Subgroups — #46854733

Order 35008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₀₉₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₅₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₅₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₉₄	C₄	1	1	yes	characteristic
5	C₂×C₅₄₇⋊C₈	—	2	1	no	—
6	C₄⋊Dic₅₄₇	C₄	1	1	yes	characteristic
7	Dic₅₄₇⋊C₄	—	2	1	no	—
8	C₄×Dic₅₄₇	—	2	1	no	—
9	C₂×C₈×C₅₄₇	—	2	1	no	—
10	C₄²×C₅₄₇	C₂²	1	1	yes	characteristic
11	Dic₁₀₉₄	—	2	1	no	—
12	Dic₁₀₉₄	C₈	1	2	yes	complemented
13	C₂×Dic₅₄₇	—	2	1	no	—
14	C₂×Dic₅₄₇	—	2	1	no	—
15	C₅₄₇⋊C₈	—	4	1	no	—
16	C₂×C₄×C₅₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅₄₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₅₄₇	D₄	1	1	yes	characteristic
19	C₈×C₅₄₇	—	2	2	no	—
20	C₂²×C₅₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₅₄₇	—	2	1	no	—
22	C₄×C₅₄₇	C₂×C₈	1	1	yes	characteristic
23	C₄×C₅₄₇	M₁₆	1	1	yes	characteristic
24	C₄×C₅₄₇	SD₁₆	1	1	yes	characteristic
25	C₄×C₅₄₇	Q₁₆	1	1	yes	characteristic
26	Dic₅₄₇	—	2	2	no	—
27	Dic₅₄₇	—	4	1	no	—
28	C₂×C₅₄₇	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₅₄₇	#103	1	1	yes	characteristic
30	C₂×C₅₄₇	#104	1	1	yes	characteristic
31	C₅₄₇	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	547	1	no	maximal, Sylow
33	C₄×Q₈	—	547	1	no	—
34	C₄⋊C₈	—	547	1	no	—
35	C₄×C₈	D₅₄₇	1	1	yes	characteristic
36	C₂×Q₈	—	547	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	—	1094	1	no	—
39	C₄⋊C₄	—	547	1	no	—
40	C₄⋊C₄	—	1094	1	no	—
41	C₄²	—	1094	1	no	—
42	C₄²	C₂×D₅₄₇	1	1	yes	characteristic
43	Q₈	—	547	2	no	—
44	Q₈	—	1094	1	no	—
45	C₂×C₄	—	1094	1	no	—
46	C₂×C₄	—	1094	1	no	—
47	C₂×C₄	C₄×D₅₄₇	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₅₄₇	1	1	yes	characteristic
49	C₂×C₄	D₂₁₈₈	1	1	yes	characteristic
50	C₈	—	2	2	no	—
51	C₈	—	2188	1	no	—
52	C₂²	(C₂×D₅₄₇)⋊C₄	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	1094	2	no	—
55	C₄	—	2188	1	no	—
56	C₄	C₈×D₅₄₇	1	1	yes	characteristic
57	C₄	#22576759	1	1	yes	characteristic
58	C₄	#22576765	1	1	yes	characteristic
59	C₄	Dic₂₁₈₈	1	1	yes	characteristic
60	C₂	(C₂×D₅₄₇)⋊C₈	1	1	yes	characteristic
61	C₂	#31775927	1	1	yes	characteristic
62	C₂	#31775930	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₁₈₈
commutator	C₄×C₅₄₇	C₂×C₈
Frattini	C₄²	C₂×D₅₄₇
Fitting	C₄×C₈×C₅₄₇	C₂
socle, prime radical	C₂²×C₅₄₇	C₂²⋊C₄
cosocle	C₄²×C₅₄₇	C₂²
hypercenter	C₄×C₈	D₅₄₇
hypocenter	C₅₄₇	Q₈⋊C₈
LCS	G ▷ C₄×C₅₄₇ ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
12. Dic₁₀₉₄	C₈	semidirect
31. C₅₄₇	Q₈⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₁₀₉₄	2
C₄⋊(C₅₄₇⋊C₈)	2
C₄×C₈×C₅₄₇	2
Q₈⋊C₈	547