Subgroups — #45688290

Order 33344.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659775	C₂	1	2	yes	maximal, complemented
2	#30659704	C₂	1	1	yes	maximal, characteristic
3	C₂×#16861967	—	2	2	no	—
4	C₂×D₂₀₈₄	C₄	1	1	yes	characteristic
5	C₂×C₂²⋊D₅₂₁	—	2	2	no	—
6	C₄×Dic₅₂₁	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₅₂₁	C₄	1	1	yes	characteristic
8	#16861967	—	4	2	no	—
9	C₂²×D₅₂₁	—	2	1	no	—
10	D₂₀₈₄	—	4	1	no	—
11	C₂²⋊D₅₂₁	—	4	2	no	—
12	C₂²⋊D₅₂₁	—	4	2	no	—
13	C₂×Dic₅₂₁	D₄	1	2	yes	—
14	C₂³×C₅₂₁	—	2	1	no	—
15	D₄×C₅₂₁	—	4	1	no	—
16	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₅₂₁	—	4	1	no	—
18	C₂²×C₅₂₁	—	4	2	no	—
19	C₂²×C₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×D₅₂₁	—	4	1	no	—
21	C₂×D₅₂₁	—	4	2	no	—
22	C₄×C₅₂₁	—	2	1	no	—
23	Dic₅₂₁	D₈	1	2	yes	—
24	Dic₅₂₁	SD₁₆	1	2	yes	—
25	C₂×C₅₂₁	—	8	1	no	—
26	C₂×C₅₂₁	#100	1	1	yes	characteristic
27	C₂×C₅₂₁	#102	1	2	yes	—
28	D₅₂₁	—	8	1	no	—
29	C₅₂₁	#331	1	1	yes	characteristic, complemented, Sylow
30	#331	—	521	1	no	maximal, Sylow
31	#127	—	521	1	no	—
32	C₄⋊C₈	—	521	2	no	—
33	C₂×D₄	—	521	1	no	—
34	C₂×D₄	—	1042	2	no	—
35	C₂×D₄	#14523438	1	1	yes	characteristic
36	C₂×C₈	—	1042	2	no	—
37	C₄²	—	521	1	no	—
38	C₂³	—	2	1	no	—
39	C₂³	—	1042	1	no	—
40	D₄	—	4	1	no	—
41	D₄	—	2084	1	no	—
42	D₄	—	2084	2	no	—
43	D₄	—	2084	2	no	—
44	C₂×C₄	—	521	2	no	—
45	C₂×C₄	C₂×#14523438	1	1	yes	characteristic
46	C₈	—	2084	2	no	—
47	C₂²	—	4	1	no	—
48	C₂²	—	4	2	no	—
49	C₂²	—	2084	1	no	—
50	C₂²	—	2084	2	no	—
51	C₂²	C₂²⋊#14523438	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	521	2	no	—
54	C₄	—	521	2	no	—
55	C₂	—	8	1	no	—
56	C₂	—	4168	1	no	—
57	C₂	#30659768	1	1	yes	characteristic
58	C₂	#30659770	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²⋊#14523438
commutator	C₂×C₄×C₅₂₁	C₂×C₄
Frattini	C₂×C₄	C₂×#14523438
Fitting	C₂×D₄×C₅₂₁	C₄
socle	C₂²×C₅₂₁	C₂²⋊C₄
prime radical	#30659704	C₂
cosocle	C₄×Dic₅₂₁	C₂²
hypercenter	C₂×D₄	#14523438
hypocenter	C₅₂₁	#331
LCS	G ▷ C₂×C₄×C₅₂₁ ▷ C₂²×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #30659775	C₂	semidirect
29. C₅₂₁	#331	semidirect

Maximal subgroups

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

subgroup	index
#30659775	2
#30659704	2
#331	521