Subgroups — #72317127

Order 4096.

At least 18063 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

The subgroup lattice has 481 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317123	C₂	1	1	yes	maximal, characteristic, complemented
2	#72314482	C₂	1	1	yes	maximal, characteristic, complemented
3	#72312179	C₂	1	1	yes	maximal, characteristic, complemented
4	#72310395	C₂	1	1	yes	maximal, characteristic, complemented
5	#72310339	C₂	1	1	yes	maximal, characteristic, complemented
6	#72310327	C₂	1	1	yes	maximal, characteristic, complemented
7	#72310304	C₂	1	1	yes	maximal, characteristic, complemented
8	#72310290	C₂	1	1	yes	maximal, characteristic, complemented
9	#72309539	C₂	1	1	yes	maximal, characteristic, complemented
10	#72309452	C₂	1	1	yes	maximal, characteristic, complemented
11	#72309379	C₂	1	1	yes	maximal, characteristic, complemented
12	#72309310	C₂	1	1	yes	maximal, characteristic, complemented
13	#72266814	C₂	1	1	yes	maximal, characteristic
14	#72266813	C₄	1	1	yes	characteristic, complemented
15	#72266811	C₄	1	1	yes	characteristic, complemented
16	#72266809	C₄	1	1	yes	characteristic, complemented
17	#72266809	C₄	1	1	yes	characteristic, complemented
18	#72266809	C₄	1	1	yes	characteristic, complemented
19	#72266809	C₄	1	1	yes	characteristic, complemented
20	#72266804	C₄	1	1	yes	characteristic, complemented
21	#72266073	C₂²	1	1	yes	characteristic, complemented
22	#72266028	C₂²	1	1	yes	characteristic, complemented
23	#72264815	C₂	1	1	yes	maximal, characteristic
24	#72251565	C₂	1	1	yes	maximal, characteristic
25	#72251103	C₄	1	1	yes	characteristic, complemented
26	#72237398	C₂²	1	1	yes	characteristic
27	#72234663	C₂²	1	1	yes	characteristic
28	#72225617	C₂²	1	1	yes	characteristic
29	#72225617	C₂²	1	1	yes	characteristic
30	#72225617	C₂²	1	1	yes	characteristic
31	#72225617	C₂²	1	1	yes	characteristic
32	#72219418	C₂²	1	1	yes	characteristic, complemented
33	#72219415	C₂²	1	1	yes	characteristic, complemented
34	#72219414	C₂²	1	1	yes	characteristic, complemented
35	#72219414	C₂²	1	1	yes	characteristic, complemented
36	#72219301	C₂²	1	1	yes	characteristic
37	#72219251	C₂²	1	1	yes	characteristic, complemented
38	#72219248	C₂²	1	1	yes	characteristic, complemented
39	#72219243	C₂²	1	1	yes	characteristic
40	#72219237	C₂²	1	1	yes	characteristic
41	#72219229	C₂²	1	1	yes	characteristic, complemented
42	#72219228	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#8534	C₂²	1	1	yes	characteristic
44	#72218498	C₂²	1	1	yes	characteristic, complemented
45	#72218455	C₂²	1	1	yes	characteristic
46	#72218381	C₂²	1	1	yes	characteristic, complemented
47	#72218381	C₂²	1	1	yes	characteristic, complemented
48	#72218313	C₂²	1	1	yes	characteristic, complemented
49	#72218313	C₂²	1	1	yes	characteristic, complemented
50	#72218306	C₂²	1	1	yes	characteristic
51	#72218306	C₂²	1	1	yes	characteristic
