Subgroups — #72337601

Order 8192.

Only the 914 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 566 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337600	C₂	1	2	yes	maximal, complemented
2	#72337595	C₂	1	2	yes	maximal, complemented
3	#72337587	C₂	1	2	yes	maximal, complemented
4	#72337573	C₂	1	2	yes	maximal, complemented
5	#72334286	C₂	1	1	yes	maximal, characteristic, complemented
6	#72329062	C₂	1	1	yes	maximal, characteristic
7	#72327645	C₄	1	2	yes	complemented
8	#72327645	C₄	1	2	yes	complemented
9	#72327288	C₂²	1	2	yes	—
10	#72327288	C₂²	1	2	yes	—
11	#72327248	D₄	1	2	yes	—
12	#72327248	D₄	1	2	yes	—
13	#72327244	D₄	1	2	yes	—
14	#72327244	D₄	1	2	yes	—
15	#72327231	D₄	1	2	yes	—
16	#72327231	D₄	1	2	yes	—
17	#72326786	D₄	1	2	yes	—
18	#72326786	D₄	1	2	yes	—
19	#72318215	D₄	1	2	yes	—
20	#72318215	D₄	1	2	yes	—
21	#72313138	C₄	1	1	yes	characteristic, complemented
22	#72310618	C₂	1	1	yes	maximal, characteristic, complemented
23	#72310535	C₂²	1	2	yes	complemented
24	#72309341	C₄	1	1	yes	characteristic, complemented
25	#72309335	C₂×C₄	1	2	yes	—
26	#72309335	C₂×C₄	1	2	yes	—
27	#72302118	C₂	1	1	yes	maximal, characteristic, complemented
28	#72302078	C₂²	1	1	yes	characteristic, complemented
29	#72302062	C₂²	1	1	yes	characteristic, complemented
30	#72302047	C₂²	1	1	yes	characteristic, complemented
31	#72302019	C₂²	1	1	yes	characteristic, complemented
32	#72283093	C₂×C₄	1	2	yes	—
33	#72283093	C₂×C₄	1	2	yes	—
34	#72256276	C₂	1	1	yes	maximal, characteristic, complemented
35	#72238419	C₂	1	1	yes	maximal, characteristic, complemented
36	#72237771	C₂²	1	2	yes	complemented
37	#72237771	C₂²	1	2	yes	complemented
38	#72237770	C₂²	1	2	yes	complemented
39	#72237770	C₂²	1	2	yes	complemented
40	#72237770	C₂²	1	2	yes	complemented
41	#72237630	C₂²	1	1	yes	characteristic, complemented
42	#72237628	C₂²	1	1	yes	characteristic
43	#72237624	D₄	1	2	yes	—
44	#72237620	D₄	1	2	yes	—
45	#72237618	D₄	1	1	yes	characteristic
46	#72237612	C₂×C₄	1	2	yes	—
47	#72236376	C₄	1	1	yes	characteristic, complemented
48	#72234688	C₂²	1	1	yes	characteristic, complemented
49	#72234668	D₄	1	1	yes	characteristic
50	#72234665	C₂²	1	1	yes	characteristic
51	#72234663	D₄	1	1	yes	characteristic
52	#72234625	D₄	1	1	yes	characteristic
53	#72234619	C₂×C₄	1	1	yes	characteristic
54	#72234619	C₂×C₄	1	1	yes	characteristic
55	#72234591	D₄	1	1	yes	characteristic
56	#72234591	D₄	1	1	yes	characteristic
57	#72232884	D₄	1	1	yes	characteristic
58	#72232592	D₄	1	1	yes	characteristic
59	#72226360	C₂	1	1	yes	maximal, characteristic, complemented
60	#72226357	C₂²	1	2	yes	complemented
61	#72226352	C₂²	1	2	yes	complemented
62	#72226352	C₂²	1	2	yes	complemented
63	#72226352	C₂²	1	2	yes	complemented
64	#72225883	C₂²	1	1	yes	characteristic, complemented
65	#72225873	C₂³	1	2	yes	complemented
66	#72225873	C₂³	1	2	yes	complemented
67	#72225781	C₂²	1	1	yes	characteristic, complemented
68	#72225777	C₂³	1	1	yes	characteristic, complemented
69	#72225776	C₂³	1	1	yes	characteristic, complemented
70	#72225776	C₂³	1	1	yes	characteristic, complemented
71	#72225776	C₂³	1	1	yes	characteristic, complemented
72	#72225733	C₂³	1	2	yes	—
73	#72225660	D₄	1	2	yes	—
74	#72225660	D₄	1	2	yes	—
