Subgroups — C₂×C₃×D₃×#121 #11900266

Order 1152.

5269 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#939	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#930	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#121	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₃×#895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#884	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂²×C₃×#121	—	3	1	no	maximal
14	C₂×D₃×#121	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂⁴×C₃×D₃	C₂²	1	2	yes	—
16	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
19	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×#67	C₂²	1	2	yes	complemented
21	C₂²×C₃×#67	C₂²	1	2	yes	complemented
22	C₂²×C₃×#67	C₂²	1	2	yes	complemented
23	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×D₃×D₄	—	2	8	no	—
25	C₂×C₃×D₃×D₄	—	2	16	no	—
26	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
27	C₂×C₃×D₃×D₄	C₂²	1	16	yes	complemented
28	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
29	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₃×C₄×D₃	—	2	8	no	—
31	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
32	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄×D₃	C₂²	1	8	yes	complemented
35	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
37	C₃²×#121	C₂²	1	8	yes	complemented
38	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₃×#217	C₂²	1	2	yes	complemented
41	C₃×#939	C₂²	1	16	yes	complemented
42	C₃×#938	C₂²	1	8	yes	complemented
43	C₃×#930	C₂²	1	8	yes	complemented
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
46	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
48	C₃×#895	C₂²	1	8	yes	complemented
49	C₃×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
50	C₃×#884	C₂²	1	16	yes	complemented
51	C₃×D₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
52	C₂³×C₃×D₄	—	3	2	no	—
53	C₂³×C₃×D₄	—	3	1	no	—
54	C₂⁴×C₃×C₄	—	3	1	no	—
55	C₂²×D₃×D₄	C₂×C₃	1	2	yes	complemented
56	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂³×C₄×D₃	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×C₃×#121	—	2	1	no	—
59	C₂×C₃×#121	—	3	1	no	—
60	C₂×C₃×#121	—	3	2	no	—
61	C₂×C₃×#121	—	3	1	no	—
62	C₂×C₃×#121	—	3	16	no	—
63	C₂×C₃×#121	—	3	1	no	—
64	C₂×C₃×#121	—	3	2	no	—
65	C₂×C₃×#121	D₃	1	1	yes	characteristic, direct product factor
66	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
68	C₂²×C₃×C₂²⋊C₄	—	3	2	no	—
69	C₂×#939	C₂×C₃	1	2	yes	complemented
70	C₂×#938	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×#930	C₂×C₃	1	1	yes	characteristic, complemented
72	D₃×#121	C₂×C₃	1	16	yes	direct product factor
73	C₂×#895	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#884	C₂×C₃	1	2	yes	complemented
76	C₂×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
77	C₂⁴×C₃²	C₂³	1	2	yes	—
78	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
79	C₂³×C₃×D₃	—	2	4	no	—
80	C₂³×C₃×D₃	—	2	4	no	—
81	C₂³×C₃×D₃	—	2	8	no	—
82	C₂³×C₃×D₃	—	2	8	no	—
83	C₂³×C₃×D₃	—	2	8	no	—
84	C₂³×C₃×D₃	D₄	1	8	yes	complemented
85	C₂³×C₃×D₃	C₂³	1	8	yes	—
86	C₂³×C₃×D₃	C₂³	1	2	yes	—
87	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
88	C₂³×C₃×D₃	C₂³	1	4	yes	—
89	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
90	C₂×C₃²×D₄	—	2	8	no	—
91	C₂×C₃²×D₄	—	2	4	no	—
92	C₂×C₃²×D₄	C₂³	1	4	yes	complemented
93	C₂×C₃²×D₄	C₂³	1	8	yes	complemented
94	C₂²×C₃²×C₄	—	2	4	no	—
95	C₂²×C₃²×C₄	C₂³	1	2	yes	—
96	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
99	C₂×C₃×#67	—	2	8	no	—
100	C₂×C₃×#67	—	2	8	no	—
101	C₂×C₃×#67	—	2	8	no	—
102	C₂×C₃×#67	C₂³	1	8	yes	complemented
103	C₂×C₃×#67	C₂³	1	8	yes	complemented
104	C₂×C₃×#67	C₂³	1	8	yes	complemented
105	C₂²×C₃×Dic₃	—	2	4	no	—
106	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
107	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
108	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
109	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
110	C₃×D₃×D₄	—	2	64	no	—
111	C₃×D₃×D₄	—	2	32	no	—
112	C₂×C₃×D₁₂	—	2	8	no	—
113	C₂×C₃×D₁₂	—	2	4	no	—
114	C₂×C₃×D₁₂	C₂³	1	8	yes	complemented
115	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
116	C₂×C₃×C₄×D₃	—	2	4	no	—
117	C₂×C₃×C₄×D₃	—	2	8	no	—
118	C₂×C₃×C₄×D₃	—	2	4	no	—
119	C₂×C₃×C₄×D₃	—	2	4	no	—
120	C₂×C₃×C₄×D₃	—	2	32	no	—
121	C₂×C₃×C₄×D₃	D₄	1	8	yes	complemented
