Subgroups — #72315710

Order 4096.

Only the 947 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 534 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315417	C₂	1	2	yes	maximal, complemented
2	#72315362	C₂	1	2	yes	maximal, complemented
3	#72315298	C₂	1	2	yes	maximal, complemented
4	#72315258	C₂	1	2	yes	maximal, complemented
5	#72315164	C₂	1	1	yes	maximal, characteristic, complemented
6	#72315084	C₂	1	1	yes	maximal, characteristic, complemented
7	#72314961	C₂	1	2	yes	maximal, complemented
8	#72314824	C₂	1	2	yes	maximal, complemented
9	#72314791	C₂	1	2	yes	maximal, complemented
10	#72314748	C₂²	1	2	yes	complemented
11	#72314748	C₂²	1	2	yes	complemented
12	#72314734	C₂²	1	2	yes	complemented
13	#72314708	C₂	1	2	yes	maximal, complemented
14	#72314665	C₂²	1	2	yes	complemented
15	#72310290	C₂	1	1	yes	maximal, characteristic, complemented
16	#72266873	C₂	1	1	yes	maximal, characteristic, complemented
17	#72262357	C₂	1	1	yes	maximal, characteristic, complemented
18	#72262349	C₂	1	1	yes	maximal, characteristic, complemented
19	#72258094	C₂²	1	2	yes	complemented
20	#72258094	C₂²	1	2	yes	complemented
21	#72258019	C₂²	1	2	yes	complemented
22	#72258019	C₂²	1	2	yes	complemented
23	#72256195	C₂²	1	2	yes	complemented
24	#72256193	C₂²	1	2	yes	complemented
25	#72256048	C₂²	1	2	yes	complemented
26	#72256043	C₂²	1	2	yes	complemented
27	#72255986	C₂²	1	2	yes	complemented
28	#72255977	C₂²	1	2	yes	complemented
29	#72255849	C₂²	1	2	yes	complemented
30	#72255841	C₂²	1	2	yes	complemented
31	#72255841	C₂²	1	2	yes	complemented
32	#72255793	C₂²	1	2	yes	complemented
33	#72255778	C₂²	1	2	yes	complemented
34	#72255777	C₂²	1	2	yes	complemented
35	#72255774	C₂²	1	2	yes	complemented
36	#72255772	C₂²	1	2	yes	complemented
37	#72251547	C₂	1	1	yes	maximal, characteristic, complemented
38	#72251533	C₂²	1	2	yes	complemented
39	#72251530	C₂²	1	2	yes	complemented
40	#72251528	C₂²	1	2	yes	complemented
41	#72251527	C₂²	1	2	yes	complemented
42	#72240489	C₂	1	1	yes	maximal, characteristic, complemented
43	#72240132	C₂²	1	2	yes	complemented
44	#72240132	C₂²	1	2	yes	complemented
45	#72238344	C₂	1	1	yes	maximal, characteristic, complemented
46	#72238343	C₂²	1	2	yes	complemented
47	#72238343	C₂²	1	2	yes	complemented
48	#72238342	C₂²	1	2	yes	complemented
49	#72238342	C₂²	1	2	yes	complemented
50	#72237423	C₂	1	1	yes	maximal, characteristic, complemented
51	#72237402	C₂²	1	2	yes	—
52	#72237402	C₂²	1	2	yes	—
53	#72237402	C₂²	1	2	yes	—
54	#72237402	C₂²	1	2	yes	—
55	#72237400	C₂²	1	1	yes	characteristic
56	#72237398	C₂²	1	1	yes	characteristic
57	#72237398	C₂²	1	1	yes	characteristic
58	#72237045	C₂²	1	2	yes	complemented
59	#72237045	C₂²	1	2	yes	complemented
60	#72236928	C₂²	1	2	yes	complemented
61	#72236928	C₂²	1	2	yes	complemented
62	#72232884	C₂²	1	1	yes	characteristic
63	#72225747	C₂	1	1	yes	maximal, characteristic, complemented
64	#72225745	C₂²	1	1	yes	characteristic, complemented
65	#72225744	C₂²	1	1	yes	characteristic, complemented
66	#72225743	C₂²	1	1	yes	characteristic, complemented
67	#72225742	C₂²	1	1	yes	characteristic, complemented
68	#72225742	C₂²	1	1	yes	characteristic, complemented
69	#72225741	C₂²	1	1	yes	characteristic, complemented
70	#72225740	C₂²	1	1	yes	characteristic, complemented
71	C₂×#7266798	C₂²	1	1	yes	characteristic, complemented
72	#72225667	C₂²	1	1	yes	characteristic, complemented