75	#72225655	C₂³	1	1	yes	characteristic
76	#72225655	C₂³	1	1	yes	characteristic
77	#72224136	D₄	1	1	yes	characteristic
78	#72224136	D₄	1	1	yes	characteristic
79	C₂×#72217546	C₂²	1	1	yes	characteristic
80	C₂×#417744	D₄	1	2	yes	—
81	C₂×#417493	C₂×C₄	1	2	yes	—
82	C₂×#417493	D₄	1	2	yes	—
83	C₂×#374022	D₄	1	1	yes	characteristic
84	C₂×#359428	C₂×C₄	1	1	yes	characteristic
85	C₂×#359428	D₄	1	1	yes	characteristic
86	C₂×#7670203	C₂³	1	1	yes	characteristic
87	#72218920	C₂×C₄	1	2	yes	—
88	#72218920	C₂×C₄	1	2	yes	—
89	#72217947	C₄	1	1	yes	characteristic, complemented
90	#72217789	C₂×C₄	1	1	yes	characteristic
91	C₂³×#2846	C₂×C₄	1	1	yes	characteristic
92	C₂³×#2846	D₄	1	1	yes	characteristic
93	#72217730	C₂×C₄	1	2	yes	—
94	#72217730	C₂×C₄	1	2	yes	—
95	#72217511	C₂×C₄	1	1	yes	characteristic
96	#72217511	C₂×C₄	1	1	yes	characteristic
97	#72217511	C₂×C₄	1	1	yes	characteristic
98	C₂×#449475	C₂³	1	2	yes	—
99	#72216646	D₄	1	2	yes	—
100	#72216646	D₄	1	2	yes	—
101	#72216064	D₄	1	1	yes	characteristic
102	#72216064	D₄	1	1	yes	characteristic
103	C₂×#6342371	D₄	1	1	yes	characteristic
104	#72210024	D₄	1	2	yes	—
105	#72210024	D₄	1	2	yes	—
106	C₂⁹	C₂²⋊C₄	1	1	yes	characteristic, complemented
107	#10586404	C₂²⋊C₄	1	1	yes	characteristic
108	#10586404	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×#62817	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×#62817	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×#62817	C₂²⋊C₄	1	1	yes	characteristic, complemented
112	#10586066	C₂×D₄	1	1	yes	characteristic
113	#10586066	C₂×D₄	1	1	yes	characteristic
114	C₂²×#3484	C₂×D₄	1	1	yes	characteristic
115	C₂²×#3484	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×#120	C₂²×C₄	1	1	yes	characteristic
117	C₂⁴×#120	C₂×D₄	1	1	yes	characteristic
118	#8093108	C₂²⋊C₄	1	2	yes	complemented
119	#8093108	C₂²⋊C₄	1	2	yes	complemented
120	#8093107	C₂²⋊C₄	1	2	yes	complemented
121	#8093107	C₂²⋊C₄	1	2	yes	complemented
122	#7670230	C₂²⋊C₄	1	2	yes	complemented
123	#7670230	C₂²⋊C₄	1	2	yes	complemented
124	#7670203	C₂²⋊C₄	1	2	yes	complemented
125	#7670203	C₂²⋊C₄	1	2	yes	complemented
126	#7642273	C₂²×C₄	1	2	yes	—
127	#7642244	C₂²×C₄	1	1	yes	characteristic
128	#7642244	C₂²×C₄	1	1	yes	characteristic
129	#7642244	C₂²×C₄	1	1	yes	characteristic
130	#7642244	C₂²×C₄	1	1	yes	characteristic
131	C₂²×#2846	C₂²⋊C₄	1	2	yes	complemented
132	C₂²×#2846	C₂²⋊C₄	1	2	yes	complemented
133	C₂²×#2846	C₂²×C₄	1	2	yes	—
134	C₂²×#2846	C₂×D₄	1	2	yes	—
135	C₂²×#2846	C₂×D₄	1	2	yes	—
136	C₂²×#2846	C₂×D₄	1	1	yes	characteristic
137	#7630944	C₂²⋊C₄	1	2	yes	complemented
138	#7630939	C₂²⋊C₄	1	1	yes	characteristic
139	#7630939	C₂²⋊C₄	1	1	yes	characteristic
140	#7630939	C₂²⋊C₄	1	1	yes	characteristic
141	#7630939	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×#35390	C₂×D₄	1	1	yes	characteristic
143	C₂×#35348	C₂²×C₄	1	1	yes	characteristic
144	C₂×#35348	C₂×D₄	1	1	yes	characteristic
145	C₂×#35346	C₂⁴	1	1	yes	characteristic
146	C₂×#34981	C₂×D₄	1	1	yes	characteristic
147	C₂×#34981	C₂×D₄	1	1	yes	characteristic
148	C₂×#34980	C₂×D₄	1	1	yes	characteristic
149	C₂×#34980	C₂×D₄	1	1	yes	characteristic
150	#7626202	C₂²⋊C₄	1	1	yes	characteristic
151	#7626202	C₂²⋊C₄	1	1	yes	characteristic
