Subgroups — #44442475

Order 29504.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414110	C₂	1	1	yes	maximal, characteristic
2	#28414051	C₂	1	2	yes	maximal
3	#28414049	C₂	1	2	yes	maximal
4	C₄×#16814779	C₂	1	1	yes	maximal, characteristic
5	#125×C₄₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#16814779	C₂²	1	1	yes	characteristic
7	C₂×#16814779	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₆₁	C₂²	1	2	yes	—
9	#20301480	—	2	2	no	—
10	C₄⋊C₄×C₄₆₁	—	2	2	no	—
11	C₄⋊C₄×C₄₆₁	C₂²	1	2	yes	—
12	C₄²×C₄₆₁	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₆₁	—	2	2	no	—
14	#16814779	Q₈	1	2	yes	—
15	#16814779	Q₈	1	2	yes	—
16	C₂×C₄×C₄₆₁	—	2	2	no	—
17	C₂×C₄×C₄₆₁	D₄	1	2	yes	—
18	C₂×C₄×C₄₆₁	C₂³	1	1	yes	characteristic
19	C₂²×C₄₆₁	C₂×D₄	1	1	yes	characteristic
20	C₄×C₄₆₁	—	2	2	no	—
21	C₄×C₄₆₁	—	4	2	no	—
22	C₄×C₄₆₁	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₄₆₁	C₂×Q₈	1	1	yes	characteristic
24	Dic₄₆₁	—	4	2	no	—
25	C₂×C₄₆₁	C₄⋊Q₈	1	1	yes	characteristic
26	C₂×C₄₆₁	#135	1	2	yes	—
27	C₄₆₁	#499	1	1	yes	characteristic, complemented, Sylow
28	#499	—	461	1	no	maximal, Sylow
29	#125	—	461	1	no	—
30	#125	D₄₆₁	1	1	yes	characteristic
31	#107	—	461	2	no	—
32	#106	—	461	2	no	—
33	C₄×C₈	—	461	1	no	—
34	C₂×C₈	—	461	1	no	—
35	C₂×C₈	—	461	1	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	922	2	no	—
38	C₄⋊C₄	—	461	2	no	—
39	C₄⋊C₄	C₂×D₄₆₁	1	2	yes	—
40	C₄²	C₂×D₄₆₁	1	1	yes	characteristic
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	922	2	no	—
43	C₂×C₄	C₂²⋊D₄₆₁	1	2	yes	—
44	C₂×C₄	C₂²×D₄₆₁	1	1	yes	characteristic
45	C₈	—	461	2	no	—
46	C₈	—	461	2	no	—
47	C₂²	C₂×C₂²⋊D₄₆₁	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	4	2	no	—
50	C₄	—	1844	2	no	—
51	C₄	Q₈×D₄₆₁	1	1	yes	characteristic
52	C₄	Q₈×D₄₆₁	1	1	yes	characteristic
53	C₂	#28414116	1	1	yes	characteristic
54	C₂	#28414138	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₆₁
commutator, cosocle	C₂×C₄×C₄₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₆₁
Fitting	#125×C₄₆₁	C₂
socle, prime radical	C₂²×C₄₆₁	C₂×D₄
hypercenter	#125	D₄₆₁
hypocenter	C₄₆₁	#499
LCS	G ▷ C₂×C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
27. C₄₆₁	#499	semidirect

Maximal subgroups

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

subgroup	index
#28414110	2
#28414051	2
#28414049	2
C₄×#16814779	2
#125×C₄₆₁	2
#499	461