Subgroups — #72341497

Order 2048.

At least 8265 conjugacy classes of subgroups; only the 4044 normal subgroups are shown.

The subgroup lattice has 813 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341488	C₂	1	2	yes	maximal, complemented
2	#72341486	C₂	1	2	yes	maximal, complemented
3	#72341484	C₂	1	2	yes	maximal, complemented
4	#72341482	C₂	1	8	yes	maximal, complemented
5	#72341481	C₂	1	2	yes	maximal, complemented
6	#72341479	C₂	1	2	yes	maximal, complemented
7	#72341476	C₂	1	2	yes	maximal, complemented
8	#72341465	C₂	1	2	yes	maximal, complemented
9	#72341294	C₂	1	1	yes	maximal, characteristic, complemented
10	#72318239	C₂	1	2	yes	maximal, complemented
11	#72318202	C₂	1	2	yes	maximal, complemented
12	#72317829	C₂	1	16	yes	maximal, complemented
13	#72312619	C₂	1	1	yes	maximal, characteristic, complemented
14	#72312133	C₂	1	1	yes	maximal, characteristic, complemented
15	#72311618	C₂	1	2	yes	maximal, complemented
16	#72311606	C₂	1	2	yes	maximal, complemented
17	#72311264	C₂	1	2	yes	maximal, complemented
18	#72249427	C₂	1	8	yes	maximal, complemented
19	#72236657	C₂	1	2	yes	maximal, complemented
20	#72234146	C₂	1	2	yes	maximal, complemented
21	#10586106	C₂²	1	1	yes	characteristic, complemented
22	C₂×#60391	C₂²	1	1	yes	characteristic, complemented
23	C₂×#60388	C₂²	1	1	yes	characteristic
24	#9910716	C₂²	1	8	yes	complemented
25	#8932413	C₂²	1	2	yes	complemented
26	#8928621	C₂²	1	2	yes	complemented
27	#8756105	C₂²	1	2	yes	complemented
28	#7986316	C₂²	1	4	yes	complemented
29	#7985555	C₂²	1	4	yes	complemented
30	#7742598	C₂²	1	2	yes	—
31	#7739366	C₂²	1	2	yes	complemented
32	#7737411	C₂²	1	2	yes	complemented
33	#7711153	C₂²	1	2	yes	complemented
34	#7672684	C₂²	1	1	yes	characteristic
35	C₂×#33559	C₂²	1	4	yes	complemented
36	C₂²×#2196	C₂²	1	4	yes	complemented
37	#6629393	C₂²	1	4	yes	complemented
38	#6628972	C₂²	1	1	yes	characteristic, complemented
39	#6628903	C₂²	1	4	yes	complemented
40	#6628896	C₂²	1	4	yes	complemented
41	#6628874	C₂²	1	1	yes	characteristic, complemented
42	#6628873	C₂²	1	1	yes	characteristic, complemented
43	#6591508	C₂²	1	16	yes	complemented
44	#6573716	C₂²	1	16	yes	complemented
45	#6573695	C₂²	1	8	yes	complemented
46	#6573661	C₂²	1	8	yes	complemented
47	#6487653	C₂²	1	4	yes	complemented
48	#6470247	C₂²	1	4	yes	complemented
49	#6470234	C₂²	1	4	yes	complemented
50	#6443332	C₂²	1	1	yes	characteristic, complemented
51	#6442555	C₂²	1	1	yes	characteristic, complemented
52	#6437971	C₂²	1	1	yes	characteristic, complemented
53	#6437970	C₂²	1	1	yes	characteristic, complemented
54	#6437455	C₂²	1	1	yes	characteristic, complemented
55	#6437452	C₂²	1	1	yes	characteristic
56	#6385981	C₂²	1	2	yes	complemented
57	#6379034	C₂²	1	1	yes	characteristic, complemented
58	C₄×#3018	C₂²	1	1	yes	characteristic, complemented
59	#512122	C₂²	1	4	yes	complemented
60	#512118	C₂²	1	4	yes	complemented
61	#511914	C₂²	1	8	yes	complemented
62	#511787	C₂²	1	4	yes	complemented
63	#511771	C₂²	1	4	yes	complemented
64	#508199	C₂²	1	8	yes	complemented
65	#508101	C₂²	1	8	yes	complemented
66	#508095	C₂²	1	8	yes	complemented
67	#503578	C₂²	1	4	yes	complemented
68	#503238	C₂²	1	16	yes	complemented
69	#503194	C₂²	1	4	yes	complemented
70	#502835	C₂²	1	16	yes	complemented
71	#502788	C₂²	1	8	yes	complemented
72	#502727	C₂²	1	16	yes	complemented
73	#502718	C₂²	1	16	yes	complemented
74	#501172	C₂²	1	16	yes	complemented
75	#501164	C₂²	1	16	yes	complemented
76	#501105	C₂²	1	8	yes	complemented
77	#501097	C₂²	1	8	yes	complemented
78	#501085	C₂²	1	8	yes	complemented
79	#501084	C₂²	1	8	yes	complemented
80	#500954	C₂²	1	4	yes	complemented
81	#500823	C₂²	1	16	yes	complemented
82	#500769	C₂²	1	4	yes	complemented
83	#500544	C₂²	1	16	yes	complemented
84	#500497	C₂²	1	8	yes	complemented
85	#500364	C₂²	1	4	yes	complemented
86	#500192	C₂²	1	4	yes	complemented
87	#500179	C₂²	1	4	yes	complemented
88	#500174	C₂²	1	4	yes	complemented
89	#500075	C₂²	1	16	yes	complemented
90	#500066	C₂²	1	16	yes	complemented
91	#500016	C₂²	1	4	yes	complemented
92	#500016	C₂²	1	4	yes	complemented
93	#500016	C₂²	1	4	yes	complemented
94	#499844	C₂²	1	4	yes	complemented
95	#499844	C₂²	1	4	yes	complemented
96	#499844	C₂²	1	8	yes	complemented
97	#499844	C₂²	1	4	yes	complemented
98	#499843	C₂²	1	8	yes	complemented
99	#499840	C₂²	1	4	yes	complemented
100	#499840	C₂²	1	4	yes	complemented
101	#499840	C₂²	1	8	yes	complemented
102	#499840	C₂²	1	4	yes	complemented
103	#499832	C₂²	1	8	yes	complemented
104	#499831	C₂²	1	4	yes	complemented
105	#499831	C₂²	1	4	yes	complemented
106	#499831	C₂²	1	4	yes	complemented
107	#499803	C₂²	1	16	yes	complemented
108	#499795	C₂²	1	16	yes	complemented
109	#499288	C₂²	1	8	yes	complemented
110	#498933	C₂²	1	8	yes	complemented
111	#498927	C₂²	1	8	yes	complemented
112	#497515	C₂²	1	16	yes	complemented
113	#497357	C₂²	1	16	yes	complemented
114	#497308	C₂²	1	8	yes	complemented
115	#497300	C₂²	1	8	yes	complemented
116	#496513	C₂²	1	4	yes	complemented
117	#496312	C₂²	1	2	yes	complemented
118	#496247	C₂²	1	4	yes	complemented
119	#496240	C₂²	1	4	yes	complemented
