Subgroups — #44442484

Order 29504.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414117	C₂	1	1	yes	maximal, characteristic
2	#28414109	C₂	1	1	yes	maximal, characteristic
3	#28414051	C₂	1	1	yes	maximal, characteristic
4	#28414050	C₂	1	1	yes	maximal, characteristic
5	#28414049	C₂	1	1	yes	maximal, characteristic
6	#28414028	C₂	1	1	yes	maximal, characteristic
7	#107×C₄₆₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₂₂	—	2	1	no	—
9	C₂×#16814779	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₆₁	—	2	1	no	—
11	C₄⋊Dic₄₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₆₁	C₂²	1	1	yes	characteristic
13	#20301480	—	2	1	no	—
14	#20301480	—	2	1	no	—
15	C₄×Dic₄₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₄₆₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₄₆₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₄₆₁	C₂²	1	1	yes	characteristic
19	Dic₉₂₂	—	4	2	no	—
20	C₂×Dic₄₆₁	—	2	1	no	—
21	C₂×Dic₄₆₁	—	2	1	no	—
22	C₂×Dic₄₆₁	D₄	1	1	yes	characteristic
23	C₂×Dic₄₆₁	D₄	1	1	yes	characteristic
24	#16814779	Q₈	1	2	yes	complemented
25	C₂×C₄×C₄₆₁	—	2	1	no	—
26	C₂×C₄×C₄₆₁	—	2	1	no	—
27	C₂×C₄×C₄₆₁	C₂³	1	1	yes	characteristic
28	C₈×C₄₆₁	Q₈	1	2	yes	complemented
29	C₂²×C₄₆₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₄₆₁	—	4	1	no	—
31	C₄×C₄₆₁	—	4	1	no	—
32	C₄×C₄₆₁	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₄₆₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₄₆₁	—	2	1	no	—
35	Dic₄₆₁	—	2	1	no	—
36	Dic₄₆₁	—	4	1	no	—
37	Dic₄₆₁	—	4	1	no	—
38	C₂×C₄₆₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₄₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₄₆₁	#137	1	1	yes	characteristic
41	C₄₆₁	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	461	1	no	maximal, Sylow
43	C₄⋊Q₈	—	461	1	no	—
44	#125	—	461	1	no	—
45	#107	—	461	1	no	—
46	#107	D₄₆₁	1	1	yes	characteristic
47	#106	—	461	1	no	—
48	#106	—	461	1	no	—
49	#97	—	461	1	no	—
50	C₂×Q₈	—	922	1	no	—
51	C₂×C₈	—	461	1	no	—
52	C₂×C₈	C₂×D₄₆₁	1	1	yes	characteristic
53	C₄⋊C₄	—	922	1	no	—
54	C₄⋊C₄	—	922	1	no	—
55	C₄⋊C₄	—	922	1	no	—
56	C₄⋊C₄	—	461	1	no	—
57	C₄⋊C₄	—	461	1	no	—
58	C₄⋊C₄	C₂×D₄₆₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₄₆₁	1	1	yes	characteristic
60	C₄²	—	461	1	no	—
61	Q₈	—	1844	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	922	1	no	—
65	C₂×C₄	—	922	1	no	—
66	C₂×C₄	—	461	1	no	—
67	C₂×C₄	—	461	1	no	—
68	C₂×C₄	C₂²×D₄₆₁	1	1	yes	characteristic
69	C₈	—	461	2	no	—
70	C₈	Dic₉₂₂	1	2	yes	complemented
71	C₂²	D₄×D₄₆₁	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	1844	1	no	—
75	C₄	—	1844	1	no	—
76	C₄	—	922	1	no	—
77	C₄	—	922	1	no	—
78	C₄	Q₈×D₄₆₁	1	1	yes	characteristic
79	C₄	C₂×Dic₉₂₂	1	1	yes	characteristic
80	C₂	#28414117	1	1	yes	characteristic
81	C₂	#28414142	1	1	yes	characteristic
82	C₂	#28414150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₆₁
commutator, cosocle	C₂×C₄×C₄₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₆₁
Fitting	#107×C₄₆₁	C₂
socle, prime radical	C₂²×C₄₆₁	C₂×D₄
hypercenter	#107	D₄₆₁
hypocenter	C₄₆₁	#501
LCS	G ▷ C₂×C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
24. #16814779	Q₈	semidirect
28. C₈×C₄₆₁	Q₈	semidirect
41. C₄₆₁	#501	semidirect
70. C₈	Dic₉₂₂	semidirect

Maximal subgroups

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

subgroup	index
#28414117	2
#28414109	2
#28414051	2
#28414050	2
#28414049	2
#28414028	2
#107×C₄₆₁	2
#501	461