Subgroups — #72312260

Order 2048.

At least 8359 conjugacy classes of subgroups; only the 4028 normal subgroups are shown.

The subgroup lattice has 879 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312253	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312243	C₂	1	4	yes	maximal, complemented
3	#72312235	C₂	1	4	yes	maximal, complemented
4	#72312213	C₂	1	4	yes	maximal, complemented
5	#72312191	C₂	1	2	yes	maximal, complemented
6	#72312183	C₂	1	2	yes	maximal, complemented
7	#72312155	C₂	1	1	yes	maximal, characteristic, complemented
8	#72312145	C₂	1	1	yes	maximal, characteristic, complemented
9	#72312101	C₂	1	4	yes	maximal, complemented
10	#72312087	C₂	1	8	yes	maximal, complemented
11	#72312036	C₂	1	8	yes	maximal, complemented
12	#72311647	C₂	1	1	yes	maximal, characteristic, complemented
13	#72311639	C₂	1	1	yes	maximal, characteristic, complemented
14	#72311243	C₂	1	4	yes	maximal, complemented
15	#72256267	C₂	1	4	yes	maximal, complemented
16	#72236711	C₂	1	2	yes	maximal, complemented
17	#72236702	C₂	1	2	yes	maximal, complemented
18	#72236649	C₂	1	1	yes	maximal, characteristic, complemented
19	#72236637	C₂	1	1	yes	maximal, characteristic, complemented
20	#72234425	C₂	1	4	yes	maximal, complemented
21	#72233169	C₂	1	4	yes	maximal, complemented
22	#10586097	C₂²	1	1	yes	characteristic, complemented
23	#8902653	C₂²	1	4	yes	complemented
24	#8701557	C₂²	1	2	yes	complemented
25	#8509007	C₂²	1	2	yes	complemented
26	#8195763	C₂²	1	2	yes	complemented
27	#8096139	C₂²	1	2	yes	complemented
28	#8062884	C₂²	1	4	yes	complemented
29	#7968183	C₂²	1	4	yes	complemented
30	#7829344	C₂²	1	4	yes	complemented
31	#7737411	C₂²	1	2	yes	—
32	#7703052	C₂²	1	1	yes	characteristic, complemented
33	#7695992	C₂²	1	2	yes	complemented
34	#7672703	C₂²	1	1	yes	characteristic
35	#7667013	C₂²	1	1	yes	characteristic, complemented
36	#6629390	C₂²	1	2	yes	complemented
37	#6629390	C₂²	1	2	yes	complemented
38	#6629110	C₂²	1	1	yes	characteristic, complemented
39	#6628896	C₂²	1	8	yes	complemented
40	#6628876	C₂²	1	2	yes	complemented
41	#6591514	C₂²	1	8	yes	complemented
42	#6591514	C₂²	1	8	yes	complemented
43	#6591494	C₂²	1	4	yes	complemented
44	#6591488	C₂²	1	4	yes	complemented
45	#6591466	C₂²	1	4	yes	complemented
46	#6591460	C₂²	1	4	yes	complemented
47	D₄×B(4,𝔽₂)	C₂²	1	8	yes	complemented
48	D₄×B(4,𝔽₂)	C₂²	1	8	yes	complemented
49	#6487648	C₂²	1	2	yes	complemented
50	#6487648	C₂²	1	2	yes	complemented
51	#6470234	C₂²	1	8	yes	complemented
52	#6446732	C₂²	1	1	yes	characteristic, complemented
53	#6442555	C₂²	1	1	yes	characteristic, complemented
54	#6440362	C₂²	1	2	yes	complemented
55	#6437975	C₂²	1	2	yes	complemented
56	#6385980	C₂²	1	2	yes	complemented
57	#6379033	C₂²	1	1	yes	characteristic, complemented
58	C₄×#3018	C₂²	1	1	yes	characteristic, complemented
59	#6370747	C₂²	1	2	yes	complemented
60	#512151	C₂²	1	16	yes	complemented
61	#511911	C₂²	1	4	yes	complemented
62	#511908	C₂²	1	4	yes	complemented
63	#508193	C₂²	1	4	yes	complemented
64	#508192	C₂²	1	4	yes	complemented
65	#508143	C₂²	1	8	yes	complemented
66	#508062	C₂²	1	8	yes	complemented
67	#503585	C₂²	1	2	yes	complemented
68	#503579	C₂²	1	2	yes	complemented
69	#503576	C₂²	1	8	yes	complemented
70	#503567	C₂²	1	8	yes	complemented
71	#503201	C₂²	1	2	yes	complemented
72	#503194	C₂²	1	2	yes	complemented
73	#502786	C₂²	1	4	yes	complemented
74	#502780	C₂²	1	4	yes	complemented
75	#502774	C₂²	1	8	yes	complemented
76	#502766	C₂²	1	8	yes	complemented
77	#502725	C₂²	1	16	yes	complemented
78	#502711	C₂²	1	16	yes	complemented
79	#502685	C₂²	1	16	yes	complemented
80	#502667	C₂²	1	8	yes	complemented
81	#502661	C₂²	1	8	yes	complemented
82	#501164	C₂²	1	16	yes	complemented
83	#501156	C₂²	1	16	yes	complemented
84	#500961	C₂²	1	2	yes	complemented
85	#500955	C₂²	1	2	yes	complemented
86	#500952	C₂²	1	8	yes	complemented
87	#500943	C₂²	1	8	yes	complemented
88	#500776	C₂²	1	2	yes	complemented
89	#500769	C₂²	1	2	yes	complemented
90	#500495	C₂²	1	4	yes	complemented
91	#500489	C₂²	1	4	yes	complemented
92	#500483	C₂²	1	8	yes	complemented
93	#500475	C₂²	1	8	yes	complemented
94	#500382	C₂²	1	8	yes	complemented
95	#500364	C₂²	1	2	yes	complemented
96	#500358	C₂²	1	2	yes	complemented
97	#500185	C₂²	1	2	yes	complemented
98	#500174	C₂²	1	2	yes	complemented
99	#500073	C₂²	1	16	yes	complemented
100	#500059	C₂²	1	16	yes	complemented
101	#500034	C₂²	1	8	yes	complemented
102	#500034	C₂²	1	8	yes	complemented
103	#500034	C₂²	1	8	yes	complemented
104	#500033	C₂²	1	16	yes	complemented
105	#500016	C₂²	1	2	yes	complemented
106	#500016	C₂²	1	4	yes	complemented
107	#500015	C₂²	1	8	yes	complemented
108	#500010	C₂²	1	2	yes	complemented
109	#500010	C₂²	1	4	yes	complemented
110	#500009	C₂²	1	8	yes	complemented
111	#499851	C₂²	1	2	yes	complemented
112	#499851	C₂²	1	4	yes	complemented
113	#499844	C₂²	1	2	yes	complemented
114	#499844	C₂²	1	4	yes	complemented
115	#499795	C₂²	1	16	yes	complemented
116	#499787	C₂²	1	16	yes	complemented
117	#499282	C₂²	1	4	yes	complemented
118	#499281	C₂²	1	4	yes	complemented
119	#498984	C₂²	1	8	yes	complemented
120	C₂×#13343	C₂²	1	8	yes	complemented
121	#497498	C₂²	1	4	yes	complemented
122	#497496	C₂²	1	4	yes	complemented
123	#497492	C₂²	1	4	yes	complemented
124	#497490	C₂²	1	4	yes	complemented
125	#497484	C₂²	1	8	yes	complemented
