Subgroups — #72310453

Order 4096.

At least 26970 conjugacy classes of subgroups; only the 543 normal subgroups are shown.

The subgroup lattice has 472 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72310388	C₂	1	1	yes	maximal, characteristic, complemented
2	#72310339	C₂	1	1	yes	maximal, characteristic, complemented
3	#72310304	C₂	1	1	yes	maximal, characteristic, complemented
4	#72309591	C₂	1	1	yes	maximal, characteristic, complemented
5	#72309382	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266881	C₂	1	1	yes	maximal, characteristic, complemented
7	#72266073	C₂²	1	1	yes	characteristic, complemented
8	#72266028	C₂²	1	1	yes	characteristic, complemented
9	#72262357	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251565	C₂	1	1	yes	maximal, characteristic, complemented
11	#72238346	C₂	1	1	yes	maximal, characteristic, complemented
12	#72237398	C₂²	1	1	yes	characteristic, complemented
13	#72237032	C₂	1	1	yes	maximal, characteristic, complemented
14	#72234663	C₂²	1	1	yes	characteristic, complemented
15	#72225648	C₂	1	1	yes	maximal, characteristic
16	#72225647	C₄	1	1	yes	characteristic, complemented
17	#72225646	C₄	1	1	yes	characteristic, complemented
18	#72225644	C₄	1	1	yes	characteristic, complemented
19	#72225641	C₄	1	1	yes	characteristic, complemented
20	#72225639	C₄	1	1	yes	characteristic, complemented
21	#72225635	C₄	1	1	yes	characteristic, complemented
22	#72225619	C₂²	1	1	yes	characteristic
23	#72225617	C₂²	1	1	yes	characteristic
24	#72219445	C₂	1	1	yes	maximal, characteristic, complemented
25	#72219418	C₂²	1	1	yes	characteristic, complemented
26	#72219414	C₂²	1	1	yes	characteristic, complemented
27	#72219301	C₂²	1	1	yes	characteristic, complemented
28	#72219157	C₄	1	1	yes	characteristic, complemented
29	#72218522	C₂	1	1	yes	maximal, characteristic, complemented
30	#72218518	C₂²	1	1	yes	characteristic, complemented
31	#72218498	C₂²	1	1	yes	characteristic, complemented
32	#72218477	C₂	1	1	yes	maximal, characteristic, complemented
33	#72218455	C₂²	1	1	yes	characteristic
34	#72218451	C₂²	1	1	yes	characteristic, complemented
35	#72218393	C₂	1	1	yes	maximal, characteristic, complemented
36	#72218381	C₂²	1	1	yes	characteristic, complemented
37	#72218381	C₂²	1	1	yes	characteristic, complemented
38	#72218375	C₂²	1	1	yes	characteristic, complemented
39	#72218313	C₂²	1	1	yes	characteristic, complemented
40	#72218306	C₂²	1	1	yes	characteristic, complemented
41	#72218180	C₂²	1	1	yes	characteristic, complemented
42	#72218180	C₂²	1	1	yes	characteristic, complemented
43	#72218069	C₂²	1	1	yes	characteristic, complemented
44	#72218069	C₂²	1	1	yes	characteristic, complemented
45	#72218057	C₂²	1	1	yes	characteristic
46	#72218057	C₂²	1	1	yes	characteristic
47	#72218057	C₂²	1	1	yes	characteristic
48	#72218057	C₂²	1	1	yes	characteristic, complemented
49	#72218057	C₂²	1	1	yes	characteristic, complemented
50	#72218057	C₂²	1	1	yes	characteristic, complemented
51	#72218057	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#23900	C₂²	1	1	yes	characteristic
53	C₂×#6499874	C₄	1	1	yes	characteristic, complemented
54	#72217511	C₂²	1	1	yes	characteristic
55	#72216064	C₂²	1	1	yes	characteristic
56	#72215858	C₂²	1	1	yes	characteristic
