Subgroups — #72265776

Order 2048.

At least 16083 conjugacy classes of subgroups; only the 746 normal subgroups are shown.

The subgroup lattice has 463 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265773	C₂	1	2	yes	maximal, complemented
2	#72265770	C₂	1	2	yes	maximal, complemented
3	#72265743	C₂	1	1	yes	maximal, characteristic, complemented
4	#72258238	C₂	1	2	yes	maximal, complemented
5	#72258234	C₂	1	2	yes	maximal, complemented
6	#72232845	C₂	1	1	yes	maximal, characteristic
7	#72219300	C₂	1	1	yes	maximal, characteristic, complemented
8	#72219294	C₂	1	1	yes	maximal, characteristic, complemented
9	#72218846	C₂	1	1	yes	maximal, characteristic, complemented
10	#72218455	C₂	1	1	yes	maximal, characteristic, complemented
11	#72218057	C₂	1	1	yes	maximal, characteristic, complemented
12	#7792764	C₄	1	2	yes	complemented
13	#7792761	C₄	1	2	yes	complemented
14	#7763452	C₂²	1	2	yes	—
15	#7763449	C₂²	1	2	yes	—
16	#7708354	C₄	1	2	yes	complemented
17	#7708349	C₄	1	2	yes	complemented
18	#7630939	C₂²	1	1	yes	characteristic
19	C₂×#34980	C₂²	1	1	yes	characteristic
20	C₂²×#2403	C₂²	1	1	yes	characteristic
21	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
22	#517411	C₂²	1	1	yes	characteristic, complemented
23	#494713	C₂²	1	2	yes	complemented
24	#494713	C₂²	1	2	yes	complemented
25	C₂×#13086	C₂²	1	2	yes	complemented
26	C₂×#13086	C₂²	1	2	yes	complemented
27	#493879	C₂²	1	2	yes	complemented
28	#493357	C₂²	1	2	yes	complemented
29	#392113	C₂²	1	1	yes	characteristic, complemented
30	#392109	C₂²	1	1	yes	characteristic, complemented
31	#357894	C₂²	1	1	yes	characteristic, complemented
32	C₂×#11172	C₂²	1	1	yes	characteristic, complemented
33	#357530	C₂²	1	1	yes	characteristic, complemented
34	C₂×#10972	C₂²	1	1	yes	characteristic, complemented
35	C₂×#9495	C₂²	1	2	yes	complemented
36	C₂×#9495	C₂²	1	2	yes	complemented
37	#201322	C₂²	1	2	yes	complemented
38	#201322	C₂²	1	2	yes	complemented
39	C₂⁵×D₄	D₄	1	1	yes	characteristic
40	C₂⁵×D₄	C₂³	1	1	yes	characteristic
41	C₂×#3484	C₂×C₄	1	1	yes	characteristic
42	C₂×#3484	D₄	1	1	yes	characteristic
43	C₂×#3484	D₄	1	1	yes	characteristic
44	C₂×#3532	C₂×C₄	1	2	yes	—
45	C₂²×#534	D₄	1	1	yes	characteristic
46	C₂²×#534	C₂³	1	1	yes	characteristic
47	C₂³×#120	C₂×C₄	1	1	yes	characteristic
48	C₂³×#120	D₄	1	1	yes	characteristic
49	C₂³×#120	D₄	1	1	yes	characteristic
50	C₂³×#99	C₂³	1	1	yes	characteristic
51	C₂³×#99	C₂³	1	1	yes	characteristic
52	#59370	D₄	1	2	yes	—
53	#59191	D₄	1	2	yes	—
54	#58992	D₄	1	2	yes	—
55	#58990	D₄	1	2	yes	—
56	#50856	D₄	1	2	yes	—
