Subgroups — #72337740

Order 8192.

Only the 766 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 483 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337739	C₂	1	1	yes	maximal, characteristic, complemented
2	#72337595	C₂	1	2	yes	maximal, complemented
3	#72337573	C₂	1	1	yes	maximal, characteristic, complemented
4	#72337419	C₂	1	1	yes	maximal, characteristic
5	#72337418	C₄	1	1	yes	characteristic, complemented
6	#72337417	C₄	1	1	yes	characteristic, complemented
7	#72337417	C₄	1	2	yes	complemented
8	#72337255	C₄	1	1	yes	characteristic, complemented
9	#72334280	C₂	1	2	yes	maximal, complemented
10	#72334279	C₂²	1	1	yes	characteristic, complemented
11	#72327288	C₂²	1	1	yes	characteristic
12	#72327288	C₂²	1	2	yes	—
13	#72327248	C₂×C₄	1	1	yes	characteristic
14	#72327248	C₂×C₄	1	2	yes	—
15	#72327244	D₄	1	1	yes	characteristic
16	#72327244	D₄	1	2	yes	—
17	#72327231	C₂×C₄	1	1	yes	characteristic
18	#72327231	C₂×C₄	1	2	yes	—
19	#72326786	D₄	1	1	yes	characteristic
20	#72326786	D₄	1	2	yes	—
21	#72326041	C₂	1	1	yes	maximal, characteristic, complemented
22	#72321821	C₂	1	1	yes	maximal, characteristic, complemented
23	#72318234	C₄	1	1	yes	characteristic, complemented
24	#72318234	C₄	1	2	yes	complemented
25	#72318215	C₂×C₄	1	1	yes	characteristic
26	#72318215	C₂×C₄	1	2	yes	—
27	#72310536	C₂	1	2	yes	maximal, complemented
28	#72310535	C₂²	1	2	yes	complemented
29	#72310532	C₂²	1	1	yes	characteristic, complemented
30	#72310518	C₂	1	1	yes	maximal, characteristic, complemented
31	#72310517	C₂²	1	2	yes	complemented
32	#72309392	C₂²	1	2	yes	complemented
33	#72309392	C₂²	1	1	yes	characteristic, complemented
34	#72309335	D₄	1	1	yes	characteristic
35	#72309335	D₄	1	2	yes	—
36	#72305078	C₂	1	1	yes	maximal, characteristic, complemented
37	#72303878	C₂²	1	1	yes	characteristic, complemented
38	#72302062	C₂²	1	2	yes	complemented
39	#72302019	C₂²	1	1	yes	characteristic, complemented
40	#72283093	D₄	1	1	yes	characteristic
41	#72283093	D₄	1	2	yes	—
42	#72266818	C₂²	1	1	yes	characteristic
43	#72266813	D₄	1	1	yes	characteristic
44	#72240522	D₄	1	1	yes	characteristic
45	#72240522	D₄	1	2	yes	—
46	#72237783	C₂	1	2	yes	maximal, complemented
47	#72237782	C₂²	1	1	yes	characteristic, complemented
48	#72237771	C₂²	1	1	yes	characteristic, complemented
49	#72237771	C₂²	1	2	yes	complemented
50	#72237770	C₂²	1	2	yes	complemented
51	#72237770	C₂²	1	2	yes	complemented
52	#72237769	C₂²	1	2	yes	—
53	#72237769	C₂²	1	1	yes	characteristic
54	#72237754	D₄	1	2	yes	—
55	#72237754	D₄	1	2	yes	—
56	#72237754	D₄	1	2	yes	—
57	#72237749	D₄	1	2	yes	—
58	#72237749	D₄	1	1	yes	characteristic
59	#72237746	D₄	1	2	yes	—
60	#72237746	D₄	1	2	yes	—
61	#72237746	D₄	1	2	yes	—