120	#496205	C₂²	1	2	yes	complemented
121	#496204	C₂²	1	2	yes	complemented
122	#495744	C₂²	1	8	yes	complemented
123	#495583	C₂²	1	4	yes	complemented
124	#494689	C₂²	1	4	yes	complemented
125	#494682	C₂²	1	4	yes	complemented
126	#494596	C₂²	1	4	yes	complemented
127	#494592	C₂²	1	4	yes	complemented
128	#493957	C₂²	1	2	yes	complemented
129	#493432	C₂²	1	2	yes	complemented
130	#493430	C₂²	1	2	yes	complemented
131	C₂×2₋¹⁺⁶	C₂³	1	1	yes	characteristic, complemented
132	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
133	#62987	C₂³	1	8	yes	complemented
134	#62859	C₂³	1	1	yes	characteristic, complemented
135	#62852	C₂³	1	1	yes	characteristic
136	#62812	C₂³	1	1	yes	characteristic, complemented
137	C₂×#3500	D₄	1	1	yes	characteristic, complemented
138	C₂×#3500	C₂³	1	1	yes	characteristic
139	C₂×#3499	C₂³	1	1	yes	characteristic
140	C₂×#3498	C₂³	1	1	yes	characteristic
141	C₂×#3549	C₂³	1	2	yes	complemented
142	C₂²×D₄²	C₂³	1	2	yes	—
143	C₂²×H(3,𝔽₄)	D₄	1	2	yes	complemented
144	C₄×#585	C₂³	1	1	yes	characteristic, complemented
145	C₂×#3027	C₂³	1	8	yes	—
146	C₂²×B(4,𝔽₂)	C₂³	1	8	yes	complemented
147	C₂×#3022	C₂³	1	1	yes	characteristic, complemented
148	C₂×#3022	C₂³	1	1	yes	characteristic, complemented
149	C₂×#3022	C₂³	1	4	yes	complemented
150	C₂×#3022	C₂³	1	1	yes	characteristic, complemented
151	C₂×#3021	C₂³	1	1	yes	characteristic
152	C₂×#3021	C₂³	1	1	yes	characteristic
153	C₂×#3021	C₂³	1	1	yes	characteristic
154	C₂×#3019	C₂³	1	4	yes	—
155	C₂×#3018	C₂³	1	1	yes	characteristic
156	C₂×#3018	C₂³	1	4	yes	—
157	C₂×#3018	C₂³	1	1	yes	characteristic
158	C₂×#3018	C₂³	1	1	yes	characteristic
159	C₂²×#453	C₂³	1	4	yes	—
160	C₂×#2889	C₂³	1	1	yes	characteristic, complemented
161	C₂×#2888	C₂³	1	1	yes	characteristic
162	#59817	C₂³	1	2	yes	complemented
163	#59816	C₂³	1	2	yes	complemented
164	#59126	C₂³	1	4	yes	—
165	#59041	C₂³	1	4	yes	—
166	#59041	C₂³	1	4	yes	complemented
167	#52004	C₂³	1	4	yes	—
168	#52004	C₂³	1	4	yes	—
169	#51749	C₂³	1	4	yes	—
170	#51749	C₂³	1	4	yes	complemented
171	#50274	C₂³	1	8	yes	complemented
172	#49545	C₂³	1	8	yes	complemented
173	#48922	C₂³	1	8	yes	—
174	#47929	C₂³	1	8	yes	complemented
175	#46287	C₂³	1	4	yes	—
176	#46073	C₂³	1	4	yes	complemented
177	#45741	C₂³	1	8	yes	complemented
178	#45439	C₂³	1	8	yes	—
179	#39357	D₄	1	4	yes	complemented
180	#39357	C₂³	1	4	yes	—
181	#38028	D₄	1	8	yes	complemented
182	#38028	C₂³	1	8	yes	—
183	#37645	D₄	1	8	yes	complemented
184	#37645	C₂³	1	8	yes	—
185	#37536	D₄	1	4	yes	complemented
186	#37419	C₂³	1	4	yes	complemented
187	#37187	D₄	1	4	yes	complemented
188	#37150	C₂³	1	4	yes	complemented
189	#36702	D₄	1	4	yes	complemented
190	#36702	C₂³	1	4	yes	—
191	C₂×#2858	D₄	1	1	yes	characteristic, complemented
192	#36122	D₄	1	4	yes	complemented
193	#36121	C₂³	1	4	yes	—
194	#35676	D₄	1	1	yes	characteristic, complemented
195	#35676	C₂³	1	1	yes	characteristic
196	#35676	C₂³	1	4	yes	—
197	#35616	D₄	1	1	yes	characteristic, complemented
198	#35616	C₂³	1	1	yes	characteristic
199	#35346	C₂³	1	4	yes	—
200	#35327	D₄	1	1	yes	characteristic, complemented
201	#35327	C₂³	1	1	yes	characteristic
202	#35316	D₄	1	1	yes	characteristic, complemented
203	#35272	D₄	1	1	yes	characteristic, complemented
204	#35129	C₂³	1	4	yes	—
205	#34493	C₂³	1	4	yes	complemented
206	#34366	D₄	1	2	yes	complemented
207	#34364	C₂³	1	2	yes	—
208	#34155	C₂³	1	2	yes	complemented
209	C₄×#532	D₄	1	1	yes	characteristic, complemented
210	C₄×#532	C₂³	1	1	yes	characteristic
211	C₂×#2199	C₂³	1	8	yes	—
212	C₂×#2199	C₂³	1	8	yes	—
213	C₂×#2199	C₂³	1	8	yes	complemented
214	C₂×#2196	C₂³	1	8	yes	—
215	C₂×#2196	C₂³	1	8	yes	—
216	C₂×#2196	C₂³	1	8	yes	complemented
217	C₂×#2196	C₂³	1	8	yes	complemented
218	C₂×#2196	C₂³	1	8	yes	complemented
219	C₂×#2196	C₂³	1	8	yes	complemented
220	C₂×#2129	C₂³	1	4	yes	complemented
221	C₂×#2127	C₂³	1	4	yes	—
222	C₂×#2126	C₂³	1	4	yes	complemented
223	C₂²×#353	C₂³	1	4	yes	—
224	C₂×#2122	C₂³	1	8	yes	complemented
225	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
226	#33021	C₂³	1	8	yes	complemented
227	#32975	C₂³	1	8	yes	complemented
228	#32926	C₂³	1	8	yes	—
229	#32924	C₂³	1	8	yes	complemented
230	#32899	C₂³	1	8	yes	complemented
231	#32899	C₂³	1	16	yes	complemented
232	#32899	C₂³	1	8	yes	complemented
233	#32899	C₂³	1	8	yes	complemented
234	#32898	C₂³	1	16	yes	—
235	#32891	C₂³	1	8	yes	complemented
236	#32890	C₂³	1	8	yes	complemented
237	#25899	C₂³	1	8	yes	complemented
238	#25771	C₂³	1	8	yes	—
239	#25743	C₂³	1	8	yes	complemented
240	#24414	C₂³	1	8	yes	complemented
241	#24413	C₂³	1	8	yes	complemented
242	#24406	C₂³	1	16	yes	complemented
243	#24404	C₂³	1	16	yes	—
244	#24262	C₂³	1	16	yes	complemented
245	#24224	C₂³	1	4	yes	complemented
246	#24222	C₂³	1	4	yes	—
247	#24058	C₂³	1	8	yes	complemented
248	#24057	C₂³	1	8	yes	complemented
249	#23914	C₂³	1	4	yes	complemented
250	#23912	C₂³	1	4	yes	—
251	#23908	C₂³	1	4	yes	—
252	#23906	C₂³	1	4	yes	—
253	#23904	C₂³	1	8	yes	—
254	#23900	C₂³	1	8	yes	complemented
255	#22408	C₂³	1	8	yes	complemented
256	#22405	C₂³	1	16	yes	complemented
257	#21482	C₂³	1	16	yes	complemented
