Subgroups — #72310440

Order 4096.

At least 21007 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

The subgroup lattice has 442 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72310339	C₂	1	1	yes	maximal, characteristic, complemented
2	#72310334	C₂	1	1	yes	maximal, characteristic, complemented
3	#72310299	C₂	1	1	yes	maximal, characteristic, complemented
4	#72310290	C₂	1	1	yes	maximal, characteristic, complemented
5	#72309539	C₂	1	1	yes	maximal, characteristic, complemented
6	#72309382	C₂	1	1	yes	maximal, characteristic, complemented
7	#72266887	C₂	1	1	yes	maximal, characteristic, complemented
8	#72266073	C₂²	1	1	yes	characteristic
9	#72266028	C₂²	1	1	yes	characteristic
10	#72265757	C₂	1	1	yes	maximal, characteristic, complemented
11	#72262357	C₂	1	1	yes	maximal, characteristic, complemented
12	#72238346	C₂	1	1	yes	maximal, characteristic, complemented
13	#72237398	C₂²	1	1	yes	characteristic
14	#72234663	C₂²	1	1	yes	characteristic
15	#72225747	C₂	1	1	yes	maximal, characteristic
16	#72225745	C₄	1	1	yes	characteristic, complemented
17	#72225744	C₄	1	1	yes	characteristic, complemented
18	#72225743	C₄	1	1	yes	characteristic, complemented
19	#72225742	C₄	1	1	yes	characteristic, complemented
20	#72225742	C₄	1	1	yes	characteristic, complemented
21	#72225741	C₄	1	1	yes	characteristic, complemented
22	#72225740	C₄	1	1	yes	characteristic, complemented
23	C₂×#7266798	C₄	1	1	yes	characteristic, complemented
24	#72225667	C₂²	1	1	yes	characteristic
25	#72225617	C₂²	1	1	yes	characteristic
26	#72219445	C₂	1	1	yes	maximal, characteristic, complemented
27	#72219418	C₂²	1	1	yes	characteristic
28	#72219414	C₂²	1	1	yes	characteristic
29	#72219301	C₂²	1	1	yes	characteristic
30	#72219301	C₂²	1	1	yes	characteristic
31	#72218856	C₂	1	1	yes	maximal, characteristic, complemented
32	#72218522	C₂	1	1	yes	maximal, characteristic, complemented
33	#72218518	C₂²	1	1	yes	characteristic
34	#72218498	C₂²	1	1	yes	characteristic
35	#72218498	C₂²	1	1	yes	characteristic
36	#72218451	C₂²	1	1	yes	characteristic
37	#72218393	C₂	1	1	yes	maximal, characteristic, complemented
38	#72218381	C₂²	1	1	yes	characteristic
39	#72218381	C₂²	1	1	yes	characteristic
40	#72218381	C₂²	1	1	yes	characteristic
41	#72218381	C₂²	1	1	yes	characteristic
42	#72218381	C₂²	1	1	yes	characteristic
43	#72218381	C₂²	1	1	yes	characteristic
44	#72218381	C₂²	1	1	yes	characteristic
45	#72218375	C₂²	1	1	yes	characteristic
46	#72218313	C₂²	1	1	yes	characteristic
47	#72218313	C₂²	1	1	yes	characteristic
48	#72218306	C₂²	1	1	yes	characteristic
49	#72218198	C₂²	1	1	yes	characteristic
50	#72218180	C₂²	1	1	yes	characteristic
51	#72218069	C₂²	1	1	yes	characteristic
52	#72218057	C₂²	1	1	yes	characteristic
53	#72218057	C₂²	1	1	yes	characteristic
54	C₂²×#23900	C₂²	1	1	yes	characteristic
55	#72217789	C₂²	1	1	yes	characteristic
56	#72215858	C₂²	1	1	yes	characteristic
57	#72215179	C₂²	1	1	yes	characteristic
58	#72213862	C₂²	1	1	yes	characteristic
59	C₂²×#3484	C₂³	1	1	yes	characteristic
60	C₂⁴×#120	C₂³	1	1	yes	characteristic
61	C₂²×#2846	D₄	1	1	yes	characteristic
62	C₂²×#2846	D₄	1	1	yes	characteristic
63	#7630939	C₂³	1	1	yes	characteristic
64	C₂×#32873	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×#23895	C₂×C₄	1	1	yes	characteristic
66	C₂×#23895	C₂×C₄	1	1	yes	characteristic
67	C₂×#23895	D₄	1	1	yes	characteristic
