Subgroups — #72266685

Order 8192.

Only the 456 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 374 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266683	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266681	C₂	1	1	yes	maximal, characteristic, complemented
3	#72266679	C₂	1	1	yes	maximal, characteristic, complemented
4	#72266631	C₂	1	1	yes	maximal, characteristic, complemented
5	#72266468	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266390	C₂	1	1	yes	maximal, characteristic
7	#72266385	C₂²	1	1	yes	characteristic
8	#72266377	C₄	1	2	yes	complemented
9	#72266364	C₄	1	2	yes	complemented
10	#72266342	C₂	1	1	yes	maximal, characteristic, complemented
11	#72266321	C₂	1	1	yes	maximal, characteristic, complemented
12	#72266300	C₂	1	1	yes	maximal, characteristic, complemented
13	#72266290	C₂	1	1	yes	maximal, characteristic, complemented
14	#72266289	C₂²	1	1	yes	characteristic, complemented
15	#72266289	C₂²	1	1	yes	characteristic, complemented
16	#72266230	C₂	1	1	yes	maximal, characteristic, complemented
17	#72266223	C₂²	1	1	yes	characteristic, complemented
18	#72266203	C₂	1	1	yes	maximal, characteristic, complemented
19	#72266202	C₂²	1	1	yes	characteristic, complemented
20	#72266200	C₂²	1	1	yes	characteristic, complemented
21	#72266198	C₂²	1	1	yes	characteristic, complemented
22	#72266197	C₂²	1	1	yes	characteristic
23	#72266184	C₂	1	1	yes	maximal, characteristic, complemented
24	#72266172	C₂²	1	1	yes	characteristic
25	#72266151	C₂²	1	1	yes	characteristic
26	#72266135	C₂²	1	1	yes	characteristic, complemented
27	#72266134	C₂²	1	1	yes	characteristic
28	#72266133	C₂²	1	1	yes	characteristic, complemented
29	#72266093	C₂	1	1	yes	maximal, characteristic, complemented
30	#72266086	C₂²	1	1	yes	characteristic, complemented
31	#72266085	C₂²	1	1	yes	characteristic, complemented
32	#72266068	C₂²	1	1	yes	characteristic, complemented
33	#72266023	C₂²	1	1	yes	characteristic
34	#72266021	D₄	1	1	yes	characteristic, complemented
35	#72266021	D₄	1	1	yes	characteristic, complemented
36	#72266010	D₄	1	1	yes	characteristic, complemented
37	#72262607	C₂²	1	1	yes	characteristic
38	#72259008	D₄	1	1	yes	characteristic, complemented
39	#72259008	D₄	1	1	yes	characteristic, complemented
40	#72259004	C₂×C₄	1	1	yes	characteristic, complemented
41	#72258969	C₂×C₄	1	1	yes	characteristic, complemented
42	#72258504	C₂²	1	1	yes	characteristic
43	#72255884	C₄	1	2	yes	complemented
44	#72240620	C₂²	1	1	yes	characteristic
45	#72240619	D₄	1	1	yes	characteristic
46	#72240619	D₄	1	1	yes	characteristic
47	#72238594	D₄	1	2	yes	—
48	#72238594	D₄	1	2	yes	—
49	#72236906	C₂²	1	1	yes	characteristic, complemented
50	#72236870	C₂²	1	1	yes	characteristic
