Subgroups — C₁₁×#22275 #14599468

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2328	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1961	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1880	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1877	C₂	1	4	yes	maximal, complemented
8	C₁₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×SD₁₆	C₂²	1	4	yes	—
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
15	C₁₁×#492	C₄	1	8	yes	complemented
16	C₂×C₁₁×#103	C₂²	1	4	yes	—
17	C₂×C₁₁×#102	C₂²	1	4	yes	—
18	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#391	C₂²	1	2	yes	—
21	C₁₁×#390	C₂²	1	2	yes	—
22	C₁₁×#387	—	2	4	no	—
23	C₁₁×#386	—	2	4	no	—
24	C₁₁×#382	C₂²	1	1	yes	characteristic
25	C₁₁×#382	C₂²	1	1	yes	characteristic
26	C₁₁×#376	C₂²	1	1	yes	characteristic
27	C₁₁×#340	C₂²	1	4	yes	—
28	C₁₁×#336	C₂²	1	2	yes	—
29	C₁₁×#336	C₂²	1	2	yes	—
30	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
31	C₂²×D₄×C₁₁	—	2	2	no	—
32	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₁	—	2	2	no	—
34	C₂×C₁₁×SD₁₆	—	4	4	no	—
35	C₂×C₁₁×SD₁₆	—	4	4	no	—
36	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
37	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
41	C₁₁×#127	—	2	2	no	—
42	C₁₁×#127	C₂×C₄	1	4	yes	—
43	C₄×Q₈×C₁₁	—	4	4	no	—
44	C₄×D₄×C₁₁	—	4	4	no	—
45	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
48	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
49	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
50	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
51	C₂×C₄²×C₁₁	—	2	2	no	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
55	C₁₁×#103	—	4	4	no	—
56	C₁₁×#102	—	4	4	no	—
57	C₁₁×#97	—	2	2	no	—
58	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
59	C₁₁×#95	—	2	2	no	—
60	C₁₁×#95	—	2	2	no	—
61	C₁₁×#95	—	2	4	no	—
62	C₁₁×#95	D₄	1	4	yes	—
63	#22275	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂⁴×C₁₁	—	2	2	no	—
65	C₂×Q₈×C₁₁	—	2	2	no	—
66	C₂×Q₈×C₁₁	—	2	4	no	—
67	C₂×Q₈×C₁₁	—	2	4	no	—
68	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
69	C₂×D₄×C₁₁	—	2	8	no	—
70	C₂×D₄×C₁₁	—	2	2	no	—
71	C₂×D₄×C₁₁	—	2	4	no	—
72	C₂×D₄×C₁₁	—	2	4	no	—
73	C₂×D₄×C₁₁	—	8	4	no	—
74	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₁₁	—	2	2	no	—
76	C₂²×C₄×C₁₁	—	2	2	no	—
77	C₂²×C₄×C₁₁	—	2	2	no	—
78	C₂²×C₄×C₁₁	—	4	4	no	—
79	C₂²×C₄×C₁₁	—	8	4	no	—
80	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
84	C₁₁×SD₁₆	—	4	16	no	—
85	C₂×C₈×C₁₁	—	2	2	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
91	C₁₁×C₄⋊C₄	—	2	8	no	—
92	C₁₁×C₄⋊C₄	—	2	4	no	—
93	C₁₁×C₄⋊C₄	—	2	4	no	—
94	C₁₁×C₄⋊C₄	—	4	4	no	—
95	C₁₁×C₂²⋊C₄	—	4	4	no	—
96	C₁₁×C₂²⋊C₄	—	8	4	no	—
97	C₄²×C₁₁	—	2	2	no	—
98	C₄²×C₁₁	—	2	2	no	—
99	C₄²×C₁₁	—	4	4	no	—
100	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
101	C₄²×C₁₁	#41	1	2	yes	—
102	C₂×#492	C₂×C₁₁	1	1	yes	characteristic
103	#2328	C₂×C₁₁	1	1	yes	characteristic
104	#2327	C₂×C₁₁	1	1	yes	characteristic, complemented
105	#1961	C₂×C₁₁	1	1	yes	characteristic
106	#1960	C₂×C₁₁	1	1	yes	characteristic, complemented
107	#1880	C₂×C₁₁	1	4	yes	complemented
108	#1877	C₂×C₁₁	1	4	yes	complemented
109	#1835	C₂×C₁₁	1	1	yes	characteristic, complemented
110	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
111	C₂³×C₁₁	—	2	4	no	—
112	C₂³×C₁₁	—	4	2	no	—
113	C₂³×C₁₁	—	4	2	no	—
114	C₂³×C₁₁	—	4	4	no	—
115	C₂³×C₁₁	—	4	4	no	—