73	#72225617	C₂²	1	1	yes	characteristic, complemented
74	#72219445	C₂	1	1	yes	maximal, characteristic, complemented
75	#72219418	C₂²	1	1	yes	characteristic, complemented
76	#72219414	C₂²	1	1	yes	characteristic, complemented
77	#72219301	C₂²	1	1	yes	characteristic
78	#72219301	C₂²	1	1	yes	characteristic
79	#72219158	C₂²	1	2	yes	complemented
80	#72219158	C₂²	1	2	yes	complemented
81	#72218868	C₂	1	1	yes	maximal, characteristic, complemented
82	#72218847	C₂	1	1	yes	maximal, characteristic, complemented
83	#72218521	C₂²	1	2	yes	complemented
84	#72218521	C₂²	1	2	yes	complemented
85	#72218518	C₂²	1	1	yes	characteristic, complemented
86	#72218498	C₂²	1	1	yes	characteristic, complemented
87	#72218498	C₂²	1	1	yes	characteristic, complemented
88	#72218391	C₂²	1	2	yes	complemented
89	#72218391	C₂²	1	2	yes	complemented
90	#72218381	C₂²	1	1	yes	characteristic, complemented
91	#72218381	C₂²	1	1	yes	characteristic, complemented
92	#72218313	C₂²	1	1	yes	characteristic, complemented
93	#72218306	C₂²	1	1	yes	characteristic
94	#72218306	C₂²	1	1	yes	characteristic
95	#72218222	C₂	1	1	yes	maximal, characteristic, complemented
96	#72218215	C₂²	1	2	yes	complemented
97	#72218215	C₂²	1	2	yes	complemented
98	#72218206	C₂²	1	2	yes	complemented
99	#72218206	C₂²	1	2	yes	complemented
100	#72218198	C₂²	1	1	yes	characteristic, complemented
101	#72218180	C₂²	1	1	yes	characteristic, complemented
102	C₂×#139750	C₂²	1	2	yes	complemented
103	C₂×#139750	C₂²	1	2	yes	complemented
104	#72218057	C₂²	1	1	yes	characteristic, complemented
105	C₂²×#23900	C₂²	1	1	yes	characteristic
106	C₂²×#23900	C₂²	1	1	yes	characteristic
107	#72217875	C₂²	1	1	yes	characteristic
108	C₂×#144378	C₂²	1	2	yes	complemented
109	C₂×#144378	C₂²	1	2	yes	complemented
110	C₂×#139731	C₂²	1	2	yes	complemented
111	C₂×#139731	C₂²	1	2	yes	complemented
112	#72217789	C₂²	1	1	yes	characteristic, complemented
113	#72215858	C₂²	1	1	yes	characteristic, complemented
114	#72215179	C₂²	1	1	yes	characteristic, complemented
115	#72213862	C₂²	1	1	yes	characteristic
116	#72213862	C₂²	1	1	yes	characteristic
117	#72210555	C₂²	1	1	yes	characteristic
118	#72210555	C₂²	1	1	yes	characteristic
119	#72210555	C₂²	1	1	yes	characteristic
120	#72210555	C₂²	1	1	yes	characteristic
121	#72210555	C₂²	1	1	yes	characteristic
122	#72210511	C₂²	1	1	yes	characteristic
123	#10586422	C₂³	1	2	yes	—
124	#10586422	C₂³	1	2	yes	—
125	C₂²×#3484	C₂³	1	1	yes	characteristic
126	C₂²×#3484	C₂³	1	1	yes	characteristic
127	C₂²×#3484	C₂³	1	1	yes	characteristic
128	C₂⁴×#120	C₂³	1	1	yes	characteristic
129	C₂²×#2846	D₄	1	2	yes	complemented
130	#7630939	C₂³	1	1	yes	characteristic
131	C₂×#32873	C₂³	1	1	yes	characteristic, complemented
132	C₂×#23895	D₄	1	2	yes	complemented
133	C₂×#23895	C₂³	1	1	yes	characteristic
134	C₂×#23895	C₂³	1	1	yes	characteristic
135	C₂×#23895	C₂³	1	2	yes	—
136	#6437621	D₄	1	2	yes	complemented
137	C₂×#23900	D₄	1	2	yes	complemented
138	C₂×#23900	D₄	1	2	yes	complemented
139	C₂×#23900	C₂³	1	1	yes	characteristic
140	C₂×#23900	C₂³	1	1	yes	characteristic
141	C₂×#23900	C₂³	1	1	yes	characteristic
142	C₂×#23900	C₂³	1	1	yes	characteristic
143	C₂×#23900	C₂³	1	2	yes	—
144	C₂×#23900	C₂³	1	2	yes	—
145	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
146	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
147	#6437445	C₂³	1	2	yes	—
148	C₂×#21776	D₄	1	2	yes	complemented