57	#72215179	C₂²	1	1	yes	characteristic, complemented
58	#72213862	C₂²	1	1	yes	characteristic
59	C₂×#62817	C₂×C₄	1	1	yes	characteristic, complemented
60	#10586066	D₄	1	1	yes	characteristic
61	C₂²×#3484	C₂³	1	1	yes	characteristic
62	C₂⁴×#120	C₂³	1	1	yes	characteristic
63	C₂×#60399	C₂×C₄	1	1	yes	characteristic
64	C₂×#60399	D₄	1	1	yes	characteristic
65	#7642244	C₂×C₄	1	1	yes	characteristic, complemented
66	#7642244	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂²×#2846	D₄	1	1	yes	characteristic
68	C₂²×#2846	D₄	1	1	yes	characteristic
69	#7630939	C₂³	1	1	yes	characteristic
70	#7630939	C₂³	1	1	yes	characteristic
71	#7630939	C₂³	1	1	yes	characteristic
72	#7626202	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×#23895	C₂×C₄	1	1	yes	characteristic
74	C₂×#23895	C₂×C₄	1	1	yes	characteristic
75	C₂×#23895	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂×#23895	D₄	1	1	yes	characteristic
77	C₂×#23895	D₄	1	1	yes	characteristic
78	#6437621	D₄	1	1	yes	characteristic
79	#6437621	D₄	1	1	yes	characteristic
80	C₂×#23900	C₂×C₄	1	1	yes	characteristic
81	C₂×#23900	C₂×C₄	1	1	yes	characteristic
82	C₂×#23900	C₂×C₄	1	1	yes	characteristic
83	C₂×#23900	C₂×C₄	1	1	yes	characteristic
84	C₂×#23900	C₂×C₄	1	1	yes	characteristic, complemented
85	C₂×#23900	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×#23900	D₄	1	1	yes	characteristic
87	C₂×#23900	D₄	1	1	yes	characteristic
88	C₂×#23900	D₄	1	1	yes	characteristic
89	C₂×#23900	D₄	1	1	yes	characteristic
90	#6431795	C₂×C₄	1	1	yes	characteristic
91	#6431795	C₂×C₄	1	1	yes	characteristic
92	#6431795	D₄	1	1	yes	characteristic
93	#6431795	D₄	1	1	yes	characteristic
94	C₂×#21776	C₂×C₄	1	1	yes	characteristic, complemented
95	#6371558	C₂×C₄	1	1	yes	characteristic
96	#6371558	D₄	1	1	yes	characteristic
97	#6371504	D₄	1	1	yes	characteristic
98	#6371504	D₄	1	1	yes	characteristic
99	C₂²×#1898	D₄	1	1	yes	characteristic
100	C₂²×#1898	D₄	1	1	yes	characteristic
101	#6370693	D₄	1	1	yes	characteristic
102	C₂²×#1781	C₂³	1	1	yes	characteristic
103	C₂²×#1781	C₂³	1	1	yes	characteristic
104	C₂²×#1781	C₂³	1	1	yes	characteristic
105	C₂²×#1781	C₂³	1	1	yes	characteristic
106	#517411	C₂³	1	1	yes	characteristic
107	#494713	D₄	1	4	yes	complemented
108	#494713	D₄	1	4	yes	complemented
109	#392113	C₂³	1	1	yes	characteristic
110	#392109	C₂³	1	1	yes	characteristic
111	#392109	C₂³	1	1	yes	characteristic
112	#392109	C₂³	1	1	yes	characteristic
113	#392109	C₂³	1	1	yes	characteristic
114	#382544	C₂×C₄	1	1	yes	characteristic, complemented
115	#382434	C₂×C₄	1	1	yes	characteristic, complemented
116	#373637	C₂×C₄	1	1	yes	characteristic, complemented
117	#359549	C₂×C₄	1	1	yes	characteristic
118	#359549	C₂×C₄	1	1	yes	characteristic
119	#359549	C₂×C₄	1	1	yes	characteristic, complemented
120	#359549	C₂×C₄	1	1	yes	characteristic, complemented
121	#359549	D₄	1	1	yes	characteristic
122	#359549	D₄	1	1	yes	characteristic
123	#359501	C₂×C₄	1	1	yes	characteristic, complemented
124	#359501	C₂×C₄	1	1	yes	characteristic, complemented
125	#359442	D₄	1	1	yes	characteristic
126	#359442	D₄	1	1	yes	characteristic
127	#355096	C₂×C₄	1	1	yes	characteristic, complemented
128	C₂⁸	C₂×D₄	1	1	yes	characteristic
129	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
130	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