62	#72237743	D₄	1	2	yes	—
63	#72237743	D₄	1	1	yes	characteristic
64	#72237740	C₂×C₄	1	2	yes	—
65	#72237740	C₂×C₄	1	1	yes	characteristic
66	#72237732	C₂×C₄	1	2	yes	—
67	#72237732	C₂×C₄	1	2	yes	—
68	#72237732	C₂×C₄	1	2	yes	—
69	#72237724	C₂×C₄	1	2	yes	—
70	#72237724	C₂×C₄	1	1	yes	characteristic
71	#72237724	C₂×C₄	1	1	yes	characteristic
72	#72237724	C₂×C₄	1	2	yes	—
73	#72237724	C₂×C₄	1	1	yes	characteristic
74	#72237724	D₄	1	2	yes	—
75	#72237724	D₄	1	1	yes	characteristic
76	#72237724	D₄	1	1	yes	characteristic
77	#72237617	C₂²	1	2	yes	complemented
78	C₂×#97550	C₂³	1	1	yes	characteristic
79	#72234672	C₂²	1	2	yes	complemented
80	#72234670	C₂³	1	1	yes	characteristic
81	#72226357	C₂²	1	1	yes	characteristic, complemented
82	#72226352	C₂²	1	2	yes	complemented
83	#72225873	C₂³	1	2	yes	—
84	#72225873	C₂³	1	1	yes	characteristic
85	#72225777	C₂³	1	1	yes	characteristic
86	#72225776	C₂³	1	2	yes	—
87	#72225733	C₂³	1	1	yes	characteristic
88	#72225733	C₂³	1	2	yes	—
89	#72225660	C₂×C₄	1	1	yes	characteristic
90	#72225660	C₂×C₄	1	2	yes	—
91	#72225655	C₂³	1	1	yes	characteristic
92	#72225655	C₂³	1	2	yes	—
93	#72218920	D₄	1	1	yes	characteristic
94	#72218920	D₄	1	2	yes	—
95	#72217730	D₄	1	1	yes	characteristic
96	#72217730	D₄	1	2	yes	—
97	C₂×#449475	C₂³	1	1	yes	characteristic
98	#72216646	D₄	1	1	yes	characteristic
99	#72216646	D₄	1	2	yes	—
100	#72210507	D₄	1	2	yes	—
101	#72210507	D₄	1	1	yes	characteristic
102	#72210026	D₄	1	2	yes	—
103	#72210026	D₄	1	1	yes	characteristic
104	#72210024	D₄	1	1	yes	characteristic
105	#72210024	D₄	1	2	yes	—
106	#10586066	C₂×D₄	1	1	yes	characteristic
107	#10586066	C₂×D₄	1	2	yes	—
108	#8093108	C₂²⋊C₄	1	1	yes	characteristic
109	#8093108	C₂²⋊C₄	1	2	yes	complemented
110	#8093107	C₂²⋊C₄	1	1	yes	characteristic
111	#8093107	C₂²⋊C₄	1	2	yes	complemented
112	#7670230	C₂²⋊C₄	1	1	yes	characteristic
113	#7670230	C₂²⋊C₄	1	2	yes	complemented
114	#7670203	C₂²⋊C₄	1	1	yes	characteristic
115	#7670203	C₂²⋊C₄	1	2	yes	complemented
116	#7642273	C₂×D₄	1	1	yes	characteristic
117	#7642273	C₂×D₄	1	2	yes	—
118	#7642244	C₂×D₄	1	1	yes	characteristic
119	#7642244	C₂×D₄	1	2	yes	—
120	#7642244	C₂×D₄	1	1	yes	characteristic
121	#7642244	C₂×D₄	1	2	yes	—
122	C₂²×#2846	C₂×D₄	1	1	yes	characteristic
123	C₂²×#2846	C₂×D₄	1	2	yes	—
124	C₂×#35346	C₂⁴	1	1	yes	characteristic
125	#7513948	C₂²⋊C₄	1	2	yes	complemented
126	#7513948	C₂²⋊C₄	1	2	yes	complemented
127	#7513948	C₂²⋊C₄	1	2	yes	complemented
128	#6631461	C₂²⋊C₄	1	2	yes	complemented
129	#6631461	C₂²⋊C₄	1	1	yes	characteristic, complemented
130	#6629262	C₂×D₄	1	1	yes	characteristic
131	#6629262	C₂×D₄	1	2	yes	—
132	#6629262	C₂×D₄	1	1	yes	characteristic
133	#6629262	C₂×D₄	1	2	yes	—