126	#497484	C₂²	1	8	yes	complemented
127	D₄×AΣL(1,𝔽₁₆)	C₂²	1	8	yes	complemented
128	D₄×AΣL(1,𝔽₁₆)	C₂²	1	8	yes	complemented
129	#496508	C₂²	1	2	yes	complemented
130	#496508	C₂²	1	2	yes	complemented
131	#496398	C₂²	1	2	yes	complemented
132	#496240	C₂²	1	8	yes	complemented
133	#496200	C₂²	1	4	yes	complemented
134	C₄×#2199	C₂²	1	4	yes	complemented
135	C₄×#2196	C₂²	1	4	yes	complemented
136	#495580	C₂²	1	2	yes	complemented
137	#495580	C₂²	1	2	yes	complemented
138	#494682	C₂²	1	8	yes	complemented
139	#494575	C₂²	1	16	yes	complemented
140	#493957	C₂²	1	1	yes	characteristic, complemented
141	#493957	C₂²	1	1	yes	characteristic, complemented
142	#493867	C₂²	1	4	yes	complemented
143	C₂×H(7,𝔽₂)	C₂³	1	2	yes	—
144	D₄×H(5,𝔽₂)	C₂³	1	4	yes	—
145	D₄×H(5,𝔽₂)	C₂³	1	4	yes	—
146	#62852	C₂³	1	2	yes	—
147	#62812	C₂³	1	1	yes	characteristic
148	C₂×#3511	D₄	1	1	yes	characteristic, complemented
149	C₂×#3498	C₂³	1	1	yes	characteristic
150	C₂²×D₄²	D₄	1	2	yes	complemented
151	C₄×#585	C₂³	1	1	yes	characteristic
152	C₂²×B(4,𝔽₂)	C₂³	1	16	yes	—
153	C₂×#3018	C₂³	1	1	yes	characteristic
154	C₂×#3018	C₂³	1	2	yes	—
155	C₂×#2888	C₂³	1	2	yes	—
156	#60045	C₂³	1	2	yes	—
157	#59945	C₂³	1	2	yes	complemented
158	#59864	C₂³	1	1	yes	characteristic, complemented
159	#59816	C₂³	1	1	yes	characteristic, complemented
160	#59814	C₂³	1	4	yes	complemented
161	#59199	C₂³	1	4	yes	complemented
162	#59041	C₂³	1	2	yes	—
163	#59000	C₂³	1	4	yes	complemented
164	#58990	C₂³	1	8	yes	complemented
165	#52301	C₂³	1	2	yes	complemented
166	#52103	C₂³	1	2	yes	complemented
167	C₂×#2679	C₂³	1	4	yes	complemented
168	#51940	C₂³	1	8	yes	complemented
169	#51815	C₂³	1	8	yes	—
170	#48143	C₂³	1	8	yes	complemented
171	#48113	C₂³	1	8	yes	complemented
172	#46338	C₂³	1	2	yes	complemented
173	#46287	C₂³	1	2	yes	—
174	#46225	C₂³	1	2	yes	—
175	#46152	C₂³	1	1	yes	characteristic, complemented
176	#46089	C₂³	1	4	yes	complemented
177	#45996	C₂³	1	1	yes	characteristic, complemented
178	#45645	C₂³	1	4	yes	complemented
179	#45493	C₂³	1	4	yes	complemented
180	#45439	C₂³	1	8	yes	complemented
181	#38957	C₂³	1	2	yes	—
182	#38956	D₄	1	2	yes	complemented
183	#38953	C₂³	1	2	yes	—
184	#38952	D₄	1	2	yes	complemented
185	#38904	D₄	1	4	yes	complemented
186	#38904	D₄	1	4	yes	complemented
187	#38904	C₂³	1	4	yes	—
188	#38904	C₂³	1	4	yes	—
189	#37134	C₂³	1	4	yes	complemented
190	#36702	D₄	1	8	yes	complemented
191	C₂×#2858	D₄	1	1	yes	characteristic, complemented
192	#36419	D₄	1	2	yes	complemented
193	#36412	D₄	1	2	yes	complemented
194	#36289	C₂³	1	2	yes	—
195	#36260	C₂³	1	2	yes	—
196	D₄×#120	D₄	1	4	yes	complemented
197	D₄×#120	D₄	1	4	yes	complemented
198	D₄×#120	C₂³	1	4	yes	—
199	D₄×#120	C₂³	1	4	yes	—
200	#35531	D₄	1	2	yes	complemented
201	#35513	C₂³	1	2	yes	—
202	#35346	C₂³	1	8	yes	—
203	#35279	C₂³	1	1	yes	characteristic
204	#35272	D₄	1	1	yes	characteristic, complemented
205	#35256	D₄	1	2	yes	complemented
206	#35237	D₄	1	2	yes	complemented
207	#35237	D₄	1	2	yes	complemented
208	#34963	C₂³	1	2	yes	—
209	#34963	C₂³	1	2	yes	—
210	#34364	D₄	1	2	yes	complemented
211	#34356	C₂³	1	8	yes	complemented
212	C₄×H(3,𝔽₄)	C₂³	1	2	yes	complemented
213	#34258	C₂³	1	2	yes	—
214	C₄×D₄²	C₂³	1	2	yes	complemented
215	C₄×#532	D₄	1	1	yes	characteristic, complemented
216	C₄×#532	C₂³	1	1	yes	characteristic
217	C₂×#2199	C₂³	1	4	yes	—
218	C₂×#2199	C₂³	1	8	yes	complemented
219	C₂×#2196	C₂³	1	4	yes	—
220	C₂×#2196	C₂³	1	8	yes	complemented
221	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	16	yes	complemented
222	#33021	C₂³	1	4	yes	—
223	#33021	C₂³	1	4	yes	—
224	#32976	C₂³	1	4	yes	—
225	#32976	C₂³	1	4	yes	—
226	#32971	C₂³	1	4	yes	—
227	#32969	C₂³	1	4	yes	—
228	#32926	C₂³	1	4	yes	—
229	#32926	C₂³	1	4	yes	—
230	#32899	C₂³	1	4	yes	—
231	#32899	C₂³	1	4	yes	—
232	#32899	C₂³	1	8	yes	—
233	#32899	C₂³	1	8	yes	—
234	#32898	C₂³	1	16	yes	—
235	#32898	C₂³	1	16	yes	—
236	#32891	C₂³	1	8	yes	—
237	#32888	C₂³	1	8	yes	—
238	#25900	C₂³	1	4	yes	—
239	#25900	C₂³	1	4	yes	—
240	#25870	C₂³	1	4	yes	—
241	#25869	C₂³	1	4	yes	—
242	#25771	C₂³	1	4	yes	—
243	#25771	C₂³	1	4	yes	—
244	#24413	C₂³	1	8	yes	—
245	#24412	C₂³	1	8	yes	—
246	#24404	C₂³	1	16	yes	—
247	#24404	C₂³	1	16	yes	—
248	#24260	C₂³	1	8	yes	—
249	#24260	C₂³	1	8	yes	—
250	#24224	C₂³	1	2	yes	—
251	#24224	C₂³	1	2	yes	—
252	#24222	C₂³	1	2	yes	—
253	#24222	C₂³	1	2	yes	—
254	#24058	C₂³	1	16	yes	—
255	#24022	C₂³	1	8	yes	—
256	#24018	C₂³	1	8	yes	—
257	#23900	C₂³	1	16	yes	—
258	D₄×#100	C₂³	1	4	yes	—
259	D₄×#100	C₂³	1	4	yes	—
260	D₄×#99	C₂³	1	8	yes	—
261	D₄×#99	C₂³	1	8	yes	—
262	C₄×B(4,𝔽₂)	C₂³	1	8	yes	—
263	C₄×B(4,𝔽₂)	C₂³	1	8	yes	—
264	C₄×#455	C₂³	1	2	yes	—
265	C₄×#455	C₂³	1	2	yes	—
266	C₄×#453	C₂³	1	2	yes	—
267	C₄×#453	C₂³	1	2	yes	—
268	#20952	C₂³	1	1	yes	characteristic
269	#20858	C₂³	1	2	yes	—
270	#20855	C₂³	1	1	yes	characteristic
271	#20723	C₂³	1	2	yes	—
272	#20723	C₂³	1	2	yes	—
273	#20637	C₂³	1	1	yes	characteristic
274	#20618	C₂³	1	2	yes	—
275	#20618	C₂³	1	2	yes	—
276	#20618	C₂³	1	2	yes	—
277	#20616	C₂³	1	8	yes	—
278	#20615	C₂³	1	2	yes	—
279	#20615	C₂³	1	1	yes	characteristic
280	C₂×#1792	C₂³	1	8	yes	—
281	#20609	C₂³	1	16	yes	—
282	#20592	C₂³	1	2	yes	—
283	#20585	C₂³	1	8	yes	—
284	C₄×#413	C₂³	1	1	yes	characteristic
285	#13463	C₂³	1	4	yes	complemented
286	#13462	C₂³	1	16	yes	complemented
287	#13461	C₂³	1	4	yes	complemented
