Subgroups — #72312718

Order 4096.

At least 21526 conjugacy classes of subgroups; only the 519 normal subgroups are shown.

The subgroup lattice has 466 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312643	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312430	C₂	1	1	yes	maximal, characteristic, complemented
3	#72312360	C₂	1	1	yes	maximal, characteristic, complemented
4	#72312179	C₂	1	1	yes	maximal, characteristic, complemented
5	#72310388	C₂	1	1	yes	maximal, characteristic, complemented
6	#72310377	C₂	1	1	yes	maximal, characteristic, complemented
7	#72310337	C₂	1	1	yes	maximal, characteristic, complemented
8	#72309929	C₂	1	1	yes	maximal, characteristic, complemented
9	#72309519	C₂	1	1	yes	maximal, characteristic, complemented
10	#72309374	C₂	1	1	yes	maximal, characteristic, complemented
11	#72309310	C₂	1	1	yes	maximal, characteristic, complemented
12	#72266943	C₂	1	1	yes	maximal, characteristic, complemented
13	#72266073	C₂²	1	1	yes	characteristic, complemented
14	#72264815	C₂	1	1	yes	maximal, characteristic, complemented
15	#72259008	C₂²	1	1	yes	characteristic, complemented
16	#72251212	C₂	1	1	yes	maximal, characteristic
17	#72251108	C₄	1	1	yes	characteristic, complemented
18	#72251073	C₄	1	1	yes	characteristic, complemented
19	#72251054	C₄	1	1	yes	characteristic, complemented
20	#72240471	C₄	1	1	yes	characteristic, complemented
21	#72238611	C₄	1	1	yes	characteristic, complemented
22	#72238346	C₂	1	1	yes	maximal, characteristic, complemented
23	#72237903	C₄	1	1	yes	characteristic, complemented
24	#72234953	C₄	1	1	yes	characteristic, complemented
25	#72234693	C₄	1	1	yes	characteristic, complemented
26	#72234663	C₂²	1	1	yes	characteristic, complemented
27	#72234661	C₂²	1	1	yes	characteristic
28	#72225650	C₂²	1	1	yes	characteristic
29	#72225619	C₂²	1	1	yes	characteristic
30	#72225617	C₂²	1	1	yes	characteristic
31	C₂×#115348	C₂²	1	1	yes	characteristic, complemented
32	#72224136	C₂²	1	1	yes	characteristic
33	#72219415	C₂²	1	1	yes	characteristic, complemented
34	#72219414	C₂²	1	1	yes	characteristic, complemented
35	#72219310	C₂²	1	1	yes	characteristic, complemented
36	#72219300	C₂²	1	1	yes	characteristic, complemented
37	#72219299	C₂²	1	1	yes	characteristic, complemented
38	#72219251	C₂²	1	1	yes	characteristic, complemented
39	#72219243	C₂²	1	1	yes	characteristic, complemented
40	#72219243	C₂²	1	1	yes	characteristic, complemented
41	#72219237	C₂²	1	1	yes	characteristic
42	#72219229	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#8534	C₂²	1	1	yes	characteristic, complemented
44	#72218381	C₂²	1	1	yes	characteristic, complemented
45	#72218313	C₂²	1	1	yes	characteristic, complemented
46	#72218313	C₂²	1	1	yes	characteristic, complemented
47	#72218306	C₂²	1	1	yes	characteristic, complemented
48	#72218069	C₂²	1	1	yes	characteristic
49	#72218069	C₂²	1	1	yes	characteristic
50	#72218069	C₂²	1	1	yes	characteristic
51	#72218069	C₂²	1	1	yes	characteristic, complemented
52	#72218069	C₂²	1	1	yes	characteristic, complemented
