	no	—
105	C₂×C₃×#638	—	2	1	no	—
106	C₂×C₃×#638	—	2	2	no	—
107	C₂×C₃×#638	—	2	2	no	—
108	C₂×C₃×#638	—	2	8	no	—
109	C₂²×C₃×C₃⋊Dic₃	—	2	1	no	—
110	C₂²×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
111	C₃×#3832	—	2	2	no	—
112	C₃×#3832	C₂³	1	4	yes	complemented
113	C₃×Q₈×C₃⋊D₃	—	2	2	no	—
114	C₃×Q₈×C₃⋊D₃	C₂³	1	4	yes	complemented
115	C₃×#3830	—	2	8	no	—
116	C₃×#3830	—	2	2	no	—
117	C₃×#3830	C₂³	1	4	yes	complemented
118	C₃×D₄×C₃⋊D₃	—	2	8	no	—
119	C₃×D₄×C₃⋊D₃	—	2	4	no	—
120	C₃×D₄×C₃⋊D₃	—	2	8	no	—
121	C₃×D₄×C₃⋊D₃	—	2	8	no	—
122	C₃×D₄×C₃⋊D₃	—	2	4	no	—
123	C₃×D₄×C₃⋊D₃	—	2	2	no	—
124	C₃×D₄×C₃⋊D₃	C₂³	1	8	yes	—
125	C₃×D₄×C₃⋊D₃	C₂³	1	8	yes	complemented
126	C₃×D₄×C₃⋊D₃	C₂³	1	4	yes	complemented
127	C₃×#3828	—	2	2	no	—
128	C₃×#3828	—	2	8	no	—
129	C₃×#3828	C₂³	1	4	yes	complemented
130	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
131	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
132	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
133	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
135	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic, complemented
136	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
137	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
138	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
139	C₂×C₃×C₄×C₃⋊D₃	—	2	8	no	—
140	C₂×C₃×C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₃⋊D₃	D₄	1	4	yes	—
143	C₂×C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄×C₃⋊D₃	C₂³	1	4	yes	—
146	C₂×C₃×#634	—	2	1	no	—
147	C₂×C₃×#634	C₂³	1	1	yes	characteristic, complemented
148	C₃³×SD₁₆	C₂³	1	8	yes	complemented
149	C₃³×D₈	C₂³	1	8	yes	complemented
150	C₃³×M₁₆	C₂³	1	4	yes	complemented
151	C₂×C₃³×C₈	C₂³	1	2	yes	complemented
152	C₃×#3755	C₂³	1	8	yes	complemented
153	C₃×#3754	C₂³	1	8	yes	complemented
154	C₃×#3753	C₂³	1	8	yes	complemented
155	C₃×#3753	C₂³	1	8	yes	complemented
156	C₃×#3748	C₂³	1	4	yes	complemented
157	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	complemented
158	C₃×#3745	C₂³	1	8	yes	complemented
159	C₃×#3744	C₂³	1	8	yes	complemented
160	C₃×#3743	C₂³	1	8	yes	complemented
161	C₃×C₈×C₃⋊D₃	C₂³	1	8	yes	complemented
162	C₂²×C₃×AGL(1,ℤ/8)	—	9	1	no	—
163	C₂×D₃×AGL(1,ℤ/8)	—	3	4	no	—
164	C₂⁴×C₃⋊D₃	—	2	1	no	—
165	C₂⁴×C₃×D₃	—	6	4	no	—
166	C₂×C₃²×#41	—	2	4	no	—
167	C₂×C₃²×#41	C₂×D₃	1	4	yes	complemented
168	C₂×C₃²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂²×C₃²×D₄	—	2	4	no	—
170	C₂²×C₃²×D₄	C₂×D₃	1	4	yes	complemented
171	C₂²×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂²×#638	—	2	1	no	—
173	#41×C₃⋊D₃	—	2	4	no	—
174	#41×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
175	C₂×#3832	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₂×Q₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×#3830	—	2	1	no	—
178	C₂×#3830	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂×D₄×C₃⋊D₃	—	2	1	no	—
180	C₂×D₄×C₃⋊D₃	—	2	1	no	—
181	C₂×D₄×C₃⋊D₃	—	2	4	no	—
182	C₂×D₄×C₃⋊D₃	—	2	1	no	—
183	C₂×D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
184	C₂×D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
185	C₂×D₄×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
186	C₂×D₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×#3828	—	2	1	no	—
188	C₂×#3828	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂²×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂²×C₄×C₃⋊D₃	—	2	1	no	—
191	C₂²×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
192	C₂²×C₃×#67	—	6	4	no	—
193	C₃×D₃×#41	—	3	32	no	—
194	C₃×D₃×#41	—	6	16	no	—
195	C₂×C₃×#239	—	3	4	no	—
196	C₂×C₃×D₃×Q₈	—	3	4	no	—
197	C₂×C₃×#237	—	3	4	no	—
198	C₂×C₃×#237	—	6	4	no	—
199	C₂×C₃×D₃×D₄	—	3	8	no	—
200	C₂×C₃×D₃×D₄	—	3	8	no	—
201	C₂×C₃×D₃×D₄	—	3	4	no	—
202	C₂×C₃×D₃×D₄	—	3	32	no	—
203	C₂×C₃×D₃×D₄	—	6	4	no	—
204	C₂×C₃×D₃×D₄	—	6	4	no	—
205	C₂×C₃×D₃×D₄	—	6	4	no	—
206	C₂×C₃×D₃×D₄	—	6	16	no	—
207	C₂×C₃×#235	—	3	4	no	—
208	C₂×C₃×#235	—	6	4	no	—
209	C₂²×C₃×D₁₂	—	3	4	no	—
210	C₂²×C₃×C₄×D₃	—	3	4	no	—
211	C₂²×C₃×C₄×D₃	—	6	4	no	—
212	C₃²×AGL(1,ℤ/8)	—	2	32	no	—
213	C₃²×AGL(1,ℤ/8)	C₂×D₃	1	32	yes	complemented
214	C₃²×AGL(1,ℤ/8)	C₂²×C₃	1	8	yes	complemented
215	C₂×C₃²×SD₁₆	—	2	8	no	—
216	C₂×C₃²×SD₁₆	C₂×D₃	1	8	yes	complemented
217	C₂×C₃²×SD₁₆	C₂²×C₃	1	2	yes	complemented
218	C₂×C₃²×D₈	—	2	8	no	—
219	C₂×C₃²×D₈	C₂×D₃	1	8	yes	complemented
220	C₂×C₃²×D₈	C₂²×C₃	1	2	yes	complemented
221	C₂×C₃²×M₁₆	—	2	4	no	—
222	C₂×C₃²×M₁₆	C₂×D₃	1	4	yes	complemented
223	C₂×C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
224	#64158	C₂²×C₃	1	8	yes	complemented
225	C₂×#3755	C₂²×C₃	1	2	yes	complemented
226	C₂×#3754	C₂²×C₃	1	2	yes	complemented
227	#64141	C₂²×C₃	1	8	yes	complemented
228	C₂×#3753	C₂²×C₃	1	2	yes	complemented
229	C₂×#3753	C₂²×C₃	1	2	yes	complemented
230	C₂×#3748	C₂²×C₃	1	1	yes	characteristic, complemented
231	#64123	C₂²×C₃	1	16	yes	complemented
232	SD₁₆×C₃⋊D₃	C₂²×C₃	1	16	yes	complemented
233	#64120	C₂²×C₃	1	16	yes	complemented
234	D₈×C₃⋊D₃	C₂²×C₃	1	16	yes	complemented
235	#64117	C₂²×C₃	1	8	yes	complemented
236	M₁₆×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
237	C₂×#3745	C₂²×C₃	1	2	yes	complemented
238	C₂×#3744	C₂²×C₃	1	2	yes	complemented
239	C₂×#3743	C₂²×C₃	1	2	yes	complemented
240	C₂×C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
241	C₃×#949	—	3	32	no	—
242	C₂×C₃×#215	—	3	8	no	—
243	C₂×C₃×#214	—	3	8	no	—
244	C₃×#932	—	3	32	no	—
245	C₂×C₃×#213	—	3	8	no	—
246	C₂×C₃×#213	—	3	8	no	—
247	C₂×C₃×#208	—	3	4	no	—
248	C₃×#914	—	3	64	no	—
249	C₃×D₃×SD₁₆	—	3	64	no	—
250	C₃×#911	—	3	64	no	—
251	C₃×D₃×D₈	—	3	64	no	—
252	C₃×#908	—	3	32	no	—
253	C₃×D₃×M₁₆	—	3	32	no	—
254	C₂×C₃×D₂₄	—	3	8	no	—
255	C₂×C₃×#204	—	3	8	no	—
256	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
257	C₂×C₃×D₃×C₈	—	3	8	no	—
258	C₂³×C₃³	—	2	2	no	—
259	C₂³×C₃³	—	2	4	no	—
260	C₂³×C₃³	—	2	1	no	—
261	C₂³×C₃³	—	4	4	no	—
262	C₂³×C₃³	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
264	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
265	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
266	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
267	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
268	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
269	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
270	C₂²×C₃×C₃⋊D₃	—	4	8	no	—
271	C₂²×C₃×C₃⋊D₃	—	4	32	no	—
272	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
273	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
274	C₂²×C₃×C₃⋊D₃	—	4	8	no	—
275	C₂²×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₃×C₃⋊D₃	C₂×D₄	1	4	yes	—