131	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
132	#62842	C₂²⋊C₄	1	1	yes	characteristic, complemented
133	#62842	C₂²⋊C₄	1	1	yes	characteristic, complemented
134	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
135	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
136	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
137	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
138	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
139	C₂×#3484	C₂×D₄	1	1	yes	characteristic
140	C₂×#3484	C₂×D₄	1	1	yes	characteristic
141	C₂×#3484	C₂×D₄	1	1	yes	characteristic
142	C₂×#3484	C₂×D₄	1	1	yes	characteristic
143	C₂×#3484	C₂×D₄	1	1	yes	characteristic
144	C₂×#3484	C₂×D₄	1	1	yes	characteristic
145	C₂×#3484	C₂×D₄	1	1	yes	characteristic
146	C₂×#3484	C₂×D₄	1	1	yes	characteristic
147	C₂×#3484	C₂×D₄	1	1	yes	characteristic
148	C₂×#3484	C₂×D₄	1	1	yes	characteristic
149	C₂×#3484	C₂×D₄	1	1	yes	characteristic
150	C₂×#3484	C₂×D₄	1	1	yes	characteristic
151	C₂²×#534	C₂×D₄	1	1	yes	characteristic
152	C₂²×#534	C₂×D₄	1	1	yes	characteristic
153	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
154	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
155	C₂³×#120	C₂×D₄	1	1	yes	characteristic
156	C₂³×#120	C₂×D₄	1	1	yes	characteristic
157	C₂³×#120	C₂×D₄	1	1	yes	characteristic
158	C₂³×#120	C₂×D₄	1	1	yes	characteristic
159	#62652	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	C₂²×#518	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
165	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
167	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
168	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
169	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
170	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
171	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
172	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
173	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	C₂³×#99	C₂×D₄	1	2	yes	complemented
175	C₂³×#99	C₂×D₄	1	2	yes	complemented
176	#36614	#41	1	2	yes	—
177	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
185	#35222	C₂×D₄	1	2	yes	—
186	#35222	C₂×D₄	1	2	yes	—
187	#35222	#41	1	2	yes	—
188	#34171	C₂²×C₄	1	1	yes	characteristic
189	#34171	C₂²×C₄	1	1	yes	characteristic
190	#34171	C₂²×C₄	1	1	yes	characteristic
191	#34171	C₂×D₄	1	1	yes	characteristic
192	#34171	C₂×D₄	1	1	yes	characteristic
193	#34171	C₂×D₄	1	1	yes	characteristic
194	#34171	C₂×D₄	1	1	yes	characteristic
195	#34171	C₂×D₄	1	1	yes	characteristic
196	#34171	C₂×D₄	1	1	yes	characteristic
197	C₂²×#379	C₂×D₄	1	1	yes	characteristic
198	C₂²×#379	C₂×D₄	1	1	yes	characteristic
199	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
200	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
201	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
202	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
203	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
204	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
205	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
206	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
207	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
208	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
