Subgroups — #72261086

Order 2048.

At least 9002 conjugacy classes of subgroups; only the 778 normal subgroups are shown.

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	#72261073	C₂	1	1	yes	maximal, characteristic, complemented
2	#72261064	C₂	1	2	yes	maximal, complemented
3	#72238584	C₂	1	1	yes	maximal, characteristic
4	#72234078	C₂	1	1	yes	maximal, characteristic, complemented
5	#72233187	C₂	1	2	yes	maximal, complemented
6	#72233002	C₂	1	2	yes	maximal, complemented
7	#72232863	C₂	1	2	yes	maximal, complemented
8	#72232764	C₂	1	4	yes	maximal, complemented
9	C₂×#63011	C₂²	1	1	yes	characteristic
10	C₂×#41²	C₄	1	1	yes	characteristic, complemented
11	#7739388	C₂²	1	1	yes	characteristic
12	#7739367	C₄	1	1	yes	characteristic, complemented
13	#7737957	C₄	1	2	yes	complemented
14	#7737955	C₂²	1	2	yes	—
15	#7712669	C₄	1	2	yes	complemented
16	#7711937	C₄	1	1	yes	characteristic, complemented
17	#7672702	C₂²	1	1	yes	characteristic
18	#7671874	C₂²	1	2	yes	—
19	#7627216	C₄	1	1	yes	characteristic, complemented
20	#494721	C₂²	1	4	yes	complemented
21	#494701	C₂²	1	2	yes	complemented
22	#493878	C₂²	1	1	yes	characteristic, complemented
23	#493867	C₂²	1	2	yes	complemented
24	#493430	C₂²	1	2	yes	complemented
25	#493424	C₂²	1	4	yes	complemented
26	#492900	C₂²	1	1	yes	characteristic, complemented
27	#359601	C₂²	1	2	yes	complemented
28	#359591	C₂²	1	4	yes	complemented
29	#214619	C₂²	1	4	yes	complemented
30	#213852	C₂²	1	2	yes	complemented
31	C₂×#3498	C₂³	1	1	yes	characteristic
32	C₂×#3484	C₂³	1	2	yes	—
33	C₂×#3549	C₂×C₄	1	1	yes	characteristic
34	C₂×#3543	D₄	1	2	yes	—
35	C₂×#3537	C₂×C₄	1	2	yes	—
36	C₂×#3532	D₄	1	4	yes	—
37	C₂×#3483	C₂×C₄	1	1	yes	characteristic
38	C₂×#3481	C₂×C₄	1	1	yes	characteristic
39	C₂×#3481	C₂×C₄	1	2	yes	—
40	C₂²×D₄²	D₄	1	2	yes	—
41	C₂×#3444	C₂×C₄	1	2	yes	—
42	C₂×#3444	C₂×C₄	1	1	yes	characteristic
43	C₂×#2883	C₂³	1	2	yes	—
44	#59084	D₄	1	2	yes	—
45	#59056	D₄	1	2	yes	—
46	#59006	D₄	1	4	yes	—
47	#58990	D₄	1	4	yes	—
48	#51896	D₄	1	4	yes	—
49	#50856	D₄	1	4	yes	—
50	#50635	D₄	1	4	yes	—
51	#37273	C₂×C₄	1	2	yes	—
52	#37273	C₂×C₄	1	2	yes	—
53	#37269	C₂×C₄	1	2	yes	—
54	#36626	D₄	1	2	yes	—
55	C₂×#2856	D₄	1	1	yes	characteristic
56	#35563	C₂×C₄	1	1	yes	characteristic
57	#35563	D₄	1	1	yes	characteristic
58	#35556	D₄	1	2	yes	—
59	#35533	C₂×C₄	1	2	yes	—
60	#35515	D₄	1	2	yes	—
61	#35513	C₂³	1	2	yes	—
62	#35512	D₄	1	1	yes	characteristic
63	#35512	C₂³	1	1	yes	characteristic
64	#35285	D₄	1	1	yes	characteristic
65	#35280	D₄	1	1	yes	characteristic
