Subgroups — C₃×C₃⋊D₃×#442 #72244981

Order 3456.

4176 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₄×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
3	C₃³×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#10592851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#10592713	C₂	1	2	yes	maximal, complemented
6	C₃×#10592568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₃⋊D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#10592484	C₂	1	2	yes	maximal, complemented
9	C₃×C₃⋊D₃×#102	C₂	1	2	yes	maximal, complemented
10	C₃×#10592410	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₃⋊D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₃×#442	—	3	4	no	maximal
13	C₃⋊D₃×#442	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×C₃⋊D₃	—	2	2	no	—
16	C₂×C₃³×D₈	C₂²	1	1	yes	characteristic
17	C₃³×C₄×D₄	C₂²	1	2	yes	complemented
18	C₃×D₄×C₃⋊Dic₃	C₂²	1	2	yes	complemented
19	C₂×C₃×#3753	C₂²	1	2	yes	—
20	C₃×C₄×#638	—	2	2	no	—
21	C₃×D₈×C₃⋊D₃	C₄	1	8	yes	complemented
22	C₂×C₃×#3745	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
25	C₃×#64102	C₂²	1	2	yes	complemented
26	C₃×C₄⋊C₄×C₃⋊D₃	C₂²	1	2	yes	—
27	C₃×#64090	—	2	2	no	—
28	C₃×C₂²⋊C₄×C₃⋊D₃	—	2	2	no	—
29	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
30	C₃×C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
31	C₃³×#106	C₂²	1	1	yes	characteristic, complemented
32	C₃³×#102	C₂²	1	2	yes	complemented
33	C₃³×#97	C₂²	1	1	yes	characteristic, complemented
34	C₃×#63659	C₂²	1	2	yes	complemented
35	C₃×#63648	C₂²	1	2	yes	complemented
36	C₃×#63644	C₂²	1	1	yes	characteristic, complemented
37	C₃×#63642	C₂²	1	1	yes	characteristic, complemented
38	C₃×#63642	C₂²	1	1	yes	characteristic, complemented
39	C₃×#63636	C₂²	1	2	yes	complemented
40	C₃×#63635	C₂²	1	2	yes	complemented
41	C₃×#63630	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
43	C₄×D₄×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
44	C₂×C₃×D₃×D₈	—	3	4	no	—
45	C₃×C₄×D₃×D₄	—	3	8	no	—
46	C₃²×#442	—	2	4	no	—
47	C₃²×#442	D₃	1	4	yes	complemented
48	C₃²×#442	C₂×C₃	1	1	yes	characteristic, complemented
49	#10592851	C₂×C₃	1	1	yes	characteristic, complemented
50	#10592713	C₂×C₃	1	2	yes	complemented
51	#10592568	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃⋊D₃×#106	C₂×C₃	1	1	yes	characteristic, complemented
53	#10592484	C₂×C₃	1	2	yes	complemented
54	C₃⋊D₃×#102	C₂×C₃	1	2	yes	complemented
55	#10592410	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃⋊D₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
57	C₃×#5152	—	3	4	no	—
58	C₃×#5014	—	3	8	no	—
59	C₃×#4869	—	3	4	no	—
60	C₃×D₃×#106	—	3	4	no	—
61	C₃×#4785	—	3	8	no	—
62	C₃×D₃×#102	—	3	8	no	—
63	C₃×#4711	—	3	4	no	—
64	C₃×D₃×#97	—	3	4	no	—
65	C₂³×C₃×C₃⋊D₃	—	2	2	no	—
66	C₂×C₃³×D₄	C₂³	1	2	yes	—
67	C₂²×C₃³×C₄	—	2	2	no	—
68	C₂×C₃×#638	—	2	2	no	—
69	C₂²×C₃×C₃⋊Dic₃	—	2	2	no	—
70	C₃×D₄×C₃⋊D₃	—	2	4	no	—
71	C₃×D₄×C₃⋊D₃	C₂×C₄	1	8	yes	complemented
72	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
74	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
75	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
76	C₂×C₃×C₄×C₃⋊D₃	—	4	8	no	—
77	C₂×C₃×C₄×C₃⋊D₃	D₄	1	2	yes	—
78	C₂×C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
79	C₃³×D₈	C₂×C₄	1	4	yes	complemented
80	C₂×C₃³×C₈	C₂³	1	1	yes	characteristic
81	C₂×C₃³×C₈	C₂³	1	1	yes	characteristic
82	C₃³×C₄⋊C₄	C₂³	1	2	yes	—
83	C₃³×C₂²⋊C₄	—	2	2	no	—
84	C₃³×C₄²	C₂³	1	1	yes	characteristic
85	C₃×#3757	—	2	2	no	—
86	C₃×#3753	C₂×C₄	1	8	yes	complemented
87	C₃×#3752	—	2	2	no	—
88	C₃×#3752	—	2	2	no	—
89	C₃×C₄⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
90	C₃×#3750	—	2	2	no	—
91	C₃×C₄×C₃⋊Dic₃	D₄	1	2	yes	—