288	#13424	C₂³	1	8	yes	complemented
289	#13422	C₂³	1	8	yes	complemented
290	#13419	C₂³	1	16	yes	complemented
291	#13419	C₂³	1	4	yes	complemented
292	#13419	C₂³	1	4	yes	complemented
293	#13377	C₂³	1	4	yes	—
294	#13377	C₂³	1	8	yes	complemented
295	#13376	C₂³	1	16	yes	—
296	#13376	C₂³	1	16	yes	complemented
297	#13376	C₂³	1	16	yes	complemented
298	#13375	C₂³	1	4	yes	—
299	#13375	C₂³	1	8	yes	complemented
300	#13348	C₂³	1	8	yes	—
301	#13348	C₂³	1	16	yes	complemented
302	#13346	C₂³	1	8	yes	—
303	#13346	C₂³	1	16	yes	complemented
304	#13343	C₂³	1	16	yes	—
305	#13343	C₂³	1	4	yes	—
306	#13343	C₂³	1	4	yes	—
307	#13343	C₂³	1	8	yes	complemented
308	#13343	C₂³	1	8	yes	complemented
309	#13343	C₂³	1	16	yes	complemented
310	#13343	C₂³	1	16	yes	complemented
311	#13299	C₂³	1	8	yes	complemented
312	#13298	C₂³	1	8	yes	complemented
313	#13295	C₂³	1	4	yes	complemented
314	#13295	C₂³	1	4	yes	complemented
315	#13292	C₂³	1	4	yes	complemented
316	#13292	C₂³	1	4	yes	complemented
317	#13221	C₂³	1	4	yes	complemented
318	#13221	C₂³	1	4	yes	complemented
319	#13218	C₂³	1	4	yes	complemented
320	#13218	C₂³	1	4	yes	complemented
321	#13090	C₂³	1	16	yes	complemented
322	#13088	C₂³	1	16	yes	complemented
323	#13086	C₂³	1	16	yes	complemented
324	#13086	C₂³	1	16	yes	complemented
325	#13083	C₂³	1	4	yes	—
326	#13083	C₂³	1	8	yes	—
327	#13083	C₂³	1	4	yes	—
328	#13083	C₂³	1	8	yes	—
329	#13083	C₂³	1	4	yes	—
330	#13083	C₂³	1	4	yes	—
331	#13082	C₂³	1	16	yes	complemented
332	#13082	C₂³	1	16	yes	complemented
333	#13050	C₂³	1	4	yes	—
334	#13050	C₂³	1	8	yes	complemented
335	#13047	C₂³	1	4	yes	—
336	#13047	C₂³	1	8	yes	complemented
337	#13043	C₂³	1	16	yes	—
338	#13043	C₂³	1	8	yes	—
339	#13043	C₂³	1	16	yes	complemented
340	#13043	C₂³	1	16	yes	complemented
341	#13043	C₂³	1	16	yes	complemented
342	#13041	C₂³	1	8	yes	—
343	#13041	C₂³	1	16	yes	—
344	#13041	C₂³	1	16	yes	complemented
345	#13041	C₂³	1	16	yes	complemented
346	#13041	C₂³	1	16	yes	complemented
347	#12967	C₂³	1	4	yes	complemented
348	#12964	C₂³	1	4	yes	complemented
349	#12960	C₂³	1	16	yes	complemented
350	#12960	C₂³	1	8	yes	complemented
351	#12958	C₂³	1	8	yes	complemented
352	#12958	C₂³	1	16	yes	complemented
353	#12859	C₂³	1	8	yes	—
354	#12858	C₂³	1	8	yes	complemented
355	#12857	C₂³	1	2	yes	—
356	#12857	C₂³	1	2	yes	—
357	#12856	C₂³	1	8	yes	complemented
358	#12854	C₂³	1	16	yes	complemented
359	#12798	C₂³	1	2	yes	complemented
360	#12798	C₂³	1	2	yes	complemented
361	#12797	C₂³	1	2	yes	complemented
362	#12797	C₂³	1	2	yes	complemented
363	#12793	C₂³	1	8	yes	complemented
364	#12793	C₂³	1	8	yes	complemented
365	#12763	C₂³	1	4	yes	complemented
366	#12759	C₂³	1	4	yes	complemented
367	#12695	C₂³	1	2	yes	—
368	#12695	C₂³	1	2	yes	—
369	#12687	C₂³	1	16	yes	complemented
370	C₄×#354	C₂³	1	2	yes	complemented
371	C₄×#354	C₂³	1	2	yes	complemented
372	C₄×#353	C₂³	1	2	yes	complemented
373	C₄×#353	C₂³	1	2	yes	complemented
374	C₄×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
375	C₄×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
376	#12582	C₂³	1	8	yes	complemented
377	C₂×#1393	C₂³	1	8	yes	complemented
378	#12574	C₂³	1	16	yes	complemented
379	C₂×#585	C₂⁴	1	1	yes	characteristic
380	C₂×#585	C₂⁴	1	2	yes	—
381	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
382	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
383	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
384	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
385	C₂×H(3,𝔽₄)	C₂⁴	1	2	yes	—
386	#3496	C₂⁴	1	2	yes	—
387	#3496	C₂⁴	1	2	yes	—
388	#3484	C₂⁴	1	8	yes	—
389	C₂×#556	C₂×D₄	1	2	yes	complemented
390	C₂×#555	C₂×D₄	1	2	yes	complemented
391	C₂×#554	C₂×D₄	1	2	yes	complemented
392	C₂×#550	C₂×D₄	1	2	yes	—
393	C₂×#550	C₂×D₄	1	2	yes	—
394	C₂×#547	C₂×D₄	1	2	yes	complemented
395	C₂×D₄²	C₂×D₄	1	4	yes	—
396	C₂×D₄²	C₂×D₄	1	4	yes	—
397	C₂×D₄²	C₂⁴	1	2	yes	—
398	C₂×D₄²	C₂⁴	1	2	yes	—
399	C₂×D₄²	C₂⁴	1	2	yes	—
400	C₂×#537	C₂×D₄	1	2	yes	complemented
401	C₂×#535	C₂×D₄	1	2	yes	—
402	C₂×#535	C₂×D₄	1	4	yes	—
403	C₂×#535	C₂×D₄	1	2	yes	complemented
404	C₂×#532	C₂×D₄	1	2	yes	—
405	C₂×#532	C₂×D₄	1	1	yes	characteristic
406	C₂×#532	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
408	C₂²×#127	C₂×D₄	1	2	yes	—
409	C₂²×#127	C₂×D₄	1	1	yes	characteristic
410	C₂²×#121	C₂×D₄	1	4	yes	complemented
411	C₂²×#121	C₂×D₄	1	4	yes	complemented
412	C₂²×#120	C₂×D₄	1	8	yes	complemented
413	C₂²×#120	C₂×D₄	1	8	yes	complemented
414	C₂²×#120	C₂⁴	1	8	yes	—
415	C₄×H(5,𝔽₂)	C₂⁴	1	2	yes	—
416	C₄×H(5,𝔽₂)	C₂⁴	1	2	yes	—
417	#3428	C₂⁴	1	1	yes	characteristic
418	C₂×#520	C₂×D₄	1	2	yes	complemented
419	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
420	C₂×C₄×#41	C₂×D₄	1	2	yes	complemented
421	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×D₄	C₂×D₄	1	2	yes	complemented
423	C₂²×C₄×D₄	C₂×D₄	1	2	yes	complemented
424	C₂×B(4,𝔽₂)	C₂⁴	1	8	yes	—
425	C₂×B(4,𝔽₂)	C₂⁴	1	8	yes	—
426	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
427	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
428	C₂×#455	C₂⁴	1	2	yes	—
429	C₂×#455	C₂⁴	1	4	yes	—
430	C₂×#453	C₂⁴	1	2	yes	—
431	C₂×#453	C₂⁴	1	4	yes	—
432	C₂×#413	C₂⁴	1	1	yes	characteristic
433	C₂×#413	C₂⁴	1	2	yes	—
434	C₂×#413	C₂⁴	1	1	yes	characteristic
435	C₂²×#100	C₂⁴	1	8	yes	—
436	C₂²×#99	C₂⁴	1	16	yes	—
437	#2858	C₂×D₄	1	2	yes	complemented
438	#2858	C₂×D₄	1	2	yes	complemented