209	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
210	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
211	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
212	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
213	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
214	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
215	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
216	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
217	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
218	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
219	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
220	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
221	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
222	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
223	C₂×#1781	C₂×D₄	1	1	yes	characteristic
224	C₂×#1781	C₂×D₄	1	1	yes	characteristic
225	C₂×#1781	C₂×D₄	1	1	yes	characteristic
226	C₂×#1781	C₂×D₄	1	1	yes	characteristic
227	C₂×#1781	C₂×D₄	1	1	yes	characteristic
228	C₂×#1781	C₂×D₄	1	1	yes	characteristic
229	C₂×#1781	C₂×D₄	1	2	yes	complemented
230	C₂×#1781	C₂×D₄	1	2	yes	complemented
231	#20354	C₂²⋊C₄	1	1	yes	characteristic, complemented
232	#20354	C₂²⋊C₄	1	1	yes	characteristic, complemented
233	#20354	C₂²⋊C₄	1	1	yes	characteristic, complemented
234	#20354	C₂²⋊C₄	1	1	yes	characteristic, complemented
235	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂⁷	C₂²×D₄	1	1	yes	characteristic
238	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
245	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
246	C₂⁴×D₄	#120	1	1	yes	characteristic
247	C₂⁴×D₄	#120	1	1	yes	characteristic
248	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
249	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
250	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
251	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
252	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
253	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
254	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
255	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
256	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
257	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
261	C₂×#535	C₄×D₄	1	2	yes	—
262	C₂×#535	#120	1	2	yes	—
263	C₂×#535	#121	1	2	yes	—
264	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×#534	#120	1	1	yes	characteristic
269	C₂×#534	#120	1	1	yes	characteristic
270	C₂×#534	#120	1	1	yes	characteristic
271	C₂×#534	#120	1	1	yes	characteristic
272	C₂×#525	C₄×D₄	1	2	yes	—
273	C₂×#525	#121	1	2	yes	—
274	C₂×#525	#123	1	2	yes	—
275	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×#120	#120	1	1	yes	characteristic
280	C₂²×#120	#120	1	1	yes	characteristic
281	C₂²×#120	#120	1	1	yes	characteristic
282	C₂²×#120	#120	1	1	yes	characteristic
283	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×#518	#120	1	1	yes	characteristic
295	C₂×#518	#120	1	1	yes	characteristic
296	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
299	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
300	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	#2846	#99	1	4	yes	complemented
305	#2309	C₄×D₄	1	2	yes	—
