Subgroups — #45688347

Order 33344.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659781	C₂	1	1	yes	maximal, characteristic, complemented
2	#30659779	C₂	1	1	yes	maximal, characteristic, complemented
3	#30659731	C₂	1	1	yes	maximal, characteristic
4	#22552374	—	2	1	no	—
5	#22552367	—	2	1	no	—
6	#22552365	—	2	1	no	—
7	#22552351	—	2	1	no	—
8	D₄₁₆₈	C₄	1	1	yes	characteristic
9	C₈×D₅₂₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₅₂₁	C₄	1	1	yes	characteristic
11	#16861967	—	4	1	no	—
12	D₂₀₈₄	—	2	1	no	—
13	D₂₀₈₄	—	4	1	no	—
14	C₄×D₅₂₁	—	4	1	no	—
15	C₄×D₅₂₁	D₄	1	1	yes	characteristic
16	#16861960	D₄	1	1	yes	characteristic
17	Q₈×C₅₂₁	—	2	1	no	—
18	C₈×C₅₂₁	C₂×C₄	1	1	yes	characteristic
19	C₂×D₅₂₁	—	4	1	no	—
20	C₂×D₅₂₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₅₂₁	—	4	1	no	—
22	C₄×C₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₅₂₁	D₈	1	1	yes	characteristic
24	C₂×C₅₂₁	#102	1	1	yes	characteristic
25	D₅₂₁	—	2	1	no	—
26	D₅₂₁	—	8	1	no	—
27	C₅₂₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	521	1	no	maximal, Sylow
29	#135	—	521	1	no	—
30	C₂×C₁₆	—	521	1	no	—
31	#108	—	521	1	no	—
32	#41	—	1042	1	no	—
33	Q₁₆	#14523438	1	1	yes	characteristic
34	SD₁₆	—	1042	1	no	—
35	D₈	—	521	1	no	—
36	M₁₆	—	1042	1	no	—
37	C₂×C₈	—	521	1	no	—
38	C₁₆	—	1042	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	1042	1	no	—
41	D₄	—	2084	1	no	—
42	C₂×C₄	—	521	1	no	—
43	C₂×C₄	—	2084	1	no	—
44	C₈	—	521	1	no	—
45	C₈	—	2084	1	no	—
46	C₈	C₂×#14523438	1	1	yes	characteristic
47	C₂²	—	521	1	no	—
48	C₂²	—	2084	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	521	1	no	—
51	C₄	C₂²⋊#14523438	1	1	yes	characteristic
52	C₂	—	1042	1	no	—
53	C₂	—	4168	1	no	—
54	C₂	#30659770	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30659770
commutator	C₈×C₅₂₁	C₂×C₄
Frattini	C₈	C₂×#14523438
Fitting	Q₁₆×C₅₂₁	C₄
socle	C₂×C₅₂₁	#102
prime radical	#30659731	C₂
cosocle	C₈×D₅₂₁	C₂²
hypercenter	Q₁₆	#14523438
hypocenter	C₅₂₁	#359
LCS	G ▷ C₈×C₅₂₁ ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #30659781	C₂	semidirect
2. #30659779	C₂	semidirect
27. C₅₂₁	#359	semidirect

Maximal subgroups

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

subgroup	index
#30659781	2
#30659779	2
#30659731	2
#359	521