Subgroups — C₁₁×#7548 #14584741

Order 2816.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1425	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1424	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₁×#368	—	2	1	no	—
6	C₁₁×#366	—	2	1	no	—
7	C₁₁×C₆₄	C₄	1	2	yes	complemented
8	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
9	C₁₁×#108	—	4	1	no	—
10	C₁₁×#107	—	4	1	no	—
11	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
13	#7548	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₁₁×M₁₆	—	8	1	no	—
15	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
16	C₁₁×C₄⋊C₄	—	8	1	no	—
17	C₁₁×C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
19	M₁₂₈	C₂×C₁₁	1	1	yes	characteristic
20	#1425	C₂×C₁₁	1	1	yes	characteristic
21	#1424	C₂×C₁₁	1	1	yes	characteristic
22	C₂×C₄×C₁₁	—	16	1	no	—
23	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
24	C₈×C₁₁	—	16	1	no	—
25	C₈×C₁₁	#107	1	1	yes	characteristic
26	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
27	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
28	#368	—	2	1	no	—
29	#366	—	2	1	no	—
30	C₆₄	C₄×C₁₁	1	2	yes	complemented
31	C₂²×C₁₁	SD₆₄	1	1	yes	characteristic
32	C₄×C₁₁	—	32	1	no	—
33	C₄×C₁₁	#366	1	1	yes	characteristic
34	C₄×C₁₁	SD₆₄	1	1	yes	characteristic
35	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
36	#108	—	4	1	no	—
37	#107	—	4	1	no	—
38	C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
39	C₃₂	Q₈×C₁₁	1	1	yes	characteristic
40	C₂×C₁₁	—	2	1	no	—
41	C₂×C₁₁	#1424	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
44	C₄⋊C₄	—	8	1	no	—
45	C₁₆	C₁₁×C₄⋊C₄	1	1	yes	characteristic
46	C₁₆	C₁₁×Q₁₆	1	1	yes	characteristic
47	C₁₁	#7548	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₄	—	16	1	no	—
49	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
50	C₈	—	16	1	no	—
51	C₈	C₁₁×#107	1	1	yes	characteristic
52	C₈	C₁₁×Q₃₂	1	1	yes	characteristic
53	C₂²	C₁₁×SD₆₄	1	1	yes	characteristic
54	C₄	—	32	1	no	—
55	C₄	C₁₁×#366	1	1	yes	characteristic
56	C₄	C₁₁×SD₆₄	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	C₁₁×#1424	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#1424
commutator	C₃₂	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₁
prime radical	C₂²×C₁₁	SD₆₄
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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
7. C₁₁×C₆₄	C₄	semidirect
13. #7548	C₁₁	direct (N × H)
30. C₆₄	C₄×C₁₁	semidirect
47. C₁₁	#7548	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×M₁₂₈	2
C₁₁×#1425	2
C₁₁×#1424	2
#7548	11

Subgroups — C11×#7548 #14584741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7548 #14584741