57	#50646	D₄	1	2	yes	—
58	#48922	D₄	1	2	yes	—
59	#48143	D₄	1	2	yes	—
60	#48113	D₄	1	2	yes	—
61	#48088	D₄	1	2	yes	—
62	#47848	D₄	1	2	yes	—
63	#47827	D₄	1	2	yes	—
64	#45727	D₄	1	2	yes	—
65	#45568	D₄	1	2	yes	—
66	#45455	D₄	1	2	yes	—
67	#45439	D₄	1	2	yes	—
68	#36747	C₂×C₄	1	2	yes	—
69	#36737	C₂×C₄	1	2	yes	—
70	#36714	C₂×C₄	1	2	yes	—
71	#36702	C₂×C₄	1	2	yes	—
72	#36614	D₄	1	2	yes	—
73	#35222	C₂×C₄	1	2	yes	—
74	#35222	D₄	1	2	yes	—
75	#35222	C₂³	1	2	yes	—
76	#34980	C₂×C₄	1	2	yes	—
77	#34980	C₂×C₄	1	2	yes	—
78	#34980	D₄	1	2	yes	—
79	#34980	D₄	1	2	yes	—
80	C₂×#2403	C₂×C₄	1	2	yes	—
81	C₂×#2403	D₄	1	2	yes	—
82	C₂×#2403	D₄	1	2	yes	—
83	C₂×#2403	C₂³	1	2	yes	—
84	#34407	C₂×C₄	1	2	yes	—
85	#34406	C₂×C₄	1	2	yes	—
86	#34356	C₂×C₄	1	2	yes	—
87	#34171	C₂×C₄	1	1	yes	characteristic
88	#34171	D₄	1	1	yes	characteristic
89	#34171	D₄	1	1	yes	characteristic
90	C₂×#2308	D₄	1	1	yes	characteristic
91	C₂×#2308	C₂³	1	1	yes	characteristic
92	C₂×#2308	C₂³	1	1	yes	characteristic
93	C₂×#2308	C₂³	1	1	yes	characteristic
94	C₂²×#386	C₂×C₄	1	1	yes	characteristic
95	C₂²×#386	D₄	1	1	yes	characteristic
96	C₂²×#379	D₄	1	1	yes	characteristic
97	C₂²×#379	D₄	1	1	yes	characteristic
98	C₂×#1783	C₂³	1	2	yes	—
99	C₂×#1781	C₂³	1	2	yes	—
100	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
101	C₂⁷	C₂×D₄	1	1	yes	characteristic
102	C₂⁷	C₂×D₄	1	1	yes	characteristic
103	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	complemented
105	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
114	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
119	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
120	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂×H(3,𝔽₄)	C₂²⋊C₄	1	2	yes	complemented
122	C₂×#560	C₂²⋊C₄	1	2	yes	complemented
123	C₂×#551	C₂²⋊C₄	1	2	yes	complemented
124	C₂×D₄²	C₂²⋊C₄	1	2	yes	complemented
125	C₂×#535	C₂²⋊C₄	1	2	yes	complemented
126	C₂×#535	C₂²×C₄	1	2	yes	—
127	C₂×#535	C₂×D₄	1	2	yes	—
128	C₂×#534	C₂²⋊C₄	1	2	yes	—
129	C₂×#534	C₂²⋊C₄	1	2	yes	—
130	C₂×#534	C₂²×C₄	1	2	yes	—
131	C₂×#534	C₂×D₄	1	2	yes	—
132	C₂×#534	C₂×D₄	1	2	yes	—
133	C₂×#534	C₂×D₄	1	2	yes	—
134	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
135	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
136	C₂×#525	C₂×D₄	1	2	yes	—
137	C₂²×#123	C₂×D₄	1	2	yes	—
138	C₂²×#120	C₂²⋊C₄	1	2	yes	—
139	C₂²×#120	C₂²⋊C₄	1	2	yes	—
140	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
141	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
142	C₂²×#120	C₂²×C₄	1	2	yes	—
143	C₂²×#120	C₂×D₄	1	2	yes	—