51	#72236821	C₂²	1	1	yes	characteristic
52	#72236821	C₂²	1	1	yes	characteristic
53	#72236816	D₄	1	2	yes	complemented
54	#72236812	D₄	1	2	yes	complemented
55	#72236800	C₂²	1	1	yes	characteristic
56	#72236034	C₂²	1	1	yes	characteristic
57	#72235937	C₂³	1	1	yes	characteristic
58	#72235930	C₂³	1	1	yes	characteristic
59	#72235847	D₄	1	1	yes	characteristic, complemented
60	#72235847	D₄	1	1	yes	characteristic, complemented
61	#72233780	D₄	1	1	yes	characteristic
62	#72233780	D₄	1	1	yes	characteristic
63	#72226375	C₂	1	1	yes	maximal, characteristic, complemented
64	#72226364	C₂²	1	1	yes	characteristic, complemented
65	#72226359	C₂²	1	1	yes	characteristic
66	#72226161	C₂²	1	1	yes	characteristic, complemented
67	#72225904	C₂²	1	1	yes	characteristic, complemented
68	#72225881	C₂³	1	1	yes	characteristic
69	#72225818	C₂²	1	1	yes	characteristic, complemented
70	#72225783	D₄	1	1	yes	characteristic, complemented
71	C₂×#188035	C₂³	1	1	yes	characteristic
72	#72225773	C₂²	1	1	yes	characteristic
73	#72225773	C₂²	1	1	yes	characteristic
74	#72225773	C₂²	1	1	yes	characteristic
75	#72225711	C₂²	1	1	yes	characteristic
76	#72225649	C₂×C₄	1	2	yes	complemented
77	#72225621	C₂³	1	1	yes	characteristic
78	#72225611	C₄	1	2	yes	complemented
79	#72219423	C₂×C₄	1	2	yes	complemented
80	#72219423	D₄	1	2	yes	complemented
81	#72219377	C₂³	1	1	yes	characteristic
82	#72219377	C₂³	1	1	yes	characteristic
83	#72219377	C₂³	1	1	yes	characteristic
84	#72219307	C₂³	1	1	yes	characteristic
85	#72219307	C₂³	1	1	yes	characteristic
86	#72219307	C₂³	1	1	yes	characteristic
87	#72219307	C₂³	1	1	yes	characteristic
88	C₂×#7631286	C₂³	1	1	yes	characteristic
89	C₂×#7631286	C₂³	1	1	yes	characteristic
90	C₂×#647656	C₂³	1	1	yes	characteristic
91	C₂²×#62817	C₂×C₄	1	1	yes	characteristic, complemented
92	#72218854	C₂×C₄	1	2	yes	complemented
93	#72218846	C₂×C₄	1	2	yes	complemented
94	#72218795	C₂×C₄	1	2	yes	complemented
95	#72218518	C₂×C₄	1	2	yes	complemented
96	#72218518	D₄	1	2	yes	complemented
97	#72218467	C₂×C₄	1	2	yes	complemented
98	#72218467	C₂×C₄	1	2	yes	complemented
99	#72218467	C₂×C₄	1	2	yes	complemented
100	#72217875	C₂×C₄	1	1	yes	characteristic, complemented
101	#72214832	C₂×C₄	1	2	yes	—
102	#72214832	C₂×C₄	1	2	yes	—
103	#72214832	C₂×C₄	1	2	yes	complemented
104	C₂⁴×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
106	C₂²×#3484	C₂²×C₄	1	1	yes	characteristic
107	C₂²×#3484	C₂²×C₄	1	1	yes	characteristic
108	C₂²×#3484	C₂²×C₄	1	1	yes	characteristic
109	C₂³×D₄²	C₂⁴	1	1	yes	characteristic
110	C₂⁴×#120	C₂²×C₄	1	1	yes	characteristic
111	C₂⁴×#120	C₂×D₄	1	1	yes	characteristic
112	C₂²×#2846	#41	1	1	yes	characteristic
113	C₂×#35347	#41	1	1	yes	characteristic