439	#2858	C₂×D₄	1	2	yes	complemented
440	#2858	C₂×D₄	1	2	yes	complemented
441	#2856	C₂×D₄	1	4	yes	complemented
442	#2850	C₂×D₄	1	4	yes	complemented
443	#2847	C₂×D₄	1	4	yes	complemented
444	#2847	C₂×D₄	1	4	yes	complemented
445	#2847	C₂×D₄	1	4	yes	complemented
446	#2847	C₂×D₄	1	4	yes	complemented
447	#2846	C₂×D₄	1	8	yes	complemented
448	#2846	C₂×D₄	1	8	yes	complemented
449	#2804	C₂⁴	1	2	yes	—
450	#2748	C₂⁴	1	8	yes	—
451	#2684	C₂⁴	1	4	yes	—
452	#2683	C₂⁴	1	2	yes	—
453	#2679	C₂⁴	1	2	yes	—
454	#2679	C₂⁴	1	8	yes	—
455	#2679	C₂⁴	1	2	yes	—
456	#2669	C₂⁴	1	4	yes	—
457	#2622	C₂×D₄	1	8	yes	complemented
458	#2622	C₂×D₄	1	8	yes	complemented
459	#2620	C₂×D₄	1	4	yes	complemented
460	#2619	C₂×D₄	1	4	yes	complemented
461	#2568	C₂×D₄	1	2	yes	complemented
462	#2567	C₂×D₄	1	2	yes	complemented
463	#2563	C₂⁴	1	2	yes	—
464	#2548	C₂×D₄	1	2	yes	complemented
465	#2548	C₂×D₄	1	2	yes	complemented
466	#2542	C₂⁴	1	2	yes	—
467	#2541	C₂×D₄	1	2	yes	complemented
468	#2541	C₂×D₄	1	2	yes	complemented
469	#2504	C₂×D₄	1	4	yes	complemented
470	#2504	C₂×D₄	1	4	yes	complemented
471	#2504	C₂×D₄	1	4	yes	complemented
472	#2501	C₂×D₄	1	4	yes	complemented
473	#2500	C₂×D₄	1	4	yes	complemented
474	#2500	C₂×D₄	1	4	yes	complemented
475	#2487	C₂×D₄	1	2	yes	complemented
476	#2487	C₂×D₄	1	2	yes	complemented
477	#2487	C₂⁴	1	2	yes	—
478	#2487	C₂⁴	1	2	yes	—
479	#2482	C₂×D₄	1	4	yes	complemented
480	#2482	C₂×D₄	1	4	yes	complemented
481	#2435	C₂⁴	1	4	yes	—
482	#2433	C₂×D₄	1	4	yes	complemented
483	#2433	C₂×D₄	1	4	yes	complemented
484	#2433	C₂⁴	1	4	yes	—
485	#2432	C₂×D₄	1	4	yes	complemented
486	#2431	C₂×D₄	1	4	yes	complemented
487	#2410	C₂×D₄	1	8	yes	complemented
488	#2410	C₂×D₄	1	8	yes	complemented
489	#2410	C₂×D₄	1	8	yes	complemented
490	#2410	C₂×D₄	1	8	yes	complemented
491	#2408	C₂×D₄	1	2	yes	complemented
492	#2408	C₂×D₄	1	2	yes	complemented
493	#2408	C₂⁴	1	2	yes	—
494	#2408	C₂⁴	1	2	yes	—
495	#2404	C₂×D₄	1	8	yes	complemented
496	#2404	C₂×D₄	1	8	yes	complemented
497	#2404	C₂⁴	1	4	yes	—
498	#2404	C₂⁴	1	4	yes	—
499	#2403	C₂×D₄	1	8	yes	complemented
500	#2403	C₂×D₄	1	8	yes	complemented
501	#2403	C₂⁴	1	8	yes	—
502	#2403	C₂⁴	1	8	yes	—
503	#2379	C₂⁴	1	2	yes	—
504	#2375	C₂⁴	1	4	yes	—
505	#2375	C₂⁴	1	8	yes	—
506	#2366	C₂⁴	1	2	yes	—
507	#2358	C₂⁴	1	4	yes	—
508	#2358	C₂⁴	1	8	yes	—
509	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
510	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
511	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
512	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
513	#2317	C₂×D₄	1	2	yes	complemented
514	#2311	C₂×D₄	1	4	yes	complemented
515	#2311	C₂⁴	1	2	yes	—
516	#2309	C₂×D₄	1	2	yes	complemented
517	#2309	C₂⁴	1	4	yes	—
518	#2308	C₂×D₄	1	8	yes	complemented
519	#2308	C₂×D₄	1	8	yes	complemented
520	#2308	C₂⁴	1	8	yes	—
521	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
522	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
523	C₄×#127	C₂⁴	1	1	yes	characteristic
524	C₄×#127	C₂⁴	1	1	yes	characteristic
525	C₄×#124	C₂×D₄	1	1	yes	characteristic, complemented
526	C₄×#124	C₂×D₄	1	1	yes	characteristic, complemented
527	C₄×#124	C₂⁴	1	1	yes	characteristic
528	C₄×#124	C₂⁴	1	1	yes	characteristic
529	C₄×#120	C₂×D₄	1	4	yes	complemented
530	C₄×#120	C₂×D₄	1	4	yes	complemented
531	C₄×#120	C₂⁴	1	4	yes	—
532	C₄×#120	C₂⁴	1	4	yes	—
533	#2297	C₂×D₄	1	4	yes	complemented
534	#2297	C₂×D₄	1	1	yes	characteristic, complemented
535	#2297	C₂×D₄	1	2	yes	complemented
536	#2297	C₂⁴	1	1	yes	characteristic
537	#2293	C₂×D₄	1	2	yes	complemented
538	#2293	C₂×D₄	1	2	yes	complemented
539	C₂×#390	C₂×D₄	1	2	yes	complemented
540	C₂×#390	C₂×D₄	1	2	yes	complemented
541	C₂×#390	C₂⁴	1	4	yes	—
542	#2285	C₂×D₄	1	1	yes	characteristic, complemented
543	#2285	C₂×D₄	1	1	yes	characteristic, complemented
544	#2283	C₂×D₄	1	2	yes	complemented
545	#2283	C₂×D₄	1	2	yes	complemented
546	C₄²×D₄	C₂×D₄	1	2	yes	complemented
547	C₄²×D₄	C₂×D₄	1	2	yes	complemented
548	C₂×C₄³	C₂×D₄	1	1	yes	characteristic, complemented
549	C₂×#354	C₂⁴	1	4	yes	—
550	C₂×#354	C₂⁴	1	4	yes	—
551	C₂×#353	C₂⁴	1	4	yes	—
552	C₂×#353	C₂⁴	1	4	yes	—
553	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
554	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	—
555	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
556	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	—
557	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
558	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
559	#1889	C₂⁴	1	8	yes	—
560	#1889	C₂⁴	1	8	yes	—
561	#1887	C₂⁴	1	2	yes	—
562	#1885	C₂⁴	1	2	yes	—
563	#1867	C₂⁴	1	8	yes	—
564	#1867	C₂⁴	1	8	yes	—
565	#1856	C₂⁴	1	8	yes	—
566	#1856	C₂⁴	1	2	yes	—
567	#1856	C₂⁴	1	2	yes	—
568	#1800	C₂⁴	1	2	yes	—
569	#1800	C₂⁴	1	2	yes	—
570	#1799	C₂⁴	1	4	yes	—
571	#1799	C₂⁴	1	4	yes	—
572	#1792	C₂⁴	1	8	yes	—
573	#1792	C₂⁴	1	8	yes	—
574	#1792	C₂⁴	1	2	yes	—
575	#1792	C₂⁴	1	8	yes	—
576	#1792	C₂⁴	1	4	yes	—
577	#1792	C₂⁴	1	2	yes	—
578	#1792	C₂⁴	1	4	yes	—
579	#1790	C₂⁴	1	8	yes	—
580	#1790	C₂⁴	1	16	yes	—
581	#1790	C₂⁴	1	8	yes	—
582	#1790	C₂⁴	1	16	yes	—
583	#1783	C₂⁴	1	8	yes	—
584	#1782	C₂⁴	1	4	yes	—
585	#1782	C₂⁴	1	4	yes	—
586	#1781	C₂⁴	1	16	yes	—
587	C₄×#100	C₂⁴	1	2	yes	—
588	C₄×#100	C₂⁴	1	2	yes	—
589	C₄×#99	C₂⁴	1	4	yes	—
590	C₄×#99	C₂⁴	1	4	yes	—
591	#1393	C₂⁴	1	4	yes	—
592	#1393	C₂⁴	1	4	yes	—