66	#35256	D₄	1	2	yes	—
67	#35254	C₂×C₄	1	2	yes	—
68	#35254	C₂×C₄	1	1	yes	characteristic
69	#35254	D₄	1	1	yes	characteristic
70	#35223	D₄	1	2	yes	—
71	#35222	D₄	1	2	yes	—
72	#34368	C₂×C₄	1	1	yes	characteristic
73	#34360	C₂×C₄	1	2	yes	—
74	#34269	D₄	1	2	yes	—
75	#34258	D₄	1	1	yes	characteristic
76	#34258	C₂³	1	1	yes	characteristic
77	#34207	C₂×C₄	1	1	yes	characteristic
78	#34200	C₂×C₄	1	2	yes	—
79	C₄×#525	D₄	1	1	yes	characteristic
80	C₂²×#390	D₄	1	2	yes	—
81	#20592	C₂³	1	2	yes	—
82	#20585	C₂³	1	4	yes	—
83	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
84	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
85	C₂⁴×D₄	C₂×D₄	1	2	yes	—
86	C₂×H(3,𝔽₄)	C₂²⋊C₄	1	2	yes	—
87	C₂×#560	C₂²⋊C₄	1	4	yes	—
88	C₂×#559	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×#559	C₂²⋊C₄	1	2	yes	complemented
90	C₂×Q₈²	C₂²⋊C₄	1	1	yes	characteristic, complemented
91	C₂×#555	C₂²⋊C₄	1	2	yes	complemented
92	C₂×#555	C₂²⋊C₄	1	1	yes	characteristic, complemented
93	C₂×#551	C₂²⋊C₄	1	2	yes	—
94	C₂×#551	C₂²⋊C₄	1	2	yes	complemented
95	C₂×#551	C₂²⋊C₄	1	2	yes	complemented
96	C₂×D₄²	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
98	C₂×D₄²	C₂²⋊C₄	1	2	yes	—
99	C₂×D₄²	C₂²⋊C₄	1	2	yes	complemented
100	C₂×#537	C₂×D₄	1	2	yes	—
101	C₂×#535	C₂²⋊C₄	1	2	yes	complemented
102	C₂×#535	C₂²×C₄	1	1	yes	characteristic
103	C₂×#535	C₂²×C₄	1	2	yes	—
104	C₂×#535	C₂×D₄	1	1	yes	characteristic
105	C₂×#535	C₂×D₄	1	2	yes	—
106	C₂×#535	C₂×D₄	1	2	yes	—
107	C₂×#535	C₂×D₄	1	2	yes	—
108	C₂×#535	C₂×D₄	1	2	yes	—
109	C₂×#534	C₂×D₄	1	4	yes	—
110	C₂×#534	C₂×D₄	1	4	yes	—
111	C₂×#533	C₂²⋊C₄	1	1	yes	characteristic, complemented
112	C₂×#533	C₂²⋊C₄	1	2	yes	complemented
113	C₂×#532	C₂²×C₄	1	1	yes	characteristic
114	C₂×#532	C₂²×C₄	1	2	yes	—
115	C₂×#532	C₂×D₄	1	2	yes	—
116	C₂²×#127	C₂×D₄	1	2	yes	—
117	C₂²×#127	C₂×D₄	1	1	yes	characteristic
118	C₂×#525	C₂²⋊C₄	1	2	yes	complemented
119	C₂×#525	C₂²⋊C₄	1	1	yes	characteristic, complemented
120	C₂×#525	C₂²×C₄	1	2	yes	—
121	C₂×#525	C₂²×C₄	1	1	yes	characteristic
122	C₂×#525	C₂×D₄	1	1	yes	characteristic
123	C₂×#525	C₂×D₄	1	2	yes	—
124	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic, complemented
125	C₂²×#121	C₂×D₄	1	1	yes	characteristic
126	C₂²×#120	C₂×D₄	1	4	yes	—
127	C₂²×#120	C₂×D₄	1	4	yes	—
128	C₂×#520	C₂²⋊C₄	1	1	yes	characteristic, complemented
129	C₂×#520	C₂²×C₄	1	1	yes	characteristic
130	C₂×#518	C₂×D₄	1	2	yes	—
131	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
132	C₂×C₄×#41	C₂²⋊C₄	1	2	yes	complemented
