Subgroups — #72261407

Order 2048.

At least 13115 conjugacy classes of subgroups; only the 728 normal subgroups are shown.

The subgroup lattice has 469 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261400	C₂	1	1	yes	maximal, characteristic, complemented
2	#72261186	C₂	1	1	yes	maximal, characteristic
3	#72261063	C₂	1	1	yes	maximal, characteristic, complemented
4	#72260988	C₂	1	1	yes	maximal, characteristic, complemented
5	#72234969	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234187	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233510	C₂	1	2	yes	maximal, complemented
8	#72233338	C₂	1	2	yes	maximal, complemented
9	#72233200	C₂	1	2	yes	maximal, complemented
10	#72232787	C₂	1	1	yes	maximal, characteristic, complemented
11	#72232749	C₂	1	2	yes	maximal, complemented
12	#8395045	C₄	1	2	yes	complemented
13	#8362477	C₄	1	2	yes	complemented
14	#8176294	C₂²	1	2	yes	—
15	#8093976	C₄	1	1	yes	characteristic, complemented
16	#8093116	C₄	1	1	yes	characteristic, complemented
17	#7772012	C₂²	1	2	yes	—
18	#7682006	C₄	1	1	yes	characteristic, complemented
19	#7670308	C₄	1	1	yes	characteristic, complemented
20	#7644628	C₂²	1	1	yes	characteristic
21	C₂×#38080	C₂²	1	1	yes	characteristic
22	#7631286	C₂²	1	1	yes	characteristic
23	#6385971	C₂²	1	1	yes	characteristic, complemented
24	#496231	C₂²	1	2	yes	complemented
25	#496225	C₂²	1	2	yes	complemented
26	C₂×#13088	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13088	C₂²	1	1	yes	characteristic, complemented
28	#494695	C₂²	1	2	yes	complemented
29	C₂×#13086	C₂²	1	2	yes	complemented
30	C₂×#12858	C₂²	1	1	yes	characteristic, complemented
31	C₂×#12582	C₂²	1	1	yes	characteristic, complemented
32	#374058	C₂²	1	2	yes	complemented
33	#374038	C₂²	1	2	yes	complemented
34	#359869	C₂²	1	2	yes	complemented
35	#359579	C₂²	1	1	yes	characteristic, complemented
36	#359579	C₂²	1	1	yes	characteristic, complemented
37	#201701	C₂²	1	2	yes	complemented
38	#201664	C₂²	1	2	yes	complemented
39	#201293	C₂²	1	2	yes	complemented
40	#188087	C₂²	1	1	yes	characteristic, complemented
41	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
42	C₂×#3484	D₄	1	1	yes	characteristic
43	C₂²×#553	D₄	1	1	yes	characteristic
44	C₂²×D₄²	C₂³	1	1	yes	characteristic
45	C₂³×#99	C₂³	1	1	yes	characteristic
46	C₂³×#99	C₂³	1	1	yes	characteristic
47	#59940	C₂×C₄	1	2	yes	—
48	#59940	C₂×C₄	1	2	yes	—
49	#59814	C₂×C₄	1	2	yes	—
50	#59623	D₄	1	2	yes	—
51	#59126	C₂×C₄	1	2	yes	—
52	#58990	D₄	1	2	yes	—
53	#51993	D₄	1	2	yes	—
54	#51945	D₄	1	2	yes	—
55	#51940	D₄	1	2	yes	—
56	#51940	D₄	1	2	yes	—
57	#50646	D₄	1	2	yes	—
58	#48143	D₄	1	2	yes	—
59	#48088	D₄	1	2	yes	—
60	#47827	D₄	1	2	yes	—
61	#46334	C₂×C₄	1	2	yes	—
62	#46324	C₂×C₄	1	2	yes	—
63	#46089	C₂×C₄	1	2	yes	—