122	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
123	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
124	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
125	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
126	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
127	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
128	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
129	C₃×#217	C₂³	1	8	yes	complemented
130	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
131	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
132	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
133	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
134	C₂²×#121	—	3	1	no	Sylow
135	C₂⁵×C₃	—	3	1	no	—
136	C₂⁵×C₃	—	3	2	no	—
137	C₂⁴×D₃	C₂²×C₃	1	2	yes	—
138	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₃×D₄	—	2	1	no	—
140	C₂²×C₃×D₄	—	2	2	no	—
141	C₂²×C₃×D₄	—	3	2	no	—
142	C₂²×C₃×D₄	—	3	2	no	—
143	C₂²×C₃×D₄	—	3	2	no	—
144	C₂²×C₃×D₄	—	3	8	no	—
145	C₂²×C₃×D₄	—	3	16	no	—
146	C₂²×C₃×D₄	—	3	2	no	—
147	C₂²×C₃×D₄	—	3	1	no	—
148	C₂²×C₃×D₄	—	6	8	no	—
149	C₂²×C₃×D₄	—	6	16	no	—
150	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
151	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
152	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
154	C₂³×C₃×C₄	—	2	1	no	—
155	C₂³×C₃×C₄	—	3	1	no	—
156	C₂³×C₃×C₄	—	3	1	no	—
157	C₂³×C₃×C₄	—	3	1	no	—
158	C₂³×C₃×C₄	—	3	1	no	—
159	C₂³×C₃×C₄	—	3	1	no	—
160	C₂³×C₃×C₄	—	3	2	no	—
161	C₂³×C₃×C₄	—	3	8	no	—
162	C₂³×C₃×C₄	—	6	8	no	—
163	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂²×#67	C₂²×C₃	1	2	yes	complemented
166	C₂²×#67	C₂²×C₃	1	2	yes	complemented
167	C₂²×#67	C₂²×C₃	1	2	yes	complemented
168	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×D₃×D₄	—	2	16	no	—
170	C₂×D₃×D₄	—	2	8	no	—
171	C₂×D₃×D₄	C₂²×C₃	1	16	yes	complemented
172	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
173	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
174	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂²×C₄×D₃	—	2	8	no	—
176	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
177	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
178	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
179	C₂²×C₄×D₃	C₂²×C₃	1	8	yes	complemented
180	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₃×#121	—	2	8	no	—
183	C₃×#121	—	3	8	no	—
184	C₃×#121	—	3	16	no	—
185	C₃×#121	—	3	8	no	—
186	C₃×#121	—	3	8	no	—
187	C₃×#121	—	3	16	no	—
188	C₃×#121	C₂×D₃	1	8	yes	direct product factor
189	C₃×#121	C₂²×C₃	1	8	yes	complemented
190	C₂×C₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₃×C₄⋊C₄	—	3	2	no	—
192	C₂×C₃×C₄⋊C₄	—	3	1	no	—
193	C₂×C₃×C₄⋊C₄	—	3	8	no	—
194	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
195	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
198	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
199	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
200	C₂×C₃×C₂²⋊C₄	—	3	16	no	—
201	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
202	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
203	C₂×#217	C₂²×C₃	1	2	yes	complemented
204	#939	C₂²×C₃	1	16	yes	complemented
205	#938	C₂²×C₃	1	8	yes	complemented
206	#930	C₂²×C₃	1	8	yes	complemented
207	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
208	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
209	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
211	#895	C₂²×C₃	1	8	yes	complemented
212	D₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
213	#884	C₂²×C₃	1	16	yes	complemented
214	D₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
215	C₂³×C₃²	—	2	2	no	—
216	C₂³×C₃²	—	2	2	no	—
217	C₂³×C₃²	—	2	4	no	—
218	C₂³×C₃²	—	2	4	no	—
219	C₂³×C₃²	—	2	4	no	—
220	C₂³×C₃²	C₂×D₄	1	4	yes	complemented
221	C₂³×C₃²	C₂⁴	1	4	yes	—
222	C₂³×C₃²	C₂⁴	1	2	yes	—
223	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
224	C₂²×C₃×D₃	—	2	2	no	—
225	C₂²×C₃×D₃	—	2	2	no	—
226	C₂²×C₃×D₃	—	2	32	no	—
227	C₂²×C₃×D₃	—	2	8	no	—
228	C₂²×C₃×D₃	—	2	8	no	—
229	C₂²×C₃×D₃	—	2	4	no	—
230	C₂²×C₃×D₃	—	2	4	no	—
231	C₂²×C₃×D₃	—	2	4	no	—
232	C₂²×C₃×D₃	—	2	16	no	—
233	C₂²×C₃×D₃	—	2	16	no	—
234	C₂²×C₃×D₃	—	2	16	no	—
235	C₂²×C₃×D₃	—	4	32	no	—
236	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
237	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
238	C₂²×C₃×D₃	C₂×D₄	1	16	yes	complemented
