Subgroups — #45688404

Order 33344.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22552373	C₂	1	2	yes	maximal, complemented
2	#30659765	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄×D₅₂₁	C₂	1	1	yes	maximal, characteristic
4	#22552373	—	2	4	no	—
5	C₂×#16861967	C₂²	1	4	yes	complemented
6	C₂³×D₅₂₁	C₄	1	1	yes	characteristic
7	C₂²×Dic₅₂₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₅₂₁	—	2	4	no	—
9	C₂×C₄×D₅₂₁	C₄	1	2	yes	—
10	C₂×C₄×D₅₂₁	C₂²	1	2	yes	—
11	C₂²×C₄×C₅₂₁	C₄	1	1	yes	characteristic
12	#16861967	—	2	4	no	—
13	C₂²×D₅₂₁	—	2	2	no	—
14	C₂²×D₅₂₁	—	2	4	no	—
15	C₂²×D₅₂₁	C₂×C₄	1	2	yes	—
16	C₂×Dic₅₂₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₅₂₁	D₄	1	4	yes	—
18	C₂×Dic₅₂₁	C₂³	1	1	yes	characteristic
19	C₄×D₅₂₁	—	2	4	no	—
20	C₄×D₅₂₁	—	2	4	no	—
21	C₂³×C₅₂₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₅₂₁	—	2	2	no	—
23	C₂×C₄×C₅₂₁	C₂×C₄	1	2	yes	—
24	C₂²×C₅₂₁	—	2	2	no	—
25	C₂²×C₅₂₁	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₅₂₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₅₂₁	—	2	8	no	—
28	C₂×D₅₂₁	—	2	2	no	—
29	C₂×D₅₂₁	—	2	2	no	—
30	C₂×D₅₂₁	M₁₆	1	4	yes	complemented
31	C₄×C₅₂₁	—	2	2	no	—
32	Dic₅₂₁	C₂²⋊C₄	1	2	yes	—
33	Dic₅₂₁	C₂×D₄	1	2	yes	—
34	C₂×C₅₂₁	—	2	2	no	—
35	C₂×C₅₂₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₅₂₁	C₂×M₁₆	1	2	yes	—
37	D₅₂₁	—	2	4	no	—
38	C₅₂₁	#407	1	1	yes	characteristic, complemented, Sylow
39	#407	—	521	1	no	maximal, Sylow
40	C₂³×C₄	—	521	1	no	—
41	C₂×M₁₆	—	521	2	no	—
42	C₂²⋊C₈	—	521	4	no	—
43	C₂⁴	—	521	1	no	—
44	C₂²×C₄	—	521	1	no	—
45	C₂²×C₄	—	521	2	no	—
46	C₂²×C₄	—	521	2	no	—
47	C₂²×C₄	—	1042	4	no	—
48	C₂²×C₄	#14523438	1	1	yes	characteristic
49	M₁₆	—	1042	4	no	—
50	C₂×C₈	—	521	4	no	—
51	C₂³	—	521	2	no	—
52	C₂³	—	1042	4	no	—
53	C₂³	—	1042	2	no	—
54	C₂³	C₂×#14523438	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	521	4	no	—
57	C₂×C₄	—	521	1	no	—
58	C₂×C₄	—	521	1	no	—
59	C₂×C₄	—	1042	4	no	—
60	C₂×C₄	—	1042	4	no	—
61	C₂×C₄	C₂×#14523438	1	2	yes	—
62	C₈	—	1042	4	no	—
63	C₂²	—	2	2	no	—
64	C₂²	—	521	4	no	—
65	C₂²	—	1042	8	no	—
66	C₂²	—	1042	2	no	—
67	C₂²	—	1042	2	no	—
68	C₂²	C₂²⋊#14523438	1	2	yes	—
69	C₂²	C₂²×#14523438	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	521	2	no	—
72	C₄	—	521	2	no	—
73	C₂	—	2	2	no	—
74	C₂	—	1042	4	no	—
75	C₂	C₂×C₂²⋊#14523438	1	1	yes	characteristic
76	C₂	D₅₂₁⋊M₁₆	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#14523438
commutator, socle	C₂²×C₅₂₁	C₂²×C₄
Fitting	C₂²×C₄×C₅₂₁	C₄
prime radical	C₂³×D₅₂₁	C₄
cosocle	C₂×Dic₅₂₁	C₂³
hypercenter	C₂²×C₄	#14523438
hypocenter	C₅₂₁	#407
LCS	G ▷ C₂²×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#22552373	C₂	semidirect
2. #30659765	C₂	semidirect
5. C₂×#16861967	C₂²	semidirect
30. C₂×D₅₂₁	M₁₆	semidirect
38. C₅₂₁	#407	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22552373	2
#30659765	2
C₂²×C₄×D₅₂₁	2
#407	521