Subgroups — #46831057

Order 34624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₄₁⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	#31772707	C₂	1	1	yes	maximal, characteristic
3	C₂×#22575819	C₂	1	1	yes	maximal, characteristic
4	#22575846	—	2	1	no	—
5	#22575845	C₄	1	2	yes	complemented
6	D₅₄₁⋊C₈	—	2	1	no	—
7	C₄⋊#14524194	—	2	1	no	—
8	C₂²⋊#14524194	C₄	1	2	yes	—
9	C₄×#14524194	—	2	1	no	—
10	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
11	#22575819	—	2	1	no	—
12	#22575819	—	2	1	no	—
13	C₂×#16864513	C₄	1	1	yes	characteristic, complemented
14	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
15	C₂×#14524194	—	2	2	no	—
16	#16864520	—	2	2	no	—
17	C₂²×D₅₄₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₅₄₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₅₄₁	D₄	1	1	yes	characteristic
20	C₄×D₅₄₁	D₄	1	1	yes	characteristic
21	C₄×D₅₄₁	D₄	1	1	yes	characteristic
22	C₄×D₅₄₁	Q₈	1	1	yes	characteristic
23	#16864513	—	2	1	no	—
24	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
25	C₈×C₅₄₁	—	2	1	no	—
26	C₂²×C₅₄₁	C₄²	1	1	yes	characteristic
27	C₂×D₅₄₁	—	4	1	no	—
28	C₂×D₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₅₄₁	C₄⋊C₄	1	1	yes	characteristic
30	#14524194	—	4	2	no	—
31	C₄×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
33	Dic₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₅₄₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₅₄₁	—	2	1	no	—
36	C₂×C₅₄₁	#95	1	1	yes	characteristic
37	D₅₄₁	—	2	1	no	—
38	D₅₄₁	—	2	1	no	—
39	C₅₄₁	#344	1	1	yes	characteristic, complemented, Sylow
40	#344	—	541	1	no	maximal, Sylow
41	C₂×M₁₆	—	541	1	no	—
42	C₂×M₁₆	—	541	1	no	—
43	#117	—	541	1	no	—
44	C₂²×C₄	—	541	1	no	—
45	M₁₆	—	541	2	no	—
46	M₁₆	—	1082	1	no	—
47	M₁₆	—	1082	1	no	—
48	M₁₆	—	1082	1	no	—
49	C₂×C₈	—	541	1	no	—
50	C₂×C₈	—	1082	1	no	—
51	C₂×C₈	#14524194	1	1	yes	characteristic, complemented
52	C₄⋊C₄	—	1082	1	no	—
53	C₂²⋊C₄	—	541	2	no	—
54	C₄²	—	1082	1	no	—
55	C₂³	—	541	1	no	—
56	C₂×C₄	—	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	—	1082	2	no	—
62	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	1082	2	no	—
65	C₈	—	1082	1	no	—
66	C₂²	—	541	1	no	—
67	C₂²	—	541	1	no	—
68	C₂²	—	2164	1	no	—
69	C₂²	C₄×#14524194	1	1	yes	characteristic
70	C₄	—	541	1	no	—
71	C₄	—	541	1	no	—
72	C₄	—	2164	2	no	—
73	C₄	C₂²⋊#14524194	1	1	yes	characteristic
74	C₄	C₄⋊#14524194	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	1082	1	no	—
77	C₂	—	1082	1	no	—
78	C₂	(C₂×#14524194)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#14524194
commutator	C₂²×C₅₄₁	C₄²
Frattini	C₂×C₄	C₂×#14524194
Fitting	C₂×C₈×C₅₄₁	C₄
socle	C₂×C₅₄₁	#95
prime radical	C₂²×D₅₄₁	C₂×C₄
cosocle	C₂×C₄×D₅₄₁	C₂²
hypercenter	C₂×C₈	#14524194
hypocenter	C₅₄₁	#344
LCS	G ▷ C₂²×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
5. #22575845	C₄	semidirect
13. C₂×#16864513	C₄	semidirect
14. C₂×C₈×C₅₄₁	C₄	semidirect
39. C₅₄₁	#344	semidirect
51. 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
D₅₄₁⋊M₁₆	2
#31772707	2
C₂×#22575819	2
#344	541