593	#1393	C₂⁴	1	16	yes	—
594	#1393	C₂⁴	1	16	yes	—
595	#1393	C₂⁴	1	4	yes	—
596	#1393	C₂⁴	1	4	yes	—
597	#1390	C₂⁴	1	8	yes	—
598	#1390	C₂⁴	1	8	yes	—
599	#1390	C₂⁴	1	16	yes	—
600	#1390	C₂⁴	1	16	yes	—
601	#1390	C₂⁴	1	8	yes	—
602	#1390	C₂⁴	1	8	yes	—
603	C₂⁶	C₂²×D₄	1	8	yes	—
604	C₂×H(5,𝔽₂)	C₂⁵	1	4	yes	—
605	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
606	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
607	C₂²×#41	C₂²×D₄	1	4	yes	—
608	C₂²×#41	C₂²×D₄	1	4	yes	—
609	C₂²×#41	C₂²×D₄	1	2	yes	—
610	C₂²×#41	C₂⁵	1	1	yes	characteristic
611	C₂³×D₄	#120	1	2	yes	—
612	C₂³×D₄	#120	1	2	yes	—
613	C₂³×D₄	C₂²×D₄	1	8	yes	—
614	C₂³×D₄	C₂²×D₄	1	4	yes	—
615	C₂³×D₄	C₂²×D₄	1	4	yes	—
616	C₂³×D₄	C₂²×D₄	1	4	yes	—
617	C₂³×D₄	C₂²×D₄	1	2	yes	—
618	C₂³×D₄	C₂²×D₄	1	2	yes	—
619	C₂³×D₄	C₂²×D₄	1	8	yes	—
620	C₂³×D₄	C₂²×D₄	1	8	yes	—
621	C₂³×D₄	C₂²×D₄	1	2	yes	—
622	C₂³×D₄	C₂⁵	1	4	yes	—
623	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
624	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
625	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
626	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
627	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
628	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
629	C₂×#127	#120	1	4	yes	—
630	C₂×#127	#120	1	4	yes	—
631	C₂×#127	#120	1	2	yes	—
632	C₂×#127	#120	1	4	yes	—
633	C₂×#127	#120	1	2	yes	—
634	C₂×#127	#120	1	1	yes	characteristic
635	C₂×#127	C₂²×D₄	1	2	yes	—
636	C₂×#127	C₂²×D₄	1	2	yes	—
637	C₂×#127	C₂²×D₄	1	4	yes	—
638	C₂×#127	C₂⁵	1	1	yes	characteristic
639	C₂×#124	#120	1	2	yes	—
640	C₂×#124	#120	1	4	yes	—
641	C₂×#124	C₂²×D₄	1	1	yes	characteristic
642	C₂×#124	C₂²×D₄	1	4	yes	—
643	C₂×#124	C₂⁵	1	1	yes	characteristic
644	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
645	C₂×#121	#120	1	2	yes	—
646	C₂×#121	#120	1	2	yes	—
647	C₂×#121	#120	1	8	yes	—
648	C₂×#121	#120	1	8	yes	—
649	C₂×#121	C₂²×D₄	1	4	yes	—
650	C₂×#121	C₂²×D₄	1	4	yes	—
651	C₂×#121	C₂²×D₄	1	4	yes	—
652	C₂×#121	C₂²×D₄	1	4	yes	—
653	C₂×#121	C₂²×D₄	1	4	yes	—
654	C₂×#120	#120	1	8	yes	—
655	C₂×#120	C₂²×D₄	1	8	yes	—
656	C₂×#120	C₂²×D₄	1	8	yes	—
657	C₂×#120	C₂²×D₄	1	4	yes	—
658	C₂×#120	C₂²×D₄	1	4	yes	—
659	C₂×#120	C₂²×D₄	1	8	yes	—
660	C₂×#120	C₂²×D₄	1	8	yes	—
661	C₂×#120	C₂²×D₄	1	8	yes	—
662	C₂×#120	C₂²×D₄	1	8	yes	—
663	C₂×#120	C₂⁵	1	4	yes	—
664	C₂×#120	C₂⁵	1	4	yes	—
665	#518	C₂⁵	1	2	yes	—
666	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
667	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
668	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
669	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
670	C₂×C₄×D₄	#120	1	4	yes	—
671	C₂×C₄×D₄	#120	1	4	yes	—
672	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
673	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
674	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
675	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
676	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
677	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
678	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
679	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
680	C₂×#117	C₂²×D₄	1	1	yes	characteristic
681	C₂×#117	C₂²×D₄	1	4	yes	—
682	C₂×#117	C₂²×D₄	1	1	yes	characteristic
683	C₂×#117	C₂²×D₄	1	2	yes	—
684	C₂×#117	C₂²×D₄	1	2	yes	—
685	C₂×#117	C₂²×D₄	1	4	yes	—
686	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
687	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
688	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
689	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
690	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
691	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
692	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
693	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
694	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
695	C₂²×C₄²	C₂²×D₄	1	2	yes	—
696	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
697	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
698	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
699	C₂²×C₄²	C₂²×D₄	1	4	yes	—
700	C₂×#100	C₂⁵	1	2	yes	—
701	C₂×#100	C₂⁵	1	4	yes	—
702	C₂×#100	C₂⁵	1	2	yes	—
703	C₂×#99	C₂⁵	1	8	yes	—
704	C₂×#99	C₂⁵	1	8	yes	—
705	#391	C₂²×D₄	1	1	yes	characteristic
706	#391	C₂²×D₄	1	1	yes	characteristic
707	#391	C₂²×D₄	1	4	yes	—
708	#391	C₂²×D₄	1	1	yes	characteristic
709	#391	C₂²×D₄	1	1	yes	characteristic
710	#390	C₂²×D₄	1	4	yes	—
711	#390	C₂²×D₄	1	4	yes	—
712	#390	C₂²×D₄	1	4	yes	—
713	#390	C₂²×D₄	1	4	yes	—
714	#390	C₂²×D₄	1	4	yes	—
715	#390	C₂²×D₄	1	4	yes	—
716	#390	C₂²×D₄	1	1	yes	characteristic
717	#390	C₂²×D₄	1	1	yes	characteristic
718	#390	C₂⁵	1	1	yes	characteristic
719	#390	C₂⁵	1	1	yes	characteristic
720	#390	C₂⁵	1	4	yes	—
721	#386	C₂²×D₄	1	4	yes	—
722	#386	C₂²×D₄	1	4	yes	—
723	#386	C₂²×D₄	1	8	yes	—
724	#386	C₂²×D₄	1	8	yes	—
725	#386	C₂²×D₄	1	8	yes	—
726	#386	C₂²×D₄	1	8	yes	—
727	#386	C₂⁵	1	4	yes	—
728	#386	C₂⁵	1	4	yes	—
729	#385	C₂²×D₄	1	4	yes	—
730	#385	C₂²×D₄	1	4	yes	—
731	#385	C₂²×D₄	1	4	yes	—
732	#385	C₂²×D₄	1	4	yes	—
733	#384	C₂²×D₄	1	1	yes	characteristic
734	#384	C₂²×D₄	1	1	yes	characteristic
735	#384	C₂²×D₄	1	4	yes	—
736	#382	C₂²×D₄	1	4	yes	—
737	#382	C₂²×D₄	1	1	yes	characteristic
738	#382	C₂²×D₄	1	1	yes	characteristic
739	#381	C₂²×D₄	1	4	yes	—