114	C₂×#35347	#41	1	1	yes	characteristic
115	C₂×#35347	#41	1	1	yes	characteristic
116	C₂×#35346	C₂×D₄	1	1	yes	characteristic
117	C₂×#35346	C₂×D₄	1	1	yes	characteristic
118	C₂×#35346	C₂×D₄	1	1	yes	characteristic
119	C₂×#34980	C₂×D₄	1	2	yes	—
120	C₂×#34980	C₂×D₄	1	1	yes	characteristic
121	C₂×#34980	C₂×D₄	1	1	yes	characteristic
122	C₂²×#2403	C₂²×C₄	1	2	yes	—
123	C₂²×#2403	C₂×D₄	1	1	yes	characteristic
124	C₂²×#2403	C₂×D₄	1	1	yes	characteristic
125	C₂×#34256	#41	1	1	yes	characteristic
126	C₂×#34256	#41	1	1	yes	characteristic
127	C₂×#34171	C₂×D₄	1	1	yes	characteristic
128	C₂×#34171	C₂×D₄	1	1	yes	characteristic
129	C₂×#21746	C₂×D₄	1	1	yes	characteristic
130	C₂×#21746	C₂×D₄	1	1	yes	characteristic
131	C₂×#21746	C₂×D₄	1	1	yes	characteristic
132	C₂×#21746	C₂×D₄	1	1	yes	characteristic
133	#612424	C₂²⋊C₄	1	2	yes	—
134	#612424	C₂²⋊C₄	1	2	yes	—
135	#612424	C₂²⋊C₄	1	2	yes	—
136	#612424	C₂²⋊C₄	1	2	yes	—
137	#517411	C₂²×C₄	1	1	yes	characteristic
138	#517411	C₂×D₄	1	1	yes	characteristic
139	#517411	C₂×D₄	1	1	yes	characteristic
140	#517411	C₂×D₄	1	1	yes	characteristic
141	#517411	C₂×D₄	1	1	yes	characteristic
142	#517411	C₂×D₄	1	1	yes	characteristic
143	#517411	C₂×D₄	1	1	yes	characteristic
144	#515362	#41	1	1	yes	characteristic
145	#515285	C₂×D₄	1	1	yes	characteristic
146	C₂×#14134	#41	1	1	yes	characteristic
147	C₂×#13867	C₂²×C₄	1	1	yes	characteristic
148	C₂×#13867	C₂×D₄	1	1	yes	characteristic
149	#392109	C₂²×C₄	1	2	yes	—
150	#392109	C₂²×C₄	1	2	yes	—
151	#392109	C₂×D₄	1	2	yes	—
152	#392109	C₂×D₄	1	2	yes	—
153	#382422	C₂×D₄	1	2	yes	—
154	#382422	C₂×D₄	1	2	yes	—
155	#382422	C₂×D₄	1	2	yes	—
156	#359428	C₂²⋊C₄	1	2	yes	—
157	#359428	C₂²⋊C₄	1	2	yes	—
158	#359428	C₂²⋊C₄	1	2	yes	—
159	#359428	C₂²⋊C₄	1	2	yes	—
160	#154094	C₂²×C₄	1	2	yes	—
161	C₂⁸	C₄×D₄	1	1	yes	characteristic, complemented
162	C₂³×H(5,𝔽₂)	C₄×D₄	1	1	yes	characteristic
163	C₂³×H(5,𝔽₂)	C₄×D₄	1	1	yes	characteristic
164	C₂³×H(5,𝔽₂)	C₄×D₄	1	1	yes	characteristic, complemented
165	C₂³×H(5,𝔽₂)	#121	1	1	yes	characteristic
166	C₂³×H(5,𝔽₂)	#121	1	1	yes	characteristic
167	C₂⁵×D₄	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂⁵×D₄	#120	1	1	yes	characteristic
169	C₂⁵×D₄	#120	1	1	yes	characteristic
170	C₂⁵×D₄	C₂³×C₄	1	1	yes	characteristic
171	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
172	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
173	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
174	C₂²×#534	C₄×D₄	1	1	yes	characteristic
175	C₂²×#534	C₄×D₄	1	1	yes	characteristic
176	C₂²×#534	C₄×D₄	1	1	yes	characteristic
177	C₂²×#534	C₄×D₄	1	1	yes	characteristic
178	C₂³×#127	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂³×#121	C₂×#41	1	1	yes	characteristic