134	#6628896	C₂×D₄	1	1	yes	characteristic
135	#6628896	C₂×D₄	1	2	yes	—
136	#6628896	C₂×D₄	1	1	yes	characteristic
137	#6628896	C₂×D₄	1	2	yes	—
138	#6451874	C₂×D₄	1	2	yes	—
139	#6451874	C₂×D₄	1	2	yes	—
140	#6451874	C₂×D₄	1	2	yes	—
141	#6437629	C₂²⋊C₄	1	2	yes	complemented
142	#6437629	C₂²⋊C₄	1	1	yes	characteristic, complemented
143	#6437629	C₂²⋊C₄	1	2	yes	complemented
144	#6437629	C₂²⋊C₄	1	2	yes	complemented
145	#6437629	C₂²⋊C₄	1	2	yes	complemented
146	#6437629	C₂²⋊C₄	1	2	yes	complemented
147	#6437629	C₂²⋊C₄	1	1	yes	characteristic, complemented
148	#6437629	C₂²⋊C₄	1	2	yes	complemented
149	#6437629	C₂²⋊C₄	1	1	yes	characteristic, complemented
150	#6432953	C₂²×C₄	1	1	yes	characteristic
151	#6432953	C₂²×C₄	1	2	yes	—
152	#6432953	C₂²×C₄	1	1	yes	characteristic
153	#6432953	C₂²×C₄	1	2	yes	—
154	#6432953	C₂×D₄	1	1	yes	characteristic
155	#6432953	C₂×D₄	1	1	yes	characteristic
156	#6432953	C₂×D₄	1	2	yes	—
157	#6432953	C₂×D₄	1	2	yes	—
158	#6374210	C₂×D₄	1	1	yes	characteristic
159	#6374210	C₂×D₄	1	2	yes	—
160	#6374210	C₂×D₄	1	1	yes	characteristic
161	#6374210	C₂×D₄	1	2	yes	—
162	#6370693	C₂×D₄	1	1	yes	characteristic
163	#6370693	C₂×D₄	1	2	yes	—
164	#449521	C₂²⋊C₄	1	1	yes	characteristic
165	#449521	C₂²⋊C₄	1	1	yes	characteristic
166	#449521	C₂²⋊C₄	1	2	yes	complemented
167	#449521	C₂²⋊C₄	1	2	yes	complemented
168	#449475	C₂²⋊C₄	1	1	yes	characteristic
169	#449475	C₂²⋊C₄	1	1	yes	characteristic
170	#449475	C₂²⋊C₄	1	2	yes	complemented
171	#449475	C₂²⋊C₄	1	2	yes	complemented
172	#449475	C₂²×C₄	1	1	yes	characteristic
173	#449475	C₂²×C₄	1	1	yes	characteristic
174	#449475	C₂×D₄	1	1	yes	characteristic
175	#449475	C₂×D₄	1	2	yes	—
176	#449475	C₂×D₄	1	1	yes	characteristic
177	#449475	C₂×D₄	1	2	yes	—
178	#449090	C₂²⋊C₄	1	2	yes	complemented
179	#449090	C₂²⋊C₄	1	2	yes	complemented
180	#449090	C₂²⋊C₄	1	2	yes	complemented
181	#436464	C₂²⋊C₄	1	2	yes	complemented
182	#436464	C₂²⋊C₄	1	2	yes	complemented
183	#436464	C₂²⋊C₄	1	2	yes	complemented
184	#432839	C₂²⋊C₄	1	2	yes	complemented
185	#432839	C₂²⋊C₄	1	2	yes	complemented
186	#432839	C₂²⋊C₄	1	2	yes	complemented
187	#418911	C₂²⋊C₄	1	2	yes	complemented
188	#418911	C₂²⋊C₄	1	2	yes	complemented
189	#418911	C₂²⋊C₄	1	2	yes	complemented
190	#418213	C₂²⋊C₄	1	1	yes	characteristic
191	#418213	C₂²⋊C₄	1	2	yes	complemented
192	#418132	C₂²⋊C₄	1	1	yes	characteristic
193	#418132	C₂²⋊C₄	1	2	yes	complemented
194	#417896	C₂²⋊C₄	1	1	yes	characteristic
195	#417896	C₂²⋊C₄	1	2	yes	complemented
196	#417896	C₂²×C₄	1	1	yes	characteristic
197	#417896	C₂²×C₄	1	2	yes	—
198	#417896	C₂×D₄	1	1	yes	characteristic
199	#417896	C₂×D₄	1	2	yes	—
200	#417896	C₂×D₄	1	2	yes	—
201	#417896	C₂×D₄	1	2	yes	—
202	#417896	C₂×D₄	1	2	yes	—