740	#381	C₂²×D₄	1	4	yes	—
741	#380	C₂²×D₄	1	2	yes	—
742	#380	C₂²×D₄	1	2	yes	—
743	#380	C₂²×D₄	1	2	yes	—
744	#380	C₂²×D₄	1	2	yes	—
745	#379	C₂²×D₄	1	8	yes	—
746	#379	C₂²×D₄	1	8	yes	—
747	#379	C₂²×D₄	1	4	yes	—
748	#379	C₂²×D₄	1	4	yes	—
749	#379	C₂²×D₄	1	4	yes	—
750	#379	C₂²×D₄	1	4	yes	—
751	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
752	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
753	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
754	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
755	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
756	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
757	C₄³	C₂²×D₄	1	1	yes	characteristic
758	C₄³	C₂²×D₄	1	1	yes	characteristic
759	C₄³	C₂²×D₄	1	1	yes	characteristic
760	C₄³	C₂²×D₄	1	1	yes	characteristic
761	C₂⁵	C₂×#120	1	4	yes	—
762	C₂⁵	C₂³×D₄	1	8	yes	—
763	C₂⁵	C₂³×D₄	1	4	yes	—
764	C₂⁵	C₂³×D₄	1	4	yes	—
765	H(5,𝔽₂)	#585	1	4	yes	—
766	C₂²×Q₈	C₂×#120	1	2	yes	—
767	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
768	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
769	C₂²×D₄	C₂×#120	1	4	yes	—
770	C₂²×D₄	C₂×#120	1	4	yes	—
771	C₂²×D₄	C₂×#120	1	4	yes	—
772	C₂²×D₄	C₂×#120	1	8	yes	—
773	C₂²×D₄	C₂×#120	1	4	yes	—
774	C₂²×D₄	C₂×#120	1	8	yes	—
775	C₂²×D₄	C₂×#120	1	8	yes	—
776	C₂²×D₄	C₂×#120	1	2	yes	—
777	C₂²×D₄	C₂×#120	1	2	yes	—
778	C₂²×D₄	C₂×#120	1	2	yes	—
779	C₂²×D₄	C₂×#120	1	4	yes	—
780	C₂²×D₄	C₂×#120	1	4	yes	—
781	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
782	C₂²×D₄	C₂³×D₄	1	4	yes	—
783	C₂²×D₄	C₂³×D₄	1	2	yes	—
784	C₂²×D₄	C₂³×D₄	1	8	yes	—
785	C₂²×D₄	C₂⁶	1	1	yes	characteristic
786	C₂³×C₄	C₂×#120	1	1	yes	characteristic
787	C₂³×C₄	C₂×#120	1	1	yes	characteristic
788	C₂³×C₄	C₂×#120	1	8	yes	—
789	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
790	C₂³×C₄	C₂³×D₄	1	4	yes	—
791	C₂³×C₄	C₂³×D₄	1	2	yes	—
792	C₂³×C₄	C₂³×D₄	1	2	yes	—
793	C₂³×C₄	C₂³×D₄	1	2	yes	—
794	C₂³×C₄	C₂³×D₄	1	4	yes	—
795	C₂³×C₄	C₂³×D₄	1	4	yes	—
796	#127	B(4,𝔽₂)	1	2	yes	—
797	#127	B(4,𝔽₂)	1	2	yes	—
798	#127	B(4,𝔽₂)	1	2	yes	—
799	#127	B(4,𝔽₂)	1	2	yes	—
800	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
801	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
802	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
803	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
806	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
807	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
808	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
810	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
811	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
813	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
814	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
815	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
816	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
817	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
818	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
820	C₂×C₄²	C₂×#120	1	1	yes	characteristic
821	C₂×C₄²	C₂×#120	1	2	yes	—
822	C₂×C₄²	C₂×#120	1	2	yes	—
823	C₂×C₄²	C₂×#120	1	2	yes	—
824	C₂×C₄²	C₂×#120	1	1	yes	characteristic
825	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
826	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
827	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
828	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
829	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
830	C₂×C₄²	C₂³×D₄	1	4	yes	—
831	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
832	C₂⁴	C₂²×#120	1	8	yes	—
833	C₂⁴	C₂²×#120	1	4	yes	—
834	C₂⁴	C₂²×#120	1	1	yes	characteristic
835	C₂⁴	C₂⁴×D₄	1	2	yes	—
836	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
837	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
838	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
839	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
840	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
841	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
842	C₂×D₄	C₂×#585	1	2	yes	—
843	C₂×D₄	H(7,𝔽₂)	1	2	yes	—
844	C₂²×C₄	C₂²×#120	1	2	yes	—
845	C₂²×C₄	C₂²×#120	1	4	yes	—
846	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
847	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
848	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
849	C₂²×C₄	C₂²×#120	1	2	yes	—
850	C₂²×C₄	C₂²×#120	1	2	yes	—
851	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
852	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
854	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
855	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
856	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
857	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
858	C₂³	C₂²×B(4,𝔽₂)	1	8	yes	—
859	C₂³	#60399	1	2	yes	—
860	C₂³	C₂³×#120	1	1	yes	characteristic
861	C₂³	#62987	1	4	yes	—
862	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
863	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
864	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
865	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
866	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
867	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
868	C₂×C₄	#62811	1	1	yes	characteristic
869	C₂×C₄	#62852	1	1	yes	characteristic
870	C₂²	#7631838	1	1	yes	characteristic