258	C₄×#455	C₂³	1	4	yes	complemented
259	C₄×#453	C₂³	1	4	yes	—
260	#20956	C₂³	1	1	yes	characteristic
261	#20955	C₂³	1	1	yes	characteristic, complemented
262	#20952	C₂³	1	1	yes	characteristic
263	#20855	C₂³	1	1	yes	characteristic, complemented
264	#20723	C₂³	1	4	yes	complemented
265	#20637	C₂³	1	1	yes	characteristic, complemented
266	#20615	C₂³	1	1	yes	characteristic, complemented
267	#20615	C₂³	1	1	yes	characteristic, complemented
268	#20615	C₂³	1	1	yes	characteristic, complemented
269	#20609	C₂³	1	8	yes	complemented
270	#20608	C₂³	1	8	yes	complemented
271	#20593	C₂³	1	1	yes	characteristic, complemented
272	#20592	C₂³	1	1	yes	characteristic
273	#20587	C₂³	1	4	yes	complemented
274	#20585	C₂³	1	4	yes	—
275	C₄×#413	C₂³	1	1	yes	characteristic, complemented
276	#13461	C₂³	1	8	yes	complemented
277	#13424	C₂³	1	16	yes	complemented
278	#13424	C₂³	1	16	yes	complemented
279	#13422	C₂³	1	16	yes	complemented
280	#13419	C₂³	1	8	yes	complemented
281	#13375	C₂³	1	8	yes	complemented
282	#13375	C₂³	1	8	yes	complemented
283	#13375	C₂³	1	8	yes	complemented
284	#13348	C₂³	1	16	yes	complemented
285	#13348	C₂³	1	16	yes	complemented
286	#13348	C₂³	1	16	yes	complemented
287	#13348	C₂³	1	16	yes	complemented
288	#13348	C₂³	1	16	yes	complemented
289	#13348	C₂³	1	16	yes	complemented
290	#13346	C₂³	1	16	yes	—
291	#13346	C₂³	1	16	yes	—
292	#13346	C₂³	1	16	yes	complemented
293	#13343	C₂³	1	8	yes	—
294	#13343	C₂³	1	8	yes	—
295	#13343	C₂³	1	8	yes	complemented
296	#13296	C₂³	1	8	yes	complemented
297	#13293	C₂³	1	8	yes	complemented
298	#13225	C₂³	1	16	yes	complemented
299	#13221	C₂³	1	8	yes	complemented
300	#13218	C₂³	1	8	yes	complemented
301	#13090	C₂³	1	16	yes	complemented
302	#13089	C₂³	1	16	yes	complemented
303	#13087	C₂³	1	16	yes	complemented
304	#13086	C₂³	1	16	yes	—
305	#13083	C₂³	1	8	yes	complemented
306	#13083	C₂³	1	8	yes	complemented
307	#13083	C₂³	1	8	yes	complemented
308	#13083	C₂³	1	8	yes	complemented
309	#13083	C₂³	1	16	yes	complemented
310	#13082	C₂³	1	16	yes	—
311	#13049	C₂³	1	8	yes	complemented
312	#13049	C₂³	1	8	yes	complemented
313	#13049	C₂³	1	8	yes	complemented
314	#13048	C₂³	1	8	yes	complemented
315	#13048	C₂³	1	8	yes	complemented
316	#13048	C₂³	1	8	yes	complemented
317	#13047	C₂³	1	8	yes	—
318	#13047	C₂³	1	8	yes	—
319	#13047	C₂³	1	8	yes	complemented
320	#13043	C₂³	1	16	yes	complemented
321	#13043	C₂³	1	16	yes	complemented
322	#13043	C₂³	1	16	yes	complemented
323	#12966	C₂³	1	8	yes	complemented
324	#12965	C₂³	1	8	yes	complemented
325	#12964	C₂³	1	8	yes	complemented
326	#12960	C₂³	1	16	yes	complemented
327	#12857	C₂³	1	4	yes	complemented
328	#12854	C₂³	1	8	yes	complemented
329	#12853	C₂³	1	8	yes	complemented
330	#12798	C₂³	1	4	yes	complemented
331	#12797	C₂³	1	4	yes	complemented
332	#12795	C₂³	1	16	yes	complemented
333	#12763	C₂³	1	8	yes	complemented
334	#12759	C₂³	1	8	yes	complemented
335	#12759	C₂³	1	8	yes	complemented
336	#12698	C₂³	1	4	yes	complemented
337	#12698	C₂³	1	4	yes	complemented
338	#12697	C₂³	1	4	yes	—
339	#12696	C₂³	1	4	yes	—
340	#12695	C₂³	1	4	yes	—
341	#12695	C₂³	1	4	yes	complemented
342	#12693	C₂³	1	4	yes	—
343	#12691	C₂³	1	8	yes	complemented
344	#12687	C₂³	1	8	yes	complemented
345	C₄×#354	C₂³	1	4	yes	complemented
346	C₄×#353	C₂³	1	4	yes	complemented
347	#12622	C₂³	1	16	yes	complemented
348	#12574	C₂³	1	8	yes	complemented
349	#12573	C₂³	1	8	yes	complemented
350	C₂×#585	C₂⁴	1	1	yes	characteristic
351	C₂×#585	C₂⁴	1	4	yes	—
352	C₂×#585	C₂⁴	1	1	yes	characteristic
353	C₂×#585	C₂⁴	1	1	yes	characteristic
354	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
355	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
356	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
357	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
358	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
359	C₂×H(3,𝔽₄)	C₂⁴	1	4	yes	—
360	#3496	C₂⁴	1	4	yes	—
361	#3485	C₂⁴	1	4	yes	—
362	#3484	C₂⁴	1	4	yes	—
363	C₂×#548	C₂×D₄	1	4	yes	—
364	C₂×#548	C₂×D₄	1	4	yes	complemented
365	C₂×#546	C₂×D₄	1	8	yes	—
366	C₂×#546	C₂×D₄	1	4	yes	complemented
367	C₂×#546	C₂⁴	1	4	yes	—
368	C₂×D₄²	C₂⁴	1	4	yes	—
369	C₂×D₄²	C₂⁴	1	4	yes	—
370	C₂×#536	C₂×D₄	1	2	yes	—
371	C₂×#536	C₂×D₄	1	1	yes	characteristic
372	C₂×#536	C₂×D₄	1	1	yes	characteristic
373	C₂×#536	C₂×D₄	1	1	yes	characteristic, complemented
374	C₂×#536	C₂×D₄	1	2	yes	complemented
375	C₂×#536	C₂⁴	1	1	yes	characteristic
376	C₂×#536	C₂⁴	1	2	yes	—
377	C₂×#535	C₂×D₄	1	1	yes	characteristic
378	C₂×#535	C₂×D₄	1	2	yes	—
379	C₂×#535	C₂×D₄	1	1	yes	characteristic
380	C₂×#535	C₂×D₄	1	2	yes	—
381	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
382	C₂×#535	C₂×D₄	1	4	yes	complemented
383	C₂×#535	C₂⁴	1	1	yes	characteristic
384	C₂×#535	C₂⁴	1	2	yes	—
385	C₂×#535	C₂⁴	1	4	yes	—
386	C₂×#532	C₂×D₄	1	2	yes	—
387	C₂×#532	C₂×D₄	1	2	yes	—
388	C₂×#532	C₂×D₄	1	1	yes	characteristic
389	C₂×#532	C₂⁴	1	2	yes	—
390	C₂×#532	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
392	C₂²×C₄⋊Q₈	C₂×D₄	1	2	yes	complemented
393	C₂²×#127	C₂×D₄	1	1	yes	characteristic
394	C₂²×#127	C₂⁴	1	2	yes	—