203	#417824	C₂²⋊C₄	1	1	yes	characteristic
204	#417824	C₂²⋊C₄	1	2	yes	complemented
205	#417824	C₂²×C₄	1	1	yes	characteristic
206	#417824	C₂²×C₄	1	2	yes	—
207	#417824	C₂×D₄	1	1	yes	characteristic
208	#417824	C₂×D₄	1	2	yes	—
209	#417824	C₂×D₄	1	2	yes	—
210	#417824	C₂×D₄	1	2	yes	—
211	#417824	C₂×D₄	1	2	yes	—
212	#391735	C₂²⋊C₄	1	1	yes	characteristic
213	#391735	C₂²⋊C₄	1	2	yes	complemented
214	#391709	C₂²⋊C₄	1	1	yes	characteristic
215	#391709	C₂²⋊C₄	1	2	yes	complemented
216	#388001	C₂²⋊C₄	1	2	yes	complemented
217	#388001	C₂²⋊C₄	1	2	yes	complemented
218	#388001	C₂²⋊C₄	1	2	yes	complemented
219	#382422	C₂×D₄	1	1	yes	characteristic
220	#382422	C₂×D₄	1	2	yes	—
221	#375666	C₂²⋊C₄	1	1	yes	characteristic
222	#375666	C₂²⋊C₄	1	2	yes	complemented
223	#374004	C₂²⋊C₄	1	1	yes	characteristic
224	#374004	C₂²⋊C₄	1	2	yes	complemented
225	#359705	C₂×D₄	1	2	yes	—
226	#359705	C₂×D₄	1	2	yes	—
227	#359705	C₂×D₄	1	2	yes	—
228	C₂×#10965	C₂×D₄	1	1	yes	characteristic
229	C₂×#10965	C₂×D₄	1	2	yes	—
230	#357285	C₂²⋊C₄	1	2	yes	complemented
231	#357285	C₂²⋊C₄	1	1	yes	characteristic, complemented
232	#357285	C₂²⋊C₄	1	1	yes	characteristic, complemented
233	#357285	C₂²⋊C₄	1	2	yes	complemented
234	#357285	C₂²⋊C₄	1	1	yes	characteristic, complemented
235	#356055	C₂²⋊C₄	1	2	yes	complemented
236	#356055	C₂²⋊C₄	1	1	yes	characteristic, complemented
237	C₂⁸	#120	1	1	yes	characteristic
238	C₂×H(7,𝔽₂)	#120	1	2	yes	—
239	C₂×H(7,𝔽₂)	#120	1	1	yes	characteristic
240	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
241	#62842	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	#62842	C₂×C₂²⋊C₄	1	2	yes	—
243	#62842	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	#62842	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂×#3490	#120	1	1	yes	characteristic
246	C₂×#3490	#120	1	2	yes	—
247	C₂×#3484	#120	1	1	yes	characteristic
248	C₂×#3484	#120	1	1	yes	characteristic
249	C₂×#3484	#120	1	2	yes	—
250	C₂×#3484	#120	1	2	yes	—
251	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
252	C₂³×#120	C₂²×D₄	1	2	yes	—
253	#62652	#120	1	2	yes	—
254	#62652	#120	1	1	yes	characteristic
255	C₂×#2846	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×#2846	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×#2846	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×#2846	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×#2846	#120	1	1	yes	characteristic
260	C₂×#2846	#120	1	2	yes	—
261	C₂×#2846	#120	1	1	yes	characteristic
262	C₂×#2846	#120	1	2	yes	—
263	#35390	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	#35390	C₂×C₂²⋊C₄	1	2	yes	—
265	#35390	#120	1	1	yes	characteristic
266	#35390	#120	1	2	yes	—
