Subgroups — #45687742

Order 33344.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659699	C₂	1	1	yes	maximal, characteristic
2	#30659673	C₂	1	1	yes	maximal, characteristic
3	#30659641	C₂	1	1	yes	maximal, characteristic
4	#30659637	C₂	1	1	yes	maximal, characteristic
5	#30659633	C₂	1	1	yes	maximal, characteristic
6	#30659631	C₂	1	1	yes	maximal, characteristic
7	#106×C₅₂₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₀₄₂	C₂²	1	1	yes	characteristic
9	C₂×#16861960	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₅₂₁	—	2	1	no	—
11	C₄⋊Dic₅₂₁	C₂²	1	1	yes	characteristic
12	#22552343	—	2	1	no	—
13	#22552343	—	2	1	no	—
14	C₄×Dic₅₂₁	—	2	1	no	—
15	C₄×Dic₅₂₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₅₂₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₅₂₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₅₂₁	C₂²	1	1	yes	characteristic
19	Dic₁₀₄₂	—	2	1	no	—
20	Dic₁₀₄₂	Q₈	1	2	yes	—
21	C₂×Dic₅₂₁	—	2	1	no	—
22	C₂×Dic₅₂₁	—	2	1	no	—
23	C₂×Dic₅₂₁	D₄	1	1	yes	characteristic
24	C₂×Dic₅₂₁	D₄	1	1	yes	characteristic
25	#16861960	—	2	1	no	—
26	C₂×C₄×C₅₂₁	—	2	1	no	—
27	C₂×C₄×C₅₂₁	—	2	1	no	—
28	C₂×C₄×C₅₂₁	C₂³	1	1	yes	characteristic
29	C₈×C₅₂₁	—	2	1	no	—
30	C₂²×C₅₂₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₅₂₁	—	4	1	no	—
32	C₄×C₅₂₁	—	4	1	no	—
33	C₄×C₅₂₁	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₅₂₁	#41	1	1	yes	characteristic
35	Dic₅₂₁	—	2	2	no	—
36	Dic₅₂₁	—	2	1	no	—
37	Dic₅₂₁	—	2	1	no	—
38	Dic₅₂₁	—	4	1	no	—
39	C₂×C₅₂₁	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₅₂₁	#135	1	1	yes	characteristic
41	C₂×C₅₂₁	#137	1	1	yes	characteristic
42	C₅₂₁	#479	1	1	yes	characteristic, complemented, Sylow
43	#479	—	521	1	no	maximal, Sylow
44	#125	—	521	1	no	—
45	C₄×Q₈	—	521	1	no	—
46	#107	—	521	1	no	—
47	#106	D₅₂₁	1	1	yes	characteristic
48	C₄⋊C₈	—	521	1	no	—
49	#103	—	521	1	no	—
50	#103	—	521	1	no	—
51	C₂×Q₈	—	521	1	no	—
52	C₂×C₈	—	521	1	no	—
53	C₂×C₈	C₂×D₅₂₁	1	1	yes	characteristic
54	C₄⋊C₄	—	521	1	no	—
55	C₄⋊C₄	—	1042	1	no	—
56	C₄⋊C₄	—	1042	1	no	—
57	C₄⋊C₄	—	1042	1	no	—
58	C₄⋊C₄	C₂×D₅₂₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₅₂₁	1	1	yes	characteristic
60	C₄²	—	521	1	no	—
61	C₄²	—	1042	1	no	—
62	Q₈	—	521	2	no	—
63	Q₈	—	1042	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	521	1	no	—
67	C₂×C₄	—	521	1	no	—
68	C₂×C₄	—	1042	1	no	—
69	C₂×C₄	—	1042	1	no	—
70	C₂×C₄	C₂²×D₅₂₁	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	1042	1	no	—
73	C₂²	D₄×D₅₂₁	1	1	yes	characteristic
74	C₄	—	4	1	no	—
75	C₄	—	4	1	no	—
76	C₄	—	1042	2	no	—
77	C₄	—	1042	1	no	—
78	C₄	—	1042	1	no	—
79	C₄	—	2084	1	no	—
80	C₄	Q₈×D₅₂₁	1	1	yes	characteristic
81	C₄	#22552364	1	1	yes	characteristic
82	C₂	#30659686	1	1	yes	characteristic
83	C₂	#30659729	1	1	yes	characteristic
84	C₂	#30659737	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₂₁
commutator, cosocle	C₂×C₄×C₅₂₁	C₂³
Frattini	C₂×C₄	C₂²×D₅₂₁
Fitting	#106×C₅₂₁	C₂
socle, prime radical	C₂²×C₅₂₁	C₂×D₄
hypercenter	#106	D₅₂₁
hypocenter	C₅₂₁	#479
LCS	G ▷ C₂×C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
42. C₅₂₁	#479	semidirect

Maximal subgroups

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

subgroup	index
#30659699	2
#30659673	2
#30659641	2
#30659637	2
#30659633	2
#30659631	2
#106×C₅₂₁	2
#479	521