Subgroups — C₁₁×#13737 #14590930

Order 2816.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2258	C₂	1	1	yes	maximal, characteristic
2	C₁₁×M₁₂₈	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₁×C₆₄	C₂	1	3	yes	maximal, complemented
4	C₁₁×#504	C₄	1	1	yes	characteristic
5	C₁₁×M₆₄	C₄	1	3	yes	—
6	C₂×C₁₁×C₃₂	C₂²	1	3	yes	—
7	C₁₁×C₆₄	C₂²	1	3	yes	—
8	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
9	C₁₁×#131	C₈	1	1	yes	characteristic
10	C₁₁×M₃₂	C₈	1	3	yes	—
11	C₂×C₁₁×C₁₆	C₂×C₄	1	3	yes	—
12	C₁₁×C₃₂	C₂×C₄	1	3	yes	—
13	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
14	#13737	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₁₁×#41	C₁₆	1	1	yes	characteristic
16	C₁₁×M₁₆	C₁₆	1	3	yes	—
17	C₂×C₈×C₁₁	C₂×C₈	1	3	yes	—
18	C₁₁×C₁₆	C₂×C₈	1	3	yes	—
19	C₁₁×C₁₆	C₂²×C₄	1	1	yes	characteristic
20	#2258	C₂×C₁₁	1	1	yes	characteristic
21	M₁₂₈	C₂×C₁₁	1	3	yes	complemented
22	C₂×C₆₄	C₂×C₁₁	1	3	yes	complemented
23	Q₈×C₁₁	C₃₂	1	1	yes	characteristic
24	D₄×C₁₁	C₃₂	1	3	yes	—
25	C₂×C₄×C₁₁	C₂×C₁₆	1	3	yes	—
26	C₈×C₁₁	C₂×C₁₆	1	3	yes	—
27	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
28	#504	C₄×C₁₁	1	1	yes	characteristic
29	M₆₄	C₄×C₁₁	1	3	yes	—
30	C₂×C₃₂	C₂²×C₁₁	1	3	yes	—
31	C₆₄	C₂²×C₁₁	1	3	yes	—
32	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
33	C₂²×C₁₁	C₂×C₃₂	1	3	yes	—
34	C₄×C₁₁	C₂×C₃₂	1	3	yes	—
35	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
36	#131	C₈×C₁₁	1	1	yes	characteristic
37	M₃₂	C₈×C₁₁	1	3	yes	—
38	C₂×C₁₆	C₂×C₄×C₁₁	1	3	yes	—
39	C₃₂	C₂×C₄×C₁₁	1	3	yes	—
40	C₃₂	C₂³×C₁₁	1	1	yes	characteristic
41	C₂×C₁₁	—	2	3	no	—
42	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
43	#41	C₁₁×C₁₆	1	1	yes	characteristic
44	M₁₆	C₁₁×C₁₆	1	3	yes	—
45	C₂×C₈	C₂×C₈×C₁₁	1	3	yes	—
46	C₁₆	C₂×C₈×C₁₁	1	3	yes	—
47	C₁₆	C₂²×C₄×C₁₁	1	1	yes	characteristic
48	C₁₁	#13737	1	1	yes	characteristic, direct product factor, Sylow
49	Q₈	C₁₁×C₃₂	1	1	yes	characteristic
50	D₄	C₁₁×C₃₂	1	3	yes	—
51	C₂×C₄	C₂×C₁₁×C₁₆	1	3	yes	—
52	C₈	C₂×C₁₁×C₁₆	1	3	yes	—
53	C₈	C₂²×C₈×C₁₁	1	1	yes	characteristic
54	C₂²	C₂×C₁₁×C₃₂	1	3	yes	—
55	C₄	C₂×C₁₁×C₃₂	1	3	yes	—
56	C₄	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×C₁₁×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₁₁×C₆₄	C₂²
commutator	C₂	C₂²×C₁₁×C₃₂
Frattini, cosocle	C₃₂	C₂³×C₁₁
socle	C₂×C₁₁	C₂²×C₃₂
prime radical	C₁₁×#41	C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₁×C₆₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×M₁₂₈	C₂	semidirect
3. C₂×C₁₁×C₆₄	C₂	semidirect
14. #13737	C₁₁	direct (N × H)
21. M₁₂₈	C₂×C₁₁	semidirect
22. C₂×C₆₄	C₂×C₁₁	semidirect
48. C₁₁	#13737	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×#2258	2
C₁₁×M₁₂₈	2
C₂×C₁₁×C₆₄	2
#13737	11

Subgroups — C11×#13737 #14590930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13737 #14590930