152	#7626202	C₂²⋊C₄	1	1	yes	characteristic, complemented
153	C₂×#34198	C₂×D₄	1	1	yes	characteristic
154	C₂×#34198	C₂×D₄	1	1	yes	characteristic
155	C₂³×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	C₂³×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	#6629262	C₂×D₄	1	2	yes	—
158	#6629262	C₂×D₄	1	2	yes	—
159	#6628896	C₂×D₄	1	2	yes	—
160	#6628896	C₂×D₄	1	2	yes	—
161	#6453039	C₂²⋊C₄	1	2	yes	complemented
162	#6451874	C₂²⋊C₄	1	2	yes	complemented
163	#6451874	C₂×D₄	1	2	yes	—
164	#6451874	C₂×D₄	1	2	yes	—
165	#6432953	C₂×D₄	1	2	yes	—
166	#6432953	C₂×D₄	1	2	yes	—
167	#6432953	C₂×D₄	1	2	yes	—
168	#6432953	C₂×D₄	1	2	yes	—
169	#6374210	C₂×D₄	1	1	yes	characteristic
170	#6374210	C₂×D₄	1	1	yes	characteristic
171	#6374210	C₂×D₄	1	1	yes	characteristic
172	#6374210	C₂×D₄	1	1	yes	characteristic
173	#6374128	C₂²⋊C₄	1	1	yes	characteristic
174	#6374128	C₂²⋊C₄	1	1	yes	characteristic
175	C₂×#21746	C₂²⋊C₄	1	1	yes	characteristic, complemented
176	C₂×#21746	C₂²⋊C₄	1	1	yes	characteristic, complemented
177	#6371504	C₂²⋊C₄	1	1	yes	characteristic
178	#6371504	C₂²⋊C₄	1	1	yes	characteristic
179	#6371504	C₂²⋊C₄	1	1	yes	characteristic
180	#6371504	C₂²⋊C₄	1	1	yes	characteristic
181	#6370693	C₂×D₄	1	1	yes	characteristic
182	#6370693	C₂×D₄	1	1	yes	characteristic
183	C₂×#14679	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	C₂×#14679	C₂²⋊C₄	1	2	yes	complemented
185	#449521	C₂²⋊C₄	1	2	yes	complemented
186	#449521	C₂²⋊C₄	1	2	yes	complemented
187	#449521	C₂²⋊C₄	1	2	yes	complemented
188	#449521	C₂²⋊C₄	1	2	yes	complemented
189	#449475	C₂²⋊C₄	1	2	yes	complemented
190	#449475	C₂²⋊C₄	1	2	yes	complemented
191	#449475	C₂²⋊C₄	1	2	yes	complemented
192	#449475	C₂²⋊C₄	1	2	yes	complemented
193	#449475	C₂×D₄	1	2	yes	—
194	#449475	C₂×D₄	1	2	yes	—
195	#449475	C₂×D₄	1	2	yes	—
196	#449475	C₂×D₄	1	2	yes	—
197	#449475	C₂×D₄	1	2	yes	—
198	#449475	C₂×D₄	1	2	yes	—
199	#449475	C₂×D₄	1	2	yes	—
200	#449475	C₂×D₄	1	2	yes	—
201	#418213	C₂²⋊C₄	1	2	yes	complemented
202	#418213	C₂²⋊C₄	1	2	yes	complemented
203	#418132	C₂²⋊C₄	1	2	yes	complemented
204	#418132	C₂²⋊C₄	1	2	yes	complemented
205	#417896	C₂²⋊C₄	1	2	yes	complemented
206	#417896	C₂²⋊C₄	1	2	yes	complemented
207	#417896	C₂×D₄	1	2	yes	—
208	#417896	C₂×D₄	1	2	yes	—
209	#417896	C₂×D₄	1	2	yes	—
210	#417896	C₂×D₄	1	2	yes	—
211	#417824	C₂²⋊C₄	1	2	yes	complemented
212	#417824	C₂²⋊C₄	1	2	yes	complemented
213	#417824	C₂×D₄	1	2	yes	—
214	#417824	C₂×D₄	1	2	yes	—
215	#417824	C₂×D₄	1	2	yes	—
216	#417824	C₂×D₄	1	2	yes	—
217	#392207	C₂²⋊C₄	1	2	yes	complemented
218	#391735	C₂²⋊C₄	1	2	yes	complemented
219	#391735	C₂²⋊C₄	1	2	yes	complemented
220	#391709	C₂²⋊C₄	1	2	yes	complemented
221	#391709	C₂²⋊C₄	1	2	yes	complemented
222	#382422	C₂²×C₄	1	2	yes	—
223	#375666	C₂²⋊C₄	1	2	yes	complemented
224	#375666	C₂²⋊C₄	1	2	yes	complemented
225	#374004	C₂²⋊C₄	1	2	yes	complemented
226	#374004	C₂²⋊C₄	1	2	yes	complemented
227	#359921	C₂²⋊C₄	1	2	yes	complemented
228	#359705	C₂²⋊C₄	1	2	yes	complemented
229	#359705	C₂×D₄	1	2	yes	—
230	#359705	C₂×D₄	1	2	yes	—
231	C₂×#11196	C₂²⋊C₄	1	2	yes	complemented
232	C₂×#10965	C₂²⋊C₄	1	2	yes	complemented
233	C₂×#10965	C₂²⋊C₄	1	2	yes	complemented
234	C₂×#10965	C₂²×C₄	1	2	yes	—