277	C₂²×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
278	C₃³×Q₈	—	2	1	no	—
279	C₃³×Q₈	C₂⁴	1	2	yes	complemented
280	C₃³×D₄	—	2	4	no	—
281	C₃³×D₄	—	2	2	no	—
282	C₃³×D₄	—	2	4	no	—
283	C₃³×D₄	—	2	1	no	—
284	C₃³×D₄	C₂⁴	1	4	yes	—
285	C₃³×D₄	C₂⁴	1	2	yes	complemented
286	C₂×C₃³×C₄	—	2	1	no	—
287	C₂×C₃³×C₄	—	2	4	no	—
288	C₂×C₃³×C₄	C₂×D₄	1	1	yes	characteristic
289	C₂×C₃³×C₄	C₂×D₄	1	2	yes	—
290	C₂×C₃³×C₄	C₂⁴	1	1	yes	characteristic
291	C₂×C₃³×C₄	C₂⁴	1	2	yes	—
292	C₃×#638	—	2	4	no	—
293	C₃×#638	—	2	4	no	—
294	C₃×#638	—	2	4	no	—
295	C₃×#638	—	2	8	no	—
296	C₃×#638	—	2	8	no	—
297	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
298	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
299	C₂×C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
300	C₂×C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
301	C₂×C₃×C₃⋊Dic₃	C₂×D₄	1	4	yes	—
302	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
303	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
304	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
305	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
306	C₃×C₄⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
307	C₃×C₄⋊(C₃⋊D₃)	C₂⁴	1	2	yes	complemented
308	C₃×C₄×C₃⋊D₃	—	2	4	no	—
309	C₃×C₄×C₃⋊D₃	—	2	4	no	—
310	C₃×C₄×C₃⋊D₃	—	2	4	no	—
311	C₃×C₄×C₃⋊D₃	C₂×D₄	1	4	yes	—
312	C₃×C₄×C₃⋊D₃	C₂×D₄	1	4	yes	—
313	C₃×C₄×C₃⋊D₃	C₂×D₄	1	2	yes	—
314	C₃×C₄×C₃⋊D₃	C₂×D₄	1	2	yes	—
315	C₃×C₄×C₃⋊D₃	C₂⁴	1	2	yes	—
316	C₃×C₄×C₃⋊D₃	C₂⁴	1	2	yes	—
317	C₃×#634	—	2	1	no	—
318	C₃×#634	—	2	4	no	—
319	C₃×#634	C₂⁴	1	2	yes	complemented
320	C₃³×C₈	C₂⁴	1	4	yes	complemented
321	C₃×C₃⋊(C₃⋊C₈)	C₂⁴	1	4	yes	complemented
322	C₂²×C₃×#41	—	9	1	no	—
323	C₂³×C₃×D₄	—	9	1	no	—
324	C₂×D₃×#41	—	3	4	no	—
325	C₂²×D₃×D₄	—	3	4	no	—
326	C₂×C₃×AGL(1,ℤ/8)	—	2	4	no	—
327	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
328	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
329	C₂×C₃×AGL(1,ℤ/8)	—	9	16	no	—
330	C₂×C₃×AGL(1,ℤ/8)	—	9	2	no	—
331	C₂×C₃×AGL(1,ℤ/8)	—	9	2	no	—
332	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
333	C₂×C₃×AGL(1,ℤ/8)	C₃×D₃	1	4	yes	complemented
334	C₂×C₃×AGL(1,ℤ/8)	C₃⋊D₃	1	1	yes	characteristic, direct product factor
335	C₂²×C₃×SD₁₆	—	9	2	no	—
336	C₂²×C₃×D₈	—	9	2	no	—
337	C₂²×C₃×M₁₆	—	9	1	no	—
338	C₂×#949	—	3	4	no	—
339	C₂×#932	—	3	4	no	—
340	D₃×AGL(1,ℤ/8)	—	3	64	no	—
341	C₂×#914	—	3	8	no	—
342	C₂×D₃×SD₁₆	—	3	8	no	—
343	C₂×#911	—	3	8	no	—
344	C₂×D₃×D₈	—	3	8	no	—
345	C₂×#908	—	3	4	no	—
346	C₂×D₃×M₁₆	—	3	4	no	—
347	C₂⁴×C₃²	—	2	4	no	—
348	C₂⁴×C₃²	—	2	1	no	—
349	C₂⁴×C₃²	—	4	4	no	—
350	C₂³×C₃⋊D₃	—	2	1	no	—
351	C₂³×C₃⋊D₃	—	2	1	no	—
352	C₂³×C₃⋊D₃	—	2	2	no	—
353	C₂³×C₃⋊D₃	—	2	2	no	—
354	C₂³×C₃⋊D₃	—	2	8	no	—
355	C₂³×C₃⋊D₃	—	4	8	no	—
356	C₂³×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
357	C₂³×C₃×D₃	—	3	4	no	—
358	C₂³×C₃×D₃	—	6	4	no	—
359	C₂³×C₃×D₃	—	6	8	no	—
360	C₂³×C₃×D₃	—	6	8	no	—
361	C₂³×C₃×D₃	—	6	32	no	—
362	C₂³×C₃×D₃	—	6	4	no	—
363	C₂³×C₃×D₃	—	12	32	no	—
364	C₃²×#41	—	2	8	no	—
365	C₃²×#41	—	2	2	no	—
366	C₃²×#41	—	2	16	no	—
367	C₃²×#41	—	4	8	no	—
368	C₃²×#41	C₂²×D₃	1	16	yes	complemented
369	C₃²×#41	C₂³×C₃	1	4	yes	complemented
370	C₂×C₃²×Q₈	—	2	4	no	—
371	C₂×C₃²×Q₈	C₂²×D₃	1	4	yes	complemented
372	C₂×C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
373	C₂×C₃²×D₄	—	2	4	no	—
374	C₂×C₃²×D₄	—	2	1	no	—
375	C₂×C₃²×D₄	—	2	8	no	—
376	C₂×C₃²×D₄	—	2	16	no	—
377	C₂×C₃²×D₄	—	2	4	no	—
378	C₂×C₃²×D₄	—	2	4	no	—
379	C₂×C₃²×D₄	—	2	8	no	—
380	C₂×C₃²×D₄	—	2	1	no	—
381	C₂×C₃²×D₄	—	2	2	no	—
382	C₂×C₃²×D₄	—	4	4	no	—
383	C₂×C₃²×D₄	—	4	8	no	—
384	C₂×C₃²×D₄	—	4	4	no	—
385	C₂×C₃²×D₄	C₂²×D₃	1	8	yes	—
386	C₂×C₃²×D₄	C₂²×D₃	1	16	yes	complemented
387	C₂×C₃²×D₄	C₂²×D₃	1	4	yes	complemented
388	C₂×C₃²×D₄	C₂³×C₃	1	2	yes	—
389	C₂×C₃²×D₄	C₂³×C₃	1	4	yes	complemented
390	C₂×C₃²×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
391	C₂²×C₃²×C₄	—	2	4	no	—
392	C₂²×C₃²×C₄	—	2	4	no	—
393	C₂²×C₃²×C₄	—	2	1	no	—
394	C₂²×C₃²×C₄	—	4	4	no	—
395	C₂²×C₃²×C₄	C₂²×D₃	1	4	yes	—
396	C₂²×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
397	C₂×#638	—	2	1	no	—
398	C₂×#638	—	2	1	no	—
399	C₂×#638	—	2	1	no	—
400	C₂×#638	—	2	2	no	—
401	C₂×#638	—	2	2	no	—
402	C₂×#638	—	2	8	no	—
403	C₂²×C₃⋊Dic₃	—	2	1	no	—
404	C₂²×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
405	#3832	—	2	2	no	—
406	#3832	C₂³×C₃	1	4	yes	complemented
407	Q₈×C₃⋊D₃	—	2	2	no	—
408	Q₈×C₃⋊D₃	C₂³×C₃	1	4	yes	complemented
409	#3830	—	2	8	no	—
410	#3830	—	2	2	no	—
411	#3830	C₂³×C₃	1	4	yes	complemented
412	D₄×C₃⋊D₃	—	2	8	no	—
413	D₄×C₃⋊D₃	—	2	4	no	—
414	D₄×C₃⋊D₃	—	2	8	no	—
415	D₄×C₃⋊D₃	—	2	8	no	—
416	D₄×C₃⋊D₃	—	2	4	no	—
417	D₄×C₃⋊D₃	—	2	2	no	—
418	D₄×C₃⋊D₃	C₂³×C₃	1	8	yes	—
419	D₄×C₃⋊D₃	C₂³×C₃	1	8	yes	complemented
420	D₄×C₃⋊D₃	C₂³×C₃	1	4	yes	complemented
421	#3828	—	2	2	no	—
422	#3828	—	2	8	no	—
423	#3828	C₂³×C₃	1	4	yes	complemented
424	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
425	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
426	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
427	C₂×C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	complemented
429	C₂×C₄⋊(C₃⋊D₃)	C₂³×C₃	1	1	yes	characteristic, complemented
430	C₂×C₄×C₃⋊D₃	—	2	1	no	—
431	C₂×C₄×C₃⋊D₃	—	2	1	no	—
432	C₂×C₄×C₃⋊D₃	—	2	1	no	—
433	C₂×C₄×C₃⋊D₃	—	2	8	no	—
434	C₂×C₄×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
435	C₂×C₄×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
436	C₂×C₄×C₃⋊D₃	C₃×D₄	1	4	yes	—
437	C₂×C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₄×C₃⋊D₃	C₂³×C₃	1	4	yes	—
440	C₂×#634	—	2	1	no	—
441	C₂×#634	C₂³×C₃	1	1	yes	characteristic, complemented
442	C₂×C₃×#67	—	6	4	no	—
443	C₂×C₃×#67	—	6	8	no	—
444	C₂×C₃×#67	—	6	8	no	—
445	C₂×C₃×#67	—	6	32	no	—
446	C₂×C₃×#67	—	6	4	no	—
447	C₂×C₃×#67	—	6	4	no	—
448	C₂²×C₃×Dic₃	—	3	4	no	—
449	C₂²×C₃×Dic₃	—	6	4	no	—
450	C₃×#239	—	3	16	no	—
451	C₃×#239	—	6	8	no	—
452	C₃×D₃×Q₈	—	3	16	no	—
453	C₃×D₃×Q₈	—	6	8	no	—
454	C₃×#237	—	3	16	no	—
455	C₃×#237	—	6	8	no	—
456	C₃×#237	—	6	32	no	—
457	C₃×D₃×D₄	—	3	32	no	—
458	C₃×D₃×D₄	—	3	32	no	—
459	C₃×D₃×D₄	—	3	16	no	—
460	C₃×D₃×D₄	—	6	32	no	—
461	C₃×D₃×D₄	—	6	32	no	—
462	C₃×D₃×D₄	—	6	16	no	—
463	C₃×D₃×D₄	—	6	16	no	—
464	C₃×D₃×D₄	—	6	8	no	—
465	C₃×D₃×D₄	—	6	32	no	—
466	C₃×#235	—	3	16	no	—
467	C₃×#235	—	6	32	no	—
468	C₃×#235	—	6	8	no	—
469	C₂×C₃×D₁₂	—	3	8	no	—
470	C₂×C₃×D₁₂	—	3	4	no	—
471	C₂×C₃×D₁₂	—	3	16	no	—
472	C₂×C₃×D₁₂	—	6	4	no	—
473	C₂×C₃×D₁₂	—	6	4	no	—
474	C₂×C₃×D₁₂	—	6	8	no	—
475	C₂×C₃×C₄×D₃	—	3	4	no	—
476	C₂×C₃×C₄×D₃	—	3	4	no	—
477	C₂×C₃×C₄×D₃	—	3	16	no	—