239	C₂²×C₃×D₃	C₂×D₄	1	4	yes	complemented
240	C₂²×C₃×D₃	#41	1	4	yes	—
241	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
242	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
243	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
244	C₃²×D₄	—	2	16	no	—
245	C₃²×D₄	—	2	8	no	—
246	C₂×C₃²×C₄	—	2	2	no	—
247	C₂×C₃²×C₄	—	2	4	no	—
248	C₂×C₃²×C₄	—	2	8	no	—
249	C₂×C₃²×C₄	C₂×D₄	1	4	yes	complemented
250	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
251	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
252	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
253	C₃×#67	—	2	16	no	—
254	C₃×#67	—	2	16	no	—
255	C₃×#67	—	2	16	no	—
256	C₂×C₃×Dic₃	—	2	2	no	—
257	C₂×C₃×Dic₃	—	2	4	no	—
258	C₂×C₃×Dic₃	—	2	8	no	—
259	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	complemented
260	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
261	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
262	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
263	C₃×D₁₂	—	2	16	no	—
264	C₃×D₁₂	—	2	8	no	—
265	C₃×C₄×D₃	—	2	8	no	—
266	C₃×C₄×D₃	—	2	16	no	—
267	C₃×C₄×D₃	—	2	8	no	—
268	C₃×C₄×D₃	—	2	8	no	—
269	C₃×C₄×D₃	C₂×D₄	1	16	yes	complemented
270	C₂³×D₄	—	3	1	no	—
271	C₂³×D₄	—	3	2	no	—
272	C₂⁴×C₄	—	3	1	no	—
273	C₂×#121	—	3	1	no	—
274	C₂×#121	—	3	2	no	—
275	C₂×#121	—	3	1	no	—
276	C₂×#121	—	3	16	no	—
277	C₂×#121	—	3	1	no	—
278	C₂×#121	—	3	2	no	—
279	C₂×#121	C₃×D₃	1	1	yes	characteristic, direct product factor
280	C₂²×C₄⋊C₄	—	3	1	no	—
281	C₂²×C₂²⋊C₄	—	3	2	no	—
282	C₂⁴×C₃	—	2	1	no	—
283	C₂⁴×C₃	—	2	2	no	—
284	C₂⁴×C₃	—	3	1	no	—
285	C₂⁴×C₃	—	3	8	no	—
286	C₂⁴×C₃	—	3	4	no	—
287	C₂⁴×C₃	—	3	1	no	—
288	C₂⁴×C₃	—	3	8	no	—
289	C₂⁴×C₃	—	3	2	no	—
290	C₂⁴×C₃	—	6	4	no	—
291	C₂⁴×C₃	—	6	4	no	—
292	C₂⁴×C₃	—	6	8	no	—
293	C₂⁴×C₃	—	6	8	no	—
294	C₂⁴×C₃	—	6	8	no	—
295	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
296	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
297	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
298	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
299	C₂³×D₃	—	2	4	no	—
300	C₂³×D₃	—	2	4	no	—
301	C₂³×D₃	—	2	8	no	—
302	C₂³×D₃	—	2	8	no	—
303	C₂³×D₃	—	2	8	no	—
304	C₂³×D₃	C₃×D₄	1	8	yes	complemented
305	C₂³×D₃	C₂³×C₃	1	8	yes	—
306	C₂³×D₃	C₂³×C₃	1	2	yes	—
307	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
308	C₂³×D₃	C₂³×C₃	1	4	yes	—
309	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₃×D₄	—	2	8	no	—
311	C₂×C₃×D₄	—	2	8	no	—
312	C₂×C₃×D₄	—	2	4	no	—
313	C₂×C₃×D₄	—	2	4	no	—
314	C₂×C₃×D₄	—	2	4	no	—
315	C₂×C₃×D₄	—	2	8	no	—
316	C₂×C₃×D₄	—	3	8	no	—
317	C₂×C₃×D₄	—	3	8	no	—
318	C₂×C₃×D₄	—	3	8	no	—
319	C₂×C₃×D₄	—	3	8	no	—
320	C₂×C₃×D₄	—	3	4	no	—
321	C₂×C₃×D₄	—	4	4	no	—
322	C₂×C₃×D₄	—	4	8	no	—
323	C₂×C₃×D₄	—	6	8	no	—
324	C₂×C₃×D₄	—	6	32	no	—
325	C₂×C₃×D₄	—	6	8	no	—
326	C₂×C₃×D₄	—	6	64	no	—
327	C₂×C₃×D₄	—	6	8	no	—
328	C₂×C₃×D₄	—	6	8	no	—
329	C₂×C₃×D₄	—	6	4	no	—
330	C₂×C₃×D₄	C₂²×D₃	1	8	yes	complemented
331	C₂×C₃×D₄	C₂²×D₃	1	4	yes	complemented
332	C₂×C₃×D₄	C₂³×C₃	1	4	yes	complemented
333	C₂×C₃×D₄	C₂³×C₃	1	8	yes	complemented
334	C₂²×C₃×C₄	—	2	4	no	—
335	C₂²×C₃×C₄	—	2	4	no	—
336	C₂²×C₃×C₄	—	2	1	no	—
337	C₂²×C₃×C₄	—	2	1	no	—
338	C₂²×C₃×C₄	—	2	2	no	—
339	C₂²×C₃×C₄	—	2	4	no	—
340	C₂²×C₃×C₄	—	3	1	no	—
341	C₂²×C₃×C₄	—	3	8	no	—
342	C₂²×C₃×C₄	—	3	4	no	—
343	C₂²×C₃×C₄	—	3	4	no	—
344	C₂²×C₃×C₄	—	3	1	no	—
345	C₂²×C₃×C₄	—	3	2	no	—
346	C₂²×C₃×C₄	—	3	4	no	—
347	C₂²×C₃×C₄	—	3	8	no	—
348	C₂²×C₃×C₄	—	3	4	no	—
349	C₂²×C₃×C₄	—	3	4	no	—
350	C₂²×C₃×C₄	—	4	4	no	—
351	C₂²×C₃×C₄	—	6	4	no	—
352	C₂²×C₃×C₄	—	6	32	no	—
353	C₂²×C₃×C₄	—	6	4	no	—
354	C₂²×C₃×C₄	—	6	8	no	—
355	C₂²×C₃×C₄	—	6	4	no	—
356	C₂²×C₃×C₄	—	6	4	no	—
357	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
359	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
361	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
362	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
365	C₂×#67	—	2	8	no	—
366	C₂×#67	—	2	8	no	—
367	C₂×#67	—	2	8	no	—
368	C₂×#67	C₂³×C₃	1	8	yes	complemented
369	C₂×#67	C₂³×C₃	1	8	yes	complemented
370	C₂×#67	C₂³×C₃	1	8	yes	complemented
371	C₂²×Dic₃	—	2	4	no	—
372	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
373	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
374	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
375	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