395	C₂²×#124	C₂×D₄	1	1	yes	characteristic
396	C₂²×#124	C₂×D₄	1	1	yes	characteristic
397	C₂²×#124	C₂×D₄	1	2	yes	—
398	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
399	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
400	C₂²×#124	C₂×D₄	1	4	yes	complemented
401	C₂²×#124	C₂×D₄	1	4	yes	complemented
402	C₂²×#124	C₂×D₄	1	8	yes	complemented
403	C₂²×#120	C₂×D₄	1	4	yes	—
404	C₂²×#120	C₂×D₄	1	4	yes	—
405	C₂²×#120	C₂×D₄	1	8	yes	complemented
406	C₂²×#120	C₂⁴	1	4	yes	—
407	C₄×H(5,𝔽₂)	C₂⁴	1	4	yes	—
408	#3428	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
410	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
411	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
412	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
413	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
414	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
415	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
416	C₂×#455	C₂⁴	1	2	yes	—
417	C₂×#455	C₂⁴	1	4	yes	—
418	C₂×#455	C₂⁴	1	4	yes	—
419	C₂×#455	C₂⁴	1	4	yes	—
420	C₂×#455	C₂⁴	1	2	yes	—
421	C₂×#455	C₂⁴	1	2	yes	—
422	C₂×#453	C₂⁴	1	2	yes	—
423	C₂×#453	C₂⁴	1	2	yes	—
424	C₂×#453	C₂⁴	1	4	yes	—
425	C₂×#453	C₂⁴	1	4	yes	—
426	C₂×#453	C₂⁴	1	2	yes	—
427	C₂×#453	C₂⁴	1	4	yes	—
428	C₂×#413	C₂⁴	1	1	yes	characteristic
429	C₂×#413	C₂⁴	1	4	yes	—
430	C₂×#413	C₂⁴	1	1	yes	characteristic
431	C₂×#413	C₂⁴	1	1	yes	characteristic
432	C₂×#413	C₂⁴	1	1	yes	characteristic
433	C₂²×#100	C₂⁴	1	4	yes	—
434	C₂×#410	C₂⁴	1	8	yes	—
435	C₂²×#99	C₂⁴	1	8	yes	—
436	#2858	C₂×D₄	1	4	yes	complemented
437	#2858	C₂×D₄	1	4	yes	complemented
438	#2857	C₂×D₄	1	4	yes	complemented
439	#2856	C₂×D₄	1	4	yes	complemented
440	#2853	C₂×D₄	1	8	yes	complemented
441	#2846	C₂×D₄	1	8	yes	complemented
442	#2684	C₂⁴	1	8	yes	—
443	#2684	C₂⁴	1	8	yes	—
444	#2683	C₂⁴	1	4	yes	—
445	#2679	C₂⁴	1	4	yes	—
446	#2669	C₂⁴	1	8	yes	—
447	#2622	C₂×D₄	1	8	yes	complemented
448	#2621	C₂×D₄	1	4	yes	complemented
449	#2619	C₂×D₄	1	4	yes	complemented
450	#2617	C₂×D₄	1	8	yes	complemented
451	#2617	C₂×D₄	1	8	yes	complemented
452	#2613	C₂×D₄	1	8	yes	complemented
453	#2545	C₂×D₄	1	4	yes	complemented
454	#2545	C₂×D₄	1	4	yes	complemented
455	#2544	C₂×D₄	1	4	yes	complemented
456	#2544	C₂⁴	1	4	yes	—
457	#2482	C₂×D₄	1	8	yes	complemented
458	#2436	C₂×D₄	1	8	yes	complemented
459	#2436	C₂×D₄	1	4	yes	complemented
460	#2436	C₂×D₄	1	4	yes	complemented
461	#2435	C₂×D₄	1	4	yes	complemented
462	#2435	C₂⁴	1	4	yes	—
463	#2433	C₂×D₄	1	8	yes	complemented
464	#2432	C₂×D₄	1	4	yes	—
465	#2432	C₂×D₄	1	4	yes	complemented
466	#2431	C₂×D₄	1	4	yes	complemented
467	#2431	C₂⁴	1	4	yes	—
468	#2411	C₂×D₄	1	8	yes	complemented
469	#2411	C₂×D₄	1	8	yes	complemented
470	#2410	C₂×D₄	1	8	yes	complemented
471	#2410	C₂×D₄	1	8	yes	complemented
472	#2409	C₂×D₄	1	4	yes	complemented
473	#2409	C₂⁴	1	4	yes	—
474	#2408	C₂×D₄	1	4	yes	complemented
475	#2408	C₂⁴	1	4	yes	—
476	#2404	C₂×D₄	1	8	yes	—
477	#2404	C₂×D₄	1	8	yes	complemented
478	#2404	C₂×D₄	1	8	yes	complemented
479	#2404	C₂⁴	1	8	yes	—
480	#2404	C₂⁴	1	8	yes	—
481	#2403	C₂×D₄	1	8	yes	—
482	#2403	C₂⁴	1	8	yes	—
483	#2380	C₂⁴	1	4	yes	—
484	#2375	C₂⁴	1	8	yes	—
485	#2372	C₂⁴	1	4	yes	—
486	#2366	C₂⁴	1	4	yes	—
487	#2342	C₂×D₄	1	8	yes	complemented
488	#2342	C₂×D₄	1	8	yes	complemented
489	#2321	C₂×D₄	1	8	yes	complemented
490	#2321	C₂⁴	1	8	yes	—
491	#2310	C₂×D₄	1	1	yes	characteristic, complemented
492	#2310	C₂×D₄	1	1	yes	characteristic, complemented
493	#2310	C₂×D₄	1	4	yes	complemented
494	#2309	C₂×D₄	1	1	yes	characteristic
495	#2309	C₂×D₄	1	1	yes	characteristic, complemented
496	#2308	C₂×D₄	1	4	yes	—
497	#2308	C₂×D₄	1	4	yes	—
498	#2308	C₂⁴	1	4	yes	—
499	C₄×C₄⋊Q₈	C₂×D₄	1	2	yes	complemented
500	C₄×#127	C₂⁴	1	2	yes	—
501	C₄×#124	C₂×D₄	1	2	yes	complemented
502	C₄×#124	C₂⁴	1	2	yes	—
503	#2297	C₂×D₄	1	1	yes	characteristic
504	#2297	C₂×D₄	1	1	yes	characteristic, complemented
505	#2297	C₂×D₄	1	4	yes	complemented
506	#2297	C₂×D₄	1	1	yes	characteristic, complemented
507	#2297	C₂⁴	1	1	yes	characteristic
508	#2297	C₂⁴	1	4	yes	—
509	#2293	C₂×D₄	1	4	yes	complemented
510	#2285	C₂×D₄	1	1	yes	characteristic, complemented
511	#2285	C₂×D₄	1	1	yes	characteristic, complemented
512	#2283	C₂×D₄	1	4	yes	complemented
513	C₄²×D₄	C₂×D₄	1	4	yes	complemented
514	C₂×C₄³	C₂×D₄	1	1	yes	characteristic, complemented
515	C₂×#354	C₂⁴	1	8	yes	—
516	C₂×#354	C₂⁴	1	8	yes	—
517	C₂×#354	C₂⁴	1	8	yes	—
518	C₂×#353	C₂⁴	1	8	yes	—
519	C₂×#353	C₂⁴	1	8	yes	—
520	C₂×#353	C₂⁴	1	8	yes	—
521	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	—
522	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	—
523	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	—
524	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	—
525	#1889	C₂⁴	1	16	yes	—
526	#1887	C₂⁴	1	4	yes	—
527	#1887	C₂⁴	1	2	yes	—
528	#1885	C₂⁴	1	4	yes	—
529	#1885	C₂⁴	1	2	yes	—
530	#1867	C₂⁴	1	16	yes	—
531	#1856	C₂⁴	1	4	yes	—
532	#1800	C₂⁴	1	4	yes	—
533	#1799	C₂⁴	1	8	yes	—
534	#1792	C₂⁴	1	4	yes	—
535	#1792	C₂⁴	1	4	yes	—
536	#1792	C₂⁴	1	4	yes	—
537	#1790	C₂⁴	1	16	yes	—
538	#1790	C₂⁴	1	16	yes	—
539	#1790	C₂⁴	1	16	yes	—