267	#35367	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	#35367	C₂×C₂²⋊C₄	1	2	yes	—
269	#35367	#120	1	1	yes	characteristic
270	#35367	#120	1	2	yes	—
271	#35350	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	#35350	C₂×C₂²⋊C₄	1	2	yes	—
273	#35350	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	#35350	C₂×C₂²⋊C₄	1	2	yes	—
275	#35350	#120	1	1	yes	characteristic
276	#35350	#120	1	2	yes	—
277	#35350	#120	1	2	yes	—
278	#35350	#120	1	1	yes	characteristic
279	#35346	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	#35346	C₂×C₂²⋊C₄	1	2	yes	—
281	#35346	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	#35346	C₂×C₂²⋊C₄	1	2	yes	—
283	#35346	#120	1	1	yes	characteristic
284	#35346	#120	1	2	yes	—
285	#35346	#120	1	2	yes	—
286	#35346	#120	1	1	yes	characteristic
287	#35346	C₂³×C₄	1	1	yes	characteristic
288	#35346	C₂²×D₄	1	1	yes	characteristic
289	#35346	C₂²×D₄	1	2	yes	—
290	#35346	C₂²×D₄	1	1	yes	characteristic
291	#35346	C₂²×D₄	1	1	yes	characteristic
292	#35346	C₂²×D₄	1	2	yes	—
293	#34176	#120	1	1	yes	characteristic
294	#34176	#120	1	2	yes	—
295	#34171	#120	1	1	yes	characteristic
296	#34171	#120	1	1	yes	characteristic
297	#34171	#120	1	2	yes	—
298	#34171	#120	1	2	yes	—
299	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
300	C₂×#2308	C₂²×D₄	1	2	yes	—
301	C₂²×#379	#120	1	1	yes	characteristic
302	C₂²×#379	#120	1	2	yes	—
303	#23468	C₂×C₂²⋊C₄	1	2	yes	—
304	#23468	C₂×C₂²⋊C₄	1	2	yes	—
305	#23468	C₂×C₂²⋊C₄	1	2	yes	—
306	#23468	#120	1	2	yes	—
307	#23468	#120	1	2	yes	—
308	#23468	#120	1	2	yes	—
309	#23444	C₂×C₂²⋊C₄	1	2	yes	—
310	#23444	C₂×C₂²⋊C₄	1	2	yes	—
311	#23444	C₂×C₂²⋊C₄	1	2	yes	—
312	#23444	#120	1	2	yes	—
313	#23444	#120	1	2	yes	—
314	#23444	#120	1	2	yes	—
315	#20689	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	#20689	C₂×C₂²⋊C₄	1	2	yes	—
317	#20689	C₂×C₂²⋊C₄	1	2	yes	—
318	#20689	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	#20689	#120	1	1	yes	characteristic
320	#20689	#120	1	2	yes	—
321	#20689	#120	1	2	yes	—
322	#20689	#120	1	1	yes	characteristic
323	C₂×#1819	#120	1	2	yes	—
324	C₂×#1819	#120	1	2	yes	—
325	C₂×#1819	#120	1	2	yes	—
326	#20585	C₂×C₂²⋊C₄	1	2	yes	—
327	#20585	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	#20585	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	#20585	C₂×C₂²⋊C₄	1	2	yes	—
330	#20585	C₂×C₂²⋊C₄	1	2	yes	—
331	#20585	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	#20585	C₂×C₂²⋊C₄	1	2	yes	—
333	#20585	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	#20585	#120	1	1	yes	characteristic
335	#20585	#120	1	2	yes	—
336	#20585	#120	1	2	yes	—
337	#20585	#120	1	1	yes	characteristic
338	#20585	#120	1	2	yes	—
339	#20585	#120	1	1	yes	characteristic