68	C₂×#23895	D₄	1	1	yes	characteristic
69	#6437621	D₄	1	1	yes	characteristic
70	#6437621	D₄	1	1	yes	characteristic
71	C₂×#23900	C₂×C₄	1	1	yes	characteristic
72	C₂×#23900	C₂×C₄	1	1	yes	characteristic
73	C₂×#23900	C₂×C₄	1	1	yes	characteristic
74	C₂×#23900	C₂×C₄	1	1	yes	characteristic
75	C₂×#23900	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂×#23900	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×#23900	D₄	1	1	yes	characteristic
78	C₂×#23900	D₄	1	1	yes	characteristic
79	C₂×#23900	D₄	1	1	yes	characteristic
80	C₂×#23900	D₄	1	1	yes	characteristic
81	C₂×#21776	C₂×C₄	1	1	yes	characteristic
82	C₂×#21776	C₂×C₄	1	1	yes	characteristic
83	C₂×#21776	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂×#21776	D₄	1	1	yes	characteristic
85	C₂×#21776	D₄	1	1	yes	characteristic
86	C₂×#21746	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×#21746	C₂×C₄	1	1	yes	characteristic, complemented
88	C₂²×#1898	D₄	1	1	yes	characteristic
89	C₂²×#1898	D₄	1	1	yes	characteristic
90	#6370693	D₄	1	1	yes	characteristic
91	#6370693	D₄	1	1	yes	characteristic
92	C₂²×#1781	C₂³	1	1	yes	characteristic
93	C₂²×#1781	C₂³	1	1	yes	characteristic
94	C₂²×#1781	C₂³	1	1	yes	characteristic
95	C₂²×#1781	C₂³	1	1	yes	characteristic
96	#517411	C₂³	1	1	yes	characteristic
97	#392231	D₄	1	1	yes	characteristic
98	#392231	D₄	1	1	yes	characteristic
99	#392113	C₂³	1	1	yes	characteristic
100	#392109	C₂³	1	1	yes	characteristic
101	#392109	C₂³	1	1	yes	characteristic
102	#392109	C₂³	1	1	yes	characteristic
103	#392109	C₂³	1	1	yes	characteristic
104	#392109	C₂³	1	1	yes	characteristic
105	#392109	C₂³	1	1	yes	characteristic
106	#392030	C₂×C₄	1	1	yes	characteristic, complemented
107	#392030	C₂×C₄	1	1	yes	characteristic, complemented
108	#392030	C₂×C₄	1	1	yes	characteristic, complemented
109	#382544	C₂×C₄	1	1	yes	characteristic, complemented
110	#382434	C₂×C₄	1	1	yes	characteristic
111	#382434	C₂×C₄	1	1	yes	characteristic
112	#382434	C₂×C₄	1	1	yes	characteristic, complemented
113	#382434	D₄	1	1	yes	characteristic
114	#382434	D₄	1	1	yes	characteristic
115	#382422	C₂×C₄	1	1	yes	characteristic, complemented
116	#382422	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	D₄	1	1	yes	characteristic
120	#359549	D₄	1	1	yes	characteristic
121	#359501	C₂×C₄	1	1	yes	characteristic, complemented
122	#359501	C₂×C₄	1	1	yes	characteristic, complemented
123	#359442	D₄	1	1	yes	characteristic
124	#359442	D₄	1	1	yes	characteristic
125	#355096	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂⁸	C₂×D₄	1	1	yes	characteristic
127	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
128	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
129	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
130	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
131	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
132	C₂×#3484	C₂×D₄	1	1	yes	characteristic
133	C₂×#3484	C₂×D₄	1	1	yes	characteristic
134	C₂×#3484	C₂×D₄	1	1	yes	characteristic
135	C₂×#3484	C₂×D₄	1	1	yes	characteristic
136	C₂×#3484	C₂×D₄	1	1	yes	characteristic
137	C₂×#3484	C₂×D₄	1	1	yes	characteristic
138	C₂×#3484	C₂×D₄	1	1	yes	characteristic
139	C₂×#3484	C₂×D₄	1	1	yes	characteristic
140	C₂²×#534	C₂×D₄	1	1	yes	characteristic
141	C₂²×#534	C₂×D₄	1	1	yes	characteristic
142	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