149	C₂×#21776	C₂³	1	2	yes	—
150	C₂×#21776	C₂³	1	1	yes	characteristic
151	C₂×#21776	C₂³	1	1	yes	characteristic
152	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
153	C₂×#21746	C₂³	1	1	yes	characteristic, complemented
154	C₂×#21746	C₂³	1	1	yes	characteristic, complemented
155	C₂²×#1898	D₄	1	2	yes	complemented
156	#6370693	D₄	1	2	yes	complemented
157	C₂²×#1781	C₂³	1	1	yes	characteristic
158	C₂²×#1781	C₂³	1	1	yes	characteristic
159	#616961	C₂³	1	2	yes	—
160	#616961	C₂³	1	2	yes	—
161	#517411	C₂³	1	1	yes	characteristic
162	C₂×#12707	C₂³	1	2	yes	—
163	C₂×#12707	C₂³	1	2	yes	—
164	C₂×#12707	C₂³	1	2	yes	—
165	C₂×#12707	C₂³	1	2	yes	—
166	C₂×#12707	C₂³	1	2	yes	complemented
167	C₂×#12705	C₂³	1	2	yes	—
168	C₂×#12705	C₂³	1	2	yes	—
169	C₂×#12705	C₂³	1	2	yes	—
170	C₂×#12705	C₂³	1	2	yes	—
171	#493370	C₂³	1	2	yes	—
172	#493370	C₂³	1	2	yes	—
173	#493370	C₂³	1	2	yes	—
174	#493370	C₂³	1	2	yes	—
175	#493370	C₂³	1	2	yes	—
176	#493370	C₂³	1	2	yes	—
177	C₂×#12687	C₂³	1	2	yes	complemented
178	C₂×#12687	C₂³	1	2	yes	complemented
179	#392231	D₄	1	2	yes	complemented
180	#392113	C₂³	1	1	yes	characteristic
181	#392109	C₂³	1	1	yes	characteristic
182	#392109	C₂³	1	1	yes	characteristic
183	#392109	C₂³	1	1	yes	characteristic
184	#392109	C₂³	1	1	yes	characteristic
185	#392109	C₂³	1	1	yes	characteristic
186	#392109	C₂³	1	1	yes	characteristic
187	#392030	C₂³	1	1	yes	characteristic, complemented
188	#392030	C₂³	1	1	yes	characteristic, complemented
189	#392030	C₂³	1	1	yes	characteristic, complemented
190	#382544	C₂³	1	1	yes	characteristic, complemented
191	#382434	D₄	1	2	yes	complemented
192	#382434	C₂³	1	2	yes	—
193	#382434	C₂³	1	1	yes	characteristic
194	#382434	C₂³	1	1	yes	characteristic
195	#382434	C₂³	1	1	yes	characteristic, complemented
196	#382422	C₂³	1	1	yes	characteristic, complemented
197	#382422	C₂³	1	1	yes	characteristic, complemented
198	#359549	D₄	1	2	yes	complemented
199	#359549	C₂³	1	1	yes	characteristic
200	#359549	C₂³	1	1	yes	characteristic
201	#359549	C₂³	1	2	yes	—
202	#359509	C₂³	1	2	yes	—
203	#359501	C₂³	1	1	yes	characteristic, complemented
204	#359501	C₂³	1	1	yes	characteristic, complemented
205	#359442	D₄	1	2	yes	complemented
206	#355096	C₂³	1	1	yes	characteristic, complemented
207	#347047	D₄	1	8	yes	complemented
208	#347045	D₄	1	8	yes	complemented
209	#188050	C₂³	1	2	yes	—
210	#188050	C₂³	1	2	yes	—
211	C₂×#8541	C₂³	1	2	yes	complemented
212	C₂×#8541	C₂³	1	2	yes	complemented
213	#187944	C₂³	1	2	yes	—
214	#187944	C₂³	1	2	yes	—
215	#187944	C₂³	1	2	yes	—
216	#187944	C₂³	1	2	yes	—
217	#187944	C₂³	1	2	yes	complemented
218	#146479	C₂³	1	2	yes	complemented
219	#128033	C₂³	1	2	yes	complemented
220	#128033	C₂³	1	2	yes	complemented
221	C₂×#7316	C₂³	1	2	yes	complemented
222	C₂×#7316	C₂³	1	2	yes	complemented
223	C₂×#7314	C₂³	1	2	yes	complemented
224	C₂×#7314	C₂³	1	2	yes	complemented
225	C₂×#7310	C₂³	1	2	yes	complemented
226	C₂×#7310	C₂³	1	2	yes	complemented
227	C₂×#7310	C₂³	1	2	yes	complemented
228	C₂×#7310	C₂³	1	2	yes	complemented
229	C₂×#7310	C₂³	1	2	yes	complemented
230	C₂×#7310	C₂³	1	2	yes	complemented
231	#128009	C₂³	1	2	yes	complemented
232	#128009	C₂³	1	2	yes	complemented
233	#128009	C₂³	1	2	yes	complemented
234	#128009	C₂³	1	2	yes	complemented
235	#107114	C₂³	1	2	yes	complemented
236	C₂⁸	C₂×D₄	1	1	yes	characteristic
237	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