144	C₂²×#120	C₂×D₄	1	2	yes	—
145	C₂×#518	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂×#518	C₂²⋊C₄	1	1	yes	characteristic, complemented
147	C₂×#518	C₂²⋊C₄	1	1	yes	characteristic, complemented
148	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
149	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
150	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
153	#2804	C₂²⋊C₄	1	2	yes	complemented
154	#2748	C₂²⋊C₄	1	2	yes	complemented
155	#2748	C₂²⋊C₄	1	2	yes	complemented
156	#2717	C₂²⋊C₄	1	2	yes	complemented
157	#2709	C₂²⋊C₄	1	2	yes	complemented
158	#2697	C₂²⋊C₄	1	2	yes	complemented
159	#2697	C₂²⋊C₄	1	2	yes	complemented
160	#2684	C₂²⋊C₄	1	2	yes	complemented
161	#2684	C₂²⋊C₄	1	2	yes	complemented
162	#2684	C₂²⋊C₄	1	2	yes	complemented
163	#2683	C₂²⋊C₄	1	2	yes	complemented
164	#2679	C₂²⋊C₄	1	2	yes	complemented
165	#2679	C₂²⋊C₄	1	2	yes	complemented
166	#2669	C₂²⋊C₄	1	2	yes	complemented
167	#2669	C₂²⋊C₄	1	2	yes	complemented
168	#2669	C₂²⋊C₄	1	2	yes	complemented
169	#2435	C₂×D₄	1	2	yes	—
170	#2435	C₂×D₄	1	2	yes	—
171	#2435	C₂×D₄	1	2	yes	—
172	#2435	C₂×D₄	1	2	yes	—
173	#2433	C₂×D₄	1	2	yes	—
174	#2433	C₂×D₄	1	2	yes	—
175	#2433	C₂×D₄	1	2	yes	—
176	#2433	C₂×D₄	1	2	yes	—
177	#2403	C₂×D₄	1	2	yes	—
178	#2403	C₂×D₄	1	2	yes	—
179	#2403	C₂×D₄	1	2	yes	—
180	#2403	C₂×D₄	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	#2380	C₂²⋊C₄	1	2	yes	complemented
186	#2379	C₂²⋊C₄	1	2	yes	complemented
187	#2376	C₂²⋊C₄	1	2	yes	complemented
188	#2375	C₂²⋊C₄	1	2	yes	complemented
189	#2375	C₂²⋊C₄	1	2	yes	complemented
190	#2375	C₂²⋊C₄	1	2	yes	complemented
191	#2374	C₂²⋊C₄	1	2	yes	complemented
192	#2372	C₂²⋊C₄	1	2	yes	complemented
193	#2366	C₂²⋊C₄	1	2	yes	complemented
194	#2358	C₂²⋊C₄	1	2	yes	complemented
195	#2358	C₂²⋊C₄	1	2	yes	complemented
196	#2358	C₂²⋊C₄	1	2	yes	complemented
197	#2309	C₂²⋊C₄	1	2	yes	complemented
198	#2309	C₂²×C₄	1	2	yes	—
199	#2309	C₂×D₄	1	2	yes	—
200	#2308	C₂²⋊C₄	1	2	yes	—
201	#2308	C₂²⋊C₄	1	2	yes	—
202	#2308	C₂²×C₄	1	2	yes	—
203	#2308	C₂×D₄	1	2	yes	—
204	#2308	C₂×D₄	1	2	yes	—
205	#2308	C₂×D₄	1	2	yes	—
206	C₂×#386	C₂²⋊C₄	1	2	yes	complemented
207	C₂×#386	C₂²⋊C₄	1	2	yes	complemented
208	C₂×#386	C₂²×C₄	1	2	yes	—
209	C₂×#386	C₂×D₄	1	2	yes	—
210	C₂×#386	C₂×D₄	1	2	yes	—
211	C₂×#386	C₂×D₄	1	2	yes	—
212	#2280	C₂²⋊C₄	1	2	yes	complemented
213	#2280	C₂²⋊C₄	1	2	yes	complemented
214	#2280	C₂×D₄	1	2	yes	—
215	C₂×#379	C₂²⋊C₄	1	2	yes	—
216	C₂×#379	C₂²⋊C₄	1	2	yes	—
217	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
218	C₂×#379	C₂×D₄	1	2	yes	—