64	#46089	C₂×C₄	1	2	yes	—
65	#45727	D₄	1	2	yes	—
66	#45438	D₄	1	2	yes	—
67	#37436	D₄	1	2	yes	—
68	#37232	C₂×C₄	1	2	yes	—
69	#37117	D₄	1	2	yes	—
70	#36747	D₄	1	2	yes	—
71	#36714	D₄	1	2	yes	—
72	C₂×#2856	C₂×C₄	1	1	yes	characteristic
73	#35527	C₂×C₄	1	2	yes	—
74	#35512	D₄	1	2	yes	—
75	#35351	C₂×C₄	1	1	yes	characteristic
76	#35350	D₄	1	1	yes	characteristic
77	#35347	C₂×C₄	1	1	yes	characteristic
78	#35347	C₂×C₄	1	1	yes	characteristic
79	#35347	C₂×C₄	1	1	yes	characteristic
80	#35346	D₄	1	1	yes	characteristic
81	#35346	D₄	1	1	yes	characteristic
82	#35346	D₄	1	1	yes	characteristic
83	#34980	D₄	1	2	yes	—
84	#34980	C₂³	1	2	yes	—
85	C₂×#2541	C₂×C₄	1	1	yes	characteristic
86	C₂×#2566	D₄	1	1	yes	characteristic
87	C₂×#2500	D₄	1	1	yes	characteristic
88	C₂×#2504	C₂×C₄	1	1	yes	characteristic
89	C₂×#2433	D₄	1	1	yes	characteristic
90	C₂×#2433	C₂³	1	1	yes	characteristic
91	C₂×#2403	C₂³	1	2	yes	—
92	C₂×#2641	C₂×C₄	1	1	yes	characteristic
93	C₂×#2619	D₄	1	1	yes	characteristic
94	#34407	D₄	1	2	yes	—
95	#34356	D₄	1	2	yes	—
96	#34171	D₄	1	1	yes	characteristic
97	#34171	C₂³	1	2	yes	—
98	C₂×#2328	D₄	1	1	yes	characteristic
99	C₂×#2309	C₂³	1	1	yes	characteristic
100	C₂×#2308	D₄	1	1	yes	characteristic
101	C₂²×#390	D₄	1	1	yes	characteristic
102	C₂×#2290	D₄	1	1	yes	characteristic
103	C₂×#1783	C₂³	1	2	yes	—
104	C₂×#1781	C₂³	1	1	yes	characteristic
105	C₂×#1781	C₂³	1	1	yes	characteristic
106	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
109	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	2	yes	—
114	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
115	C₂×#560	C₂²⋊C₄	1	2	yes	complemented
116	C₂×D₄²	C₂²⋊C₄	1	2	yes	complemented
117	C₂×#534	C₂²⋊C₄	1	2	yes	complemented
118	C₂×#534	C₂×D₄	1	2	yes	—
119	C₂×#534	C₂×D₄	1	2	yes	—
120	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
121	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
122	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
123	C₂²×#127	C₂×D₄	1	1	yes	characteristic
124	C₂²×#125	C₂²⋊C₄	1	1	yes	characteristic, complemented
125	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic, complemented
126	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
127	C₂²×#121	C₂×D₄	1	1	yes	characteristic
128	C₂²×#121	C₂×D₄	1	1	yes	characteristic
129	C₂²×#121	C₂×D₄	1	1	yes	characteristic
130	C₂²×#121	C₂×D₄	1	1	yes	characteristic
131	C₂²×#120	C₂×D₄	1	2	yes	—
132	C₂²×#120	C₂×D₄	1	2	yes	—
133	C₂²×#120	C₂×D₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	1	yes	characteristic
138	C₂×#518	C₂²⋊C₄	1	1	yes	characteristic, complemented
139	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
140	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂²×#117	C₂×D₄	1	1	yes	characteristic
143	C₂²×#117	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