238	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
239	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
240	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
241	#62832	C₂×D₄	1	4	yes	—
242	#62824	C₂×D₄	1	4	yes	—
243	C₂×#3484	C₂×D₄	1	2	yes	—
244	C₂×#3484	C₂×D₄	1	2	yes	—
245	C₂×#3484	C₂×D₄	1	1	yes	characteristic
246	C₂×#3484	C₂×D₄	1	1	yes	characteristic
247	C₂×#3484	C₂×D₄	1	1	yes	characteristic
248	C₂×#3484	C₂×D₄	1	1	yes	characteristic
249	C₂×#3484	#41	1	2	yes	complemented
250	C₂×#3484	C₂⁴	1	1	yes	characteristic
251	C₂×#3484	C₂⁴	1	1	yes	characteristic
252	C₂×#3484	C₂⁴	1	1	yes	characteristic
253	C₂×#3484	C₂⁴	1	2	yes	—
254	C₂²×#535	C₂⁴	1	2	yes	—
255	C₂²×#534	C₂×D₄	1	2	yes	—
256	C₂²×#525	#41	1	2	yes	complemented
257	C₂³×#120	C₂×D₄	1	2	yes	—
258	C₂³×#120	C₂×D₄	1	1	yes	characteristic
259	C₂³×#120	C₂×D₄	1	1	yes	characteristic
260	C₂³×#120	C₂⁴	1	1	yes	characteristic
261	C₂³×#120	C₂⁴	1	1	yes	characteristic
262	C₂²×#518	C₂×D₄	1	1	yes	characteristic
263	C₂²×#518	#41	1	1	yes	characteristic, complemented
264	C₂²×#518	#41	1	1	yes	characteristic, complemented
265	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
266	C₂×#3026	C₂×D₄	1	2	yes	complemented
267	C₂×#3026	C₂×D₄	1	2	yes	complemented
268	C₂×#2883	C₂×D₄	1	2	yes	complemented
269	C₂×#2883	C₂×D₄	1	2	yes	complemented
270	C₂×#2846	C₂×D₄	1	2	yes	—
271	C₂×#2846	C₂×D₄	1	2	yes	—
272	C₂×#2846	C₂×D₄	1	2	yes	—
273	C₂×#2846	C₂×D₄	1	2	yes	—
274	#34171	C₂×D₄	1	1	yes	characteristic
275	#34171	C₂×D₄	1	1	yes	characteristic
276	#34171	C₂⁴	1	1	yes	characteristic
277	C₂²×#379	C₂×D₄	1	2	yes	—
278	#23900	C₂×D₄	1	8	yes	—
279	#23900	C₂×D₄	1	8	yes	—
280	C₂×#1913	C₂×D₄	1	2	yes	complemented
281	C₂×#1913	C₂×D₄	1	2	yes	complemented
282	C₂×#1913	C₂×D₄	1	2	yes	complemented
283	C₂×#1913	C₂×D₄	1	2	yes	complemented
284	C₂×#1898	C₂×D₄	1	2	yes	—
285	C₂×#1898	C₂×D₄	1	2	yes	—
286	C₂×#1898	C₂×D₄	1	2	yes	—
287	C₂×#1898	C₂×D₄	1	2	yes	—
288	#20960	C₂×D₄	1	2	yes	complemented
289	#20960	C₂×D₄	1	2	yes	complemented
290	C₂×#1828	C₂×D₄	1	2	yes	complemented
291	C₂×#1828	C₂×D₄	1	2	yes	complemented
292	C₂×#1828	C₂×D₄	1	2	yes	complemented
293	C₂×#1828	C₂×D₄	1	2	yes	complemented
294	C₂×#1783	C₂⁴	1	2	yes	—
295	#20585	C₂×D₄	1	2	yes	complemented
296	#20585	C₂×D₄	1	2	yes	complemented
297	C₂×#1781	C₂×D₄	1	2	yes	—
298	C₂×#1781	C₂×D₄	1	2	yes	—
299	C₂×#1781	C₂×D₄	1	2	yes	—
300	C₂×#1781	C₂×D₄	1	2	yes	—
301	C₂×#1781	C₂×D₄	1	2	yes	—
302	C₂×#1781	C₂×D₄	1	2	yes	—
303	C₂×#1781	C₂×D₄	1	2	yes	—
304	C₂×#1781	C₂⁴	1	2	yes	—
305	C₂×#1781	C₂⁴	1	2	yes	—
306	C₂×#1781	C₂⁴	1	2	yes	—
307	C₂×#1781	C₂⁴	1	1	yes	characteristic
308	C₂×#1781	C₂⁴	1	1	yes	characteristic
309	C₂×#1781	C₂⁴	1	1	yes	characteristic
310	C₂×#1781	C₂⁴	1	1	yes	characteristic
311	C₂×#1781	C₂⁴	1	1	yes	characteristic
312	C₂×#1781	C₂⁴	1	1	yes	characteristic
313	C₂×#1781	C₂⁴	1	1	yes	characteristic
314	C₂×#1781	C₂⁴	1	1	yes	characteristic
315	C₂×#1781	C₂⁴	1	2	yes	—
316	#15259	C₂×D₄	1	4	yes	—
317	#15258	C₂×D₄	1	4	yes	—
318	#14335	C₂⁴	1	2	yes	—
319	#8546	C₂×D₄	1	4	yes	—
320	#8544	C₂×D₄	1	4	yes	—
321	#8534	C₂×D₄	1	8	yes	—
322	#8534	C₂×D₄	1	8	yes	—
323	C₂⁷	C₂²×D₄	1	1	yes	characteristic
324	C₂⁷	C₂²×D₄	1	1	yes	characteristic
325	C₂⁷	C₂²×D₄	1	1	yes	characteristic
326	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
328	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
329	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