52	#72218198	C₂²	1	1	yes	characteristic, complemented
53	#72218180	C₂²	1	1	yes	characteristic
54	#72218069	C₂²	1	1	yes	characteristic
55	#72218069	C₂²	1	1	yes	characteristic
56	#72218057	C₂²	1	1	yes	characteristic
57	#72218057	C₂²	1	1	yes	characteristic
58	#72216064	C₂²	1	1	yes	characteristic
59	#10586066	C₂×C₄	1	1	yes	characteristic
60	C₂²×#3484	C₂³	1	1	yes	characteristic
61	C₂×#60399	D₄	1	1	yes	characteristic
62	C₂×#60399	D₄	1	1	yes	characteristic
63	#7630939	C₂³	1	1	yes	characteristic
64	#7630939	C₂³	1	1	yes	characteristic
65	#7626202	D₄	1	1	yes	characteristic
66	#7626202	D₄	1	1	yes	characteristic
67	#6431795	D₄	1	1	yes	characteristic
68	#6431795	D₄	1	1	yes	characteristic
69	#6431795	D₄	1	1	yes	characteristic
70	#6431795	D₄	1	1	yes	characteristic
71	#6374251	D₄	1	1	yes	characteristic
72	#6374251	D₄	1	1	yes	characteristic
73	C₂×#21776	C₂×C₄	1	1	yes	characteristic
74	C₂×#21776	C₂×C₄	1	1	yes	characteristic
75	C₂×#21776	C₂×C₄	1	1	yes	characteristic
76	C₂×#21776	C₂×C₄	1	1	yes	characteristic
77	C₂×#21776	D₄	1	1	yes	characteristic
78	C₂×#21776	D₄	1	1	yes	characteristic
79	C₂×#21776	D₄	1	1	yes	characteristic
80	C₂×#21776	D₄	1	1	yes	characteristic
81	#6374128	D₄	1	1	yes	characteristic
82	#6374128	D₄	1	1	yes	characteristic
83	C₂×#21746	D₄	1	1	yes	characteristic
84	C₂×#21746	D₄	1	1	yes	characteristic
85	#6371558	D₄	1	1	yes	characteristic
86	#6371558	D₄	1	1	yes	characteristic
87	#6371504	C₂×C₄	1	1	yes	characteristic
88	#6371504	C₂×C₄	1	1	yes	characteristic
89	#6371007	C₂×C₄	1	1	yes	characteristic
90	#6371007	C₂×C₄	1	1	yes	characteristic
91	#6370693	C₂×C₄	1	1	yes	characteristic
92	#6370693	C₂×C₄	1	1	yes	characteristic
93	#6370693	C₂×C₄	1	1	yes	characteristic
94	#6370693	C₂×C₄	1	1	yes	characteristic
95	#6370693	C₂×C₄	1	1	yes	characteristic
96	C₂²×#1781	C₂³	1	1	yes	characteristic
97	C₂²×#1781	C₂³	1	1	yes	characteristic
98	C₂²×#1781	C₂³	1	1	yes	characteristic
99	C₂²×#1781	C₂³	1	1	yes	characteristic
100	#517411	C₂³	1	1	yes	characteristic
101	C₂²×#1438	C₂³	1	1	yes	characteristic
102	#392231	C₂×C₄	1	1	yes	characteristic
103	#392231	C₂×C₄	1	1	yes	characteristic
104	#392113	C₂³	1	1	yes	characteristic
105	#392113	C₂³	1	1	yes	characteristic
106	#392109	C₂³	1	1	yes	characteristic
107	#392109	C₂³	1	1	yes	characteristic
108	#392109	C₂³	1	1	yes	characteristic
109	#392109	C₂³	1	1	yes	characteristic
110	#382544	C₂×C₄	1	1	yes	characteristic
111	#382544	C₂×C₄	1	1	yes	characteristic
112	#382544	C₂×C₄	1	1	yes	characteristic
113	#382544	C₂×C₄	1	1	yes	characteristic
114	#382434	C₂×C₄	1	1	yes	characteristic
115	#382434	C₂×C₄	1	1	yes	characteristic
116	#382434	C₂×C₄	1	1	yes	characteristic
117	#382434	C₂×C₄	1	1	yes	characteristic
118	#382434	D₄	1	1	yes	characteristic
119	#382434	D₄	1	1	yes	characteristic
120	#382434	D₄	1	1	yes	characteristic
121	#382434	D₄	1	1	yes	characteristic