235	C₂×#10965	C₂×D₄	1	2	yes	—
236	C₂×#10965	C₂×D₄	1	2	yes	—
237	C₂⁸	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂⁸	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂×H(7,𝔽₂)	#120	1	1	yes	characteristic
240	C₂×H(7,𝔽₂)	#120	1	1	yes	characteristic
241	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
242	C₂⁵×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂⁵×D₄	#120	1	1	yes	characteristic
244	#62842	#120	1	1	yes	characteristic
245	#62842	#120	1	1	yes	characteristic
246	#62842	#120	1	1	yes	characteristic
247	#62842	#120	1	1	yes	characteristic
248	C₂×#3490	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂×#3484	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×#3484	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×#3484	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×#3484	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×#3532	#99	1	4	yes	—
254	C₂²×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×#534	#120	1	1	yes	characteristic
256	C₂²×#534	#120	1	1	yes	characteristic
257	C₂²×#534	#120	1	1	yes	characteristic
258	C₂²×#534	#120	1	1	yes	characteristic
259	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂³×#120	#120	1	1	yes	characteristic
264	C₂³×#120	#120	1	1	yes	characteristic
265	C₂³×#120	#120	1	1	yes	characteristic
266	C₂³×#120	#120	1	1	yes	characteristic
267	C₂³×#120	C₂³×C₄	1	1	yes	characteristic
268	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
269	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
270	#62652	#120	1	1	yes	characteristic
271	#62652	#120	1	1	yes	characteristic
272	C₂²×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×#518	#120	1	1	yes	characteristic
274	C₂⁴×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂⁴×C₂²⋊C₄	#120	1	1	yes	characteristic
276	#36614	#99	1	2	yes	—
277	C₂×#2846	#99	1	2	yes	—
278	C₂×#2846	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×#2846	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂×#2846	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂×#2846	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂×#2846	#120	1	2	yes	—
283	C₂×#2846	#120	1	2	yes	—
284	C₂×#2846	#120	1	2	yes	—
285	C₂×#2846	#120	1	2	yes	—
286	C₂×#2846	#120	1	2	yes	—
287	C₂×#2846	#120	1	2	yes	—
288	C₂×#2846	#120	1	2	yes	—
289	C₂×#2846	#120	1	2	yes	—
290	#35390	C₂×C₂²⋊C₄	1	2	yes	—
291	#35390	C₂×C₂²⋊C₄	1	2	yes	—
292	#35367	C₂×C₂²⋊C₄	1	2	yes	—
293	#35367	C₂×C₂²⋊C₄	1	2	yes	—
294	#35350	C₂×C₂²⋊C₄	1	2	yes	—
295	#35350	C₂×C₂²⋊C₄	1	2	yes	—
296	#35350	C₂×C₂²⋊C₄	1	2	yes	—
297	#35350	C₂×C₂²⋊C₄	1	2	yes	—
298	#35346	C₂×C₂²⋊C₄	1	2	yes	—
299	#35346	C₂×C₂²⋊C₄	1	2	yes	—
300	#35346	C₂×C₂²⋊C₄	1	2	yes	—
301	#35346	C₂×C₂²⋊C₄	1	2	yes	—
302	#35346	C₂²×D₄	1	2	yes	—
303	#35346	C₂²×D₄	1	2	yes	—
304	#35346	C₂²×D₄	1	2	yes	—
305	#35346	C₂²×D₄	1	2	yes	—
306	#35222	#99	1	2	yes	—
307	#34980	#99	1	2	yes	—
308	#34356	#99	1	4	yes	—
309	#34176	C₂×C₂²⋊C₄	1	2	yes	—
310	#34171	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	#34171	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	#34171	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	#34171	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×#2315	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×#2315	#120	1	1	yes	characteristic