180	C₂³×#121	C₂×#41	1	1	yes	characteristic
181	C₂³×#121	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂³×#121	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
188	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
189	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
190	C₂³×#120	C₂×#41	1	1	yes	characteristic
191	C₂²×#518	C₄×D₄	1	1	yes	characteristic
192	C₂²×#518	C₄×D₄	1	1	yes	characteristic
193	C₂²×#518	C₄×D₄	1	1	yes	characteristic, complemented
194	C₂³×C₄×D₄	C₂×#41	1	1	yes	characteristic
195	C₂³×C₄×D₄	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂⁴×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic, complemented
197	C₂⁴×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic, complemented
198	C₂×#2846	#99	1	4	yes	complemented
199	C₂×#2308	C₄×D₄	1	1	yes	characteristic, complemented
200	C₂×#2308	C₄×D₄	1	1	yes	characteristic, complemented
201	C₂×#2308	#121	1	1	yes	characteristic
202	C₂×#2308	#121	1	1	yes	characteristic
203	C₂×#2308	#121	1	1	yes	characteristic
204	C₂×#2308	#121	1	1	yes	characteristic
205	C₂×#2308	#121	1	1	yes	characteristic
206	C₂×#2308	#121	1	1	yes	characteristic
207	C₂²×#386	#123	1	1	yes	characteristic
208	C₂²×#386	#123	1	1	yes	characteristic
209	C₂²×#386	#123	1	1	yes	characteristic
210	C₂²×#386	#123	1	1	yes	characteristic
211	C₂²×#379	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂²×#379	C₄×D₄	1	1	yes	characteristic, complemented
213	C₂²×#379	#120	1	1	yes	characteristic
214	C₂²×#379	#120	1	1	yes	characteristic
215	#14694	#99	1	4	yes	complemented
216	#14679	C₂×C₂²⋊C₄	1	2	yes	—
217	#14679	C₂×C₂²⋊C₄	1	2	yes	—
218	#14679	#120	1	2	yes	—
219	#14679	#120	1	2	yes	—
220	C₂⁷	C₂×#99	1	2	yes	complemented
221	C₂⁷	B(4,𝔽₂)	1	1	yes	characteristic
222	C₂⁷	B(4,𝔽₂)	1	1	yes	characteristic
223	C₂⁷	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂⁷	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂⁷	C₂×#120	1	1	yes	characteristic
226	C₂⁷	C₂×#120	1	1	yes	characteristic
227	C₂⁴×D₄	#386	1	1	yes	characteristic
228	C₂⁴×D₄	#386	1	1	yes	characteristic
229	C₂⁴×D₄	#386	1	1	yes	characteristic
230	C₂⁴×D₄	#386	1	1	yes	characteristic
231	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic
232	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic
233	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic
234	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic
235	C₂⁴×D₄	C₂×C₄×D₄	1	1	yes	characteristic
236	C₂⁴×D₄	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂⁴×D₄	C₂×C₄×D₄	1	1	yes	characteristic
238	C₂⁴×D₄	#518	1	1	yes	characteristic
239	C₂⁴×D₄	C₂×#121	1	1	yes	characteristic
240	C₂⁴×D₄	#525	1	1	yes	characteristic
241	C₂⁴×D₄	#535	1	1	yes	characteristic
