Subgroups — C₁₁×#33457 #14610650

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×SD₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2175	C₂	1	4	yes	maximal, complemented
5	C₄×C₁₁×SD₃₂	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2158	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#2140	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
12	C₁₁×#519	—	2	1	no	—
13	C₁₁×#518	—	2	1	no	—
14	C₂×C₁₁×SD₃₂	C₄	1	8	yes	complemented
15	C₂×C₁₁×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₁₁×SD₃₂	C₂²	1	2	yes	—
17	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
19	C₁₁×#442	—	2	2	no	—
20	C₁₁×#441	—	2	2	no	—
21	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
22	C₄×C₁₁×D₈	C₂²	1	4	yes	—
23	C₁₁×#427	C₂²	1	1	yes	characteristic
24	C₁₁×#427	C₂²	1	1	yes	characteristic
25	C₁₁×#419	—	2	1	no	—
26	C₁₁×#418	—	2	1	no	—
27	C₁₁×#405	C₂²	1	1	yes	characteristic
28	C₁₁×#367	C₂²	1	2	yes	complemented
29	C₁₁×#366	C₂²	1	2	yes	complemented
30	C₁₁×#358	C₂²	1	4	yes	complemented
31	C₁₁×#357	C₂²	1	4	yes	—
32	C₁₁×#346	C₂²	1	2	yes	complemented
33	C₄×C₁₁×C₁₆	C₂²	1	2	yes	complemented
34	C₂²×Q₈×C₁₁	—	2	1	no	—
35	C₂²×D₄×C₁₁	—	2	1	no	—
36	C₂×C₁₁×Q₁₆	—	2	1	no	—
37	C₂×C₁₁×Q₁₆	—	2	2	no	—
38	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
39	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
40	C₂×C₁₁×D₈	—	2	1	no	—
41	C₂×C₁₁×D₈	—	2	2	no	—
42	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
43	C₂×C₁₁×D₈	C₂³	1	2	yes	—
44	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₄×Q₈×C₁₁	—	2	4	no	—
47	C₄×Q₈×C₁₁	—	4	2	no	—
48	C₄×D₄×C₁₁	—	2	4	no	—
49	C₄×D₄×C₁₁	—	4	2	no	—
50	C₁₁×#117	—	2	1	no	—
51	C₁₁×#117	—	2	1	no	—
52	C₁₁×#117	—	4	2	no	—
53	C₁₁×#117	D₄	1	1	yes	characteristic
54	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
55	C₁₁×SD₃₂	C₂×C₄	1	8	yes	complemented
56	C₁₁×SD₃₂	C₂×C₄	1	8	yes	complemented
57	C₁₁×M₃₂	—	2	2	no	—
58	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	complemented
59	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
60	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
62	C₁₁×#107	C₂³	1	2	yes	—
63	C₁₁×#107	C₂³	1	2	yes	—
64	C₁₁×#106	—	2	1	no	—
65	C₁₁×#106	—	2	1	no	—
66	C₁₁×#103	—	2	4	no	—
67	C₁₁×#102	—	2	4	no	—
68	C₁₁×#97	D₄	1	2	yes	—
69	C₄×C₈×C₁₁	C₂³	1	2	yes	—
70	#33457	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₁	—	4	1	no	—
72	C₂×Q₈×C₁₁	—	2	4	no	—
73	C₂×Q₈×C₁₁	—	2	2	no	—
74	C₂×Q₈×C₁₁	—	4	1	no	—
75	C₂×Q₈×C₁₁	—	4	2	no	—
76	C₂×D₄×C₁₁	—	2	4	no	—
77	C₂×D₄×C₁₁	—	2	2	no	—
78	C₂×D₄×C₁₁	—	4	1	no	—
79	C₂×D₄×C₁₁	—	4	2	no	—
80	C₂²×C₄×C₁₁	—	4	1	no	—
81	C₂²×C₄×C₁₁	—	4	4	no	—
82	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₁₁×Q₁₆	—	2	4	no	—
84	C₁₁×Q₁₆	—	2	2	no	—
85	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	—
86	C₁₁×D₈	—	2	4	no	—
87	C₁₁×D₈	—	2	2	no	—