478	C₂×C₃×C₄×D₃	—	3	4	no	—
479	C₂×C₃×C₄×D₃	—	3	4	no	—
480	C₂×C₃×C₄×D₃	—	3	16	no	—
481	C₂×C₃×C₄×D₃	—	6	32	no	—
482	C₂×C₃×C₄×D₃	—	6	4	no	—
483	C₂×C₃×C₄×D₃	—	6	4	no	—
484	C₂×C₃×C₄×D₃	—	6	4	no	—
485	C₂×C₃×Dic₆	—	3	4	no	—
486	C₂×C₃×Dic₆	—	6	4	no	—
487	C₃²×SD₁₆	—	2	32	no	—
488	C₃²×SD₁₆	C₂²×D₃	1	32	yes	complemented
489	C₃²×SD₁₆	C₂³×C₃	1	8	yes	complemented
490	C₃²×D₈	—	2	32	no	—
491	C₃²×D₈	C₂²×D₃	1	32	yes	complemented
492	C₃²×D₈	C₂³×C₃	1	8	yes	complemented
493	C₃²×M₁₆	—	2	16	no	—
494	C₃²×M₁₆	C₂²×D₃	1	16	yes	complemented
495	C₃²×M₁₆	C₂³×C₃	1	4	yes	complemented
496	C₂×C₃²×C₈	—	2	8	no	—
497	C₂×C₃²×C₈	C₂²×D₃	1	8	yes	complemented
498	C₂×C₃²×C₈	C₂³×C₃	1	2	yes	complemented
499	#3755	C₂³×C₃	1	8	yes	complemented
500	#3754	C₂³×C₃	1	8	yes	complemented
501	#3753	C₂³×C₃	1	8	yes	complemented
502	#3753	C₂³×C₃	1	8	yes	complemented
503	#3748	C₂³×C₃	1	4	yes	complemented
504	C₂×C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	complemented
505	#3745	C₂³×C₃	1	8	yes	complemented
506	#3744	C₂³×C₃	1	8	yes	complemented
507	#3743	C₂³×C₃	1	8	yes	complemented
508	C₈×C₃⋊D₃	C₂³×C₃	1	8	yes	complemented
509	C₃×#215	—	3	32	no	—
510	C₃×#214	—	3	32	no	—
511	C₃×#213	—	3	32	no	—
512	C₃×#213	—	3	32	no	—
513	C₃×#208	—	3	16	no	—
514	C₂×C₃×C₃⋊C₈	—	3	8	no	—
515	C₃×D₂₄	—	3	32	no	—
516	C₃×#204	—	3	32	no	—
517	C₃×ΓL(1,𝔽₂₅)	—	3	32	no	—
518	C₃×D₃×C₈	—	3	32	no	—
519	C₂²×AGL(1,ℤ/8)	—	9	1	no	Sylow
520	C₂²×C₃³	—	2	2	no	—
521	C₂²×C₃³	—	2	2	no	—
522	C₂²×C₃³	—	2	4	no	—
523	C₂²×C₃³	—	4	8	no	—
524	C₂²×C₃³	—	4	4	no	—
525	C₂²×C₃³	—	4	2	no	—
526	C₂²×C₃³	C₂²×D₄	1	2	yes	—
527	C₂²×C₃³	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₃×C₃⋊D₃	—	2	2	no	—
529	C₂×C₃×C₃⋊D₃	—	2	8	no	—
530	C₂×C₃×C₃⋊D₃	—	2	2	no	—
531	C₂×C₃×C₃⋊D₃	—	2	4	no	—
532	C₂×C₃×C₃⋊D₃	—	4	16	no	—
533	C₂×C₃×C₃⋊D₃	—	4	8	no	—
534	C₂×C₃×C₃⋊D₃	—	4	2	no	—
535	C₂×C₃×C₃⋊D₃	—	4	4	no	—
536	C₂×C₃×C₃⋊D₃	—	4	8	no	—
537	C₂×C₃×C₃⋊D₃	—	4	16	no	—
538	C₂×C₃×C₃⋊D₃	AGL(1,ℤ/8)	1	4	yes	direct product factor
539	C₂×C₃×C₃⋊D₃	C₂²×D₄	1	2	yes	—
540	C₂×C₃×C₃⋊D₃	C₂²×D₄	1	2	yes	—
541	C₃³×C₄	—	2	2	no	—
542	C₃³×C₄	C₂²×D₄	1	1	yes	characteristic
543	C₃³×C₄	C₂²×D₄	1	2	yes	—
544	C₃³×C₄	C₂⁵	1	1	yes	characteristic
545	C₃×C₃⋊Dic₃	—	2	2	no	—
546	C₃×C₃⋊Dic₃	C₂²×D₄	1	2	yes	—
547	C₃×C₃⋊Dic₃	C₂²×D₄	1	2	yes	—
548	C₂⁵×C₃	—	18	1	no	—
549	C₂⁴×D₃	—	6	4	no	—
550	C₂×C₃×#41	—	2	4	no	—
551	C₂×C₃×#41	—	9	8	no	—
552	C₂×C₃×#41	—	9	1	no	—
553	C₂×C₃×#41	—	9	1	no	—
554	C₂×C₃×#41	—	9	1	no	—
555	C₂×C₃×#41	—	18	1	no	—
556	C₂×C₃×#41	—	18	1	no	—
557	C₂×C₃×#41	—	18	4	no	—
558	C₂×C₃×#41	C₂×C₃×D₃	1	4	yes	complemented
559	C₂×C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
560	C₂²×C₃×Q₈	—	9	1	no	—
561	C₂²×C₃×D₄	—	2	4	no	—
562	C₂²×C₃×D₄	—	9	2	no	—
563	C₂²×C₃×D₄	—	9	2	no	—
564	C₂²×C₃×D₄	—	9	1	no	—
565	C₂²×C₃×D₄	—	9	8	no	—
566	C₂²×C₃×D₄	—	9	1	no	—
567	C₂²×C₃×D₄	—	18	1	no	—
568	C₂²×C₃×D₄	—	18	4	no	—
569	C₂²×C₃×D₄	—	18	1	no	—
570	C₂²×C₃×D₄	—	18	1	no	—
571	C₂²×C₃×D₄	—	18	1	no	—
572	C₂²×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
573	C₂²×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
574	C₂³×C₃×C₄	—	9	1	no	—
575	C₂³×C₃×C₄	—	18	1	no	—
576	C₂²×#67	—	6	4	no	—
577	D₃×#41	—	3	32	no	—
578	D₃×#41	—	6	16	no	—
579	C₂×#239	—	3	4	no	—
580	C₂×D₃×Q₈	—	3	4	no	—
581	C₂×#237	—	3	4	no	—
582	C₂×#237	—	6	4	no	—
583	C₂×D₃×D₄	—	3	8	no	—
584	C₂×D₃×D₄	—	3	8	no	—
585	C₂×D₃×D₄	—	3	32	no	—
586	C₂×D₃×D₄	—	3	4	no	—
587	C₂×D₃×D₄	—	6	4	no	—
588	C₂×D₃×D₄	—	6	4	no	—
589	C₂×D₃×D₄	—	6	16	no	—
590	C₂×D₃×D₄	—	6	4	no	—
591	C₂×#235	—	3	4	no	—
592	C₂×#235	—	6	4	no	—
593	C₂²×D₁₂	—	3	4	no	—
594	C₂²×C₄×D₃	—	3	4	no	—
595	C₂²×C₄×D₃	—	6	4	no	—
596	C₃×AGL(1,ℤ/8)	—	2	32	no	—
597	C₃×AGL(1,ℤ/8)	—	9	8	no	—
598	C₃×AGL(1,ℤ/8)	—	9	8	no	—
599	C₃×AGL(1,ℤ/8)	—	9	16	no	—
600	C₃×AGL(1,ℤ/8)	—	9	16	no	—
601	C₃×AGL(1,ℤ/8)	—	9	8	no	—
602	C₃×AGL(1,ℤ/8)	C₂×C₃×D₃	1	32	yes	complemented
603	C₃×AGL(1,ℤ/8)	C₂×C₃⋊D₃	1	8	yes	direct product factor
604	C₂×C₃×SD₁₆	—	2	8	no	—
605	C₂×C₃×SD₁₆	—	9	2	no	—
606	C₂×C₃×SD₁₆	—	9	2	no	—
607	C₂×C₃×SD₁₆	—	9	16	no	—
608	C₂×C₃×SD₁₆	—	9	2	no	—
609	C₂×C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
610	C₂×C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
611	C₂×C₃×D₈	—	2	8	no	—
612	C₂×C₃×D₈	—	9	2	no	—
613	C₂×C₃×D₈	—	9	2	no	—
614	C₂×C₃×D₈	—	9	16	no	—
615	C₂×C₃×D₈	—	9	2	no	—
616	C₂×C₃×D₈	C₂×C₃×D₃	1	8	yes	complemented
617	C₂×C₃×D₈	C₂×C₃⋊D₃	1	2	yes	complemented
618	C₂×C₃×M₁₆	—	2	4	no	—
619	C₂×C₃×M₁₆	—	9	1	no	—
620	C₂×C₃×M₁₆	—	9	8	no	—
621	C₂×C₃×M₁₆	—	9	2	no	—
622	C₂×C₃×M₁₆	C₂×C₃×D₃	1	4	yes	complemented
623	C₂×C₃×M₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
624	C₂²×C₃×C₈	—	9	2	no	—
625	#949	—	3	32	no	—
626	C₂×#215	—	3	8	no	—
627	C₂×#214	—	3	8	no	—
628	#932	—	3	32	no	—
629	C₂×#213	—	3	8	no	—
630	C₂×#213	—	3	8	no	—
631	C₂×#208	—	3	4	no	—
632	#914	—	3	64	no	—
633	D₃×SD₁₆	—	3	64	no	—
634	#911	—	3	64	no	—
635	D₃×D₈	—	3	64	no	—
636	#908	—	3	32	no	—
637	D₃×M₁₆	—	3	32	no	—
638	C₂×D₂₄	—	3	8	no	—
639	C₂×#204	—	3	8	no	—
640	C₂×ΓL(1,𝔽₂₅)	—	3	8	no	—
641	C₂×D₃×C₈	—	3	8	no	—
642	C₂³×C₃²	—	2	2	no	—
643	C₂³×C₃²	—	2	4	no	—
644	C₂³×C₃²	—	2	1	no	—
645	C₂³×C₃²	—	2	4	no	—
646	C₂³×C₃²	—	2	8	no	—
647	C₂³×C₃²	—	2	16	no	—
648	C₂³×C₃²	—	2	4	no	—
649	C₂³×C₃²	—	4	8	no	—
650	C₂³×C₃²	—	4	16	no	—
651	C₂³×C₃²	—	4	4	no	—
652	C₂³×C₃²	—	4	4	no	—
653	C₂³×C₃²	—	4	16	no	—
654	C₂³×C₃²	—	8	16	no	—
655	C₂³×C₃²	D₃×D₄	1	4	yes	—
656	C₂³×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
657	C₂²×C₃⋊D₃	—	2	4	no	—
658	C₂²×C₃⋊D₃	—	2	2	no	—
659	C₂²×C₃⋊D₃	—	2	4	no	—
660	C₂²×C₃⋊D₃	—	2	1	no	—
661	C₂²×C₃⋊D₃	—	2	8	no	—
662	C₂²×C₃⋊D₃	—	2	8	no	—
663	C₂²×C₃⋊D₃	—	2	4	no	—
664	C₂²×C₃⋊D₃	—	4	8	no	—
665	C₂²×C₃⋊D₃	—	4	32	no	—
666	C₂²×C₃⋊D₃	—	4	4	no	—
667	C₂²×C₃⋊D₃	—	4	8	no	—
668	C₂²×C₃⋊D₃	—	4	4	no	—
669	C₂²×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
670	C₂²×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	—
671	C₂²×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
672	C₂²×C₃×D₃	—	3	4	no	—
673	C₂²×C₃×D₃	—	3	4	no	—
674	C₂²×C₃×D₃	—	3	16	no	—
675	C₂²×C₃×D₃	—	6	16	no	—
676	C₂²×C₃×D₃	—	6	32	no	—
677	C₂²×C₃×D₃	—	6	32	no	—
678	C₂²×C₃×D₃	—	6	16	no	—
679	C₂²×C₃×D₃	—	6	16	no	—
680	C₂²×C₃×D₃	—	6	8	no	—
681	C₂²×C₃×D₃	—	6	4	no	—
682	C₂²×C₃×D₃	—	12	32	no	—
683	C₂²×C₃×D₃	—	12	16	no	—
684	C₂²×C₃×D₃	—	12	128	no	—
685	C₂²×C₃×D₃	—	12	32	no	—
686	C₂²×C₃×D₃	—	12	16	no	—
687	C₃²×Q₈	—	2	1	no	—
688	C₃²×Q₈	—	2	8	no	—
689	C₃²×Q₈	—	2	4	no	—
690	C₃²×Q₈	—	4	4	no	—
691	C₃²×Q₈	C₂³×D₃	1	8	yes	complemented
692	C₃²×Q₈	C₂⁴×C₃	1	2	yes	complemented
693	C₃²×D₄	—	2	4	no	—
694	C₃²×D₄	—	2	2	no	—
695	C₃²×D₄	—	2	4	no	—