122	#355096	C₂×C₄	1	1	yes	characteristic
123	#355096	C₂×C₄	1	1	yes	characteristic
124	#355096	C₂×C₄	1	1	yes	characteristic
125	#355096	C₂×C₄	1	1	yes	characteristic
126	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
128	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
129	#62842	C₂²⋊C₄	1	1	yes	characteristic
130	#62842	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
132	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
133	C₂×#3484	C₂×D₄	1	1	yes	characteristic
134	C₂×#3484	C₂×D₄	1	1	yes	characteristic
135	C₂×#3484	C₂×D₄	1	1	yes	characteristic
136	C₂×#3484	C₂×D₄	1	1	yes	characteristic
137	C₂×#3484	C₂×D₄	1	1	yes	characteristic
138	C₂×#3484	C₂×D₄	1	1	yes	characteristic
139	C₂×#3484	C₂×D₄	1	1	yes	characteristic
140	C₂×#3484	C₂×D₄	1	1	yes	characteristic
141	C₂×#3484	C₂×D₄	1	1	yes	characteristic
142	C₂×#3484	C₂×D₄	1	1	yes	characteristic
143	C₂×#3484	C₂×D₄	1	1	yes	characteristic
144	C₂×#3484	C₂×D₄	1	1	yes	characteristic
145	C₂²×#534	C₂×D₄	1	1	yes	characteristic
146	C₂²×#534	C₂×D₄	1	1	yes	characteristic
147	C₂³×#120	C₂×D₄	1	1	yes	characteristic
148	C₂³×#120	C₂×D₄	1	1	yes	characteristic
149	#62652	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×#518	C₂²×C₄	1	1	yes	characteristic
151	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
163	#36614	#41	1	2	yes	—
164	C₂×#2846	#41	1	2	yes	—
165	#35222	#41	1	2	yes	—
166	#35222	#41	1	2	yes	—
167	#35222	#41	1	2	yes	—
168	#34980	#41	1	2	yes	—
169	#34980	#41	1	2	yes	—
170	#34980	#41	1	2	yes	—
171	#34176	C₂²⋊C₄	1	1	yes	characteristic
172	#34176	C₂²⋊C₄	1	1	yes	characteristic
173	#34176	C₂²⋊C₄	1	1	yes	characteristic
174	#34176	C₂²⋊C₄	1	1	yes	characteristic
175	#34171	C₂²⋊C₄	1	1	yes	characteristic
176	#34171	C₂²⋊C₄	1	1	yes	characteristic
177	#34171	C₂²⋊C₄	1	1	yes	characteristic
178	#34171	C₂²⋊C₄	1	1	yes	characteristic
179	#34171	C₂²×C₄	1	1	yes	characteristic
180	#34171	C₂²×C₄	1	1	yes	characteristic
181	#34171	C₂×D₄	1	1	yes	characteristic
182	#34171	C₂×D₄	1	1	yes	characteristic
183	#34171	C₂×D₄	1	1	yes	characteristic
184	#34171	C₂×D₄	1	1	yes	characteristic
185	C₂²×#379	C₂×D₄	1	1	yes	characteristic
186	C₂²×#379	C₂×D₄	1	1	yes	characteristic
187	C₂²×#379	C₂×D₄	1	1	yes	characteristic
188	C₂²×#379	C₂×D₄	1	1	yes	characteristic
189	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
190	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
191	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
192	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
193	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
196	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
200	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
201	#20585	C₂²⋊C₄	1	1	yes	characteristic
202	#20585	C₂²⋊C₄	1	1	yes	characteristic
203	#20585	C₂²⋊C₄	1	1	yes	characteristic
204	#20585	C₂²⋊C₄	1	1	yes	characteristic