88	C₁₁×D₈	C₂²×C₄	1	4	yes	—
89	C₁₁×M₁₆	—	2	2	no	—
90	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
92	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	#41	1	2	yes	—
94	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
95	C₁₁×C₄⋊C₄	—	2	2	no	—
96	C₁₁×C₄⋊C₄	—	2	2	no	—
97	C₁₁×C₄⋊C₄	—	4	4	no	—
98	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
99	C₁₁×C₂²⋊C₄	—	4	1	no	—
100	C₁₁×C₂²⋊C₄	—	4	1	no	—
101	C₁₁×C₂²⋊C₄	—	4	4	no	—
102	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
103	C₄²×C₁₁	—	4	1	no	—
104	C₄²×C₁₁	—	4	1	no	—
105	C₄²×C₁₁	—	4	4	no	—
106	C₄²×C₁₁	C₂×D₄	1	2	yes	—
107	C₁₁×C₁₆	—	2	2	no	—
108	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
109	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
110	C₂²×SD₃₂	C₂×C₁₁	1	1	yes	characteristic
111	#2950	C₂×C₁₁	1	1	yes	characteristic, complemented
112	#2948	C₂×C₁₁	1	1	yes	characteristic
113	#2175	C₂×C₁₁	1	4	yes	complemented
114	C₄×SD₃₂	C₂×C₁₁	1	4	yes	complemented
115	#2158	C₂×C₁₁	1	1	yes	characteristic, complemented
116	#2141	C₂×C₁₁	1	1	yes	characteristic, complemented
117	#2140	C₂×C₁₁	1	1	yes	characteristic
118	#2108	C₂×C₁₁	1	1	yes	characteristic, complemented
119	C₂³×C₁₁	—	4	2	no	—
120	C₂³×C₁₁	—	4	4	no	—
121	C₂³×C₁₁	—	16	2	no	—
122	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
123	Q₈×C₁₁	—	2	4	no	—
124	Q₈×C₁₁	—	4	2	no	—
125	Q₈×C₁₁	—	4	4	no	—
126	D₄×C₁₁	—	2	4	no	—
127	D₄×C₁₁	—	4	2	no	—
128	D₄×C₁₁	—	4	4	no	—
129	C₂×C₄×C₁₁	—	4	2	no	—
130	C₂×C₄×C₁₁	—	4	4	no	—
131	C₂×C₄×C₁₁	—	4	2	no	—
132	C₂×C₄×C₁₁	—	4	2	no	—
133	C₂×C₄×C₁₁	—	16	4	no	—
134	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
135	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
136	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
137	C₂×C₄×C₁₁	#135	1	2	yes	—
138	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
139	C₈×C₁₁	—	2	2	no	—
140	C₈×C₁₁	C₄×D₄	1	2	yes	—
141	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
142	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
143	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
144	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
145	#519	—	2	1	no	—
146	#518	—	2	1	no	—
147	C₂×SD₃₂	C₄×C₁₁	1	8	yes	complemented
148	C₂×SD₃₂	C₂²×C₁₁	1	2	yes	—
149	C₂×SD₃₂	C₂²×C₁₁	1	2	yes	—
150	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
151	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
152	#442	—	2	2	no	—
153	#441	—	2	2	no	—
154	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
155	C₄×D₈	C₂²×C₁₁	1	4	yes	—
156	#427	C₂²×C₁₁	1	1	yes	characteristic
157	#427	C₂²×C₁₁	1	1	yes	characteristic
158	#419	—	2	1	no	—
159	#418	—	2	1	no	—
160	#405	C₂²×C₁₁	1	1	yes	characteristic
161	#367	C₂²×C₁₁	1	2	yes	complemented
162	#366	C₂²×C₁₁	1	2	yes	complemented
163	#358	C₂²×C₁₁	1	4	yes	complemented