306	#2309	#120	1	2	yes	—
307	#2309	#121	1	2	yes	—
308	#2280	C₄×D₄	1	2	yes	—
309	#2280	#121	1	2	yes	—
310	#2280	#123	1	2	yes	—
311	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	#1898	#99	1	4	yes	complemented
316	C₂⁶	C₂×#99	1	2	yes	—
317	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
318	C₂⁶	#458	1	1	yes	characteristic
319	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
320	C₂⁶	#518	1	1	yes	characteristic
321	C₂⁶	C₂×#120	1	1	yes	characteristic
322	C₂⁶	C₂×#120	1	1	yes	characteristic
323	C₂⁶	#534	1	1	yes	characteristic
324	C₂⁶	#534	1	1	yes	characteristic
325	C₂⁶	D₄²	1	1	yes	characteristic
326	C₂⁶	D₄²	1	1	yes	characteristic
327	C₂⁶	D₄²	1	1	yes	characteristic
328	C₂⁶	D₄²	1	1	yes	characteristic
329	C₂⁶	#546	1	1	yes	characteristic
330	C₂⁶	#546	1	1	yes	characteristic
331	C₂⁶	#546	1	1	yes	characteristic
332	C₂²×#41	#386	1	2	yes	—
333	C₂³×D₄	#379	1	1	yes	characteristic
334	C₂³×D₄	#379	1	1	yes	characteristic
335	C₂³×D₄	#379	1	1	yes	characteristic
336	C₂³×D₄	#379	1	1	yes	characteristic
337	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
338	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
339	C₂³×D₄	#458	1	1	yes	characteristic
340	C₂³×D₄	#458	1	1	yes	characteristic
341	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
342	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
343	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂³×D₄	#518	1	1	yes	characteristic
345	C₂³×D₄	C₂×#120	1	1	yes	characteristic
346	C₂³×D₄	C₂×#120	1	1	yes	characteristic
347	C₂³×D₄	C₂×#120	1	1	yes	characteristic
348	C₂³×D₄	C₂×#121	1	1	yes	characteristic
349	C₂³×D₄	#534	1	1	yes	characteristic
350	C₂³×D₄	#534	1	1	yes	characteristic
351	C₂³×D₄	D₄²	1	1	yes	characteristic
352	C₂³×D₄	D₄²	1	1	yes	characteristic
353	C₂³×D₄	D₄²	1	1	yes	characteristic
354	C₂³×D₄	D₄²	1	1	yes	characteristic
355	C₂³×D₄	#546	1	1	yes	characteristic
356	C₂³×D₄	#546	1	1	yes	characteristic
357	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
358	C₂⁴×C₄	#458	1	1	yes	characteristic
359	C₂⁴×C₄	C₂×C₄×D₄	1	1	yes	characteristic
360	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
361	C₂⁴×C₄	C₂×#123	1	1	yes	characteristic
362	C₂⁴×C₄	#546	1	1	yes	characteristic
363	C₂⁴×C₄	#546	1	1	yes	characteristic
364	C₂⁴×C₄	#546	1	1	yes	characteristic
365	C₂×#127	B(4,𝔽₂)	1	4	yes	—
366	C₂×#124	B(4,𝔽₂)	1	4	yes	—
367	C₂×#120	C₂×#99	1	2	yes	—
368	C₂×#120	C₂×#99	1	2	yes	—
369	C₂×#120	B(4,𝔽₂)	1	2	yes	—
370	C₂×#120	#458	1	2	yes	—
371	C₂×#117	#386	1	2	yes	—
372	C₂×#117	#386	1	2	yes	—
373	C₂×#117	#386	1	2	yes	—
374	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
379	#379	C₂×#99	1	2	yes	—
380	#379	C₂×#99	1	2	yes	—
381	C₂⁵	#1790	1	1	yes	characteristic
382	C₂⁵	#1790	1	1	yes	characteristic
383	C₂⁵	#1790	1	1	yes	characteristic
384	C₂⁵	#1790	1	1	yes	characteristic
385	C₂⁵	C₂×#379	1	1	yes	characteristic
386	C₂⁵	#2308	1	1	yes	characteristic
387	C₂⁵	D₄×C₂²⋊C₄	1	1	yes	characteristic
388	C₂⁵	D₄×C₂²⋊C₄	1	1	yes	characteristic
389	C₂⁵	D₄×C₂²⋊C₄	1	1	yes	characteristic
390	C₂⁵	#2403	1	1	yes	characteristic
391	C₂⁵	#2403	1	1	yes	characteristic
392	C₂⁵	#2405	1	1	yes	characteristic
393	C₂⁵	#2410	1	1	yes	characteristic
394	C₂⁵	#2410	1	1	yes	characteristic
395	C₂⁵	#2410	1	1	yes	characteristic
396	C₂⁵	C₂²×#99	1	1	yes	characteristic
