Subgroups — C₁₁×#23842 #14601035

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2331	C₂	1	2	yes	maximal
2	C₁₁×#2085	C₂	1	2	yes	maximal
3	C₁₁×#2085	C₂	1	2	yes	maximal
4	C₁₁×#2058	C₂	1	2	yes	maximal
5	C₁₁×#2057	C₂	1	2	yes	maximal
6	C₁₁×#1776	C₂	1	2	yes	maximal
7	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₁×#106	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂×C₁₁×#107	C₂²	1	2	yes	—
12	C₂×C₁₁×#107	C₂²	1	2	yes	—
13	C₂×C₁₁×#106	C₂²	1	2	yes	—
14	C₂×C₁₁×#106	C₂²	1	2	yes	—
15	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#391	—	2	2	no	—
18	C₁₁×#391	—	2	2	no	—
19	C₁₁×#389	C₂²	1	2	yes	—
20	C₁₁×#389	C₂²	1	2	yes	—
21	C₁₁×#387	—	2	2	no	—
22	C₁₁×#387	—	2	2	no	—
23	C₁₁×#382	C₂²	1	2	yes	—
24	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
25	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
26	C₁₁×#376	C₂²	1	1	yes	characteristic
27	C₁₁×#340	C₂²	1	1	yes	characteristic
28	C₁₁×#340	C₂²	1	1	yes	characteristic
29	C₁₁×#340	C₂²	1	1	yes	characteristic
30	C₁₁×#340	C₂²	1	1	yes	characteristic
31	C₁₁×#340	C₂²	1	2	yes	—
32	C₁₁×#340	C₂²	1	2	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₁	—	2	2	no	—
36	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₁₁×C₄⋊Q₈	—	2	4	no	—
40	C₁₁×C₄⋊Q₈	—	2	4	no	—
41	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
46	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
47	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₁	—	2	2	no	—
49	C₂×C₄²×C₁₁	—	2	2	no	—
50	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
52	C₁₁×#107	—	2	4	no	—
53	C₁₁×#107	—	2	4	no	—
54	C₁₁×#106	—	2	4	no	—
55	C₁₁×#106	—	2	4	no	—
56	C₁₁×#97	Q₈	1	4	yes	complemented
57	C₄×C₈×C₁₁	Q₈	1	4	yes	complemented
58	C₁₁×#95	—	2	2	no	—
59	C₁₁×#95	—	2	2	no	—
60	C₁₁×#95	—	2	2	no	—
61	C₁₁×#95	—	2	2	no	—
62	C₁₁×#95	—	2	2	no	—
63	C₁₁×#95	—	2	2	no	—
64	C₁₁×#95	D₄	1	1	yes	characteristic
65	C₁₁×#95	D₄	1	2	yes	—
66	C₁₁×#95	D₄	1	1	yes	characteristic
67	#23842	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×Q₈×C₁₁	—	2	8	no	—
69	C₂×Q₈×C₁₁	—	8	2	no	—
70	C₂×Q₈×C₁₁	—	8	2	no	—
71	C₂²×C₄×C₁₁	—	2	2	no	—
72	C₂²×C₄×C₁₁	—	2	2	no	—
73	C₂²×C₄×C₁₁	—	2	2	no	—
74	C₂²×C₄×C₁₁	—	2	2	no	—
75	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	2	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	2	2	no	—
84	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
85	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
86	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
87	C₁₁×C₄⋊C₄	—	2	8	no	—
88	C₁₁×C₄⋊C₄	—	2	2	no	—
89	C₁₁×C₄⋊C₄	—	2	2	no	—
90	C₁₁×C₄⋊C₄	—	2	2	no	—
91	C₁₁×C₄⋊C₄	—	2	2	no	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	2	no	—
94	C₁₁×C₄⋊C₄	—	8	2	no	—
95	C₁₁×C₄⋊C₄	—	8	2	no	—
96	C₁₁×C₄⋊C₄	#41	1	4	yes	—
97	C₁₁×C₄⋊C₄	#41	1	4	yes	—
98	C₄²×C₁₁	—	2	2	no	—
99	C₄²×C₁₁	—	2	2	no	—
100	C₄²×C₁₁	—	8	2	no	—
101	C₄²×C₁₁	—	8	2	no	—
102	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
103	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
104	#2331	C₂×C₁₁	1	2	yes	—
105	#2085	C₂×C₁₁	1	2	yes	—
106	#2085	C₂×C₁₁	1	2	yes	—
107	#2058	C₂×C₁₁	1	2	yes	—
108	#2057	C₂×C₁₁	1	2	yes	—