92	C₃×C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
95	C₃×#3745	C₂×C₄	1	4	yes	complemented
96	C₃×C₈×C₃⋊D₃	—	2	2	no	—
97	C₃×C₈×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
98	C₂×C₃×#442	—	9	1	no	—
99	D₃×#442	—	3	4	no	—
100	C₂×D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
101	C₂²×C₄×C₃⋊D₃	—	2	2	no	—
102	C₂×C₃×D₃×D₄	—	3	8	no	—
103	C₂²×C₃×C₄×D₃	—	6	8	no	—
104	C₂×C₃²×D₈	—	2	4	no	—
105	C₂×C₃²×D₈	C₂×D₃	1	4	yes	—
106	C₂×C₃²×D₈	C₂²×C₃	1	1	yes	characteristic
107	C₃²×C₄×D₄	—	2	8	no	—
108	C₃²×C₄×D₄	C₂×D₃	1	8	yes	complemented
109	C₃²×C₄×D₄	C₂²×C₃	1	2	yes	complemented
110	D₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
111	C₂×#3753	C₂²×C₃	1	2	yes	—
112	C₄×#638	—	2	2	no	—
113	D₈×C₃⋊D₃	C₃×C₄	1	8	yes	complemented
114	C₂×#3745	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
117	#64102	C₂²×C₃	1	2	yes	complemented
118	C₄⋊C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
119	#64090	—	2	2	no	—
120	C₂²⋊C₄×C₃⋊D₃	—	2	2	no	—
121	C₄×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	complemented
122	C₄²×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
123	C₃×D₄×Dic₃	—	3	8	no	—
124	C₂×C₃×#213	—	3	8	no	—
125	C₃×C₄×#67	—	6	8	no	—
126	C₃×D₃×D₈	—	3	32	no	—
127	C₂×C₃×D₂₄	—	3	4	no	—
128	C₂×C₃×D₃×C₈	—	3	4	no	—
129	C₂×C₃×D₃×C₈	—	3	4	no	—
130	C₃×#893	—	3	8	no	—
131	C₃×D₃×C₄⋊C₄	—	3	8	no	—
132	C₃×#67⋊C₄	—	6	8	no	—
133	C₃×D₃×C₂²⋊C₄	—	6	8	no	—
134	C₃×C₄×D₁₂	—	3	8	no	—
135	C₃×C₄²×D₃	—	3	4	no	—
136	C₃²×#106	—	2	4	no	—
137	C₃²×#106	C₂×D₃	1	4	yes	complemented
138	C₃²×#106	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₃²×#102	—	2	8	no	—
140	C₃²×#102	C₂×D₃	1	8	yes	complemented
141	C₃²×#102	C₂²×C₃	1	2	yes	complemented
142	C₃²×#97	—	2	4	no	—
143	C₃²×#97	C₂×D₃	1	4	yes	complemented
144	C₃²×#97	C₂²×C₃	1	1	yes	characteristic, complemented
145	#63659	C₂²×C₃	1	2	yes	complemented
146	#63648	C₂²×C₃	1	2	yes	complemented
147	#63644	C₂²×C₃	1	1	yes	characteristic, complemented
148	#63642	C₂²×C₃	1	1	yes	characteristic, complemented
149	#63642	C₂²×C₃	1	1	yes	characteristic, complemented
150	#63636	C₂²×C₃	1	2	yes	complemented
151	#63635	C₂²×C₃	1	2	yes	complemented
152	#63630	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₃×#832	—	3	8	no	—
154	C₃×#821	—	3	8	no	—
155	C₃×#817	—	3	4	no	—
156	C₃×#815	—	3	4	no	—
157	C₃×#815	—	3	4	no	—
158	C₃×#809	—	3	8	no	—
159	C₃×#808	—	3	8	no	—
160	C₃×#803	—	3	4	no	—
161	C₂³×C₃³	—	2	2	no	—
162	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
163	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
164	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
165	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
166	C₂²×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
167	C₃³×D₄	—	2	2	no	—
168	C₃³×D₄	C₂²×C₄	1	4	yes	complemented
169	C₂×C₃³×C₄	—	2	2	no	—
170	C₂×C₃³×C₄	—	4	4	no	—
171	C₂×C₃³×C₄	C₂×D₄	1	2	yes	—
172	C₂×C₃³×C₄	C₂⁴	1	1	yes	characteristic
173	C₃×#638	—	2	8	no	—
174	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
175	C₂×C₃×C₃⋊Dic₃	—	4	4	no	—
176	C₂×C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
178	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
179	C₃×C₄⋊(C₃⋊D₃)	C₂²×C₄	1	4	yes	complemented
180	C₃×C₄×C₃⋊D₃	—	2	4	no	—
181	C₃×C₄×C₃⋊D₃	—	4	4	no	—
182	C₃×C₄×C₃⋊D₃	—	4	4	no	—
183	C₃×C₄×C₃⋊D₃	—	4	4	no	—
184	C₃×C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
185	C₃×C₄×C₃⋊D₃	#41	1	2	yes	—
186	C₃³×C₈	—	2	1	no	—
187	C₃³×C₈	C₂²×C₄	1	2	yes	complemented
188	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
189	C₃×C₃⋊(C₃⋊C₈)	C₂²×C₄	1	2	yes	complemented
190	C₂²×C₃×D₈	—	9	1	no	—
191	C₂×C₃×C₄×D₄	—	9	2	no	—
192	C₂×D₃×D₈	—	3	4	no	—
193	C₄×D₃×D₄	—	3	8	no	—
