Subgroups — C₁₁×#13741 #14590934

Order 2816.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2262	C₂	1	2	yes	maximal, complemented
2	C₁₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×SD₁₂₈	C₂	1	2	yes	maximal, complemented
4	C₁₁×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#508	—	2	2	no	—
7	C₁₁×Q₆₄	C₂²	1	2	yes	—
8	C₁₁×SD₆₄	—	2	2	no	—
9	C₁₁×D₃₂	C₂²	1	2	yes	—
10	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
12	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
13	C₁₁×#135	—	4	2	no	—
14	C₁₁×Q₃₂	—	2	2	no	—
15	C₁₁×SD₃₂	—	4	2	no	—
16	C₁₁×D₁₆	—	2	2	no	—
17	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
18	C₁₁×C₃₂	D₄	1	1	yes	characteristic
19	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
20	#13741	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₁₁×#41	—	8	2	no	—
22	C₁₁×Q₁₆	—	4	2	no	—
23	C₁₁×SD₁₆	—	8	2	no	—
24	C₁₁×D₈	—	4	2	no	—
25	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
26	C₁₁×C₁₆	D₈	1	1	yes	characteristic
27	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
28	#2262	C₂×C₁₁	1	2	yes	complemented
29	Q₁₂₈	C₂×C₁₁	1	1	yes	characteristic, complemented
30	SD₁₂₈	C₂×C₁₁	1	2	yes	complemented
31	D₆₄	C₂×C₁₁	1	1	yes	characteristic, complemented
32	C₂×C₆₄	C₂×C₁₁	1	1	yes	characteristic, complemented
33	Q₈×C₁₁	—	8	2	no	—
34	D₄×C₁₁	—	8	2	no	—
35	D₄×C₁₁	—	16	2	no	—
36	C₂×C₄×C₁₁	—	16	2	no	—
37	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
38	C₈×C₁₁	D₁₆	1	1	yes	characteristic
39	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
40	#508	—	2	2	no	—
41	Q₆₄	C₂²×C₁₁	1	2	yes	—
42	SD₆₄	—	2	2	no	—
43	D₃₂	C₂²×C₁₁	1	2	yes	—
44	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
45	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
46	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
47	C₂²×C₁₁	—	16	2	no	—
48	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
49	C₄×C₁₁	—	16	2	no	—
50	C₄×C₁₁	D₃₂	1	1	yes	characteristic
51	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
52	#135	—	4	2	no	—
53	Q₃₂	—	2	2	no	—
54	SD₃₂	—	4	2	no	—
55	D₁₆	—	2	2	no	—
56	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
57	C₃₂	D₄×C₁₁	1	1	yes	characteristic
58	C₃₂	C₂³×C₁₁	1	1	yes	characteristic
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	—	32	2	no	—
61	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
62	#41	—	8	2	no	—
63	Q₁₆	—	4	2	no	—
64	SD₁₆	—	8	2	no	—
65	D₈	—	4	2	no	—
66	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
67	C₁₆	C₁₁×D₈	1	1	yes	characteristic
68	C₁₆	C₂×D₄×C₁₁	1	1	yes	characteristic
69	C₁₁	#13741	1	1	yes	characteristic, direct product factor, Sylow
70	Q₈	—	8	2	no	—
71	D₄	—	8	2	no	—
72	D₄	—	16	2	no	—
73	C₂×C₄	—	16	2	no	—
74	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
75	C₈	C₁₁×D₁₆	1	1	yes	characteristic
76	C₈	C₂×C₁₁×D₈	1	1	yes	characteristic
77	C₂²	—	16	2	no	—
78	C₂²	C₁₁×D₃₂	1	1	yes	characteristic
79	C₄	—	16	2	no	—
80	C₄	C₁₁×D₃₂	1	1	yes	characteristic
81	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	32	2	no	—
84	C₂	C₂×C₁₁×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂³×C₁₁
socle	C₂×C₁₁	C₂×D₃₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ C₂×C₁₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2262	C₂	semidirect
2. C₁₁×Q₁₂₈	C₂	semidirect
3. C₁₁×SD₁₂₈	C₂	semidirect
4. C₁₁×D₆₄	C₂	semidirect
5. C₂×C₁₁×C₆₄	C₂	semidirect
20. #13741	C₁₁	direct (N × H)
28. #2262	C₂×C₁₁	semidirect
29. Q₁₂₈	C₂×C₁₁	semidirect
30. SD₁₂₈	C₂×C₁₁	semidirect
31. D₆₄	C₂×C₁₁	semidirect
32. C₂×C₆₄	C₂×C₁₁	semidirect
69. C₁₁	#13741	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×#2262	2
C₁₁×Q₁₂₈	2
C₁₁×SD₁₂₈	2
C₁₁×D₆₄	2
C₂×C₁₁×C₆₄	2
#13741	11

Subgroups — C11×#13741 #14590934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13741 #14590934