109	#1776	C₂×C₁₁	1	2	yes	—
110	C₄×#107	C₂×C₁₁	1	1	yes	characteristic
111	C₄×#106	C₂×C₁₁	1	1	yes	characteristic
112	#1746	C₂×C₁₁	1	1	yes	characteristic
113	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
114	Q₈×C₁₁	—	8	8	no	—
115	C₂×C₄×C₁₁	—	2	1	no	—
116	C₂×C₄×C₁₁	—	2	2	no	—
117	C₂×C₄×C₁₁	—	2	1	no	—
118	C₂×C₄×C₁₁	—	2	2	no	—
119	C₂×C₄×C₁₁	—	2	2	no	—
120	C₂×C₄×C₁₁	—	2	4	no	—
121	C₂×C₄×C₁₁	—	2	4	no	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	2	no	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	—	4	2	no	—
128	C₂×C₄×C₁₁	—	4	2	no	—
129	C₂×C₄×C₁₁	—	4	2	no	—
130	C₂×C₄×C₁₁	—	4	2	no	—
131	C₂×C₄×C₁₁	—	4	2	no	—
132	C₂×C₄×C₁₁	—	4	2	no	—
133	C₂×C₄×C₁₁	—	4	2	no	—
134	C₂×C₄×C₁₁	—	4	2	no	—
135	C₂×C₄×C₁₁	—	4	2	no	—
136	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
137	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
138	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
141	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
142	C₈×C₁₁	—	2	2	no	—
143	C₈×C₁₁	—	2	4	no	—
144	C₈×C₁₁	—	2	2	no	—
145	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
146	C₂×#107	C₂²×C₁₁	1	2	yes	—
147	C₂×#107	C₂²×C₁₁	1	2	yes	—
148	C₂×#106	C₂²×C₁₁	1	2	yes	—
149	C₂×#106	C₂²×C₁₁	1	2	yes	—
150	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
151	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
152	#391	—	2	2	no	—
153	#391	—	2	2	no	—
154	#389	C₂²×C₁₁	1	2	yes	—
155	#389	C₂²×C₁₁	1	2	yes	—
156	#387	—	2	2	no	—
157	#387	—	2	2	no	—
158	#382	C₂²×C₁₁	1	2	yes	—
159	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
160	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
161	#376	C₂²×C₁₁	1	1	yes	characteristic
162	#340	C₂²×C₁₁	1	1	yes	characteristic
163	#340	C₂²×C₁₁	1	2	yes	—
164	#340	C₂²×C₁₁	1	1	yes	characteristic
165	#340	C₂²×C₁₁	1	1	yes	characteristic
166	#340	C₂²×C₁₁	1	1	yes	characteristic
167	#340	C₂²×C₁₁	1	2	yes	—
168	#336	C₂²×C₁₁	1	2	yes	—
169	#336	C₂²×C₁₁	1	2	yes	—
170	C₂²×C₁₁	#525	1	2	yes	—
171	C₂²×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
172	C₂²×C₁₁	#576	1	1	yes	characteristic
173	C₂²×C₁₁	#577	1	2	yes	—
174	C₂²×C₁₁	#578	1	1	yes	characteristic
175	C₄×C₁₁	—	2	2	no	—
176	C₄×C₁₁	—	2	2	no	—
177	C₄×C₁₁	—	4	2	no	—
178	C₄×C₁₁	—	4	4	no	—
179	C₄×C₁₁	—	4	4	no	—
180	C₄×C₁₁	—	4	2	no	—
181	C₄×C₁₁	—	8	2	no	—
182	C₄×C₁₁	—	8	2	no	—
183	C₄×C₁₁	#533	1	1	yes	characteristic
184	C₄×C₁₁	#533	1	1	yes	characteristic
185	C₄×C₁₁	#533	1	2	yes	—
186	C₂²×Q₈	—	2	2	no	—
187	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
188	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
189	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
190	C₄⋊Q₈	—	2	4	no	—
191	C₄⋊Q₈	—	2	4	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
196	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
197	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
198	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
199	C₂×C₄²	—	2	2	no	—
200	C₂×C₄²	—	2	2	no	—
201	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
202	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
203	#107	—	2	4	no	—
