Subgroups — #46855443

Order 35008.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31776025	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×D₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#31775948	C₂	1	1	yes	maximal, characteristic, complemented
4	#31775947	C₂	1	1	yes	maximal, characteristic, complemented
5	#31775945	C₂	1	1	yes	maximal, characteristic, complemented
6	#31775941	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₃₂×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#22576777	—	2	1	no	—
9	Q₈×D₅₄₇	—	2	1	no	—
10	Dic₂₁₈₈	C₂²	1	1	yes	characteristic
11	#22576766	—	2	1	no	—
12	#22576763	—	2	1	no	—
13	D₄₃₇₆	C₂²	1	1	yes	characteristic
14	C₈×D₅₄₇	C₂²	1	1	yes	characteristic
15	C₅₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
16	Q₁₆×C₅₄₇	C₂²	1	1	yes	characteristic
17	Q₁₆×C₅₄₇	C₂²	1	1	yes	characteristic
18	C₁₆×C₅₄₇	C₂²	1	1	yes	characteristic
19	Dic₁₀₉₄	—	2	1	no	—
20	Dic₁₀₉₄	—	4	1	no	—
21	D₂₁₈₈	—	2	1	no	—
22	D₂₁₈₈	—	4	1	no	—
23	C₄×D₅₄₇	—	4	1	no	—
24	C₄×D₅₄₇	—	4	1	no	—
25	C₄×D₅₄₇	D₄	1	1	yes	characteristic
26	C₅₄₇⋊C₈	D₄	1	1	yes	characteristic
27	Q₈×C₅₄₇	—	2	1	no	—
28	Q₈×C₅₄₇	—	2	1	no	—
29	C₈×C₅₄₇	C₂³	1	1	yes	characteristic
30	C₂×D₅₄₇	—	4	1	no	—
31	C₂×D₅₄₇	D₈	1	1	yes	characteristic
32	C₄×C₅₄₇	—	4	1	no	—
33	C₄×C₅₄₇	—	4	1	no	—
34	C₄×C₅₄₇	C₂×D₄	1	1	yes	characteristic
35	Dic₅₄₇	—	4	1	no	—
36	Dic₅₄₇	D₈	1	1	yes	characteristic
37	C₂×C₅₄₇	C₂×D₈	1	1	yes	characteristic
38	D₅₄₇	—	2	1	no	—
39	D₅₄₇	—	8	1	no	—
40	C₅₄₇	#510	1	1	yes	characteristic, complemented, Sylow
41	#510	—	547	1	no	maximal, Sylow
42	#135	—	547	1	no	—
43	C₂×Q₁₆	—	547	1	no	—
44	Q₃₂	—	547	1	no	—
45	Q₃₂	D₅₄₇	1	1	yes	characteristic, complemented
46	SD₃₂	—	547	1	no	—
47	SD₃₂	—	547	1	no	—
48	M₃₂	—	547	1	no	—
49	#41	—	1094	1	no	—
50	C₂×Q₈	—	1094	1	no	—
51	Q₁₆	—	547	1	no	—
52	Q₁₆	—	1094	1	no	—
53	Q₁₆	C₂×D₅₄₇	1	1	yes	characteristic
54	Q₁₆	C₂×D₅₄₇	1	1	yes	characteristic
55	SD₁₆	—	1094	1	no	—
56	D₈	—	547	1	no	—
57	C₂×C₈	—	547	1	no	—
58	C₁₆	—	547	1	no	—
59	C₁₆	C₂×D₅₄₇	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	2	1	no	—
62	Q₈	—	1094	1	no	—
63	Q₈	—	2188	1	no	—
64	D₄	—	1094	1	no	—
65	D₄	—	2188	1	no	—
66	C₂×C₄	—	547	1	no	—
67	C₂×C₄	—	2188	1	no	—
68	C₂×C₄	—	2188	1	no	—
69	C₈	—	547	1	no	—
70	C₈	C₂²×D₅₄₇	1	1	yes	characteristic
71	C₂²	—	547	1	no	—
72	C₂²	—	2188	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	4	1	no	—
75	C₄	—	547	1	no	—
76	C₄	—	2188	1	no	—
77	C₄	D₄×D₅₄₇	1	1	yes	characteristic
78	C₂	—	4376	1	no	—
79	C₂	—	1094	1	no	—
80	C₂	D₈×D₅₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₅₄₇
commutator, cosocle	C₈×C₅₄₇	C₂³
Frattini	C₈	C₂²×D₅₄₇
Fitting	Q₃₂×C₅₄₇	C₂
socle	C₂×C₅₄₇	C₂×D₈
prime radical	#31776025	C₂
hypercenter	Q₃₂	D₅₄₇
hypocenter	C₅₄₇	#510
LCS	G ▷ C₈×C₅₄₇ ▷ C₄×C₅₄₇ ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Q₁₆×D₅₄₇	C₂	semidirect
3. #31775948	C₂	semidirect
4. #31775947	C₂	semidirect
5. #31775945	C₂	semidirect
6. #31775941	C₂	semidirect
7. Q₃₂×C₅₄₇	C₂	semidirect
40. C₅₄₇	#510	semidirect
45. Q₃₂	D₅₄₇	semidirect

Maximal subgroups

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

subgroup	index
#31776025	2
Q₁₆×D₅₄₇	2
#31775948	2
#31775947	2
#31775945	2
#31775941	2
Q₃₂×C₅₄₇	2
#510	547