Subgroups — C₁₁×#21484 #14598677

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3573	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3025	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2930	C₂	1	3	yes	maximal, complemented
4	C₁₁×#1891	C₂	1	3	yes	maximal, complemented
5	C₁₁×#1868	C₂	1	3	yes	maximal, complemented
6	C₁₁×#1791	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1757	C₂	1	3	yes	maximal, complemented
8	C₁₁×#585	C₂²	1	1	yes	characteristic
9	C₁₁×#568	—	2	6	no	—
10	C₁₁×#568	C₂²	1	3	yes	—
11	C₂×C₁₁×#131	—	2	6	no	—
12	C₂×C₁₁×#131	C₂²	1	3	yes	—
13	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₁₁×#525	C₂²	1	3	yes	—
15	C₁₁×#458	C₄	1	4	yes	—
16	C₁₁×B(4,𝔽₂)	C₄	1	4	yes	—
17	C₁₁×#436	—	2	6	no	—
18	C₁₁×#435	—	2	6	no	—
19	C₁₁×#424	C₂²	1	3	yes	complemented
20	C₁₁×#413	C₂²	1	3	yes	—
21	C₁₁×#410	C₂²	1	3	yes	—
22	C₁₁×#408	C₂²	1	3	yes	—
23	C₁₁×#407	C₂²	1	3	yes	complemented
24	C₁₁×#405	C₂²	1	3	yes	complemented
25	C₁₁×#344	C₂²	1	6	yes	complemented
26	C₁₁×2₋¹⁺⁴	—	2	3	no	—
27	C₁₁×H(5,𝔽₂)	—	2	3	no	—
28	C₁₁×H(5,𝔽₂)	C₂×C₄	1	4	yes	—
29	C₂×C₁₁×#41	—	2	6	no	—
30	C₂×C₁₁×#41	C₂³	1	3	yes	—
31	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
32	C₁₁×#131	—	2	4	no	—
33	C₁₁×#131	—	2	12	no	—
34	C₁₁×#131	—	2	6	no	—
35	C₁₁×#131	—	2	12	no	—
36	C₁₁×#131	—	2	6	no	—
37	C₂×C₁₁×M₁₆	—	2	12	no	—
38	C₂×C₁₁×M₁₆	—	2	6	no	—
39	C₂×C₁₁×M₁₆	—	2	3	no	—
40	C₂×C₁₁×M₁₆	—	2	3	no	—
41	C₂×C₁₁×M₁₆	D₄	1	6	yes	complemented
42	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
43	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
44	C₂²×C₈×C₁₁	—	2	4	no	—
45	C₂²×C₈×C₁₁	D₄	1	6	yes	complemented
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₁₁×#123	C₂×C₄	1	6	yes	—
49	C₁₁×C₂²⋊Q₈	—	2	3	no	—
50	C₁₁×#121	—	2	3	no	—
51	C₁₁×#120	C₂×C₄	1	6	yes	—
52	C₄×D₄×C₁₁	—	2	6	no	—
53	C₁₁×#117	C₂³	1	3	yes	—
54	C₁₁×C₄⋊C₈	—	2	6	no	—
55	C₁₁×#101	—	2	3	no	—
56	C₁₁×#100	—	2	3	no	—
57	C₁₁×#99	C₂×C₄	1	12	yes	—
58	C₁₁×C₂²⋊C₈	—	2	6	no	—
59	C₁₁×C₂²⋊C₈	—	2	6	no	—
60	C₁₁×#97	—	2	3	no	—
61	C₄×C₈×C₁₁	—	2	3	no	—
62	#21484	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₁₁×#41	—	2	4	no	—
65	C₁₁×#41	—	2	12	no	—
66	C₁₁×#41	—	2	12	no	—
67	C₁₁×#41	—	2	6	no	—
68	C₁₁×#41	—	2	6	no	—
69	C₂×Q₈×C₁₁	—	2	6	no	—
70	C₂×Q₈×C₁₁	#41	1	3	yes	—
71	C₂×D₄×C₁₁	—	2	6	no	—
72	C₂×D₄×C₁₁	—	2	12	no	—
73	C₂×D₄×C₁₁	—	2	6	no	—
74	C₂×D₄×C₁₁	C₂²×C₄	1	6	yes	—
75	C₂×D₄×C₁₁	#41	1	3	yes	—
76	C₂²×C₄×C₁₁	—	2	4	no	—