194	C₃×#442	—	2	4	no	—
195	C₃×#442	—	9	1	no	—
196	C₃×#442	—	9	2	no	—
197	C₃×#442	—	9	1	no	—
198	C₃×#442	—	9	2	no	—
199	C₃×#442	—	9	1	no	—
200	C₃×#442	C₃×D₃	1	4	yes	complemented
201	C₃×#442	C₃⋊D₃	1	1	yes	characteristic, direct product factor
202	C₂×C₃×#106	—	9	1	no	—
203	C₂×C₃×#102	—	9	2	no	—
204	C₂×C₃×#97	—	9	1	no	—
205	#5152	—	3	4	no	—
206	#5014	—	3	8	no	—
207	#4869	—	3	4	no	—
208	D₃×#106	—	3	4	no	—
209	#4785	—	3	8	no	—
210	D₃×#102	—	3	8	no	—
211	#4711	—	3	4	no	—
212	D₃×#97	—	3	4	no	—
213	C₂³×C₃⋊D₃	—	2	2	no	—
214	C₂³×C₃×D₃	—	6	8	no	—
215	C₂×C₃²×D₄	—	2	8	no	—
216	C₂×C₃²×D₄	C₂²×D₃	1	8	yes	—
217	C₂×C₃²×D₄	C₂³×C₃	1	2	yes	—
218	C₂²×C₃²×C₄	—	2	8	no	—
219	C₂²×C₃²×C₄	—	2	2	no	—
220	C₂²×C₃²×C₄	—	4	8	no	—
221	C₂×#638	—	2	2	no	—
222	C₂²×C₃⋊Dic₃	—	2	2	no	—
223	D₄×C₃⋊D₃	—	2	4	no	—
224	D₄×C₃⋊D₃	C₂×C₃×C₄	1	8	yes	complemented
225	C₂×C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
226	C₂×C₄×C₃⋊D₃	—	2	2	no	—
227	C₂×C₄×C₃⋊D₃	—	2	2	no	—
228	C₂×C₄×C₃⋊D₃	—	2	2	no	—
229	C₂×C₄×C₃⋊D₃	—	4	8	no	—
230	C₂×C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
231	C₂×C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
232	C₂×C₃×#67	—	6	8	no	—
233	C₂²×C₃×Dic₃	—	6	8	no	—
234	C₃×D₃×D₄	—	3	32	no	—
235	C₃×D₃×D₄	—	6	16	no	—
236	C₂×C₃×D₁₂	—	3	8	no	—
237	C₂×C₃×C₄×D₃	—	3	4	no	—
238	C₂×C₃×C₄×D₃	—	3	8	no	—
239	C₂×C₃×C₄×D₃	—	6	8	no	—
240	C₂×C₃×C₄×D₃	—	6	8	no	—
241	C₂×C₃×C₄×D₃	—	6	8	no	—
242	C₂×C₃×C₄×D₃	—	12	32	no	—
243	C₃²×D₈	—	2	16	no	—
244	C₃²×D₈	C₄×D₃	1	16	yes	complemented
245	C₃²×D₈	C₂×C₃×C₄	1	4	yes	complemented
246	C₂×C₃²×C₈	—	2	4	no	—
247	C₂×C₃²×C₈	—	2	4	no	—
248	C₂×C₃²×C₈	C₂²×D₃	1	4	yes	—
249	C₂×C₃²×C₈	C₂²×D₃	1	4	yes	—
250	C₂×C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
251	C₂×C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
252	C₃²×C₄⋊C₄	—	2	8	no	—
253	C₃²×C₄⋊C₄	C₂²×D₃	1	8	yes	—
254	C₃²×C₄⋊C₄	C₂³×C₃	1	2	yes	—
255	C₃²×C₂²⋊C₄	—	2	8	no	—
256	C₃²×C₂²⋊C₄	—	2	2	no	—
257	C₃²×C₂²⋊C₄	—	4	8	no	—
258	C₃²×C₄²	—	2	4	no	—
259	C₃²×C₄²	C₂²×D₃	1	4	yes	—
260	C₃²×C₄²	C₂³×C₃	1	1	yes	characteristic
261	#3757	—	2	2	no	—
262	#3753	C₂×C₃×C₄	1	8	yes	complemented
263	#3752	—	2	2	no	—
264	#3752	—	2	2	no	—
265	C₄⋊(C₃⋊Dic₃)	C₂³×C₃	1	2	yes	—
266	#3750	—	2	2	no	—
267	C₄×C₃⋊Dic₃	C₃×D₄	1	2	yes	—
268	C₄×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
271	#3745	C₂×C₃×C₄	1	4	yes	complemented
272	C₈×C₃⋊D₃	—	2	2	no	—
273	C₈×C₃⋊D₃	C₂×C₃×C₄	1	4	yes	complemented
274	C₃×#217	—	6	8	no	—
275	C₃×#213	—	3	32	no	—
276	C₃×(C₂×D₃)⋊C₄	—	6	8	no	—
277	C₃×(C₂×D₃)⋊C₄	—	6	8	no	—
278	C₃×C₄⋊Dic₃	—	3	8	no	—
279	C₃×Dic₃⋊C₄	—	6	8	no	—
280	C₃×C₄×Dic₃	—	3	8	no	—
281	C₃×C₄×Dic₃	—	3	4	no	—
282	C₂×C₃×C₃⋊C₈	—	3	4	no	—
283	C₂×C₃×C₃⋊C₈	—	3	4	no	—
284	C₃×D₂₄	—	3	16	no	—
285	C₃×D₃×C₈	—	3	16	no	—
286	C₃×D₃×C₈	—	6	8	no	—
287	C₂×#442	—	9	1	no	Sylow
288	C₂²×C₃³	—	2	4	no	—
289	C₂²×C₃³	—	4	2	no	—
290	C₂²×C₃³	—	4	2	no	—
291	C₂²×C₃³	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₃×C₃⋊D₃	—	2	4	no	—
293	C₂×C₃×C₃⋊D₃	—	4	2	no	—
294	C₂×C₃×C₃⋊D₃	—	4	2	no	—
295	C₂×C₃×C₃⋊D₃	—	4	16	no	—
296	C₂×C₃×C₃⋊D₃	C₄×D₄	1	2	yes	—
297	C₂×C₃×C₃⋊D₃	AGL(1,ℤ/8)	1	4	yes	—
298	C₃³×C₄	—	2	2	no	—
299	C₃³×C₄	—	4	2	no	—
300	C₃³×C₄	C₂³×C₄	1	1	yes	characteristic
301	C₃³×C₄	C₂×#41	1	1	yes	characteristic
302	C₃×C₃⋊Dic₃	—	2	2	no	—
303	C₃×C₃⋊Dic₃	—	4	2	no	—
304	C₃×C₃⋊Dic₃	C₄×D₄	1	2	yes	—
305	C₂²×C₃×D₄	—	9	2	no	—
306	C₂³×C₃×C₄	—	18	2	no	—
307	C₂×D₃×D₄	—	3	8	no	—
308	C₂²×C₄×D₃	—	6	8	no	—
309	C₂×C₃×D₈	—	2	4	no	—
310	C₂×C₃×D₈	—	9	2	no	—
311	C₂×C₃×D₈	—	9	8	no	—
312	C₂×C₃×D₈	—	9	1	no	—
313	C₂×C₃×D₈	C₂×C₃×D₃	1	4	yes	—
314	C₂×C₃×D₈	C₂×C₃⋊D₃	1	1	yes	characteristic
315	C₂²×C₃×C₈	—	9	1	no	—
316	C₂²×C₃×C₈	—	9	1	no	—
317	C₃×C₄×D₄	—	2	8	no	—