540	#1785	C₂⁴	1	4	yes	—
541	#1783	C₂⁴	1	4	yes	—
542	#1782	C₂⁴	1	8	yes	—
543	#1782	C₂⁴	1	8	yes	—
544	#1781	C₂⁴	1	8	yes	—
545	C₄×#100	C₂⁴	1	4	yes	—
546	C₄×#99	C₂⁴	1	8	yes	—
547	#1393	C₂⁴	1	8	yes	—
548	#1393	C₂⁴	1	8	yes	—
549	#1390	C₂⁴	1	16	yes	—
550	#1390	C₂⁴	1	16	yes	—
551	#1390	C₂⁴	1	16	yes	—
552	#1390	C₂⁴	1	16	yes	—
553	C₂⁶	C₂²×D₄	1	4	yes	—
554	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
555	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
556	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
557	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
558	C₂²×#41	C₂²×D₄	1	2	yes	—
559	C₂²×#41	C₂²×D₄	1	2	yes	—
560	C₂²×#41	C₂²×D₄	1	2	yes	—
561	C₂²×#41	C₂²×D₄	1	4	yes	—
562	C₂²×#41	C₂²×D₄	1	2	yes	—
563	C₂²×#41	C₂²×D₄	1	2	yes	—
564	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
565	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
566	C₂²×#41	C₂⁵	1	1	yes	characteristic
567	C₂²×#41	C₂⁵	1	2	yes	—
568	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
569	C₂³×Q₈	C₂²×D₄	1	2	yes	—
570	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
571	C₂³×Q₈	C₂²×D₄	1	2	yes	—
572	C₂³×Q₈	C₂²×D₄	1	2	yes	—
573	C₂³×Q₈	C₂²×D₄	1	4	yes	—
574	C₂³×D₄	C₂²×D₄	1	4	yes	—
575	C₂³×D₄	C₂²×D₄	1	2	yes	—
576	C₂³×D₄	C₂²×D₄	1	2	yes	—
577	C₂³×D₄	C₂²×D₄	1	4	yes	—
578	C₂³×D₄	C₂²×D₄	1	8	yes	—
579	C₂³×D₄	C₂²×D₄	1	4	yes	—
580	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
581	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
582	C₂³×D₄	C₂⁵	1	2	yes	—
583	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
584	C₂×C₄⋊Q₈	#120	1	2	yes	—
585	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
587	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
588	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
589	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
590	C₂×#127	#120	1	1	yes	characteristic
591	C₂×#127	#120	1	2	yes	—
592	C₂×#127	C₂²×D₄	1	2	yes	—
593	C₂×#127	C₂²×D₄	1	2	yes	—
594	C₂×#127	C₂²×D₄	1	2	yes	—
595	C₂×#127	C₂⁵	1	2	yes	—
596	C₂×#127	C₂⁵	1	1	yes	characteristic
597	C₂×#124	#120	1	1	yes	characteristic
598	C₂×#124	#120	1	2	yes	—
599	C₂×#124	#120	1	8	yes	—
600	C₂×#124	#120	1	2	yes	—
601	C₂×#124	#120	1	2	yes	—
602	C₂×#124	#120	1	2	yes	—
603	C₂×#124	#120	1	1	yes	characteristic
604	C₂×#124	C₂²×D₄	1	2	yes	—
605	C₂×#124	C₂²×D₄	1	1	yes	characteristic
606	C₂×#124	C₂²×D₄	1	4	yes	—
607	C₂×#124	C₂²×D₄	1	2	yes	—
608	C₂×#124	C₂²×D₄	1	2	yes	—
609	C₂×#124	C₂²×D₄	1	4	yes	—
610	C₂×#124	C₂²×D₄	1	4	yes	—
611	C₂×#124	C₂²×D₄	1	4	yes	—
612	C₂×#124	C₂⁵	1	2	yes	—
613	C₂×#124	C₂⁵	1	1	yes	characteristic
614	C₂×#123	#120	1	4	yes	—
615	C₂×#123	C₂²×D₄	1	8	yes	—
616	C₂×C₂²⋊Q₈	#120	1	8	yes	—
617	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
618	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
619	C₂×#121	#120	1	4	yes	—
620	C₂×#121	#120	1	8	yes	—
621	C₂×#121	C₂²×D₄	1	4	yes	—
622	C₂×#121	C₂²×D₄	1	8	yes	—
623	C₂×#121	C₂²×D₄	1	4	yes	—
624	C₂×#120	#120	1	4	yes	—
625	C₂×#120	C₂²×D₄	1	8	yes	—
626	C₂×#120	C₂²×D₄	1	8	yes	—
627	C₂×#120	C₂²×D₄	1	8	yes	—
628	C₂×#120	C₂²×D₄	1	8	yes	—
629	C₂×#120	C₂²×D₄	1	8	yes	—
630	C₂×#120	C₂²×D₄	1	8	yes	—
631	C₂×#120	C₂⁵	1	8	yes	—
632	#518	C₂⁵	1	2	yes	—
633	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
634	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
635	C₂×C₄×D₄	#120	1	8	yes	—
636	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
637	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
638	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
639	C₂×C₄×D₄	C₂⁵	1	2	yes	—
640	C₂×#117	C₂²×D₄	1	1	yes	characteristic
641	C₂×#117	C₂²×D₄	1	4	yes	—
642	C₂×#117	C₂²×D₄	1	4	yes	—
643	C₂×#117	C₂²×D₄	1	1	yes	characteristic
644	C₂×#117	C₂²×D₄	1	2	yes	—
645	C₂×#117	C₂²×D₄	1	1	yes	characteristic
646	C₂×#117	C₂²×D₄	1	1	yes	characteristic
647	C₂×#117	C₂²×D₄	1	2	yes	—
648	C₂×#117	C₂²×D₄	1	2	yes	—
649	C₂²×C₂²⋊C₄	#120	1	4	yes	—
650	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
651	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
652	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
653	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
654	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
655	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
656	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
657	C₂²×C₄²	C₂²×D₄	1	2	yes	—
658	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
659	C₂²×C₄²	C₂²×D₄	1	2	yes	—
660	C₂²×C₄²	C₂²×D₄	1	2	yes	—
661	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
662	C₂²×C₄²	C₂²×D₄	1	4	yes	—
663	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
664	#453	H(5,𝔽₂)	1	8	yes	—
665	C₂×#100	C₂⁵	1	2	yes	—
666	C₂×#100	C₂⁵	1	2	yes	—
667	C₂×#100	C₂⁵	1	2	yes	—
668	C₂×#100	C₂⁵	1	2	yes	—
669	C₂×#99	C₂⁵	1	16	yes	—
670	#391	C₂²×D₄	1	2	yes	—
671	#391	C₂²×D₄	1	4	yes	—
672	#391	C₂²×D₄	1	2	yes	—
673	#391	C₂²×D₄	1	4	yes	—
674	#390	C₂²×D₄	1	4	yes	—
675	#390	C₂²×D₄	1	2	yes	—
676	#390	C₂²×D₄	1	4	yes	—
677	#390	C₂⁵	1	2	yes	—
678	#386	C₂²×D₄	1	8	yes	—
679	#386	C₂²×D₄	1	8	yes	—
680	#386	C₂²×D₄	1	8	yes	—
681	#386	C₂²×D₄	1	8	yes	—
682	#386	C₂²×D₄	1	8	yes	—