871	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
872	C₂²	C₂×#60399	1	1	yes	characteristic
873	C₄	#7622880	1	2	yes	—
874	C₄	#7622886	1	2	yes	—
875	C₂	C₂×#7622880	1	1	yes	characteristic
876	C₂	C₂×#7622886	1	1	yes	characteristic
877	C₂	#72311903	1	1	yes	characteristic

	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×#127 ◁ C₂×#3498 ◁ 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. #72312253	C₂	semidirect
2. #72312243	C₂	semidirect
3. #72312235	C₂	semidirect
4. #72312213	C₂	semidirect
5. #72312191	C₂	semidirect
6. #72312183	C₂	semidirect
7. #72312155	C₂	semidirect
8. #72312145	C₂	semidirect
9. #72312101	C₂	semidirect
10. #72312087	C₂	semidirect
11. #72312036	C₂	semidirect
12. #72311647	C₂	semidirect
13. #72311639	C₂	semidirect
14. #72311243	C₂	semidirect
15. #72256267	C₂	semidirect
16. #72236711	C₂	semidirect
17. #72236702	C₂	semidirect
18. #72236649	C₂	semidirect
19. #72236637	C₂	semidirect
20. #72234425	C₂	semidirect
21. #72233169	C₂	semidirect
22. #10586097	C₂²	semidirect
23. #8902653	C₂²	semidirect
24. #8701557	C₂²	semidirect
25. #8509007	C₂²	semidirect
26. #8195763	C₂²	semidirect
27. #8096139	C₂²	semidirect
28. #8062884	C₂²	semidirect
29. #7968183	C₂²	semidirect
30. #7829344	C₂²	semidirect
32. #7703052	C₂²	semidirect
33. #7695992	C₂²	semidirect
35. #7667013	C₂²	semidirect
36. #6629390	C₂²	semidirect
37. #6629390	C₂²	semidirect
38. #6629110	C₂²	semidirect
39. #6628896	C₂²	semidirect
40. #6628876	C₂²	semidirect
41. #6591514	C₂²	semidirect
42. #6591514	C₂²	semidirect
43. #6591494	C₂²	semidirect
44. #6591488	C₂²	semidirect
45. #6591466	C₂²	semidirect
46. #6591460	C₂²	semidirect
47. D₄×B(4,𝔽₂)	C₂²	semidirect
48. D₄×B(4,𝔽₂)	C₂²	semidirect
49. #6487648	C₂²	semidirect
50. #6487648	C₂²	semidirect
51. #6470234	C₂²	semidirect
52. #6446732	C₂²	semidirect
53. #6442555	C₂²	semidirect
54. #6440362	C₂²	semidirect
55. #6437975	C₂²	semidirect
56. #6385980	C₂²	semidirect
57. #6379033	C₂²	semidirect
58. C₄×#3018	C₂²	semidirect
59. #6370747	C₂²	semidirect
60. #512151	C₂²	semidirect
61. #511911	C₂²	semidirect
62. #511908	C₂²	semidirect
63. #508193	C₂²	semidirect
64. #508192	C₂²	semidirect
65. #508143	C₂²	semidirect
66. #508062	C₂²	semidirect
67. #503585	C₂²	semidirect
68. #503579	C₂²	semidirect
69. #503576	C₂²	semidirect
70. #503567	C₂²	semidirect
71. #503201	C₂²	semidirect
72. #503194	C₂²	semidirect
73. #502786	C₂²	semidirect
74. #502780	C₂²	semidirect
75. #502774	C₂²	semidirect
76. #502766	C₂²	semidirect
77. #502725	C₂²	semidirect
78. #502711	C₂²	semidirect
79. #502685	C₂²	semidirect
80. #502667	C₂²	semidirect
81. #502661	C₂²	semidirect
82. #501164	C₂²	semidirect
83. #501156	C₂²	semidirect
84. #500961	C₂²	semidirect
85. #500955	C₂²	semidirect
86. #500952	C₂²	semidirect
87. #500943	C₂²	semidirect
88. #500776	C₂²	semidirect
89. #500769	C₂²	semidirect
90. #500495	C₂²	semidirect
91. #500489	C₂²	semidirect
92. #500483	C₂²	semidirect
93. #500475	C₂²	semidirect
94. #500382	C₂²	semidirect
95. #500364	C₂²	semidirect
96. #500358	C₂²	semidirect
97. #500185	C₂²	semidirect
98. #500174	C₂²	semidirect
99. #500073	C₂²	semidirect
100. #500059	C₂²	semidirect
101. #500034	C₂²	semidirect
102. #500034	C₂²	semidirect
103. #500034	C₂²	semidirect
104. #500033	C₂²	semidirect
105. #500016	C₂²	semidirect
106. #500016	C₂²	semidirect
107. #500015	C₂²	semidirect
108. #500010	C₂²	semidirect
109. #500010	C₂²	semidirect
110. #500009	C₂²	semidirect
111. #499851	C₂²	semidirect
112. #499851	C₂²	semidirect
113. #499844	C₂²	semidirect
114. #499844	C₂²	semidirect
115. #499795	C₂²	semidirect
116. #499787	C₂²	semidirect
117. #499282	C₂²	semidirect
118. #499281	C₂²	semidirect
119. #498984	C₂²	semidirect
120. C₂×#13343	C₂²	semidirect
121. #497498	C₂²	semidirect
122. #497496	C₂²	semidirect
123. #497492	C₂²	semidirect
124. #497490	C₂²	semidirect
125. #497484	C₂²	semidirect
126. #497484	C₂²	semidirect
127. D₄×AΣL(1,𝔽₁₆)	C₂²	semidirect
128. D₄×AΣL(1,𝔽₁₆)	C₂²	semidirect
129. #496508	C₂²	semidirect
130. #496508	C₂²	semidirect
131. #496398	C₂²	semidirect
132. #496240	C₂²	semidirect
133. #496200	C₂²	semidirect
134. C₄×#2199	C₂²	semidirect
135. C₄×#2196	C₂²	semidirect
136. #495580	C₂²	semidirect
137. #495580	C₂²	semidirect
138. #494682	C₂²	semidirect
139. #494575	C₂²	semidirect
140. #493957	C₂²	semidirect
141. #493957	C₂²	semidirect
142. #493867	C₂²	semidirect
148. C₂×#3511	D₄	semidirect
150. C₂²×D₄²	D₄	semidirect
157. #59945	C₂³	semidirect
158. #59864	C₂³	semidirect
159. #59816	C₂³	semidirect
160. #59814	C₂³	semidirect
161. #59199	C₂³	semidirect
163. #59000	C₂³	semidirect
164. #58990	C₂³	semidirect
165. #52301	C₂³	semidirect
166. #52103	C₂³	semidirect
167. C₂×#2679	C₂³	semidirect
168. #51940	C₂³	semidirect
170. #48143	C₂³	semidirect
171. #48113	C₂³	semidirect
172. #46338	C₂³	semidirect
175. #46152	C₂³	semidirect
176. #46089	C₂³	semidirect
177. #45996	C₂³	semidirect
178. #45645	C₂³	semidirect
179. #45493	C₂³	semidirect
180. #45439	C₂³	semidirect
182. #38956	D₄	semidirect
184. #38952	D₄	semidirect
185. #38904	D₄	semidirect
186. #38904	D₄	semidirect
189. #37134	C₂³	semidirect
190. #36702	D₄	semidirect
191. C₂×#2858	D₄	semidirect
192. #36419	D₄	semidirect
193. #36412	D₄	semidirect
196. D₄×#120	D₄	semidirect
197. D₄×#120	D₄	semidirect
200. #35531	D₄	semidirect
204. #35272	D₄	semidirect