318	C₃×C₄×D₄	—	9	2	no	—
319	C₃×C₄×D₄	—	9	2	no	—
320	C₃×C₄×D₄	—	9	2	no	—
321	C₃×C₄×D₄	—	18	2	no	—
322	C₃×C₄×D₄	—	18	2	no	—
323	C₃×C₄×D₄	C₂×C₃×D₃	1	8	yes	complemented
324	C₃×C₄×D₄	C₂×C₃⋊D₃	1	2	yes	complemented
325	C₂×C₃×C₄⋊C₄	—	9	2	no	—
326	C₂×C₃×C₂²⋊C₄	—	18	2	no	—
327	C₂×C₃×C₄²	—	9	1	no	—
328	D₄×Dic₃	—	3	8	no	—
329	C₂×#213	—	3	8	no	—
330	C₄×#67	—	6	8	no	—
331	D₃×D₈	—	3	32	no	—
332	C₂×D₂₄	—	3	4	no	—
333	C₂×D₃×C₈	—	3	4	no	—
334	C₂×D₃×C₈	—	3	4	no	—
335	#893	—	3	8	no	—
336	D₃×C₄⋊C₄	—	3	8	no	—
337	#67⋊C₄	—	6	8	no	—
338	D₃×C₂²⋊C₄	—	6	8	no	—
339	C₄×D₁₂	—	3	8	no	—
340	C₄²×D₃	—	3	4	no	—
341	C₃×#106	—	2	4	no	—
342	C₃×#106	—	9	1	no	—
343	C₃×#106	—	9	2	no	—
344	C₃×#106	C₂×C₃×D₃	1	4	yes	complemented
345	C₃×#106	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
346	C₃×#102	—	2	8	no	—
347	C₃×#102	—	9	2	no	—
348	C₃×#102	—	9	2	no	—
349	C₃×#102	—	9	2	no	—
350	C₃×#102	C₂×C₃×D₃	1	8	yes	complemented
351	C₃×#102	C₂×C₃⋊D₃	1	2	yes	complemented
352	C₃×#97	—	2	4	no	—
353	C₃×#97	—	9	1	no	—
354	C₃×#97	—	9	1	no	—
355	C₃×#97	—	9	1	no	—
356	C₃×#97	C₂×C₃×D₃	1	4	yes	complemented
357	C₃×#97	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
358	#832	—	3	8	no	—
359	#821	—	3	8	no	—
360	#817	—	3	4	no	—
361	#815	—	3	4	no	—
362	#815	—	3	4	no	—
363	#809	—	3	8	no	—
364	#808	—	3	8	no	—
365	#803	—	3	4	no	—
366	C₂³×C₃²	—	2	2	no	—
367	C₂³×C₃²	—	2	8	no	—
368	C₂³×C₃²	—	4	8	no	—
369	C₂²×C₃⋊D₃	—	2	2	no	—
370	C₂²×C₃⋊D₃	—	2	8	no	—
371	C₂²×C₃⋊D₃	—	4	4	no	—
372	C₂²×C₃⋊D₃	—	4	4	no	—
373	C₂²×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
374	C₂²×C₃×D₃	—	3	4	no	—
375	C₂²×C₃×D₃	—	6	32	no	—
376	C₂²×C₃×D₃	—	6	8	no	—
377	C₂²×C₃×D₃	—	12	16	no	—
378	C₂²×C₃×D₃	—	12	16	no	—
379	C₃²×D₄	—	2	2	no	—
380	C₃²×D₄	—	2	16	no	—
381	C₃²×D₄	—	2	8	no	—
382	C₃²×D₄	—	4	8	no	—
383	C₃²×D₄	C₂×C₄×D₃	1	16	yes	complemented
384	C₃²×D₄	C₂²×C₃×C₄	1	4	yes	complemented
385	C₂×C₃²×C₄	—	2	2	no	—
386	C₂×C₃²×C₄	—	2	4	no	—
387	C₂×C₃²×C₄	—	2	8	no	—
388	C₂×C₃²×C₄	—	2	8	no	—
389	C₂×C₃²×C₄	—	4	8	no	—
390	C₂×C₃²×C₄	—	4	4	no	—
391	C₂×C₃²×C₄	—	4	16	no	—
392	C₂×C₃²×C₄	—	8	16	no	—
393	C₂×C₃²×C₄	D₃×D₄	1	8	yes	—
394	C₂×C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
395	C₂×C₃²×C₄	C₂³×D₃	1	4	yes	—
396	C₂×C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
397	#638	—	2	8	no	—
398	C₂×C₃⋊Dic₃	—	2	2	no	—
399	C₂×C₃⋊Dic₃	—	4	4	no	—
400	C₂×C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
401	C₂×C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
402	C₄⋊(C₃⋊D₃)	—	2	2	no	—
403	C₄⋊(C₃⋊D₃)	C₂²×C₃×C₄	1	4	yes	complemented
404	C₄×C₃⋊D₃	—	2	4	no	—
405	C₄×C₃⋊D₃	—	4	4	no	—
406	C₄×C₃⋊D₃	—	4	4	no	—
407	C₄×C₃⋊D₃	—	4	4	no	—
408	C₄×C₃⋊D₃	C₂²×C₃×C₄	1	2	yes	—
409	C₄×C₃⋊D₃	C₃×#41	1	2	yes	—
410	C₃×#67	—	6	32	no	—
411	C₂×C₃×Dic₃	—	3	4	no	—
412	C₂×C₃×Dic₃	—	3	8	no	—
413	C₂×C₃×Dic₃	—	6	8	no	—
414	C₂×C₃×Dic₃	—	12	16	no	—
415	C₃×D₁₂	—	3	16	no	—
416	C₃×D₁₂	—	6	8	no	—
417	C₃×C₄×D₃	—	3	8	no	—
418	C₃×C₄×D₃	—	3	8	no	—
419	C₃×C₄×D₃	—	6	16	no	—
420	C₃×C₄×D₃	—	12	16	no	—
421	C₃×C₄×D₃	—	12	16	no	—
422	C₃×C₄×D₃	—	12	16	no	—
423	C₃²×C₈	—	2	1	no	—
424	C₃²×C₈	—	2	8	no	—
425	C₃²×C₈	—	2	4	no	—
426	C₃²×C₈	—	4	4	no	—
427	C₃²×C₈	C₂×C₄×D₃	1	8	yes	complemented
428	C₃²×C₈	C₂²×C₃×C₄	1	2	yes	complemented
429	C₃⋊(C₃⋊C₈)	—	2	1	no	—
430	C₃⋊(C₃⋊C₈)	C₂²×C₃×C₄	1	2	yes	complemented
431	C₃×C₃⋊C₈	—	3	8	no	—
432	C₃×C₃⋊C₈	—	6	4	no	—
433	C₂²×D₈	—	9	1	no	—
434	C₂×C₄×D₄	—	9	2	no	—
435	#442	—	9	1	no	—
436	#442	—	9	2	no	—
437	#442	—	9	1	no	—
438	#442	—	9	2	no	—
439	#442	—	9	1	no	—
440	#442	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
441	C₂×#106	—	9	1	no	—
442	C₂×#102	—	9	2	no	—
443	C₂×#97	—	9	1	no	—
444	C₂×C₃³	—	4	4	no	—
445	C₂×C₃³	C₂×C₄×D₄	1	1	yes	characteristic
