Subgroups — C₁₁×#62624 #14639817

Order 2816.

2038 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3573	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3407	C₂	1	15	yes	maximal, complemented
3	C₂×C₁₁×#504	C₂	1	15	yes	maximal, complemented
4	C₁₁×#585	C₄	1	1	yes	characteristic
5	C₁₁×#568	C₄	1	15	yes	—
6	C₂×C₁₁×#131	C₂²	1	15	yes	—
7	C₁₁×#504	C₂²	1	20	yes	complemented
8	C₁₁×#504	C₂²	1	60	yes	complemented
9	C₂×C₁₁×M₃₂	C₂²	1	45	yes	complemented
10	C₂²×C₁₁×C₁₆	C₂²	1	15	yes	complemented
11	C₁₁×2₋¹⁺⁴	C₈	1	6	yes	—
12	C₁₁×H(5,𝔽₂)	C₈	1	10	yes	—
13	C₂×C₁₁×#41	C₂×C₄	1	15	yes	—
14	C₁₁×#131	C₂×C₄	1	60	yes	—
15	C₁₁×#131	C₂³	1	20	yes	—
16	C₂×C₁₁×M₁₆	C₂×C₄	1	45	yes	—
17	C₂²×C₈×C₁₁	C₂³	1	15	yes	—
18	C₁₁×M₃₂	C₂³	1	60	yes	—
19	C₂×C₁₁×C₁₆	C₂³	1	45	yes	—
20	C₂×C₁₁×C₁₆	C₂³	1	15	yes	—
21	#62624	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₁₁×#41	C₂×C₈	1	60	yes	—
23	C₁₁×#41	C₂²×C₄	1	20	yes	—
24	C₂×Q₈×C₁₁	C₂×C₈	1	15	yes	—
25	C₂×D₄×C₁₁	C₂×C₈	1	45	yes	—
26	C₂²×C₄×C₁₁	C₂²×C₄	1	15	yes	—
27	C₁₁×M₁₆	C₂²×C₄	1	60	yes	—
28	C₂×C₈×C₁₁	C₂²×C₄	1	45	yes	—
29	C₂×C₈×C₁₁	C₂⁴	1	15	yes	—
30	C₁₁×C₁₆	C₂⁴	1	15	yes	—
31	C₁₁×C₁₆	C₂⁴	1	1	yes	characteristic
32	#3573	C₂×C₁₁	1	1	yes	characteristic
33	#3407	C₂×C₁₁	1	15	yes	complemented
34	C₂×#504	C₂×C₁₁	1	15	yes	complemented
35	C₂³×C₁₁	C₂²×C₈	1	15	yes	—
36	Q₈×C₁₁	C₂²×C₈	1	20	yes	—
37	D₄×C₁₁	C₂²×C₈	1	60	yes	—
38	C₂×C₄×C₁₁	C₂²×C₈	1	45	yes	—
39	C₂×C₄×C₁₁	C₂³×C₄	1	15	yes	—
40	C₈×C₁₁	C₂³×C₄	1	15	yes	—
41	C₈×C₁₁	C₂⁵	1	1	yes	characteristic
42	#585	C₄×C₁₁	1	1	yes	characteristic
43	#568	C₄×C₁₁	1	15	yes	—
44	C₂×#131	C₂²×C₁₁	1	15	yes	—
45	#504	C₂²×C₁₁	1	20	yes	complemented
46	#504	C₂²×C₁₁	1	60	yes	complemented
47	C₂×M₃₂	C₂²×C₁₁	1	45	yes	complemented
48	C₂²×C₁₆	C₂²×C₁₁	1	15	yes	complemented
49	C₂²×C₁₁	—	4	15	no	—
50	C₂²×C₁₁	C₂³×C₈	1	15	yes	—
51	C₄×C₁₁	C₂³×C₈	1	15	yes	—
52	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
53	2₋¹⁺⁴	C₈×C₁₁	1	6	yes	—
54	H(5,𝔽₂)	C₈×C₁₁	1	10	yes	—
55	C₂×#41	C₂×C₄×C₁₁	1	15	yes	—
56	#131	C₂×C₄×C₁₁	1	60	yes	—
57	#131	C₂³×C₁₁	1	20	yes	—
58	C₂×M₁₆	C₂×C₄×C₁₁	1	45	yes	—
59	C₂²×C₈	C₂³×C₁₁	1	15	yes	—
60	M₃₂	C₂³×C₁₁	1	60	yes	—
61	C₂×C₁₆	C₂³×C₁₁	1	15	yes	—
62	C₂×C₁₆	C₂³×C₁₁	1	45	yes	—
63	C₂×C₁₁	—	2	15	no	—
64	C₂×C₁₁	C₂⁴×C₈	1	1	yes	characteristic
65	#41	C₂×C₈×C₁₁	1	60	yes	—
66	#41	C₂²×C₄×C₁₁	1	20	yes	—
67	C₂×Q₈	C₂×C₈×C₁₁	1	15	yes	—
68	C₂×D₄	C₂×C₈×C₁₁	1	45	yes	—
69	C₂²×C₄	C₂²×C₄×C₁₁	1	15	yes	—
70	M₁₆	C₂²×C₄×C₁₁	1	60	yes	—
71	C₂×C₈	C₂²×C₄×C₁₁	1	45	yes	—
72	C₂×C₈	C₂⁴×C₁₁	1	15	yes	—
73	C₁₆	C₂⁴×C₁₁	1	1	yes	characteristic
74	C₁₆	C₂⁴×C₁₁	1	15	yes	—
75	C₁₁	#62624	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³	C₂²×C₈×C₁₁	1	15	yes	—
77	Q₈	C₂²×C₈×C₁₁	1	20	yes	—
78	D₄	C₂²×C₈×C₁₁	1	60	yes	—
79	C₂×C₄	C₂²×C₈×C₁₁	1	45	yes	—
80	C₂×C₄	C₂³×C₄×C₁₁	1	15	yes	—
81	C₈	C₂³×C₄×C₁₁	1	15	yes	—
82	C₈	C₂⁵×C₁₁	1	1	yes	characteristic
83	C₂²	—	4	15	no	—
84	C₂²	C₂³×C₈×C₁₁	1	15	yes	—
85	C₄	C₂³×C₈×C₁₁	1	15	yes	—
86	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
87	C₂	—	2	15	no	—
88	C₂	C₂⁴×C₈×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₁₁×C₁₆	C₂⁴
commutator	C₂	C₂⁴×C₈×C₁₁
Frattini, cosocle	C₈	C₂⁵×C₁₁
socle	C₂×C₁₁	C₂⁴×C₈
prime radical	C₁₁×#585	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3407	C₂	semidirect
3. C₂×C₁₁×#504	C₂	semidirect
7. C₁₁×#504	C₂²	semidirect
8. C₁₁×#504	C₂²	semidirect
9. C₂×C₁₁×M₃₂	C₂²	semidirect
10. C₂²×C₁₁×C₁₆	C₂²	semidirect
21. #62624	C₁₁	direct (N × H)
33. #3407	C₂×C₁₁	semidirect
34. C₂×#504	C₂×C₁₁	semidirect
45. #504	C₂²×C₁₁	semidirect
46. #504	C₂²×C₁₁	semidirect
47. C₂×M₃₂	C₂²×C₁₁	semidirect
48. C₂²×C₁₆	C₂²×C₁₁	semidirect
75. C₁₁	#62624	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×#3407	2
C₂×C₁₁×#504	2
#62624	11

Subgroups — C11×#62624 #14639817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#62624 #14639817