Subgroups — #46855806

Order 35008.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31776048	C₂	1	2	yes	maximal, complemented
2	#31776030	C₂	1	6	yes	maximal, complemented
3	#31776024	C₂	1	3	yes	maximal, complemented
4	C₂×D₄₃₇₆	C₂	1	3	yes	maximal, complemented
5	#131×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#22576777	—	2	2	no	—
7	#22576776	C₂²	1	6	yes	complemented
8	C₂×D₂₁₈₈	C₂²	1	6	yes	complemented
9	D₄×D₅₄₇	—	2	6	no	—
10	Dic₂₁₈₈	C₂²	1	1	yes	characteristic, complemented
11	#22576765	C₂²	1	6	yes	complemented
12	D₄₃₇₆	C₂²	1	3	yes	complemented
13	D₄₃₇₆	C₂²	1	6	yes	complemented
14	#41×C₅₄₇	C₂²	1	1	yes	characteristic
15	M₁₆×C₅₄₇	C₂²	1	3	yes	complemented
16	C₂×C₈×C₅₄₇	C₂²	1	3	yes	complemented
17	C₂²×D₅₄₇	—	2	6	no	—
18	Dic₁₀₉₄	C₂³	1	2	yes	—
19	D₂₁₈₈	—	2	6	no	—
20	D₂₁₈₈	C₂³	1	6	yes	—
21	C₂²⋊D₅₄₇	—	2	6	no	—
22	C₄×D₅₄₇	—	2	6	no	—
23	Q₈×C₅₄₇	D₄	1	1	yes	characteristic
24	D₄×C₅₄₇	D₄	1	3	yes	—
25	C₂×C₄×C₅₄₇	C₂³	1	3	yes	—
26	C₈×C₅₄₇	C₂³	1	1	yes	characteristic
27	C₈×C₅₄₇	C₂³	1	3	yes	—
28	C₂²×C₅₄₇	C₂×D₄	1	3	yes	—
29	C₂×D₅₄₇	—	2	6	no	—
30	C₂×D₅₄₇	—	8	6	no	—
31	C₄×C₅₄₇	C₂×D₄	1	3	yes	—
32	C₄×C₅₄₇	C₂⁴	1	1	yes	characteristic
33	Dic₅₄₇	—	2	2	no	—
34	C₂×C₅₄₇	—	2	3	no	—
35	C₂×C₅₄₇	C₂²×D₄	1	1	yes	characteristic
36	D₅₄₇	—	4	6	no	—
37	C₅₄₇	#576	1	1	yes	characteristic, complemented, Sylow
38	#576	—	547	1	no	maximal, Sylow
39	H(5,𝔽₂)	—	547	2	no	—
40	AGL(1,ℤ/8)	—	547	6	no	—
41	#135	—	547	3	no	—
42	C₂×D₈	—	547	3	no	—
43	#131	D₅₄₇	1	1	yes	characteristic, complemented
44	#41	—	547	6	no	—
45	#41	—	1094	2	no	—
46	#41	C₂×D₅₄₇	1	1	yes	characteristic
47	C₂×D₄	—	547	6	no	—
48	C₂×D₄	—	1094	6	no	—
49	Q₁₆	—	547	1	no	—
50	SD₁₆	—	547	6	no	—
51	D₈	—	547	3	no	—
52	D₈	—	547	6	no	—
53	M₁₆	C₂×D₅₄₇	1	3	yes	complemented
54	C₂×C₈	C₂×D₅₄₇	1	3	yes	complemented
55	C₂³	—	1094	6	no	—
56	Q₈	—	547	2	no	—
57	Q₈	D₂₁₈₈	1	1	yes	characteristic
58	D₄	—	547	6	no	—
59	D₄	—	1094	6	no	—
60	D₄	—	1094	6	no	—
61	D₄	D₂₁₈₈	1	3	yes	—
62	C₂×C₄	—	1094	6	no	—
63	C₂×C₄	C₂²×D₅₄₇	1	3	yes	—
64	C₈	C₂²×D₅₄₇	1	1	yes	characteristic
65	C₈	C₂²×D₅₄₇	1	3	yes	—
66	C₂²	—	4376	6	no	—
67	C₂²	—	1094	6	no	—
68	C₂²	C₂×D₂₁₈₈	1	3	yes	—
69	C₄	—	1094	2	no	—
70	C₄	C₂×D₂₁₈₈	1	3	yes	—
71	C₄	C₂³×D₅₄₇	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	2188	6	no	—
74	C₂	C₂²×D₂₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₂₁₈₈
commutator, cosocle	C₄×C₅₄₇	C₂⁴
Frattini	C₄	C₂³×D₅₄₇
Fitting	#131×C₅₄₇	C₂
socle	C₂×C₅₄₇	C₂²×D₄
hypercenter	#131	D₅₄₇
hypocenter	C₅₄₇	#576
LCS	G ▷ C₄×C₅₄₇ ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #31776048	C₂	semidirect
2. #31776030	C₂	semidirect
3. #31776024	C₂	semidirect
4. C₂×D₄₃₇₆	C₂	semidirect
5. #131×C₅₄₇	C₂	semidirect
7. #22576776	C₂²	semidirect
8. C₂×D₂₁₈₈	C₂²	semidirect
10. Dic₂₁₈₈	C₂²	semidirect
11. #22576765	C₂²	semidirect
12. D₄₃₇₆	C₂²	semidirect
13. D₄₃₇₆	C₂²	semidirect
15. M₁₆×C₅₄₇	C₂²	semidirect
16. C₂×C₈×C₅₄₇	C₂²	semidirect
37. C₅₄₇	#576	semidirect
43. #131	D₅₄₇	semidirect
53. M₁₆	C₂×D₅₄₇	semidirect
54. C₂×C₈	C₂×D₅₄₇	semidirect

Maximal subgroups

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

subgroup	index
#31776048	2
#31776030	2
#31776024	2
C₂×D₄₃₇₆	2
#131×C₅₄₇	2
#576	547