Subgroups — #46831185

Order 34624.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772707	C₂	1	2	yes	maximal
2	#31772697	C₂	1	2	yes	maximal, complemented
3	#31772696	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#14524194	C₂²	1	4	yes	—
6	C₂²⋊#14524194	—	2	2	no	—
7	C₄×#14524194	—	2	2	no	—
8	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
9	C₂×#16864513	C₄	1	1	yes	characteristic, complemented
10	C₈×D₅₄₁	C₄	1	1	yes	characteristic, complemented
11	C₈×D₅₄₁	C₄	1	1	yes	characteristic, complemented
12	C₈×D₅₄₁	C₂²	1	1	yes	characteristic
13	C₈×D₅₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
15	C₂×#14524194	—	2	4	no	—
16	C₂²×D₅₄₁	D₄	1	1	yes	characteristic
17	C₂×Dic₅₄₁	Q₈	1	1	yes	characteristic
18	C₄×D₅₄₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₅₄₁	D₄	1	1	yes	characteristic
20	C₄×D₅₄₁	Q₈	1	1	yes	characteristic
21	C₄×D₅₄₁	C₂³	1	1	yes	characteristic
22	#16864513	C₂×C₄	1	1	yes	characteristic
23	#16864513	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
25	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
26	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₅₄₁	—	2	2	no	—
29	C₂×D₅₄₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₅₄₁	C₂×D₄	1	1	yes	characteristic
31	#14524194	—	4	4	no	—
32	C₄×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
34	Dic₅₄₁	C₄⋊C₄	1	1	yes	characteristic
35	Dic₅₄₁	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₅₄₁	—	2	1	no	—
37	C₂×C₅₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	D₅₄₁	—	2	1	no	—
39	D₅₄₁	#135	1	2	yes	—
40	C₅₄₁	#427	1	1	yes	characteristic, complemented, Sylow
41	#427	—	541	1	no	maximal, Sylow
42	C₂²×C₈	—	541	1	no	—
43	#117	—	541	2	no	—
44	#107	—	541	2	no	—
45	#106	—	541	2	no	—
46	C₂²×C₄	—	541	1	no	—
47	C₂×C₈	—	541	1	no	—
48	C₂×C₈	—	541	1	no	—
49	C₂×C₈	—	541	1	no	—
50	C₂×C₈	—	541	1	no	—
51	C₂×C₈	—	541	1	no	—
52	C₂×C₈	#14524194	1	1	yes	characteristic, complemented
53	C₄⋊C₄	—	541	4	no	—
54	C₂²⋊C₄	—	1082	2	no	—
55	C₄²	—	1082	2	no	—
56	C₂³	—	541	1	no	—
57	C₂×C₄	—	541	1	no	—
58	C₂×C₄	—	541	1	no	—
59	C₂×C₄	—	541	1	no	—
60	C₂×C₄	—	541	1	no	—
61	C₂×C₄	—	541	1	no	—
62	C₂×C₄	—	1082	4	no	—
63	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
64	C₈	—	541	1	no	—
65	C₈	—	541	1	no	—
66	C₈	C₂×#14524194	1	1	yes	characteristic
67	C₈	C₂×#14524194	1	1	yes	characteristic
68	C₂²	—	541	1	no	—
69	C₂²	—	541	1	no	—
70	C₂²	—	1082	2	no	—
71	C₂²	C₄⋊#14524194	1	1	yes	characteristic
72	C₄	—	541	1	no	—
73	C₄	—	541	1	no	—
74	C₄	—	2164	4	no	—
75	C₄	C₄⋊#14524194	1	1	yes	characteristic
76	C₄	C₂²×#14524194	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	541	2	no	—
79	C₂	—	1082	1	no	—
80	C₂	C₂×C₄⋊#14524194	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#14524194
commutator	C₄×C₅₄₁	C₂²×C₄
Frattini	C₄	C₂²×#14524194
Fitting	C₂×C₈×C₅₄₁	C₄
socle	C₂×C₅₄₁	C₂×C₄⋊C₄
prime radical	C₂²×D₅₄₁	D₄
cosocle	C₄×D₅₄₁	C₂³
hypercenter	C₂×C₈	#14524194
hypocenter	C₅₄₁	#427
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #31772697	C₂	semidirect
3. #31772696	C₂	semidirect
9. C₂×#16864513	C₄	semidirect
10. C₈×D₅₄₁	C₄	semidirect
11. C₈×D₅₄₁	C₄	semidirect
14. C₂×C₈×C₅₄₁	C₄	semidirect
40. C₅₄₁	#427	semidirect
52. C₂×C₈	#14524194	semidirect

Maximal subgroups

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

subgroup	index
#31772707	2
#31772697	2
#31772696	2
C₂×C₈×D₅₄₁	2
#427	541