77	C₂²×C₄×C₁₁	—	2	3	no	—
78	C₂²×C₄×C₁₁	—	2	3	no	—
79	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
81	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
82	C₁₁×M₁₆	—	2	12	no	—
83	C₁₁×M₁₆	—	2	12	no	—
84	C₁₁×M₁₆	—	2	6	no	—
85	C₁₁×M₁₆	—	2	6	no	—
86	C₁₁×M₁₆	—	4	1	no	—
87	C₁₁×M₁₆	—	4	3	no	—
88	C₂×C₈×C₁₁	—	2	12	no	—
89	C₂×C₈×C₁₁	—	2	6	no	—
90	C₂×C₈×C₁₁	—	2	6	no	—
91	C₂×C₈×C₁₁	—	2	3	no	—
92	C₂×C₈×C₁₁	—	2	3	no	—
93	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
94	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
95	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
96	C₁₁×C₄⋊C₄	—	2	6	no	—
97	C₁₁×C₄⋊C₄	—	2	3	no	—
98	C₁₁×C₂²⋊C₄	—	2	6	no	—
99	C₁₁×C₂²⋊C₄	—	2	6	no	—
100	C₁₁×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
101	C₄²×C₁₁	—	2	3	no	—
102	#3573	C₂×C₁₁	1	1	yes	characteristic, complemented
103	#3025	C₂×C₁₁	1	1	yes	characteristic
104	#2930	C₂×C₁₁	1	3	yes	complemented
105	#1891	C₂×C₁₁	1	3	yes	complemented
106	#1868	C₂×C₁₁	1	3	yes	complemented
107	#1791	C₂×C₁₁	1	1	yes	characteristic, complemented
108	#1757	C₂×C₁₁	1	3	yes	complemented
109	C₂³×C₁₁	—	2	4	no	—
110	C₂³×C₁₁	—	2	3	no	—
111	C₂³×C₁₁	—	8	1	no	—
112	C₂³×C₁₁	C₄×D₄	1	6	yes	—
113	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
114	Q₈×C₁₁	—	2	4	no	—
115	Q₈×C₁₁	—	2	6	no	—
116	D₄×C₁₁	—	2	12	no	—
117	D₄×C₁₁	—	2	12	no	—
118	D₄×C₁₁	—	2	6	no	—
119	D₄×C₁₁	—	8	6	no	—
120	C₂×C₄×C₁₁	—	2	12	no	—
121	C₂×C₄×C₁₁	—	2	6	no	—
122	C₂×C₄×C₁₁	—	2	6	no	—
123	C₂×C₄×C₁₁	—	2	6	no	—
124	C₂×C₄×C₁₁	—	2	3	no	—
125	C₂×C₄×C₁₁	—	4	1	no	—
126	C₂×C₄×C₁₁	—	4	3	no	—
127	C₂×C₄×C₁₁	C₄×D₄	1	6	yes	—
128	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
129	C₂×C₄×C₁₁	C₂×#41	1	3	yes	—
130	C₈×C₁₁	—	2	6	no	—
131	C₈×C₁₁	—	4	1	no	—
132	C₈×C₁₁	—	4	3	no	—
133	C₈×C₁₁	#120	1	1	yes	characteristic
134	C₈×C₁₁	#120	1	3	yes	—
135	#585	C₂²×C₁₁	1	1	yes	characteristic
136	#568	—	2	6	no	—
137	#568	C₂²×C₁₁	1	3	yes	—
138	C₂×#131	—	2	6	no	—
139	C₂×#131	C₂²×C₁₁	1	3	yes	—
140	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
141	#525	C₂²×C₁₁	1	3	yes	—
142	#458	C₄×C₁₁	1	4	yes	—
143	B(4,𝔽₂)	C₄×C₁₁	1	4	yes	—
144	#436	—	2	6	no	—
145	#435	—	2	6	no	—
146	#424	C₂²×C₁₁	1	3	yes	complemented
147	#413	C₂²×C₁₁	1	3	yes	—
148	#410	C₂²×C₁₁	1	3	yes	—
149	#408	C₂²×C₁₁	1	3	yes	—
150	#407	C₂²×C₁₁	1	3	yes	complemented
151	#405	C₂²×C₁₁	1	3	yes	complemented
152	#344	C₂²×C₁₁	1	6	yes	complemented
153	C₂²×C₁₁	—	2	6	no	—
154	C₂²×C₁₁	—	4	1	no	—
