Subgroups — #46830582

Order 34624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772627	C₂	1	1	yes	maximal, characteristic
2	#31772619	C₂	1	1	yes	maximal, characteristic
3	#31772562	C₂	1	1	yes	maximal, characteristic
4	#31772561	C₂	1	1	yes	maximal, characteristic
5	#31772559	C₂	1	1	yes	maximal, characteristic
6	#31772538	C₂	1	1	yes	maximal, characteristic
7	#106×C₅₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₀₈₂	—	2	1	no	—
9	C₂×#16864513	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₅₄₁	—	2	1	no	—
11	C₄⋊Dic₅₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₅₄₁	C₂²	1	1	yes	characteristic
13	#22575815	—	2	1	no	—
14	#22575815	—	2	1	no	—
15	C₄×Dic₅₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₅₄₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₅₄₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₅₄₁	C₂²	1	1	yes	characteristic
19	Dic₁₀₈₂	—	4	2	no	—
20	C₂×Dic₅₄₁	—	2	1	no	—
21	C₂×Dic₅₄₁	—	2	1	no	—
22	C₂×Dic₅₄₁	D₄	1	1	yes	characteristic
23	C₂×Dic₅₄₁	D₄	1	1	yes	characteristic
24	#16864513	Q₈	1	2	yes	complemented
25	C₂×C₄×C₅₄₁	—	2	1	no	—
26	C₂×C₄×C₅₄₁	—	2	1	no	—
27	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
28	C₈×C₅₄₁	Q₈	1	2	yes	complemented
29	C₂²×C₅₄₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₅₄₁	—	4	1	no	—
31	C₄×C₅₄₁	—	4	1	no	—
32	C₄×C₅₄₁	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₅₄₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₅₄₁	—	2	1	no	—
35	Dic₅₄₁	—	2	1	no	—
36	Dic₅₄₁	—	4	1	no	—
37	Dic₅₄₁	—	4	1	no	—
38	C₂×C₅₄₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₅₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₅₄₁	#137	1	1	yes	characteristic
41	C₅₄₁	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	541	1	no	maximal, Sylow
43	C₄⋊Q₈	—	541	1	no	—
44	#125	—	541	1	no	—
45	#107	—	541	1	no	—
46	#107	—	541	1	no	—
47	#106	—	541	1	no	—
48	#106	D₅₄₁	1	1	yes	characteristic
49	#97	—	541	1	no	—
50	C₂×Q₈	—	1082	1	no	—
51	C₂×C₈	—	541	1	no	—
52	C₂×C₈	C₂×D₅₄₁	1	1	yes	characteristic
53	C₄⋊C₄	—	541	1	no	—
54	C₄⋊C₄	—	541	1	no	—
55	C₄⋊C₄	—	1082	1	no	—
56	C₄⋊C₄	—	1082	1	no	—
57	C₄⋊C₄	—	1082	1	no	—
58	C₄⋊C₄	C₂×D₅₄₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₅₄₁	1	1	yes	characteristic
60	C₄²	—	541	1	no	—
61	Q₈	—	2164	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	541	1	no	—
65	C₂×C₄	—	541	1	no	—
66	C₂×C₄	—	1082	1	no	—
67	C₂×C₄	—	1082	1	no	—
68	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
69	C₈	—	541	2	no	—
70	C₈	Dic₁₀₈₂	1	2	yes	complemented
71	C₂²	D₄×D₅₄₁	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	1082	1	no	—
75	C₄	—	1082	1	no	—
76	C₄	—	2164	1	no	—
77	C₄	—	2164	1	no	—
78	C₄	Q₈×D₅₄₁	1	1	yes	characteristic
79	C₄	C₂×Dic₁₀₈₂	1	1	yes	characteristic
80	C₂	#31772627	1	1	yes	characteristic
81	C₂	#31772655	1	1	yes	characteristic
82	C₂	#31772657	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₄₁
commutator, cosocle	C₂×C₄×C₅₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₅₄₁
Fitting	#106×C₅₄₁	C₂
socle, prime radical	C₂²×C₅₄₁	C₂×D₄
hypercenter	#106	D₅₄₁
hypocenter	C₅₄₁	#501
LCS	G ▷ C₂×C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
24. #16864513	Q₈	semidirect
28. C₈×C₅₄₁	Q₈	semidirect
41. C₅₄₁	#501	semidirect
70. C₈	Dic₁₀₈₂	semidirect

Maximal subgroups

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

subgroup	index
#31772627	2
#31772619	2
#31772562	2
#31772561	2
#31772559	2
#31772538	2
#106×C₅₄₁	2
#501	541