204	#107	—	2	4	no	—
205	#106	—	2	4	no	—
206	#106	—	2	4	no	—
207	#97	Q₈×C₁₁	1	4	yes	complemented
208	C₄×C₈	Q₈×C₁₁	1	4	yes	complemented
209	#95	—	2	2	no	—
210	#95	—	2	2	no	—
211	#95	—	2	2	no	—
212	#95	—	2	2	no	—
213	#95	—	2	2	no	—
214	#95	—	2	2	no	—
215	#95	D₄×C₁₁	1	1	yes	characteristic
216	#95	D₄×C₁₁	1	2	yes	—
217	#95	D₄×C₁₁	1	1	yes	characteristic
218	C₂×C₁₁	#2399	1	1	yes	characteristic
219	C₂×C₁₁	#3118	1	2	yes	—
220	C₂×C₁₁	#3121	1	2	yes	—
221	C₂×C₁₁	#3163	1	1	yes	characteristic
222	C₂×C₁₁	#3164	1	1	yes	characteristic
223	C₂×Q₈	—	2	8	no	—
224	C₂×Q₈	—	8	2	no	—
225	C₂×Q₈	—	8	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
231	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
232	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
234	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
240	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
241	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
242	C₄⋊C₄	—	2	8	no	—
243	C₄⋊C₄	—	2	2	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₄⋊C₄	—	2	2	no	—
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	8	2	no	—
250	C₄⋊C₄	—	8	2	no	—
251	C₄⋊C₄	C₁₁×#41	1	4	yes	—
252	C₄⋊C₄	C₁₁×#41	1	4	yes	—
253	C₄²	—	2	2	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	8	2	no	—
256	C₄²	—	8	2	no	—
257	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
258	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
259	C₁₁	#23842	1	1	yes	characteristic, direct product factor, Sylow
260	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
261	Q₈	—	8	8	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
284	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
285	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
286	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
287	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
288	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
289	C₈	—	2	2	no	—
290	C₈	—	2	4	no	—
291	C₈	—	2	2	no	—
292	C₂²	C₁₁×#525	1	2	yes	—
293	C₂²	C₂×C₁₁×C₄⋊Q₈	1	1	yes	characteristic
294	C₂²	C₁₁×#576	1	1	yes	characteristic
295	C₂²	C₁₁×#577	1	2	yes	—
296	C₂²	C₁₁×#578	1	1	yes	characteristic
297	C₄	—	2	2	no	—
298	C₄	—	2	2	no	—
299	C₄	—	4	2	no	—
300	C₄	—	4	4	no	—
301	C₄	—	4	4	no	—
302	C₄	—	4	2	no	—
303	C₄	—	8	2	no	—
304	C₄	—	8	2	no	—
305	C₄	C₁₁×#533	1	1	yes	characteristic
306	C₄	C₁₁×#533	1	2	yes	—
307	C₄	C₁₁×#533	1	1	yes	characteristic
308	C₂	C₁₁×#2399	1	1	yes	characteristic
309	C₂	C₁₁×#3118	1	2	yes	—
310	C₂	C₁₁×#3121	1	2	yes	—
311	C₂	C₁₁×#3163	1	1	yes	characteristic
312	C₂	C₁₁×#3164	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₁₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
56. C₁₁×#97	Q₈	semidirect
57. C₄×C₈×C₁₁	Q₈	semidirect
67. #23842	C₁₁	direct (N × H)
207. #97	Q₈×C₁₁	semidirect
208. C₄×C₈	Q₈×C₁₁	semidirect
259. C₁₁	#23842	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2331	2
C₁₁×#2085	2
C₁₁×#2058	2
C₁₁×#2057	2
C₁₁×#1776	2
C₄×C₁₁×#107	2
C₄×C₁₁×#106	2
C₁₁×#1746	2
#23842	11

Subgroups — C11×#23842 #14601035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23842 #14601035