376	D₃×D₄	—	2	64	no	—
377	D₃×D₄	—	2	32	no	—
378	C₂×D₁₂	—	2	8	no	—
379	C₂×D₁₂	—	2	4	no	—
380	C₂×D₁₂	C₂³×C₃	1	8	yes	complemented
381	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
382	C₂×C₄×D₃	—	2	4	no	—
383	C₂×C₄×D₃	—	2	8	no	—
384	C₂×C₄×D₃	—	2	4	no	—
385	C₂×C₄×D₃	—	2	4	no	—
386	C₂×C₄×D₃	—	2	32	no	—
387	C₂×C₄×D₃	C₃×D₄	1	8	yes	complemented
388	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
389	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
390	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
391	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
392	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
393	C₃×C₄⋊C₄	—	2	4	no	—
394	C₃×C₄⋊C₄	—	3	8	no	—
395	C₃×C₄⋊C₄	—	3	4	no	—
396	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
397	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
398	C₃×C₂²⋊C₄	—	2	8	no	—
399	C₃×C₂²⋊C₄	—	3	8	no	—
400	C₃×C₂²⋊C₄	—	3	8	no	—
401	C₃×C₂²⋊C₄	—	3	8	no	—
402	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
403	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
404	#217	C₂³×C₃	1	8	yes	complemented
405	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
406	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
407	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
408	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
409	C₂²×C₃²	—	2	8	no	—
410	C₂²×C₃²	—	2	2	no	—
411	C₂²×C₃²	—	2	2	no	—
412	C₂²×C₃²	—	2	4	no	—
413	C₂²×C₃²	—	2	4	no	—
414	C₂²×C₃²	—	2	4	no	—
415	C₂²×C₃²	—	4	8	no	—
416	C₂²×C₃²	C₂²×D₄	1	2	yes	—
417	C₂²×C₃²	C₂²×D₄	1	2	yes	—
418	C₂²×C₃²	C₂²×D₄	1	4	yes	complemented
419	C₂²×C₃²	C₂×#41	1	2	yes	—
420	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
421	C₂×C₃×D₃	—	2	8	no	—
422	C₂×C₃×D₃	—	2	2	no	—
423	C₂×C₃×D₃	—	2	2	no	—
424	C₂×C₃×D₃	—	2	32	no	—
425	C₂×C₃×D₃	—	2	4	no	—
426	C₂×C₃×D₃	—	2	4	no	—
427	C₂×C₃×D₃	—	2	4	no	—
428	C₂×C₃×D₃	—	4	8	no	—
429	C₂×C₃×D₃	—	4	32	no	—
430	C₂×C₃×D₃	#121	1	16	yes	direct product factor
431	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
432	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
433	C₂×C₃×D₃	C₂²×D₄	1	4	yes	complemented
434	C₂×C₃×D₃	C₂×#41	1	4	yes	—
435	C₃²×C₄	—	2	2	no	—
436	C₃²×C₄	—	2	4	no	—
437	C₃²×C₄	C₂²×D₄	1	4	yes	complemented
438	C₃×Dic₃	—	2	2	no	—
439	C₃×Dic₃	—	2	4	no	—
440	C₃×Dic₃	C₂²×D₄	1	4	yes	complemented
441	C₂⁵	—	3	1	no	—
442	C₂⁵	—	3	2	no	—
443	C₂²×D₄	—	3	2	no	—
444	C₂²×D₄	—	3	2	no	—
445	C₂²×D₄	—	3	2	no	—
446	C₂²×D₄	—	3	8	no	—
447	C₂²×D₄	—	3	16	no	—
448	C₂²×D₄	—	3	2	no	—
449	C₂²×D₄	—	3	1	no	—
450	C₂²×D₄	—	6	8	no	—
451	C₂²×D₄	—	6	16	no	—
452	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
453	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
454	C₂³×C₄	—	3	1	no	—
455	C₂³×C₄	—	3	1	no	—
456	C₂³×C₄	—	3	1	no	—
457	C₂³×C₄	—	3	2	no	—
458	C₂³×C₄	—	3	1	no	—
459	C₂³×C₄	—	3	1	no	—
460	C₂³×C₄	—	3	8	no	—
461	C₂³×C₄	—	6	8	no	—
462	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
463	#121	—	3	8	no	—
464	#121	—	3	16	no	—
465	#121	—	3	8	no	—
466	#121	—	3	8	no	—
467	#121	—	3	16	no	—
468	#121	C₂×C₃×D₃	1	8	yes	direct product factor
469	C₂×C₄⋊C₄	—	3	2	no	—
470	C₂×C₄⋊C₄	—	3	1	no	—
471	C₂×C₄⋊C₄	—	3	8	no	—
472	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
473	C₂×C₂²⋊C₄	—	3	2	no	—
474	C₂×C₂²⋊C₄	—	3	2	no	—
475	C₂×C₂²⋊C₄	—	3	2	no	—
476	C₂×C₂²⋊C₄	—	3	16	no	—
477	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
478	C₂³×C₃	—	2	2	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	—	2	4	no	—
483	C₂³×C₃	—	2	4	no	—
484	C₂³×C₃	—	2	4	no	—
485	C₂³×C₃	—	2	4	no	—
486	C₂³×C₃	—	2	4	no	—
487	C₂³×C₃	—	2	4	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	2	2	no	—
490	C₂³×C₃	—	2	4	no	—
491	C₂³×C₃	—	2	4	no	—
492	C₂³×C₃	—	3	4	no	—
493	C₂³×C₃	—	3	4	no	—
494	C₂³×C₃	—	3	4	no	—
495	C₂³×C₃	—	3	2	no	—
496	C₂³×C₃	—	3	4	no	—
497	C₂³×C₃	—	3	16	no	—
498	C₂³×C₃	—	3	2	no	—
499	C₂³×C₃	—	3	4	no	—
500	C₂³×C₃	—	4	2	no	—
501	C₂³×C₃	—	4	2	no	—
502	C₂³×C₃	—	4	4	no	—
503	C₂³×C₃	—	4	4	no	—
504	C₂³×C₃	—	4	4	no	—
505	C₂³×C₃	—	6	8	no	—
506	C₂³×C₃	—	6	8	no	—
507	C₂³×C₃	—	6	32	no	—
508	C₂³×C₃	—	6	16	no	—
509	C₂³×C₃	—	6	16	no	—
510	C₂³×C₃	—	6	16	no	—
511	C₂³×C₃	—	6	2	no	—
512	C₂³×C₃	—	6	2	no	—
513	C₂³×C₃	—	6	4	no	—
514	C₂³×C₃	—	6	4	no	—
515	C₂³×C₃	—	6	4	no	—
516	C₂³×C₃	—	12	32	no	—
517	C₂³×C₃	D₃×D₄	1	4	yes	complemented
518	C₂³×C₃	C₂×C₃×D₄	1	4	yes	complemented