397	C₂⁵	C₂²×#99	1	1	yes	characteristic
398	C₂⁵	#2883	1	1	yes	characteristic
399	C₂⁵	#2883	1	1	yes	characteristic
400	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
401	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
402	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
403	C₂⁵	C₂×#458	1	1	yes	characteristic
404	C₂⁵	C₂×#458	1	1	yes	characteristic
405	C₂⁵	C₂×#458	1	1	yes	characteristic
406	C₂⁵	#3026	1	1	yes	characteristic
407	C₂⁵	#3026	1	1	yes	characteristic
408	C₂²×Q₈	#1889	1	2	yes	complemented
409	C₂²×D₄	#1781	1	2	yes	—
410	C₂²×D₄	#1790	1	2	yes	—
411	C₂²×D₄	#1889	1	2	yes	complemented
412	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
413	C₂³×C₄	#1790	1	1	yes	characteristic
414	C₂³×C₄	#1790	1	1	yes	characteristic
415	C₂³×C₄	#1790	1	1	yes	characteristic
416	C₂³×C₄	#1790	1	1	yes	characteristic
417	C₂³×C₄	C₂×#386	1	1	yes	characteristic
418	C₂³×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
419	C₂³×C₄	#2405	1	1	yes	characteristic
420	C₂³×C₄	#2410	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	#1781	1	2	yes	—
422	C₂×C₂²⋊C₄	#1790	1	2	yes	—
423	C₂×C₄²	#1889	1	4	yes	complemented
424	C₂⁴	#8534	1	2	yes	—
425	C₂⁴	#13867	1	1	yes	characteristic
426	C₂⁴	C₂×#1781	1	1	yes	characteristic
427	C₂⁴	#20585	1	1	yes	characteristic
428	C₂⁴	C₂×#1790	1	1	yes	characteristic
429	C₂⁴	C₂×#1790	1	1	yes	characteristic
430	C₂⁴	C₂×#1790	1	1	yes	characteristic
431	C₂⁴	#20609	1	1	yes	characteristic
432	C₂⁴	#21776	1	2	yes	—
433	C₂⁴	D₄×#99	1	1	yes	characteristic
434	C₂⁴	D₄×#99	1	1	yes	characteristic
435	C₂⁴	D₄×#99	1	1	yes	characteristic
436	C₂⁴	D₄×#99	1	1	yes	characteristic
437	C₂⁴	#23895	1	2	yes	—
438	C₂⁴	#23900	1	2	yes	—
439	C₂⁴	#23900	1	2	yes	—
440	C₂⁴	#23900	1	1	yes	characteristic
441	C₂⁴	#23901	1	1	yes	characteristic
442	C₂⁴	#24056	1	1	yes	characteristic
443	C₂⁴	#24056	1	1	yes	characteristic
444	C₂⁴	#24404	1	1	yes	characteristic
445	C₂⁴	#24404	1	1	yes	characteristic
446	C₂⁴	#24405	1	1	yes	characteristic
447	C₂⁴	#24405	1	1	yes	characteristic
448	C₂²×C₄	#8534	1	2	yes	—
449	C₂²×C₄	C₂×#1889	1	2	yes	—
450	C₂³	C₂×#8534	1	1	yes	characteristic
451	C₂³	#187928	1	1	yes	characteristic
452	C₂³	#187934	1	1	yes	characteristic
453	C₂³	#187940	1	1	yes	characteristic
454	C₂³	#245225	1	2	yes	—
455	C₂³	#245226	1	2	yes	—
456	C₂³	#359501	1	1	yes	characteristic
457	C₂³	#359528	1	1	yes	characteristic
458	C₂³	#359531	1	1	yes	characteristic
459	C₂³	#359549	1	1	yes	characteristic
460	C₂³	#359552	1	1	yes	characteristic
461	C₂³	#359579	1	1	yes	characteristic
462	C₂³	#359591	1	1	yes	characteristic
463	C₂²	#72216625	1	1	yes	characteristic
464	C₂²	#72225626	1	1	yes	characteristic
465	C₂²	#72232787	1	1	yes	characteristic
466	C₂²	#72232821	1	1	yes	characteristic
467	C₂²	#72233304	1	1	yes	characteristic
468	C₂²	#72236754	1	1	yes	characteristic
469	C₂²	#72240111	1	1	yes	characteristic
470	C₂	#72258963	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72258963
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72225648	C₂
LCS	G ▷ C₂⁴×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72310388	C₂	semidirect
2. #72310339	C₂	semidirect
3. #72310304	C₂	semidirect
4. #72309591	C₂	semidirect
5. #72309382	C₂	semidirect
6. #72266881	C₂	semidirect
7. #72266073	C₂²	semidirect
