Subgroups — C₁₁×#7546 #14584739

Order 2816.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1423	C₂	1	2	yes	maximal
3	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
4	C₁₁×#366	—	2	2	no	—
5	C₁₁×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
7	C₁₁×#107	—	4	2	no	—
8	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
10	#7546	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
12	C₁₁×C₄⋊C₄	—	8	2	no	—
13	C₁₁×C₁₆	C₄⋊C₄	1	1	yes	characteristic
14	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
15	C₂×C₆₄	C₂×C₁₁	1	1	yes	characteristic
16	#1423	C₂×C₁₁	1	2	yes	—
17	C₂×C₄×C₁₁	—	16	2	no	—
18	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
19	C₈×C₁₁	#107	1	1	yes	characteristic
20	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
21	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
22	#366	—	2	2	no	—
23	C₆₄	C₄×C₁₁	1	2	yes	complemented
24	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
25	C₄×C₁₁	—	32	2	no	—
26	C₄×C₁₁	#366	1	1	yes	characteristic
27	C₄×C₁₁	Q₆₄	1	1	yes	characteristic
28	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
29	#107	—	4	2	no	—
30	C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
31	C₃₂	Q₈×C₁₁	1	1	yes	characteristic
32	C₂×C₁₁	#1423	1	1	yes	characteristic
33	C₂×C₁₁	SD₁₂₈	1	2	yes	—
34	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
35	C₄⋊C₄	—	8	2	no	—
36	C₁₆	C₁₁×C₄⋊C₄	1	1	yes	characteristic
37	C₁₆	C₁₁×Q₁₆	1	1	yes	characteristic
38	C₁₁	#7546	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₄	—	16	2	no	—
40	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
41	C₈	C₁₁×#107	1	1	yes	characteristic
42	C₈	C₁₁×Q₃₂	1	1	yes	characteristic
43	C₂²	C₁₁×D₃₂	1	1	yes	characteristic
44	C₄	—	32	2	no	—
45	C₄	C₁₁×#366	1	1	yes	characteristic
46	C₄	C₁₁×Q₆₄	1	1	yes	characteristic
47	C₂	C₁₁×#1423	1	1	yes	characteristic
48	C₂	C₁₁×SD₁₂₈	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	D₃₂
commutator	C₃₂	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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
5. C₁₁×C₆₄	C₄	semidirect
10. #7546	C₁₁	direct (N × H)
23. C₆₄	C₄×C₁₁	semidirect
38. C₁₁	#7546	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×C₆₄	2
C₁₁×#1423	2
#7546	11

Subgroups — C11×#7546 #14584739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7546 #14584739