330	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
331	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
332	C₂³×#41	C₂×#41	1	2	yes	—
333	C₂⁴×D₄	#120	1	2	yes	—
334	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
336	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
337	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
338	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
339	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
340	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
341	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
342	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
345	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
346	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
347	#3484	C₂²×D₄	1	4	yes	—
348	#3484	C₂²×D₄	1	4	yes	—
349	#3484	H(5,𝔽₂)	1	4	yes	—
350	#3484	H(5,𝔽₂)	1	4	yes	—
351	C₂×#534	#120	1	2	yes	—
352	C₂×#534	#120	1	2	yes	—
353	C₂×#534	C₂²×D₄	1	2	yes	—
354	C₂×#534	C₂²×D₄	1	2	yes	—
355	C₂²×#127	C₂²×D₄	1	2	yes	—
356	C₂²×#127	H(5,𝔽₂)	1	2	yes	—
357	C₂²×#124	C₂²×D₄	1	2	yes	—
358	C₂²×#124	H(5,𝔽₂)	1	2	yes	—
359	C₂²×#120	#120	1	2	yes	—
360	C₂²×#120	#120	1	2	yes	—
361	C₂²×#120	C₂²×D₄	1	2	yes	—
362	C₂²×#120	C₂²×D₄	1	2	yes	—
363	C₂²×#120	C₂²×D₄	1	4	yes	—
364	C₂×#518	#120	1	2	yes	—
365	C₂×#518	C₂²×D₄	1	1	yes	characteristic
366	C₂×#518	C₂²×D₄	1	1	yes	characteristic
367	C₂×#518	C₂²×D₄	1	1	yes	characteristic
368	C₂×#518	C₂²×D₄	1	1	yes	characteristic
369	C₂×#518	C₂²×D₄	1	1	yes	characteristic
370	C₂×#518	C₂×#41	1	2	yes	—
371	C₂²×#117	C₂×#41	1	2	yes	—
372	C₂³×C₂²⋊C₄	#120	1	2	yes	—
373	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
374	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
375	C₂²×#99	C₂²×D₄	1	2	yes	—
376	C₂²×#99	C₂²×D₄	1	2	yes	—
377	C₂²×#99	C₂²×D₄	1	2	yes	—
378	C₂²×#99	C₂²×D₄	1	2	yes	—
379	C₂²×#99	C₂²×D₄	1	2	yes	—
380	C₂²×#99	C₂²×D₄	1	2	yes	—
381	#2846	#120	1	8	yes	complemented
382	C₂×#379	C₂²×D₄	1	2	yes	—
383	C₂×#379	C₂²×D₄	1	2	yes	—
384	#1898	#120	1	8	yes	complemented
385	#1781	C₂²×D₄	1	4	yes	—
386	#1781	C₂²×D₄	1	4	yes	—
387	#1438	C₂²×D₄	1	4	yes	—
388	C₂⁶	B(4,𝔽₂)	1	2	yes	—
389	C₂⁶	C₂×#120	1	1	yes	characteristic
390	C₂⁶	C₂×#120	1	1	yes	characteristic
391	C₂⁶	C₂×#120	1	2	yes	—
392	C₂⁶	#535	1	1	yes	characteristic
393	C₂⁶	#535	1	1	yes	characteristic
394	C₂⁶	#546	1	1	yes	characteristic
395	C₂⁶	#546	1	1	yes	characteristic
396	C₂⁶	#546	1	1	yes	characteristic
397	C₂⁶	#546	1	1	yes	characteristic
398	C₂⁶	#546	1	1	yes	characteristic
399	C₂⁶	#546	1	1	yes	characteristic
400	C₂⁶	#546	1	1	yes	characteristic
401	C₂⁶	C₂³×D₄	1	1	yes	characteristic
402	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×H(5,𝔽₂)	D₄²	1	4	yes	—
404	C₂×H(5,𝔽₂)	#546	1	4	yes	complemented
405	C₂³×Q₈	#546	1	2	yes	complemented
406	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
407	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
408	C₂³×D₄	C₂×#120	1	1	yes	characteristic
409	C₂³×D₄	C₂×#120	1	1	yes	characteristic
410	C₂³×D₄	C₂×#120	1	2	yes	—
411	C₂³×D₄	C₂×#120	1	2	yes	—
412	C₂³×D₄	#525	1	1	yes	characteristic
413	C₂³×D₄	#525	1	1	yes	characteristic
414	C₂³×D₄	#535	1	1	yes	characteristic
415	C₂³×D₄	#535	1	1	yes	characteristic
416	C₂³×D₄	#546	1	1	yes	characteristic
417	C₂³×D₄	#546	1	1	yes	characteristic
418	C₂³×D₄	#546	1	1	yes	characteristic
419	C₂³×D₄	#546	1	1	yes	characteristic