696	C₃²×D₄	—	2	1	no	—
697	C₃²×D₄	—	2	16	no	—
698	C₃²×D₄	—	2	8	no	—
699	C₃²×D₄	—	2	16	no	—
700	C₃²×D₄	—	2	8	no	—
701	C₃²×D₄	—	2	16	no	—
702	C₃²×D₄	—	2	4	no	—
703	C₃²×D₄	—	4	8	no	—
704	C₃²×D₄	—	4	16	no	—
705	C₃²×D₄	—	4	4	no	—
706	C₃²×D₄	—	4	16	no	—
707	C₃²×D₄	C₂³×D₃	1	16	yes	—
708	C₃²×D₄	C₂³×D₃	1	8	yes	complemented
709	C₃²×D₄	C₂⁴×C₃	1	4	yes	—
710	C₃²×D₄	C₂⁴×C₃	1	2	yes	complemented
711	C₂×C₃²×C₄	—	2	1	no	—
712	C₂×C₃²×C₄	—	2	4	no	—
713	C₂×C₃²×C₄	—	2	4	no	—
714	C₂×C₃²×C₄	—	2	8	no	—
715	C₂×C₃²×C₄	—	2	4	no	—
716	C₂×C₃²×C₄	—	2	8	no	—
717	C₂×C₃²×C₄	—	2	4	no	—
718	C₂×C₃²×C₄	—	2	16	no	—
719	C₂×C₃²×C₄	—	4	16	no	—
720	C₂×C₃²×C₄	—	4	4	no	—
721	C₂×C₃²×C₄	D₃×D₄	1	4	yes	—
722	C₂×C₃²×C₄	D₃×D₄	1	8	yes	—
723	C₂×C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
724	C₂×C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
725	C₂×C₃²×C₄	C₂³×D₃	1	4	yes	—
726	C₂×C₃²×C₄	C₂³×D₃	1	8	yes	—
727	C₂×C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
728	C₂×C₃²×C₄	C₂⁴×C₃	1	2	yes	—
729	#638	—	2	4	no	—
730	#638	—	2	4	no	—
731	#638	—	2	4	no	—
732	#638	—	2	8	no	—
733	#638	—	2	8	no	—
734	C₂×C₃⋊Dic₃	—	2	1	no	—
735	C₂×C₃⋊Dic₃	—	2	4	no	—
736	C₂×C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
737	C₂×C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
738	C₂×C₃⋊Dic₃	C₂×C₃×D₄	1	4	yes	—
739	C₄⋊(C₃⋊D₃)	—	2	4	no	—
740	C₄⋊(C₃⋊D₃)	—	2	2	no	—
741	C₄⋊(C₃⋊D₃)	—	2	4	no	—
742	C₄⋊(C₃⋊D₃)	—	2	1	no	—
743	C₄⋊(C₃⋊D₃)	C₂⁴×C₃	1	4	yes	—
744	C₄⋊(C₃⋊D₃)	C₂⁴×C₃	1	2	yes	complemented
745	C₄×C₃⋊D₃	—	2	4	no	—
746	C₄×C₃⋊D₃	—	2	4	no	—
747	C₄×C₃⋊D₃	—	2	4	no	—
748	C₄×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	—
749	C₄×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	—
750	C₄×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
751	C₄×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
752	C₄×C₃⋊D₃	C₂⁴×C₃	1	2	yes	—
753	C₄×C₃⋊D₃	C₂⁴×C₃	1	2	yes	—
754	#634	—	2	1	no	—
755	#634	—	2	4	no	—
756	#634	C₂⁴×C₃	1	2	yes	complemented
757	C₃×#67	—	6	16	no	—
758	C₃×#67	—	6	32	no	—
759	C₃×#67	—	6	32	no	—
760	C₃×#67	—	6	16	no	—
761	C₃×#67	—	6	16	no	—
762	C₂×C₃×Dic₃	—	3	4	no	—
763	C₂×C₃×Dic₃	—	3	4	no	—
764	C₂×C₃×Dic₃	—	3	16	no	—
765	C₂×C₃×Dic₃	—	6	16	no	—
766	C₂×C₃×Dic₃	—	6	4	no	—
767	C₃×D₁₂	—	3	16	no	—
768	C₃×D₁₂	—	3	8	no	—
769	C₃×D₁₂	—	6	16	no	—
770	C₃×D₁₂	—	6	8	no	—
771	C₃×D₁₂	—	6	16	no	—
772	C₃×D₁₂	—	6	4	no	—
773	C₃×C₄×D₃	—	3	16	no	—
774	C₃×C₄×D₃	—	3	16	no	—
775	C₃×C₄×D₃	—	3	8	no	—
776	C₃×C₄×D₃	—	3	8	no	—
777	C₃×C₄×D₃	—	3	8	no	—
778	C₃×C₄×D₃	—	3	8	no	—
779	C₃×C₄×D₃	—	6	16	no	—
780	C₃×C₄×D₃	—	6	16	no	—
781	C₃×C₄×D₃	—	6	16	no	—
782	C₃×Dic₆	—	3	8	no	—
783	C₃×Dic₆	—	6	16	no	—
784	C₃×Dic₆	—	6	4	no	—
785	C₃²×C₈	—	2	16	no	—
786	C₃²×C₈	C₂³×D₃	1	16	yes	complemented
787	C₃²×C₈	C₂⁴×C₃	1	4	yes	complemented
788	C₃⋊(C₃⋊C₈)	C₂⁴×C₃	1	4	yes	complemented
789	C₃×C₃⋊C₈	—	3	16	no	—
790	C₂²×#41	—	9	1	no	—
791	C₂³×D₄	—	9	1	no	—
792	C₂×AGL(1,ℤ/8)	—	9	1	no	—
793	C₂×AGL(1,ℤ/8)	—	9	1	no	—
794	C₂×AGL(1,ℤ/8)	—	9	16	no	—
795	C₂×AGL(1,ℤ/8)	—	9	2	no	—
796	C₂×AGL(1,ℤ/8)	—	9	2	no	—
797	C₂×AGL(1,ℤ/8)	—	9	1	no	—
798	C₂×AGL(1,ℤ/8)	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
799	C₂²×SD₁₆	—	9	2	no	—
800	C₂²×D₈	—	9	2	no	—
801	C₂²×M₁₆	—	9	1	no	—
802	C₂×C₃³	—	2	2	no	—
803	C₂×C₃³	—	4	4	no	—
804	C₂×C₃³	—	4	2	no	—
805	C₂×C₃³	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
806	C₂×C₃³	C₂³×D₄	1	1	yes	characteristic
807	C₃×C₃⋊D₃	—	2	2	no	—
808	C₃×C₃⋊D₃	—	4	2	no	—
809	C₃×C₃⋊D₃	—	4	4	no	—
810	C₃×C₃⋊D₃	C₂×AGL(1,ℤ/8)	1	4	yes	direct product factor
811	C₂⁴×C₃	—	2	4	no	—
812	C₂⁴×C₃	—	2	1	no	—
813	C₂⁴×C₃	—	4	4	no	—
814	C₂⁴×C₃	—	9	1	no	—
815	C₂⁴×C₃	—	18	8	no	—
816	C₂⁴×C₃	—	18	2	no	—
817	C₂⁴×C₃	—	18	2	no	—
818	C₂⁴×C₃	—	18	1	no	—
819	C₂⁴×C₃	—	18	1	no	—
820	C₂⁴×C₃	—	36	8	no	—
821	C₂³×D₃	—	3	4	no	—
822	C₂³×D₃	—	6	4	no	—
823	C₂³×D₃	—	6	8	no	—
824	C₂³×D₃	—	6	8	no	—
825	C₂³×D₃	—	6	32	no	—
826	C₂³×D₃	—	6	4	no	—
827	C₂³×D₃	—	12	32	no	—
828	C₃×#41	—	2	8	no	—
829	C₃×#41	—	2	2	no	—
830	C₃×#41	—	2	16	no	—
831	C₃×#41	—	4	8	no	—
832	C₃×#41	—	9	4	no	—
833	C₃×#41	—	9	4	no	—
834	C₃×#41	—	9	4	no	—
835	C₃×#41	—	18	8	no	—
836	C₃×#41	—	18	8	no	—
837	C₃×#41	—	18	2	no	—
838	C₃×#41	—	18	2	no	—
839	C₃×#41	—	18	2	no	—
840	C₃×#41	C₂²×C₃×D₃	1	16	yes	complemented
841	C₃×#41	C₂²×C₃⋊D₃	1	4	yes	complemented
842	C₂×C₃×Q₈	—	2	4	no	—
843	C₂×C₃×Q₈	—	9	4	no	—
844	C₂×C₃×Q₈	—	9	1	no	—
845	C₂×C₃×Q₈	—	18	1	no	—
846	C₂×C₃×Q₈	—	18	2	no	—
847	C₂×C₃×Q₈	C₂²×C₃×D₃	1	4	yes	complemented
848	C₂×C₃×Q₈	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
849	C₂×C₃×D₄	—	2	4	no	—
850	C₂×C₃×D₄	—	2	1	no	—
851	C₂×C₃×D₄	—	2	4	no	—
852	C₂×C₃×D₄	—	2	8	no	—
853	C₂×C₃×D₄	—	2	2	no	—
854	C₂×C₃×D₄	—	2	1	no	—
855	C₂×C₃×D₄	—	2	8	no	—
856	C₂×C₃×D₄	—	2	4	no	—
857	C₂×C₃×D₄	—	2	16	no	—
858	C₂×C₃×D₄	—	4	4	no	—
859	C₂×C₃×D₄	—	4	8	no	—
860	C₂×C₃×D₄	—	4	4	no	—
861	C₂×C₃×D₄	—	9	8	no	—
862	C₂×C₃×D₄	—	9	8	no	—
863	C₂×C₃×D₄	—	9	4	no	—
864	C₂×C₃×D₄	—	9	1	no	—
865	C₂×C₃×D₄	—	9	2	no	—
866	C₂×C₃×D₄	—	9	4	no	—
867	C₂×C₃×D₄	—	18	1	no	—
868	C₂×C₃×D₄	—	18	8	no	—
869	C₂×C₃×D₄	—	18	4	no	—
870	C₂×C₃×D₄	—	18	4	no	—
871	C₂×C₃×D₄	—	18	8	no	—
872	C₂×C₃×D₄	—	18	2	no	—
873	C₂×C₃×D₄	—	18	8	no	—
874	C₂×C₃×D₄	—	18	2	no	—
875	C₂×C₃×D₄	—	18	2	no	—
876	C₂×C₃×D₄	—	18	1	no	—
877	C₂×C₃×D₄	—	18	8	no	—
878	C₂×C₃×D₄	—	18	1	no	—
879	C₂×C₃×D₄	—	18	1	no	—
880	C₂×C₃×D₄	—	18	2	no	—
881	C₂×C₃×D₄	—	18	1	no	—
882	C₂×C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
883	C₂×C₃×D₄	C₂²×C₃×D₃	1	16	yes	complemented
884	C₂×C₃×D₄	C₂²×C₃×D₃	1	4	yes	complemented
885	C₂×C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
886	C₂×C₃×D₄	C₂²×C₃⋊D₃	1	4	yes	complemented
887	C₂×C₃×D₄	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
888	C₂²×C₃×C₄	—	2	4	no	—
889	C₂²×C₃×C₄	—	2	1	no	—
890	C₂²×C₃×C₄	—	2	4	no	—
891	C₂²×C₃×C₄	—	4	4	no	—
892	C₂²×C₃×C₄	—	9	1	no	—
893	C₂²×C₃×C₄	—	9	1	no	—
894	C₂²×C₃×C₄	—	9	4	no	—
895	C₂²×C₃×C₄	—	9	1	no	—
896	C₂²×C₃×C₄	—	9	1	no	—
897	C₂²×C₃×C₄	—	9	4	no	—
898	C₂²×C₃×C₄	—	9	1	no	—
899	C₂²×C₃×C₄	—	18	1	no	—
900	C₂²×C₃×C₄	—	18	8	no	—
901	C₂²×C₃×C₄	—	18	1	no	—
902	C₂²×C₃×C₄	—	18	1	no	—
903	C₂²×C₃×C₄	—	18	1	no	—
904	C₂²×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
905	C₂²×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
906	C₂×#67	—	6	4	no	—
907	C₂×#67	—	6	8	no	—
908	C₂×#67	—	6	8	no	—
909	C₂×#67	—	6	32	no	—
910	C₂×#67	—	6	4	no	—
911	C₂×#67	—	6	4	no	—
912	C₂²×Dic₃	—	3	4	no	—
913	C₂²×Dic₃	—	6	4	no	—
914	#239	—	3	16	no	—
915	#239	—	6	8	no	—
916	D₃×Q₈	—	3	16	no	—
917	D₃×Q₈	—	6	8	no	—
918	#237	—	3	16	no	—
919	#237	—	6	8	no	—
