Subgroups — C₂₁₁⋊#564 #27213901

Order 13504.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269969	C₂	1	2	yes	maximal
2	#20269968	C₂	1	4	yes	maximal
3	#20269967	C₂	1	4	yes	maximal
4	#20269967	C₂	1	4	yes	maximal
5	#125×C₂₁₁	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Dic₂₁₁	C₂²	1	2	yes	—
7	C₄⋊Dic₂₁₁	C₂²	1	4	yes	—
8	C₄⋊Dic₂₁₁	C₂²	1	2	yes	—
9	Dic₂₁₁⋊C₄	C₂²	1	4	yes	—
10	Dic₂₁₁⋊C₄	C₂²	1	4	yes	—
11	Dic₂₁₁⋊C₄	C₂²	1	4	yes	—
12	Dic₂₁₁⋊C₄	C₂²	1	4	yes	—
13	C₄×Dic₂₁₁	C₂²	1	4	yes	—
14	C₄⋊C₄×C₂₁₁	C₂²	1	2	yes	—
15	C₄⋊C₄×C₂₁₁	C₂²	1	4	yes	—
16	C₄²×C₂₁₁	C₂²	1	1	yes	characteristic
17	C₂×Dic₂₁₁	C₂³	1	4	yes	—
18	C₂×Dic₂₁₁	C₂³	1	4	yes	—
19	C₂×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₂₁₁	C₂³	1	2	yes	—
21	C₂×C₄×C₂₁₁	C₂³	1	4	yes	—
22	C₂²×C₂₁₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₂₁₁	—	2	2	no	—
24	C₄×C₂₁₁	—	2	4	no	—
25	C₄×C₂₁₁	—	2	1	no	—
26	Dic₂₁₁	—	2	4	no	—
27	Dic₂₁₁	—	2	4	no	—
28	C₂×C₂₁₁	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₂₁₁	2₋¹⁺⁴	1	1	yes	characteristic
30	C₂₁₁	#564	1	1	yes	characteristic, complemented, Sylow
31	#564	—	211	1	no	maximal, Sylow
32	#125	—	211	4	no	—
33	#125	—	211	4	no	—
34	#125	—	211	4	no	—
35	#125	—	211	2	no	—
36	#125	D₂₁₁	1	1	yes	characteristic
37	C₄⋊C₄	—	211	4	no	—
38	C₄⋊C₄	—	211	4	no	—
39	C₄⋊C₄	—	211	4	no	—
40	C₄⋊C₄	—	211	4	no	—
41	C₄⋊C₄	—	211	4	no	—
42	C₄⋊C₄	—	211	2	no	—
43	C₄⋊C₄	—	211	2	no	—
44	C₄⋊C₄	C₂×D₂₁₁	1	2	yes	—
45	C₄⋊C₄	C₂×D₂₁₁	1	4	yes	—
46	C₄²	—	211	4	no	—
47	C₄²	C₂×D₂₁₁	1	1	yes	characteristic
48	C₂×C₄	—	211	4	no	—
49	C₂×C₄	—	211	4	no	—
50	C₂×C₄	C₂²×D₂₁₁	1	4	yes	—
51	C₂×C₄	C₂²×D₂₁₁	1	2	yes	—
52	C₂×C₄	C₂²×D₂₁₁	1	1	yes	characteristic
53	C₂²	C₂³×D₂₁₁	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	422	4	no	—
58	C₄	—	422	4	no	—
59	C₂	#20270024	1	2	yes	—
60	C₂	#20270025	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₁₁
commutator, socle, prime radical, cosocle	C₂²×C₂₁₁	C₂⁴
Fitting	#125×C₂₁₁	C₂
hypercenter	#125	D₂₁₁
hypocenter	C₂₁₁	#564
LCS	G ▷ C₂²×C₂₁₁ ▷ C₂₁₁
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
30. C₂₁₁	#564	semidirect

Maximal subgroups

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

subgroup	index
#20269969	2
#20269968	2
#20269967	2
#125×C₂₁₁	2
#564	211

Subgroups — C211⋊#564 #27213901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₁₁⋊#564 #27213901