Subgroups — #14907026

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13081718	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10622757	C₂	1	1	yes	maximal, characteristic
3	#13070456	C₂	1	4	yes	maximal, complemented
4	#13070451	C₂	1	4	yes	maximal, complemented
5	C₂×#10622149	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070245	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070244	C₂	1	1	yes	maximal, characteristic, complemented
8	M₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
11	C₂×#67003	C₄	1	1	yes	characteristic
12	C₂×#66954	C₂²	1	1	yes	characteristic
13	C₁₁×#504	—	2	2	no	—
14	C₁₁×#504	C₂²	1	4	yes	complemented
15	C₂×C₁₁×M₃₂	—	2	2	no	—
16	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×#66901	C₄	1	1	yes	characteristic
19	#10622757	C₄	1	2	yes	—
20	#10622757	C₄	1	2	yes	—
21	#10622757	C₂²	1	2	yes	—
22	#10622757	C₂²	1	2	yes	—
23	C₂×#66889	C₄	1	1	yes	characteristic
24	C₂×#66886	C₄	1	1	yes	characteristic
25	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
26	C₂×#66876	C₂²	1	1	yes	characteristic
27	C₂×#66876	C₂²	1	1	yes	characteristic
28	#10622520	—	2	2	no	—
29	D₁₁×M₃₂	—	2	2	no	—
30	#10622514	C₂²	1	4	yes	complemented
31	#10622199	C₂²	1	4	yes	complemented
32	#10622153	C₂²	1	4	yes	complemented
33	#10622149	C₂²	1	2	yes	complemented
34	#10622149	C₂²	1	2	yes	complemented
35	#10622140	C₂²	1	2	yes	complemented
36	C₁₆×Dic₁₁	C₂²	1	2	yes	complemented
37	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
38	C₂×#4339	C₂×C₄	1	1	yes	characteristic
39	C₁₁×#131	—	2	1	no	—
40	C₁₁×#131	—	2	1	no	—
41	C₁₁×#131	C₂×C₄	1	2	yes	—
42	C₁₁×#131	C₂³	1	2	yes	—
43	C₂×C₁₁×M₁₆	—	2	1	no	—
44	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	—	2	1	no	—
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	#67003	C₈	1	2	yes	—
48	#67003	C₈	1	2	yes	—
49	#67003	C₂×C₄	1	2	yes	—
50	#67003	C₂×C₄	1	2	yes	—
51	C₂×#4326	C₈	1	1	yes	characteristic
52	C₂×#4325	C₈	1	1	yes	characteristic
53	C₂×#4324	C₈	1	1	yes	characteristic
54	C₂×#4323	C₈	1	1	yes	characteristic
55	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×#4318	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
58	#66954	—	2	1	no	—
59	#66954	—	2	1	no	—
60	#66954	C₂×C₄	1	2	yes	—
61	#66954	C₂³	1	2	yes	—
62	C₂×#4313	—	2	1	no	—
63	C₂×C₈×D₁₁	—	2	1	no	—
64	C₁₁×M₃₂	—	2	1	no	—
65	C₁₁×M₃₂	—	2	4	no	—
66	C₁₁×M₃₂	D₄	1	2	yes	—
67	C₁₁×M₃₂	D₄	1	2	yes	—
68	C₁₁×M₃₂	C₂³	1	2	yes	—
69	C₂×C₁₁×C₁₆	—	2	1	no	—
70	C₂×C₁₁×C₁₆	—	2	4	no	—
71	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
72	#66901	C₂×C₄	1	2	yes	—
73	#66901	C₂×C₄	1	2	yes	—
74	#66889	C₂×C₄	1	2	yes	—
75	#66889	C₂×C₄	1	2	yes	—
76	#66886	C₂×C₄	1	2	yes	—
77	#66886	C₂×C₄	1	2	yes	—
78	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
81	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
82	#66876	—	2	1	no	—
83	#66876	—	2	1	no	—
84	#66876	—	2	1	no	—
85	#66876	C₂³	1	2	yes	—
86	C₂×C₁₁⋊C₁₆	—	2	1	no	—
87	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
88	#66862	—	2	4	no	—
89	C₁₆×D₁₁	—	2	4	no	—
90	#33443	—	11	1	no	maximal, Sylow
91	C₁₁×#41	—	2	1	no	—
92	C₁₁×#41	—	2	1	no	—
93	C₁₁×#41	C₂×C₈	1	2	yes	—
94	C₁₁×#41	C₂²×C₄	1	2	yes	—
95	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
96	C₂×D₄×C₁₁	—	2	1	no	—
