Subgroups — #44537129

Order 31424.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628336	C₂	1	2	yes	maximal
2	#30628271	C₂	1	1	yes	maximal, characteristic
3	#30628270	C₂	1	2	yes	maximal
4	C₈×Dic₄₉₁	C₂	1	1	yes	maximal, characteristic
5	#107×C₄₉₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₈₂	—	2	2	no	—
7	C₂×C₄₉₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₉₁	C₂²	1	2	yes	—
9	Dic₄₉₁⋊C₄	—	2	2	no	—
10	C₄×Dic₄₉₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₉₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₉₁	C₂²	1	2	yes	—
13	Dic₉₈₂	—	4	4	no	—
14	C₂×Dic₄₉₁	—	2	2	no	—
15	C₂×Dic₄₉₁	D₄	1	1	yes	characteristic
16	C₂×Dic₄₉₁	D₄	1	1	yes	characteristic
17	C₄₉₁⋊C₈	Q₈	1	2	yes	complemented
18	C₂×C₄×C₄₉₁	—	2	2	no	—
19	C₂×C₄×C₄₉₁	C₂³	1	1	yes	characteristic
20	C₈×C₄₉₁	Q₈	1	2	yes	complemented
21	C₂²×C₄₉₁	C₂×D₄	1	1	yes	characteristic
22	C₄×C₄₉₁	—	4	2	no	—
23	C₄×C₄₉₁	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₄₉₁	C₂×Q₈	1	1	yes	characteristic
25	Dic₄₉₁	—	4	2	no	—
26	Dic₄₉₁	D₈	1	2	yes	—
27	Dic₄₉₁	Q₁₆	1	2	yes	—
28	C₂×C₄₉₁	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₄₉₁	C₂×D₈	1	1	yes	characteristic
30	C₂×C₄₉₁	C₂×Q₁₆	1	1	yes	characteristic
31	C₄₉₁	#500	1	1	yes	characteristic, complemented, Sylow
32	#500	—	491	1	no	maximal, Sylow
33	C₄⋊Q₈	—	491	2	no	—
34	#107	—	491	1	no	—
35	#107	—	491	2	no	—
36	#107	D₄₉₁	1	1	yes	characteristic
37	C₄×C₈	—	491	1	no	—
38	C₂×Q₈	—	982	2	no	—
39	C₂×C₈	—	491	1	no	—
40	C₂×C₈	C₂×D₄₉₁	1	1	yes	characteristic
41	C₄⋊C₄	—	982	2	no	—
42	C₄⋊C₄	—	491	2	no	—
43	C₄⋊C₄	C₂×D₄₉₁	1	2	yes	—
44	C₄²	—	491	1	no	—
45	Q₈	—	1964	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	982	2	no	—
48	C₂×C₄	—	491	1	no	—
49	C₂×C₄	—	491	1	no	—
50	C₂×C₄	C₂²×D₄₉₁	1	1	yes	characteristic
51	C₈	—	491	2	no	—
52	C₈	Dic₉₈₂	1	2	yes	complemented
53	C₂²	D₄×D₄₉₁	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	1964	2	no	—
56	C₄	—	491	2	no	—
57	C₄	—	491	2	no	—
58	C₄	Q₈×D₄₉₁	1	1	yes	characteristic
59	C₄	C₂×Dic₉₈₂	1	1	yes	characteristic
60	C₂	#30628336	1	1	yes	characteristic
61	C₂	D₈×D₄₉₁	1	1	yes	characteristic
62	C₂	Q₁₆×D₄₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₉₁
commutator, cosocle	C₂×C₄×C₄₉₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₉₁
Fitting	#107×C₄₉₁	C₂
socle, prime radical	C₂²×C₄₉₁	C₂×D₄
hypercenter	#107	D₄₉₁
hypocenter	C₄₉₁	#500
LCS	G ▷ C₂×C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
17. C₄₉₁⋊C₈	Q₈	semidirect
20. C₈×C₄₉₁	Q₈	semidirect
31. C₄₉₁	#500	semidirect
52. C₈	Dic₉₈₂	semidirect

Maximal subgroups

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

subgroup	index
#30628336	2
#30628271	2
#30628270	2
C₈×Dic₄₉₁	2
#107×C₄₉₁	2
#500	491