Subgroups — C₁₁×C₁₁⋊#3874 #31827686

Order 18150.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₅₅	—	3	1	no	maximal, Hall
3	C₅²×C₁₁²	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁⋊#3874	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₁₁×#3874	—	11	1	no	maximal
6	C₁₁×D₅₅	—	3	1	no	—
7	C₅×C₁₁×D₁₁	—	15	1	no	—
8	C₁₁×C₅²⋊C₃	—	2	5	no	—
9	C₁₁×C₅²⋊C₃	D₁₁	1	1	yes	characteristic, complemented
10	C₁₁×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
11	C₁₁×D₃₃	—	25	1	no	maximal, Hall
12	C₅×C₁₁²	—	3	1	no	—
13	C₅×C₁₁²	—	6	1	no	—
14	C₅×D₅₅	—	3	1	no	—
15	C₅×D₅×C₁₁	—	33	1	no	—
16	C₃×C₁₁²	—	50	1	no	Hall
17	C₅²×C₁₁	—	2	5	no	—
18	C₅²×C₁₁	D₃×C₁₁	1	1	yes	characteristic, complemented
19	C₅²×C₁₁	D₃₃	1	1	yes	characteristic, complemented
20	C₁₁×D₁₁	—	15	1	no	Hall
21	#3874	—	11	1	no	Hall
22	C₁₁²	#3874	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₅×C₁₁	—	165	1	no	—
24	D₅₅	—	3	1	no	—
25	C₅×D₁₁	—	15	1	no	—
26	D₅×C₁₁	—	33	1	no	—
27	C₅²⋊C₃	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
28	D₃₃	—	25	1	no	—
29	D₃×C₁₁	—	275	1	no	—
30	C₅×C₁₁	—	3	1	no	—
31	C₅×C₁₁	—	6	5	no	—
32	C₅×C₁₁	—	6	1	no	—
33	C₅×C₁₁	—	6	5	no	—
34	C₅×C₁₁	—	6	1	no	—
35	C₅×C₁₁	—	6	1	no	—
36	C₅×D₅	—	33	1	no	Hall
37	C₃×C₁₁	—	25	1	no	—
38	C₃×C₁₁	—	50	5	no	—
39	C₃×C₁₁	—	50	1	no	—
40	C₅²	C₁₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₁	—	165	1	no	—
42	D₁₁	—	15	1	no	—
43	C₁₁	—	2	5	no	—
44	C₁₁	C₁₁×#3874	1	1	yes	characteristic, complemented
45	C₁₁	C₁₁⋊#3874	1	1	yes	characteristic, direct product factor
46	C₂×C₅	—	165	1	no	—
47	D₅	—	33	1	no	—
48	D₃	—	275	1	no	Hall
49	C₅	—	3	1	no	—
50	C₅	—	6	1	no	—
51	C₃	—	50	1	no	Sylow
52	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₁₁⋊#3874
commutator, cosocle, hypocenter	C₁₁×C₅²⋊C₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁²	D₃
LCS	G ▷ C₁₁×C₅²⋊C₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₅²⋊C₃	C₂	semidirect
3. C₅²×C₁₁²	D₃	semidirect
4. C₁₁⋊#3874	C₁₁	direct (N × H)
9. C₁₁×C₅²⋊C₃	D₁₁	semidirect
10. C₁₁×C₅²⋊C₃	C₂×C₁₁	semidirect
18. C₅²×C₁₁	D₃×C₁₁	semidirect
19. C₅²×C₁₁	D₃₃	semidirect
22. C₁₁²	#3874	semidirect
27. C₅²⋊C₃	C₁₁×D₁₁	semidirect
40. C₅²	C₁₁×D₃₃	semidirect
44. C₁₁	C₁₁×#3874	semidirect
45. C₁₁	C₁₁⋊#3874	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁²×C₅²⋊C₃	2
C₅×C₁₁×D₅₅	3
C₁₁⋊#3874	11
C₁₁×#3874	11
C₁₁×D₃₃	25

Subgroups — C11×C11⋊#3874 #31827686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₁⋊#3874 #31827686