143	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
144	C₂³×#120	C₂×D₄	1	1	yes	characteristic
145	C₂³×#120	C₂×D₄	1	1	yes	characteristic
146	C₂³×#120	C₂×D₄	1	1	yes	characteristic
147	C₂³×#120	C₂×D₄	1	1	yes	characteristic
148	C₂²×#518	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
150	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
151	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
152	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
153	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic, complemented
154	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
158	C₂³×#99	#41	1	2	yes	complemented
159	C₂³×#99	#41	1	2	yes	complemented
160	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
168	#34171	C₂²×C₄	1	1	yes	characteristic
169	#34171	C₂×D₄	1	1	yes	characteristic
170	#34171	C₂×D₄	1	1	yes	characteristic
171	C₂²×#379	C₂×D₄	1	1	yes	characteristic
172	C₂²×#379	C₂×D₄	1	1	yes	characteristic
173	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
176	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
177	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
178	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
179	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
180	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic, complemented
181	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
185	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
186	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
189	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
190	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
191	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
192	#20960	C₂²⋊C₄	1	1	yes	characteristic, complemented
193	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
194	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
195	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
196	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
197	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
198	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
199	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
200	C₂×#1828	C₂²⋊C₄	1	1	yes	characteristic, complemented
201	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
202	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
203	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
204	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
205	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
206	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
207	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
208	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
209	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
210	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
211	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
212	C₂×#1781	C₂²×C₄	1	1	yes	characteristic
213	C₂×#1781	C₂×D₄	1	1	yes	characteristic
214	C₂×#1781	C₂×D₄	1	1	yes	characteristic
215	C₂×#1781	C₂×D₄	1	1	yes	characteristic
216	C₂×#1781	C₂×D₄	1	1	yes	characteristic
217	C₂×#1781	C₂×D₄	1	1	yes	characteristic
218	C₂×#1781	C₂×D₄	1	1	yes	characteristic
219	C₂×#1781	C₂×D₄	1	1	yes	characteristic
220	C₂×#1781	C₂×D₄	1	1	yes	characteristic
221	C₂×#1781	C₂×D₄	1	1	yes	characteristic
222	C₂×#1781	C₂×D₄	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	#41	1	2	yes	complemented