53	#72218069	C₂²	1	1	yes	characteristic, complemented
54	#72218069	C₂²	1	1	yes	characteristic, complemented
55	#72218057	C₂²	1	1	yes	characteristic, complemented
56	#72218057	C₂²	1	1	yes	characteristic, complemented
57	#72216064	C₂²	1	1	yes	characteristic
58	#72213862	C₂²	1	1	yes	characteristic
59	#10586404	C₂×C₄	1	1	yes	characteristic, complemented
60	#10586066	D₄	1	1	yes	characteristic
61	C₂²×#3484	C₂³	1	1	yes	characteristic
62	C₂×#60399	C₂×C₄	1	1	yes	characteristic
63	C₂×#60399	D₄	1	1	yes	characteristic
64	#7641845	D₄	1	1	yes	characteristic
65	#7641845	D₄	1	1	yes	characteristic
66	#7630939	C₂³	1	1	yes	characteristic
67	#7630939	C₂³	1	1	yes	characteristic
68	#7630939	C₂³	1	1	yes	characteristic
69	C₂×#34980	C₂³	1	1	yes	characteristic
70	#6440460	C₂×C₄	1	1	yes	characteristic
71	#6440460	C₂×C₄	1	1	yes	characteristic
72	#6440460	C₂×C₄	1	1	yes	characteristic, complemented
73	#6440460	D₄	1	1	yes	characteristic
74	#6440460	D₄	1	1	yes	characteristic
75	C₂×#23895	C₂×C₄	1	1	yes	characteristic
76	C₂×#23895	C₂×C₄	1	1	yes	characteristic
77	C₂×#23895	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×#23895	D₄	1	1	yes	characteristic
79	C₂×#23895	D₄	1	1	yes	characteristic
80	#6437621	C₂×C₄	1	1	yes	characteristic
81	#6437621	C₂×C₄	1	1	yes	characteristic
82	#6437621	C₂×C₄	1	1	yes	characteristic, complemented
83	#6437621	D₄	1	1	yes	characteristic
84	#6437621	D₄	1	1	yes	characteristic
85	#6437621	D₄	1	1	yes	characteristic
86	#6437621	D₄	1	1	yes	characteristic
87	#6431795	C₂×C₄	1	1	yes	characteristic
88	#6431795	C₂×C₄	1	1	yes	characteristic
89	#6431795	D₄	1	1	yes	characteristic
90	#6431795	D₄	1	1	yes	characteristic
91	#6374210	C₂×C₄	1	1	yes	characteristic, complemented
92	#6374210	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×#21776	C₂×C₄	1	1	yes	characteristic, complemented
94	#6374128	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×#21746	D₄	1	1	yes	characteristic
96	C₂×#21746	D₄	1	1	yes	characteristic
97	#6371558	C₂×C₄	1	1	yes	characteristic
98	#6371558	D₄	1	1	yes	characteristic
99	#6371504	D₄	1	1	yes	characteristic
100	#6371504	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	C₂²×#1438	C₂³	1	1	yes	characteristic
107	#392113	C₂³	1	1	yes	characteristic
108	#392113	C₂³	1	1	yes	characteristic
109	#392113	C₂³	1	1	yes	characteristic
110	#392109	C₂³	1	1	yes	characteristic
111	#392109	C₂³	1	1	yes	characteristic
112	#382544	C₂×C₄	1	1	yes	characteristic, complemented
113	#382434	C₂×C₄	1	1	yes	characteristic, complemented
114	#373637	C₂×C₄	1	1	yes	characteristic, complemented
115	#359811	C₂×C₄	1	1	yes	characteristic, complemented
116	#359549	C₂×C₄	1	1	yes	characteristic
117	#359549	C₂×C₄	1	1	yes	characteristic
118	#359549	C₂×C₄	1	1	yes	characteristic, complemented
119	#359549	C₂×C₄	1	1	yes	characteristic, complemented
120	#359549	D₄	1	1	yes	characteristic
121	#359549	D₄	1	1	yes	characteristic
122	#359442	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	#147567	D₄	1	4	yes	complemented
127	#147567	D₄	1	4	yes	complemented
128	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