219	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂⁶	#120	1	1	yes	characteristic
225	C₂⁶	#120	1	1	yes	characteristic
226	C₂⁶	#120	1	1	yes	characteristic
227	C₂⁶	#120	1	1	yes	characteristic
228	C₂⁶	#120	1	1	yes	characteristic
229	C₂⁶	#120	1	1	yes	characteristic
230	C₂⁶	#120	1	1	yes	characteristic
231	C₂⁶	#120	1	1	yes	characteristic
232	C₂⁶	C₂²×D₄	1	1	yes	characteristic
233	C₂⁶	C₂²×D₄	1	1	yes	characteristic
234	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂³×D₄	#120	1	1	yes	characteristic
243	C₂³×D₄	#120	1	1	yes	characteristic
244	C₂³×D₄	#120	1	1	yes	characteristic
245	C₂³×D₄	#120	1	1	yes	characteristic
246	C₂³×D₄	#120	1	1	yes	characteristic
247	C₂³×D₄	#120	1	2	yes	—
248	C₂³×D₄	#120	1	1	yes	characteristic
249	C₂³×D₄	#120	1	2	yes	—
250	C₂³×D₄	#120	1	2	yes	—
251	C₂³×D₄	#120	1	2	yes	—
252	C₂³×D₄	#120	1	2	yes	—
253	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
254	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
255	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
256	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
257	C₂³×D₄	C₂²×D₄	1	2	yes	—
258	C₂³×D₄	C₂²×D₄	1	2	yes	—
259	C₂³×D₄	C₂²×D₄	1	2	yes	—
260	C₂³×D₄	C₂²×D₄	1	2	yes	—
261	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂⁴×C₄	#120	1	1	yes	characteristic
265	C₂⁴×C₄	#120	1	1	yes	characteristic
266	C₂⁴×C₄	#120	1	1	yes	characteristic
267	C₂⁴×C₄	#120	1	1	yes	characteristic
268	C₂⁴×C₄	#120	1	1	yes	characteristic
269	C₂⁴×C₄	#120	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
271	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂×#127	#120	1	2	yes	—
274	C₂×#127	#120	1	2	yes	—
275	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×#124	#120	1	2	yes	—
278	C₂×#124	#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×C₂²⋊Q₈	#120	1	2	yes	—
284	C₂×C₂²⋊Q₈	#120	1	2	yes	—
285	C₂×#121	#120	1	2	yes	—
286	C₂×#121	#120	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	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×#120	C₂×C₂²⋊C₄	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×#120	#120	1	2	yes	—
298	C₂×#120	#120	1	2	yes	—
299	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂²×C₂²⋊C₄	#120	1	2	yes	—
308	C₂²×C₂²⋊C₄	#120	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	2	yes	—
313	C₂²×C₂²⋊C₄	#120	1	2	yes	—
314	#390	C₂×C₂²⋊C₄	1	2	yes	—
315	#390	C₂×C₂²⋊C₄	1	2	yes	—
316	#390	C₂×C₂²⋊C₄	1	2	yes	—
317	#390	C₂×C₂²⋊C₄	1	2	yes	—
318	#390	#120	1	2	yes	—
319	#390	#120	1	2	yes	—
320	#390	#120	1	2	yes	—
321	#390	#120	1	2	yes	—
322	#386	C₂×C₂²⋊C₄	1	2	yes	—
323	#386	C₂×C₂²⋊C₄	1	2	yes	—