228	#14679	#41	1	2	yes	complemented
229	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂⁷	C₂²×D₄	1	1	yes	characteristic
232	C₂⁷	C₂×#41	1	1	yes	characteristic
233	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
237	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
238	C₂⁴×D₄	#120	1	1	yes	characteristic
239	C₂⁴×D₄	#120	1	1	yes	characteristic
240	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
241	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
242	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
243	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
244	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
245	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
246	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
247	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
248	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
249	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂⁴×D₄	2₋¹⁺⁴	1	1	yes	characteristic
252	C₂⁵×C₄	2₋¹⁺⁴	1	1	yes	characteristic
253	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×#534	#120	1	1	yes	characteristic
258	C₂×#534	#120	1	1	yes	characteristic
259	C₂×#534	#120	1	1	yes	characteristic
260	C₂×#534	#120	1	1	yes	characteristic
261	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×#120	#120	1	1	yes	characteristic
266	C₂²×#120	#120	1	1	yes	characteristic
267	C₂²×#120	#120	1	1	yes	characteristic
268	C₂²×#120	#120	1	1	yes	characteristic
269	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×#518	#120	1	1	yes	characteristic
275	C₂×#518	#120	1	1	yes	characteristic
276	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
279	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
280	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	#2846	#99	1	4	yes	complemented
293	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	#1898	#99	1	4	yes	complemented
298	C₂⁶	C₂×#99	1	2	yes	—
299	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
300	C₂⁶	#458	1	1	yes	characteristic
301	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
302	C₂⁶	C₄×#41	1	1	yes	characteristic
303	C₂⁶	C₂×#120	1	1	yes	characteristic
304	C₂⁶	C₂×#120	1	1	yes	characteristic
305	C₂⁶	#525	1	1	yes	characteristic
306	C₂⁶	#532	1	1	yes	characteristic
307	C₂⁶	#546	1	1	yes	characteristic
308	C₂⁶	#546	1	1	yes	characteristic
309	C₂⁶	#546	1	1	yes	characteristic
310	C₂⁶	#546	1	1	yes	characteristic
311	C₂⁶	#547	1	1	yes	characteristic
312	C₂⁶	#547	1	1	yes	characteristic
313	C₂⁶	#547	1	1	yes	characteristic
314	C₂³×D₄	#379	1	1	yes	characteristic
315	C₂³×D₄	#379	1	1	yes	characteristic
316	C₂³×D₄	#379	1	1	yes	characteristic
317	C₂³×D₄	#379	1	1	yes	characteristic
318	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
319	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
320	C₂³×D₄	#458	1	1	yes	characteristic
321	C₂³×D₄	#458	1	1	yes	characteristic
322	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
323	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
324	C₂³×D₄	C₄×#41	1	1	yes	characteristic
325	C₂³×D₄	#520	1	1	yes	characteristic
326	C₂³×D₄	C₂×#120	1	1	yes	characteristic
327	C₂³×D₄	C₂×#120	1	1	yes	characteristic
328	C₂³×D₄	#525	1	1	yes	characteristic
329	C₂³×D₄	#532	1	1	yes	characteristic
330	C₂³×D₄	#535	1	1	yes	characteristic
331	C₂³×D₄	#537	1	1	yes	characteristic
332	C₂³×D₄	#546	1	1	yes	characteristic