145	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	#2804	C₂²⋊C₄	1	2	yes	complemented
147	#2804	C₂²⋊C₄	1	2	yes	complemented
148	#2748	C₂²⋊C₄	1	2	yes	complemented
149	#2748	C₂²⋊C₄	1	2	yes	complemented
150	#2748	C₂²⋊C₄	1	2	yes	complemented
151	#2709	C₂²⋊C₄	1	2	yes	complemented
152	#2697	C₂²⋊C₄	1	2	yes	complemented
153	#2697	C₂²⋊C₄	1	2	yes	complemented
154	#2697	C₂²⋊C₄	1	2	yes	complemented
155	#2683	C₂²⋊C₄	1	2	yes	complemented
156	#2679	C₂²⋊C₄	1	2	yes	complemented
157	#2679	C₂²⋊C₄	1	2	yes	complemented
158	#2679	C₂²⋊C₄	1	2	yes	complemented
159	#2669	C₂²⋊C₄	1	2	yes	complemented
160	#2669	C₂²⋊C₄	1	2	yes	complemented
161	#2669	C₂²⋊C₄	1	2	yes	complemented
162	#2483	C₂²⋊C₄	1	2	yes	complemented
163	#2433	C₂×D₄	1	2	yes	—
164	#2433	C₂×D₄	1	2	yes	—
165	#2433	C₂×D₄	1	2	yes	—
166	#2433	C₂×D₄	1	2	yes	—
167	#2405	C₂²⋊C₄	1	2	yes	—
168	#2405	C₂²⋊C₄	1	2	yes	—
169	#2405	C₂²⋊C₄	1	2	yes	complemented
170	#2405	C₂²⋊C₄	1	2	yes	complemented
171	#2405	C₂²×C₄	1	2	yes	—
172	#2405	C₂×D₄	1	2	yes	—
173	#2405	C₂×D₄	1	2	yes	—
174	#2405	C₂×D₄	1	2	yes	—
175	#2403	C₂²⋊C₄	1	2	yes	—
176	#2403	C₂²⋊C₄	1	2	yes	—
177	#2403	C₂²⋊C₄	1	2	yes	complemented
178	#2403	C₂²×C₄	1	2	yes	—
179	#2403	C₂²×C₄	1	2	yes	—
180	#2403	C₂²×C₄	1	2	yes	—
181	#2403	C₂×D₄	1	2	yes	—
182	#2403	C₂×D₄	1	2	yes	—
183	#2403	C₂×D₄	1	2	yes	—
184	#2403	C₂×D₄	1	2	yes	—
185	#2403	C₂×D₄	1	2	yes	—
186	#2403	C₂×D₄	1	2	yes	—
187	#2403	C₂×D₄	1	2	yes	—
188	#2403	C₂×D₄	1	2	yes	—
189	#2403	C₂×D₄	1	2	yes	—
190	#2380	C₂²⋊C₄	1	2	yes	complemented
191	#2376	C₂²⋊C₄	1	2	yes	complemented
192	#2375	C₂²⋊C₄	1	2	yes	complemented
193	#2375	C₂²⋊C₄	1	2	yes	complemented
194	#2375	C₂²⋊C₄	1	2	yes	complemented
195	#2375	C₂²⋊C₄	1	2	yes	complemented
196	#2375	C₂²⋊C₄	1	2	yes	complemented
197	#2374	C₂²⋊C₄	1	2	yes	complemented
198	#2374	C₂²⋊C₄	1	2	yes	complemented
199	#2366	C₂²⋊C₄	1	2	yes	complemented
200	#2358	C₂²⋊C₄	1	2	yes	complemented
201	#2358	C₂²⋊C₄	1	2	yes	complemented
202	#2358	C₂²⋊C₄	1	2	yes	complemented
203	#2358	C₂²⋊C₄	1	2	yes	complemented
204	#2309	C₂²⋊C₄	1	2	yes	—
205	#2309	C₂×D₄	1	2	yes	—
206	#2309	C₂×D₄	1	2	yes	—
207	#2309	C₂×D₄	1	2	yes	—
208	#2309	C₂×D₄	1	2	yes	—
209	#2308	C₂²⋊C₄	1	1	yes	characteristic
210	#2308	C₂²⋊C₄	1	1	yes	characteristic
211	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
212	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
213	#2308	C₂²⋊C₄	1	2	yes	complemented
214	#2308	C₂×D₄	1	2	yes	—
215	#2308	C₂×D₄	1	2	yes	—
216	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic, complemented
217	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic, complemented
218	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic, complemented
219	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic, complemented