97	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	—	2	1	no	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊D₁₁	—	2	1	no	—
101	C₂²×Dic₁₁	—	2	1	no	—
102	#4339	—	2	1	no	—
103	#4339	—	2	1	no	—
104	#4339	C₂×C₈	1	2	yes	—
105	#4339	C₂²×C₄	1	2	yes	—
106	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₁₁	—	2	1	no	—
108	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
109	C₁₁×M₁₆	—	2	2	no	—
110	C₁₁×M₁₆	—	2	2	no	—
111	C₁₁×M₁₆	—	2	1	no	—
112	C₁₁×M₁₆	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
120	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
121	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
122	#4326	C₂×C₈	1	2	yes	—
123	#4326	C₂×C₈	1	2	yes	—
124	#4325	C₂×C₈	1	2	yes	—
125	#4325	C₂×C₈	1	2	yes	—
126	#4324	C₂×C₈	1	2	yes	—
127	#4324	C₂×C₈	1	2	yes	—
128	#4323	C₂×C₈	1	2	yes	—
129	#4323	C₂×C₈	1	2	yes	—
130	C₄×Dic₁₁	—	2	1	no	—
131	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
133	#4318	—	2	1	no	—
134	#4318	C₂²×C₄	1	2	yes	—
135	C₂×C₁₁⋊C₈	—	2	1	no	—
136	C₂×C₁₁⋊C₈	C₂×C₈	1	1	yes	characteristic
137	C₂×C₁₁⋊C₈	C₂×C₈	1	1	yes	characteristic
138	C₂×C₁₁⋊C₈	C₂×C₈	1	1	yes	characteristic
139	C₂×C₁₁⋊C₈	C₂×C₈	1	1	yes	characteristic
140	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	#4313	—	2	2	no	—
143	#4313	—	2	2	no	—
144	C₈×D₁₁	—	2	2	no	—
145	C₈×D₁₁	—	2	2	no	—
146	C₁₁×C₁₆	—	2	2	no	—
147	C₁₁×C₁₆	C₂×D₄	1	4	yes	—
148	C₁₁⋊C₁₆	—	2	2	no	—
149	C₁₁⋊C₁₆	—	2	2	no	—
150	#3407	—	11	1	no	—
151	#3407	D₁₁	1	1	yes	characteristic, complemented
152	C₂×#443	—	11	1	no	—
153	#2171	—	11	4	no	—
154	#2170	—	11	4	no	—
155	C₂×#364	—	11	1	no	—
156	#2117	—	11	1	no	—
157	#2117	—	11	1	no	—
158	C₄×M₃₂	—	11	1	no	—
159	C₂³×C₁₁	—	2	1	no	—
160	C₂³×C₁₁	#131	1	1	yes	characteristic
161	C₂²×D₁₁	—	2	1	no	—
162	Q₈×C₁₁	—	2	1	no	—
163	Q₈×C₁₁	C₂²×C₈	1	2	yes	—
164	D₄×C₁₁	—	2	2	no	—
165	D₄×C₁₁	—	2	2	no	—
166	D₄×C₁₁	—	2	1	no	—
167	D₄×C₁₁	C₂²×C₈	1	2	yes	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
175	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂²⋊D₁₁	—	2	2	no	—
178	C₂²⋊D₁₁	—	2	2	no	—
179	C₂×Dic₁₁	—	2	1	no	—
180	C₂×Dic₁₁	—	2	1	no	—
181	C₂×Dic₁₁	—	2	1	no	—
182	C₂×Dic₁₁	—	4	2	no	—
183	D₄₄	—	2	1	no	—
184	D₄₄	C₂²×C₈	1	2	yes	—
185	C₄×D₁₁	—	2	2	no	—
186	C₄×D₁₁	—	2	2	no	—
187	Dic₂₂	—	2	1	no	—
188	Dic₂₂	C₂²×C₈	1	2	yes	—
189	C₈×C₁₁	—	2	2	no	—
190	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
191	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
192	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
194	C₁₁⋊C₈	—	2	2	no	—
195	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
196	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
197	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
198	C₁₁⋊C₈	C₂²×C₈	1	1	yes	characteristic
199	C₂×#135	—	11	1	no	—
200	C₂×#131	—	11	1	no	—
201	C₂×#131	C₂×D₁₁	1	1	yes	characteristic
202	#504	—	2	2	no	—
203	#504	—	11	4	no	—
204	#504	—	22	2	no	—
205	#504	C₂×D₁₁	1	4	yes	complemented
206	C₂×M₃₂	—	2	2	no	—
207	C₂×M₃₂	—	11	1	no	—
208	C₂×M₃₂	—	11	1	no	—
209	C₂×M₃₂	—	22	2	no	—
210	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
211	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
212	#443	—	11	2	no	—
213	#443	—	11	2	no	—
214	#443	—	11	2	no	—
215	#443	—	11	2	no	—
