Subgroups — C₁₁×#22282 #14599475

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2932	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1963	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1876	C₂	1	8	yes	maximal, complemented
5	C₁₁×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#135	C₂²	1	4	yes	—
8	C₂×C₁₁×#131	C₂²	1	4	yes	—
9	C₁₁×#532	C₂²	1	2	yes	—
10	C₁₁×#495	C₄	1	4	yes	complemented
11	C₁₁×#494	C₄	1	1	yes	characteristic, complemented
12	C₁₁×#493	C₄	1	1	yes	characteristic, complemented
13	C₁₁×#492	C₄	1	2	yes	complemented
14	C₁₁×#435	—	2	8	no	—
15	C₁₁×#423	C₂²	1	2	yes	—
16	C₂×C₁₁×#104	C₂²	1	8	yes	—
17	C₁₁×#408	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×#376	C₂²	1	1	yes	characteristic
21	C₁₁×#341	C₂²	1	4	yes	—
22	C₁₁×#336	C₂²	1	4	yes	—
23	C₂×C₁₁×#41	C₂³	1	4	yes	—
24	C₁₁×#135	—	4	8	no	—
25	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
26	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	—
27	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
28	C₁₁×#131	—	4	8	no	—
29	C₂×C₁₁×M₁₆	—	2	4	no	—
30	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
31	C₂²×C₈×C₁₁	—	2	4	no	—
32	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
34	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
35	C₁₁×#127	C₂×C₄	1	2	yes	—
36	C₁₁×#124	C₂×C₄	1	4	yes	—
37	C₁₁×#121	—	2	4	no	—
38	C₄×D₄×C₁₁	—	2	4	no	—
39	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×C₄⋊C₈	—	2	4	no	—
42	C₁₁×#104	—	4	8	no	—
43	C₁₁×C₂²⋊C₈	—	2	8	no	—
44	C₁₁×#97	D₄	1	4	yes	—
45	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
48	C₁₁×#95	—	2	2	no	—
49	#22282	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₁₁×#41	—	2	8	no	—
51	C₁₁×#41	—	2	8	no	—
52	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
53	C₂×D₄×C₁₁	—	2	4	no	—
54	C₂×D₄×C₁₁	—	2	4	no	—
55	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	—	2	2	no	—
58	C₂²×C₄×C₁₁	#41	1	2	yes	—
59	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
60	C₁₁×Q₁₆	—	4	4	no	—
61	C₁₁×SD₁₆	—	4	8	no	—
62	C₁₁×D₈	—	4	4	no	—
63	C₁₁×M₁₆	—	2	8	no	—
64	C₁₁×M₁₆	—	4	8	no	—
65	C₂×C₈×C₁₁	—	2	4	no	—
66	C₂×C₈×C₁₁	—	2	4	no	—
67	C₂×C₈×C₁₁	—	2	4	no	—
68	C₂×C₈×C₁₁	—	4	8	no	—
69	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
70	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
71	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
72	C₁₁×C₄⋊C₄	—	2	4	no	—
73	C₁₁×C₂²⋊C₄	—	2	8	no	—
74	C₄²×C₁₁	—	2	4	no	—
75	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₁	C₂×D₄	1	2	yes	—
78	#3147	C₂×C₁₁	1	1	yes	characteristic
79	#2932	C₂×C₁₁	1	2	yes	complemented
80	#1963	C₂×C₁₁	1	2	yes	complemented
81	#1876	C₂×C₁₁	1	8	yes	complemented
82	#1837	C₂×C₁₁	1	1	yes	characteristic, complemented
83	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
84	C₂³×C₁₁	—	2	4	no	—
85	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
86	Q₈×C₁₁	—	2	8	no	—
87	D₄×C₁₁	—	2	8	no	—
88	D₄×C₁₁	—	4	8	no	—
89	D₄×C₁₁	—	8	4	no	—
90	C₂×C₄×C₁₁	—	2	4	no	—
91	C₂×C₄×C₁₁	—	4	2	no	—
92	C₂×C₄×C₁₁	—	4	4	no	—
93	C₂×C₄×C₁₁	—	4	4	no	—
94	C₂×C₄×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	4	2	no	—
96	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
101	C₈×C₁₁	—	2	2	no	—
102	C₈×C₁₁	—	2	2	no	—
103	C₈×C₁₁	—	2	4	no	—
104	C₈×C₁₁	—	4	4	no	—
105	C₂×#135	C₂²×C₁₁	1	4	yes	—
106	C₂×#131	C₂²×C₁₁	1	4	yes	—
107	#532	C₂²×C₁₁	1	2	yes	—
108	#495	C₄×C₁₁	1	4	yes	complemented
109	#494	C₄×C₁₁	1	1	yes	characteristic, complemented
110	#493	C₄×C₁₁	1	1	yes	characteristic, complemented
111	#492	C₄×C₁₁	1	2	yes	complemented
112	#435	—	2	8	no	—
113	#423	C₂²×C₁₁	1	2	yes	—
114	C₂×#104	C₂²×C₁₁	1	8	yes	—
115	#408	C₂²×C₁₁	1	4	yes	—
116	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
118	#376	C₂²×C₁₁	1	1	yes	characteristic
119	#341	C₂²×C₁₁	1	4	yes	—
120	#336	C₂²×C₁₁	1	4	yes	—
121	C₂²×C₁₁	—	2	2	no	—
122	C₂²×C₁₁	—	4	4	no	—
123	C₂²×C₁₁	—	4	8	no	—
124	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
125	C₂²×C₁₁	#540	1	2	yes	—
126	C₄×C₁₁	—	2	2	no	—