316	C₂×#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×#2308	#120	1	1	yes	characteristic
318	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
319	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
320	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
321	C₂²×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×#379	C₂×C₂²⋊C₄	1	2	yes	—
323	C₂²×#379	C₂×C₂²⋊C₄	1	2	yes	—
324	C₂²×#379	C₂×C₂²⋊C₄	1	2	yes	—
325	C₂²×#379	#120	1	1	yes	characteristic
326	C₂²×#379	#120	1	1	yes	characteristic
327	C₂×#2273	#120	1	1	yes	characteristic
328	#23468	#120	1	2	yes	—
329	#23468	#120	1	2	yes	—
330	#23468	#120	1	2	yes	—
331	#23468	#120	1	2	yes	—
332	#23444	#120	1	2	yes	—
333	#23444	#120	1	2	yes	—
334	#23444	#120	1	2	yes	—
335	#23444	#120	1	2	yes	—
336	#20689	#120	1	2	yes	—
337	#20689	#120	1	2	yes	—
338	#20689	#120	1	2	yes	—
339	#20689	#120	1	2	yes	—
340	C₂×#1819	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂×#1819	C₂×C₂²⋊C₄	1	2	yes	—
342	#20585	#120	1	2	yes	—
343	#20585	#120	1	2	yes	—
344	#20585	#120	1	2	yes	—
345	#20585	#120	1	2	yes	—
346	#20585	#120	1	2	yes	—
347	#20585	#120	1	2	yes	—
348	#20585	#120	1	2	yes	—
349	#20585	#120	1	2	yes	—
350	#10965	C₂×C₂²⋊C₄	1	2	yes	—
351	#10965	C₂×C₂²⋊C₄	1	2	yes	—
352	#10965	C₂×C₂²⋊C₄	1	2	yes	—
353	#10965	C₂×C₂²⋊C₄	1	2	yes	—
354	#10965	C₂×C₂²⋊C₄	1	2	yes	—
355	#10965	C₂×C₂²⋊C₄	1	2	yes	—
356	#10965	C₂×C₂²⋊C₄	1	2	yes	—
357	#10965	C₂×C₂²⋊C₄	1	2	yes	—
358	#10965	#120	1	2	yes	—
359	#10965	#120	1	2	yes	—
360	#10965	#120	1	2	yes	—
361	#10965	#120	1	2	yes	—
362	#10965	#120	1	2	yes	—
363	#10965	#120	1	2	yes	—
364	#10965	#120	1	2	yes	—
365	#10965	#120	1	2	yes	—
366	#10938	#120	1	2	yes	—
367	#10938	#120	1	2	yes	—
368	#10938	#120	1	2	yes	—
369	#10938	#120	1	2	yes	—
370	#10938	#120	1	2	yes	—
371	#10938	#120	1	2	yes	—
372	#10938	#120	1	2	yes	—
373	#10938	#120	1	2	yes	—
374	C₂⁷	#379	1	2	yes	—
375	C₂⁷	#379	1	2	yes	—
376	C₂⁷	#379	1	1	yes	characteristic
377	C₂⁷	#379	1	1	yes	characteristic
378	C₂⁷	C₂×#99	1	1	yes	characteristic
379	C₂⁷	B(4,𝔽₂)	1	1	yes	characteristic
380	C₂⁷	C₂²×C₂²⋊C₄	1	1	yes	characteristic
381	C₂²×H(5,𝔽₂)	#379	1	1	yes	characteristic
382	C₂²×H(5,𝔽₂)	#379	1	1	yes	characteristic
383	C₂²×H(5,𝔽₂)	#379	1	1	yes	characteristic
384	C₂²×H(5,𝔽₂)	#379	1	1	yes	characteristic
385	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
386	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
387	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
388	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
389	C₂⁴×D₄	#379	1	1	yes	characteristic
390	C₂⁴×D₄	#379	1	1	yes	characteristic
391	C₂⁴×D₄	C₂×#99	1	1	yes	characteristic
392	C₂⁴×D₄	C₂×#99	1	1	yes	characteristic
393	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic
394	C₂⁴×D₄	#458	1	1	yes	characteristic
395	C₂⁴×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
396	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
397	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
398	C₂⁵×C₄	C₂×#99	1	1	yes	characteristic
399	C₂⁵×C₄	#458	1	1	yes	characteristic
400	C₂×H(3,𝔽₄)	AΣL(1,𝔽₁₆)	1	4	yes	complemented
401	C₂×#560	AΣL(1,𝔽₁₆)	1	4	yes	complemented
402	C₂×#551	AΣL(1,𝔽₁₆)	1	4	yes	complemented