340	#20585	#120	1	2	yes	—
341	#20585	#120	1	1	yes	characteristic
342	#10965	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	#10965	C₂×C₂²⋊C₄	1	2	yes	—
344	#10965	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	#10965	C₂×C₂²⋊C₄	1	2	yes	—
346	#10965	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	#10965	C₂×C₂²⋊C₄	1	2	yes	—
348	#10965	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	#10965	C₂×C₂²⋊C₄	1	2	yes	—
350	#10965	#120	1	2	yes	—
351	#10965	#120	1	2	yes	—
352	#10965	#120	1	2	yes	—
353	#10965	#120	1	2	yes	—
354	#10965	#120	1	2	yes	—
355	#10965	#120	1	2	yes	—
356	#10938	C₂×C₂²⋊C₄	1	2	yes	—
357	#10938	C₂×C₂²⋊C₄	1	2	yes	—
358	#10938	C₂×C₂²⋊C₄	1	2	yes	—
359	#10938	C₂×C₂²⋊C₄	1	2	yes	—
360	#10938	C₂×C₂²⋊C₄	1	2	yes	—
361	#10938	C₂×C₂²⋊C₄	1	2	yes	—
362	#10938	#120	1	2	yes	—
363	#10938	#120	1	2	yes	—
364	#10938	#120	1	2	yes	—
365	#10938	#120	1	2	yes	—
366	#10938	#120	1	2	yes	—
367	#10938	#120	1	2	yes	—
368	C₂⁷	#379	1	1	yes	characteristic
369	C₂⁷	#379	1	1	yes	characteristic
370	C₂⁷	C₂×#120	1	1	yes	characteristic
371	C₂²×H(5,𝔽₂)	#379	1	1	yes	characteristic
372	C₂²×H(5,𝔽₂)	#379	1	1	yes	characteristic
373	C₂²×H(5,𝔽₂)	#379	1	2	yes	—
374	C₂²×H(5,𝔽₂)	#379	1	2	yes	—
375	C₂²×H(5,𝔽₂)	C₂²×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×H(5,𝔽₂)	C₂×#120	1	2	yes	—
377	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
378	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
379	C₂⁴×D₄	C₂×#120	1	2	yes	—
380	C₂×#543	#379	1	1	yes	characteristic
381	C₂×#543	#379	1	2	yes	—
382	C₂×#534	#379	1	1	yes	characteristic
383	C₂×#534	#379	1	2	yes	—
384	C₂²×#120	C₂²×C₂²⋊C₄	1	1	yes	characteristic
385	C₂²×#120	C₂²×C₂²⋊C₄	1	2	yes	—
386	C₂²×#120	C₂×#120	1	1	yes	characteristic
387	C₂²×#120	C₂×#120	1	2	yes	—
388	C₂²×#120	C₂×#120	1	1	yes	characteristic
389	C₂²×#120	C₂×#120	1	2	yes	—
390	C₂²×#120	C₂×#120	1	1	yes	characteristic
391	C₂²×#120	C₂×#120	1	2	yes	—
392	C₂×#518	#379	1	1	yes	characteristic
393	C₂×#518	#379	1	1	yes	characteristic
394	C₂×#518	#379	1	2	yes	—
395	C₂×#518	#379	1	2	yes	—
396	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
397	C₂³×C₂²⋊C₄	C₂×#120	1	2	yes	—
398	#2309	#458	1	4	yes	—
399	#2308	#379	1	1	yes	characteristic
400	#2308	#379	1	2	yes	—
401	#2308	#379	1	1	yes	characteristic
402	#2308	#379	1	2	yes	—
403	#2308	#379	1	2	yes	—
404	#2308	#379	1	2	yes	—
405	#2308	#379	1	1	yes	characteristic
406	#2308	#379	1	1	yes	characteristic
407	#2308	#458	1	2	yes	—
408	#2308	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	#2308	C₂²×C₂²⋊C₄	1	2	yes	—
410	#2308	C₂×#120	1	1	yes	characteristic
411	#2308	C₂×#120	1	2	yes	—
412	#2308	C₂×#120	1	2	yes	—
413	#2308	C₂×#120	1	2	yes	—
414	#2308	C₂×#120	1	2	yes	—
