Subgroups — C₁₁×#7547 #14584740

Order 2816.

60 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×#1425	C₂	1	2	yes	maximal
3	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
4	C₁₁×#368	—	2	2	no	—
5	C₁₁×C₆₄	C₄	1	2	yes	—
6	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
7	C₁₁×#108	—	4	2	no	—
8	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
10	#7547	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₁₁×M₁₆	—	8	2	no	—
12	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
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	#1425	C₂×C₁₁	1	2	yes	—
17	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
18	C₈×C₁₁	—	16	2	no	—
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	#368	—	2	2	no	—
23	C₆₄	C₄×C₁₁	1	2	yes	—
24	C₂²×C₁₁	Q₆₄	1	1	yes	characteristic
25	C₄×C₁₁	#366	1	1	yes	characteristic
26	C₄×C₁₁	D₃₂	1	1	yes	characteristic
27	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
28	#108	—	4	2	no	—
29	C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
30	C₃₂	Q₈×C₁₁	1	1	yes	characteristic
31	C₂×C₁₁	—	2	1	no	—
32	C₂×C₁₁	#1423	1	1	yes	characteristic
33	M₁₆	—	8	2	no	—
34	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
35	C₁₆	C₁₁×C₄⋊C₄	1	1	yes	characteristic
36	C₁₆	C₁₁×Q₁₆	1	1	yes	characteristic
37	C₁₁	#7547	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
39	C₈	—	16	2	no	—
40	C₈	C₁₁×#107	1	1	yes	characteristic
41	C₈	C₁₁×Q₃₂	1	1	yes	characteristic
42	C₂²	C₁₁×Q₆₄	1	1	yes	characteristic
43	C₄	C₁₁×#366	1	1	yes	characteristic
44	C₄	C₁₁×D₃₂	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	C₁₁×#1423	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	D₃₂
commutator	C₃₂	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₁
socle	C₂×C₁₁	#1423
prime radical	C₂²×C₁₁	Q₆₄
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
10. #7547	C₁₁	direct (N × H)
37. C₁₁	#7547	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×#1425	2
#7547	11

Subgroups — C11×#7547 #14584740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7547 #14584740