130	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
131	#62842	C₂²⋊C₄	1	1	yes	characteristic
132	#62842	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×#3484	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	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	C₂²×#534	C₂²×C₄	1	1	yes	characteristic
151	C₂²×#534	C₂×D₄	1	1	yes	characteristic
152	C₂²×#534	C₂×D₄	1	1	yes	characteristic
153	C₂²×#534	C₂×D₄	1	1	yes	characteristic
154	C₂³×#120	C₂×D₄	1	1	yes	characteristic
155	C₂³×#120	C₂×D₄	1	1	yes	characteristic
156	C₂³×#120	C₂×D₄	1	1	yes	characteristic
157	#62652	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×#518	C₂×D₄	1	1	yes	characteristic
159	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#3026	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
168	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#2846	#41	1	2	yes	—
172	#34992	C₂²⋊C₄	1	1	yes	characteristic
173	#34992	C₂²⋊C₄	1	1	yes	characteristic
174	#34992	C₂²⋊C₄	1	1	yes	characteristic
175	#34992	C₂²⋊C₄	1	1	yes	characteristic
176	#34980	C₂²⋊C₄	1	1	yes	characteristic
177	#34980	C₂²⋊C₄	1	1	yes	characteristic
178	#34980	C₂²⋊C₄	1	1	yes	characteristic
179	#34980	C₂²⋊C₄	1	1	yes	characteristic
180	#34980	C₂×D₄	1	2	yes	—
181	#34980	C₂×D₄	1	2	yes	—
182	#34980	#41	1	2	yes	—
183	#34171	C₂²×C₄	1	1	yes	characteristic
184	#34171	C₂²×C₄	1	1	yes	characteristic
185	#34171	C₂²×C₄	1	1	yes	characteristic
186	#34171	C₂×D₄	1	1	yes	characteristic
187	#34171	C₂×D₄	1	1	yes	characteristic
188	#34171	C₂×D₄	1	1	yes	characteristic
189	#34171	C₂×D₄	1	1	yes	characteristic
190	#34171	C₂×D₄	1	1	yes	characteristic
191	#34171	C₂×D₄	1	1	yes	characteristic
192	C₂×#2308	C₂²×C₄	1	1	yes	characteristic
193	C₂×#2308	C₂×D₄	1	1	yes	characteristic
194	C₂²×#379	C₂×D₄	1	1	yes	characteristic
195	C₂²×#379	C₂×D₄	1	1	yes	characteristic
196	C₂²×#379	C₂×D₄	1	1	yes	characteristic
197	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
200	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
201	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
202	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
203	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
204	C₂×#1913	C₂²⋊C₄	1	1	yes	characteristic
205	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
206	C₂×#1898	C₂²⋊C₄	1	1	yes	characteristic
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	#20960	C₂²⋊C₄	1	1	yes	characteristic
214	#20960	C₂²⋊C₄	1	1	yes	characteristic
215	#20960	C₂²⋊C₄	1	1	yes	characteristic
216	#20960	C₂²⋊C₄	1	1	yes	characteristic
217	C₂×#1783	C₂×D₄	1	2	yes	complemented
218	C₂×#1783	C₂×D₄	1	2	yes	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
232	#20354	C₂²⋊C₄	1	1	yes	characteristic
233	#20354	C₂²⋊C₄	1	1	yes	characteristic
234	#20354	C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁷	C₂²×D₄	1	1	yes	characteristic
236	C₂⁷	C₂×#41	1	1	yes	characteristic
237	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	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)	#120	1	1	yes	characteristic