415	#2280	B(4,𝔽₂)	1	2	yes	—
416	C₂×#379	#379	1	1	yes	characteristic
417	C₂×#379	#379	1	2	yes	—
418	C₂×#379	#379	1	1	yes	characteristic
419	C₂×#379	#379	1	2	yes	—
420	C₂×#379	B(4,𝔽₂)	1	4	yes	—
421	#2273	#379	1	1	yes	characteristic
422	#2273	#379	1	2	yes	—
423	#2273	#379	1	1	yes	characteristic
424	#2273	#379	1	2	yes	—
425	C₂×#342	#379	1	2	yes	—
426	C₂×#342	#379	1	2	yes	—
427	C₂×#342	#379	1	2	yes	—
428	C₂×#342	#379	1	2	yes	—
429	C₂×#342	#379	1	2	yes	—
430	C₂×#342	#379	1	2	yes	—
431	C₂⁶	C₂×#379	1	1	yes	characteristic
432	C₂⁶	#2846	1	1	yes	characteristic
433	C₂⁶	#2846	1	1	yes	characteristic
434	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
435	C₂⁶	#3026	1	1	yes	characteristic
436	C₂³×D₄	C₂×#379	1	1	yes	characteristic
437	C₂³×D₄	C₂×#379	1	2	yes	—
438	C₂³×D₄	#2846	1	1	yes	characteristic
439	C₂³×D₄	#2846	1	2	yes	—
440	C₂³×D₄	C₂×#458	1	1	yes	characteristic
441	C₂³×D₄	C₂×#458	1	2	yes	—
442	C₂³×D₄	#3026	1	2	yes	—
443	C₂³×D₄	#3026	1	1	yes	characteristic
444	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
445	C₂⁴×C₄	#3026	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂×#379	1	2	yes	—
447	C₂²×C₂²⋊C₄	C₂×#379	1	1	yes	characteristic
448	C₂²×C₂²⋊C₄	#2846	1	2	yes	—
449	C₂²×C₂²⋊C₄	#2846	1	1	yes	characteristic
450	#381	#1790	1	2	yes	—
451	#381	#1790	1	2	yes	—
452	#379	#1790	1	4	yes	—
453	#379	#1790	1	4	yes	—
454	C₂⁵	#14679	1	1	yes	characteristic
455	C₂⁵	C₂×#1790	1	2	yes	—
456	C₂⁵	#20609	1	1	yes	characteristic
457	C₂⁵	#32898	1	2	yes	—
458	C₂⁵	#32898	1	1	yes	characteristic
459	C₂⁵	#32898	1	2	yes	—
460	C₂⁵	#32900	1	1	yes	characteristic
461	C₂⁵	#32900	1	2	yes	—
462	C₂⁵	#32900	1	1	yes	characteristic
463	C₂³×C₄	C₂×#1790	1	1	yes	characteristic
464	C₂³×C₄	#20609	1	2	yes	—
465	C₂³×C₄	#32898	1	1	yes	characteristic
466	C₂³×C₄	#32900	1	2	yes	—
467	C₂⁴	#347047	1	1	yes	characteristic
468	C₂⁴	#347056	1	1	yes	characteristic
469	C₂⁴	#347056	1	2	yes	—
470	C₂⁴	#392125	1	1	yes	characteristic
471	C₂⁴	#392125	1	2	yes	—
472	C₂⁴	#511790	1	4	yes	—
473	C₂²×C₄	#511790	1	2	yes	—
474	C₂³	#72218475	1	1	yes	characteristic
475	C₂³	#72218475	1	2	yes	—
476	C₂³	#72238343	1	1	yes	characteristic
477	C₂³	#72238343	1	2	yes	—
478	C₂³	#72265024	1	1	yes	characteristic
479	C₂²	#72265783	1	1	yes	characteristic
480	C₂²	#72265783	1	2	yes	—
481	C₂	#72266707	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266707
commutator	#35346	C₂³×C₄
Frattini, cosocle	C₂×#35346	C₂⁴
prime radical	#72337419	C₂
LCS	G ▷ #35346 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#35346 ◁ 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. #72337739	C₂	semidirect
2. #72337595	C₂	semidirect
3. #72337573	C₂	semidirect
5. #72337418	C₄	semidirect