519	C₂³×C₃	C₂³×D₃	1	4	yes	—
520	C₂³×C₃	C₂³×D₃	1	2	yes	—
521	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
522	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
523	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
524	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
525	C₂²×D₃	—	2	2	no	—
526	C₂²×D₃	—	2	2	no	—
527	C₂²×D₃	—	2	32	no	—
528	C₂²×D₃	—	2	8	no	—
529	C₂²×D₃	—	2	8	no	—
530	C₂²×D₃	—	2	4	no	—
531	C₂²×D₃	—	2	4	no	—
532	C₂²×D₃	—	2	4	no	—
533	C₂²×D₃	—	2	16	no	—
534	C₂²×D₃	—	2	16	no	—
535	C₂²×D₃	—	2	16	no	—
536	C₂²×D₃	—	4	32	no	—
537	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
538	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
539	C₂²×D₃	C₂×C₃×D₄	1	16	yes	complemented
540	C₂²×D₃	C₂×C₃×D₄	1	4	yes	complemented
541	C₂²×D₃	C₃×#41	1	4	yes	—
542	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
543	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
544	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
545	C₃×D₄	—	2	16	no	—
546	C₃×D₄	—	2	16	no	—
547	C₃×D₄	—	2	8	no	—
548	C₃×D₄	—	2	8	no	—
549	C₃×D₄	—	4	8	no	—
550	C₃×D₄	—	4	16	no	—
551	C₃×D₄	—	6	16	no	—
552	C₃×D₄	—	6	16	no	—
553	C₃×D₄	—	6	16	no	—
554	C₃×D₄	—	6	16	no	—
555	C₃×D₄	—	6	8	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	4	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	4	no	—
560	C₂×C₃×C₄	—	2	8	no	—
561	C₂×C₃×C₄	—	2	8	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	4	no	—
565	C₂×C₃×C₄	—	2	4	no	—
566	C₂×C₃×C₄	—	3	4	no	—
567	C₂×C₃×C₄	—	3	2	no	—
568	C₂×C₃×C₄	—	3	16	no	—
569	C₂×C₃×C₄	—	3	2	no	—
570	C₂×C₃×C₄	—	3	4	no	—
571	C₂×C₃×C₄	—	4	8	no	—
572	C₂×C₃×C₄	—	4	2	no	—
573	C₂×C₃×C₄	—	4	4	no	—
574	C₂×C₃×C₄	—	6	8	no	—
575	C₂×C₃×C₄	—	6	8	no	—
576	C₂×C₃×C₄	—	6	16	no	—
577	C₂×C₃×C₄	—	6	8	no	—
578	C₂×C₃×C₄	—	6	2	no	—
579	C₂×C₃×C₄	—	6	4	no	—
580	C₂×C₃×C₄	—	6	8	no	—
581	C₂×C₃×C₄	D₃×D₄	1	4	yes	complemented
582	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	complemented
583	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
584	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
585	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
586	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
587	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
588	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
589	#67	—	2	16	no	—
590	#67	—	2	16	no	—
591	#67	—	2	16	no	—
592	C₂×Dic₃	—	2	2	no	—
593	C₂×Dic₃	—	2	4	no	—
594	C₂×Dic₃	—	2	8	no	—
595	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	complemented
596	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
597	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
598	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
599	D₁₂	—	2	16	no	—
600	D₁₂	—	2	8	no	—
601	C₄×D₃	—	2	8	no	—
602	C₄×D₃	—	2	16	no	—
603	C₄×D₃	—	2	8	no	—
604	C₄×D₃	—	2	8	no	—
605	C₄×D₃	C₂×C₃×D₄	1	16	yes	complemented
606	C₂×C₃²	—	2	4	no	—
607	C₂×C₃²	—	4	4	no	—
608	C₂×C₃²	C₂×#121	1	4	yes	complemented
609	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
610	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
611	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
612	C₃×D₃	—	2	4	no	—
613	C₃×D₃	—	4	4	no	—
614	C₃×D₃	C₂×#121	1	8	yes	direct product factor
615	C₂⁴	—	3	1	no	—
616	C₂⁴	—	3	4	no	—
617	C₂⁴	—	3	1	no	—
618	C₂⁴	—	3	8	no	—
619	C₂⁴	—	3	8	no	—
620	C₂⁴	—	3	2	no	—
621	C₂⁴	—	6	4	no	—
622	C₂⁴	—	6	4	no	—
623	C₂⁴	—	6	8	no	—
624	C₂⁴	—	6	8	no	—
625	C₂⁴	—	6	8	no	—
626	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
627	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	3	8	no	—
631	C₂×D₄	—	3	8	no	—
632	C₂×D₄	—	3	8	no	—
633	C₂×D₄	—	3	8	no	—
634	C₂×D₄	—	3	4	no	—
635	C₂×D₄	—	6	8	no	—
636	C₂×D₄	—	6	32	no	—
637	C₂×D₄	—	6	8	no	—
638	C₂×D₄	—	6	64	no	—
639	C₂×D₄	—	6	8	no	—
640	C₂×D₄	—	6	8	no	—
641	C₂×D₄	—	6	4	no	—
642	C₂×D₄	C₂²×C₃×D₃	1	8	yes	complemented
643	C₂×D₄	C₂²×C₃×D₃	1	4	yes	complemented
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	3	4	no	—
647	C₂²×C₄	—	3	8	no	—
648	C₂²×C₄	—	3	1	no	—
649	C₂²×C₄	—	3	2	no	—
650	C₂²×C₄	—	3	4	no	—
651	C₂²×C₄	—	3	4	no	—
652	C₂²×C₄	—	3	8	no	—
653	C₂²×C₄	—	3	4	no	—
654	C₂²×C₄	—	3	4	no	—
655	C₂²×C₄	—	6	4	no	—
656	C₂²×C₄	—	6	32	no	—
657	C₂²×C₄	—	6	4	no	—
658	C₂²×C₄	—	6	8	no	—
659	C₂²×C₄	—	6	4	no	—
660	C₂²×C₄	—	6	4	no	—
661	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