920	#237	—	6	32	no	—
921	D₃×D₄	—	3	32	no	—
922	D₃×D₄	—	3	32	no	—
923	D₃×D₄	—	3	16	no	—
924	D₃×D₄	—	6	32	no	—
925	D₃×D₄	—	6	32	no	—
926	D₃×D₄	—	6	16	no	—
927	D₃×D₄	—	6	16	no	—
928	D₃×D₄	—	6	8	no	—
929	D₃×D₄	—	6	32	no	—
930	#235	—	3	16	no	—
931	#235	—	6	32	no	—
932	#235	—	6	8	no	—
933	C₂×D₁₂	—	3	8	no	—
934	C₂×D₁₂	—	3	4	no	—
935	C₂×D₁₂	—	3	16	no	—
936	C₂×D₁₂	—	6	4	no	—
937	C₂×D₁₂	—	6	4	no	—
938	C₂×D₁₂	—	6	8	no	—
939	C₂×C₄×D₃	—	3	4	no	—
940	C₂×C₄×D₃	—	3	4	no	—
941	C₂×C₄×D₃	—	3	16	no	—
942	C₂×C₄×D₃	—	3	4	no	—
943	C₂×C₄×D₃	—	3	4	no	—
944	C₂×C₄×D₃	—	3	16	no	—
945	C₂×C₄×D₃	—	6	32	no	—
946	C₂×C₄×D₃	—	6	4	no	—
947	C₂×C₄×D₃	—	6	4	no	—
948	C₂×C₄×D₃	—	6	4	no	—
949	C₂×Dic₆	—	3	4	no	—
950	C₂×Dic₆	—	6	4	no	—
951	C₃×SD₁₆	—	2	32	no	—
952	C₃×SD₁₆	—	9	8	no	—
953	C₃×SD₁₆	—	9	8	no	—
954	C₃×SD₁₆	—	9	8	no	—
955	C₃×SD₁₆	C₂²×C₃×D₃	1	32	yes	complemented
956	C₃×SD₁₆	C₂²×C₃⋊D₃	1	8	yes	complemented
957	C₃×D₈	—	2	32	no	—
958	C₃×D₈	—	9	8	no	—
959	C₃×D₈	—	9	8	no	—
960	C₃×D₈	—	9	8	no	—
961	C₃×D₈	C₂²×C₃×D₃	1	32	yes	complemented
962	C₃×D₈	C₂²×C₃⋊D₃	1	8	yes	complemented
963	C₃×M₁₆	—	2	16	no	—
964	C₃×M₁₆	—	9	4	no	—
965	C₃×M₁₆	—	9	8	no	—
966	C₃×M₁₆	C₂²×C₃×D₃	1	16	yes	complemented
967	C₃×M₁₆	C₂²×C₃⋊D₃	1	4	yes	complemented
968	C₂×C₃×C₈	—	2	8	no	—
969	C₂×C₃×C₈	—	9	2	no	—
970	C₂×C₃×C₈	—	9	8	no	—
971	C₂×C₃×C₈	C₂²×C₃×D₃	1	8	yes	complemented
972	C₂×C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
973	#215	—	3	32	no	—
974	#214	—	3	32	no	—
975	#213	—	3	32	no	—
976	#213	—	3	32	no	—
977	#208	—	3	16	no	—
978	C₂×C₃⋊C₈	—	3	8	no	—
979	D₂₄	—	3	32	no	—
980	#204	—	3	32	no	—
981	ΓL(1,𝔽₂₅)	—	3	32	no	—
982	D₃×C₈	—	3	32	no	—
983	C₂²×C₃²	—	2	2	no	—
984	C₂²×C₃²	—	2	2	no	—
985	C₂²×C₃²	—	2	4	no	—
986	C₂²×C₃²	—	2	4	no	—
987	C₂²×C₃²	—	2	8	no	—
988	C₂²×C₃²	—	2	8	no	—
989	C₂²×C₃²	—	2	8	no	—
990	C₂²×C₃²	—	2	16	no	—
991	C₂²×C₃²	—	4	8	no	—
992	C₂²×C₃²	—	4	8	no	—
993	C₂²×C₃²	—	4	16	no	—
994	C₂²×C₃²	—	4	8	no	—
995	C₂²×C₃²	—	4	4	no	—
996	C₂²×C₃²	—	4	2	no	—
997	C₂²×C₃²	—	4	32	no	—
998	C₂²×C₃²	—	4	16	no	—
999	C₂²×C₃²	—	4	8	no	—
1000	C₂²×C₃²	—	8	8	no	—
1001	C₂²×C₃²	—	8	16	no	—
1002	C₂²×C₃²	—	8	32	no	—
1003	C₂²×C₃²	C₂×D₃×D₄	1	8	yes	—
1004	C₂²×C₃²	C₂×D₃×D₄	1	4	yes	—
1005	C₂²×C₃²	C₂²×C₃×D₄	1	2	yes	—
1006	C₂²×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
1007	C₂×C₃⋊D₃	—	2	2	no	—
1008	C₂×C₃⋊D₃	—	2	8	no	—
1009	C₂×C₃⋊D₃	—	2	2	no	—
1010	C₂×C₃⋊D₃	—	2	4	no	—
1011	C₂×C₃⋊D₃	—	4	16	no	—
1012	C₂×C₃⋊D₃	—	4	8	no	—
1013	C₂×C₃⋊D₃	—	4	2	no	—
1014	C₂×C₃⋊D₃	—	4	4	no	—
1015	C₂×C₃⋊D₃	—	4	8	no	—
1016	C₂×C₃⋊D₃	—	4	16	no	—
1017	C₂×C₃⋊D₃	C₃×AGL(1,ℤ/8)	1	4	yes	direct product factor
1018	C₂×C₃⋊D₃	C₂²×C₃×D₄	1	2	yes	—
1019	C₂×C₃⋊D₃	C₂²×C₃×D₄	1	2	yes	—
1020	C₂×C₃×D₃	—	3	8	no	—
1021	C₂×C₃×D₃	—	3	16	no	—
1022	C₂×C₃×D₃	—	3	8	no	—
1023	C₂×C₃×D₃	—	6	32	no	—
1024	C₂×C₃×D₃	—	6	8	no	—
1025	C₂×C₃×D₃	—	6	8	no	—
1026	C₂×C₃×D₃	—	6	16	no	—
1027	C₂×C₃×D₃	—	12	32	no	—
1028	C₂×C₃×D₃	—	12	64	no	—
1029	C₂×C₃×D₃	—	12	64	no	—
1030	C₂×C₃×D₃	—	12	32	no	—
1031	C₂×C₃×D₃	—	12	8	no	—
1032	C₂×C₃×D₃	—	12	16	no	—
1033	C₃²×C₄	—	2	2	no	—
1034	C₃²×C₄	—	2	8	no	—
1035	C₃²×C₄	—	2	4	no	—
1036	C₃²×C₄	—	2	4	no	—
1037	C₃²×C₄	—	2	8	no	—
1038	C₃²×C₄	—	4	8	no	—
1039	C₃²×C₄	C₂×D₃×D₄	1	4	yes	—
1040	C₃²×C₄	C₂×D₃×D₄	1	8	yes	—
1041	C₃²×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1042	C₃²×C₄	C₂²×C₃×D₄	1	2	yes	—
1043	C₃²×C₄	C₂⁴×D₃	1	4	yes	—
1044	C₃²×C₄	C₂⁵×C₃	1	1	yes	characteristic
1045	C₃⋊Dic₃	—	2	2	no	—
1046	C₃⋊Dic₃	C₂²×C₃×D₄	1	2	yes	—
1047	C₃⋊Dic₃	C₂²×C₃×D₄	1	2	yes	—
1048	C₃×Dic₃	—	3	8	no	—
1049	C₃×Dic₃	—	3	8	no	—
1050	C₃×Dic₃	—	6	8	no	—
1051	C₂⁵	—	18	1	no	—
1052	C₂×#41	—	9	8	no	—
1053	C₂×#41	—	9	1	no	—
1054	C₂×#41	—	9	1	no	—
1055	C₂×#41	—	9	1	no	—
1056	C₂×#41	—	18	1	no	—
1057	C₂×#41	—	18	1	no	—
1058	C₂×#41	—	18	4	no	—
1059	C₂×#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
1060	C₂²×Q₈	—	9	1	no	—
1061	C₂²×D₄	—	9	2	no	—
1062	C₂²×D₄	—	9	2	no	—
1063	C₂²×D₄	—	9	1	no	—
1064	C₂²×D₄	—	9	8	no	—
1065	C₂²×D₄	—	9	1	no	—
1066	C₂²×D₄	—	18	1	no	—
1067	C₂²×D₄	—	18	1	no	—
1068	C₂²×D₄	—	18	4	no	—
1069	C₂²×D₄	—	18	1	no	—
1070	C₂²×D₄	—	18	1	no	—
1071	C₂²×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
1072	C₂³×C₄	—	9	1	no	—
1073	C₂³×C₄	—	18	1	no	—
1074	AGL(1,ℤ/8)	—	9	8	no	—
1075	AGL(1,ℤ/8)	—	9	8	no	—
1076	AGL(1,ℤ/8)	—	9	16	no	—
1077	AGL(1,ℤ/8)	—	9	16	no	—
1078	AGL(1,ℤ/8)	—	9	8	no	—
1079	AGL(1,ℤ/8)	C₂×C₃×C₃⋊D₃	1	8	yes	direct product factor
1080	C₂×SD₁₆	—	9	2	no	—
1081	C₂×SD₁₆	—	9	2	no	—
1082	C₂×SD₁₆	—	9	16	no	—
1083	C₂×SD₁₆	—	9	2	no	—
1084	C₂×SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
1085	C₂×D₈	—	9	2	no	—
1086	C₂×D₈	—	9	2	no	—
1087	C₂×D₈	—	9	16	no	—
1088	C₂×D₈	—	9	2	no	—
1089	C₂×D₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
1090	C₂×M₁₆	—	9	1	no	—
1091	C₂×M₁₆	—	9	8	no	—
1092	C₂×M₁₆	—	9	2	no	—
1093	C₂×M₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
1094	C₂²×C₈	—	9	2	no	—
1095	C₃³	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
1096	C₂³×C₃	—	2	4	no	—
1097	C₂³×C₃	—	2	8	no	—
1098	C₂³×C₃	—	2	16	no	—
1099	C₂³×C₃	—	2	4	no	—
1100	C₂³×C₃	—	2	1	no	—
1101	C₂³×C₃	—	2	2	no	—
1102	C₂³×C₃	—	2	4	no	—
1103	C₂³×C₃	—	4	4	no	—
1104	C₂³×C₃	—	4	8	no	—
1105	C₂³×C₃	—	4	16	no	—
1106	C₂³×C₃	—	4	4	no	—
1107	C₂³×C₃	—	4	16	no	—
1108	C₂³×C₃	—	8	16	no	—
1109	C₂³×C₃	—	9	1	no	—
1110	C₂³×C₃	—	9	4	no	—
1111	C₂³×C₃	—	9	1	no	—
1112	C₂³×C₃	—	18	4	no	—
1113	C₂³×C₃	—	18	4	no	—
1114	C₂³×C₃	—	18	8	no	—
1115	C₂³×C₃	—	18	8	no	—
1116	C₂³×C₃	—	18	4	no	—
1117	C₂³×C₃	—	18	1	no	—
1118	C₂³×C₃	—	18	2	no	—
1119	C₂³×C₃	—	36	4	no	—
1120	C₂³×C₃	—	36	4	no	—
1121	C₂³×C₃	—	36	8	no	—
1122	C₂³×C₃	—	36	32	no	—
1123	C₂³×C₃	—	36	8	no	—
1124	C₂³×C₃	C₃×D₃×D₄	1	4	yes	—
1125	C₂³×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
1126	C₂²×D₃	—	3	4	no	—
1127	C₂²×D₃	—	3	4	no	—
1128	C₂²×D₃	—	3	16	no	—
1129	C₂²×D₃	—	6	16	no	—
1130	C₂²×D₃	—	6	16	no	—
1131	C₂²×D₃	—	6	32	no	—
1132	C₂²×D₃	—	6	32	no	—
1133	C₂²×D₃	—	6	4	no	—
1134	C₂²×D₃	—	6	16	no	—
1135	C₂²×D₃	—	6	8	no	—
1136	C₂²×D₃	—	12	16	no	—
1137	C₂²×D₃	—	12	32	no	—
1138	C₂²×D₃	—	12	128	no	—
1139	C₂²×D₃	—	12	32	no	—
1140	C₂²×D₃	—	12	16	no	—
1141	C₃×Q₈	—	2	4	no	—
1142	C₃×Q₈	—	2	1	no	—
1143	C₃×Q₈	—	2	8	no	—
1144	C₃×Q₈	—	4	4	no	—
1145	C₃×Q₈	—	9	2	no	—
1146	C₃×Q₈	—	18	4	no	—
1147	C₃×Q₈	—	18	1	no	—
1148	C₃×Q₈	C₂³×C₃×D₃	1	8	yes	complemented
1149	C₃×Q₈	C₂³×C₃⋊D₃	1	2	yes	complemented
1150	C₃×D₄	—	2	16	no	—
1151	C₃×D₄	—	2	4	no	—
1152	C₃×D₄	—	2	8	no	—
1153	C₃×D₄	—	2	16	no	—
1154	C₃×D₄	—	2	4	no	—
1155	C₃×D₄	—	2	2	no	—
1156	C₃×D₄	—	2	4	no	—
1157	C₃×D₄	—	2	1	no	—
1158	C₃×D₄	—	2	16	no	—
1159	C₃×D₄	—	2	8	no	—