220	C₂×#390	C₂²×C₄	1	1	yes	characteristic
221	C₂×#390	C₂²×C₄	1	1	yes	characteristic
222	C₂×#390	C₂²×C₄	1	1	yes	characteristic
223	C₂×#390	C₂×D₄	1	1	yes	characteristic
224	C₂×#390	C₂×D₄	1	1	yes	characteristic
225	C₂×#390	C₂×D₄	1	1	yes	characteristic
226	C₂×#386	C₂×D₄	1	2	yes	—
227	C₂×#386	C₂×D₄	1	2	yes	—
228	C₂×#384	C₂²⋊C₄	1	1	yes	characteristic, complemented
229	C₂×#382	C₂²⋊C₄	1	1	yes	characteristic, complemented
230	C₂×#382	C₂²⋊C₄	1	1	yes	characteristic, complemented
231	C₂×#379	C₂×D₄	1	2	yes	—
232	C₂×#379	C₂×D₄	1	2	yes	—
233	C₂×C₄×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
234	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
235	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
236	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic, complemented
237	C₂⁶	#120	1	1	yes	characteristic
238	C₂⁶	#120	1	1	yes	characteristic
239	C₂⁶	#120	1	2	yes	—
240	C₂⁶	C₂²×D₄	1	1	yes	characteristic
241	C₂⁶	C₂²×D₄	1	1	yes	characteristic
242	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂³×D₄	#120	1	1	yes	characteristic
254	C₂³×D₄	#120	1	1	yes	characteristic
255	C₂³×D₄	#120	1	1	yes	characteristic
256	C₂³×D₄	#120	1	1	yes	characteristic
257	C₂³×D₄	#120	1	1	yes	characteristic
258	C₂³×D₄	#120	1	2	yes	—
259	C₂³×D₄	#120	1	2	yes	—
260	C₂³×D₄	#120	1	2	yes	—
261	C₂³×D₄	#120	1	2	yes	—
262	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
263	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
264	C₂³×D₄	C₂²×D₄	1	2	yes	—
265	C₂³×D₄	C₂²×D₄	1	2	yes	—
266	C₂³×D₄	C₂²×D₄	1	2	yes	—
267	C₂³×D₄	C₂²×D₄	1	2	yes	—
268	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
270	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂⁴×C₄	#120	1	1	yes	characteristic
272	C₂⁴×C₄	#120	1	1	yes	characteristic
273	C₂⁴×C₄	#120	1	2	yes	—
274	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
275	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×#127	#120	1	2	yes	—
278	C₂×#127	#120	1	2	yes	—
279	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂×#123	#120	1	2	yes	—
282	C₂×#123	#120	1	2	yes	—
283	C₂×#121	#120	1	2	yes	—
284	C₂×#121	#120	1	2	yes	—
285	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
286	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×#120	#120	1	2	yes	—
292	C₂×#120	#120	1	2	yes	—
293	C₂×#120	#120	1	2	yes	—
294	C₂×#120	#120	1	2	yes	—
295	C₂×#120	#120	1	2	yes	—
296	C₂×#120	#120	1	2	yes	—
297	C₂×#117	#120	1	2	yes	—
298	C₂×#117	#120	1	2	yes	—
299	C₂×#117	#120	1	2	yes	—
300	C₂×#117	#120	1	2	yes	—
301	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
306	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
311	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
313	C₂²×C₂²⋊C₄	#120	1	2	yes	—
314	C₂²×C₂²⋊C₄	#120	1	2	yes	—