164	#357	C₂²×C₁₁	1	4	yes	—
165	#346	C₂²×C₁₁	1	2	yes	complemented
166	C₄×C₁₆	C₂²×C₁₁	1	2	yes	complemented
167	C₂²×C₁₁	—	2	2	no	—
168	C₂²×C₁₁	—	4	4	no	—
169	C₂²×C₁₁	—	8	4	no	—
170	C₂²×C₁₁	—	16	4	no	—
171	C₂²×C₁₁	C₄×D₈	1	2	yes	—
172	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
173	C₄×C₁₁	—	2	4	no	—
174	C₄×C₁₁	—	4	4	no	—
175	C₄×C₁₁	—	8	2	no	—
176	C₄×C₁₁	—	8	2	no	—
177	C₄×C₁₁	C₄×D₈	1	2	yes	—
178	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
180	C₂²×Q₈	—	2	1	no	—
181	C₂²×D₄	—	2	1	no	—
182	C₂×Q₁₆	—	2	1	no	—
183	C₂×Q₁₆	—	2	2	no	—
184	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
185	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
186	C₂×D₈	—	2	1	no	—
187	C₂×D₈	—	2	2	no	—
188	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
189	C₂×D₈	C₂³×C₁₁	1	2	yes	—
190	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
192	C₄×Q₈	—	2	4	no	—
193	C₄×Q₈	—	4	2	no	—
194	C₄×D₄	—	2	4	no	—
195	C₄×D₄	—	4	2	no	—
196	#117	—	2	1	no	—
197	#117	—	2	1	no	—
198	#117	—	4	2	no	—
199	#117	D₄×C₁₁	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	—	4	2	no	—
201	SD₃₂	C₂×C₄×C₁₁	1	8	yes	complemented
202	SD₃₂	C₂×C₄×C₁₁	1	8	yes	complemented
203	M₃₂	—	2	2	no	—
204	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
205	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
206	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
207	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
208	#107	C₂³×C₁₁	1	2	yes	—
209	#107	C₂³×C₁₁	1	2	yes	—
210	#106	—	2	1	no	—
211	#106	—	2	1	no	—
212	#103	—	2	4	no	—
213	#102	—	2	4	no	—
214	#97	D₄×C₁₁	1	2	yes	—
215	C₄×C₈	C₂³×C₁₁	1	2	yes	—
216	C₂×C₁₁	—	2	2	no	—
217	C₂×C₁₁	—	8	4	no	—
218	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
219	C₂×C₁₁	#3416	1	2	yes	—
220	C₂⁴	—	4	1	no	—
221	C₂×Q₈	—	2	4	no	—
222	C₂×Q₈	—	2	2	no	—
223	C₂×Q₈	—	4	1	no	—
224	C₂×Q₈	—	4	2	no	—
225	C₂×D₄	—	2	4	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	4	1	no	—
228	C₂×D₄	—	4	2	no	—
229	C₂²×C₄	—	4	1	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
232	Q₁₆	—	2	4	no	—
233	Q₁₆	—	2	2	no	—
234	Q₁₆	C₂²×C₄×C₁₁	1	4	yes	—
235	D₈	—	2	4	no	—
236	D₈	—	2	2	no	—
237	D₈	C₂²×C₄×C₁₁	1	4	yes	—
238	M₁₆	—	2	2	no	—
239	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
240	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
241	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
242	C₂×C₈	C₁₁×#41	1	2	yes	—
243	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	4	4	no	—
247	C₄⋊C₄	C₁₁×D₈	1	2	yes	—
248	C₂²⋊C₄	—	4	1	no	—
249	C₂²⋊C₄	—	4	1	no	—
250	C₂²⋊C₄	—	4	4	no	—
251	C₂²⋊C₄	C₁₁×D₈	1	2	yes	—
252	C₄²	—	4	1	no	—
253	C₄²	—	4	1	no	—
254	C₄²	—	4	4	no	—
255	C₄²	C₂×D₄×C₁₁	1	2	yes	—
256	C₁₆	—	2	2	no	—
257	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
258	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