1160	C₃×D₄	—	4	8	no	—
1161	C₃×D₄	—	4	16	no	—
1162	C₃×D₄	—	4	4	no	—
1163	C₃×D₄	—	4	16	no	—
1164	C₃×D₄	—	9	2	no	—
1165	C₃×D₄	—	9	4	no	—
1166	C₃×D₄	—	18	4	no	—
1167	C₃×D₄	—	18	8	no	—
1168	C₃×D₄	—	18	8	no	—
1169	C₃×D₄	—	18	4	no	—
1170	C₃×D₄	—	18	4	no	—
1171	C₃×D₄	—	18	4	no	—
1172	C₃×D₄	—	18	4	no	—
1173	C₃×D₄	—	18	2	no	—
1174	C₃×D₄	—	18	1	no	—
1175	C₃×D₄	C₂³×C₃×D₃	1	16	yes	—
1176	C₃×D₄	C₂³×C₃×D₃	1	8	yes	complemented
1177	C₃×D₄	C₂³×C₃⋊D₃	1	4	yes	—
1178	C₃×D₄	C₂³×C₃⋊D₃	1	2	yes	complemented
1179	C₂×C₃×C₄	—	2	4	no	—
1180	C₂×C₃×C₄	—	2	1	no	—
1181	C₂×C₃×C₄	—	2	16	no	—
1182	C₂×C₃×C₄	—	2	4	no	—
1183	C₂×C₃×C₄	—	2	4	no	—
1184	C₂×C₃×C₄	—	2	8	no	—
1185	C₂×C₃×C₄	—	2	4	no	—
1186	C₂×C₃×C₄	—	2	8	no	—
1187	C₂×C₃×C₄	—	4	16	no	—
1188	C₂×C₃×C₄	—	4	4	no	—
1189	C₂×C₃×C₄	—	9	4	no	—
1190	C₂×C₃×C₄	—	9	1	no	—
1191	C₂×C₃×C₄	—	9	1	no	—
1192	C₂×C₃×C₄	—	9	4	no	—
1193	C₂×C₃×C₄	—	9	2	no	—
1194	C₂×C₃×C₄	—	9	2	no	—
1195	C₂×C₃×C₄	—	9	4	no	—
1196	C₂×C₃×C₄	—	9	2	no	—
1197	C₂×C₃×C₄	—	9	2	no	—
1198	C₂×C₃×C₄	—	18	4	no	—
1199	C₂×C₃×C₄	—	18	4	no	—
1200	C₂×C₃×C₄	—	18	4	no	—
1201	C₂×C₃×C₄	—	18	1	no	—
1202	C₂×C₃×C₄	—	18	4	no	—
1203	C₂×C₃×C₄	C₃×D₃×D₄	1	4	yes	—
1204	C₂×C₃×C₄	C₃×D₃×D₄	1	8	yes	—
1205	C₂×C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
1206	C₂×C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
1207	C₂×C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
1208	C₂×C₃×C₄	C₂³×C₃×D₃	1	8	yes	—
1209	C₂×C₃×C₄	C₂³×C₃⋊D₃	1	2	yes	—
1210	C₂×C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
1211	#67	—	6	16	no	—
1212	#67	—	6	32	no	—
1213	#67	—	6	32	no	—
1214	#67	—	6	16	no	—
1215	#67	—	6	16	no	—
1216	C₂×Dic₃	—	3	4	no	—
1217	C₂×Dic₃	—	3	4	no	—
1218	C₂×Dic₃	—	3	16	no	—
1219	C₂×Dic₃	—	6	16	no	—
1220	C₂×Dic₃	—	6	4	no	—
1221	D₁₂	—	3	16	no	—
1222	D₁₂	—	3	8	no	—
1223	D₁₂	—	6	16	no	—
1224	D₁₂	—	6	8	no	—
1225	D₁₂	—	6	16	no	—
1226	D₁₂	—	6	4	no	—
1227	C₄×D₃	—	3	16	no	—
1228	C₄×D₃	—	3	16	no	—
1229	C₄×D₃	—	3	8	no	—
1230	C₄×D₃	—	3	8	no	—
1231	C₄×D₃	—	3	8	no	—
1232	C₄×D₃	—	3	8	no	—
1233	C₄×D₃	—	6	16	no	—
1234	C₄×D₃	—	6	16	no	—
1235	C₄×D₃	—	6	16	no	—
1236	Dic₆	—	3	8	no	—
1237	Dic₆	—	6	16	no	—
1238	Dic₆	—	6	4	no	—
1239	C₃×C₈	—	2	16	no	—
1240	C₃×C₈	—	9	4	no	—
1241	C₃×C₈	C₂³×C₃×D₃	1	16	yes	complemented
1242	C₃×C₈	C₂³×C₃⋊D₃	1	4	yes	complemented
1243	C₃⋊C₈	—	3	16	no	—
1244	C₂×C₃²	—	2	2	no	—
1245	C₂×C₃²	—	2	8	no	—
1246	C₂×C₃²	—	2	4	no	—
1247	C₂×C₃²	—	2	8	no	—
1248	C₂×C₃²	—	4	8	no	—
1249	C₂×C₃²	—	4	4	no	—
1250	C₂×C₃²	—	4	2	no	—
1251	C₂×C₃²	—	4	16	no	—
1252	C₂×C₃²	—	4	8	no	—
1253	C₂×C₃²	—	8	8	no	—
1254	C₂×C₃²	—	8	16	no	—
1255	C₂×C₃²	D₃×AGL(1,ℤ/8)	1	8	yes	complemented
1256	C₂×C₃²	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	complemented
1257	C₂×C₃²	C₂²×D₃×D₄	1	4	yes	—
1258	C₂×C₃²	C₂³×C₃×D₄	1	1	yes	characteristic
1259	C₃⋊D₃	—	2	2	no	—
1260	C₃⋊D₃	—	4	2	no	—
1261	C₃⋊D₃	—	4	4	no	—
1262	C₃⋊D₃	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	direct product factor
1263	C₃×D₃	—	3	16	no	—
1264	C₃×D₃	—	6	8	no	—
1265	C₃×D₃	—	12	8	no	—
1266	C₃×D₃	—	12	16	no	—
1267	C₂⁴	—	2	1	no	—
1268	C₂⁴	—	9	1	no	—
1269	C₂⁴	—	18	1	no	—
1270	C₂⁴	—	18	2	no	—
1271	C₂⁴	—	18	2	no	—
1272	C₂⁴	—	18	8	no	—
1273	C₂⁴	—	18	1	no	—
1274	C₂⁴	—	36	8	no	—
1275	#41	—	2	2	no	—
1276	#41	—	9	4	no	—
1277	#41	—	9	4	no	—
1278	#41	—	9	4	no	—
1279	#41	—	18	8	no	—
1280	#41	—	18	8	no	—
1281	#41	—	18	2	no	—
1282	#41	—	18	2	no	—
1283	#41	—	18	2	no	—
1284	#41	C₂²×C₃×C₃⋊D₃	1	4	yes	complemented
1285	C₂×Q₈	—	9	4	no	—
1286	C₂×Q₈	—	9	1	no	—
1287	C₂×Q₈	—	18	1	no	—
1288	C₂×Q₈	—	18	2	no	—
1289	C₂×Q₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
1290	C₂×D₄	—	2	1	no	—
1291	C₂×D₄	—	2	1	no	—
1292	C₂×D₄	—	2	2	no	—
1293	C₂×D₄	—	9	8	no	—
1294	C₂×D₄	—	9	8	no	—
1295	C₂×D₄	—	9	4	no	—
1296	C₂×D₄	—	9	1	no	—
1297	C₂×D₄	—	9	2	no	—
1298	C₂×D₄	—	9	4	no	—
1299	C₂×D₄	—	18	1	no	—
1300	C₂×D₄	—	18	8	no	—
1301	C₂×D₄	—	18	4	no	—
1302	C₂×D₄	—	18	4	no	—
1303	C₂×D₄	—	18	8	no	—
1304	C₂×D₄	—	18	2	no	—
1305	C₂×D₄	—	18	2	no	—
1306	C₂×D₄	—	18	2	no	—
1307	C₂×D₄	—	18	8	no	—
1308	C₂×D₄	—	18	1	no	—
1309	C₂×D₄	—	18	8	no	—
1310	C₂×D₄	—	18	1	no	—
1311	C₂×D₄	—	18	1	no	—
1312	C₂×D₄	—	18	1	no	—
1313	C₂×D₄	—	18	2	no	—
1314	C₂×D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
1315	C₂×D₄	C₂²×C₃×C₃⋊D₃	1	4	yes	complemented
1316	C₂×D₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
1317	C₂²×C₄	—	2	1	no	—
1318	C₂²×C₄	—	9	1	no	—
1319	C₂²×C₄	—	9	1	no	—
1320	C₂²×C₄	—	9	1	no	—
1321	C₂²×C₄	—	9	4	no	—
1322	C₂²×C₄	—	9	1	no	—
1323	C₂²×C₄	—	9	1	no	—
1324	C₂²×C₄	—	9	4	no	—
1325	C₂²×C₄	—	18	1	no	—
1326	C₂²×C₄	—	18	8	no	—
1327	C₂²×C₄	—	18	1	no	—
1328	C₂²×C₄	—	18	1	no	—
1329	C₂²×C₄	—	18	1	no	—
1330	C₂²×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
1331	SD₁₆	—	9	8	no	—
1332	SD₁₆	—	9	8	no	—
1333	SD₁₆	—	9	8	no	—
1334	SD₁₆	C₂²×C₃×C₃⋊D₃	1	8	yes	complemented
1335	D₈	—	9	8	no	—
1336	D₈	—	9	8	no	—
1337	D₈	—	9	8	no	—
1338	D₈	C₂²×C₃×C₃⋊D₃	1	8	yes	complemented
1339	M₁₆	—	9	4	no	—
1340	M₁₆	—	9	8	no	—
1341	M₁₆	C₂²×C₃×C₃⋊D₃	1	4	yes	complemented
1342	C₂×C₈	—	9	2	no	—
1343	C₂×C₈	—	9	8	no	—
1344	C₂×C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	complemented
1345	C₂²×C₃	—	2	8	no	—
1346	C₂²×C₃	—	2	2	no	—
1347	C₂²×C₃	—	2	8	no	—
1348	C₂²×C₃	—	2	16	no	—
1349	C₂²×C₃	—	2	2	no	—
1350	C₂²×C₃	—	2	4	no	—
1351	C₂²×C₃	—	2	4	no	—
1352	C₂²×C₃	—	2	8	no	—
1353	C₂²×C₃	—	4	8	no	—
1354	C₂²×C₃	—	4	8	no	—
1355	C₂²×C₃	—	4	16	no	—
1356	C₂²×C₃	—	4	32	no	—
1357	C₂²×C₃	—	4	8	no	—
1358	C₂²×C₃	—	4	16	no	—
1359	C₂²×C₃	—	4	8	no	—
1360	C₂²×C₃	—	4	4	no	—
1361	C₂²×C₃	—	4	2	no	—
1362	C₂²×C₃	—	8	16	no	—
1363	C₂²×C₃	—	8	8	no	—
1364	C₂²×C₃	—	8	32	no	—
1365	C₂²×C₃	—	9	2	no	—
1366	C₂²×C₃	—	9	4	no	—
1367	C₂²×C₃	—	9	2	no	—
1368	C₂²×C₃	—	18	8	no	—
1369	C₂²×C₃	—	18	2	no	—
1370	C₂²×C₃	—	18	2	no	—
1371	C₂²×C₃	—	18	4	no	—
1372	C₂²×C₃	—	36	8	no	—
1373	C₂²×C₃	—	36	16	no	—
1374	C₂²×C₃	—	36	8	no	—
1375	C₂²×C₃	—	36	16	no	—
1376	C₂²×C₃	—	36	4	no	—
1377	C₂²×C₃	—	36	2	no	—
1378	C₂²×C₃	C₂×C₃×D₃×D₄	1	8	yes	—
1379	C₂²×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
1380	C₂²×C₃	C₂×D₄×C₃⋊D₃	1	2	yes	—
1381	C₂²×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
1382	C₂×D₃	—	3	16	no	—
1383	C₂×D₃	—	3	8	no	—
1384	C₂×D₃	—	3	8	no	—
1385	C₂×D₃	—	6	32	no	—
1386	C₂×D₃	—	6	8	no	—
1387	C₂×D₃	—	6	8	no	—
1388	C₂×D₃	—	6	16	no	—
1389	C₂×D₃	—	12	64	no	—
1390	C₂×D₃	—	12	32	no	—
1391	C₂×D₃	—	12	64	no	—
1392	C₂×D₃	—	12	32	no	—
1393	C₂×D₃	—	12	16	no	—
1394	C₂×D₃	—	12	8	no	—
1395	C₃×C₄	—	2	8	no	—
1396	C₃×C₄	—	2	2	no	—
1397	C₃×C₄	—	2	8	no	—
1398	C₃×C₄	—	2	4	no	—
1399	C₃×C₄	—	2	4	no	—
