Subgroups — C₇⋊(C₁₁⋊(C₁₁⋊#157)) #44479178

Order 30492.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₁₁²	—	6	2	no	—
4	C₁₁⋊(C₁₁⋊#157)	—	7	1	no	maximal, Hall
5	C₇⋊(C₁₁⋊Dic₁₁)	—	9	1	no	maximal, Hall
6	C₇⋊(C₁₁⋊#157)	—	11	12	no	maximal
7	C₃×C₇×C₁₁²	—	2	2	no	—
8	C₁₁²×C₃⋊D₃	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₁²	—	9	1	no	—
10	C₇×C₁₁×C₃⋊D₃	D₁₁	1	12	yes	—
11	C₃²×C₁₁²	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁²	#157	1	1	yes	characteristic, complemented, Hall
13	D₃×C₁₁²	—	6	2	no	—
14	C₃²×C₇×C₁₁	Dic₁₁	1	12	yes	complemented
15	C₁₁⋊Dic₁₁	—	63	1	no	Hall
16	D₃×C₇×C₁₁	—	6	24	no	—
17	C₁₁⋊#157	—	77	12	no	—
18	C₃×C₁₁²	—	2	2	no	—
19	Dic₇₇	—	99	12	no	—
20	C₇⋊#157	—	121	1	no	Hall
21	C₂×C₁₁²	—	9	1	no	—
22	C₃×C₇×C₁₁	—	2	24	no	—
23	C₁₁×C₃⋊D₃	D₇₇	1	12	yes	—
24	C₂×C₇×C₁₁	—	9	12	no	—
25	C₇×C₃⋊D₃	C₁₁⋊D₁₁	1	1	yes	characteristic
26	C₁₁²	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
27	C₃²×C₁₁	Dic₇₇	1	12	yes	complemented
28	C₇×C₁₁	C₁₁⋊#157	1	12	yes	complemented
29	D₃×C₁₁	—	6	24	no	—
30	C₃²×C₇	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Hall
31	Dic₁₁	—	693	12	no	—
32	D₃×C₇	—	6	2	no	—
33	#157	—	847	1	no	Hall
34	C₃×C₁₁	—	2	24	no	—
35	Dic₇	—	1089	1	no	Hall
36	C₂×C₁₁	—	9	12	no	—
37	C₃×C₇	—	2	2	no	—
38	C₃⋊D₃	C₇⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic
39	C₂×C₇	—	9	1	no	—
40	C₁₁	C₇⋊(C₁₁⋊#157)	1	12	yes	complemented
41	C₃²	C₇⋊(C₁₁⋊Dic₁₁)	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₁₁⋊(C₁₁⋊#157)	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	6	2	no	—
44	C₄	—	7623	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₁₁²	C₄
prime radical, cosocle	C₇×C₁₁²×C₃⋊D₃	C₂
LCS	G ▷ C₃²×C₇×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇×C₁₁²	C₄	semidirect
11. C₃²×C₁₁²	Dic₇	semidirect
12. C₇×C₁₁²	#157	semidirect
14. C₃²×C₇×C₁₁	Dic₁₁	semidirect
26. C₁₁²	C₇⋊#157	semidirect
27. C₃²×C₁₁	Dic₇₇	semidirect
28. C₇×C₁₁	C₁₁⋊#157	semidirect
30. C₃²×C₇	C₁₁⋊Dic₁₁	semidirect
40. C₁₁	C₇⋊(C₁₁⋊#157)	semidirect
41. C₃²	C₇⋊(C₁₁⋊Dic₁₁)	semidirect
42. C₇	C₁₁⋊(C₁₁⋊#157)	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁²×C₃⋊D₃	2
C₁₁⋊(C₁₁⋊#157)	7
C₇⋊(C₁₁⋊Dic₁₁)	9
C₇⋊(C₁₁⋊#157)	11

Subgroups — C7⋊(C11⋊(C11⋊#157)) #44479178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊(C₁₁⋊(C₁₁⋊#157)) #44479178