Subgroups — C₁₁⋊#11758267 #24924790

Order 10780.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#5997	—	5	1	no	maximal, Hall
4	C₁₁×C₇⋊D₇	D₅	1	1	yes	characteristic
5	#11758267	—	11	1	no	maximal, Hall
6	C₅×C₁₁×D₇	—	14	4	no	—
7	C₇²×C₁₁	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇⋊D₇	D₁₁	1	1	yes	characteristic
9	C₅×C₇×C₁₁	—	2	4	no	—
10	C₅×C₇²	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	Dic₅₅	—	49	1	no	maximal, Hall
12	#5997	—	55	1	no	Hall
13	C₁₁×D₇	—	14	4	no	—
14	C₂×C₅×C₁₁	—	49	1	no	—
15	C₇⋊D₇	D₅₅	1	1	yes	characteristic
16	C₇×C₁₁	—	2	4	no	—
17	C₅×D₇	—	14	4	no	—
18	C₅×C₁₁	#5997	1	1	yes	characteristic, complemented, Hall
19	C₇²	Dic₅₅	1	1	yes	characteristic, complemented, Sylow
20	Dic₁₁	—	245	1	no	Hall
21	C₅×C₇	—	2	4	no	—
22	C₂×C₁₁	—	49	1	no	—
23	Dic₅	—	539	1	no	Hall
24	D₇	—	14	4	no	—
25	C₁₁	#11758267	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	49	1	no	—
27	C₇	—	2	4	no	—
28	C₅	C₁₁⋊#5997	1	1	yes	characteristic, complemented, Sylow
29	C₄	—	2695	1	no	Sylow
30	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇²×C₁₁	C₄
prime radical, cosocle	C₅×C₁₁×C₇⋊D₇	C₂
LCS	G ▷ C₅×C₇²×C₁₁
UCS	C₁

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