155	C₂²×C₁₁	—	4	6	no	—
156	C₂²×C₁₁	—	4	3	no	—
157	C₂²×C₁₁	—	4	3	no	—
158	C₂²×C₁₁	—	4	1	no	—
159	C₂²×C₁₁	—	8	4	no	—
160	C₂²×C₁₁	C₂×C₄×D₄	1	3	yes	—
161	C₄×C₁₁	—	2	6	no	—
162	C₄×C₁₁	—	4	6	no	—
163	C₄×C₁₁	—	4	1	no	—
164	C₄×C₁₁	C₂×#120	1	1	yes	characteristic
165	C₄×C₁₁	#525	1	3	yes	—
166	2₋¹⁺⁴	—	2	3	no	—
167	H(5,𝔽₂)	—	2	3	no	—
168	H(5,𝔽₂)	C₂×C₄×C₁₁	1	4	yes	—
169	C₂×#41	—	2	6	no	—
170	C₂×#41	C₂³×C₁₁	1	3	yes	—
171	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
172	#131	—	2	4	no	—
173	#131	—	2	12	no	—
174	#131	—	2	6	no	—
175	#131	—	2	12	no	—
176	#131	—	2	6	no	—
177	C₂×M₁₆	—	2	12	no	—
178	C₂×M₁₆	—	2	6	no	—
179	C₂×M₁₆	—	2	3	no	—
180	C₂×M₁₆	—	2	3	no	—
181	C₂×M₁₆	D₄×C₁₁	1	6	yes	complemented
182	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
183	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
184	C₂²×C₈	—	2	4	no	—
185	C₂²×C₈	D₄×C₁₁	1	6	yes	complemented
186	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
187	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
188	#123	C₂×C₄×C₁₁	1	6	yes	—
189	C₂²⋊Q₈	—	2	3	no	—
190	#121	—	2	3	no	—
191	#120	C₂×C₄×C₁₁	1	6	yes	—
192	C₄×D₄	—	2	6	no	—
193	#117	C₂³×C₁₁	1	3	yes	—
194	C₄⋊C₈	—	2	6	no	—
195	#101	—	2	3	no	—
196	#100	—	2	3	no	—
197	#99	C₂×C₄×C₁₁	1	12	yes	—
198	C₂²⋊C₈	—	2	6	no	—
199	C₂²⋊C₈	—	2	6	no	—
200	#97	—	2	3	no	—
201	C₄×C₈	—	2	3	no	—
202	C₂×C₁₁	—	2	3	no	—
203	C₂×C₁₁	—	4	6	no	—
204	C₂×C₁₁	—	8	1	no	—
205	C₂×C₁₁	C₄×#120	1	1	yes	characteristic
206	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
207	#41	—	2	4	no	—
208	#41	—	2	12	no	—
209	#41	—	2	12	no	—
210	#41	—	2	6	no	—
211	#41	—	2	6	no	—
212	C₂×Q₈	—	2	6	no	—
213	C₂×Q₈	C₁₁×#41	1	3	yes	—
214	C₂×D₄	—	2	6	no	—
215	C₂×D₄	—	2	12	no	—
216	C₂×D₄	—	2	6	no	—
217	C₂×D₄	C₂²×C₄×C₁₁	1	6	yes	—
218	C₂×D₄	C₁₁×#41	1	3	yes	—
219	C₂²×C₄	—	2	4	no	—
220	C₂²×C₄	—	2	3	no	—
221	C₂²×C₄	—	2	3	no	—
222	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
223	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
224	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
225	M₁₆	—	2	12	no	—
226	M₁₆	—	2	6	no	—
227	M₁₆	—	2	12	no	—
228	M₁₆	—	2	6	no	—
229	M₁₆	—	4	1	no	—
230	M₁₆	—	4	3	no	—
231	C₂×C₈	—	2	12	no	—
232	C₂×C₈	—	2	6	no	—
233	C₂×C₈	—	2	6	no	—
234	C₂×C₈	—	2	3	no	—
235	C₂×C₈	—	2	3	no	—
236	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
237	C₂×C₈	C₂×D₄×C₁₁	1	3	yes	—
238	C₂×C₈	C₂×D₄×C₁₁	1	3	yes	—
239	C₄⋊C₄	—	2	6	no	—
240	C₄⋊C₄	—	2	3	no	—
241	C₂²⋊C₄	—	2	6	no	—
