Subgroups — #46855433

Order 35008.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31776024	C₂	1	2	yes	maximal, complemented
2	Dic₄₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#31775947	C₂	1	2	yes	maximal, complemented
4	D₈₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#22576776	—	2	2	no	—
7	Dic₂₁₈₈	C₂²	1	2	yes	—
8	#22576765	—	2	2	no	—
9	D₄₃₇₆	C₂²	1	2	yes	—
10	C₂×C₈×C₅₄₇	C₂²	1	1	yes	characteristic
11	C₁₆×C₅₄₇	C₂²	1	1	yes	characteristic
12	C₁₆×C₅₄₇	C₂²	1	1	yes	characteristic
13	Dic₁₀₉₄	—	2	2	no	—
14	D₂₁₈₈	—	2	2	no	—
15	C₂²⋊D₅₄₇	—	4	2	no	—
16	C₄×D₅₄₇	—	4	2	no	—
17	C₂×C₄×C₅₄₇	D₄	1	1	yes	characteristic
18	C₈×C₅₄₇	D₄	1	1	yes	characteristic
19	C₈×C₅₄₇	C₂³	1	1	yes	characteristic
20	C₂²×C₅₄₇	D₈	1	1	yes	characteristic
21	C₂×D₅₄₇	—	4	2	no	—
22	C₄×C₅₄₇	D₈	1	1	yes	characteristic
23	C₄×C₅₄₇	C₂×D₄	1	1	yes	characteristic
24	Dic₅₄₇	—	4	2	no	—
25	C₂×C₅₄₇	—	2	1	no	—
26	C₂×C₅₄₇	C₂×D₈	1	1	yes	characteristic
27	D₅₄₇	—	8	2	no	—
28	C₅₄₇	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	547	1	no	maximal, Sylow
30	#135	—	547	2	no	—
31	Q₃₂	—	547	1	no	—
32	SD₃₂	—	547	2	no	—
33	D₁₆	—	547	1	no	—
34	C₂×C₁₆	D₅₄₇	1	1	yes	characteristic, complemented
35	#41	—	1094	2	no	—
36	Q₁₆	—	547	2	no	—
37	SD₁₆	—	1094	2	no	—
38	D₈	—	547	2	no	—
39	C₂×C₈	C₂×D₅₄₇	1	1	yes	characteristic
40	C₁₆	C₂×D₅₄₇	1	1	yes	characteristic
41	C₁₆	C₂×D₅₄₇	1	1	yes	characteristic
42	Q₈	—	1094	2	no	—
43	D₄	—	1094	2	no	—
44	D₄	—	2188	2	no	—
45	C₂×C₄	—	2188	2	no	—
46	C₂×C₄	D₂₁₈₈	1	1	yes	characteristic
47	C₈	D₂₁₈₈	1	1	yes	characteristic
48	C₈	C₂²×D₅₄₇	1	1	yes	characteristic
49	C₂²	—	2188	2	no	—
50	C₂²	D₄₃₇₆	1	1	yes	characteristic
51	C₄	—	2188	2	no	—
52	C₄	D₄₃₇₆	1	1	yes	characteristic
53	C₄	C₂×D₂₁₈₈	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	4376	2	no	—
56	C₂	C₂×D₄₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄₃₇₆
commutator, cosocle	C₈×C₅₄₇	C₂³
Frattini	C₈	C₂²×D₅₄₇
Fitting	C₂×C₁₆×C₅₄₇	C₂
socle	C₂×C₅₄₇	C₂×D₈
hypercenter	C₂×C₁₆	D₅₄₇
hypocenter	C₅₄₇	#508
LCS	G ▷ C₈×C₅₄₇ ▷ C₄×C₅₄₇ ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #31776024	C₂	semidirect
2. Dic₄₃₇₆	C₂	semidirect
3. #31775947	C₂	semidirect
4. D₈₇₅₂	C₂	semidirect
5. C₂×C₁₆×C₅₄₇	C₂	semidirect
28. C₅₄₇	#508	semidirect
34. C₂×C₁₆	D₅₄₇	semidirect

Maximal subgroups

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

subgroup	index
#31776024	2
Dic₄₃₇₆	2
#31775947	2
D₈₇₅₂	2
C₂×C₁₆×C₅₄₇	2
#508	547