116	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
117	Q₈×C₁₁	—	2	8	no	—
118	Q₈×C₁₁	—	4	4	no	—
119	D₄×C₁₁	—	2	8	no	—
120	D₄×C₁₁	—	4	4	no	—
121	D₄×C₁₁	—	8	8	no	—
122	C₂×C₄×C₁₁	—	2	4	no	—
123	C₂×C₄×C₁₁	—	2	4	no	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	4	no	—
127	C₂×C₄×C₁₁	—	2	4	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	4	no	—
133	C₂×C₄×C₁₁	—	4	4	no	—
134	C₂×C₄×C₁₁	—	8	8	no	—
135	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
136	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
139	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
140	C₈×C₁₁	—	2	4	no	—
141	C₈×C₁₁	—	4	2	no	—
142	C₂²×SD₁₆	C₂²×C₁₁	1	4	yes	—
143	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
144	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
145	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
146	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
147	#492	C₄×C₁₁	1	8	yes	complemented
148	C₂×#103	C₂²×C₁₁	1	4	yes	—
149	C₂×#102	C₂²×C₁₁	1	4	yes	—
150	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
151	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
152	#391	C₂²×C₁₁	1	2	yes	—
153	#390	C₂²×C₁₁	1	2	yes	—
154	#387	—	2	4	no	—
155	#386	—	2	4	no	—
156	#382	C₂²×C₁₁	1	1	yes	characteristic
157	#382	C₂²×C₁₁	1	1	yes	characteristic
158	#376	C₂²×C₁₁	1	1	yes	characteristic
159	#340	C₂²×C₁₁	1	4	yes	—
160	#336	C₂²×C₁₁	1	2	yes	—
161	#336	C₂²×C₁₁	1	2	yes	—
162	C₂²×C₁₁	—	4	4	no	—
163	C₂²×C₁₁	—	4	8	no	—
164	C₂²×C₁₁	—	8	4	no	—
165	C₂²×C₁₁	—	8	2	no	—
166	C₂²×C₁₁	—	8	2	no	—
167	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
168	C₂²×C₁₁	#535	1	1	yes	characteristic
169	C₂²×C₁₁	#535	1	1	yes	characteristic
170	C₂²×C₁₁	#577	1	4	yes	—
171	C₄×C₁₁	—	2	4	no	—
172	C₄×C₁₁	—	4	4	no	—
173	C₄×C₁₁	—	4	2	no	—
174	C₄×C₁₁	—	4	2	no	—
175	C₄×C₁₁	—	8	2	no	—
176	C₄×C₁₁	—	8	2	no	—
177	C₄×C₁₁	#518	1	2	yes	—
178	C₄×C₁₁	#540	1	2	yes	—
179	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
180	C₂²×D₄	—	2	2	no	—
181	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
182	C₂³×C₄	—	2	2	no	—
183	C₂×SD₁₆	—	4	4	no	—
184	C₂×SD₁₆	—	4	4	no	—
185	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
186	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
187	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
188	C₄⋊Q₈	—	2	2	no	—
189	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
190	#127	—	2	2	no	—
191	#127	C₂×C₄×C₁₁	1	4	yes	—
192	C₄×Q₈	—	4	4	no	—
193	C₄×D₄	—	4	4	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	—	2	2	no	—
196	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
197	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
198	C₂×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₂²⋊C₄	—	2	4	no	—
200	C₂×C₄²	—	2	2	no	—
201	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
202	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
203	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
204	#103	—	4	4	no	—
205	#102	—	4	4	no	—
206	#97	—	2	2	no	—
207	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
208	#95	—	2	2	no	—
209	#95	—	2	2	no	—
210	#95	—	2	4	no	—
211	#95	D₄×C₁₁	1	4	yes	—
212	C₂×C₁₁	—	8	4	no	—
213	C₂×C₁₁	#2328	1	1	yes	characteristic
214	C₂×C₁₁	#2949	1	2	yes	—
215	C₂×C₁₁	#3221	1	2	yes	—
216	C₂×C₁₁	#3222	1	2	yes	—
217	C₂⁴	—	2	2	no	—
218	C₂×Q₈	—	2	2	no	—
219	C₂×Q₈	—	2	4	no	—
220	C₂×Q₈	—	2	4	no	—