205. #35256	D₄	semidirect
206. #35237	D₄	semidirect
207. #35237	D₄	semidirect
210. #34364	D₄	semidirect
211. #34356	C₂³	semidirect
212. C₄×H(3,𝔽₄)	C₂³	semidirect
214. C₄×D₄²	C₂³	semidirect
215. C₄×#532	D₄	semidirect
218. C₂×#2199	C₂³	semidirect
220. C₂×#2196	C₂³	semidirect
221. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
285. #13463	C₂³	semidirect
286. #13462	C₂³	semidirect
287. #13461	C₂³	semidirect
288. #13424	C₂³	semidirect
289. #13422	C₂³	semidirect
290. #13419	C₂³	semidirect
291. #13419	C₂³	semidirect
292. #13419	C₂³	semidirect
294. #13377	C₂³	semidirect
296. #13376	C₂³	semidirect
297. #13376	C₂³	semidirect
299. #13375	C₂³	semidirect
301. #13348	C₂³	semidirect
303. #13346	C₂³	semidirect
307. #13343	C₂³	semidirect
308. #13343	C₂³	semidirect
309. #13343	C₂³	semidirect
310. #13343	C₂³	semidirect
311. #13299	C₂³	semidirect
312. #13298	C₂³	semidirect
313. #13295	C₂³	semidirect
314. #13295	C₂³	semidirect
315. #13292	C₂³	semidirect
316. #13292	C₂³	semidirect
317. #13221	C₂³	semidirect
318. #13221	C₂³	semidirect
319. #13218	C₂³	semidirect
320. #13218	C₂³	semidirect
321. #13090	C₂³	semidirect
322. #13088	C₂³	semidirect
323. #13086	C₂³	semidirect
324. #13086	C₂³	semidirect
331. #13082	C₂³	semidirect
332. #13082	C₂³	semidirect
334. #13050	C₂³	semidirect
336. #13047	C₂³	semidirect
339. #13043	C₂³	semidirect
340. #13043	C₂³	semidirect
341. #13043	C₂³	semidirect
344. #13041	C₂³	semidirect
345. #13041	C₂³	semidirect
346. #13041	C₂³	semidirect
347. #12967	C₂³	semidirect
348. #12964	C₂³	semidirect
349. #12960	C₂³	semidirect
350. #12960	C₂³	semidirect
351. #12958	C₂³	semidirect
352. #12958	C₂³	semidirect
354. #12858	C₂³	semidirect
357. #12856	C₂³	semidirect
358. #12854	C₂³	semidirect
359. #12798	C₂³	semidirect
360. #12798	C₂³	semidirect
361. #12797	C₂³	semidirect
362. #12797	C₂³	semidirect
363. #12793	C₂³	semidirect
364. #12793	C₂³	semidirect
365. #12763	C₂³	semidirect
366. #12759	C₂³	semidirect
369. #12687	C₂³	semidirect
370. C₄×#354	C₂³	semidirect
371. C₄×#354	C₂³	semidirect
372. C₄×#353	C₂³	semidirect
373. C₄×#353	C₂³	semidirect
374. C₄×AΣL(1,𝔽₁₆)	C₂³	semidirect
375. C₄×AΣL(1,𝔽₁₆)	C₂³	semidirect
376. #12582	C₂³	semidirect
377. C₂×#1393	C₂³	semidirect
378. #12574	C₂³	semidirect
383. C₂⁴×D₄	C₂×D₄	semidirect
384. C₂⁴×D₄	C₂×D₄	semidirect
389. C₂×#556	C₂×D₄	semidirect
390. C₂×#555	C₂×D₄	semidirect
391. C₂×#554	C₂×D₄	semidirect
394. C₂×#547	C₂×D₄	semidirect
400. C₂×#537	C₂×D₄	semidirect
403. C₂×#535	C₂×D₄	semidirect
407. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
410. C₂²×#121	C₂×D₄	semidirect
411. C₂²×#121	C₂×D₄	semidirect
412. C₂²×#120	C₂×D₄	semidirect
413. C₂²×#120	C₂×D₄	semidirect
418. C₂×#520	C₂×D₄	semidirect
419. C₂×C₄×#41	C₂×D₄	semidirect
420. C₂×C₄×#41	C₂×D₄	semidirect
422. C₂²×C₄×D₄	C₂×D₄	semidirect
423. C₂²×C₄×D₄	C₂×D₄	semidirect
437. #2858	C₂×D₄	semidirect
438. #2858	C₂×D₄	semidirect
439. #2858	C₂×D₄	semidirect
440. #2858	C₂×D₄	semidirect
441. #2856	C₂×D₄	semidirect
442. #2850	C₂×D₄	semidirect
443. #2847	C₂×D₄	semidirect
444. #2847	C₂×D₄	semidirect
445. #2847	C₂×D₄	semidirect
446. #2847	C₂×D₄	semidirect
447. #2846	C₂×D₄	semidirect
448. #2846	C₂×D₄	semidirect
457. #2622	C₂×D₄	semidirect
458. #2622	C₂×D₄	semidirect
459. #2620	C₂×D₄	semidirect
460. #2619	C₂×D₄	semidirect
461. #2568	C₂×D₄	semidirect
462. #2567	C₂×D₄	semidirect
464. #2548	C₂×D₄	semidirect
465. #2548	C₂×D₄	semidirect
467. #2541	C₂×D₄	semidirect
468. #2541	C₂×D₄	semidirect
469. #2504	C₂×D₄	semidirect
470. #2504	C₂×D₄	semidirect
471. #2504	C₂×D₄	semidirect
472. #2501	C₂×D₄	semidirect
473. #2500	C₂×D₄	semidirect
474. #2500	C₂×D₄	semidirect
475. #2487	C₂×D₄	semidirect
476. #2487	C₂×D₄	semidirect
479. #2482	C₂×D₄	semidirect
480. #2482	C₂×D₄	semidirect
482. #2433	C₂×D₄	semidirect
483. #2433	C₂×D₄	semidirect
485. #2432	C₂×D₄	semidirect
486. #2431	C₂×D₄	semidirect
487. #2410	C₂×D₄	semidirect
488. #2410	C₂×D₄	semidirect
489. #2410	C₂×D₄	semidirect
490. #2410	C₂×D₄	semidirect
491. #2408	C₂×D₄	semidirect
492. #2408	C₂×D₄	semidirect
495. #2404	C₂×D₄	semidirect
496. #2404	C₂×D₄	semidirect
499. #2403	C₂×D₄	semidirect
500. #2403	C₂×D₄	semidirect
509. D₄×C₂²⋊C₄	C₂×D₄	semidirect
510. D₄×C₂²⋊C₄	C₂×D₄	semidirect
511. D₄×C₂²⋊C₄	C₂×D₄	semidirect
512. D₄×C₂²⋊C₄	C₂×D₄	semidirect
513. #2317	C₂×D₄	semidirect
514. #2311	C₂×D₄	semidirect
516. #2309	C₂×D₄	semidirect
518. #2308	C₂×D₄	semidirect
519. #2308	C₂×D₄	semidirect
521. C₄×C₄⋊Q₈	C₂×D₄	semidirect
522. C₄×C₄⋊Q₈	C₂×D₄	semidirect
525. C₄×#124	C₂×D₄	semidirect
526. C₄×#124	C₂×D₄	semidirect
529. C₄×#120	C₂×D₄	semidirect
530. C₄×#120	C₂×D₄	semidirect
533. #2297	C₂×D₄	semidirect
534. #2297	C₂×D₄	semidirect
535. #2297	C₂×D₄	semidirect
537. #2293	C₂×D₄	semidirect
538. #2293	C₂×D₄	semidirect
539. C₂×#390	C₂×D₄	semidirect
540. C₂×#390	C₂×D₄	semidirect
542. #2285	C₂×D₄	semidirect
543. #2285	C₂×D₄	semidirect
544. #2283	C₂×D₄	semidirect
545. #2283	C₂×D₄	semidirect
546. C₄²×D₄	C₂×D₄	semidirect
547. C₄²×D₄	C₂×D₄	semidirect
548. 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
#72312253	2
#72312243	2
#72312235	2
#72312213	2
#72312191	2
#72312183	2
#72312155	2
#72312145	2
#72312101	2
#72312087	2
#72312036	2
#72311647	2
#72311639	2
#72311243	2
#72256267	2
#72236711	2
#72236702	2
#72236649	2
#72236637	2
#72234425	2
#72233169	2