8. #72266028	C₂²	semidirect
9. #72262357	C₂	semidirect
10. #72251565	C₂	semidirect
11. #72238346	C₂	semidirect
12. #72237398	C₂²	semidirect
13. #72237032	C₂	semidirect
14. #72234663	C₂²	semidirect
16. #72225647	C₄	semidirect
17. #72225646	C₄	semidirect
18. #72225644	C₄	semidirect
19. #72225641	C₄	semidirect
20. #72225639	C₄	semidirect
21. #72225635	C₄	semidirect
24. #72219445	C₂	semidirect
25. #72219418	C₂²	semidirect
26. #72219414	C₂²	semidirect
27. #72219301	C₂²	semidirect
28. #72219157	C₄	semidirect
29. #72218522	C₂	semidirect
30. #72218518	C₂²	semidirect
31. #72218498	C₂²	semidirect
32. #72218477	C₂	semidirect
34. #72218451	C₂²	semidirect
35. #72218393	C₂	semidirect
36. #72218381	C₂²	semidirect
37. #72218381	C₂²	semidirect
38. #72218375	C₂²	semidirect
39. #72218313	C₂²	semidirect
40. #72218306	C₂²	semidirect
41. #72218180	C₂²	semidirect
42. #72218180	C₂²	semidirect
43. #72218069	C₂²	semidirect
44. #72218069	C₂²	semidirect
48. #72218057	C₂²	semidirect
49. #72218057	C₂²	semidirect
50. #72218057	C₂²	semidirect
51. #72218057	C₂²	semidirect
53. C₂×#6499874	C₄	semidirect
57. #72215179	C₂²	semidirect
59. C₂×#62817	C₂×C₄	semidirect
65. #7642244	C₂×C₄	semidirect
66. #7642244	C₂×C₄	semidirect
72. #7626202	C₂×C₄	semidirect
75. C₂×#23895	C₂×C₄	semidirect
84. C₂×#23900	C₂×C₄	semidirect
85. C₂×#23900	C₂×C₄	semidirect
94. C₂×#21776	C₂×C₄	semidirect
107. #494713	D₄	semidirect
108. #494713	D₄	semidirect
114. #382544	C₂×C₄	semidirect
115. #382434	C₂×C₄	semidirect
116. #373637	C₂×C₄	semidirect
119. #359549	C₂×C₄	semidirect
120. #359549	C₂×C₄	semidirect
123. #359501	C₂×C₄	semidirect
124. #359501	C₂×C₄	semidirect
127. #355096	C₂×C₄	semidirect
129. C₂×H(7,𝔽₂)	C₂²⋊C₄	semidirect
132. #62842	C₂²⋊C₄	semidirect
133. #62842	C₂²⋊C₄	semidirect
159. #62652	C₂²⋊C₄	semidirect
162. C₂×#3026	C₂²⋊C₄	semidirect
163. C₂×#3026	C₂²⋊C₄	semidirect
164. C₂×#3026	C₂²⋊C₄	semidirect
165. C₂×#3026	C₂²⋊C₄	semidirect
166. C₂×#2883	C₂²⋊C₄	semidirect
167. C₂×#2883	C₂²⋊C₄	semidirect
168. C₂×#2883	C₂²⋊C₄	semidirect
169. C₂×#2883	C₂²⋊C₄	semidirect
170. C₂×#2883	C₂²⋊C₄	semidirect
171. C₂×#2883	C₂²⋊C₄	semidirect
172. C₂×#2883	C₂²⋊C₄	semidirect
173. C₂×#2883	C₂²⋊C₄	semidirect
174. C₂³×#99	C₂×D₄	semidirect
175. C₂³×#99	C₂×D₄	semidirect
199. C₂×#1913	C₂²⋊C₄	semidirect
200. C₂×#1913	C₂²⋊C₄	semidirect
201. C₂×#1913	C₂²⋊C₄	semidirect
202. C₂×#1913	C₂²⋊C₄	semidirect
203. C₂×#1913	C₂²⋊C₄	semidirect
204. C₂×#1913	C₂²⋊C₄	semidirect
205. C₂×#1913	C₂²⋊C₄	semidirect
206. C₂×#1913	C₂²⋊C₄	semidirect
215. #20960	C₂²⋊C₄	semidirect
216. #20960	C₂²⋊C₄	semidirect
217. #20960	C₂²⋊C₄	semidirect
218. #20960	C₂²⋊C₄	semidirect
229. C₂×#1781	C₂×D₄	semidirect
230. C₂×#1781	C₂×D₄	semidirect
231. #20354	C₂²⋊C₄	semidirect
232. #20354	C₂²⋊C₄	semidirect
233. #20354	C₂²⋊C₄	semidirect
234. #20354	C₂²⋊C₄	semidirect
304. #2846	#99	semidirect
315. #1898	#99	semidirect
408. C₂²×Q₈	#1889	semidirect
411. C₂²×D₄	#1889	semidirect
423. C₂×C₄²	#1889	semidirect

Maximal subgroups

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

subgroup	index
#72310388	2
#72310339	2
#72310304	2
#72309591	2
#72309382	2
#72266881	2
#72262357	2
#72251565	2
#72238346	2
#72237032	2
#72225648	2
#72219445	2
#72218522	2
#72218477	2
#72218393	2