205	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
206	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
207	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
208	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
209	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
210	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
211	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
212	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
213	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
214	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
215	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
216	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
217	C₂×#1781	C₂×D₄	1	1	yes	characteristic
218	C₂×#1781	C₂×D₄	1	1	yes	characteristic
219	C₂×#1781	C₂×D₄	1	1	yes	characteristic
220	C₂×#1781	C₂×D₄	1	1	yes	characteristic
221	C₂×#1781	C₂×D₄	1	1	yes	characteristic
222	C₂×#1781	C₂×D₄	1	1	yes	characteristic
223	C₂×#1781	C₂×D₄	1	1	yes	characteristic
224	C₂×#1781	C₂×D₄	1	1	yes	characteristic
225	C₂×#1781	C₂×D₄	1	1	yes	characteristic
226	C₂×#1781	C₂×D₄	1	1	yes	characteristic
227	C₂×#1781	C₂×D₄	1	1	yes	characteristic
228	C₂×#1781	C₂×D₄	1	1	yes	characteristic
229	#20354	C₂²⋊C₄	1	1	yes	characteristic
230	#20354	C₂²⋊C₄	1	1	yes	characteristic
231	#20354	C₂²⋊C₄	1	1	yes	characteristic
232	#20354	C₂²⋊C₄	1	1	yes	characteristic
233	C₂⁷	C₂²×D₄	1	1	yes	characteristic
234	C₂⁷	C₂×#41	1	1	yes	characteristic
235	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
244	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
245	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
246	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
247	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
248	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
249	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
250	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
251	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
252	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
253	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
254	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
255	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
256	C₂×#535	#117	1	2	yes	—
257	C₂×#535	#123	1	2	yes	—
258	C₂×#535	#123	1	2	yes	—
259	C₂×#534	#117	1	2	yes	—
260	C₂×#534	#120	1	1	yes	characteristic
261	C₂×#534	#120	1	1	yes	characteristic
262	C₂×#534	#120	1	1	yes	characteristic
263	C₂×#534	#120	1	1	yes	characteristic
264	C₂×#534	#120	1	1	yes	characteristic
265	C₂×#534	#120	1	1	yes	characteristic
266	C₂×#534	#120	1	1	yes	characteristic
267	C₂×#534	#120	1	1	yes	characteristic
268	C₂×#534	#123	1	2	yes	—
269	C₂×#534	#123	1	2	yes	—
270	C₂×#525	#117	1	2	yes	—
271	C₂×#525	#123	1	2	yes	—
272	C₂×#525	#123	1	2	yes	—
273	C₂²×#120	#117	1	2	yes	—
274	C₂²×#120	#120	1	1	yes	characteristic