133	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₄⋊C₄	C₂²⋊C₄	1	2	yes	complemented
136	C₂³×C₄²	C₂²⋊C₄	1	2	yes	complemented
137	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
138	#2733	C₂²⋊C₄	1	4	yes	complemented
139	#2731	C₂²⋊C₄	1	4	yes	complemented
140	#2697	C₂²⋊C₄	1	4	yes	complemented
141	#2684	C₂²⋊C₄	1	4	yes	complemented
142	#2679	C₂²⋊C₄	1	4	yes	complemented
143	#2669	C₂²⋊C₄	1	4	yes	complemented
144	#2435	C₂×D₄	1	4	yes	—
145	#2433	C₂×D₄	1	4	yes	—
146	#2432	C₂×D₄	1	4	yes	—
147	#2431	C₂×D₄	1	4	yes	—
148	#2405	C₂×D₄	1	4	yes	—
149	#2403	C₂×D₄	1	4	yes	—
150	#2379	C₂²⋊C₄	1	2	yes	complemented
151	#2376	C₂²⋊C₄	1	4	yes	complemented
152	#2369	C₂²⋊C₄	1	2	yes	complemented
153	#2358	C₂²⋊C₄	1	4	yes	complemented
154	#2317	C₂²⋊C₄	1	2	yes	complemented
155	#2316	C₂²⋊C₄	1	2	yes	complemented
156	#2316	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	#2316	C₂²⋊C₄	1	1	yes	characteristic, complemented
158	#2311	C₂²⋊C₄	1	2	yes	complemented
159	#2311	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	#2311	C₂²×C₄	1	2	yes	—
161	#2311	C₂²×C₄	1	1	yes	characteristic
162	#2311	C₂×D₄	1	1	yes	characteristic
163	#2311	C₂×D₄	1	2	yes	—
164	#2311	C₂×D₄	1	1	yes	characteristic
165	#2309	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	#2309	C₂²⋊C₄	1	1	yes	characteristic, complemented
167	#2309	C₂²⋊C₄	1	2	yes	complemented
168	#2309	C₂×D₄	1	2	yes	—
169	#2309	C₂×D₄	1	1	yes	characteristic
170	#2309	C₂×D₄	1	1	yes	characteristic
171	#2297	C₂×D₄	1	1	yes	characteristic
172	#2297	C₂×D₄	1	2	yes	—
173	#2297	C₂×D₄	1	2	yes	—
174	#2296	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	#2296	C₂²⋊C₄	1	2	yes	complemented
176	#2296	C₂²⋊C₄	1	2	yes	complemented
177	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic, complemented
178	C₂×#390	C₂²⋊C₄	1	2	yes	complemented
179	C₂×#390	C₂²⋊C₄	1	2	yes	complemented
180	C₂×#390	C₂×D₄	1	1	yes	characteristic
181	C₂×#390	C₂×D₄	1	2	yes	—
182	C₂×#390	C₂×D₄	1	2	yes	—
183	C₂×#384	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	#2280	C₂²⋊C₄	1	2	yes	complemented
185	#2280	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	#2274	C₂²⋊C₄	1	2	yes	complemented
187	C₄×#117	C₂²⋊C₄	1	1	yes	characteristic, complemented
188	C₂⁶	#120	1	4	yes	—
189	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂²×#41	#120	1	2	yes	—
192	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
193	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
194	C₂²×#41	C₂²×D₄	1	2	yes	—
195	C₂²×#41	C₂²×D₄	1	2	yes	—
196	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×D₄	#120	1	2	yes	—