1400	C₃×C₄	—	4	8	no	—
1401	C₃×C₄	—	9	2	no	—
1402	C₃×C₄	—	9	2	no	—
1403	C₃×C₄	—	18	2	no	—
1404	C₃×C₄	C₂×C₃×D₃×D₄	1	4	yes	—
1405	C₃×C₄	C₂×C₃×D₃×D₄	1	8	yes	—
1406	C₃×C₄	C₂×D₄×C₃⋊D₃	1	2	yes	—
1407	C₃×C₄	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
1408	C₃×C₄	C₂⁴×C₃×D₃	1	4	yes	—
1409	C₃×C₄	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
1410	Dic₃	—	3	8	no	—
1411	Dic₃	—	3	8	no	—
1412	Dic₃	—	6	8	no	—
1413	C₃²	—	2	4	no	—
1414	C₃²	C₂×D₃×AGL(1,ℤ/8)	1	4	yes	complemented
1415	C₃²	C₂²×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
1416	C₂³	—	2	1	no	—
1417	C₂³	—	2	2	no	—
1418	C₂³	—	2	4	no	—
1419	C₂³	—	4	4	no	—
1420	C₂³	—	9	1	no	—
1421	C₂³	—	9	4	no	—
1422	C₂³	—	9	1	no	—
1423	C₂³	—	18	4	no	—
1424	C₂³	—	18	4	no	—
1425	C₂³	—	18	8	no	—
1426	C₂³	—	18	8	no	—
1427	C₂³	—	18	1	no	—
1428	C₂³	—	18	4	no	—
1429	C₂³	—	18	2	no	—
1430	C₂³	—	36	4	no	—
1431	C₂³	—	36	8	no	—
1432	C₂³	—	36	4	no	—
1433	C₂³	—	36	32	no	—
1434	C₂³	—	36	8	no	—
1435	C₂³	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
1436	Q₈	—	2	1	no	—
1437	Q₈	—	9	2	no	—
1438	Q₈	—	18	4	no	—
1439	Q₈	—	18	1	no	—
1440	Q₈	C₂³×C₃×C₃⋊D₃	1	2	yes	complemented
1441	D₄	—	2	4	no	—
1442	D₄	—	2	2	no	—
1443	D₄	—	2	4	no	—
1444	D₄	—	2	1	no	—
1445	D₄	—	9	2	no	—
1446	D₄	—	9	4	no	—
1447	D₄	—	18	4	no	—
1448	D₄	—	18	8	no	—
1449	D₄	—	18	8	no	—
1450	D₄	—	18	4	no	—
1451	D₄	—	18	4	no	—
1452	D₄	—	18	4	no	—
1453	D₄	—	18	4	no	—
1454	D₄	—	18	2	no	—
1455	D₄	—	18	1	no	—
1456	D₄	C₂³×C₃×C₃⋊D₃	1	4	yes	—
1457	D₄	C₂³×C₃×C₃⋊D₃	1	2	yes	complemented
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	4	no	—
1460	C₂×C₄	—	9	1	no	—
1461	C₂×C₄	—	9	1	no	—
1462	C₂×C₄	—	9	4	no	—
1463	C₂×C₄	—	9	4	no	—
1464	C₂×C₄	—	9	2	no	—
1465	C₂×C₄	—	9	2	no	—
1466	C₂×C₄	—	9	4	no	—
1467	C₂×C₄	—	9	2	no	—
1468	C₂×C₄	—	9	2	no	—
1469	C₂×C₄	—	18	4	no	—
1470	C₂×C₄	—	18	4	no	—
1471	C₂×C₄	—	18	4	no	—
1472	C₂×C₄	—	18	1	no	—
1473	C₂×C₄	—	18	4	no	—
1474	C₂×C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
1475	C₂×C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
1476	C₂×C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
1477	C₂×C₄	C₂³×C₃×C₃⋊D₃	1	2	yes	—
1478	C₈	—	9	4	no	—
1479	C₈	C₂³×C₃×C₃⋊D₃	1	4	yes	complemented
1480	C₂×C₃	—	2	2	no	—
1481	C₂×C₃	—	2	8	no	—
1482	C₂×C₃	—	2	4	no	—
1483	C₂×C₃	—	2	8	no	—
1484	C₂×C₃	—	4	8	no	—
1485	C₂×C₃	—	4	4	no	—
1486	C₂×C₃	—	4	2	no	—
1487	C₂×C₃	—	4	16	no	—
1488	C₂×C₃	—	4	8	no	—
1489	C₂×C₃	—	8	16	no	—
1490	C₂×C₃	—	8	8	no	—
1491	C₂×C₃	—	9	4	no	—
1492	C₂×C₃	—	18	2	no	—
1493	C₂×C₃	—	36	4	no	—
1494	C₂×C₃	—	36	2	no	—
1495	C₂×C₃	C₃×D₃×AGL(1,ℤ/8)	1	8	yes	complemented
1496	C₂×C₃	C₃⋊D₃×AGL(1,ℤ/8)	1	2	yes	direct product factor
1497	C₂×C₃	C₂²×C₃×D₃×D₄	1	4	yes	—
1498	C₂×C₃	C₂²×D₄×C₃⋊D₃	1	1	yes	characteristic
1499	D₃	—	3	16	no	—
1500	D₃	—	6	8	no	—
1501	D₃	—	12	16	no	—
1502	D₃	—	12	8	no	—
1503	C₂²	—	2	2	no	—
1504	C₂²	—	2	2	no	—
1505	C₂²	—	2	4	no	—
1506	C₂²	—	4	8	no	—
1507	C₂²	—	4	4	no	—
1508	C₂²	—	4	2	no	—
1509	C₂²	—	9	2	no	—
1510	C₂²	—	9	4	no	—
1511	C₂²	—	9	2	no	—
1512	C₂²	—	18	8	no	—
1513	C₂²	—	18	2	no	—
1514	C₂²	—	18	2	no	—
1515	C₂²	—	18	4	no	—
1516	C₂²	—	36	8	no	—
1517	C₂²	—	36	16	no	—
1518	C₂²	—	36	8	no	—
1519	C₂²	—	36	16	no	—
1520	C₂²	—	36	4	no	—
1521	C₂²	—	36	2	no	—
1522	C₂²	C₂×C₃×D₄×C₃⋊D₃	1	2	yes	—
1523	C₂²	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
1524	C₄	—	2	2	no	—
1525	C₄	—	9	2	no	—
1526	C₄	—	9	2	no	—
1527	C₄	—	18	2	no	—
1528	C₄	C₂×C₃×D₄×C₃⋊D₃	1	2	yes	—
1529	C₄	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
1530	C₄	C₂⁴×C₃×C₃⋊D₃	1	1	yes	characteristic
1531	C₃	—	2	4	no	—
1532	C₃	C₂×C₃⋊D₃×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor
1533	C₃	C₂×C₃×D₃×AGL(1,ℤ/8)	1	4	yes	complemented
1534	C₂	—	2	2	no	—
1535	C₂	—	4	4	no	—
1536	C₂	—	4	2	no	—
1537	C₂	—	9	4	no	—
1538	C₂	—	18	2	no	—
1539	C₂	—	36	4	no	—
1540	C₂	—	36	2	no	—
1541	C₂	C₃×C₃⋊D₃×AGL(1,ℤ/8)	1	2	yes	direct product factor
1542	C₂	C₂²×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×C₃⋊D₃
Fitting	C₂×C₃³×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃³	C₂²×D₄
hypercenter	C₂×C₃×AGL(1,ℤ/8)	C₃⋊D₃
hypocenter	C₃²	C₂²×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×#41×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃×D₄×C₃⋊D₃	C₂	semidirect
3. C₂×C₃³×AGL(1,ℤ/8)	C₂	semidirect
4. C₂×C₃×#64158	C₂	semidirect
5. C₂×C₃×#64141	C₂	semidirect
6. C₃×C₃⋊D₃×AGL(1,ℤ/8)	C₂	direct (N × H)
7. C₂×C₃×#64123	C₂	semidirect
8. C₂×C₃×SD₁₆×C₃⋊D₃	C₂	semidirect
9. C₂×C₃×#64120	C₂	semidirect
10. C₂×C₃×D₈×C₃⋊D₃	C₂	semidirect
11. C₂×C₃×#64117	C₂	semidirect
12. C₂×C₃×M₁₆×C₃⋊D₃	C₂	semidirect
14. C₂×C₃⋊D₃×AGL(1,ℤ/8)	C₃	direct (N × H)
16. C₂×C₃³×#41	C₂²	semidirect
17. C₂²×C₃³×D₄	C₂²	semidirect
20. C₃×#41×C₃⋊D₃	C₂²	semidirect
21. C₂×C₃×#3832	C₂²	semidirect
22. C₂×C₃×Q₈×C₃⋊D₃	C₂²	semidirect
24. C₂×C₃×#3830	C₂²	semidirect
30. C₂×C₃×D₄×C₃⋊D₃	C₂²	semidirect
31. C₂×C₃×D₄×C₃⋊D₃	C₂²	semidirect
32. C₂×C₃×D₄×C₃⋊D₃	C₂²	semidirect
34. C₂×C₃×#3828	C₂²	semidirect
35. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
38. C₃³×AGL(1,ℤ/8)	C₂²	semidirect
39. C₂×C₃³×SD₁₆	C₂²	semidirect
40. C₂×C₃³×D₈	C₂²	semidirect
41. C₂×C₃³×M₁₆	C₂²	semidirect
42. C₃×#64158	C₂²	semidirect
43. C₂×C₃×#3755	C₂²	semidirect
44. C₂×C₃×#3754	C₂²	semidirect
45. C₃×#64141	C₂²	semidirect
46. C₂×C₃×#3753	C₂²	semidirect
47. C₂×C₃×#3753	C₂²	semidirect
48. C₂×C₃×#3748	C₂²	semidirect
49. C₃×#64123	C₂²	semidirect
50. C₃×SD₁₆×C₃⋊D₃	C₂²	semidirect
51. C₃×#64120	C₂²	semidirect
52. C₃×D₈×C₃⋊D₃	C₂²	semidirect
53. C₃×#64117	C₂²	semidirect
54. C₃×M₁₆×C₃⋊D₃	C₂²	semidirect
55. C₂×C₃×#3745	C₂²	semidirect
56. C₂×C₃×#3744	C₂²	semidirect
57. C₂×C₃×#3743	C₂²	semidirect
58. C₂×C₃×C₈×C₃⋊D₃	C₂²	semidirect
59. C₂×#41×C₃⋊D₃	C₂×C₃	semidirect
60. C₂²×D₄×C₃⋊D₃	C₂×C₃	semidirect
64. C₂×C₃²×AGL(1,ℤ/8)	D₃	semidirect
65. C₂×C₃²×AGL(1,ℤ/8)	C₂×C₃	semidirect
66. C₂×#64158	C₂×C₃	semidirect
67. C₂×#64141	C₂×C₃	semidirect
68. C₃⋊D₃×AGL(1,ℤ/8)	C₂×C₃	direct (N × H)
69. C₂×#64123	C₂×C₃	semidirect
70. C₂×SD₁₆×C₃⋊D₃	C₂×C₃	semidirect
71. C₂×#64120	C₂×C₃	semidirect
72. C₂×D₈×C₃⋊D₃	C₂×C₃	semidirect
73. C₂×#64117	C₂×C₃	semidirect
74. C₂×M₁₆×C₃⋊D₃	C₂×C₃	semidirect
93. C₃³×#41	C₂³	semidirect
94. C₂×C₃³×Q₈	C₂³	semidirect
99. C₂×C₃³×D₄	C₂³	semidirect
100. C₂×C₃³×D₄	C₂³	semidirect
112. C₃×#3832	C₂³	semidirect
114. C₃×Q₈×C₃⋊D₃	C₂³	semidirect
117. C₃×#3830	C₂³	semidirect
125. C₃×D₄×C₃⋊D₃	C₂³	semidirect
126. C₃×D₄×C₃⋊D₃	C₂³	semidirect
129. C₃×#3828	C₂³	semidirect
134. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
135. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