275	C₂²×#120	#120	1	1	yes	characteristic
276	C₂²×#120	#120	1	1	yes	characteristic
277	C₂²×#120	#120	1	1	yes	characteristic
278	C₂²×#120	#120	1	1	yes	characteristic
279	C₂²×#120	#120	1	1	yes	characteristic
280	C₂²×#120	#120	1	1	yes	characteristic
281	C₂²×#120	#120	1	1	yes	characteristic
282	C₂²×#120	#123	1	2	yes	—
283	C₂²×#120	#123	1	2	yes	—
284	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	#2309	#99	1	2	yes	complemented
305	#2309	#117	1	2	yes	—
306	#2309	#123	1	2	yes	—
307	#2309	#123	1	2	yes	—
308	#2308	#99	1	2	yes	complemented
309	#2308	#117	1	2	yes	—
310	#2308	#123	1	2	yes	—
311	#2308	#123	1	2	yes	—
312	#2280	#99	1	2	yes	complemented
313	#2280	#117	1	2	yes	—
314	#2280	#123	1	2	yes	—
315	#2280	#123	1	2	yes	—
316	C₂×#379	#99	1	2	yes	complemented
317	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×#379	#117	1	2	yes	—
326	C₂×#379	#123	1	2	yes	—
327	C₂×#379	#123	1	2	yes	—
328	C₂⁶	C₂×#99	1	1	yes	characteristic
329	C₂⁶	#410	1	1	yes	characteristic
330	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
331	C₂⁶	C₂×#117	1	1	yes	characteristic
332	C₂⁶	C₂×#120	1	1	yes	characteristic
333	C₂⁶	C₂×#120	1	1	yes	characteristic
334	C₂⁶	C₂×#123	1	1	yes	characteristic
335	C₂⁶	C₂×#123	1	1	yes	characteristic
336	C₂⁶	#525	1	1	yes	characteristic
337	C₂⁶	#525	1	1	yes	characteristic
338	C₂⁶	#525	1	1	yes	characteristic
339	C₂⁶	#525	1	1	yes	characteristic
340	C₂⁶	#525	1	1	yes	characteristic
341	C₂⁶	#525	1	1	yes	characteristic
342	C₂⁶	#525	1	1	yes	characteristic
343	C₂²×#41	#381	1	2	yes	—
344	C₂³×D₄	#379	1	1	yes	characteristic
345	C₂³×D₄	#379	1	1	yes	characteristic
346	C₂³×D₄	#379	1	1	yes	characteristic
347	C₂³×D₄	#379	1	1	yes	characteristic
348	C₂³×D₄	#381	1	2	yes	—
349	C₂³×D₄	C₂×#99	1	1	yes	characteristic
350	C₂³×D₄	C₂×#99	1	1	yes	characteristic
351	C₂³×D₄	#410	1	1	yes	characteristic
352	C₂³×D₄	#410	1	1	yes	characteristic
353	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
354	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
355	C₂³×D₄	C₂×#117	1	1	yes	characteristic
356	C₂³×D₄	C₂×#117	1	1	yes	characteristic
357	C₂³×D₄	C₂×#120	1	1	yes	characteristic
358	C₂³×D₄	C₂×#120	1	1	yes	characteristic
359	C₂³×D₄	C₂×#123	1	1	yes	characteristic
360	C₂³×D₄	C₂×#123	1	1	yes	characteristic
361	C₂³×D₄	C₂×#123	1	1	yes	characteristic
362	C₂³×D₄	C₂×#123	1	1	yes	characteristic
363	C₂³×D₄	#525	1	1	yes	characteristic
364	C₂³×D₄	#525	1	1	yes	characteristic
365	C₂³×D₄	#525	1	1	yes	characteristic
366	C₂³×D₄	#525	1	1	yes	characteristic
367	C₂³×D₄	#525	1	1	yes	characteristic
368	C₂³×D₄	#525	1	1	yes	characteristic
369	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
370	C₂⁴×C₄	#410	1	1	yes	characteristic
371	C₂⁴×C₄	C₂×#117	1	1	yes	characteristic
372	C₂⁴×C₄	C₂×#123	1	1	yes	characteristic
373	C₂⁴×C₄	C₂×#123	1	1	yes	characteristic
374	C₂⁴×C₄	#525	1	1	yes	characteristic