242	C₂⁴×D₄	D₄²	1	1	yes	characteristic
243	C₂⁴×D₄	D₄²	1	1	yes	characteristic
244	C₂⁴×D₄	D₄²	1	1	yes	characteristic
245	C₂⁴×D₄	D₄²	1	1	yes	characteristic
246	C₂⁴×D₄	D₄²	1	1	yes	characteristic
247	C₂⁴×D₄	#546	1	1	yes	characteristic
248	C₂⁴×D₄	#546	1	1	yes	characteristic
249	C₂⁴×D₄	#546	1	1	yes	characteristic
250	C₂⁴×D₄	#546	1	1	yes	characteristic
251	C₂⁵×C₄	C₂×#99	1	2	yes	complemented
252	C₂⁵×C₄	B(4,𝔽₂)	1	1	yes	characteristic
253	C₂⁵×C₄	B(4,𝔽₂)	1	1	yes	characteristic
254	C₂⁵×C₄	#518	1	1	yes	characteristic
255	C₂⁵×C₄	C₂×#123	1	1	yes	characteristic
256	C₂⁵×C₄	#525	1	1	yes	characteristic
257	C₂⁵×C₄	#534	1	1	yes	characteristic
258	C₂²×#120	C₂×#99	1	4	yes	—
259	C₂³×C₄⋊C₄	#538	1	1	yes	characteristic
260	C₂³×C₄⋊C₄	#551	1	1	yes	characteristic
261	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
262	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
263	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
264	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
265	C₂³×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
266	C₂³×C₂²⋊C₄	#525	1	1	yes	characteristic
267	C₂³×C₂²⋊C₄	D₄²	1	1	yes	characteristic
268	C₂³×C₂²⋊C₄	#546	1	1	yes	characteristic
269	C₂³×C₂²⋊C₄	#546	1	1	yes	characteristic
270	C₂³×C₂²⋊C₄	#546	1	1	yes	characteristic
271	C₂³×C₂²⋊C₄	#546	1	1	yes	characteristic
272	C₂³×C₂²⋊C₄	#551	1	1	yes	characteristic
273	C₂³×C₄²	#538	1	1	yes	characteristic
274	C₂×#379	C₂×#99	1	4	yes	complemented
275	C₂×#379	B(4,𝔽₂)	1	4	yes	complemented
276	C₂⁶	#1889	1	1	yes	characteristic
277	C₂⁶	#1889	1	1	yes	characteristic
278	C₂⁶	#1889	1	1	yes	characteristic
279	C₂⁶	#1889	1	1	yes	characteristic
280	C₂⁶	C₂×#386	1	1	yes	characteristic
281	C₂⁶	C₄×#120	1	1	yes	characteristic
282	C₂⁶	D₄×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁶	D₄×C₂²⋊C₄	1	1	yes	characteristic
284	C₂⁶	#2358	1	1	yes	characteristic
285	C₂⁶	#2403	1	1	yes	characteristic
286	C₂⁶	#2404	1	1	yes	characteristic
287	C₂⁶	#2408	1	1	yes	characteristic
288	C₂⁶	C₂²×#99	1	2	yes	—
289	C₂⁶	#2883	1	2	yes	—
290	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
291	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
292	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
293	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
294	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
295	C₂⁶	#3025	1	2	yes	—
296	C₂³×D₄	#1898	1	2	yes	—
297	C₂³×D₄	#1913	1	2	yes	—
298	C₂⁴×C₄	#1889	1	1	yes	characteristic
299	C₂⁴×C₄	#1889	1	1	yes	characteristic
300	C₂⁴×C₄	#1889	1	1	yes	characteristic
301	C₂⁴×C₄	#1889	1	1	yes	characteristic
302	C₂⁴×C₄	#2321	1	1	yes	characteristic
303	C₂⁴×C₄	#2358	1	1	yes	characteristic
304	C₂⁴×C₄	#2418	1	1	yes	characteristic
