Subgroups — #46829940

Order 34624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575820	C₂	1	2	yes	maximal
2	C₂²×C₈×C₅₄₁	C₂	1	1	yes	maximal, characteristic
3	#22575820	—	2	2	no	—
4	#22575820	C₄	1	4	yes	—
5	C₂×#16864513	—	2	2	no	—
6	C₂²×C₄×C₅₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₅₄₁	—	2	2	no	—
8	C₂×C₈×C₅₄₁	C₄	1	2	yes	—
9	#16864513	—	2	4	no	—
10	C₂³×C₅₄₁	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₅₄₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅₄₁	D₄	1	2	yes	—
14	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
15	C₈×C₅₄₁	—	2	2	no	—
16	C₂²×C₅₄₁	—	2	2	no	—
17	C₂²×C₅₄₁	C₄⋊C₄	1	2	yes	—
18	C₂²×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₅₄₁	C₄²	1	1	yes	characteristic
20	C₄×C₅₄₁	C₂²⋊C₄	1	2	yes	—
21	C₄×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₅₄₁	—	2	2	no	—
23	C₂×C₅₄₁	#95	1	1	yes	characteristic
24	C₂×C₅₄₁	#108	1	2	yes	—
25	C₅₄₁	#341	1	1	yes	characteristic, complemented, Sylow
26	#341	—	541	1	no	maximal, Sylow
27	C₂×M₁₆	—	541	2	no	—
28	C₂²×C₈	D₅₄₁	1	1	yes	characteristic
29	C₂²×C₄	C₂×D₅₄₁	1	1	yes	characteristic
30	M₁₆	—	541	4	no	—
31	M₁₆	—	1082	2	no	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	1082	2	no	—
34	C₂×C₈	Dic₅₄₁	1	2	yes	—
35	C₂³	Dic₁₀₈₂	1	1	yes	characteristic
36	C₂×C₄	C₄×D₅₄₁	1	2	yes	—
37	C₂×C₄	C₂×Dic₅₄₁	1	1	yes	characteristic
38	C₂×C₄	C₂²⋊D₅₄₁	1	2	yes	—
39	C₂×C₄	D₂₁₆₄	1	1	yes	characteristic
40	C₈	—	2	2	no	—
41	C₈	—	1082	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	#22575815	1	2	yes	—
44	C₂²	C₄⋊Dic₅₄₁	1	1	yes	characteristic
45	C₄	C₄×Dic₅₄₁	1	1	yes	characteristic
46	C₄	#22575813	1	2	yes	—
47	C₄	C₂²⋊Dic₅₄₁	1	1	yes	characteristic
48	C₂	—	2	2	no	—
49	C₂	#31772535	1	1	yes	characteristic
50	C₂	#31772564	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₂₁₆₄
commutator	C₄×C₅₄₁	C₄²
Frattini	C₂²×C₄	C₂×D₅₄₁
Fitting	C₂²×C₈×C₅₄₁	C₂
socle	C₂²×C₅₄₁	C₄⋊C₄
prime radical	C₂³×C₅₄₁	Q₈
cosocle	C₂²×C₄×C₅₄₁	C₂²
hypercenter	C₂²×C₈	D₅₄₁
hypocenter	C₅₄₁	#341
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
25. C₅₄₁	#341	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575820	2
C₂²×C₈×C₅₄₁	2
#341	541