403	C₂×D₄²	AΣL(1,𝔽₁₆)	1	4	yes	complemented
404	C₂×#543	#379	1	2	yes	—
405	C₂×#535	C₂×#99	1	2	yes	—
406	C₂×#534	#379	1	2	yes	—
407	C₂×#534	C₂×#99	1	2	yes	—
408	C₂×#525	C₂×#99	1	2	yes	—
409	C₂²×#120	C₂×#99	1	2	yes	—
410	C₂²×#120	C₂×#99	1	2	yes	—
411	C₂²×#120	C₂×#99	1	2	yes	—
412	C₂²×#120	B(4,𝔽₂)	1	2	yes	—
413	C₂²×#120	#458	1	2	yes	—
414	C₂²×#120	C₂²×C₂²⋊C₄	1	2	yes	—
415	C₂²×#120	C₂²×C₂²⋊C₄	1	2	yes	—
416	C₂²×#120	C₂×#120	1	2	yes	—
417	C₂²×#120	C₂×#120	1	2	yes	—
418	C₂²×#120	C₂×#120	1	2	yes	—
419	C₂²×#120	C₂×#120	1	2	yes	—
420	C₂×#518	#379	1	1	yes	characteristic
421	C₂×#518	#379	1	1	yes	characteristic
422	C₂×#518	#379	1	1	yes	characteristic
423	C₂×#518	#379	1	1	yes	characteristic
424	C₂³×C₂²⋊C₄	#379	1	1	yes	characteristic
425	C₂³×C₂²⋊C₄	#379	1	1	yes	characteristic
426	C₂³×C₂²⋊C₄	#379	1	1	yes	characteristic
427	C₂³×C₂²⋊C₄	#379	1	1	yes	characteristic
428	C₂³×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
429	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
430	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
431	#2309	C₂×#99	1	2	yes	—
432	#2308	#379	1	2	yes	—
433	#2308	#379	1	2	yes	—
434	#2308	#379	1	2	yes	—
435	#2308	#379	1	2	yes	—
436	#2308	C₂×#99	1	2	yes	—
437	#2308	C₂×#120	1	2	yes	—
438	#2308	C₂×#120	1	2	yes	—
439	#2308	C₂×#120	1	2	yes	—
440	#2308	C₂×#120	1	2	yes	—
441	#2308	C₂×#120	1	2	yes	—
442	#2308	C₂×#120	1	2	yes	—
443	#2280	C₂×#99	1	2	yes	—
444	C₂×#379	#379	1	2	yes	—
445	C₂×#379	#379	1	2	yes	—
446	C₂×#379	#379	1	2	yes	—
447	C₂×#379	#379	1	2	yes	—
448	C₂×#379	#379	1	2	yes	—
449	C₂×#379	#379	1	2	yes	—
450	C₂×#379	C₂×#99	1	2	yes	—
451	#2273	#379	1	2	yes	—
452	#2273	#379	1	2	yes	—
453	C₂×#342	#379	1	2	yes	—
454	C₂×#342	#379	1	2	yes	—
455	C₂×#342	#379	1	2	yes	—
456	C₂×#342	#379	1	2	yes	—
457	C₂⁶	#1781	1	2	yes	—
458	C₂⁶	#1781	1	1	yes	characteristic
459	C₂⁶	#1781	1	1	yes	characteristic
460	C₂⁶	#1781	1	1	yes	characteristic
461	C₂⁶	#1790	1	1	yes	characteristic
462	C₂⁶	#1790	1	1	yes	characteristic
463	C₂⁶	#1790	1	2	yes	—
464	C₂⁶	#1790	1	1	yes	characteristic
465	C₂⁶	C₂×#379	1	2	yes	—
466	C₂⁶	C₂×#379	1	1	yes	characteristic
467	C₂⁶	C₂²×#99	1	1	yes	characteristic
468	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
469	C₂⁶	#3026	1	1	yes	characteristic
470	C₂²×#41	#1781	1	2	yes	—
471	C₂³×D₄	#1781	1	2	yes	—
472	C₂³×D₄	C₂×#379	1	1	yes	characteristic
473	C₂³×D₄	C₂×#379	1	1	yes	characteristic
474	C₂³×D₄	#2846	1	1	yes	characteristic
475	C₂³×D₄	#2846	1	1	yes	characteristic
476	C₂³×D₄	#2846	1	1	yes	characteristic
477	C₂³×D₄	#2846	1	1	yes	characteristic
478	C₂³×D₄	C₂²×#99	1	1	yes	characteristic
479	C₂³×D₄	C₂²×#99	1	1	yes	characteristic
480	C₂³×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
481	C₂³×D₄	C₂×#458	1	1	yes	characteristic
482	C₂³×D₄	#3026	1	1	yes	characteristic
483	C₂³×D₄	#3026	1	1	yes	characteristic
484	C₂⁴×C₄	#1781	1	1	yes	characteristic
485	C₂⁴×C₄	#1790	1	1	yes	characteristic
486	C₂⁴×C₄	C₂²×#99	1	1	yes	characteristic
487	C₂⁴×C₄	C₂×#458	1	1	yes	characteristic
488	C₂⁴×C₄	#3026	1	1	yes	characteristic
489	C₂×#127	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
490	C₂×#124	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