305	C₂⁴×C₄	#2418	1	1	yes	characteristic
306	C₂⁴×C₄	#2424	1	1	yes	characteristic
307	C₂⁴×C₄	#2424	1	1	yes	characteristic
308	C₂⁴×C₄	#2534	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	#1898	1	2	yes	—
310	C₂²×C₂²⋊C₄	#1913	1	2	yes	—
311	C₂⁵	#9495	1	2	yes	—
312	C₂⁵	#13967	1	1	yes	characteristic
313	C₂⁵	C₂×#1889	1	1	yes	characteristic
314	C₂⁵	C₂×#1889	1	1	yes	characteristic
315	C₂⁵	C₂×#1898	1	1	yes	characteristic
316	C₂⁵	#20984	1	1	yes	characteristic
317	C₂⁵	C₂×#1913	1	1	yes	characteristic
318	C₂⁵	C₂×#1913	1	1	yes	characteristic
319	C₂⁵	C₄×B(4,𝔽₂)	1	2	yes	—
320	C₂⁵	D₄×#99	1	2	yes	—
321	C₂⁵	D₄×#99	1	2	yes	—
322	C₂⁵	#23895	1	1	yes	characteristic
323	C₂⁵	#23896	1	1	yes	characteristic
324	C₂⁵	#23900	1	1	yes	characteristic
325	C₂⁵	#23900	1	1	yes	characteristic
326	C₂⁵	#23900	1	1	yes	characteristic
327	C₂⁵	#23902	1	1	yes	characteristic
328	C₂⁵	#23984	1	1	yes	characteristic
329	C₂⁵	#23984	1	1	yes	characteristic
330	C₂⁵	#23996	1	1	yes	characteristic
331	C₂⁵	#23996	1	1	yes	characteristic
332	C₂⁵	#23996	1	1	yes	characteristic
333	C₂⁵	#23997	1	1	yes	characteristic
334	C₂⁵	#24260	1	2	yes	—
335	C₂³×C₄	#9495	1	2	yes	—
336	C₂⁴	#139750	1	4	yes	complemented
337	C₂⁴	C₂×#9495	1	1	yes	characteristic
338	C₂⁴	#201664	1	1	yes	characteristic
339	C₂⁴	#201678	1	1	yes	characteristic
340	C₂⁴	#201678	1	1	yes	characteristic
341	C₂⁴	#245225	1	1	yes	characteristic
342	C₂⁴	#245227	1	1	yes	characteristic
343	C₂⁴	#245229	1	1	yes	characteristic
344	C₂⁴	#245231	1	1	yes	characteristic
345	C₂⁴	#251827	1	1	yes	characteristic
346	C₂⁴	#251837	1	1	yes	characteristic
347	C₂⁴	#251859	1	1	yes	characteristic
348	C₂⁴	#251871	1	1	yes	characteristic
349	C₂⁴	#364410	1	1	yes	characteristic
350	C₂⁴	#364440	1	1	yes	characteristic
351	C₂⁴	#364471	1	1	yes	characteristic
352	C₂⁴	#364500	1	1	yes	characteristic
353	C₂⁴	#364513	1	1	yes	characteristic
354	C₂⁴	#364532	1	1	yes	characteristic
355	C₂⁴	#364545	1	1	yes	characteristic
356	C₂³	B(5,𝔽₂)	1	2	yes	—
357	C₂³	#72216620	1	1	yes	characteristic
358	C₂³	C₂×#139750	1	2	yes	—
359	C₂³	#72232995	1	1	yes	characteristic
360	C₂³	#72233066	1	1	yes	characteristic
361	C₂³	#72234593	1	1	yes	characteristic
362	C₂³	#72237497	1	1	yes	characteristic
363	C₂³	#72240426	1	1	yes	characteristic
364	C₂³	#72241183	1	1	yes	characteristic
365	C₂²	#72246304	1	1	yes	characteristic
366	C₂²	#72256294	1	1	yes	characteristic
367	C₂²	#72262328	1	1	yes	characteristic
368	C₂²	#72264854	1	1	yes	characteristic
369	C₂²	#72264962	1	1	yes	characteristic
370	C₂	#72265794	1	1	yes	characteristic
371	C₂	#72265810	1	1	yes	characteristic
372	C₂	#72265910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72264962
commutator	C₂⁵×D₄	C₂³×C₄