420	C₂³×D₄	#546	1	1	yes	characteristic
421	C₂³×D₄	#546	1	1	yes	characteristic
422	C₂³×D₄	#546	1	2	yes	complemented
423	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
424	C₂³×D₄	C₂³×D₄	1	2	yes	—
425	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
426	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
427	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
430	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
431	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
432	C₂⁴×C₄	#525	1	1	yes	characteristic
433	C₂⁴×C₄	#525	1	1	yes	characteristic
434	C₂⁴×C₄	#546	1	1	yes	characteristic
435	C₂⁴×C₄	#546	1	1	yes	characteristic
436	C₂⁴×C₄	#546	1	1	yes	characteristic
437	C₂⁴×C₄	C₂²×#41	1	1	yes	characteristic
438	#534	D₄²	1	8	yes	—
439	C₂×#120	B(4,𝔽₂)	1	8	yes	—
440	C₂×#120	C₂×#120	1	4	yes	—
441	C₂×#120	#534	1	4	yes	—
442	#518	D₄²	1	4	yes	—
443	#518	#546	1	4	yes	complemented
444	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
445	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
447	C₂²×C₄²	#546	1	2	yes	complemented
448	C₂²×C₄²	#546	1	2	yes	complemented
449	#379	C₂×#120	1	4	yes	—
450	C₂⁵	#2404	1	1	yes	characteristic
451	C₂⁵	#2404	1	1	yes	characteristic
452	C₂⁵	#2404	1	1	yes	characteristic
453	C₂⁵	#2404	1	1	yes	characteristic
454	C₂⁵	#2404	1	1	yes	characteristic
455	C₂⁵	#2404	1	1	yes	characteristic
456	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
457	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
458	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
459	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
460	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
461	C₂⁵	C₂²×#120	1	1	yes	characteristic
462	C₂⁵	C₂²×#120	1	1	yes	characteristic
463	C₂⁵	C₂×#534	1	1	yes	characteristic
464	C₂⁵	C₂×#535	1	1	yes	characteristic
465	C₂⁵	C₂×#546	1	1	yes	characteristic
466	C₂⁵	C₂×#546	1	1	yes	characteristic
467	C₂⁵	C₂×#546	1	1	yes	characteristic
468	C₂⁵	#3484	1	2	yes	—
469	C₂⁵	#3484	1	1	yes	characteristic
470	C₂⁵	#3484	1	1	yes	characteristic
471	C₂⁵	#3532	1	2	yes	—
472	C₂²×D₄	#2403	1	4	yes	—
473	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
474	C₂²×D₄	C₂×D₄²	1	2	yes	—
475	C₂²×D₄	C₂×D₄²	1	2	yes	—
476	C₂²×D₄	C₂×#546	1	2	yes	—
477	C₂²×D₄	#3484	1	2	yes	—
478	C₂²×D₄	#3484	1	2	yes	—
479	C₂²×D₄	#3484	1	2	yes	—
480	C₂²×D₄	#3490	1	2	yes	—
481	C₂²×D₄	#3532	1	2	yes	—
482	C₂³×C₄	#2404	1	1	yes	characteristic
483	C₂³×C₄	#2404	1	1	yes	characteristic
484	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
485	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
486	C₂³×C₄	C₂×#525	1	1	yes	characteristic
487	C₂³×C₄	C₂×#546	1	2	yes	—
488	C₂³×C₄	C₂×#546	1	1	yes	characteristic
489	C₂³×C₄	#3490	1	2	yes	—
490	C₂×C₂²⋊C₄	#2403	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
492	C₂⁴	#23900	1	4	yes	—
493	C₂⁴	#23984	1	1	yes	characteristic
494	C₂⁴	#23984	1	1	yes	characteristic
495	C₂⁴	#23984	1	2	yes	—
496	C₂⁴	#23984	1	2	yes	—
497	C₂⁴	#23984	1	2	yes	—
498	C₂⁴	#23996	1	2	yes	—
499	C₂⁴	#23996	1	2	yes	—
500	C₂⁴	#23996	1	2	yes	—
501	C₂⁴	C₂×#2403	1	1	yes	characteristic
502	C₂⁴	C₂×#2404	1	1	yes	characteristic
503	C₂⁴	#35346	1	1	yes	characteristic
504	C₂⁴	#36152	1	1	yes	characteristic
505	C₂⁴	#36152	1	1	yes	characteristic
506	C₂⁴	#37645	1	2	yes	—
507	C₂⁴	#37832	1	1	yes	characteristic
508	C₂⁴	#37832	1	1	yes	characteristic
509	C₂⁴	#58991	1	2	yes	—