324	#386	C₂×C₂²⋊C₄	1	2	yes	—
325	#386	C₂×C₂²⋊C₄	1	2	yes	—
326	#386	C₂×C₂²⋊C₄	1	2	yes	—
327	#386	C₂×C₂²⋊C₄	1	2	yes	—
328	#386	C₂×C₂²⋊C₄	1	2	yes	—
329	#386	C₂×C₂²⋊C₄	1	2	yes	—
330	#386	#120	1	2	yes	—
331	#386	#120	1	2	yes	—
332	#386	#120	1	2	yes	—
333	#386	#120	1	2	yes	—
334	#386	#120	1	2	yes	—
335	#386	#120	1	2	yes	—
336	#386	#120	1	2	yes	—
337	#386	#120	1	2	yes	—
338	#379	#120	1	2	yes	—
339	#379	#120	1	2	yes	—
340	#379	#120	1	2	yes	—
341	#379	#120	1	2	yes	—
342	C₄×C₂²⋊C₄	#120	1	2	yes	—
343	C₄×C₂²⋊C₄	#120	1	2	yes	—
344	C₄×C₂²⋊C₄	#120	1	2	yes	—
345	C₄×C₂²⋊C₄	#120	1	2	yes	—
346	C₂⁵	#379	1	1	yes	characteristic
347	C₂⁵	#379	1	1	yes	characteristic
348	C₂⁵	#379	1	1	yes	characteristic
349	C₂⁵	#379	1	1	yes	characteristic
350	C₂⁵	#379	1	1	yes	characteristic
351	C₂⁵	#379	1	1	yes	characteristic
352	C₂⁵	#379	1	2	yes	—
353	C₂⁵	#379	1	2	yes	—
354	C₂⁵	#379	1	2	yes	—
355	C₂⁵	B(4,𝔽₂)	1	2	yes	—
356	C₂⁵	B(4,𝔽₂)	1	2	yes	—
357	C₂⁵	#458	1	2	yes	—
358	C₂⁵	#458	1	2	yes	—
359	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
360	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
361	C₂⁵	C₂×#120	1	1	yes	characteristic
362	C₂⁵	C₂×#120	1	1	yes	characteristic
363	C₂⁵	C₂×#120	1	1	yes	characteristic
364	C₂⁵	C₂×#120	1	1	yes	characteristic
365	C₂⁵	C₂×#120	1	1	yes	characteristic
366	C₂⁵	C₂×#120	1	1	yes	characteristic
367	C₂⁵	C₂×#120	1	2	yes	—
368	C₂⁵	C₂×#120	1	2	yes	—
369	C₂⁵	C₂×#120	1	1	yes	characteristic
370	C₂²×Q₈	#379	1	2	yes	—
371	C₂²×D₄	#379	1	2	yes	—
372	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
373	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
374	C₂²×D₄	C₂×#120	1	2	yes	—
375	C₂²×D₄	C₂×#120	1	2	yes	—
376	C₂²×D₄	C₂×#120	1	2	yes	—
377	C₂²×D₄	C₂×#120	1	2	yes	—
378	C₂²×D₄	C₂×#120	1	2	yes	—
379	C₂²×D₄	C₂×#120	1	2	yes	—
380	C₂³×C₄	#379	1	1	yes	characteristic
381	C₂³×C₄	#379	1	1	yes	characteristic
382	C₂³×C₄	#379	1	2	yes	—
383	C₂³×C₄	#379	1	2	yes	—
384	C₂³×C₄	#379	1	2	yes	—
385	C₂³×C₄	#379	1	2	yes	—
386	C₂³×C₄	#379	1	2	yes	—
387	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
388	C₂³×C₄	C₂×#120	1	1	yes	characteristic
389	C₂³×C₄	C₂×#120	1	2	yes	—
390	C₂³×C₄	C₂×#120	1	2	yes	—
391	C₂×C₄⋊C₄	#379	1	2	yes	—
392	C₂×C₄⋊C₄	#379	1	2	yes	—
393	C₂×C₂²⋊C₄	#379	1	2	yes	—
394	C₂×C₂²⋊C₄	#379	1	2	yes	—
395	C₂×C₂²⋊C₄	#379	1	2	yes	—
396	C₂×C₂²⋊C₄	#379	1	2	yes	—
397	C₂×C₂²⋊C₄	#379	1	2	yes	—
398	C₂×C₂²⋊C₄	#379	1	2	yes	—
399	C₂×C₂²⋊C₄	#379	1	2	yes	—
400	C₂×C₂²⋊C₄	#379	1	2	yes	—
401	C₂×C₄²	#379	1	2	yes	—
402	C₂×C₄²	#379	1	2	yes	—
403	C₂×C₄²	#379	1	2	yes	—
404	C₂×C₄²	#379	1	2	yes	—