Frattini, cosocle	C₂³×D₄²	C₂⁴
prime radical	#72266390	C₂
LCS	G ▷ C₂⁵×D₄ ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×D₄² ◁ G
LECS	G ▷ C₂³×D₄² ▷ C₂⁵ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266683	C₂	semidirect
2. #72266681	C₂	semidirect
3. #72266679	C₂	semidirect
4. #72266631	C₂	semidirect
5. #72266468	C₂	semidirect
8. #72266377	C₄	semidirect
9. #72266364	C₄	semidirect
10. #72266342	C₂	semidirect
11. #72266321	C₂	semidirect
12. #72266300	C₂	semidirect
13. #72266290	C₂	semidirect
14. #72266289	C₂²	semidirect
15. #72266289	C₂²	semidirect
16. #72266230	C₂	semidirect
17. #72266223	C₂²	semidirect
18. #72266203	C₂	semidirect
19. #72266202	C₂²	semidirect
20. #72266200	C₂²	semidirect
21. #72266198	C₂²	semidirect
23. #72266184	C₂	semidirect
26. #72266135	C₂²	semidirect
28. #72266133	C₂²	semidirect
29. #72266093	C₂	semidirect
30. #72266086	C₂²	semidirect
31. #72266085	C₂²	semidirect
32. #72266068	C₂²	semidirect
34. #72266021	D₄	semidirect
35. #72266021	D₄	semidirect
36. #72266010	D₄	semidirect
38. #72259008	D₄	semidirect
39. #72259008	D₄	semidirect
40. #72259004	C₂×C₄	semidirect
41. #72258969	C₂×C₄	semidirect
43. #72255884	C₄	semidirect
49. #72236906	C₂²	semidirect
53. #72236816	D₄	semidirect
54. #72236812	D₄	semidirect
59. #72235847	D₄	semidirect
60. #72235847	D₄	semidirect
63. #72226375	C₂	semidirect
64. #72226364	C₂²	semidirect
66. #72226161	C₂²	semidirect
67. #72225904	C₂²	semidirect
69. #72225818	C₂²	semidirect
70. #72225783	D₄	semidirect
76. #72225649	C₂×C₄	semidirect
78. #72225611	C₄	semidirect
79. #72219423	C₂×C₄	semidirect
80. #72219423	D₄	semidirect
91. C₂²×#62817	C₂×C₄	semidirect
92. #72218854	C₂×C₄	semidirect
93. #72218846	C₂×C₄	semidirect
94. #72218795	C₂×C₄	semidirect
95. #72218518	C₂×C₄	semidirect
96. #72218518	D₄	semidirect
97. #72218467	C₂×C₄	semidirect
98. #72218467	C₂×C₄	semidirect
99. #72218467	C₂×C₄	semidirect
100. #72217875	C₂×C₄	semidirect
103. #72214832	C₂×C₄	semidirect
161. C₂⁸	C₄×D₄	semidirect
164. C₂³×H(5,𝔽₂)	C₄×D₄	semidirect
193. C₂²×#518	C₄×D₄	semidirect
196. C₂⁴×C₂²⋊C₄	C₄×D₄	semidirect
197. C₂⁴×C₂²⋊C₄	C₄×D₄	semidirect
198. C₂×#2846	#99	semidirect
199. C₂×#2308	C₄×D₄	semidirect
200. C₂×#2308	C₄×D₄	semidirect
212. C₂²×#379	C₄×D₄	semidirect
215. #14694	#99	semidirect
220. C₂⁷	C₂×#99	semidirect
251. C₂⁵×C₄	C₂×#99	semidirect
274. C₂×#379	C₂×#99	semidirect
275. C₂×#379	B(4,𝔽₂)	semidirect
336. C₂⁴	#139750	semidirect

Maximal subgroups

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

subgroup	index
#72266683	2
#72266681	2
#72266679	2
#72266631	2
#72266468	2
#72266390	2
#72266342	2
#72266321	2
#72266300	2
#72266290	2
#72266230	2
#72266203	2
#72266184	2
#72266093	2
#72226375	2