491	C₂×#123	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
492	C₂×#120	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
493	C₂×#120	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
494	C₂×#120	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
495	C₂×#117	#1781	1	2	yes	—
496	C₂²×C₂²⋊C₄	#1781	1	2	yes	—
497	C₂²×C₂²⋊C₄	#1781	1	2	yes	—
498	C₂²×C₂²⋊C₄	#1790	1	2	yes	—
499	C₂²×C₂²⋊C₄	C₂×#379	1	2	yes	—
500	C₂²×C₂²⋊C₄	#2846	1	2	yes	—
501	C₂²×C₂²⋊C₄	#2846	1	2	yes	—
502	#381	#1781	1	4	yes	—
503	#379	#1781	1	4	yes	—
504	C₂⁵	#8534	1	2	yes	—
505	C₂⁵	#8534	1	2	yes	—
506	C₂⁵	#12687	1	2	yes	—
507	C₂⁵	#12687	1	2	yes	—
508	C₂⁵	#12687	1	2	yes	complemented
509	C₂⁵	#12705	1	2	yes	—
510	C₂⁵	#12705	1	2	yes	—
511	C₂⁵	#14679	1	1	yes	characteristic
512	C₂⁵	C₂×#1781	1	1	yes	characteristic
513	C₂⁵	C₂×#1781	1	1	yes	characteristic
514	C₂⁵	C₂×#1781	1	1	yes	characteristic
515	C₂⁵	C₂×#1781	1	1	yes	characteristic
516	C₂⁵	C₂×#1790	1	1	yes	characteristic
517	C₂⁵	C₂×#1790	1	1	yes	characteristic
518	C₂⁵	#20609	1	1	yes	characteristic
519	C₂⁵	#20609	1	1	yes	characteristic
520	C₂⁵	#32898	1	1	yes	characteristic
521	C₂⁵	#32898	1	1	yes	characteristic
522	C₂⁵	#32898	1	1	yes	characteristic
523	C₂⁵	#32900	1	1	yes	characteristic
524	C₂²×Q₈	#12687	1	2	yes	complemented
525	C₂²×D₄	#12687	1	2	yes	complemented
526	C₂²×D₄	C₂²×AΣL(1,𝔽₁₆)	1	4	yes	—
527	C₂³×C₄	#12687	1	2	yes	complemented
528	C₂³×C₄	C₂×#1781	1	1	yes	characteristic
529	C₂³×C₄	C₂×#1781	1	1	yes	characteristic
530	C₂³×C₄	#32898	1	1	yes	characteristic
531	C₂³×C₄	#32900	1	1	yes	characteristic
532	C₂³×C₄	#32900	1	1	yes	characteristic
533	C₂³×C₄	#32900	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	#12687	1	4	yes	—
535	C₂×C₂²⋊C₄	#12687	1	4	yes	complemented
536	C₂×C₄²	#12687	1	4	yes	complemented
537	C₂⁴	#133278	1	2	yes	—
538	C₂⁴	#133278	1	2	yes	—
539	C₂⁴	#133278	1	2	yes	—
540	C₂⁴	#133278	1	2	yes	—
541	C₂⁴	C₂×#8534	1	1	yes	characteristic
542	C₂⁴	#187928	1	1	yes	characteristic
543	C₂⁴	#187928	1	1	yes	characteristic
544	C₂⁴	#187944	1	1	yes	characteristic
545	C₂⁴	#392109	1	1	yes	characteristic
546	C₂⁴	#392125	1	1	yes	characteristic
547	C₂⁴	#392125	1	1	yes	characteristic
548	C₂⁴	C₂×#12687	1	2	yes	—
549	C₂⁴	C₂×#12687	1	2	yes	—
550	C₂⁴	C₂×#12705	1	2	yes	—
551	C₂⁴	#511790	1	2	yes	—
552	C₂²×C₄	C₂×#12687	1	2	yes	—
553	C₂³	#72215179	1	1	yes	characteristic
554	C₂³	#72218306	1	1	yes	characteristic
555	C₂³	#72218467	1	1	yes	characteristic
556	C₂³	#72218475	1	1	yes	characteristic
557	C₂³	#72226038	1	2	yes	—
558	C₂³	#72232886	1	2	yes	—
559	C₂³	#72237472	1	1	yes	characteristic
560	C₂³	C₂×#133278	1	2	yes	—
561	C₂²	#72258117	1	1	yes	characteristic
562	C₂²	#72258242	1	1	yes	characteristic
563	C₂²	#72258551	1	1	yes	characteristic
564	C₂	#72266679	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266679
commutator	C₂³×#120	C₂³×C₄
Frattini, cosocle	C₂×#35346	C₂⁴
prime radical	#72329062	C₂
LCS	G ▷ C₂³×#120 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#7670203 ◁ G
LECS	G ▷ C₂×#35346 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337600	C₂	semidirect
2. #72337595	C₂	semidirect
3. #72337587	C₂	semidirect
4. #72337573	C₂	semidirect
5. #72334286	C₂	semidirect
7. #72327645	C₄	semidirect
