Subgroups — C₄₁⋊#564 #14581091

Order 2624.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050156	C₂	1	2	yes	maximal
2	#13050155	C₂	1	4	yes	maximal
3	#13050154	C₂	1	4	yes	maximal
4	#13050154	C₂	1	4	yes	maximal
5	#125×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
7	C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
8	C₄²×C₄₁	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₄₁	C₂²	1	2	yes	—
10	C₄⋊Dic₄₁	C₂²	1	4	yes	—
11	C₄⋊Dic₄₁	C₂²	1	2	yes	—
12	#10620279	C₂²	1	4	yes	—
13	#10620279	C₂²	1	4	yes	—
14	#10620279	C₂²	1	4	yes	—
15	#10620279	C₂²	1	4	yes	—
16	C₄×Dic₄₁	C₂²	1	4	yes	—
17	C₂×C₄×C₄₁	C₂³	1	4	yes	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₄₁	C₂³	1	2	yes	—
20	C₂×Dic₄₁	C₂³	1	4	yes	—
21	C₂×Dic₄₁	C₂³	1	4	yes	—
22	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₄₁	—	2	4	no	—
24	C₄×C₄₁	—	2	2	no	—
25	C₄×C₄₁	—	2	1	no	—
26	Dic₄₁	—	2	4	no	—
27	Dic₄₁	—	2	4	no	—
28	C₂×C₄₁	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
30	#564	—	41	1	no	maximal, Sylow
31	C₄₁	#564	1	1	yes	characteristic, complemented, Sylow
32	#125	—	41	4	no	—
33	#125	—	41	4	no	—
34	#125	—	41	4	no	—
35	#125	—	41	2	no	—
36	#125	D₄₁	1	1	yes	characteristic
37	C₄⋊C₄	—	41	4	no	—
38	C₄⋊C₄	—	41	4	no	—
39	C₄⋊C₄	—	41	4	no	—
40	C₄⋊C₄	—	41	4	no	—
41	C₄⋊C₄	—	41	4	no	—
42	C₄⋊C₄	—	41	2	no	—
43	C₄⋊C₄	—	41	2	no	—
44	C₄⋊C₄	C₂×D₄₁	1	2	yes	—
45	C₄⋊C₄	C₂×D₄₁	1	4	yes	—
46	C₄²	—	41	4	no	—
47	C₄²	C₂×D₄₁	1	1	yes	characteristic
48	C₂×C₄	—	41	4	no	—
49	C₂×C₄	—	41	4	no	—
50	C₂×C₄	C₂²×D₄₁	1	4	yes	—
51	C₂×C₄	C₂²×D₄₁	1	2	yes	—
52	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
53	C₂²	C₂³×D₄₁	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	82	4	no	—
58	C₄	—	82	4	no	—
59	C₂	#13050211	1	2	yes	—
60	C₂	#13050212	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₁
commutator, socle, prime radical, cosocle	C₂²×C₄₁	C₂⁴
Fitting	#125×C₄₁	C₂
hypercenter	#125	D₄₁
hypocenter	C₄₁	#564
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
31. C₄₁	#564	semidirect

Maximal subgroups

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

subgroup	index
#13050156	2
#13050155	2
#13050154	2
#125×C₄₁	2
#564	41

Subgroups — C41⋊#564 #14581091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁⋊#564 #14581091