333	C₂³×D₄	#546	1	1	yes	characteristic
334	C₂³×D₄	#546	1	1	yes	characteristic
335	C₂³×D₄	#546	1	1	yes	characteristic
336	C₂³×D₄	#547	1	1	yes	characteristic
337	C₂³×D₄	#547	1	1	yes	characteristic
338	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
339	C₂⁴×C₄	#458	1	1	yes	characteristic
340	C₂⁴×C₄	#520	1	1	yes	characteristic
341	C₂⁴×C₄	#536	1	1	yes	characteristic
342	C₂⁴×C₄	#537	1	1	yes	characteristic
343	C₂⁴×C₄	#547	1	1	yes	characteristic
344	C₂⁴×C₄	#547	1	1	yes	characteristic
345	C₂⁴×C₄	#547	1	1	yes	characteristic
346	C₂×#120	C₂×#99	1	2	yes	—
347	C₂×#120	C₂×#99	1	2	yes	—
348	C₂×#120	B(4,𝔽₂)	1	2	yes	—
349	C₂×#120	#458	1	2	yes	—
350	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
355	#379	C₂×#99	1	2	yes	—
356	#379	C₂×#99	1	2	yes	—
357	C₂⁵	#1790	1	1	yes	characteristic
358	C₂⁵	#1790	1	1	yes	characteristic
359	C₂⁵	#1790	1	1	yes	characteristic
360	C₂⁵	#1790	1	1	yes	characteristic
361	C₂⁵	C₂×#379	1	1	yes	characteristic
362	C₂⁵	#2297	1	1	yes	characteristic
363	C₂⁵	#2339	1	1	yes	characteristic
364	C₂⁵	#2339	1	1	yes	characteristic
365	C₂⁵	#2339	1	1	yes	characteristic
366	C₂⁵	#2404	1	1	yes	characteristic
367	C₂⁵	#2404	1	1	yes	characteristic
368	C₂⁵	#2406	1	1	yes	characteristic
369	C₂⁵	#2430	1	1	yes	characteristic
370	C₂⁵	#2430	1	1	yes	characteristic
371	C₂⁵	#2430	1	1	yes	characteristic
372	C₂⁵	C₂²×#99	1	1	yes	characteristic
373	C₂⁵	C₂²×#99	1	1	yes	characteristic
374	C₂⁵	#2883	1	1	yes	characteristic
375	C₂⁵	#2883	1	1	yes	characteristic
376	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
377	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
379	C₂⁵	C₂×#458	1	1	yes	characteristic
380	C₂⁵	C₂×#458	1	1	yes	characteristic
381	C₂⁵	C₂×#458	1	1	yes	characteristic
382	C₂⁵	#3026	1	1	yes	characteristic
383	C₂⁵	#3026	1	1	yes	characteristic
384	C₂²×D₄	#1781	1	2	yes	—
385	C₂²×D₄	#1790	1	2	yes	—
386	C₂³×C₄	#1790	1	1	yes	characteristic
387	C₂³×C₄	#1790	1	1	yes	characteristic
388	C₂³×C₄	#1790	1	1	yes	characteristic
389	C₂³×C₄	#1790	1	1	yes	characteristic
390	C₂³×C₄	#2311	1	1	yes	characteristic
391	C₂³×C₄	#2339	1	1	yes	characteristic
392	C₂³×C₄	#2406	1	1	yes	characteristic
393	C₂³×C₄	#2430	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	#1781	1	2	yes	—
395	C₂×C₂²⋊C₄	#1790	1	2	yes	—
396	C₂⁴	#8534	1	2	yes	—
397	C₂⁴	#13956	1	1	yes	characteristic
398	C₂⁴	C₂×#1781	1	1	yes	characteristic
399	C₂⁴	#20585	1	1	yes	characteristic
400	C₂⁴	C₂×#1790	1	1	yes	characteristic
401	C₂⁴	C₂×#1790	1	1	yes	characteristic
402	C₂⁴	C₂×#1790	1	1	yes	characteristic
403	C₂⁴	#20609	1	1	yes	characteristic
404	C₂⁴	#22476	1	1	yes	characteristic
405	C₂⁴	#22476	1	1	yes	characteristic
406	C₂⁴	#22476	1	1	yes	characteristic
407	C₂⁴	#22476	1	1	yes	characteristic
408	C₂⁴	#23984	1	1	yes	characteristic
409	C₂⁴	#23985	1	1	yes	characteristic
410	C₂⁴	#23996	1	2	yes	—
411	C₂⁴	#23996	1	2	yes	—
412	C₂⁴	#23996	1	2	yes	—
413	C₂⁴	#24112	1	1	yes	characteristic
414	C₂⁴	#24112	1	1	yes	characteristic
415	C₂⁴	#25563	1	1	yes	characteristic
416	C₂⁴	#25563	1	1	yes	characteristic
417	C₂⁴	#25565	1	1	yes	characteristic
418	C₂⁴	#25565	1	1	yes	characteristic
419	C₂²×C₄	#8534	1	2	yes	—
420	C₂³	C₂×#8534	1	1	yes	characteristic
421	C₂³	#187928	1	1	yes	characteristic
422	C₂³	#187934	1	1	yes	characteristic
423	C₂³	#187940	1	1	yes	characteristic
424	C₂³	#251827	1	2	yes	—
425	C₂³	#251829	1	2	yes	—