199	C₂³×D₄	#120	1	4	yes	—
200	C₂³×D₄	#120	1	2	yes	—
201	C₂³×D₄	C₂²×D₄	1	2	yes	—
202	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
203	C₂³×D₄	C₂²×D₄	1	2	yes	—
204	C₂³×D₄	C₂²×D₄	1	4	yes	—
205	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	#559	#99	1	4	yes	complemented
208	#551	#99	1	8	yes	complemented
209	D₄²	#99	1	4	yes	complemented
210	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×#127	#120	1	2	yes	—
216	C₂×#127	#120	1	2	yes	—
217	C₂×#127	#120	1	2	yes	—
218	C₂×#127	#120	1	4	yes	—
219	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂×#124	#120	1	2	yes	—
225	C₂×#124	#120	1	4	yes	—
226	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×#123	#120	1	4	yes	—
230	C₂×#123	#120	1	2	yes	—
231	C₂×C₂²⋊Q₈	#120	1	4	yes	—
232	C₂×#121	#120	1	4	yes	—
233	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
235	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
238	C₂×#120	#120	1	4	yes	—
239	C₂×#120	#120	1	4	yes	—
240	C₂×#120	#120	1	4	yes	—
241	C₂×#120	#120	1	2	yes	—
242	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
244	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×#117	#120	1	2	yes	—
253	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂²×C₂²⋊C₄	#120	1	4	yes	—
258	C₂²×C₂²⋊C₄	#120	1	4	yes	—
259	C₂²×C₂²⋊C₄	#120	1	2	yes	—
260	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂²×C₄²	#120	1	2	yes	—
265	#391	C₂×C₂²⋊C₄	1	4	yes	—
266	#391	#120	1	1	yes	characteristic
267	#391	#120	1	2	yes	—
268	#391	#120	1	1	yes	characteristic
269	#390	C₂×C₂²⋊C₄	1	4	yes	—
270	#390	#120	1	1	yes	characteristic
271	#390	#120	1	2	yes	—
272	#390	#120	1	2	yes	—
273	#390	#120	1	2	yes	—
274	#390	#120	1	2	yes	—
275	#390	#120	1	2	yes	—
276	#390	#120	1	4	yes	—
277	#390	#120	1	4	yes	—
278	#390	#120	1	1	yes	characteristic
279	#386	C₂×C₂²⋊C₄	1	4	yes	—
280	#386	#120	1	4	yes	—
281	#379	#120	1	4	yes	—
282	C₄×C₂²⋊C₄	#120	1	4	yes	—
283	C₄×C₂²⋊C₄	#120	1	4	yes	—
284	C₂⁵	#379	1	4	yes	—
285	C₂⁵	#379	1	2	yes	—
286	C₂⁵	#379	1	1	yes	characteristic
287	C₂⁵	C₂×#120	1	4	yes	—
288	C₂⁵	C₂×#120	1	2	yes	—
289	C₂²×Q₈	#379	1	1	yes	characteristic
290	C₂²×Q₈	#379	1	2	yes	—
291	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
293	C₂²×D₄	#379	1	2	yes	—
294	C₂²×D₄	#379	1	1	yes	characteristic
295	C₂²×D₄	#379	1	2	yes	—
296	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
297	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×D₄	C₂×#120	1	2	yes	—
299	C₂²×D₄	C₂×#120	1	4	yes	—
300	C₂²×D₄	C₂×#120	1	4	yes	—
