Subgroups — #44442992

Order 29504.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414193	C₂	1	1	yes	maximal, characteristic, complemented
2	#28414186	C₂	1	1	yes	maximal, characteristic, complemented
3	#28414137	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#14270406	—	2	1	no	—
5	#20301504	—	2	1	no	—
6	#20301500	—	2	1	no	—
7	Dic₁₈₄₄	C₄	1	1	yes	characteristic, complemented
8	#20301489	—	2	1	no	—
9	C₈×D₄₆₁	C₂²	1	1	yes	characteristic
10	D₈×C₄₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×#14270406	—	4	1	no	—
12	Dic₉₂₂	—	2	1	no	—
13	C₂²⋊D₄₆₁	—	4	1	no	—
14	C₂×Dic₄₆₁	—	4	1	no	—
15	C₄×D₄₆₁	D₄	1	1	yes	characteristic
16	#16814779	D₄	1	1	yes	characteristic
17	D₄×C₄₆₁	—	2	1	no	—
18	C₈×C₄₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄₆₁	—	4	1	no	—
20	C₂×D₄₆₁	D₈	1	1	yes	characteristic
21	#14270406	—	8	1	no	—
22	C₄×C₄₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₄₆₁	—	4	1	no	—
24	Dic₄₆₁	SD₁₆	1	1	yes	characteristic
25	C₂×C₄₆₁	—	8	1	no	—
26	C₂×C₄₆₁	#102	1	1	yes	characteristic
27	D₄₆₁	—	2	1	no	—
28	C₄₆₁	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	461	1	no	maximal, Sylow
30	#135	—	461	1	no	—
31	M₃₂	—	461	1	no	—
32	#106	—	461	1	no	—
33	#41	—	922	1	no	—
34	Q₁₆	—	461	1	no	—
35	SD₁₆	—	922	1	no	—
36	D₈	#14270406	1	1	yes	characteristic, complemented
37	C₂×C₈	—	461	1	no	—
38	C₄⋊C₄	—	922	1	no	—
39	C₁₆	—	922	1	no	—
40	Q₈	—	922	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	1844	1	no	—
43	C₂×C₄	—	1844	1	no	—
44	C₂×C₄	—	1844	1	no	—
45	C₂×C₄	—	461	1	no	—
46	C₈	—	461	1	no	—
47	C₈	C₂×#14270406	1	1	yes	characteristic
48	C₂²	—	4	1	no	—
49	C₂²	—	461	1	no	—
50	C₄	—	1844	1	no	—
51	C₄	—	3688	1	no	—
52	C₄	—	461	1	no	—
53	C₄	C₂²⋊#14270406	1	1	yes	characteristic
54	C₂	—	8	1	no	—
55	C₂	—	922	1	no	—
56	C₂	#28414180	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28414180
commutator	C₈×C₄₆₁	C₂×C₄
Frattini	C₈	C₂×#14270406
Fitting	D₈×C₄₆₁	C₄
socle	C₂×C₄₆₁	#102
prime radical	#28414137	C₂
cosocle	C₈×D₄₆₁	C₂²
hypercenter	D₈	#14270406
hypocenter	C₄₆₁	#360
LCS	G ▷ C₈×C₄₆₁ ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #28414193	C₂	semidirect
2. #28414186	C₂	semidirect
7. Dic₁₈₄₄	C₄	semidirect
10. D₈×C₄₆₁	C₄	semidirect
28. C₄₆₁	#360	semidirect
36. D₈	#14270406	semidirect

Maximal subgroups

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

subgroup	index
#28414193	2
#28414186	2
#28414137	2
#360	461