662	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
663	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
664	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
665	C₄⋊C₄	—	3	8	no	—
666	C₄⋊C₄	—	3	4	no	—
667	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
668	C₂²⋊C₄	—	3	8	no	—
669	C₂²⋊C₄	—	3	8	no	—
670	C₂²⋊C₄	—	3	8	no	—
671	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	2	2	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	2	8	no	—
677	C₂²×C₃	—	2	8	no	—
678	C₂²×C₃	—	2	4	no	—
679	C₂²×C₃	—	2	4	no	—
680	C₂²×C₃	—	2	4	no	—
681	C₂²×C₃	—	2	4	no	—
682	C₂²×C₃	—	2	4	no	—
683	C₂²×C₃	—	2	4	no	—
684	C₂²×C₃	—	2	2	no	—
685	C₂²×C₃	—	2	2	no	—
686	C₂²×C₃	—	2	4	no	—
687	C₂²×C₃	—	2	2	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	3	4	no	—
690	C₂²×C₃	—	3	4	no	—
691	C₂²×C₃	—	3	4	no	—
692	C₂²×C₃	—	3	16	no	—
693	C₂²×C₃	—	3	4	no	—
694	C₂²×C₃	—	4	2	no	—
695	C₂²×C₃	—	4	8	no	—
696	C₂²×C₃	—	4	2	no	—
697	C₂²×C₃	—	4	4	no	—
698	C₂²×C₃	—	4	4	no	—
699	C₂²×C₃	—	4	4	no	—
700	C₂²×C₃	—	4	8	no	—
701	C₂²×C₃	—	4	8	no	—
702	C₂²×C₃	—	6	32	no	—
703	C₂²×C₃	—	6	2	no	—
704	C₂²×C₃	—	6	2	no	—
705	C₂²×C₃	—	6	8	no	—
706	C₂²×C₃	—	6	4	no	—
707	C₂²×C₃	—	6	4	no	—
708	C₂²×C₃	—	6	4	no	—
709	C₂²×C₃	—	8	8	no	—
710	C₂²×C₃	—	12	32	no	—
711	C₂²×C₃	—	12	8	no	—
712	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
713	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
714	C₂²×C₃	C₂×D₃×D₄	1	4	yes	complemented
715	C₂²×C₃	D₃×#41	1	2	yes	—
716	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
717	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
718	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	complemented
719	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
720	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
721	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
722	C₂×D₃	—	2	2	no	—
723	C₂×D₃	—	2	2	no	—
724	C₂×D₃	—	2	8	no	—
725	C₂×D₃	—	2	32	no	—
726	C₂×D₃	—	2	4	no	—
727	C₂×D₃	—	2	4	no	—
728	C₂×D₃	—	2	4	no	—
729	C₂×D₃	—	4	8	no	—
730	C₂×D₃	—	4	32	no	—
731	C₂×D₃	C₃×#121	1	16	yes	direct product factor
732	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
733	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
734	C₂×D₃	C₂²×C₃×D₄	1	4	yes	complemented
735	C₂×D₃	C₂×C₃×#41	1	4	yes	—
736	C₃×C₄	—	2	2	no	—
737	C₃×C₄	—	2	4	no	—
738	C₃×C₄	—	2	2	no	—
739	C₃×C₄	—	2	4	no	—
740	C₃×C₄	—	2	4	no	—
741	C₃×C₄	—	3	4	no	—
742	C₃×C₄	—	4	2	no	—
743	C₃×C₄	—	4	4	no	—
744	C₃×C₄	—	6	2	no	—
745	C₃×C₄	—	6	4	no	—
746	C₃×C₄	C₂×D₃×D₄	1	4	yes	complemented
747	C₃×C₄	C₂²×C₃×D₄	1	4	yes	complemented
748	Dic₃	—	2	2	no	—
749	Dic₃	—	2	4	no	—
750	Dic₃	C₂²×C₃×D₄	1	4	yes	complemented
751	C₃²	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	3	4	no	—
758	C₂³	—	3	4	no	—
759	C₂³	—	3	4	no	—
760	C₂³	—	3	2	no	—
761	C₂³	—	3	4	no	—
762	C₂³	—	3	16	no	—
763	C₂³	—	3	2	no	—
764	C₂³	—	3	4	no	—
765	C₂³	—	6	8	no	—
766	C₂³	—	6	32	no	—
767	C₂³	—	6	8	no	—
768	C₂³	—	6	16	no	—
769	C₂³	—	6	16	no	—
770	C₂³	—	6	16	no	—
771	C₂³	—	6	2	no	—
772	C₂³	—	6	2	no	—
773	C₂³	—	6	4	no	—
774	C₂³	—	6	4	no	—
775	C₂³	—	6	4	no	—
776	C₂³	—	12	32	no	—
777	C₂³	C₃×D₃×D₄	1	4	yes	complemented
778	C₂³	C₂³×C₃×D₃	1	4	yes	—
779	C₂³	C₂³×C₃×D₃	1	2	yes	—
780	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
781	D₄	—	2	16	no	—
782	D₄	—	2	8	no	—
783	D₄	—	6	16	no	—
784	D₄	—	6	16	no	—
785	D₄	—	6	16	no	—
786	D₄	—	6	16	no	—
787	D₄	—	6	8	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	8	no	—
791	C₂×C₄	—	3	4	no	—
792	C₂×C₄	—	3	2	no	—
793	C₂×C₄	—	3	16	no	—
794	C₂×C₄	—	3	2	no	—
795	C₂×C₄	—	3	4	no	—
796	C₂×C₄	—	6	8	no	—
797	C₂×C₄	—	6	8	no	—
798	C₂×C₄	—	6	16	no	—
799	C₂×C₄	—	6	8	no	—
800	C₂×C₄	—	6	2	no	—
801	C₂×C₄	—	6	4	no	—
802	C₂×C₄	—	6	8	no	—
803	C₂×C₄	C₃×D₃×D₄	1	4	yes	complemented
804	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
805	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
806	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
807	C₂×C₃	—	2	4	no	—
808	C₂×C₃	—	2	4	no	—
809	C₂×C₃	—	2	4	no	—
810	C₂×C₃	—	2	1	no	—
811	C₂×C₃	—	2	1	no	—
812	C₂×C₃	—	2	1	no	—
813	C₂×C₃	—	3	8	no	—
814	C₂×C₃	—	4	4	no	—
815	C₂×C₃	—	4	4	no	—
816	C₂×C₃	—	4	4	no	—
817	C₂×C₃	—	6	4	no	—
818	C₂×C₃	—	8	4	no	—
819	C₂×C₃	—	12	4	no	—
820	C₂×C₃	D₃×#121	1	4	yes	direct product factor
821	C₂×C₃	C₂×C₃×#121	1	4	yes	complemented