259	C₁₁	#33457	1	1	yes	characteristic, direct product factor, Sylow
260	C₂³	—	4	2	no	—
261	C₂³	—	4	4	no	—
262	C₂³	—	16	2	no	—
263	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
264	Q₈	—	2	4	no	—
265	Q₈	—	4	2	no	—
266	Q₈	—	4	4	no	—
267	D₄	—	2	4	no	—
268	D₄	—	4	2	no	—
269	D₄	—	4	4	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	16	4	no	—
275	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
276	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
277	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
278	C₂×C₄	C₁₁×#135	1	2	yes	—
279	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
280	C₈	—	2	2	no	—
281	C₈	C₄×D₄×C₁₁	1	2	yes	—
282	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
283	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
284	C₂²	—	2	2	no	—
285	C₂²	—	4	4	no	—
286	C₂²	—	8	4	no	—
287	C₂²	—	16	4	no	—
288	C₂²	C₄×C₁₁×D₈	1	2	yes	—
289	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
290	C₄	—	2	4	no	—
291	C₄	—	4	4	no	—
292	C₄	—	8	2	no	—
293	C₄	—	8	2	no	—
294	C₄	C₄×C₁₁×D₈	1	2	yes	—
295	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
296	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
297	C₂	—	2	2	no	—
298	C₂	—	8	4	no	—
299	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
300	C₂	C₁₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₁₁×#117 ◁ C₁₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2950	C₂	semidirect
4. C₁₁×#2175	C₂	semidirect
5. C₄×C₁₁×SD₃₂	C₂	semidirect
6. C₁₁×#2158	C₂	semidirect
7. C₁₁×#2141	C₂	semidirect
9. C₁₁×#2108	C₂	semidirect
14. C₂×C₁₁×SD₃₂	C₄	semidirect
21. C₄×C₁₁×Q₁₆	C₂²	semidirect
28. C₁₁×#367	C₂²	semidirect
29. C₁₁×#366	C₂²	semidirect
30. C₁₁×#358	C₂²	semidirect
32. C₁₁×#346	C₂²	semidirect
33. C₄×C₁₁×C₁₆	C₂²	semidirect
38. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
55. C₁₁×SD₃₂	C₂×C₄	semidirect
56. C₁₁×SD₃₂	C₂×C₄	semidirect
58. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
70. #33457	C₁₁	direct (N × H)
111. #2950	C₂×C₁₁	semidirect
113. #2175	C₂×C₁₁	semidirect
114. C₄×SD₃₂	C₂×C₁₁	semidirect
115. #2158	C₂×C₁₁	semidirect
116. #2141	C₂×C₁₁	semidirect
118. #2108	C₂×C₁₁	semidirect
147. C₂×SD₃₂	C₄×C₁₁	semidirect
154. C₄×Q₁₆	C₂²×C₁₁	semidirect
161. #367	C₂²×C₁₁	semidirect
162. #366	C₂²×C₁₁	semidirect
163. #358	C₂²×C₁₁	semidirect
165. #346	C₂²×C₁₁	semidirect
166. C₄×C₁₆	C₂²×C₁₁	semidirect
184. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
201. SD₃₂	C₂×C₄×C₁₁	semidirect
202. SD₃₂	C₂×C₄×C₁₁	semidirect
204. C₂×C₁₆	C₂×C₄×C₁₁	semidirect
259. C₁₁	#33457	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×SD₃₂	2
C₁₁×#2950	2
C₁₁×#2948	2
C₁₁×#2175	2
C₄×C₁₁×SD₃₂	2
C₁₁×#2158	2
C₁₁×#2141	2
C₁₁×#2140	2
C₁₁×#2108	2
#33457	11

Subgroups — C11×#33457 #14610650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33457 #14610650