446	C₂×C₃³	C₂×AGL(1,ℤ/8)	1	2	yes	—
447	C₃×C₃⋊D₃	—	4	4	no	—
448	C₃×C₃⋊D₃	#442	1	4	yes	direct product factor
449	C₂⁴×C₃	—	18	2	no	—
450	C₂³×D₃	—	6	8	no	—
451	C₂×C₃×D₄	—	2	8	no	—
452	C₂×C₃×D₄	—	9	8	no	—
453	C₂×C₃×D₄	—	9	2	no	—
454	C₂×C₃×D₄	—	18	4	no	—
455	C₂×C₃×D₄	—	18	2	no	—
456	C₂×C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
457	C₂×C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
458	C₂²×C₃×C₄	—	2	8	no	—
459	C₂²×C₃×C₄	—	2	2	no	—
460	C₂²×C₃×C₄	—	4	8	no	—
461	C₂²×C₃×C₄	—	9	1	no	—
462	C₂²×C₃×C₄	—	9	2	no	—
463	C₂²×C₃×C₄	—	18	2	no	—
464	C₂²×C₃×C₄	—	18	2	no	—
465	C₂²×C₃×C₄	—	18	2	no	—
466	C₂²×C₃×C₄	—	18	2	no	—
467	C₂²×C₃×C₄	—	36	8	no	—
468	C₂×#67	—	6	8	no	—
469	C₂²×Dic₃	—	6	8	no	—
470	D₃×D₄	—	3	32	no	—
471	D₃×D₄	—	6	16	no	—
472	C₂×D₁₂	—	3	8	no	—
473	C₂×C₄×D₃	—	3	4	no	—
474	C₂×C₄×D₃	—	3	8	no	—
475	C₂×C₄×D₃	—	6	8	no	—
476	C₂×C₄×D₃	—	6	8	no	—
477	C₂×C₄×D₃	—	6	8	no	—
478	C₂×C₄×D₃	—	12	32	no	—
479	C₃×D₈	—	2	16	no	—
480	C₃×D₈	—	9	8	no	—
481	C₃×D₈	—	9	4	no	—
482	C₃×D₈	C₃×C₄×D₃	1	16	yes	complemented
483	C₃×D₈	C₄×C₃⋊D₃	1	4	yes	complemented
484	C₂×C₃×C₈	—	2	4	no	—
485	C₂×C₃×C₈	—	2	4	no	—
486	C₂×C₃×C₈	—	9	1	no	—
487	C₂×C₃×C₈	—	9	4	no	—
488	C₂×C₃×C₈	—	9	1	no	—
489	C₂×C₃×C₈	—	18	2	no	—
490	C₂×C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
491	C₂×C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
492	C₂×C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
493	C₂×C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
494	C₃×C₄⋊C₄	—	2	8	no	—
495	C₃×C₄⋊C₄	—	9	2	no	—
496	C₃×C₄⋊C₄	—	18	2	no	—
497	C₃×C₄⋊C₄	C₂²×C₃×D₃	1	8	yes	—
498	C₃×C₄⋊C₄	C₂²×C₃⋊D₃	1	2	yes	—
499	C₃×C₂²⋊C₄	—	2	8	no	—
500	C₃×C₂²⋊C₄	—	2	2	no	—
501	C₃×C₂²⋊C₄	—	4	8	no	—
502	C₃×C₂²⋊C₄	—	18	2	no	—
503	C₃×C₂²⋊C₄	—	18	2	no	—
504	C₃×C₂²⋊C₄	—	18	2	no	—
505	C₃×C₄²	—	2	4	no	—
506	C₃×C₄²	—	9	1	no	—
507	C₃×C₄²	—	9	2	no	—
508	C₃×C₄²	C₂²×C₃×D₃	1	4	yes	—
509	C₃×C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
510	#217	—	6	8	no	—
511	#213	—	3	32	no	—
512	(C₂×D₃)⋊C₄	—	6	8	no	—
513	(C₂×D₃)⋊C₄	—	6	8	no	—
514	C₄⋊Dic₃	—	3	8	no	—
515	Dic₃⋊C₄	—	6	8	no	—
516	C₄×Dic₃	—	3	4	no	—
517	C₄×Dic₃	—	3	8	no	—
518	C₂×C₃⋊C₈	—	3	4	no	—
519	C₂×C₃⋊C₈	—	3	4	no	—
520	D₂₄	—	3	16	no	—
521	D₃×C₈	—	3	16	no	—
522	D₃×C₈	—	6	8	no	—
523	C₂²×C₃²	—	2	4	no	—
524	C₂²×C₃²	—	2	4	no	—
525	C₂²×C₃²	—	2	16	no	—
526	C₂²×C₃²	—	4	16	no	—
527	C₂²×C₃²	—	4	2	no	—
528	C₂²×C₃²	—	4	2	no	—
529	C₂²×C₃²	—	4	8	no	—
530	C₂²×C₃²	—	4	8	no	—
531	C₂²×C₃²	—	8	8	no	—
532	C₂²×C₃²	—	8	8	no	—
533	C₂²×C₃²	C₂×D₃×D₄	1	4	yes	—
534	C₂²×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
535	C₂×C₃⋊D₃	—	2	4	no	—
536	C₂×C₃⋊D₃	—	4	2	no	—
537	C₂×C₃⋊D₃	—	4	2	no	—
538	C₂×C₃⋊D₃	—	4	16	no	—
539	C₂×C₃⋊D₃	C₃×C₄×D₄	1	2	yes	—
540	C₂×C₃⋊D₃	C₃×AGL(1,ℤ/8)	1	4	yes	—
541	C₂×C₃×D₃	—	3	16	no	—
542	C₂×C₃×D₃	—	3	8	no	—
543	C₂×C₃×D₃	—	6	16	no	—
544	C₂×C₃×D₃	—	12	64	no	—
545	C₂×C₃×D₃	—	12	8	no	—
546	C₂×C₃×D₃	—	12	8	no	—
547	C₃²×C₄	—	2	2	no	—
548	C₃²×C₄	—	2	4	no	—
549	C₃²×C₄	—	2	4	no	—
550	C₃²×C₄	—	2	8	no	—
551	C₃²×C₄	—	4	8	no	—
552	C₃²×C₄	—	4	2	no	—
553	C₃²×C₄	—	4	8	no	—
554	C₃²×C₄	—	8	8	no	—
555	C₃²×C₄	C₂²×C₄×D₃	1	4	yes	—
556	C₃²×C₄	D₃×#41	1	4	yes	—
557	C₃²×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
558	C₃²×C₄	C₂×C₃×#41	1	1	yes	characteristic
559	C₃⋊Dic₃	—	2	2	no	—
560	C₃⋊Dic₃	—	4	2	no	—
561	C₃⋊Dic₃	C₃×C₄×D₄	1	2	yes	—
562	C₃×Dic₃	—	3	8	no	—
563	C₃×Dic₃	—	6	8	no	—
564	C₃×Dic₃	—	12	8	no	—
565	C₂²×D₄	—	9	2	no	—
566	C₂³×C₄	—	18	2	no	—
567	C₂×D₈	—	9	2	no	—
568	C₂×D₈	—	9	8	no	—
569	C₂×D₈	—	9	1	no	—
570	C₂×D₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
571	C₂²×C₈	—	9	1	no	—
572	C₂²×C₈	—	9	1	no	—
573	C₄×D₄	—	9	2	no	—
574	C₄×D₄	—	9	2	no	—