315	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	#120	1	2	yes	—
318	C₂²×C₂²⋊C₄	#120	1	2	yes	—
319	C₂²×C₂²⋊C₄	#120	1	2	yes	—
320	C₂²×C₂²⋊C₄	#120	1	2	yes	—
321	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	#390	C₂×C₂²⋊C₄	1	2	yes	—
327	#390	C₂×C₂²⋊C₄	1	2	yes	—
328	#390	C₂×C₂²⋊C₄	1	2	yes	—
329	#390	C₂×C₂²⋊C₄	1	2	yes	—
330	#390	C₂×C₂²⋊C₄	1	2	yes	—
331	#390	C₂×C₂²⋊C₄	1	2	yes	—
332	#390	#120	1	2	yes	—
333	#390	#120	1	2	yes	—
334	#390	#120	1	1	yes	characteristic
335	#390	#120	1	1	yes	characteristic
336	#390	#120	1	1	yes	characteristic
337	#390	#120	1	1	yes	characteristic
338	#390	#120	1	1	yes	characteristic
339	#390	#120	1	1	yes	characteristic
340	#390	#120	1	1	yes	characteristic
341	#390	#120	1	1	yes	characteristic
342	#386	C₂×C₂²⋊C₄	1	2	yes	—
343	#386	C₂×C₂²⋊C₄	1	2	yes	—
344	#386	C₂×C₂²⋊C₄	1	2	yes	—
345	#386	C₂×C₂²⋊C₄	1	2	yes	—
346	#386	C₂×C₂²⋊C₄	1	2	yes	—
347	#386	C₂×C₂²⋊C₄	1	2	yes	—
348	#386	C₂×C₂²⋊C₄	1	2	yes	—
349	#386	C₂×C₂²⋊C₄	1	2	yes	—
350	#386	#120	1	2	yes	—
351	#386	#120	1	2	yes	—
352	#386	#120	1	2	yes	—
353	#386	#120	1	2	yes	—
354	#386	#120	1	2	yes	—
355	#386	#120	1	2	yes	—
356	#386	#120	1	2	yes	—
357	#386	#120	1	2	yes	—
358	#379	C₂×C₂²⋊C₄	1	2	yes	—
359	#379	C₂×C₂²⋊C₄	1	2	yes	—
360	#379	C₂×C₂²⋊C₄	1	2	yes	—
361	#379	C₂×C₂²⋊C₄	1	2	yes	—
362	#379	#120	1	2	yes	—
363	#379	#120	1	2	yes	—
364	#379	#120	1	2	yes	—
365	#379	#120	1	2	yes	—
366	C₄×C₂²⋊C₄	#120	1	2	yes	—
367	C₄×C₂²⋊C₄	#120	1	2	yes	—
368	C₂⁵	#379	1	1	yes	characteristic
369	C₂⁵	#379	1	1	yes	characteristic
370	C₂⁵	#379	1	1	yes	characteristic
371	C₂⁵	#379	1	2	yes	—
372	C₂⁵	#379	1	2	yes	—
373	C₂⁵	#379	1	2	yes	—
374	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
375	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
376	C₂⁵	C₂×#120	1	1	yes	characteristic
377	C₂⁵	C₂×#120	1	1	yes	characteristic
378	C₂⁵	C₂×#120	1	2	yes	—
379	C₂⁵	C₂×#120	1	2	yes	—
380	C₂⁵	C₂×#120	1	2	yes	—
381	C₂⁵	C₂×#120	1	2	yes	—
382	C₂⁵	C₂×#120	1	1	yes	characteristic
383	C₂²×D₄	#379	1	2	yes	—
384	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
385	C₂²×D₄	#458	1	2	yes	—
386	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
387	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
388	C₂²×D₄	C₂×#120	1	2	yes	—
389	C₂²×D₄	C₂×#120	1	2	yes	—
390	C₂²×D₄	C₂×#120	1	2	yes	—
391	C₂²×D₄	C₂×#120	1	2	yes	—
392	C₂²×D₄	C₂×#120	1	1	yes	characteristic
393	C₂²×D₄	C₂×#120	1	1	yes	characteristic
394	C₂²×D₄	C₂×#120	1	1	yes	characteristic
395	C₂²×D₄	C₂×#120	1	1	yes	characteristic
396	C₂³×C₄	#379	1	1	yes	characteristic
397	C₂³×C₄	#379	1	1	yes	characteristic
398	C₂³×C₄	#379	1	1	yes	characteristic
399	C₂³×C₄	#379	1	1	yes	characteristic
400	C₂³×C₄	#379	1	1	yes	characteristic
401	C₂³×C₄	#379	1	2	yes	—
402	C₂³×C₄	#379	1	2	yes	—
