Subgroups — #46830002

Order 34624.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575811	C₂	1	1	yes	maximal, characteristic
2	#31772562	C₂	1	1	yes	maximal, characteristic
3	#107×C₅₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₅₄₁	—	2	1	no	—
5	#22575811	C₄	1	2	yes	complemented
6	C₂×C₈×C₅₄₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₅₄₁	—	2	1	no	—
8	C₂×Dic₅₄₁	—	4	1	no	—
9	C₂×C₄×C₅₄₁	—	4	1	no	—
10	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
11	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₅₄₁	Q₈	1	1	yes	characteristic
13	C₂²×C₅₄₁	D₈	1	1	yes	characteristic
14	C₄×C₅₄₁	—	8	1	no	—
15	C₄×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₅₄₁	Q₁₆	1	1	yes	characteristic
17	Dic₅₄₁	—	8	1	no	—
18	C₂×C₅₄₁	#107	1	1	yes	characteristic
19	C₂×C₅₄₁	SD₃₂	1	1	yes	characteristic
20	C₂×C₅₄₁	SD₃₂	1	1	yes	characteristic
21	C₅₄₁	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	541	1	no	maximal, Sylow
23	C₂×C₁₆	—	541	1	no	—
24	#107	—	541	1	no	—
25	#107	D₅₄₁	1	1	yes	characteristic
26	C₂×C₈	C₂×D₅₄₁	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	1082	1	no	—
29	C₁₆	—	541	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	2164	1	no	—
32	C₂×C₄	C₂²⋊D₅₄₁	1	1	yes	characteristic
33	C₈	C₄×D₅₄₁	1	1	yes	characteristic
34	C₈	Dic₁₀₈₂	1	1	yes	characteristic
35	C₂²	#22575821	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	4328	1	no	—
38	C₄	#22575815	1	1	yes	characteristic
39	C₄	#22575826	1	1	yes	characteristic
40	C₂	#31772561	1	1	yes	characteristic
41	C₂	#31772571	1	1	yes	characteristic
42	C₂	#31772572	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575821
commutator	C₈×C₅₄₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₅₄₁
Fitting	#107×C₅₄₁	C₂
socle, prime radical	C₂²×C₅₄₁	D₈
cosocle	C₂×C₈×C₅₄₁	C₂²
hypercenter	#107	D₅₄₁
hypocenter	C₅₄₁	#367
LCS	G ▷ C₈×C₅₄₁ ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. #22575811	C₄	semidirect
21. C₅₄₁	#367	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575811	2
#31772562	2
#107×C₅₄₁	2
#367	541