822	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
823	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
824	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
825	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
826	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
827	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
828	D₃	—	2	4	no	—
829	D₃	—	4	4	no	—
830	D₃	C₂×C₃×#121	1	8	yes	direct product factor
831	C₂²	—	2	8	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	3	16	no	—
838	C₂²	—	3	4	no	—
839	C₂²	—	3	4	no	—
840	C₂²	—	3	4	no	—
841	C₂²	—	3	4	no	—
842	C₂²	—	4	8	no	—
843	C₂²	—	6	32	no	—
844	C₂²	—	6	8	no	—
845	C₂²	—	6	2	no	—
846	C₂²	—	6	2	no	—
847	C₂²	—	6	4	no	—
848	C₂²	—	6	4	no	—
849	C₂²	—	6	4	no	—
850	C₂²	—	12	32	no	—
851	C₂²	—	12	8	no	—
852	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
853	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
854	C₂²	C₂×C₃×D₃×D₄	1	4	yes	complemented
855	C₂²	C₃×D₃×#41	1	2	yes	—
856	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
857	C₄	—	2	2	no	—
858	C₄	—	2	4	no	—
859	C₄	—	3	4	no	—
860	C₄	—	6	2	no	—
861	C₄	—	6	4	no	—
862	C₄	C₂×C₃×D₃×D₄	1	4	yes	complemented
863	C₃	—	2	1	no	—
864	C₃	C₂×D₃×#121	1	1	yes	characteristic, direct product factor
865	C₃	C₂²×C₃×#121	1	1	yes	characteristic, complemented
866	C₂	—	2	4	no	—
867	C₂	—	3	8	no	—
868	C₂	—	4	4	no	—
869	C₂	—	6	4	no	—
870	C₂	—	12	4	no	—
871	C₂	C₃×D₃×#121	1	4	yes	direct product factor
872	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
873	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
874	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#121	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#121	D₃
hypocenter	C₃	C₂²×C₃×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×D₄	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₂³×C₃×C₄×D₃	C₂	semidirect
4. C₂×C₃²×#121	C₂	semidirect
5. C₂×C₃×#939	C₂	semidirect
6. C₂×C₃×#938	C₂	semidirect
7. C₂×C₃×#930	C₂	semidirect
8. C₃×D₃×#121	C₂	direct (N × H)
9. C₂×C₃×#895	C₂	semidirect
10. C₂×C₃×D₃×C₄⋊C₄	C₂	semidirect
11. C₂×C₃×#884	C₂	semidirect
12. C₂×C₃×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂×D₃×#121	C₃	direct (N × H)
17. C₂²×C₃²×D₄	C₂²	semidirect
18. C₂²×C₃²×D₄	C₂²	semidirect
19. C₂³×C₃²×C₄	C₂²	semidirect
20. C₂²×C₃×#67	C₂²	semidirect
21. C₂²×C₃×#67	C₂²	semidirect
22. C₂²×C₃×#67	C₂²	semidirect
23. C₂³×C₃×Dic₃	C₂²	semidirect
26. C₂×C₃×D₃×D₄	C₂²	semidirect
27. C₂×C₃×D₃×D₄	C₂²	semidirect
28. C₂²×C₃×D₁₂	C₂²	semidirect
29. C₂²×C₃×D₁₂	C₂²	semidirect
34. C₂²×C₃×C₄×D₃	C₂²	semidirect
35. C₂²×C₃×C₄×D₃	C₂²	semidirect
36. C₂²×C₃×C₄×D₃	C₂²	semidirect
37. C₃²×#121	C₂²	semidirect
38. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
39. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₃×#217	C₂²	semidirect
41. C₃×#939	C₂²	semidirect
42. C₃×#938	C₂²	semidirect
43. C₃×#930	C₂²	semidirect
44. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
46. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
47. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
48. C₃×#895	C₂²	semidirect
49. C₃×D₃×C₄⋊C₄	C₂²	semidirect
50. C₃×#884	C₂²	semidirect
51. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
55. C₂²×D₃×D₄	C₂×C₃	semidirect
56. C₂²×D₃×D₄	C₂×C₃	semidirect
57. C₂³×C₄×D₃	C₂×C₃	semidirect
65. C₂×C₃×#121	D₃	direct (N × H)
66. C₂×C₃×#121	C₂×C₃	semidirect
69. C₂×#939	C₂×C₃	semidirect
70. C₂×#938	C₂×C₃	semidirect
71. C₂×#930	C₂×C₃	semidirect
72. D₃×#121	C₂×C₃	direct (N × H)
73. C₂×#895	C₂×C₃	semidirect
74. C₂×D₃×C₄⋊C₄	C₂×C₃	semidirect
75. C₂×#884	C₂×C₃	semidirect
76. C₂×D₃×C₂²⋊C₄	C₂×C₃	semidirect
84. C₂³×C₃×D₃	D₄	semidirect
92. C₂×C₃²×D₄	C₂³	semidirect
93. C₂×C₃²×D₄	C₂³	semidirect
98. C₂²×C₃²×C₄	C₂³	semidirect
102. C₂×C₃×#67	C₂³	semidirect
103. C₂×C₃×#67	C₂³	semidirect
104. C₂×C₃×#67	C₂³	semidirect
109. C₂²×C₃×Dic₃	C₂³	semidirect
114. C₂×C₃×D₁₂	C₂³	semidirect
115. C₂×C₃×D₁₂	C₂³	semidirect
121. C₂×C₃×C₄×D₃	D₄	semidirect
125. C₂×C₃×C₄×D₃	C₂³	semidirect
126. C₂×C₃×C₄×D₃	C₂³	semidirect
127. C₃²×C₄⋊C₄	C₂³	semidirect
128. C₃²×C₂²⋊C₄	C₂³	semidirect
129. C₃×#217	C₂³	semidirect
130. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
131. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
132. C₃×C₄⋊Dic₃	C₂³	semidirect
133. C₃×Dic₃⋊C₄	C₂³	semidirect
150. C₂²×C₃×D₄	C₂×D₃	semidirect