375	C₂⁴×C₄	#525	1	1	yes	characteristic
376	C₂⁴×C₄	#525	1	1	yes	characteristic
377	C₂×#120	B(4,𝔽₂)	1	2	yes	—
378	C₂×#120	B(4,𝔽₂)	1	2	yes	—
379	C₂×#120	#458	1	2	yes	—
380	C₂×#120	#458	1	2	yes	—
381	C₂×#117	#381	1	2	yes	—
382	C₂×#117	#381	1	2	yes	—
383	C₂×#117	#381	1	2	yes	—
384	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
385	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
386	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
387	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
388	C₂²×C₂²⋊C₄	#381	1	2	yes	—
389	C₂²×C₂²⋊C₄	#381	1	2	yes	—
390	C₂²×C₂²⋊C₄	#381	1	2	yes	—
391	#379	C₂×#99	1	2	yes	—
392	#379	C₂×#99	1	2	yes	—
393	#379	C₂×#99	1	2	yes	—
394	#379	C₂×#99	1	2	yes	—
395	C₂⁵	#1781	1	1	yes	characteristic
396	C₂⁵	#1781	1	1	yes	characteristic
397	C₂⁵	#1782	1	1	yes	characteristic
398	C₂⁵	#1782	1	1	yes	characteristic
399	C₂⁵	#1828	1	2	yes	complemented
400	C₂⁵	C₂×#379	1	1	yes	characteristic
401	C₂⁵	C₂×#381	1	1	yes	characteristic
402	C₂⁵	#2280	1	1	yes	characteristic
403	C₂⁵	#2280	1	1	yes	characteristic
404	C₂⁵	#2280	1	1	yes	characteristic
405	C₂⁵	#2849	1	1	yes	characteristic
406	C₂⁵	#2849	1	1	yes	characteristic
407	C₂⁵	#2849	1	1	yes	characteristic
408	C₂⁵	#2849	1	1	yes	characteristic
409	C₂⁵	#2849	1	1	yes	characteristic
410	C₂⁵	#2849	1	1	yes	characteristic
411	C₂⁵	C₂²×#99	1	1	yes	characteristic
412	C₂⁵	C₂²×#99	1	1	yes	characteristic
413	C₂⁵	C₂×#410	1	1	yes	characteristic
414	C₂⁵	C₂×#410	1	1	yes	characteristic
415	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
416	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
417	C₂⁵	C₂×#458	1	1	yes	characteristic
418	C₂⁵	C₂×#458	1	1	yes	characteristic
419	C₂⁵	#3026	1	1	yes	characteristic
420	C₂⁵	#3026	1	1	yes	characteristic
421	C₂⁵	#3026	1	1	yes	characteristic
422	C₂⁵	#3026	1	1	yes	characteristic
423	C₂²×Q₈	#1828	1	2	yes	complemented
424	C₂²×D₄	#1790	1	2	yes	—
425	C₂²×D₄	#1790	1	2	yes	—
426	C₂²×D₄	#1828	1	2	yes	complemented
427	C₂³×C₄	#1781	1	1	yes	characteristic
428	C₂³×C₄	#1781	1	1	yes	characteristic
429	C₂³×C₄	#1782	1	1	yes	characteristic
430	C₂³×C₄	#1782	1	1	yes	characteristic
431	C₂³×C₄	#1828	1	2	yes	complemented
432	C₂³×C₄	C₂×#381	1	1	yes	characteristic
433	C₂³×C₄	#2280	1	1	yes	characteristic
434	C₂³×C₄	#2849	1	1	yes	characteristic
435	C₂³×C₄	#2849	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	#1790	1	2	yes	—
437	C₂×C₂²⋊C₄	#1790	1	2	yes	—
438	C₂⁴	#8534	1	2	yes	—
439	C₂⁴	#14681	1	1	yes	characteristic
440	C₂⁴	C₂×#1781	1	1	yes	characteristic
441	C₂⁴	C₂×#1782	1	1	yes	characteristic
442	C₂⁴	C₂×#1790	1	1	yes	characteristic
443	C₂⁴	C₂×#1790	1	1	yes	characteristic
444	C₂⁴	#20609	1	1	yes	characteristic
445	C₂⁴	#20609	1	1	yes	characteristic
446	C₂⁴	C₂×#1828	1	2	yes	—
447	C₂⁴	#20722	1	1	yes	characteristic
448	C₂⁴	#20722	1	1	yes	characteristic
449	C₂⁴	#20722	1	1	yes	characteristic