147. C₂×C₃×#634	C₂³	semidirect
148. C₃³×SD₁₆	C₂³	semidirect
149. C₃³×D₈	C₂³	semidirect
150. C₃³×M₁₆	C₂³	semidirect
151. C₂×C₃³×C₈	C₂³	semidirect
152. C₃×#3755	C₂³	semidirect
153. C₃×#3754	C₂³	semidirect
154. C₃×#3753	C₂³	semidirect
155. C₃×#3753	C₂³	semidirect
156. C₃×#3748	C₂³	semidirect
157. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂³	semidirect
158. C₃×#3745	C₂³	semidirect
159. C₃×#3744	C₂³	semidirect
160. C₃×#3743	C₂³	semidirect
161. C₃×C₈×C₃⋊D₃	C₂³	semidirect
167. C₂×C₃²×#41	C₂×D₃	semidirect
168. C₂×C₃²×#41	C₂²×C₃	semidirect
170. C₂²×C₃²×D₄	C₂×D₃	semidirect
171. C₂²×C₃²×D₄	C₂²×C₃	semidirect
174. #41×C₃⋊D₃	C₂²×C₃	semidirect
175. C₂×#3832	C₂²×C₃	semidirect
176. C₂×Q₈×C₃⋊D₃	C₂²×C₃	semidirect
178. C₂×#3830	C₂²×C₃	semidirect
184. C₂×D₄×C₃⋊D₃	C₂²×C₃	semidirect
185. C₂×D₄×C₃⋊D₃	C₂²×C₃	semidirect
186. C₂×D₄×C₃⋊D₃	C₂²×C₃	semidirect
188. C₂×#3828	C₂²×C₃	semidirect
189. C₂²×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
213. C₃²×AGL(1,ℤ/8)	C₂×D₃	semidirect
214. C₃²×AGL(1,ℤ/8)	C₂²×C₃	semidirect
216. C₂×C₃²×SD₁₆	C₂×D₃	semidirect
217. C₂×C₃²×SD₁₆	C₂²×C₃	semidirect
219. C₂×C₃²×D₈	C₂×D₃	semidirect
220. C₂×C₃²×D₈	C₂²×C₃	semidirect
222. C₂×C₃²×M₁₆	C₂×D₃	semidirect
223. C₂×C₃²×M₁₆	C₂²×C₃	semidirect
224. #64158	C₂²×C₃	semidirect
225. C₂×#3755	C₂²×C₃	semidirect
226. C₂×#3754	C₂²×C₃	semidirect
227. #64141	C₂²×C₃	semidirect
228. C₂×#3753	C₂²×C₃	semidirect
229. C₂×#3753	C₂²×C₃	semidirect
230. C₂×#3748	C₂²×C₃	semidirect
231. #64123	C₂²×C₃	semidirect
232. SD₁₆×C₃⋊D₃	C₂²×C₃	semidirect
233. #64120	C₂²×C₃	semidirect
234. D₈×C₃⋊D₃	C₂²×C₃	semidirect
235. #64117	C₂²×C₃	semidirect
236. M₁₆×C₃⋊D₃	C₂²×C₃	semidirect
237. C₂×#3745	C₂²×C₃	semidirect
238. C₂×#3744	C₂²×C₃	semidirect
239. C₂×#3743	C₂²×C₃	semidirect
240. C₂×C₈×C₃⋊D₃	C₂²×C₃	semidirect
279. C₃³×Q₈	C₂⁴	semidirect
285. C₃³×D₄	C₂⁴	semidirect
307. C₃×C₄⋊(C₃⋊D₃)	C₂⁴	semidirect
319. C₃×#634	C₂⁴	semidirect
320. C₃³×C₈	C₂⁴	semidirect
321. C₃×C₃⋊(C₃⋊C₈)	C₂⁴	semidirect
333. C₂×C₃×AGL(1,ℤ/8)	C₃×D₃	semidirect
334. C₂×C₃×AGL(1,ℤ/8)	C₃⋊D₃	direct (N × H)
368. C₃²×#41	C₂²×D₃	semidirect
369. C₃²×#41	C₂³×C₃	semidirect
371. C₂×C₃²×Q₈	C₂²×D₃	semidirect
372. C₂×C₃²×Q₈	C₂³×C₃	semidirect
386. C₂×C₃²×D₄	C₂²×D₃	semidirect
387. C₂×C₃²×D₄	C₂²×D₃	semidirect
389. C₂×C₃²×D₄	C₂³×C₃	semidirect
390. C₂×C₃²×D₄	C₂³×C₃	semidirect
406. #3832	C₂³×C₃	semidirect
408. Q₈×C₃⋊D₃	C₂³×C₃	semidirect
411. #3830	C₂³×C₃	semidirect
419. D₄×C₃⋊D₃	C₂³×C₃	semidirect
420. D₄×C₃⋊D₃	C₂³×C₃	semidirect
423. #3828	C₂³×C₃	semidirect
428. C₂×C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
429. C₂×C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
441. C₂×#634	C₂³×C₃	semidirect
488. C₃²×SD₁₆	C₂²×D₃	semidirect
489. C₃²×SD₁₆	C₂³×C₃	semidirect
491. C₃²×D₈	C₂²×D₃	semidirect
492. C₃²×D₈	C₂³×C₃	semidirect
494. C₃²×M₁₆	C₂²×D₃	semidirect
495. C₃²×M₁₆	C₂³×C₃	semidirect
497. C₂×C₃²×C₈	C₂²×D₃	semidirect
498. C₂×C₃²×C₈	C₂³×C₃	semidirect
499. #3755	C₂³×C₃	semidirect
500. #3754	C₂³×C₃	semidirect
501. #3753	C₂³×C₃	semidirect
502. #3753	C₂³×C₃	semidirect
503. #3748	C₂³×C₃	semidirect
504. C₂×C₃⋊(C₃⋊C₈)	C₂³×C₃	semidirect
505. #3745	C₂³×C₃	semidirect
506. #3744	C₂³×C₃	semidirect
507. #3743	C₂³×C₃	semidirect
508. C₈×C₃⋊D₃	C₂³×C₃	semidirect
538. C₂×C₃×C₃⋊D₃	AGL(1,ℤ/8)	direct (N × H)
558. C₂×C₃×#41	C₂×C₃×D₃	semidirect
559. C₂×C₃×#41	C₂×C₃⋊D₃	semidirect
572. C₂²×C₃×D₄	C₂×C₃×D₃	semidirect
573. C₂²×C₃×D₄	C₂×C₃⋊D₃	semidirect
602. C₃×AGL(1,ℤ/8)	C₂×C₃×D₃	semidirect
603. C₃×AGL(1,ℤ/8)	C₂×C₃⋊D₃	direct (N × H)
609. C₂×C₃×SD₁₆	C₂×C₃×D₃	semidirect
610. C₂×C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
616. C₂×C₃×D₈	C₂×C₃×D₃	semidirect
617. C₂×C₃×D₈	C₂×C₃⋊D₃	semidirect
622. C₂×C₃×M₁₆	C₂×C₃×D₃	semidirect
623. C₂×C₃×M₁₆	C₂×C₃⋊D₃	semidirect
691. C₃²×Q₈	C₂³×D₃	semidirect
692. C₃²×Q₈	C₂⁴×C₃	semidirect
708. C₃²×D₄	C₂³×D₃	semidirect
710. C₃²×D₄	C₂⁴×C₃	semidirect
744. C₄⋊(C₃⋊D₃)	C₂⁴×C₃	semidirect
756. #634	C₂⁴×C₃	semidirect
786. C₃²×C₈	C₂³×D₃	semidirect
787. C₃²×C₈	C₂⁴×C₃	semidirect
788. C₃⋊(C₃⋊C₈)	C₂⁴×C₃	semidirect
798. C₂×AGL(1,ℤ/8)	C₃×C₃⋊D₃	direct (N × H)
805. C₂×C₃³	C₂×AGL(1,ℤ/8)	semidirect
810. C₃×C₃⋊D₃	C₂×AGL(1,ℤ/8)	direct (N × H)
840. C₃×#41	C₂²×C₃×D₃	semidirect
841. C₃×#41	C₂²×C₃⋊D₃	semidirect
847. C₂×C₃×Q₈	C₂²×C₃×D₃	semidirect
848. C₂×C₃×Q₈	C₂²×C₃⋊D₃	semidirect
883. C₂×C₃×D₄	C₂²×C₃×D₃	semidirect
884. C₂×C₃×D₄	C₂²×C₃×D₃	semidirect
886. C₂×C₃×D₄	C₂²×C₃⋊D₃	semidirect
887. C₂×C₃×D₄	C₂²×C₃⋊D₃	semidirect
955. C₃×SD₁₆	C₂²×C₃×D₃	semidirect
956. C₃×SD₁₆	C₂²×C₃⋊D₃	semidirect
961. C₃×D₈	C₂²×C₃×D₃	semidirect
962. C₃×D₈	C₂²×C₃⋊D₃	semidirect
966. C₃×M₁₆	C₂²×C₃×D₃	semidirect
967. C₃×M₁₆	C₂²×C₃⋊D₃	semidirect
971. C₂×C₃×C₈	C₂²×C₃×D₃	semidirect
972. C₂×C₃×C₈	C₂²×C₃⋊D₃	semidirect
1017. C₂×C₃⋊D₃	C₃×AGL(1,ℤ/8)	direct (N × H)
1059. C₂×#41	C₂×C₃×C₃⋊D₃	semidirect
1071. C₂²×D₄	C₂×C₃×C₃⋊D₃	semidirect
1079. AGL(1,ℤ/8)	C₂×C₃×C₃⋊D₃	direct (N × H)
1084. C₂×SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
1089. C₂×D₈	C₂×C₃×C₃⋊D₃	semidirect
1093. C₂×M₁₆	C₂×C₃×C₃⋊D₃	semidirect
1095. C₃³	C₂²×AGL(1,ℤ/8)	semidirect
1148. C₃×Q₈	C₂³×C₃×D₃	semidirect
1149. C₃×Q₈	C₂³×C₃⋊D₃	semidirect
1176. C₃×D₄	C₂³×C₃×D₃	semidirect
1178. C₃×D₄	C₂³×C₃⋊D₃	semidirect
1241. C₃×C₈	C₂³×C₃×D₃	semidirect
1242. C₃×C₈	C₂³×C₃⋊D₃	semidirect
1255. C₂×C₃²	D₃×AGL(1,ℤ/8)	semidirect
1256. C₂×C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
1262. C₃⋊D₃	C₂×C₃×AGL(1,ℤ/8)	direct (N × H)
1284. #41	C₂²×C₃×C₃⋊D₃	semidirect
1289. C₂×Q₈	C₂²×C₃×C₃⋊D₃	semidirect
1315. C₂×D₄	C₂²×C₃×C₃⋊D₃	semidirect
1316. C₂×D₄	C₂²×C₃×C₃⋊D₃	semidirect
1334. SD₁₆	C₂²×C₃×C₃⋊D₃	semidirect
1338. D₈	C₂²×C₃×C₃⋊D₃	semidirect
1341. M₁₆	C₂²×C₃×C₃⋊D₃	semidirect
1344. C₂×C₈	C₂²×C₃×C₃⋊D₃	semidirect
1414. C₃²	C₂×D₃×AGL(1,ℤ/8)	semidirect
1415. C₃²	C₂²×C₃×AGL(1,ℤ/8)	semidirect
1440. Q₈	C₂³×C₃×C₃⋊D₃	semidirect
1457. D₄	C₂³×C₃×C₃⋊D₃	semidirect
1479. C₈	C₂³×C₃×C₃⋊D₃	semidirect
1495. C₂×C₃	C₃×D₃×AGL(1,ℤ/8)	semidirect
1496. C₂×C₃	C₃⋊D₃×AGL(1,ℤ/8)	direct (N × H)
1532. C₃	C₂×C₃⋊D₃×AGL(1,ℤ/8)	direct (N × H)
1533. C₃	C₂×C₃×D₃×AGL(1,ℤ/8)	semidirect
1541. C₂	C₃×C₃⋊D₃×AGL(1,ℤ/8)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#41×C₃⋊D₃	2
C₂²×C₃×D₄×C₃⋊D₃	2
C₂×C₃³×AGL(1,ℤ/8)	2
C₂×C₃×#64158	2
C₂×C₃×#64141	2
C₃×C₃⋊D₃×AGL(1,ℤ/8)	2
C₂×C₃×#64123	2
C₂×C₃×SD₁₆×C₃⋊D₃	2
C₂×C₃×#64120	2
C₂×C₃×D₈×C₃⋊D₃	2
C₂×C₃×#64117	2
C₂×C₃×M₁₆×C₃⋊D₃	2
C₂×C₃×D₃×AGL(1,ℤ/8)	3
C₂×C₃⋊D₃×AGL(1,ℤ/8)	3

Subgroups — C2×C3×C3⋊D3×AGL(1,ℤ/8) #72269002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₃⋊D₃×AGL(1,ℤ/8) #72269002