683	#386	C₂⁵	1	8	yes	—
684	#385	C₂²×D₄	1	8	yes	—
685	#385	C₂²×D₄	1	8	yes	—
686	#384	C₂²×D₄	1	2	yes	—
687	#382	C₂²×D₄	1	2	yes	—
688	#381	C₂²×D₄	1	8	yes	—
689	#381	C₂²×D₄	1	8	yes	—
690	#380	C₂²×D₄	1	4	yes	—
691	#380	C₂²×D₄	1	4	yes	—
692	#379	C₂²×D₄	1	8	yes	—
693	#379	C₂²×D₄	1	8	yes	—
694	#379	C₂²×D₄	1	8	yes	—
695	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
696	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
697	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
698	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
699	C₄³	C₂²×D₄	1	2	yes	—
700	C₄³	C₂²×D₄	1	2	yes	—
701	C₂⁵	C₂×#120	1	2	yes	—
702	C₂⁵	C₂³×D₄	1	4	yes	—
703	C₂⁵	C₂³×D₄	1	8	yes	—
704	H(5,𝔽₂)	C₂×H(5,𝔽₂)	1	4	yes	—
705	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
706	C₂²×Q₈	C₂×#120	1	4	yes	—
707	C₂²×Q₈	C₂×#120	1	2	yes	—
708	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
709	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
710	C₂²×Q₈	C₂³×D₄	1	2	yes	—
711	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
712	C₂²×Q₈	C₂³×D₄	1	2	yes	—
713	C₂²×D₄	C₂×#120	1	2	yes	—
714	C₂²×D₄	C₂×#120	1	2	yes	—
715	C₂²×D₄	C₂×#120	1	1	yes	characteristic
716	C₂²×D₄	C₂×#120	1	4	yes	—
717	C₂²×D₄	C₂×#120	1	2	yes	—
718	C₂²×D₄	C₂×#120	1	4	yes	—
719	C₂²×D₄	C₂×#120	1	1	yes	characteristic
720	C₂²×D₄	C₂×#120	1	8	yes	—
721	C₂²×D₄	C₂³×D₄	1	2	yes	—
722	C₂²×D₄	C₂³×D₄	1	2	yes	—
723	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
724	C₂²×D₄	C₂³×D₄	1	2	yes	—
725	C₂²×D₄	C₂³×D₄	1	4	yes	—
726	C₂²×D₄	C₂³×D₄	1	4	yes	—
727	C₂²×D₄	C₂⁶	1	1	yes	characteristic
728	C₂³×C₄	C₂×#120	1	2	yes	—
729	C₂³×C₄	C₂×#120	1	2	yes	—
730	C₂³×C₄	C₂×#120	1	4	yes	—
731	C₂³×C₄	C₂×#120	1	4	yes	—
732	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
733	C₂³×C₄	C₂³×D₄	1	2	yes	—
734	C₂³×C₄	C₂³×D₄	1	2	yes	—
735	C₂³×C₄	C₂³×D₄	1	4	yes	—
736	C₂³×C₄	C₂³×D₄	1	2	yes	—
737	C₂³×C₄	C₂³×D₄	1	4	yes	—
738	C₂³×C₄	C₂³×D₄	1	8	yes	—
739	#127	C₂×H(5,𝔽₂)	1	4	yes	—
740	#124	B(4,𝔽₂)	1	2	yes	—
741	#124	B(4,𝔽₂)	1	2	yes	—
742	#124	B(4,𝔽₂)	1	4	yes	—
743	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
744	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
745	C₂×C₄⋊C₄	C₂×#120	1	8	yes	—
746	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
749	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
750	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
751	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
752	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
753	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
755	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
756	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
757	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
758	C₂×C₄²	C₂×#120	1	1	yes	characteristic
759	C₂×C₄²	C₂×#120	1	2	yes	—
760	C₂×C₄²	C₂×#120	1	4	yes	—
761	C₂×C₄²	C₂×#120	1	1	yes	characteristic
762	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
763	C₂×C₄²	C₂³×D₄	1	2	yes	—
764	C₂×C₄²	C₂³×D₄	1	2	yes	—
765	C₂×C₄²	C₂³×D₄	1	2	yes	—
766	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
767	C₂×C₄²	C₂³×D₄	1	2	yes	—
768	#100	C₂×H(5,𝔽₂)	1	4	yes	—
769	C₂⁴	C₂²×#120	1	4	yes	—
770	C₂⁴	C₂²×#120	1	2	yes	—
771	C₂⁴	C₂²×#120	1	2	yes	—
772	C₂⁴	C₂²×#120	1	1	yes	characteristic
773	C₂⁴	C₂⁴×D₄	1	2	yes	—
774	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
775	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
776	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
777	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
778	C₂×D₄	#3484	1	2	yes	—
779	C₂×D₄	C₂²×H(5,𝔽₂)	1	2	yes	—
780	C₂×D₄	H(7,𝔽₂)	1	2	yes	—
781	C₂²×C₄	C₂²×#120	1	2	yes	—
782	C₂²×C₄	C₂²×#120	1	2	yes	—
783	C₂²×C₄	C₂²×#120	1	4	yes	—
784	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
785	C₂²×C₄	C₂²×#120	1	2	yes	—
786	C₂²×C₄	C₂²×#120	1	4	yes	—
787	C₂²×C₄	C₂²×#120	1	2	yes	—
788	C₂²×C₄	C₂²×#120	1	2	yes	—
789	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
790	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	8	yes	—
791	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	8	yes	—
792	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
793	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
794	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
795	C₄²	#3484	1	2	yes	—
796	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
797	C₂³	#60399	1	2	yes	—
798	C₂³	C₂³×#120	1	1	yes	characteristic
799	C₂³	D₄×H(5,𝔽₂)	1	4	yes	—
800	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
801	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
802	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
803	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
804	C₂×C₄	C₂²×B(4,𝔽₂)	1	4	yes	—
805	C₂×C₄	C₂×#3484	1	1	yes	characteristic
806	C₂×C₄	#62842	1	1	yes	characteristic
807	C₂²	#7631286	1	1	yes	characteristic
808	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
809	C₂²	C₂×#60399	1	1	yes	characteristic
810	C₂	#72216616	1	1	yes	characteristic
811	C₂	#72312096	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂³×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁶
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#124 ◁ C₂×#3500 ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341488	C₂	semidirect
2. #72341486	C₂	semidirect
3. #72341484	C₂	semidirect
4. #72341482	C₂	semidirect
5. #72341481	C₂	semidirect
6. #72341479	C₂	semidirect
7. #72341476	C₂	semidirect
8. #72341465	C₂	semidirect
9. #72341294	C₂	semidirect
10. #72318239	C₂	semidirect
11. #72318202	C₂	semidirect
12. #72317829	C₂	semidirect
13. #72312619	C₂	semidirect
14. #72312133	C₂	semidirect
15. #72311618	C₂	semidirect
16. #72311606	C₂	semidirect
17. #72311264	C₂	semidirect
18. #72249427	C₂	semidirect
19. #72236657	C₂	semidirect
20. #72234146	C₂	semidirect
21. #10586106	C₂²	semidirect
22. C₂×#60391	C₂²	semidirect
24. #9910716	C₂²	semidirect
25. #8932413	C₂²	semidirect
26. #8928621	C₂²	semidirect
27. #8756105	C₂²	semidirect
28. #7986316	C₂²	semidirect
29. #7985555	C₂²	semidirect
31. #7739366	C₂²	semidirect
32. #7737411	C₂²	semidirect
33. #7711153	C₂²	semidirect
35. C₂×#33559	C₂²	semidirect
36. C₂²×#2196	C₂²	semidirect
37. #6629393	C₂²	semidirect
38. #6628972	C₂²	semidirect
39. #6628903	C₂²	semidirect
40. #6628896	C₂²	semidirect
41. #6628874	C₂²	semidirect
42. #6628873	C₂²	semidirect
43. #6591508	C₂²	semidirect
44. #6573716	C₂²	semidirect
45. #6573695	C₂²	semidirect
46. #6573661	C₂²	semidirect
47. #6487653	C₂²	semidirect
48. #6470247	C₂²	semidirect
49. #6470234	C₂²	semidirect
50. #6443332	C₂²	semidirect
51. #6442555	C₂²	semidirect
52. #6437971	C₂²	semidirect
53. #6437970	C₂²	semidirect
54. #6437455	C₂²	semidirect
56. #6385981	C₂²	semidirect
57. #6379034	C₂²	semidirect
58. C₄×#3018	C₂²	semidirect
59. #512122	C₂²	semidirect
60. #512118	C₂²	semidirect
61. #511914	C₂²	semidirect
62. #511787	C₂²	semidirect
63. #511771	C₂²	semidirect
64. #508199	C₂²	semidirect
65. #508101	C₂²	semidirect
66. #508095	C₂²	semidirect
67. #503578	C₂²	semidirect
68. #503238	C₂²	semidirect
69. #503194	C₂²	semidirect
70. #502835	C₂²	semidirect
71. #502788	C₂²	semidirect
72. #502727	C₂²	semidirect
73. #502718	C₂²	semidirect
74. #501172	C₂²	semidirect
75. #501164	C₂²	semidirect
76. #501105	C₂²	semidirect
77. #501097	C₂²	semidirect
78. #501085	C₂²	semidirect
79. #501084	C₂²	semidirect
80. #500954	C₂²	semidirect
81. #500823	C₂²	semidirect
82. #500769	C₂²	semidirect
83. #500544	C₂²	semidirect
84. #500497	C₂²	semidirect
85. #500364	C₂²	semidirect
86. #500192	C₂²	semidirect
87. #500179	C₂²	semidirect
88. #500174	C₂²	semidirect
89. #500075	C₂²	semidirect
90. #500066	C₂²	semidirect
91. #500016	C₂²	semidirect
92. #500016	C₂²	semidirect
93. #500016	C₂²	semidirect
94. #499844	C₂²	semidirect
95. #499844	C₂²	semidirect
96. #499844	C₂²	semidirect
97. #499844	C₂²	semidirect
98. #499843	C₂²	semidirect
99. #499840	C₂²	semidirect
100. #499840	C₂²	semidirect
101. #499840	C₂²	semidirect
102. #499840	C₂²	semidirect
103. #499832	C₂²	semidirect
104. #499831	C₂²	semidirect
105. #499831	C₂²	semidirect
106. #499831	C₂²	semidirect
107. #499803	C₂²	semidirect
108. #499795	C₂²	semidirect
109. #499288	C₂²	semidirect
110. #498933	C₂²	semidirect
111. #498927	C₂²	semidirect
112. #497515	C₂²	semidirect
113. #497357	C₂²	semidirect
114. #497308	C₂²	semidirect
115. #497300	C₂²	semidirect
116. #496513	C₂²	semidirect
117. #496312	C₂²	semidirect
118. #496247	C₂²	semidirect
119. #496240	C₂²	semidirect
120. #496205	C₂²	semidirect
121. #496204	C₂²	semidirect
122. #495744	C₂²	semidirect
123. #495583	C₂²	semidirect
124. #494689	C₂²	semidirect
125. #494682	C₂²	semidirect
126. #494596	C₂²	semidirect
127. #494592	C₂²	semidirect
128. #493957	C₂²	semidirect
129. #493432	C₂²	semidirect
130. #493430	C₂²	semidirect
131. C₂×2₋¹⁺⁶	C₂³	semidirect
133. #62987	C₂³	semidirect
134. #62859	C₂³	semidirect
136. #62812	C₂³	semidirect
137. C₂×#3500	D₄	semidirect
141. C₂×#3549	C₂³	semidirect
143. C₂²×H(3,𝔽₄)	D₄	semidirect
144. C₄×#585	C₂³	semidirect
146. C₂²×B(4,𝔽₂)	C₂³	semidirect
147. C₂×#3022	C₂³	semidirect
148. C₂×#3022	C₂³	semidirect
149. C₂×#3022	C₂³	semidirect
150. C₂×#3022	C₂³	semidirect
160. C₂×#2889	C₂³	semidirect
162. #59817	C₂³	semidirect
163. #59816	C₂³	semidirect
166. #59041	C₂³	semidirect
170. #51749	C₂³	semidirect
171. #50274	C₂³	semidirect
172. #49545	C₂³	semidirect
174. #47929	C₂³	semidirect
176. #46073	C₂³	semidirect
177. #45741	C₂³	semidirect
179. #39357	D₄	semidirect
181. #38028	D₄	semidirect
183. #37645	D₄	semidirect
185. #37536	D₄	semidirect
186. #37419	C₂³	semidirect
187. #37187	D₄	semidirect
188. #37150	C₂³	semidirect
189. #36702	D₄	semidirect
191. C₂×#2858	D₄	semidirect
192. #36122	D₄	semidirect
194. #35676	D₄	semidirect
197. #35616	D₄	semidirect
200. #35327	D₄	semidirect
202. #35316	D₄	semidirect
203. #35272	D₄	semidirect
205. #34493	C₂³	semidirect
206. #34366	D₄	semidirect
208. #34155	C₂³	semidirect
209. C₄×#532	D₄	semidirect
213. C₂×#2199	C₂³	semidirect
216. C₂×#2196	C₂³	semidirect
217. C₂×#2196	C₂³	semidirect
218. C₂×#2196	C₂³	semidirect
219. C₂×#2196	C₂³	semidirect
220. C₂×#2129	C₂³	semidirect
222. C₂×#2126	C₂³	semidirect
224. C₂×#2122	C₂³	semidirect
225. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
226. #33021	C₂³	semidirect
227. #32975	C₂³	semidirect
229. #32924	C₂³	semidirect
230. #32899	C₂³	semidirect
231. #32899	C₂³	semidirect
232. #32899	C₂³	semidirect
233. #32899	C₂³	semidirect
235. #32891	C₂³	semidirect
236. #32890	C₂³	semidirect
237. #25899	C₂³	semidirect
239. #25743	C₂³	semidirect
240. #24414	C₂³	semidirect
241. #24413	C₂³	semidirect
242. #24406	C₂³	semidirect
244. #24262	C₂³	semidirect
245. #24224	C₂³	semidirect
247. #24058	C₂³	semidirect
248. #24057	C₂³	semidirect
249. #23914	C₂³	semidirect
254. #23900	C₂³	semidirect
255. #22408	C₂³	semidirect
256. #22405	C₂³	semidirect
257. #21482	C₂³	semidirect
258. C₄×#455	C₂³	semidirect
261. #20955	C₂³	semidirect
263. #20855	C₂³	semidirect
264. #20723	C₂³	semidirect
265. #20637	C₂³	semidirect
266. #20615	C₂³	semidirect
267. #20615	C₂³	semidirect
268. #20615	C₂³	semidirect
269. #20609	C₂³	semidirect
270. #20608	C₂³	semidirect
271. #20593	C₂³	semidirect
273. #20587	C₂³	semidirect
275. C₄×#413	C₂³	semidirect
276. #13461	C₂³	semidirect
277. #13424	C₂³	semidirect
278. #13424	C₂³	semidirect
279. #13422	C₂³	semidirect
280. #13419	C₂³	semidirect
281. #13375	C₂³	semidirect
282. #13375	C₂³	semidirect
283. #13375	C₂³	semidirect
284. #13348	C₂³	semidirect
285. #13348	C₂³	semidirect
286. #13348	C₂³	semidirect
287. #13348	C₂³	semidirect
288. #13348	C₂³	semidirect
289. #13348	C₂³	semidirect
292. #13346	C₂³	semidirect
295. #13343	C₂³	semidirect
296. #13296	C₂³	semidirect
297. #13293	C₂³	semidirect
298. #13225	C₂³	semidirect
299. #13221	C₂³	semidirect
300. #13218	C₂³	semidirect
301. #13090	C₂³	semidirect
302. #13089	C₂³	semidirect
303. #13087	C₂³	semidirect
305. #13083	C₂³	semidirect
306. #13083	C₂³	semidirect
307. #13083	C₂³	semidirect
308. #13083	C₂³	semidirect
309. #13083	C₂³	semidirect
311. #13049	C₂³	semidirect
312. #13049	C₂³	semidirect
313. #13049	C₂³	semidirect
314. #13048	C₂³	semidirect
315. #13048	C₂³	semidirect
316. #13048	C₂³	semidirect
319. #13047	C₂³	semidirect
320. #13043	C₂³	semidirect
321. #13043	C₂³	semidirect
322. #13043	C₂³	semidirect
323. #12966	C₂³	semidirect
324. #12965	C₂³	semidirect
325. #12964	C₂³	semidirect
326. #12960	C₂³	semidirect
327. #12857	C₂³	semidirect
328. #12854	C₂³	semidirect
329. #12853	C₂³	semidirect
330. #12798	C₂³	semidirect
331. #12797	C₂³	semidirect
332. #12795	C₂³	semidirect
333. #12763	C₂³	semidirect
334. #12759	C₂³	semidirect
335. #12759	C₂³	semidirect
336. #12698	C₂³	semidirect
337. #12698	C₂³	semidirect
341. #12695	C₂³	semidirect
343. #12691	C₂³	semidirect
344. #12687	C₂³	semidirect
345. C₄×#354	C₂³	semidirect
346. C₄×#353	C₂³	semidirect
347. #12622	C₂³	semidirect
348. #12574	C₂³	semidirect
349. #12573	C₂³	semidirect
354. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
364. C₂×#548	C₂×D₄	semidirect
366. C₂×#546	C₂×D₄	semidirect
373. C₂×#536	C₂×D₄	semidirect
374. C₂×#536	C₂×D₄	semidirect
381. C₂×#535	C₂×D₄	semidirect
382. C₂×#535	C₂×D₄	semidirect
391. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
392. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
398. C₂²×#124	C₂×D₄	semidirect
399. C₂²×#124	C₂×D₄	semidirect
400. C₂²×#124	C₂×D₄	semidirect
401. C₂²×#124	C₂×D₄	semidirect
402. C₂²×#124	C₂×D₄	semidirect
405. C₂²×#120	C₂×D₄	semidirect
410. C₂×C₄×#41	C₂×D₄	semidirect
411. C₂×C₄×#41	C₂×D₄	semidirect
436. #2858	C₂×D₄	semidirect
437. #2858	C₂×D₄	semidirect
438. #2857	C₂×D₄	semidirect
439. #2856	C₂×D₄	semidirect
440. #2853	C₂×D₄	semidirect
441. #2846	C₂×D₄	semidirect
447. #2622	C₂×D₄	semidirect
448. #2621	C₂×D₄	semidirect
449. #2619	C₂×D₄	semidirect
450. #2617	C₂×D₄	semidirect
451. #2617	C₂×D₄	semidirect
452. #2613	C₂×D₄	semidirect
453. #2545	C₂×D₄	semidirect
454. #2545	C₂×D₄	semidirect
455. #2544	C₂×D₄	semidirect
457. #2482	C₂×D₄	semidirect
458. #2436	C₂×D₄	semidirect
459. #2436	C₂×D₄	semidirect
460. #2436	C₂×D₄	semidirect
461. #2435	C₂×D₄	semidirect
463. #2433	C₂×D₄	semidirect
465. #2432	C₂×D₄	semidirect
466. #2431	C₂×D₄	semidirect
468. #2411	C₂×D₄	semidirect
469. #2411	C₂×D₄	semidirect
470. #2410	C₂×D₄	semidirect
471. #2410	C₂×D₄	semidirect
472. #2409	C₂×D₄	semidirect
474. #2408	C₂×D₄	semidirect
477. #2404	C₂×D₄	semidirect
478. #2404	C₂×D₄	semidirect
487. #2342	C₂×D₄	semidirect
488. #2342	C₂×D₄	semidirect
489. #2321	C₂×D₄	semidirect
491. #2310	C₂×D₄	semidirect
492. #2310	C₂×D₄	semidirect
493. #2310	C₂×D₄	semidirect
495. #2309	C₂×D₄	semidirect
499. C₄×C₄⋊Q₈	C₂×D₄	semidirect
501. C₄×#124	C₂×D₄	semidirect
504. #2297	C₂×D₄	semidirect
505. #2297	C₂×D₄	semidirect
506. #2297	C₂×D₄	semidirect
509. #2293	C₂×D₄	semidirect
510. #2285	C₂×D₄	semidirect
511. #2285	C₂×D₄	semidirect
512. #2283	C₂×D₄	semidirect
513. C₄²×D₄	C₂×D₄	semidirect
514. C₂×C₄³	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72341488	2
#72341486	2
#72341484	2
#72341482	2
#72341481	2
#72341479	2
#72341476	2
#72341465	2
#72341294	2
#72318239	2
#72318202	2
#72317829	2
#72312619	2
#72312133	2
#72311618	2
#72311606	2
#72311264	2
#72249427	2
#72236657	2
#72234146	2