242	C₂²⋊C₄	—	2	6	no	—
243	C₂²⋊C₄	C₂²×C₄×C₁₁	1	6	yes	—
244	C₄²	—	2	3	no	—
245	C₁₁	#21484	1	1	yes	characteristic, direct product factor, Sylow
246	C₂³	—	2	4	no	—
247	C₂³	—	2	3	no	—
248	C₂³	—	8	1	no	—
249	C₂³	C₄×D₄×C₁₁	1	6	yes	—
250	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
251	Q₈	—	2	4	no	—
252	Q₈	—	2	6	no	—
253	D₄	—	2	12	no	—
254	D₄	—	2	12	no	—
255	D₄	—	2	6	no	—
256	D₄	—	8	6	no	—
257	C₂×C₄	—	2	12	no	—
258	C₂×C₄	—	2	6	no	—
259	C₂×C₄	—	2	6	no	—
260	C₂×C₄	—	2	6	no	—
261	C₂×C₄	—	2	3	no	—
262	C₂×C₄	—	4	1	no	—
263	C₂×C₄	—	4	3	no	—
264	C₂×C₄	C₄×D₄×C₁₁	1	6	yes	—
265	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
266	C₂×C₄	C₂×C₁₁×#41	1	3	yes	—
267	C₈	—	2	6	no	—
268	C₈	—	4	1	no	—
269	C₈	—	4	3	no	—
270	C₈	C₁₁×#120	1	1	yes	characteristic
271	C₈	C₁₁×#120	1	3	yes	—
272	C₂²	—	2	6	no	—
273	C₂²	—	4	1	no	—
274	C₂²	—	4	6	no	—
275	C₂²	—	4	3	no	—
276	C₂²	—	4	3	no	—
277	C₂²	—	4	1	no	—
278	C₂²	—	8	4	no	—
279	C₂²	C₂×C₄×D₄×C₁₁	1	3	yes	—
280	C₄	—	2	6	no	—
281	C₄	—	4	6	no	—
282	C₄	—	4	1	no	—
283	C₄	C₂×C₁₁×#120	1	1	yes	characteristic
284	C₄	C₁₁×#525	1	3	yes	—
285	C₂	—	2	3	no	—
286	C₂	—	4	6	no	—
287	C₂	—	8	1	no	—
288	C₂	C₄×C₁₁×#120	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	C₂×#120
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂×C₁₁	C₄×#120
prime radical	C₁₁×#3025	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3573	C₂	semidirect
3. C₁₁×#2930	C₂	semidirect
4. C₁₁×#1891	C₂	semidirect
5. C₁₁×#1868	C₂	semidirect
6. C₁₁×#1791	C₂	semidirect
7. C₁₁×#1757	C₂	semidirect
13. C₂²×C₁₁×M₁₆	C₂²	semidirect
19. C₁₁×#424	C₂²	semidirect
23. C₁₁×#407	C₂²	semidirect
24. C₁₁×#405	C₂²	semidirect
25. C₁₁×#344	C₂²	semidirect
41. C₂×C₁₁×M₁₆	D₄	semidirect
45. C₂²×C₈×C₁₁	D₄	semidirect
62. #21484	C₁₁	direct (N × H)
102. #3573	C₂×C₁₁	semidirect
104. #2930	C₂×C₁₁	semidirect
105. #1891	C₂×C₁₁	semidirect
106. #1868	C₂×C₁₁	semidirect
107. #1791	C₂×C₁₁	semidirect
108. #1757	C₂×C₁₁	semidirect
140. C₂²×M₁₆	C₂²×C₁₁	semidirect
146. #424	C₂²×C₁₁	semidirect
150. #407	C₂²×C₁₁	semidirect
151. #405	C₂²×C₁₁	semidirect
152. #344	C₂²×C₁₁	semidirect
181. C₂×M₁₆	D₄×C₁₁	semidirect
185. C₂²×C₈	D₄×C₁₁	semidirect
245. C₁₁	#21484	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×#3573	2
C₁₁×#3025	2
C₁₁×#2930	2
C₁₁×#1891	2
C₁₁×#1868	2
C₁₁×#1791	2
C₁₁×#1757	2
#21484	11

Subgroups — C11×#21484 #14598677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21484 #14598677