Subgroups — #45687283

Order 33344.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22552343	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₅₂₁	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₅₂₁	C₂	1	1	yes	maximal, characteristic
4	#30659615	C₂	1	1	yes	maximal, characteristic
5	#95×C₅₂₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₂₁	C₂²	1	2	yes	—
7	C₂²×Dic₅₂₁	C₂²	1	1	yes	characteristic
8	C₂²×Dic₅₂₁	C₂²	1	1	yes	characteristic
9	#22552343	C₄	1	8	yes	complemented
10	C₄×Dic₅₂₁	—	2	4	no	—
11	C₄×Dic₅₂₁	C₄	1	4	yes	complemented
12	C₂²×C₄×C₅₂₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅₂₁	C₂²	1	2	yes	—
14	C₂×Dic₅₂₁	—	2	2	no	—
15	C₂×Dic₅₂₁	—	2	2	no	—
16	C₂×Dic₅₂₁	C₂×C₄	1	4	yes	—
17	C₂×Dic₅₂₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₅₂₁	C₂×C₄	1	4	yes	—
19	C₂×Dic₅₂₁	C₂×C₄	1	2	yes	—
20	C₂×Dic₅₂₁	D₄	1	2	yes	—
21	C₂×Dic₅₂₁	Q₈	1	2	yes	—
22	C₂³×C₅₂₁	C₂³	1	1	yes	characteristic
23	C₂×C₄×C₅₂₁	—	2	2	no	—
24	C₂×C₄×C₅₂₁	—	2	2	no	—
25	C₂×C₄×C₅₂₁	—	2	2	no	—
26	C₂×C₄×C₅₂₁	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₅₂₁	C₂×C₄	1	4	yes	—
28	C₂²×C₅₂₁	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₅₂₁	C₂²×C₄	1	2	yes	—
30	C₂²×C₅₂₁	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₅₂₁	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₅₂₁	#41	1	2	yes	—
33	C₄×C₅₂₁	—	2	2	no	—
34	C₄×C₅₂₁	—	2	4	no	—
35	Dic₅₂₁	—	2	4	no	—
36	Dic₅₂₁	C₄²	1	4	yes	complemented
37	Dic₅₂₁	C₄⋊C₄	1	4	yes	complemented
38	C₂×C₅₂₁	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₅₂₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₅₂₁	#117	1	1	yes	characteristic
41	C₂×C₅₂₁	C₄×D₄	1	2	yes	—
42	C₂×C₅₂₁	C₄×Q₈	1	2	yes	—
43	C₅₂₁	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₄×C₄⋊C₄	—	521	1	no	maximal, Sylow
45	C₂×C₄⋊C₄	—	521	2	no	—
46	C₂×C₄²	—	521	1	no	—
47	C₂×C₄²	—	521	2	no	—
48	#95	—	521	1	no	—
49	#95	D₅₂₁	1	1	yes	characteristic
50	C₂²×C₄	—	521	1	no	—
51	C₂²×C₄	—	521	1	no	—
52	C₂²×C₄	—	521	2	no	—
53	C₂²×C₄	C₂×D₅₂₁	1	1	yes	characteristic
54	C₂²×C₄	C₂×D₅₂₁	1	2	yes	—
55	C₄⋊C₄	—	521	8	no	—
56	C₄²	—	521	4	no	—
57	C₄²	—	1042	4	no	—
58	C₂³	C₂²×D₅₂₁	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	521	2	no	—
63	C₂×C₄	—	521	2	no	—
64	C₂×C₄	—	521	4	no	—
65	C₂×C₄	—	521	2	no	—
66	C₂×C₄	—	521	2	no	—
67	C₂×C₄	—	521	4	no	—
68	C₂×C₄	—	1042	2	no	—
69	C₂×C₄	—	1042	2	no	—
70	C₂×C₄	C₄×D₅₂₁	1	2	yes	—
71	C₂×C₄	C₄×D₅₂₁	1	4	yes	—
72	C₂²	C₂×C₄×D₅₂₁	1	1	yes	characteristic
73	C₂²	C₂×C₄×D₅₂₁	1	2	yes	—
74	C₂²	D₄×D₅₂₁	1	1	yes	characteristic
75	C₂²	Q₈×D₅₂₁	1	1	yes	characteristic
76	C₂²	#22552363	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	2	4	no	—
79	C₄	—	521	4	no	—
80	C₄	—	521	4	no	—
81	C₄	—	1042	4	no	—
82	C₂	C₄²×D₅₂₁	1	1	yes	characteristic
83	C₂	C₄⋊C₄×D₅₂₁	1	1	yes	characteristic
84	C₂	#30659664	1	1	yes	characteristic
85	C₂	#30659668	1	2	yes	—
86	C₂	#30659673	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₅₂₁
commutator	C₂×C₅₂₁	C₂×C₄²
Fitting	#95×C₅₂₁	C₂
socle, prime radical, cosocle	C₂³×C₅₂₁	C₂³
hypercenter	#95	D₅₂₁
hypocenter	C₅₂₁	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
9. #22552343	C₄	semidirect
11. C₄×Dic₅₂₁	C₄	semidirect
36. Dic₅₂₁	C₄²	semidirect
37. Dic₅₂₁	C₄⋊C₄	semidirect
43. C₅₂₁	C₄×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22552343	2
C₂×C₄×Dic₅₂₁	2
#30659615	2
#95×C₅₂₁	2
C₄×C₄⋊C₄	521