450	C₂⁴	#20722	1	1	yes	characteristic
451	C₂⁴	#33020	1	1	yes	characteristic
452	C₂⁴	#33020	1	1	yes	characteristic
453	C₂⁴	#33020	1	1	yes	characteristic
454	C₂⁴	#33020	1	1	yes	characteristic
455	C₂⁴	#33022	1	1	yes	characteristic
456	C₂⁴	#33022	1	1	yes	characteristic
457	C₂⁴	#33022	1	1	yes	characteristic
458	C₂⁴	#33022	1	1	yes	characteristic
459	C₂²×C₄	#8534	1	2	yes	—
460	C₂²×C₄	C₂×#1828	1	2	yes	—
461	C₂³	C₂×#8534	1	1	yes	characteristic
462	C₂³	#187929	1	1	yes	characteristic
463	C₂³	#187929	1	1	yes	characteristic
464	C₂³	#187944	1	1	yes	characteristic
465	C₂³	#392222	1	1	yes	characteristic
466	C₂³	#392222	1	1	yes	characteristic
467	C₂³	#392231	1	1	yes	characteristic
468	C₂³	#392231	1	1	yes	characteristic
469	C₂³	#392239	1	1	yes	characteristic
470	C₂³	#392239	1	1	yes	characteristic
471	C₂³	#392245	1	1	yes	characteristic
472	C₂²	#72234592	1	1	yes	characteristic
473	C₂²	#72265195	1	1	yes	characteristic
474	C₂²	#72265195	1	1	yes	characteristic
475	C₂²	#72265195	1	1	yes	characteristic
476	C₂²	#72265195	1	1	yes	characteristic
477	C₂²	#72265754	1	1	yes	characteristic
478	C₂²	#72265917	1	1	yes	characteristic
479	C₂	#72266250	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266250
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72216064	C₂²
LCS	G ▷ C₂⁴×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72317123	C₂	semidirect
2. #72314482	C₂	semidirect
3. #72312179	C₂	semidirect
4. #72310395	C₂	semidirect
5. #72310339	C₂	semidirect
6. #72310327	C₂	semidirect
7. #72310304	C₂	semidirect
8. #72310290	C₂	semidirect
9. #72309539	C₂	semidirect
10. #72309452	C₂	semidirect
11. #72309379	C₂	semidirect
12. #72309310	C₂	semidirect
14. #72266813	C₄	semidirect
15. #72266811	C₄	semidirect
16. #72266809	C₄	semidirect
17. #72266809	C₄	semidirect
18. #72266809	C₄	semidirect
19. #72266809	C₄	semidirect
20. #72266804	C₄	semidirect
21. #72266073	C₂²	semidirect
22. #72266028	C₂²	semidirect
25. #72251103	C₄	semidirect
32. #72219418	C₂²	semidirect
33. #72219415	C₂²	semidirect
34. #72219414	C₂²	semidirect
35. #72219414	C₂²	semidirect
37. #72219251	C₂²	semidirect
38. #72219248	C₂²	semidirect
41. #72219229	C₂²	semidirect
42. #72219228	C₂²	semidirect
44. #72218498	C₂²	semidirect
46. #72218381	C₂²	semidirect
47. #72218381	C₂²	semidirect
48. #72218313	C₂²	semidirect
49. #72218313	C₂²	semidirect
52. #72218198	C₂²	semidirect
304. #2309	#99	semidirect
308. #2308	#99	semidirect
312. #2280	#99	semidirect
316. C₂×#379	#99	semidirect
399. C₂⁵	#1828	semidirect
423. C₂²×Q₈	#1828	semidirect
426. C₂²×D₄	#1828	semidirect
431. C₂³×C₄	#1828	semidirect

Maximal subgroups

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

subgroup	index
#72317123	2
#72314482	2
#72312179	2
#72310395	2
#72310339	2
#72310327	2
#72310304	2
#72310290	2
#72309539	2
#72309452	2
#72309379	2
#72309310	2
#72266814	2
#72264815	2
#72251565	2