243	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
244	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂⁴×D₄	#120	1	1	yes	characteristic
246	C₂⁴×D₄	#120	1	1	yes	characteristic
247	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
248	C₂⁴×D₄	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
256	C₂⁴×D₄	H(5,𝔽₂)	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	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#534	C₄×D₄	1	2	yes	—
265	C₂×#534	#120	1	1	yes	characteristic
266	C₂×#534	#120	1	1	yes	characteristic
267	C₂×#534	#120	1	1	yes	characteristic
268	C₂×#534	#120	1	1	yes	characteristic
269	C₂×#534	#120	1	2	yes	—
270	C₂×#534	#121	1	2	yes	—
271	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×#120	C₄×D₄	1	2	yes	—
276	C₂²×#120	#120	1	1	yes	characteristic
277	C₂²×#120	#120	1	1	yes	characteristic
278	C₂²×#120	#120	1	1	yes	characteristic
279	C₂²×#120	#120	1	1	yes	characteristic
280	C₂²×#120	#121	1	2	yes	—
281	C₂²×#120	#123	1	2	yes	—
282	C₂×#518	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
294	C₂×#518	#120	1	1	yes	characteristic
295	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	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	#2849	#99	1	2	yes	complemented
305	#2846	#99	1	2	yes	complemented
306	#2308	C₄×D₄	1	2	yes	—
307	#2308	#120	1	2	yes	—
308	#2308	#121	1	2	yes	—
309	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×#379	C₄×D₄	1	2	yes	—
314	C₂×#379	#121	1	2	yes	—
315	C₂×#379	#123	1	2	yes	—
316	#1898	#99	1	4	yes	complemented
317	C₂⁶	C₂×#99	1	1	yes	characteristic
318	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
319	C₂⁶	#458	1	1	yes	characteristic
320	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₂⁶	C₂×C₄×D₄	1	1	yes	characteristic
322	C₂⁶	C₂×#120	1	1	yes	characteristic
323	C₂⁶	C₂×#120	1	1	yes	characteristic
324	C₂⁶	C₂×#121	1	1	yes	characteristic
325	C₂⁶	C₂×#123	1	1	yes	characteristic
326	C₂⁶	D₄²	1	1	yes	characteristic
327	C₂⁶	D₄²	1	1	yes	characteristic
328	C₂⁶	#546	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	C₂⁶	#546	1	1	yes	characteristic
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	#386	1	2	yes	—
338	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
339	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
340	C₂³×D₄	#458	1	1	yes	characteristic
341	C₂³×D₄	#458	1	1	yes	characteristic
342	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
343	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
344	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
345	C₂³×D₄	#518	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×#120	1	1	yes	characteristic
349	C₂³×D₄	C₂×#121	1	1	yes	characteristic
350	C₂³×D₄	#534	1	1	yes	characteristic
351	C₂³×D₄	#534	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	D₄²	1	1	yes	characteristic
356	C₂³×D₄	#546	1	1	yes	characteristic
357	C₂³×D₄	#546	1	1	yes	characteristic
358	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
359	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
360	C₂⁴×C₄	#458	1	1	yes	characteristic
361	C₂⁴×C₄	#518	1	1	yes	characteristic