301	C₂²×D₄	C₂×#120	1	2	yes	—
302	C₂²×D₄	C₂×#120	1	2	yes	—
303	C₂²×D₄	C₂×#120	1	1	yes	characteristic
304	C₂³×C₄	#379	1	2	yes	—
305	C₂³×C₄	#379	1	1	yes	characteristic
306	C₂³×C₄	#379	1	2	yes	—
307	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
308	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
309	C₂³×C₄	C₂×#120	1	2	yes	—
310	C₂³×C₄	C₂×#120	1	4	yes	—
311	#127	C₂×#99	1	2	yes	—
312	#127	C₂×#99	1	2	yes	—
313	#124	C₂×#99	1	4	yes	—
314	#123	C₂×#99	1	4	yes	—
315	#123	C₂×#99	1	4	yes	—
316	#120	C₂×#99	1	4	yes	—
317	#120	C₂×#99	1	4	yes	—
318	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
319	C₂×C₄⋊C₄	#379	1	2	yes	—
320	C₂×C₄⋊C₄	#379	1	4	yes	—
321	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	#379	1	4	yes	—
323	C₂×C₂²⋊C₄	#379	1	2	yes	—
324	C₂×C₂²⋊C₄	#379	1	2	yes	—
325	C₂×C₂²⋊C₄	#379	1	2	yes	—
326	C₂×C₂²⋊C₄	#379	1	2	yes	—
327	C₂×C₄²	#379	1	2	yes	—
328	C₂×C₄²	#379	1	1	yes	characteristic
329	C₂×C₄²	#379	1	1	yes	characteristic
330	C₂×C₄²	#379	1	2	yes	—
331	C₂×C₄²	#379	1	1	yes	characteristic
332	C₂×C₄²	#379	1	2	yes	—
333	C₂×C₄²	#379	1	4	yes	—
334	C₂×C₄²	#379	1	2	yes	—
335	C₂×C₄²	#379	1	1	yes	characteristic
336	C₂⁴	#1781	1	4	yes	—
337	C₂⁴	C₂×#379	1	1	yes	characteristic
338	C₂⁴	C₂×#379	1	2	yes	—
339	C₂⁴	#2846	1	4	yes	—
340	C₂⁴	#2846	1	2	yes	—
341	C₂×Q₈	#1781	1	2	yes	—
342	C₂×D₄	#1781	1	2	yes	—
343	C₂×D₄	C₂²×#99	1	1	yes	characteristic
344	C₂×D₄	C₂²×#99	1	2	yes	—
345	C₂×D₄	C₂²×#99	1	1	yes	characteristic
346	C₂×D₄	#3025	1	2	yes	—
347	C₂×D₄	#3027	1	1	yes	characteristic
348	C₂×D₄	#3028	1	1	yes	characteristic
349	C₂²×C₄	#1781	1	4	yes	—
350	C₂²×C₄	C₂×#379	1	2	yes	—
351	C₂²×C₄	C₂×#379	1	1	yes	characteristic
352	C₂²×C₄	C₂×#379	1	1	yes	characteristic
353	C₂²×C₄	#2846	1	2	yes	—
354	C₂²⋊C₄	#1781	1	4	yes	—
355	C₂²⋊C₄	#1781	1	4	yes	—
356	C₄²	#1781	1	2	yes	—
357	C₄²	#1781	1	2	yes	—
358	C₂³	#14679	1	1	yes	characteristic
359	C₂³	C₂×#1781	1	2	yes	—
360	C₂³	C₂×#1781	1	2	yes	—
361	C₂³	#32899	1	2	yes	—
362	C₂³	#32901	1	2	yes	—
363	C₂×C₄	C₂×#1781	1	1	yes	characteristic
364	C₂×C₄	C₂×#1781	1	1	yes	characteristic
365	C₂×C₄	#20608	1	1	yes	characteristic
366	C₂×C₄	#20610	1	1	yes	characteristic
367	C₂²	#392109	1	1	yes	characteristic
368	C₂²	#392126	1	1	yes	characteristic
369	C₂²	#392135	1	1	yes	characteristic
370	C₂	#72258948	1	1	yes	characteristic
371	C₂	#72260467	1	1	yes	characteristic
372	C₂	#72260628	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#392135
commutator	C₂²×#41	C₂³×C₄
Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁴
prime radical	#72238584	C₂
LCS	G ▷ C₂²×#41 ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261073	C₂	semidirect
2. #72261064	C₂	semidirect
4. #72234078	C₂	semidirect
5. #72233187	C₂	semidirect
6. #72233002	C₂	semidirect
7. #72232863	C₂	semidirect
8. #72232764	C₂	semidirect
10. C₂×#41²	C₄	semidirect
12. #7739367	C₄	semidirect
13. #7737957	C₄	semidirect
15. #7712669	C₄	semidirect
16. #7711937	C₄	semidirect
19. #7627216	C₄	semidirect
20. #494721	C₂²	semidirect
21. #494701	C₂²	semidirect
22. #493878	C₂²	semidirect
23. #493867	C₂²	semidirect
24. #493430	C₂²	semidirect
25. #493424	C₂²	semidirect
26. #492900	C₂²	semidirect
27. #359601	C₂²	semidirect
28. #359591	C₂²	semidirect
29. #214619	C₂²	semidirect
30. #213852	C₂²	semidirect
89. C₂×#559	C₂²⋊C₄	semidirect
90. C₂×Q₈²	C₂²⋊C₄	semidirect
91. C₂×#555	C₂²⋊C₄	semidirect
92. C₂×#555	C₂²⋊C₄	semidirect
94. C₂×#551	C₂²⋊C₄	semidirect
95. C₂×#551	C₂²⋊C₄	semidirect
99. C₂×D₄²	C₂²⋊C₄	semidirect
101. C₂×#535	C₂²⋊C₄	semidirect
111. C₂×#533	C₂²⋊C₄	semidirect
112. C₂×#533	C₂²⋊C₄	semidirect
118. C₂×#525	C₂²⋊C₄	semidirect
119. C₂×#525	C₂²⋊C₄	semidirect
124. C₂²×#121	C₂²⋊C₄	semidirect
128. C₂×#520	C₂²⋊C₄	semidirect
131. C₂×C₄×#41	C₂²⋊C₄	semidirect
132. C₂×C₄×#41	C₂²⋊C₄	semidirect
135. C₂³×C₄⋊C₄	C₂²⋊C₄	semidirect
136. C₂³×C₄²	C₂²⋊C₄	semidirect
137. C₂³×C₄²	C₂²⋊C₄	semidirect
138. #2733	C₂²⋊C₄	semidirect
139. #2731	C₂²⋊C₄	semidirect
140. #2697	C₂²⋊C₄	semidirect
141. #2684	C₂²⋊C₄	semidirect
142. #2679	C₂²⋊C₄	semidirect
143. #2669	C₂²⋊C₄	semidirect
150. #2379	C₂²⋊C₄	semidirect
151. #2376	C₂²⋊C₄	semidirect
152. #2369	C₂²⋊C₄	semidirect
153. #2358	C₂²⋊C₄	semidirect
154. #2317	C₂²⋊C₄	semidirect
155. #2316	C₂²⋊C₄	semidirect
156. #2316	C₂²⋊C₄	semidirect
157. #2316	C₂²⋊C₄	semidirect
158. #2311	C₂²⋊C₄	semidirect
159. #2311	C₂²⋊C₄	semidirect
165. #2309	C₂²⋊C₄	semidirect
166. #2309	C₂²⋊C₄	semidirect
167. #2309	C₂²⋊C₄	semidirect
174. #2296	C₂²⋊C₄	semidirect
175. #2296	C₂²⋊C₄	semidirect
176. #2296	C₂²⋊C₄	semidirect
177. C₂×#390	C₂²⋊C₄	semidirect
178. C₂×#390	C₂²⋊C₄	semidirect
179. C₂×#390	C₂²⋊C₄	semidirect
183. C₂×#384	C₂²⋊C₄	semidirect
184. #2280	C₂²⋊C₄	semidirect
185. #2280	C₂²⋊C₄	semidirect
186. #2274	C₂²⋊C₄	semidirect
187. C₄×#117	C₂²⋊C₄	semidirect
207. #559	#99	semidirect
208. #551	#99	semidirect
209. D₄²	#99	semidirect

Maximal subgroups

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

subgroup	index
#72261073	2
#72261064	2
#72238584	2
#72234078	2
#72233187	2
#72233002	2
#72232863	2
#72232764	2