403	C₂³×C₄	#379	1	2	yes	—
404	C₂³×C₄	#379	1	2	yes	—
405	C₂³×C₄	#379	1	2	yes	—
406	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₂³×C₄	C₂×#120	1	2	yes	—
408	C₂³×C₄	C₂×#120	1	1	yes	characteristic
409	C₂³×C₄	C₂×#120	1	2	yes	—
410	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
411	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
412	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
413	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
414	C₂×C₄⋊C₄	#379	1	2	yes	—
415	C₂×C₂²⋊C₄	#379	1	2	yes	—
416	C₂×C₂²⋊C₄	#379	1	2	yes	—
417	C₂×C₂²⋊C₄	#379	1	2	yes	—
418	C₂×C₂²⋊C₄	#379	1	2	yes	—
419	C₂×C₂²⋊C₄	#379	1	2	yes	—
420	C₂×C₂²⋊C₄	#379	1	2	yes	—
421	C₂×C₂²⋊C₄	#379	1	2	yes	—
422	C₂×C₂²⋊C₄	#379	1	2	yes	—
423	C₂×C₄²	#379	1	2	yes	—
424	C₂×C₄²	#379	1	1	yes	characteristic
425	C₂×C₄²	#379	1	1	yes	characteristic
426	C₂×C₄²	#379	1	1	yes	characteristic
427	C₂×C₄²	#379	1	1	yes	characteristic
428	C₂×C₄²	#379	1	2	yes	—
429	C₂⁴	#1790	1	2	yes	—
430	C₂⁴	C₂×#379	1	1	yes	characteristic
431	C₂⁴	C₂×#379	1	2	yes	—
432	C₂⁴	C₂×#379	1	2	yes	—
433	C₂⁴	#2846	1	1	yes	characteristic
434	C₂⁴	#2846	1	1	yes	characteristic
435	C₂⁴	#2846	1	2	yes	—
436	C₂⁴	#2846	1	1	yes	characteristic
437	C₂⁴	#2846	1	1	yes	characteristic
438	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
439	C₂⁴	C₂×#458	1	1	yes	characteristic
440	C₂⁴	#3026	1	2	yes	—
441	C₂×D₄	#3025	1	1	yes	characteristic
442	C₂×D₄	#3025	1	1	yes	characteristic
443	C₂×D₄	#3027	1	1	yes	characteristic
444	C₂×D₄	#3028	1	1	yes	characteristic
445	C₂²×C₄	#1790	1	2	yes	—
446	C₂²×C₄	C₂×#379	1	1	yes	characteristic
447	C₂²×C₄	C₂×#379	1	1	yes	characteristic
448	C₂²×C₄	#2846	1	2	yes	—
449	C₂³	#12753	1	4	yes	—
450	C₂³	#14679	1	1	yes	characteristic
451	C₂³	C₂×#1790	1	1	yes	characteristic
452	C₂³	#20609	1	1	yes	characteristic
453	C₂³	#32898	1	2	yes	—
454	C₂³	#32899	1	1	yes	characteristic
455	C₂³	#32899	1	1	yes	characteristic
456	C₂³	#32900	1	2	yes	—
457	C₂³	#32901	1	1	yes	characteristic
458	C₂³	#32901	1	1	yes	characteristic
459	C₂×C₄	#20608	1	1	yes	characteristic
460	C₂×C₄	#20610	1	1	yes	characteristic
461	C₂²	#392125	1	1	yes	characteristic
462	C₂²	#392126	1	1	yes	characteristic
463	C₂²	#392135	1	1	yes	characteristic
464	C₂²	C₂×#12753	1	2	yes	—
465	C₂	#72218980	1	1	yes	characteristic
466	C₂	#72260638	1	1	yes	characteristic
467	C₂	#72260707	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#392125
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72261186	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×D₄² ◁ 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. #72261400	C₂	semidirect
3. #72261063	C₂	semidirect
4. #72260988	C₂	semidirect
5. #72234969	C₂	semidirect
6. #72234187	C₂	semidirect
7. #72233510	C₂	semidirect
8. #72233338	C₂	semidirect