362	C₂⁴×C₄	#534	1	1	yes	characteristic
363	C₂⁴×C₄	#534	1	1	yes	characteristic
364	C₂⁴×C₄	D₄²	1	1	yes	characteristic
365	C₂⁴×C₄	D₄²	1	1	yes	characteristic
366	C₂⁴×C₄	#546	1	1	yes	characteristic
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	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
373	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	#386	1	2	yes	—
376	C₂²×C₂²⋊C₄	#386	1	2	yes	—
377	C₂²×C₂²⋊C₄	#386	1	2	yes	—
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	#1913	1	2	yes	complemented
386	C₂⁵	C₂×#379	1	1	yes	characteristic
387	C₂⁵	C₂×#386	1	1	yes	characteristic
388	C₂⁵	D₄×C₂²⋊C₄	1	1	yes	characteristic
389	C₂⁵	D₄×C₂²⋊C₄	1	1	yes	characteristic
390	C₂⁵	D₄×C₂²⋊C₄	1	1	yes	characteristic
391	C₂⁵	#2403	1	1	yes	characteristic
392	C₂⁵	#2405	1	1	yes	characteristic
393	C₂⁵	#2405	1	1	yes	characteristic
394	C₂⁵	#2410	1	1	yes	characteristic
395	C₂⁵	#2410	1	1	yes	characteristic
396	C₂⁵	#2410	1	1	yes	characteristic
397	C₂⁵	C₂²×#99	1	1	yes	characteristic
398	C₂⁵	C₂²×#99	1	1	yes	characteristic
399	C₂⁵	#2883	1	1	yes	characteristic
400	C₂⁵	#2883	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×B(4,𝔽₂)	1	1	yes	characteristic
404	C₂⁵	C₂×#458	1	1	yes	characteristic
405	C₂⁵	C₂×#458	1	1	yes	characteristic
406	C₂⁵	C₂×#458	1	1	yes	characteristic
407	C₂⁵	#3026	1	1	yes	characteristic
408	C₂⁵	#3026	1	1	yes	characteristic
409	C₂²×D₄	#1781	1	2	yes	—
410	C₂²×D₄	#1790	1	2	yes	—
411	C₂³×C₄	#1790	1	1	yes	characteristic
412	C₂³×C₄	#1790	1	1	yes	characteristic
413	C₂³×C₄	#1790	1	1	yes	characteristic
414	C₂³×C₄	#1790	1	1	yes	characteristic
415	C₂³×C₄	#1913	1	2	yes	complemented
416	C₂³×C₄	#2308	1	1	yes	characteristic
417	C₂³×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
418	C₂³×C₄	#2403	1	1	yes	characteristic
419	C₂³×C₄	#2410	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	#1781	1	2	yes	—
421	C₂×C₂²⋊C₄	#1790	1	2	yes	—
422	C₂⁴	#8534	1	2	yes	—
423	C₂⁴	#13867	1	1	yes	characteristic
424	C₂⁴	C₂×#1781	1	1	yes	characteristic
425	C₂⁴	#20585	1	1	yes	characteristic
426	C₂⁴	C₂×#1790	1	1	yes	characteristic
427	C₂⁴	C₂×#1790	1	1	yes	characteristic
428	C₂⁴	C₂×#1790	1	1	yes	characteristic
429	C₂⁴	#20609	1	1	yes	characteristic
430	C₂⁴	C₂×#1913	1	2	yes	—
431	C₂⁴	D₄×#99	1	1	yes	characteristic
432	C₂⁴	D₄×#99	1	1	yes	characteristic
433	C₂⁴	D₄×#99	1	1	yes	characteristic
434	C₂⁴	D₄×#99	1	1	yes	characteristic
435	C₂⁴	#23900	1	1	yes	characteristic
436	C₂⁴	#23901	1	1	yes	characteristic
437	C₂⁴	#24056	1	1	yes	characteristic
438	C₂⁴	#24056	1	1	yes	characteristic
439	C₂⁴	#24404	1	1	yes	characteristic
440	C₂⁴	#24404	1	1	yes	characteristic
441	C₂⁴	#24405	1	1	yes	characteristic
442	C₂⁴	#24405	1	1	yes	characteristic
443	C₂²×C₄	#8534	1	2	yes	—
444	C₂²×C₄	#21776	1	2	yes	—
445	C₂²×C₄	#23895	1	2	yes	—
446	C₂³	C₂×#8534	1	1	yes	characteristic
447	C₂³	#187928	1	1	yes	characteristic
448	C₂³	#187934	1	1	yes	characteristic
449	C₂³	#187940	1	1	yes	characteristic
450	C₂³	#359442	1	1	yes	characteristic
451	C₂³	#359528	1	1	yes	characteristic
452	C₂³	#359531	1	1	yes	characteristic