221	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
222	C₂×D₄	—	2	8	no	—
223	C₂×D₄	—	2	2	no	—
224	C₂×D₄	—	2	4	no	—
225	C₂×D₄	—	2	4	no	—
226	C₂×D₄	—	8	4	no	—
227	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	—	8	4	no	—
233	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
234	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
235	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
236	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
237	SD₁₆	—	4	16	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
244	C₄⋊C₄	—	2	8	no	—
245	C₄⋊C₄	—	2	4	no	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	—	4	4	no	—
248	C₂²⋊C₄	—	4	4	no	—
249	C₂²⋊C₄	—	8	4	no	—
250	C₄²	—	2	2	no	—
251	C₄²	—	2	2	no	—
252	C₄²	—	4	4	no	—
253	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
254	C₄²	C₁₁×#41	1	2	yes	—
255	C₁₁	#22275	1	1	yes	characteristic, direct product factor, Sylow
256	C₂³	—	2	4	no	—
257	C₂³	—	4	2	no	—
258	C₂³	—	4	2	no	—
259	C₂³	—	4	4	no	—
260	C₂³	—	4	4	no	—
261	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
262	Q₈	—	2	8	no	—
263	Q₈	—	4	4	no	—
264	D₄	—	2	8	no	—
265	D₄	—	4	4	no	—
266	D₄	—	8	8	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	4	no	—
272	C₂×C₄	—	2	4	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	4	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	8	8	no	—
280	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
281	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
282	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
283	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
284	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
285	C₈	—	2	4	no	—
286	C₈	—	4	2	no	—
287	C₂²	—	4	8	no	—
288	C₂²	—	4	4	no	—
289	C₂²	—	8	4	no	—
290	C₂²	—	8	2	no	—
291	C₂²	—	8	2	no	—
292	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
293	C₂²	C₁₁×#535	1	1	yes	characteristic
294	C₂²	C₁₁×#535	1	1	yes	characteristic
295	C₂²	C₁₁×#577	1	4	yes	—
296	C₄	—	2	4	no	—
297	C₄	—	4	2	no	—
298	C₄	—	4	2	no	—
299	C₄	—	4	4	no	—
300	C₄	—	8	2	no	—
301	C₄	—	8	2	no	—
302	C₄	C₁₁×#518	1	2	yes	—
303	C₄	C₁₁×#540	1	2	yes	—
304	C₂	—	8	4	no	—
305	C₂	C₁₁×#2328	1	1	yes	characteristic
306	C₂	C₁₁×#2949	1	2	yes	—
307	C₂	C₁₁×#3221	1	2	yes	—
308	C₂	C₁₁×#3222	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×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
3. C₁₁×#2327	C₂	semidirect
5. C₁₁×#1960	C₂	semidirect
6. C₁₁×#1880	C₂	semidirect
7. C₁₁×#1877	C₂	semidirect
8. C₁₁×#1835	C₂	semidirect
9. C₁₁×#1746	C₂	semidirect
15. C₁₁×#492	C₄	semidirect
36. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
40. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
58. C₄×C₈×C₁₁	C₂×C₄	semidirect
63. #22275	C₁₁	direct (N × H)
104. #2327	C₂×C₁₁	semidirect
106. #1960	C₂×C₁₁	semidirect
107. #1880	C₂×C₁₁	semidirect
108. #1877	C₂×C₁₁	semidirect
109. #1835	C₂×C₁₁	semidirect
110. #1746	C₂×C₁₁	semidirect
147. #492	C₄×C₁₁	semidirect
185. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
189. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
207. C₄×C₈	C₂×C₄×C₁₁	semidirect
255. C₁₁	#22275	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#492	2
C₁₁×#2328	2
C₁₁×#2327	2
C₁₁×#1961	2
C₁₁×#1960	2
C₁₁×#1880	2
C₁₁×#1877	2
C₁₁×#1835	2
C₁₁×#1746	2
#22275	11

Subgroups — C11×#22275 #14599468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22275 #14599468