405	C₂⁴	#1790	1	2	yes	—
406	C₂⁴	#1790	1	2	yes	—
407	C₂⁴	#1790	1	2	yes	—
408	C₂⁴	#1790	1	2	yes	—
409	C₂⁴	C₂×#379	1	2	yes	—
410	C₂⁴	C₂×#379	1	1	yes	characteristic
411	C₂⁴	C₂×#379	1	1	yes	characteristic
412	C₂⁴	C₂×#379	1	1	yes	characteristic
413	C₂⁴	#2846	1	1	yes	characteristic
414	C₂⁴	#2846	1	2	yes	—
415	C₂⁴	#2846	1	1	yes	characteristic
416	C₂⁴	#2846	1	1	yes	characteristic
417	C₂⁴	#2846	1	1	yes	characteristic
418	C₂⁴	#2883	1	1	yes	characteristic
419	C₂⁴	#2883	1	1	yes	characteristic
420	C₂⁴	#2883	1	1	yes	characteristic
421	C₂⁴	#2883	1	1	yes	characteristic
422	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
423	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
424	C₂⁴	C₂×#458	1	1	yes	characteristic
425	C₂⁴	C₂×#458	1	1	yes	characteristic
426	C₂⁴	#3026	1	1	yes	characteristic
427	C₂⁴	#3026	1	1	yes	characteristic
428	C₂⁴	#3026	1	1	yes	characteristic
429	C₂⁴	#3026	1	1	yes	characteristic
430	C₂²×C₄	C₂×#379	1	2	yes	—
431	C₂²×C₄	#2846	1	2	yes	—
432	C₂³	#14679	1	1	yes	characteristic
433	C₂³	#20585	1	1	yes	characteristic
434	C₂³	#20585	1	1	yes	characteristic
435	C₂³	#20585	1	1	yes	characteristic
436	C₂³	#20585	1	1	yes	characteristic
437	C₂³	#20586	1	1	yes	characteristic
438	C₂³	#20586	1	1	yes	characteristic
439	C₂³	C₂×#1790	1	1	yes	characteristic
440	C₂³	C₂×#1790	1	1	yes	characteristic
441	C₂³	#20609	1	1	yes	characteristic
442	C₂³	#20609	1	1	yes	characteristic
443	C₂³	#32898	1	1	yes	characteristic
444	C₂³	#32898	1	1	yes	characteristic
445	C₂³	#32898	1	1	yes	characteristic
446	C₂³	#32898	1	1	yes	characteristic
447	C₂³	#32900	1	1	yes	characteristic
448	C₂³	#32900	1	1	yes	characteristic
449	C₂³	#32900	1	1	yes	characteristic
450	C₂³	#32900	1	1	yes	characteristic
451	C₂²	#187934	1	1	yes	characteristic
452	C₂²	#187934	1	1	yes	characteristic
453	C₂²	#187940	1	1	yes	characteristic
454	C₂²	#187949	1	1	yes	characteristic
455	C₂²	#392111	1	1	yes	characteristic
456	C₂²	#392125	1	1	yes	characteristic
457	C₂²	#392125	1	1	yes	characteristic
458	C₂²	#511790	1	2	yes	—
459	C₂	#72218475	1	1	yes	characteristic
460	C₂	#72225624	1	1	yes	characteristic
461	C₂	#72237472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#392125
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72232845	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ 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. #72265773	C₂	semidirect
2. #72265770	C₂	semidirect
3. #72265743	C₂	semidirect
4. #72258238	C₂	semidirect
5. #72258234	C₂	semidirect
7. #72219300	C₂	semidirect
8. #72219294	C₂	semidirect
