Subgroups — #44442994

Order 29504.

62 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	#28414188	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₄₆₁	C₂	1	1	yes	maximal, characteristic
4	#20301511	—	2	1	no	—
5	#20301504	—	2	1	no	—
6	D₄×D₄₆₁	—	2	1	no	—
7	D₃₆₈₈	C₄	1	1	yes	characteristic
8	#20301486	—	2	1	no	—
9	C₈×D₄₆₁	C₂²	1	1	yes	characteristic
10	D₈×C₄₆₁	C₄	1	1	yes	characteristic
11	#16814786	—	4	1	no	—
12	C₂²×D₄₆₁	—	4	1	no	—
13	D₁₈₄₄	—	2	1	no	—
14	C₂²⋊D₄₆₁	—	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	—	4	1	no	—
21	C₂×D₄₆₁	—	8	2	no	—
22	C₂×D₄₆₁	SD₁₆	1	1	yes	characteristic
23	C₄×C₄₆₁	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₄₆₁	D₈	1	1	yes	characteristic
25	C₂×C₄₆₁	—	8	1	no	—
26	C₂×C₄₆₁	#102	1	1	yes	characteristic
27	D₄₆₁	—	2	1	no	—
28	D₄₆₁	—	8	1	no	—
29	C₄₆₁	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	461	1	no	maximal, Sylow
31	C₂×D₈	—	461	1	no	—
32	M₃₂	—	461	1	no	—
33	#108	—	461	1	no	—
34	C₂×D₄	—	922	1	no	—
35	D₈	—	922	1	no	—
36	D₈	—	461	1	no	—
37	D₈	#14270406	1	1	yes	characteristic
38	M₁₆	—	922	1	no	—
39	C₂×C₈	—	461	1	no	—
40	C₁₆	—	922	1	no	—
41	C₂³	—	1844	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	1844	1	no	—
44	D₄	—	922	1	no	—
45	C₂×C₄	—	461	1	no	—
46	C₈	—	1844	1	no	—
47	C₈	—	461	1	no	—
48	C₈	C₂×#14270406	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	1844	1	no	—
51	C₂²	—	3688	2	no	—
52	C₂²	—	461	1	no	—
53	C₄	—	461	1	no	—
54	C₄	C₂²⋊#14270406	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	3688	1	no	—
57	C₂	—	922	1	no	—
58	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	D₈×D₄₆₁	C₂
cosocle	C₈×D₄₆₁	C₂²
hypercenter	D₈	#14270406
hypocenter	C₄₆₁	#361
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. #28414188	C₂	semidirect
29. C₄₆₁	#361	semidirect

Maximal subgroups

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

subgroup	index
#28414193	2
#28414188	2
D₈×D₄₆₁	2
#361	461