575	C₄×D₄	—	9	2	no	—
576	C₄×D₄	—	18	2	no	—
577	C₄×D₄	—	18	2	no	—
578	C₄×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
579	C₂×C₄⋊C₄	—	9	2	no	—
580	C₂×C₂²⋊C₄	—	18	2	no	—
581	C₂×C₄²	—	9	1	no	—
582	#106	—	9	1	no	—
583	#106	—	9	2	no	—
584	#106	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
585	#102	—	9	2	no	—
586	#102	—	9	2	no	—
587	#102	—	9	2	no	—
588	#102	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
589	#97	—	9	1	no	—
590	#97	—	9	1	no	—
591	#97	—	9	1	no	—
592	#97	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
593	C₃³	C₂×#442	1	1	yes	characteristic, complemented, Sylow
594	C₂³×C₃	—	2	8	no	—
595	C₂³×C₃	—	2	2	no	—
596	C₂³×C₃	—	4	8	no	—
597	C₂³×C₃	—	9	1	no	—
598	C₂³×C₃	—	18	8	no	—
599	C₂³×C₃	—	18	2	no	—
600	C₂³×C₃	—	36	4	no	—
601	C₂³×C₃	—	36	4	no	—
602	C₂²×D₃	—	3	4	no	—
603	C₂²×D₃	—	6	32	no	—
604	C₂²×D₃	—	6	8	no	—
605	C₂²×D₃	—	12	16	no	—
606	C₂²×D₃	—	12	16	no	—
607	C₃×D₄	—	2	8	no	—
608	C₃×D₄	—	2	2	no	—
609	C₃×D₄	—	2	16	no	—
610	C₃×D₄	—	4	8	no	—
611	C₃×D₄	—	9	4	no	—
612	C₃×D₄	—	18	8	no	—
613	C₃×D₄	—	18	2	no	—
614	C₃×D₄	C₂×C₃×C₄×D₃	1	16	yes	complemented
615	C₃×D₄	C₂×C₄×C₃⋊D₃	1	4	yes	complemented
616	C₂×C₃×C₄	—	2	8	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	4	no	—
619	C₂×C₃×C₄	—	2	8	no	—
620	C₂×C₃×C₄	—	4	8	no	—
621	C₂×C₃×C₄	—	4	4	no	—
622	C₂×C₃×C₄	—	4	16	no	—
623	C₂×C₃×C₄	—	8	16	no	—
624	C₂×C₃×C₄	—	9	1	no	—
625	C₂×C₃×C₄	—	9	2	no	—
626	C₂×C₃×C₄	—	9	2	no	—
627	C₂×C₃×C₄	—	9	2	no	—
628	C₂×C₃×C₄	—	18	4	no	—
629	C₂×C₃×C₄	—	18	2	no	—
630	C₂×C₃×C₄	—	36	4	no	—
631	C₂×C₃×C₄	—	36	4	no	—
632	C₂×C₃×C₄	—	36	4	no	—
633	C₂×C₃×C₄	—	36	4	no	—
634	C₂×C₃×C₄	C₃×D₃×D₄	1	8	yes	—
635	C₂×C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
636	C₂×C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
637	C₂×C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
638	#67	—	6	32	no	—
639	C₂×Dic₃	—	3	4	no	—
640	C₂×Dic₃	—	3	8	no	—
641	C₂×Dic₃	—	6	8	no	—
642	C₂×Dic₃	—	12	16	no	—
643	D₁₂	—	3	16	no	—
644	D₁₂	—	6	8	no	—
645	C₄×D₃	—	3	8	no	—
646	C₄×D₃	—	3	8	no	—
647	C₄×D₃	—	6	16	no	—
648	C₄×D₃	—	12	16	no	—
649	C₄×D₃	—	12	16	no	—
650	C₄×D₃	—	12	16	no	—
651	C₃×C₈	—	2	4	no	—
652	C₃×C₈	—	2	1	no	—
653	C₃×C₈	—	2	8	no	—
654	C₃×C₈	—	4	4	no	—
655	C₃×C₈	—	9	2	no	—
656	C₃×C₈	—	18	1	no	—
657	C₃×C₈	C₂×C₃×C₄×D₃	1	8	yes	complemented
658	C₃×C₈	C₂×C₄×C₃⋊D₃	1	2	yes	complemented
659	C₃⋊C₈	—	3	8	no	—
660	C₃⋊C₈	—	6	4	no	—
661	C₂×C₃²	—	2	8	no	—
662	C₂×C₃²	—	2	4	no	—
663	C₂×C₃²	—	4	4	no	—
664	C₂×C₃²	—	4	16	no	—
665	C₂×C₃²	—	8	16	no	—
666	C₂×C₃²	C₄×D₃×D₄	1	4	yes	—
667	C₂×C₃²	D₃×AGL(1,ℤ/8)	1	8	yes	—
668	C₂×C₃²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
669	C₂×C₃²	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
670	C₃⋊D₃	—	4	4	no	—
671	C₃⋊D₃	C₃×#442	1	4	yes	direct product factor
672	C₃×D₃	—	3	16	no	—
673	C₃×D₃	—	12	16	no	—
674	C₂⁴	—	18	2	no	—
675	C₂×D₄	—	9	8	no	—
676	C₂×D₄	—	9	2	no	—
677	C₂×D₄	—	18	4	no	—
678	C₂×D₄	—	18	2	no	—
679	C₂×D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	9	1	no	—
682	C₂²×C₄	—	9	2	no	—
683	C₂²×C₄	—	18	2	no	—
684	C₂²×C₄	—	18	2	no	—
685	C₂²×C₄	—	18	2	no	—
686	C₂²×C₄	—	18	2	no	—
687	C₂²×C₄	—	36	8	no	—
688	D₈	—	9	8	no	—
689	D₈	—	9	4	no	—
690	D₈	C₃×C₄×C₃⋊D₃	1	4	yes	complemented
691	C₂×C₈	—	9	1	no	—
692	C₂×C₈	—	9	4	no	—
693	C₂×C₈	—	9	1	no	—
694	C₂×C₈	—	18	2	no	—
695	C₂×C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
696	C₂×C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
697	C₄⋊C₄	—	9	2	no	—
698	C₄⋊C₄	—	18	2	no	—
699	C₄⋊C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	18	2	no	—
702	C₂²⋊C₄	—	18	2	no	—
703	C₂²⋊C₄	—	18	2	no	—
704	C₄²	—	9	1	no	—
705	C₄²	—	9	2	no	—