510	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
511	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
512	C₂²×C₄	#23900	1	4	yes	—
513	C₂²×C₄	#36098	1	2	yes	—
514	C₂²×C₄	#58991	1	2	yes	—
515	C₂³	#251827	1	4	yes	—
516	C₂³	#647657	1	1	yes	characteristic
517	C₂³	C₂×#23900	1	2	yes	—
518	C₂³	C₂×#23996	1	1	yes	characteristic
519	C₂³	C₂×#23996	1	1	yes	characteristic
520	C₂³	C₂×#23996	1	1	yes	characteristic
521	C₂³	#6451863	1	1	yes	characteristic
522	C₂³	C₂×#23984	1	1	yes	characteristic
523	C₂³	C₂×#23984	1	1	yes	characteristic
524	C₂³	#6499867	1	2	yes	—
525	C₂²	#72217617	1	1	yes	characteristic
526	C₂²	#72225632	1	1	yes	characteristic
527	C₂²	#72233156	1	1	yes	characteristic
528	C₂²	#72234644	1	1	yes	characteristic
529	C₂²	#72234955	1	1	yes	characteristic
530	C₂²	#72240110	1	1	yes	characteristic
531	C₂²	C₂×#251827	1	1	yes	characteristic
532	C₂	#72255637	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72255637
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72315417	C₂	semidirect
2. #72315362	C₂	semidirect
3. #72315298	C₂	semidirect
4. #72315258	C₂	semidirect
5. #72315164	C₂	semidirect
6. #72315084	C₂	semidirect
7. #72314961	C₂	semidirect
8. #72314824	C₂	semidirect
9. #72314791	C₂	semidirect
10. #72314748	C₂²	semidirect
11. #72314748	C₂²	semidirect
12. #72314734	C₂²	semidirect
13. #72314708	C₂	semidirect
14. #72314665	C₂²	semidirect
15. #72310290	C₂	semidirect
16. #72266873	C₂	semidirect
17. #72262357	C₂	semidirect
18. #72262349	C₂	semidirect
19. #72258094	C₂²	semidirect
20. #72258094	C₂²	semidirect
21. #72258019	C₂²	semidirect
22. #72258019	C₂²	semidirect
23. #72256195	C₂²	semidirect
24. #72256193	C₂²	semidirect
25. #72256048	C₂²	semidirect
26. #72256043	C₂²	semidirect
27. #72255986	C₂²	semidirect
28. #72255977	C₂²	semidirect
29. #72255849	C₂²	semidirect
30. #72255841	C₂²	semidirect
31. #72255841	C₂²	semidirect
32. #72255793	C₂²	semidirect
33. #72255778	C₂²	semidirect
34. #72255777	C₂²	semidirect
35. #72255774	C₂²	semidirect
36. #72255772	C₂²	semidirect
37. #72251547	C₂	semidirect
38. #72251533	C₂²	semidirect
39. #72251530	C₂²	semidirect
40. #72251528	C₂²	semidirect
41. #72251527	C₂²	semidirect
42. #72240489	C₂	semidirect
43. #72240132	C₂²	semidirect
44. #72240132	C₂²	semidirect
45. #72238344	C₂	semidirect
46. #72238343	C₂²	semidirect
47. #72238343	C₂²	semidirect
48. #72238342	C₂²	semidirect
49. #72238342	C₂²	semidirect
50. #72237423	C₂	semidirect
58. #72237045	C₂²	semidirect
59. #72237045	C₂²	semidirect
60. #72236928	C₂²	semidirect
61. #72236928	C₂²	semidirect
63. #72225747	C₂	semidirect
64. #72225745	C₂²	semidirect
65. #72225744	C₂²	semidirect
66. #72225743	C₂²	semidirect
67. #72225742	C₂²	semidirect
68. #72225742	C₂²	semidirect
69. #72225741	C₂²	semidirect
70. #72225740	C₂²	semidirect
71. C₂×#7266798	C₂²	semidirect
72. #72225667	C₂²	semidirect
73. #72225617	C₂²	semidirect
74. #72219445	C₂	semidirect
75. #72219418	C₂²	semidirect
76. #72219414	C₂²	semidirect
79. #72219158	C₂²	semidirect
80. #72219158	C₂²	semidirect
81. #72218868	C₂	semidirect
82. #72218847	C₂	semidirect
83. #72218521	C₂²	semidirect
84. #72218521	C₂²	semidirect
85. #72218518	C₂²	semidirect
86. #72218498	C₂²	semidirect
87. #72218498	C₂²	semidirect
88. #72218391	C₂²	semidirect
89. #72218391	C₂²	semidirect
90. #72218381	C₂²	semidirect
91. #72218381	C₂²	semidirect
92. #72218313	C₂²	semidirect