6. #72337417	C₄	semidirect
7. #72337417	C₄	semidirect
8. #72337255	C₄	semidirect
9. #72334280	C₂	semidirect
10. #72334279	C₂²	semidirect
21. #72326041	C₂	semidirect
22. #72321821	C₂	semidirect
23. #72318234	C₄	semidirect
24. #72318234	C₄	semidirect
27. #72310536	C₂	semidirect
28. #72310535	C₂²	semidirect
29. #72310532	C₂²	semidirect
30. #72310518	C₂	semidirect
31. #72310517	C₂²	semidirect
32. #72309392	C₂²	semidirect
33. #72309392	C₂²	semidirect
36. #72305078	C₂	semidirect
37. #72303878	C₂²	semidirect
38. #72302062	C₂²	semidirect
39. #72302019	C₂²	semidirect
46. #72237783	C₂	semidirect
47. #72237782	C₂²	semidirect
48. #72237771	C₂²	semidirect
49. #72237771	C₂²	semidirect
50. #72237770	C₂²	semidirect
51. #72237770	C₂²	semidirect
77. #72237617	C₂²	semidirect
79. #72234672	C₂²	semidirect
81. #72226357	C₂²	semidirect
82. #72226352	C₂²	semidirect
109. #8093108	C₂²⋊C₄	semidirect
111. #8093107	C₂²⋊C₄	semidirect
113. #7670230	C₂²⋊C₄	semidirect
115. #7670203	C₂²⋊C₄	semidirect
125. #7513948	C₂²⋊C₄	semidirect
126. #7513948	C₂²⋊C₄	semidirect
127. #7513948	C₂²⋊C₄	semidirect
128. #6631461	C₂²⋊C₄	semidirect
129. #6631461	C₂²⋊C₄	semidirect
141. #6437629	C₂²⋊C₄	semidirect
142. #6437629	C₂²⋊C₄	semidirect
143. #6437629	C₂²⋊C₄	semidirect
144. #6437629	C₂²⋊C₄	semidirect
145. #6437629	C₂²⋊C₄	semidirect
146. #6437629	C₂²⋊C₄	semidirect
147. #6437629	C₂²⋊C₄	semidirect
148. #6437629	C₂²⋊C₄	semidirect
149. #6437629	C₂²⋊C₄	semidirect
166. #449521	C₂²⋊C₄	semidirect
167. #449521	C₂²⋊C₄	semidirect
170. #449475	C₂²⋊C₄	semidirect
171. #449475	C₂²⋊C₄	semidirect
178. #449090	C₂²⋊C₄	semidirect
179. #449090	C₂²⋊C₄	semidirect
180. #449090	C₂²⋊C₄	semidirect
181. #436464	C₂²⋊C₄	semidirect
182. #436464	C₂²⋊C₄	semidirect
183. #436464	C₂²⋊C₄	semidirect
184. #432839	C₂²⋊C₄	semidirect
185. #432839	C₂²⋊C₄	semidirect
186. #432839	C₂²⋊C₄	semidirect
187. #418911	C₂²⋊C₄	semidirect
188. #418911	C₂²⋊C₄	semidirect
189. #418911	C₂²⋊C₄	semidirect
191. #418213	C₂²⋊C₄	semidirect
193. #418132	C₂²⋊C₄	semidirect
195. #417896	C₂²⋊C₄	semidirect
204. #417824	C₂²⋊C₄	semidirect
213. #391735	C₂²⋊C₄	semidirect
215. #391709	C₂²⋊C₄	semidirect
216. #388001	C₂²⋊C₄	semidirect
217. #388001	C₂²⋊C₄	semidirect
218. #388001	C₂²⋊C₄	semidirect
222. #375666	C₂²⋊C₄	semidirect
224. #374004	C₂²⋊C₄	semidirect
230. #357285	C₂²⋊C₄	semidirect
231. #357285	C₂²⋊C₄	semidirect
232. #357285	C₂²⋊C₄	semidirect
233. #357285	C₂²⋊C₄	semidirect
234. #357285	C₂²⋊C₄	semidirect
235. #356055	C₂²⋊C₄	semidirect
236. #356055	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72337739	2
#72337595	2
#72337573	2
#72337419	2
#72334280	2
#72326041	2
#72321821	2
#72310536	2
#72310518	2
#72305078	2
#72237783	2