706	C₄²	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
707	C₂²×C₃	—	2	16	no	—
708	C₂²×C₃	—	2	4	no	—
709	C₂²×C₃	—	2	4	no	—
710	C₂²×C₃	—	4	16	no	—
711	C₂²×C₃	—	4	8	no	—
712	C₂²×C₃	—	4	8	no	—
713	C₂²×C₃	—	4	2	no	—
714	C₂²×C₃	—	4	2	no	—
715	C₂²×C₃	—	8	8	no	—
716	C₂²×C₃	—	8	8	no	—
717	C₂²×C₃	—	9	4	no	—
718	C₂²×C₃	—	9	2	no	—
719	C₂²×C₃	—	18	4	no	—
720	C₂²×C₃	—	36	16	no	—
721	C₂²×C₃	—	36	2	no	—
722	C₂²×C₃	—	36	2	no	—
723	C₂²×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
724	C₂²×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
725	C₂×D₃	—	3	16	no	—
726	C₂×D₃	—	3	8	no	—
727	C₂×D₃	—	6	16	no	—
728	C₂×D₃	—	12	64	no	—
729	C₂×D₃	—	12	8	no	—
730	C₂×D₃	—	12	8	no	—
731	C₃×C₄	—	2	8	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	2	4	no	—
734	C₃×C₄	—	2	4	no	—
735	C₃×C₄	—	4	8	no	—
736	C₃×C₄	—	4	8	no	—
737	C₃×C₄	—	4	2	no	—
738	C₃×C₄	—	8	8	no	—
739	C₃×C₄	—	9	2	no	—
740	C₃×C₄	—	18	2	no	—
741	C₃×C₄	—	36	2	no	—
742	C₃×C₄	C₂²×C₃×C₄×D₃	1	4	yes	—
743	C₃×C₄	C₃×D₃×#41	1	4	yes	—
744	C₃×C₄	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
745	C₃×C₄	#41×C₃⋊D₃	1	1	yes	characteristic
746	Dic₃	—	3	8	no	—
747	Dic₃	—	6	8	no	—
748	Dic₃	—	12	8	no	—
749	C₃²	—	2	4	no	—
750	C₃²	D₃×#442	1	4	yes	complemented
751	C₃²	C₂×C₃×#442	1	1	yes	characteristic, complemented
752	C₂³	—	2	2	no	—
753	C₂³	—	9	1	no	—
754	C₂³	—	18	8	no	—
755	C₂³	—	18	2	no	—
756	C₂³	—	36	4	no	—
757	C₂³	—	36	4	no	—
758	D₄	—	2	2	no	—
759	D₄	—	9	4	no	—
760	D₄	—	18	8	no	—
761	D₄	—	18	2	no	—
762	D₄	C₂×C₃×C₄×C₃⋊D₃	1	4	yes	complemented
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	9	1	no	—
766	C₂×C₄	—	9	2	no	—
767	C₂×C₄	—	9	2	no	—
768	C₂×C₄	—	9	2	no	—
769	C₂×C₄	—	18	4	no	—
770	C₂×C₄	—	18	2	no	—
771	C₂×C₄	—	36	4	no	—
772	C₂×C₄	—	36	4	no	—
773	C₂×C₄	—	36	4	no	—
774	C₂×C₄	—	36	4	no	—
775	C₂×C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
776	C₂×C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
777	C₈	—	2	1	no	—
778	C₈	—	9	2	no	—
779	C₈	—	18	1	no	—
780	C₈	C₂×C₃×C₄×C₃⋊D₃	1	2	yes	complemented
781	C₂×C₃	—	2	8	no	—
782	C₂×C₃	—	2	4	no	—
783	C₂×C₃	—	4	4	no	—
784	C₂×C₃	—	4	16	no	—
785	C₂×C₃	—	8	16	no	—
786	C₂×C₃	—	9	4	no	—
787	C₂×C₃	—	36	4	no	—
788	C₂×C₃	C₃×C₄×D₃×D₄	1	4	yes	—
789	C₂×C₃	C₃×D₃×AGL(1,ℤ/8)	1	8	yes	—
790	C₂×C₃	C₄×D₄×C₃⋊D₃	1	1	yes	characteristic
791	C₂×C₃	C₃⋊D₃×AGL(1,ℤ/8)	1	2	yes	—
792	D₃	—	3	16	no	—
793	D₃	—	12	16	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	9	4	no	—
798	C₂²	—	9	2	no	—
799	C₂²	—	18	4	no	—
800	C₂²	—	36	16	no	—
801	C₂²	—	36	2	no	—
802	C₂²	—	36	2	no	—
803	C₂²	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	9	2	no	—
807	C₄	—	18	2	no	—
808	C₄	—	36	2	no	—
809	C₄	C₂²×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
810	C₄	C₃×#41×C₃⋊D₃	1	1	yes	characteristic
811	C₃	—	2	4	no	—
812	C₃	C₃⋊D₃×#442	1	1	yes	characteristic, direct product factor
813	C₃	C₃×D₃×#442	1	4	yes	complemented
814	C₂	—	4	4	no	—
815	C₂	—	9	4	no	—
816	C₂	—	36	4	no	—
817	C₂	C₃×C₄×D₄×C₃⋊D₃	1	1	yes	characteristic
818	C₂	C₃×C₃⋊D₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×C₃⋊D₃
commutator	C₃²×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#442	C₂
socle	C₂²×C₃³	C₂²×D₄
prime radical	C₂×C₃×D₈×C₃⋊D₃	C₂
cosocle	C₂×C₃²×C₄	C₂⁴×C₃
hypercenter	C₃×#442	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#442
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#442

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×D₄×C₃⋊D₃	C₂	semidirect
3. C₃³×#442	C₂	semidirect
4. C₃×#10592851	C₂	semidirect
5. C₃×#10592713	C₂	semidirect
6. C₃×#10592568	C₂	semidirect
7. C₃×C₃⋊D₃×#106	C₂	semidirect
8. C₃×#10592484	C₂	semidirect
9. C₃×C₃⋊D₃×#102	C₂	semidirect
10. C₃×#10592410	C₂	semidirect