9. #72233200	C₂	semidirect
10. #72232787	C₂	semidirect
11. #72232749	C₂	semidirect
12. #8395045	C₄	semidirect
13. #8362477	C₄	semidirect
15. #8093976	C₄	semidirect
16. #8093116	C₄	semidirect
18. #7682006	C₄	semidirect
19. #7670308	C₄	semidirect
23. #6385971	C₂²	semidirect
24. #496231	C₂²	semidirect
25. #496225	C₂²	semidirect
26. C₂×#13088	C₂²	semidirect
27. C₂×#13088	C₂²	semidirect
28. #494695	C₂²	semidirect
29. C₂×#13086	C₂²	semidirect
30. C₂×#12858	C₂²	semidirect
31. C₂×#12582	C₂²	semidirect
32. #374058	C₂²	semidirect
33. #374038	C₂²	semidirect
34. #359869	C₂²	semidirect
35. #359579	C₂²	semidirect
36. #359579	C₂²	semidirect
37. #201701	C₂²	semidirect
38. #201664	C₂²	semidirect
39. #201293	C₂²	semidirect
40. #188087	C₂²	semidirect
109. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
115. C₂×#560	C₂²⋊C₄	semidirect
116. C₂×D₄²	C₂²⋊C₄	semidirect
117. C₂×#534	C₂²⋊C₄	semidirect
120. C₂²×#127	C₂²⋊C₄	semidirect
124. C₂²×#125	C₂²⋊C₄	semidirect
125. C₂²×#121	C₂²⋊C₄	semidirect
138. C₂×#518	C₂²⋊C₄	semidirect
139. C₂²×C₄×D₄	C₂²⋊C₄	semidirect
144. C₂³×C₄⋊C₄	C₂²⋊C₄	semidirect
145. C₂³×C₄²	C₂²⋊C₄	semidirect
146. #2804	C₂²⋊C₄	semidirect
147. #2804	C₂²⋊C₄	semidirect
148. #2748	C₂²⋊C₄	semidirect
149. #2748	C₂²⋊C₄	semidirect
150. #2748	C₂²⋊C₄	semidirect
151. #2709	C₂²⋊C₄	semidirect
152. #2697	C₂²⋊C₄	semidirect
153. #2697	C₂²⋊C₄	semidirect
154. #2697	C₂²⋊C₄	semidirect
155. #2683	C₂²⋊C₄	semidirect
156. #2679	C₂²⋊C₄	semidirect
157. #2679	C₂²⋊C₄	semidirect
158. #2679	C₂²⋊C₄	semidirect
159. #2669	C₂²⋊C₄	semidirect
160. #2669	C₂²⋊C₄	semidirect
161. #2669	C₂²⋊C₄	semidirect
162. #2483	C₂²⋊C₄	semidirect
169. #2405	C₂²⋊C₄	semidirect
170. #2405	C₂²⋊C₄	semidirect
177. #2403	C₂²⋊C₄	semidirect
190. #2380	C₂²⋊C₄	semidirect
191. #2376	C₂²⋊C₄	semidirect
192. #2375	C₂²⋊C₄	semidirect
193. #2375	C₂²⋊C₄	semidirect
194. #2375	C₂²⋊C₄	semidirect
195. #2375	C₂²⋊C₄	semidirect
196. #2375	C₂²⋊C₄	semidirect
197. #2374	C₂²⋊C₄	semidirect
198. #2374	C₂²⋊C₄	semidirect
199. #2366	C₂²⋊C₄	semidirect
200. #2358	C₂²⋊C₄	semidirect
201. #2358	C₂²⋊C₄	semidirect
202. #2358	C₂²⋊C₄	semidirect
203. #2358	C₂²⋊C₄	semidirect
211. #2308	C₂²⋊C₄	semidirect
212. #2308	C₂²⋊C₄	semidirect
213. #2308	C₂²⋊C₄	semidirect
216. C₂×#390	C₂²⋊C₄	semidirect
217. C₂×#390	C₂²⋊C₄	semidirect
218. C₂×#390	C₂²⋊C₄	semidirect
219. C₂×#390	C₂²⋊C₄	semidirect
228. C₂×#384	C₂²⋊C₄	semidirect
229. C₂×#382	C₂²⋊C₄	semidirect
230. C₂×#382	C₂²⋊C₄	semidirect
233. C₂×C₄×C₄⋊C₄	C₂²⋊C₄	semidirect
234. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
236. C₂×#376	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72261400	2
#72261186	2
#72261063	2
#72260988	2
#72234969	2
#72234187	2
#72233510	2
#72233338	2
#72233200	2
#72232787	2
#72232749	2