95. #72218222	C₂	semidirect
96. #72218215	C₂²	semidirect
97. #72218215	C₂²	semidirect
98. #72218206	C₂²	semidirect
99. #72218206	C₂²	semidirect
100. #72218198	C₂²	semidirect
101. #72218180	C₂²	semidirect
102. C₂×#139750	C₂²	semidirect
103. C₂×#139750	C₂²	semidirect
104. #72218057	C₂²	semidirect
108. C₂×#144378	C₂²	semidirect
109. C₂×#144378	C₂²	semidirect
110. C₂×#139731	C₂²	semidirect
111. C₂×#139731	C₂²	semidirect
112. #72217789	C₂²	semidirect
113. #72215858	C₂²	semidirect
114. #72215179	C₂²	semidirect
129. C₂²×#2846	D₄	semidirect
131. C₂×#32873	C₂³	semidirect
132. C₂×#23895	D₄	semidirect
136. #6437621	D₄	semidirect
137. C₂×#23900	D₄	semidirect
138. C₂×#23900	D₄	semidirect
145. C₂×#23900	C₂³	semidirect
146. C₂×#23900	C₂³	semidirect
148. C₂×#21776	D₄	semidirect
152. C₂×#21776	C₂³	semidirect
153. C₂×#21746	C₂³	semidirect
154. C₂×#21746	C₂³	semidirect
155. C₂²×#1898	D₄	semidirect
156. #6370693	D₄	semidirect
166. C₂×#12707	C₂³	semidirect
177. C₂×#12687	C₂³	semidirect
178. C₂×#12687	C₂³	semidirect
179. #392231	D₄	semidirect
187. #392030	C₂³	semidirect
188. #392030	C₂³	semidirect
189. #392030	C₂³	semidirect
190. #382544	C₂³	semidirect
191. #382434	D₄	semidirect
195. #382434	C₂³	semidirect
196. #382422	C₂³	semidirect
197. #382422	C₂³	semidirect
198. #359549	D₄	semidirect
203. #359501	C₂³	semidirect
204. #359501	C₂³	semidirect
205. #359442	D₄	semidirect
206. #355096	C₂³	semidirect
207. #347047	D₄	semidirect
208. #347045	D₄	semidirect
211. C₂×#8541	C₂³	semidirect
212. C₂×#8541	C₂³	semidirect
217. #187944	C₂³	semidirect
218. #146479	C₂³	semidirect
219. #128033	C₂³	semidirect
220. #128033	C₂³	semidirect
221. C₂×#7316	C₂³	semidirect
222. C₂×#7316	C₂³	semidirect
223. C₂×#7314	C₂³	semidirect
224. C₂×#7314	C₂³	semidirect
225. C₂×#7310	C₂³	semidirect
226. C₂×#7310	C₂³	semidirect
227. C₂×#7310	C₂³	semidirect
228. C₂×#7310	C₂³	semidirect
229. C₂×#7310	C₂³	semidirect
230. C₂×#7310	C₂³	semidirect
231. #128009	C₂³	semidirect
232. #128009	C₂³	semidirect
233. #128009	C₂³	semidirect
234. #128009	C₂³	semidirect
235. #107114	C₂³	semidirect
238. C₂³×H(5,𝔽₂)	#41	semidirect
239. C₂³×H(5,𝔽₂)	#41	semidirect
249. C₂×#3484	#41	semidirect
256. C₂²×#525	#41	semidirect
263. C₂²×#518	#41	semidirect
264. C₂²×#518	#41	semidirect
266. C₂×#3026	C₂×D₄	semidirect
267. C₂×#3026	C₂×D₄	semidirect
268. C₂×#2883	C₂×D₄	semidirect
269. C₂×#2883	C₂×D₄	semidirect
280. C₂×#1913	C₂×D₄	semidirect
281. C₂×#1913	C₂×D₄	semidirect
282. C₂×#1913	C₂×D₄	semidirect
283. C₂×#1913	C₂×D₄	semidirect
288. #20960	C₂×D₄	semidirect
289. #20960	C₂×D₄	semidirect
290. C₂×#1828	C₂×D₄	semidirect
291. C₂×#1828	C₂×D₄	semidirect
292. C₂×#1828	C₂×D₄	semidirect
293. C₂×#1828	C₂×D₄	semidirect
295. #20585	C₂×D₄	semidirect
296. #20585	C₂×D₄	semidirect
381. #2846	#120	semidirect
384. #1898	#120	semidirect
404. C₂×H(5,𝔽₂)	#546	semidirect
405. C₂³×Q₈	#546	semidirect
422. C₂³×D₄	#546	semidirect
443. #518	#546	semidirect
447. C₂²×C₄²	#546	semidirect
448. C₂²×C₄²	#546	semidirect

Maximal subgroups

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

subgroup	index
#72315417	2
#72315362	2
#72315298	2
#72315258	2
#72315164	2
#72315084	2
#72314961	2
#72314824	2
#72314791	2
#72314708	2
#72310290	2
#72266873	2
#72262357	2
#72262349	2
#72251547	2
#72240489	2
#72238344	2
#72237423	2
#72225747	2
#72219445	2
#72218868	2
#72218847	2
#72218222	2