11. C₃×C₃⋊D₃×#97	C₂	semidirect
13. C₃⋊D₃×#442	C₃	direct (N × H)
17. C₃³×C₄×D₄	C₂²	semidirect
18. C₃×D₄×C₃⋊Dic₃	C₂²	semidirect
21. C₃×D₈×C₃⋊D₃	C₄	semidirect
25. C₃×#64102	C₂²	semidirect
29. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂²	semidirect
31. C₃³×#106	C₂²	semidirect
32. C₃³×#102	C₂²	semidirect
33. C₃³×#97	C₂²	semidirect
34. C₃×#63659	C₂²	semidirect
35. C₃×#63648	C₂²	semidirect
36. C₃×#63644	C₂²	semidirect
37. C₃×#63642	C₂²	semidirect
38. C₃×#63642	C₂²	semidirect
39. C₃×#63636	C₂²	semidirect
40. C₃×#63635	C₂²	semidirect
41. C₃×#63630	C₂²	semidirect
43. C₄×D₄×C₃⋊D₃	C₂×C₃	semidirect
47. C₃²×#442	D₃	semidirect
48. C₃²×#442	C₂×C₃	semidirect
49. #10592851	C₂×C₃	semidirect
50. #10592713	C₂×C₃	semidirect
51. #10592568	C₂×C₃	semidirect
52. C₃⋊D₃×#106	C₂×C₃	semidirect
53. #10592484	C₂×C₃	semidirect
54. C₃⋊D₃×#102	C₂×C₃	semidirect
55. #10592410	C₂×C₃	semidirect
56. C₃⋊D₃×#97	C₂×C₃	semidirect
71. C₃×D₄×C₃⋊D₃	C₂×C₄	semidirect
79. C₃³×D₈	C₂×C₄	semidirect
86. C₃×#3753	C₂×C₄	semidirect
95. C₃×#3745	C₂×C₄	semidirect
97. C₃×C₈×C₃⋊D₃	C₂×C₄	semidirect
108. C₃²×C₄×D₄	C₂×D₃	semidirect
109. C₃²×C₄×D₄	C₂²×C₃	semidirect
110. D₄×C₃⋊Dic₃	C₂²×C₃	semidirect
113. D₈×C₃⋊D₃	C₃×C₄	semidirect
117. #64102	C₂²×C₃	semidirect
121. C₄×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
137. C₃²×#106	C₂×D₃	semidirect
138. C₃²×#106	C₂²×C₃	semidirect
140. C₃²×#102	C₂×D₃	semidirect
141. C₃²×#102	C₂²×C₃	semidirect
143. C₃²×#97	C₂×D₃	semidirect
144. C₃²×#97	C₂²×C₃	semidirect
145. #63659	C₂²×C₃	semidirect
146. #63648	C₂²×C₃	semidirect
147. #63644	C₂²×C₃	semidirect
148. #63642	C₂²×C₃	semidirect
149. #63642	C₂²×C₃	semidirect
150. #63636	C₂²×C₃	semidirect
151. #63635	C₂²×C₃	semidirect
152. #63630	C₂²×C₃	semidirect
168. C₃³×D₄	C₂²×C₄	semidirect
179. C₃×C₄⋊(C₃⋊D₃)	C₂²×C₄	semidirect
187. C₃³×C₈	C₂²×C₄	semidirect
189. C₃×C₃⋊(C₃⋊C₈)	C₂²×C₄	semidirect
200. C₃×#442	C₃×D₃	semidirect
201. C₃×#442	C₃⋊D₃	direct (N × H)
224. D₄×C₃⋊D₃	C₂×C₃×C₄	semidirect
244. C₃²×D₈	C₄×D₃	semidirect
245. C₃²×D₈	C₂×C₃×C₄	semidirect
262. #3753	C₂×C₃×C₄	semidirect
271. #3745	C₂×C₃×C₄	semidirect
273. C₈×C₃⋊D₃	C₂×C₃×C₄	semidirect
323. C₃×C₄×D₄	C₂×C₃×D₃	semidirect
324. C₃×C₄×D₄	C₂×C₃⋊D₃	semidirect
344. C₃×#106	C₂×C₃×D₃	semidirect
345. C₃×#106	C₂×C₃⋊D₃	semidirect
350. C₃×#102	C₂×C₃×D₃	semidirect
351. C₃×#102	C₂×C₃⋊D₃	semidirect
356. C₃×#97	C₂×C₃×D₃	semidirect
357. C₃×#97	C₂×C₃⋊D₃	semidirect
383. C₃²×D₄	C₂×C₄×D₃	semidirect
384. C₃²×D₄	C₂²×C₃×C₄	semidirect
403. C₄⋊(C₃⋊D₃)	C₂²×C₃×C₄	semidirect
427. C₃²×C₈	C₂×C₄×D₃	semidirect
428. C₃²×C₈	C₂²×C₃×C₄	semidirect
430. C₃⋊(C₃⋊C₈)	C₂²×C₃×C₄	semidirect
440. #442	C₃×C₃⋊D₃	direct (N × H)
448. C₃×C₃⋊D₃	#442	direct (N × H)
482. C₃×D₈	C₃×C₄×D₃	semidirect
483. C₃×D₈	C₄×C₃⋊D₃	semidirect
578. C₄×D₄	C₂×C₃×C₃⋊D₃	semidirect
584. #106	C₂×C₃×C₃⋊D₃	semidirect
588. #102	C₂×C₃×C₃⋊D₃	semidirect
592. #97	C₂×C₃×C₃⋊D₃	semidirect
593. C₃³	C₂×#442	semidirect
614. C₃×D₄	C₂×C₃×C₄×D₃	semidirect
615. C₃×D₄	C₂×C₄×C₃⋊D₃	semidirect
657. C₃×C₈	C₂×C₃×C₄×D₃	semidirect
658. C₃×C₈	C₂×C₄×C₃⋊D₃	semidirect
671. C₃⋊D₃	C₃×#442	direct (N × H)
690. D₈	C₃×C₄×C₃⋊D₃	semidirect
750. C₃²	D₃×#442	semidirect
751. C₃²	C₂×C₃×#442	semidirect
762. D₄	C₂×C₃×C₄×C₃⋊D₃	semidirect
780. C₈	C₂×C₃×C₄×C₃⋊D₃	semidirect
812. C₃	C₃⋊D₃×#442	direct (N × H)
813. C₃	C₃×D₃×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₈×C₃⋊D₃	2
C₃×C₄×D₄×C₃⋊D₃	2
C₃³×#442	2
C₃×#10592851	2
C₃×#10592713	2
C₃×#10592568	2
C₃×C₃⋊D₃×#106	2
C₃×#10592484	2
C₃×C₃⋊D₃×#102	2
C₃×#10592410	2
C₃×C₃⋊D₃×#97	2
C₃×D₃×#442	3
C₃⋊D₃×#442	3

Subgroups — C3×C3⋊D3×#442 #72244981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊D₃×#442 #72244981