453	C₂³	#359549	1	1	yes	characteristic
454	C₂³	#359552	1	1	yes	characteristic
455	C₂³	#359579	1	1	yes	characteristic
456	C₂³	#359591	1	1	yes	characteristic
457	C₂²	#72219038	1	1	yes	characteristic
458	C₂²	#72219461	1	1	yes	characteristic
459	C₂²	#72225626	1	1	yes	characteristic
460	C₂²	#72232821	1	1	yes	characteristic
461	C₂²	#72233304	1	1	yes	characteristic
462	C₂²	#72240111	1	1	yes	characteristic
463	C₂²	#72261400	1	1	yes	characteristic
464	C₂	#72266141	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266141
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72251212	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. #72312643	C₂	semidirect
2. #72312430	C₂	semidirect
3. #72312360	C₂	semidirect
4. #72312179	C₂	semidirect
5. #72310388	C₂	semidirect
6. #72310377	C₂	semidirect
7. #72310337	C₂	semidirect
8. #72309929	C₂	semidirect
9. #72309519	C₂	semidirect
10. #72309374	C₂	semidirect
11. #72309310	C₂	semidirect
12. #72266943	C₂	semidirect
13. #72266073	C₂²	semidirect
14. #72264815	C₂	semidirect
15. #72259008	C₂²	semidirect
17. #72251108	C₄	semidirect
18. #72251073	C₄	semidirect
19. #72251054	C₄	semidirect
20. #72240471	C₄	semidirect
21. #72238611	C₄	semidirect
22. #72238346	C₂	semidirect
23. #72237903	C₄	semidirect
24. #72234953	C₄	semidirect
25. #72234693	C₄	semidirect
26. #72234663	C₂²	semidirect
31. C₂×#115348	C₂²	semidirect
33. #72219415	C₂²	semidirect
34. #72219414	C₂²	semidirect
35. #72219310	C₂²	semidirect
36. #72219300	C₂²	semidirect
37. #72219299	C₂²	semidirect
38. #72219251	C₂²	semidirect
39. #72219243	C₂²	semidirect
40. #72219243	C₂²	semidirect
42. #72219229	C₂²	semidirect
43. C₂²×#8534	C₂²	semidirect
44. #72218381	C₂²	semidirect
45. #72218313	C₂²	semidirect
46. #72218313	C₂²	semidirect
47. #72218306	C₂²	semidirect
51. #72218069	C₂²	semidirect
52. #72218069	C₂²	semidirect
53. #72218069	C₂²	semidirect
54. #72218069	C₂²	semidirect
55. #72218057	C₂²	semidirect
56. #72218057	C₂²	semidirect
59. #10586404	C₂×C₄	semidirect
72. #6440460	C₂×C₄	semidirect
77. C₂×#23895	C₂×C₄	semidirect
82. #6437621	C₂×C₄	semidirect
91. #6374210	C₂×C₄	semidirect
92. #6374210	C₂×C₄	semidirect
93. C₂×#21776	C₂×C₄	semidirect
94. #6374128	C₂×C₄	semidirect
112. #382544	C₂×C₄	semidirect
113. #382434	C₂×C₄	semidirect
114. #373637	C₂×C₄	semidirect
115. #359811	C₂×C₄	semidirect
118. #359549	C₂×C₄	semidirect
119. #359549	C₂×C₄	semidirect
122. #359442	C₂×C₄	semidirect
125. #355096	C₂×C₄	semidirect
126. #147567	D₄	semidirect
127. #147567	D₄	semidirect
217. C₂×#1783	C₂×D₄	semidirect
218. C₂×#1783	C₂×D₄	semidirect
229. C₂×#1781	C₂×D₄	semidirect
230. C₂×#1781	C₂×D₄	semidirect
304. #2849	#99	semidirect
305. #2846	#99	semidirect
316. #1898	#99	semidirect
385. C₂⁵	#1913	semidirect
415. C₂³×C₄	#1913	semidirect

Maximal subgroups

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

subgroup	index
#72312643	2
#72312430	2
#72312360	2
#72312179	2
#72310388	2
#72310377	2
#72310337	2
#72309929	2
#72309519	2
#72309374	2
#72309310	2
#72266943	2
#72264815	2
#72251212	2
#72238346	2