151. C₂²×C₃×D₄	C₂×D₃	semidirect
152. C₂²×C₃×D₄	C₂²×C₃	semidirect
153. C₂²×C₃×D₄	C₂²×C₃	semidirect
163. C₂³×C₃×C₄	C₂×D₃	semidirect
164. C₂³×C₃×C₄	C₂²×C₃	semidirect
165. C₂²×#67	C₂²×C₃	semidirect
166. C₂²×#67	C₂²×C₃	semidirect
167. C₂²×#67	C₂²×C₃	semidirect
168. C₂³×Dic₃	C₂²×C₃	semidirect
171. C₂×D₃×D₄	C₂²×C₃	semidirect
172. C₂×D₃×D₄	C₂²×C₃	semidirect
173. C₂²×D₁₂	C₂²×C₃	semidirect
174. C₂²×D₁₂	C₂²×C₃	semidirect
179. C₂²×C₄×D₃	C₂²×C₃	semidirect
180. C₂²×C₄×D₃	C₂²×C₃	semidirect
181. C₂²×C₄×D₃	C₂²×C₃	semidirect
188. C₃×#121	C₂×D₃	direct (N × H)
189. C₃×#121	C₂²×C₃	semidirect
194. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
195. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
201. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
202. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
203. C₂×#217	C₂²×C₃	semidirect
204. #939	C₂²×C₃	semidirect
205. #938	C₂²×C₃	semidirect
206. #930	C₂²×C₃	semidirect
207. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
208. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
209. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
210. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
211. #895	C₂²×C₃	semidirect
212. D₃×C₄⋊C₄	C₂²×C₃	semidirect
213. #884	C₂²×C₃	semidirect
214. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
220. C₂³×C₃²	C₂×D₄	semidirect
238. C₂²×C₃×D₃	C₂×D₄	semidirect
239. C₂²×C₃×D₃	C₂×D₄	semidirect
249. C₂×C₃²×C₄	C₂×D₄	semidirect
259. C₂×C₃×Dic₃	C₂×D₄	semidirect
269. C₃×C₄×D₃	C₂×D₄	semidirect
279. C₂×#121	C₃×D₃	direct (N × H)
304. C₂³×D₃	C₃×D₄	semidirect
330. C₂×C₃×D₄	C₂²×D₃	semidirect
331. C₂×C₃×D₄	C₂²×D₃	semidirect
332. C₂×C₃×D₄	C₂³×C₃	semidirect
333. C₂×C₃×D₄	C₂³×C₃	semidirect
360. C₂²×C₃×C₄	C₂²×D₃	semidirect
364. C₂²×C₃×C₄	C₂³×C₃	semidirect
368. C₂×#67	C₂³×C₃	semidirect
369. C₂×#67	C₂³×C₃	semidirect
370. C₂×#67	C₂³×C₃	semidirect
375. C₂²×Dic₃	C₂³×C₃	semidirect
380. C₂×D₁₂	C₂³×C₃	semidirect
381. C₂×D₁₂	C₂³×C₃	semidirect
387. C₂×C₄×D₃	C₃×D₄	semidirect
391. C₂×C₄×D₃	C₂³×C₃	semidirect
392. C₂×C₄×D₃	C₂³×C₃	semidirect
396. C₃×C₄⋊C₄	C₂²×D₃	semidirect
397. C₃×C₄⋊C₄	C₂³×C₃	semidirect
402. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
403. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
404. #217	C₂³×C₃	semidirect
405. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
406. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
407. C₄⋊Dic₃	C₂³×C₃	semidirect
408. Dic₃⋊C₄	C₂³×C₃	semidirect
418. C₂²×C₃²	C₂²×D₄	semidirect
430. C₂×C₃×D₃	#121	direct (N × H)
433. C₂×C₃×D₃	C₂²×D₄	semidirect
437. C₃²×C₄	C₂²×D₄	semidirect
440. C₃×Dic₃	C₂²×D₄	semidirect
452. C₂²×D₄	C₂×C₃×D₃	semidirect
453. C₂²×D₄	C₂×C₃×D₃	semidirect
462. C₂³×C₄	C₂×C₃×D₃	semidirect
468. #121	C₂×C₃×D₃	direct (N × H)
472. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
477. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
517. C₂³×C₃	D₃×D₄	semidirect
518. C₂³×C₃	C₂×C₃×D₄	semidirect
539. C₂²×D₃	C₂×C₃×D₄	semidirect
540. C₂²×D₃	C₂×C₃×D₄	semidirect
581. C₂×C₃×C₄	D₃×D₄	semidirect
582. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
595. C₂×Dic₃	C₂×C₃×D₄	semidirect
605. C₄×D₃	C₂×C₃×D₄	semidirect
608. C₂×C₃²	C₂×#121	semidirect
614. C₃×D₃	C₂×#121	direct (N × H)
642. C₂×D₄	C₂²×C₃×D₃	semidirect
643. C₂×D₄	C₂²×C₃×D₃	semidirect
664. C₂²×C₄	C₂²×C₃×D₃	semidirect
667. C₄⋊C₄	C₂²×C₃×D₃	semidirect
671. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
714. C₂²×C₃	C₂×D₃×D₄	semidirect
718. C₂²×C₃	C₂²×C₃×D₄	semidirect
731. C₂×D₃	C₃×#121	direct (N × H)
734. C₂×D₃	C₂²×C₃×D₄	semidirect
746. C₃×C₄	C₂×D₃×D₄	semidirect
747. C₃×C₄	C₂²×C₃×D₄	semidirect
750. Dic₃	C₂²×C₃×D₄	semidirect
751. C₃²	C₂²×#121	semidirect
777. C₂³	C₃×D₃×D₄	semidirect
803. C₂×C₄	C₃×D₃×D₄	semidirect
820. C₂×C₃	D₃×#121	direct (N × H)
821. C₂×C₃	C₂×C₃×#121	semidirect
830. D₃	C₂×C₃×#121	direct (N × H)
854. C₂²	C₂×C₃×D₃×D₄	semidirect
862. C₄	C₂×C₃×D₃×D₄	semidirect
864. C₃	C₂×D₃×#121	direct (N × H)
865. C₃	C₂²×C₃×#121	semidirect
871. C₂	C₃×D₃×#121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×D₄	2
C₂³×C₃×C₄×D₃	2
C₂×C₃²×#121	2
C₂×C₃×#939	2
C₂×C₃×#938	2
C₂×C₃×#930	2
C₃×D₃×#121	2
C₂×C₃×#895	2
C₂×C₃×D₃×C₄⋊C₄	2
C₂×C₃×#884	2
C₂×C₃×D₃×C₂²⋊C₄	2
C₂²×C₃×#121	3
C₂×D₃×#121	3

Subgroups — C2×C3×D3×#121 #11900266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×#121 #11900266