426	C₂³	#363879	1	1	yes	characteristic
427	C₂³	#363895	1	1	yes	characteristic
428	C₂³	#363909	1	1	yes	characteristic
429	C₂³	#363953	1	1	yes	characteristic
430	C₂³	#363953	1	1	yes	characteristic
431	C₂³	#363953	1	1	yes	characteristic
432	C₂³	#363969	1	1	yes	characteristic
433	C₂²	#72233182	1	1	yes	characteristic
434	C₂²	#72233199	1	1	yes	characteristic
435	C₂²	#72234957	1	1	yes	characteristic
436	C₂²	#72234960	1	1	yes	characteristic
437	C₂²	#72238859	1	1	yes	characteristic
438	C₂²	#72251608	1	1	yes	characteristic
439	C₂²	#72258403	1	1	yes	characteristic
440	C₂	#72258967	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72258967
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72225747	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. #72310339	C₂	semidirect
2. #72310334	C₂	semidirect
3. #72310299	C₂	semidirect
4. #72310290	C₂	semidirect
5. #72309539	C₂	semidirect
6. #72309382	C₂	semidirect
7. #72266887	C₂	semidirect
10. #72265757	C₂	semidirect
11. #72262357	C₂	semidirect
12. #72238346	C₂	semidirect
16. #72225745	C₄	semidirect
17. #72225744	C₄	semidirect
18. #72225743	C₄	semidirect
19. #72225742	C₄	semidirect
20. #72225742	C₄	semidirect
21. #72225741	C₄	semidirect
22. #72225740	C₄	semidirect
23. C₂×#7266798	C₄	semidirect
26. #72219445	C₂	semidirect
31. #72218856	C₂	semidirect
32. #72218522	C₂	semidirect
37. #72218393	C₂	semidirect
64. C₂×#32873	C₂×C₄	semidirect
75. C₂×#23900	C₂×C₄	semidirect
76. C₂×#23900	C₂×C₄	semidirect
83. C₂×#21776	C₂×C₄	semidirect
86. C₂×#21746	C₂×C₄	semidirect
87. C₂×#21746	C₂×C₄	semidirect
106. #392030	C₂×C₄	semidirect
107. #392030	C₂×C₄	semidirect
108. #392030	C₂×C₄	semidirect
109. #382544	C₂×C₄	semidirect
112. #382434	C₂×C₄	semidirect
115. #382422	C₂×C₄	semidirect
116. #382422	C₂×C₄	semidirect
121. #359501	C₂×C₄	semidirect
122. #359501	C₂×C₄	semidirect
125. #355096	C₂×C₄	semidirect
150. C₂×#3026	C₂²⋊C₄	semidirect
151. C₂×#3026	C₂²⋊C₄	semidirect
152. C₂×#3026	C₂²⋊C₄	semidirect
153. C₂×#3026	C₂²⋊C₄	semidirect
154. C₂×#2883	C₂²⋊C₄	semidirect
155. C₂×#2883	C₂²⋊C₄	semidirect
156. C₂×#2883	C₂²⋊C₄	semidirect
157. C₂×#2883	C₂²⋊C₄	semidirect
158. C₂³×#99	#41	semidirect
159. C₂³×#99	#41	semidirect
173. C₂×#1913	C₂²⋊C₄	semidirect
174. C₂×#1913	C₂²⋊C₄	semidirect
175. C₂×#1913	C₂²⋊C₄	semidirect
176. C₂×#1913	C₂²⋊C₄	semidirect
177. C₂×#1913	C₂²⋊C₄	semidirect
178. C₂×#1913	C₂²⋊C₄	semidirect
179. C₂×#1913	C₂²⋊C₄	semidirect
180. C₂×#1913	C₂²⋊C₄	semidirect
189. #20960	C₂²⋊C₄	semidirect
190. #20960	C₂²⋊C₄	semidirect
191. #20960	C₂²⋊C₄	semidirect
192. #20960	C₂²⋊C₄	semidirect
193. C₂×#1828	C₂²⋊C₄	semidirect
194. C₂×#1828	C₂²⋊C₄	semidirect
195. C₂×#1828	C₂²⋊C₄	semidirect
196. C₂×#1828	C₂²⋊C₄	semidirect
197. C₂×#1828	C₂²⋊C₄	semidirect
198. C₂×#1828	C₂²⋊C₄	semidirect
199. C₂×#1828	C₂²⋊C₄	semidirect
200. C₂×#1828	C₂²⋊C₄	semidirect
201. #20585	C₂²⋊C₄	semidirect
202. #20585	C₂²⋊C₄	semidirect
203. #20585	C₂²⋊C₄	semidirect
204. #20585	C₂²⋊C₄	semidirect
227. C₂×#1781	#41	semidirect
228. #14679	#41	semidirect
292. #2846	#99	semidirect
297. #1898	#99	semidirect

Maximal subgroups

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

subgroup	index
#72310339	2
#72310334	2
#72310299	2
#72310290	2
#72309539	2
#72309382	2
#72266887	2
#72265757	2
#72262357	2
#72238346	2
#72225747	2
#72219445	2
#72218856	2
#72218522	2
#72218393	2