216	C₂×#108	—	11	1	no	—
217	C₂×#104	—	11	1	no	—
218	C₂×#104	—	11	1	no	—
219	C₂×C₄×C₈	—	11	1	no	—
220	#364	—	11	2	no	—
221	#364	—	11	2	no	—
222	#350	—	11	4	no	—
223	#350	—	11	4	no	—
224	#346	—	11	2	no	—
225	C₄×C₁₆	—	11	2	no	—
226	C₂²×C₁₁	—	2	2	no	—
227	C₂²×C₁₁	—	4	1	no	—
228	C₂²×C₁₁	—	8	1	no	—
229	C₂²×C₁₁	C₈×D₄	1	1	yes	characteristic
230	C₂²×C₁₁	C₈×D₄	1	1	yes	characteristic
231	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
232	C₂×D₁₁	—	2	2	no	—
233	C₂×D₁₁	—	8	1	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
236	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
237	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
239	Dic₁₁	—	2	2	no	—
240	Dic₁₁	—	2	2	no	—
241	Dic₁₁	—	4	1	no	—
242	C₂×#41	—	11	1	no	—
243	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
244	#135	—	11	2	no	—
245	#135	—	11	2	no	—
246	#135	—	11	2	no	—
247	#135	—	11	2	no	—
248	C₂×Q₁₆	—	11	1	no	—
249	C₂×SD₁₆	—	11	1	no	—
250	C₂×SD₁₆	—	11	1	no	—
251	C₂×D₈	—	11	1	no	—
252	#131	—	2	1	no	—
253	#131	—	2	1	no	—
254	#131	—	11	2	no	—
255	#131	—	11	2	no	—
256	#131	—	22	1	no	—
257	#131	—	22	1	no	—
258	#131	C₄×D₁₁	1	2	yes	—
259	#131	C₂²×D₁₁	1	2	yes	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	11	1	no	—
262	C₂×M₁₆	—	22	1	no	—
263	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	11	1	no	—
266	C₂²×C₈	—	22	1	no	—
267	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
268	C₂×C₄²	—	11	1	no	—
269	M₃₂	—	2	1	no	—
270	M₃₂	—	2	4	no	—
271	M₃₂	—	11	2	no	—
272	M₃₂	—	22	1	no	—
273	M₃₂	—	22	1	no	—
274	M₃₂	—	22	1	no	—
275	M₃₂	—	22	4	no	—
276	M₃₂	C₂²⋊D₁₁	1	2	yes	—
277	M₃₂	C₂²⋊D₁₁	1	2	yes	—
278	M₃₂	C₂²×D₁₁	1	2	yes	—
279	C₂×C₁₆	—	2	1	no	—
280	C₂×C₁₆	—	2	4	no	—
281	C₂×C₁₆	—	11	2	no	—
282	C₂×C₁₆	—	22	1	no	—
283	C₂×C₁₆	—	22	4	no	—
284	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
285	#108	—	11	2	no	—
286	#108	—	11	2	no	—
287	#104	—	11	2	no	—
288	#104	—	11	2	no	—
289	#104	—	11	2	no	—
290	#104	—	11	2	no	—
291	C₄×C₈	—	11	1	no	—
292	C₄×C₈	—	11	1	no	—
293	C₄×C₈	—	11	1	no	—
294	C₄×C₈	—	11	1	no	—
295	C₂×C₁₁	—	2	1	no	—
296	C₂×C₁₁	—	2	1	no	—
297	C₂×C₁₁	—	2	1	no	—
298	C₂×C₁₁	—	4	2	no	—
299	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
300	D₁₁	—	4	2	no	—
301	#41	—	2	1	no	—
302	#41	—	2	1	no	—
303	#41	—	11	2	no	—
304	#41	—	11	2	no	—
305	#41	—	22	1	no	—
306	#41	—	22	1	no	—
307	#41	C₈×D₁₁	1	2	yes	—
308	#41	C₂×C₄×D₁₁	1	2	yes	—
309	C₂×Q₈	—	11	1	no	—
310	C₂×Q₈	C₈×D₁₁	1	1	yes	characteristic
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	11	1	no	—
313	C₂×D₄	—	22	1	no	—
314	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	22	1	no	—
317	C₂²×C₄	—	22	1	no	—
318	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
319	Q₁₆	—	11	2	no	—
320	Q₁₆	—	11	2	no	—
321	SD₁₆	—	11	2	no	—
322	SD₁₆	—	11	2	no	—
323	SD₁₆	—	11	2	no	—
324	SD₁₆	—	11	2	no	—
325	D₈	—	11	2	no	—
326	D₈	—	11	2	no	—
327	M₁₆	—	2	1	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	11	2	no	—
331	M₁₆	—	22	1	no	—
332	M₁₆	—	22	2	no	—
333	M₁₆	—	22	2	no	—
334	M₁₆	C₂×C₄×D₁₁	1	2	yes	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	11	1	no	—
339	C₂×C₈	—	11	1	no	—
340	C₂×C₈	—	11	1	no	—
341	C₂×C₈	—	11	1	no	—
342	C₂×C₈	—	11	1	no	—
343	C₂×C₈	—	11	1	no	—
344	C₂×C₈	—	22	1	no	—
345	C₂×C₈	—	22	2	no	—