8. #72327645	C₄	semidirect
21. #72313138	C₄	semidirect
22. #72310618	C₂	semidirect
23. #72310535	C₂²	semidirect
24. #72309341	C₄	semidirect
27. #72302118	C₂	semidirect
28. #72302078	C₂²	semidirect
29. #72302062	C₂²	semidirect
30. #72302047	C₂²	semidirect
31. #72302019	C₂²	semidirect
34. #72256276	C₂	semidirect
35. #72238419	C₂	semidirect
36. #72237771	C₂²	semidirect
37. #72237771	C₂²	semidirect
38. #72237770	C₂²	semidirect
39. #72237770	C₂²	semidirect
40. #72237770	C₂²	semidirect
41. #72237630	C₂²	semidirect
47. #72236376	C₄	semidirect
48. #72234688	C₂²	semidirect
59. #72226360	C₂	semidirect
60. #72226357	C₂²	semidirect
61. #72226352	C₂²	semidirect
62. #72226352	C₂²	semidirect
63. #72226352	C₂²	semidirect
64. #72225883	C₂²	semidirect
65. #72225873	C₂³	semidirect
66. #72225873	C₂³	semidirect
67. #72225781	C₂²	semidirect
68. #72225777	C₂³	semidirect
69. #72225776	C₂³	semidirect
70. #72225776	C₂³	semidirect
71. #72225776	C₂³	semidirect
89. #72217947	C₄	semidirect
106. C₂⁹	C₂²⋊C₄	semidirect
111. C₂×#62817	C₂²⋊C₄	semidirect
118. #8093108	C₂²⋊C₄	semidirect
119. #8093108	C₂²⋊C₄	semidirect
120. #8093107	C₂²⋊C₄	semidirect
121. #8093107	C₂²⋊C₄	semidirect
122. #7670230	C₂²⋊C₄	semidirect
123. #7670230	C₂²⋊C₄	semidirect
124. #7670203	C₂²⋊C₄	semidirect
125. #7670203	C₂²⋊C₄	semidirect
131. C₂²×#2846	C₂²⋊C₄	semidirect
132. C₂²×#2846	C₂²⋊C₄	semidirect
137. #7630944	C₂²⋊C₄	semidirect
152. #7626202	C₂²⋊C₄	semidirect
155. C₂³×#379	C₂²⋊C₄	semidirect
156. C₂³×#379	C₂²⋊C₄	semidirect
161. #6453039	C₂²⋊C₄	semidirect
162. #6451874	C₂²⋊C₄	semidirect
175. C₂×#21746	C₂²⋊C₄	semidirect
176. C₂×#21746	C₂²⋊C₄	semidirect
183. C₂×#14679	C₂²⋊C₄	semidirect
184. C₂×#14679	C₂²⋊C₄	semidirect
185. #449521	C₂²⋊C₄	semidirect
186. #449521	C₂²⋊C₄	semidirect
187. #449521	C₂²⋊C₄	semidirect
188. #449521	C₂²⋊C₄	semidirect
189. #449475	C₂²⋊C₄	semidirect
190. #449475	C₂²⋊C₄	semidirect
191. #449475	C₂²⋊C₄	semidirect
192. #449475	C₂²⋊C₄	semidirect
201. #418213	C₂²⋊C₄	semidirect
202. #418213	C₂²⋊C₄	semidirect
203. #418132	C₂²⋊C₄	semidirect
204. #418132	C₂²⋊C₄	semidirect
205. #417896	C₂²⋊C₄	semidirect
206. #417896	C₂²⋊C₄	semidirect
211. #417824	C₂²⋊C₄	semidirect
212. #417824	C₂²⋊C₄	semidirect
217. #392207	C₂²⋊C₄	semidirect
218. #391735	C₂²⋊C₄	semidirect
219. #391735	C₂²⋊C₄	semidirect
220. #391709	C₂²⋊C₄	semidirect
221. #391709	C₂²⋊C₄	semidirect
223. #375666	C₂²⋊C₄	semidirect
224. #375666	C₂²⋊C₄	semidirect
225. #374004	C₂²⋊C₄	semidirect
226. #374004	C₂²⋊C₄	semidirect
227. #359921	C₂²⋊C₄	semidirect
228. #359705	C₂²⋊C₄	semidirect
231. C₂×#11196	C₂²⋊C₄	semidirect
232. C₂×#10965	C₂²⋊C₄	semidirect
233. C₂×#10965	C₂²⋊C₄	semidirect
400. C₂×H(3,𝔽₄)	AΣL(1,𝔽₁₆)	semidirect
401. C₂×#560	AΣL(1,𝔽₁₆)	semidirect
402. C₂×#551	AΣL(1,𝔽₁₆)	semidirect
403. C₂×D₄²	AΣL(1,𝔽₁₆)	semidirect
508. C₂⁵	#12687	semidirect
524. C₂²×Q₈	#12687	semidirect
525. C₂²×D₄	#12687	semidirect
527. C₂³×C₄	#12687	semidirect
535. C₂×C₂²⋊C₄	#12687	semidirect
536. C₂×C₄²	#12687	semidirect

Maximal subgroups

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

subgroup	index
#72337600	2
#72337595	2
#72337587	2
#72337573	2
#72334286	2
#72329062	2
#72310618	2
#72302118	2
#72256276	2
#72238419	2
#72226360	2