9. #72218846	C₂	semidirect
10. #72218455	C₂	semidirect
11. #72218057	C₂	semidirect
12. #7792764	C₄	semidirect
13. #7792761	C₄	semidirect
16. #7708354	C₄	semidirect
17. #7708349	C₄	semidirect
21. C₂²×#1781	C₂²	semidirect
22. #517411	C₂²	semidirect
23. #494713	C₂²	semidirect
24. #494713	C₂²	semidirect
25. C₂×#13086	C₂²	semidirect
26. C₂×#13086	C₂²	semidirect
27. #493879	C₂²	semidirect
28. #493357	C₂²	semidirect
29. #392113	C₂²	semidirect
30. #392109	C₂²	semidirect
31. #357894	C₂²	semidirect
32. C₂×#11172	C₂²	semidirect
33. #357530	C₂²	semidirect
34. C₂×#10972	C₂²	semidirect
35. C₂×#9495	C₂²	semidirect
36. C₂×#9495	C₂²	semidirect
37. #201322	C₂²	semidirect
38. #201322	C₂²	semidirect
100. C₂⁷	C₂²⋊C₄	semidirect
103. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
104. C₂⁴×D₄	C₂²⋊C₄	semidirect
119. C₂⁵×C₄	C₂²⋊C₄	semidirect
121. C₂×H(3,𝔽₄)	C₂²⋊C₄	semidirect
122. C₂×#560	C₂²⋊C₄	semidirect
123. C₂×#551	C₂²⋊C₄	semidirect
124. C₂×D₄²	C₂²⋊C₄	semidirect
125. C₂×#535	C₂²⋊C₄	semidirect
134. C₂×#525	C₂²⋊C₄	semidirect
135. C₂×#525	C₂²⋊C₄	semidirect
140. C₂²×#120	C₂²⋊C₄	semidirect
141. C₂²×#120	C₂²⋊C₄	semidirect
145. C₂×#518	C₂²⋊C₄	semidirect
146. C₂×#518	C₂²⋊C₄	semidirect
147. C₂×#518	C₂²⋊C₄	semidirect
148. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
149. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
153. #2804	C₂²⋊C₄	semidirect
154. #2748	C₂²⋊C₄	semidirect
155. #2748	C₂²⋊C₄	semidirect
156. #2717	C₂²⋊C₄	semidirect
157. #2709	C₂²⋊C₄	semidirect
158. #2697	C₂²⋊C₄	semidirect
159. #2697	C₂²⋊C₄	semidirect
160. #2684	C₂²⋊C₄	semidirect
161. #2684	C₂²⋊C₄	semidirect
162. #2684	C₂²⋊C₄	semidirect
163. #2683	C₂²⋊C₄	semidirect
164. #2679	C₂²⋊C₄	semidirect
165. #2679	C₂²⋊C₄	semidirect
166. #2669	C₂²⋊C₄	semidirect
167. #2669	C₂²⋊C₄	semidirect
168. #2669	C₂²⋊C₄	semidirect
185. #2380	C₂²⋊C₄	semidirect
186. #2379	C₂²⋊C₄	semidirect
187. #2376	C₂²⋊C₄	semidirect
188. #2375	C₂²⋊C₄	semidirect
189. #2375	C₂²⋊C₄	semidirect
190. #2375	C₂²⋊C₄	semidirect
191. #2374	C₂²⋊C₄	semidirect
192. #2372	C₂²⋊C₄	semidirect
193. #2366	C₂²⋊C₄	semidirect
194. #2358	C₂²⋊C₄	semidirect
195. #2358	C₂²⋊C₄	semidirect
196. #2358	C₂²⋊C₄	semidirect
197. #2309	C₂²⋊C₄	semidirect
206. C₂×#386	C₂²⋊C₄	semidirect
207. C₂×#386	C₂²⋊C₄	semidirect
212. #2280	C₂²⋊C₄	semidirect
213. #2280	C₂²⋊C₄	semidirect
217. C₂×#379	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72265773	2
#72265770	2
#72265743	2
#72258238	2
#72258234	2
#72232845	2
#72219300	2
#72219294	2
#72218846	2
#72218455	2
#72218057	2