127	C₄×C₁₁	—	2	2	no	—
128	C₄×C₁₁	—	4	4	no	—
129	C₄×C₁₁	—	8	2	no	—
130	C₄×C₁₁	#518	1	2	yes	—
131	C₄×C₁₁	#535	1	2	yes	—
132	C₂×#41	C₂³×C₁₁	1	4	yes	—
133	#135	—	4	8	no	—
134	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
135	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	—
136	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
137	#131	—	4	8	no	—
138	C₂×M₁₆	—	2	4	no	—
139	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
140	C₂²×C₈	—	2	4	no	—
141	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
142	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
143	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
144	#127	C₂×C₄×C₁₁	1	2	yes	—
145	#124	C₂×C₄×C₁₁	1	4	yes	—
146	#121	—	2	4	no	—
147	C₄×D₄	—	2	4	no	—
148	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
149	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
150	C₄⋊C₈	—	2	4	no	—
151	#104	—	4	8	no	—
152	C₂²⋊C₈	—	2	8	no	—
153	#97	D₄×C₁₁	1	4	yes	—
154	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
155	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
156	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
157	#95	—	2	2	no	—
158	C₂×C₁₁	—	2	2	no	—
159	C₂×C₁₁	—	8	4	no	—
160	C₂×C₁₁	#2328	1	1	yes	characteristic
161	C₂×C₁₁	#2957	1	2	yes	—
162	#41	—	2	8	no	—
163	#41	—	2	8	no	—
164	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
165	C₂×D₄	—	2	4	no	—
166	C₂×D₄	—	2	4	no	—
167	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
168	C₂²×C₄	—	2	4	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	C₁₁×#41	1	2	yes	—
171	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
172	Q₁₆	—	4	4	no	—
173	SD₁₆	—	4	8	no	—
174	D₈	—	4	4	no	—
175	M₁₆	—	2	8	no	—
176	M₁₆	—	4	8	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	4	8	no	—
181	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
182	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
183	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
184	C₄⋊C₄	—	2	4	no	—
185	C₂²⋊C₄	—	2	8	no	—
186	C₄²	—	2	4	no	—
187	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
188	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
189	C₄²	C₂×D₄×C₁₁	1	2	yes	—
190	C₁₁	#22282	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³	—	2	4	no	—
192	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
193	Q₈	—	2	8	no	—
194	D₄	—	2	8	no	—
195	D₄	—	4	8	no	—
196	D₄	—	8	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
204	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
205	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
206	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
207	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
208	C₈	—	2	2	no	—
209	C₈	—	2	2	no	—
210	C₈	—	2	4	no	—
211	C₈	—	4	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	8	no	—
214	C₂²	—	4	4	no	—
215	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
216	C₂²	C₁₁×#540	1	2	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	4	no	—
220	C₄	—	8	2	no	—
221	C₄	C₁₁×#518	1	2	yes	—
222	C₄	C₁₁×#535	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	—	8	4	no	—
225	C₂	C₁₁×#2328	1	1	yes	characteristic
226	C₂	C₁₁×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2932	C₂	semidirect
3. C₁₁×#1963	C₂	semidirect
4. C₁₁×#1876	C₂	semidirect
5. C₁₁×#1837	C₂	semidirect
6. C₁₁×#1746	C₂	semidirect
10. C₁₁×#495	C₄	semidirect
11. C₁₁×#494	C₄	semidirect
12. C₁₁×#493	C₄	semidirect
13. C₁₁×#492	C₄	semidirect
49. #22282	C₁₁	direct (N × H)
79. #2932	C₂×C₁₁	semidirect
80. #1963	C₂×C₁₁	semidirect
81. #1876	C₂×C₁₁	semidirect
82. #1837	C₂×C₁₁	semidirect
83. #1746	C₂×C₁₁	semidirect
108. #495	C₄×C₁₁	semidirect
109. #494	C₄×C₁₁	semidirect
110. #493	C₄×C₁₁	semidirect
111. #492	C₄×C₁₁	semidirect
190. C₁₁	#22282	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×#3147	2
C₁₁×#2932	2
C₁₁×#1963	2
C₁₁×#1876	2
C₁₁×#1837	2
C₁₁×#1746	2
#22282	11

Subgroups — C11×#22282 #14599475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22282 #14599475