346	C₂×C₈	—	22	2	no	—
347	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
348	C₂×C₈	#4339	1	1	yes	characteristic
349	C₂×C₈	#4339	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
353	C₄²	—	11	1	no	—
354	C₄²	—	11	1	no	—
355	C₄²	—	22	1	no	—
356	C₁₆	—	2	2	no	—
357	C₁₆	—	22	2	no	—
358	C₁₆	—	22	2	no	—
359	C₁₆	C₂×C₂²⋊D₁₁	1	4	yes	—
360	C₁₁	#33443	1	1	yes	characteristic, complemented, Sylow
361	C₂³	—	2	1	no	—
362	C₂³	—	22	1	no	—
363	C₂³	#66954	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	11	2	no	—
366	Q₈	—	22	1	no	—
367	Q₈	C₂×C₈×D₁₁	1	2	yes	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	1	no	—
371	D₄	—	11	2	no	—
372	D₄	—	22	2	no	—
373	D₄	—	22	2	no	—
374	D₄	—	22	1	no	—
375	D₄	C₂×C₈×D₁₁	1	2	yes	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	22	1	no	—
380	C₂×C₄	—	22	1	no	—
381	C₂×C₄	—	22	2	no	—
382	C₂×C₄	—	22	2	no	—
383	C₂×C₄	—	22	1	no	—
384	C₂×C₄	—	44	2	no	—
385	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
386	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
387	C₂×C₄	#66954	1	1	yes	characteristic
388	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
389	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	11	1	no	—
393	C₈	—	11	1	no	—
394	C₈	—	11	1	no	—
395	C₈	—	11	1	no	—
396	C₈	—	22	2	no	—
397	C₈	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
398	C₈	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
399	C₈	C₂×#4339	1	1	yes	characteristic
400	C₈	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
401	C₂²	—	2	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	22	2	no	—
405	C₂²	—	88	1	no	—
406	C₂²	C₈×C₂²⋊D₁₁	1	1	yes	characteristic
407	C₂²	C₈×C₂²⋊D₁₁	1	1	yes	characteristic
408	C₂²	C₂×#66954	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	22	2	no	—
411	C₄	—	22	2	no	—
412	C₄	—	44	1	no	—
413	C₄	C₈×C₂²⋊D₁₁	1	1	yes	characteristic
414	C₄	C₈×C₂²⋊D₁₁	1	1	yes	characteristic
415	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
416	C₄	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	2	no	—
421	C₂	—	44	2	no	—
422	C₂	C₂×C₈×C₂²⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²×C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#3407	C₂
socle	C₂×C₁₁	C₂×C₈×D₄
prime radical	C₂×#67003	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#3407	D₁₁
hypocenter	C₁₁	#33443
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂ ◁ #3407

Complements

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

N	H ≅ G/N	type
1. #13081718	C₂	semidirect
3. #13070456	C₂	semidirect
4. #13070451	C₂	semidirect
5. C₂×#10622149	C₂	semidirect
6. #13070245	C₂	semidirect
7. #13070244	C₂	semidirect
8. M₃₂×Dic₁₁	C₂	semidirect
9. C₁₁×#3407	C₂	semidirect
14. C₁₁×#504	C₂²	semidirect
30. #10622514	C₂²	semidirect
31. #10622199	C₂²	semidirect
32. #10622153	C₂²	semidirect
33. #10622149	C₂²	semidirect
34. #10622149	C₂²	semidirect
35. #10622140	C₂²	semidirect
36. C₁₆×Dic₁₁	C₂²	semidirect
151. #3407	D₁₁	semidirect
205. #504	C₂×D₁₁	semidirect
360. C₁₁	#33443	semidirect

Maximal subgroups

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

subgroup	index
#13081718	2
C₂×#10622757	2
#13070456	2
#13070451	2
C₂×#10622149	2
#13070245	2
#13070244	2
M₃₂×Dic₁₁	2
C₁₁×#3407	2
#33443	11