Subgroups — #46831044

Order 34624.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₄₁⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#22575819	C₂	1	1	yes	maximal, characteristic
3	#22575846	—	2	2	no	—
4	#22575845	—	2	2	no	—
5	D₅₄₁⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
7	#22575819	—	2	2	no	—
8	C₂×#16864513	C₄	1	1	yes	characteristic
9	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic
10	#16864520	—	2	4	no	—
11	C₂²×D₅₄₁	Q₈	1	1	yes	characteristic
12	C₂×Dic₅₄₁	D₄	1	1	yes	characteristic
13	C₄×D₅₄₁	C₂×C₄	1	2	yes	—
14	C₄×D₅₄₁	D₄	1	2	yes	—
15	#16864513	—	2	1	no	—
16	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
17	C₈×C₅₄₁	—	2	1	no	—
18	C₂²×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₅₄₁	—	4	1	no	—
20	C₂×D₅₄₁	C₄⋊C₄	1	2	yes	—
21	C₄×C₅₄₁	C₄²	1	1	yes	characteristic
22	C₄×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₅₄₁	C₂²⋊C₄	1	2	yes	—
24	C₂×C₅₄₁	—	2	1	no	—
25	C₂×C₅₄₁	#95	1	1	yes	characteristic
26	D₅₄₁	—	2	2	no	—
27	C₅₄₁	#338	1	1	yes	characteristic, complemented, Sylow
28	#338	—	541	1	no	maximal, Sylow
29	C₂×M₁₆	—	541	2	no	—
30	C₂×M₁₆	—	541	1	no	—
31	C₂²×C₄	—	541	1	no	—
32	M₁₆	—	1082	2	no	—
33	M₁₆	—	1082	2	no	—
34	M₁₆	—	1082	2	no	—
35	C₂×C₈	—	541	4	no	—
36	C₂×C₈	—	541	1	no	—
37	C₂×C₈	#14524194	1	1	yes	characteristic
38	C₂³	—	541	1	no	—
39	C₂×C₄	—	541	1	no	—
40	C₂×C₄	—	541	2	no	—
41	C₂×C₄	—	541	2	no	—
42	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	1082	4	no	—
45	C₈	—	1082	1	no	—
46	C₂²	—	541	2	no	—
47	C₂²	—	2164	1	no	—
48	C₂²	C₄⋊#14524194	1	1	yes	characteristic
49	C₄	—	541	2	no	—
50	C₄	C₄×#14524194	1	1	yes	characteristic
51	C₄	C₂²⋊#14524194	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	1082	2	no	—
54	C₂	(C₂×#14524194)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#14524194
commutator	C₄×C₅₄₁	C₄²
Frattini	C₂×C₄	C₂×#14524194
Fitting	C₂×C₈×C₅₄₁	C₄
socle	C₂×C₅₄₁	#95
prime radical	C₂²×D₅₄₁	Q₈
cosocle	C₂×C₄×D₅₄₁	C₂²
hypercenter	C₂×C₈	#14524194
hypocenter	C₅₄₁	#338
LCS	G ▷ C₄×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
27. C₅₄₁	#338	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
C₂×#22575819	2
#338	541