Subgroups — #46831087

Order 34624.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₄₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#31772697	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#14524194	—	2	1	no	—
5	#22575839	—	2	1	no	—
6	D₄×D₅₄₁	—	2	1	no	—
7	D₄₃₂₈	C₄	1	1	yes	characteristic, complemented
8	#22575821	—	2	1	no	—
9	C₈×D₅₄₁	C₂²	1	1	yes	characteristic
10	D₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
11	C₂×#14524194	—	4	1	no	—
12	C₂²×D₅₄₁	—	4	1	no	—
13	D₂₁₆₄	—	2	1	no	—
14	C₂²⋊D₅₄₁	—	4	1	no	—
15	C₄×D₅₄₁	D₄	1	1	yes	characteristic
16	#16864513	D₄	1	1	yes	characteristic
17	D₄×C₅₄₁	—	2	1	no	—
18	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₅₄₁	—	4	1	no	—
20	C₂×D₅₄₁	—	4	1	no	—
21	C₂×D₅₄₁	—	8	1	no	—
22	C₂×D₅₄₁	—	8	1	no	—
23	C₂×D₅₄₁	D₈	1	1	yes	characteristic
24	#14524194	—	8	1	no	—
25	C₄×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₅₄₁	SD₁₆	1	1	yes	characteristic
27	C₂×C₅₄₁	—	8	1	no	—
28	C₂×C₅₄₁	#102	1	1	yes	characteristic
29	D₅₄₁	—	8	1	no	—
30	D₅₄₁	D₁₆	1	1	yes	characteristic
31	D₅₄₁	SD₃₂	1	1	yes	characteristic
32	C₅₄₁	#357	1	1	yes	characteristic, complemented, Sylow
33	#357	—	541	1	no	maximal, Sylow
34	C₂×D₈	—	541	1	no	—
35	C₂×C₁₆	—	541	1	no	—
36	#107	—	541	1	no	—
37	C₂×D₄	—	1082	1	no	—
38	D₈	—	541	1	no	—
39	D₈	—	1082	1	no	—
40	D₈	#14524194	1	1	yes	characteristic, complemented
41	C₂×C₈	—	541	1	no	—
42	C₄⋊C₄	—	1082	1	no	—
43	C₁₆	—	1082	1	no	—
44	C₂³	—	2164	1	no	—
45	D₄	—	2	1	no	—
46	D₄	—	1082	1	no	—
47	D₄	—	2164	1	no	—
48	C₂×C₄	—	541	1	no	—
49	C₂×C₄	—	2164	1	no	—
50	C₈	—	541	1	no	—
51	C₈	C₂×#14524194	1	1	yes	characteristic
52	C₂²	—	4	1	no	—
53	C₂²	—	541	1	no	—
54	C₂²	—	2164	1	no	—
55	C₂²	—	4328	1	no	—
56	C₂²	—	4328	1	no	—
57	C₄	—	541	1	no	—
58	C₄	—	4328	1	no	—
59	C₄	C₂²⋊#14524194	1	1	yes	characteristic
60	C₂	—	8	1	no	—
61	C₂	—	541	1	no	—
62	C₂	—	541	1	no	—
63	C₂	—	4328	1	no	—
64	C₂	#31772690	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31772690
commutator	C₈×C₅₄₁	C₂×C₄
Frattini	C₈	C₂×#14524194
Fitting	D₈×C₅₄₁	C₄
socle	C₂×C₅₄₁	#102
prime radical	D₈×D₅₄₁	C₂
cosocle	C₈×D₅₄₁	C₂²
hypercenter	D₈	#14524194
hypocenter	C₅₄₁	#357
LCS	G ▷ C₈×C₅₄₁ ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₅₄₁⋊C₁₆	C₂	semidirect
2. #31772697	C₂	semidirect
7. D₄₃₂₈	C₄	semidirect
10. D₈×C₅₄₁	C₄	semidirect
32. C₅₄₁	#357	semidirect
40. D₈	#14524194	semidirect

Maximal subgroups

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

subgroup	index
D₅₄₁⋊C₁₆	2
#31772697	2
D₈×D₅₄₁	2
#357	541