Subgroups — #46830550

Order 34624.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₃₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#22575821	C₂	1	2	yes	maximal, complemented
3	#31772624	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₂₁₆₄	C₂²	1	2	yes	—
7	C₂×C₂²⋊D₅₄₁	—	2	4	no	—
8	D₄₃₂₈	—	2	2	no	—
9	#22575821	—	2	4	no	—
10	C₂×#16864513	C₂²	1	1	yes	characteristic
11	C₄×Dic₅₄₁	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₅₄₁	C₂²	1	2	yes	—
13	D₈×C₅₄₁	—	2	2	no	—
14	C₂×C₈×C₅₄₁	C₂²	1	1	yes	characteristic
15	C₂²×D₅₄₁	—	2	2	no	—
16	D₂₁₆₄	—	2	2	no	—
17	D₂₁₆₄	—	2	2	no	—
18	C₂²⋊D₅₄₁	—	4	8	no	—
19	C₂×Dic₅₄₁	D₄	1	2	yes	—
20	#16864513	D₄	1	2	yes	complemented
21	C₂³×C₅₄₁	—	2	2	no	—
22	D₄×C₅₄₁	—	2	2	no	—
23	D₄×C₅₄₁	—	2	2	no	—
24	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
25	C₈×C₅₄₁	D₄	1	2	yes	complemented
26	C₂²×C₅₄₁	—	4	2	no	—
27	C₂²×C₅₄₁	—	4	4	no	—
28	C₂²×C₅₄₁	C₂×D₄	1	1	yes	characteristic
29	C₂×D₅₄₁	—	4	2	no	—
30	C₂×D₅₄₁	—	4	4	no	—
31	C₄×C₅₄₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₅₄₁	C₂×D₄	1	1	yes	characteristic
33	Dic₅₄₁	D₈	1	4	yes	complemented
34	C₂×C₅₄₁	—	8	2	no	—
35	C₂×C₅₄₁	#127	1	1	yes	characteristic
36	C₂×C₅₄₁	C₂×D₈	1	2	yes	—
37	D₅₄₁	—	8	2	no	—
38	C₅₄₁	#493	1	1	yes	characteristic, complemented, Sylow
39	#493	—	541	1	no	maximal, Sylow
40	C₂×D₈	—	541	2	no	—
41	C₂×D₈	—	541	1	no	—
42	C₂×D₈	D₅₄₁	1	1	yes	characteristic, complemented
43	#127	—	541	2	no	—
44	C₄×C₈	—	541	1	no	—
45	C₂×D₄	—	541	2	no	—
46	C₂×D₄	—	1082	4	no	—
47	C₂×D₄	C₂×D₅₄₁	1	2	yes	—
48	D₈	—	2	2	no	—
49	D₈	—	1082	4	no	—
50	D₈	—	1082	2	no	—
51	C₂×C₈	—	541	1	no	—
52	C₂×C₈	C₂×D₅₄₁	1	1	yes	characteristic
53	C₄²	—	541	1	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	1082	2	no	—
56	D₄	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	1082	2	no	—
59	D₄	—	1082	2	no	—
60	D₄	—	2164	8	no	—
61	C₂×C₄	—	541	2	no	—
62	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
63	C₈	—	541	2	no	—
64	C₈	C₂²⋊D₅₄₁	1	2	yes	complemented
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	2164	2	no	—
68	C₂²	—	2164	4	no	—
69	C₂²	D₄×D₅₄₁	1	1	yes	characteristic
70	C₄	—	541	4	no	—
71	C₄	D₄×D₅₄₁	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₅₄₁	1	1	yes	characteristic
73	C₂	—	8	2	no	—
74	C₂	—	4328	2	no	—
75	C₂	#31772624	1	1	yes	characteristic
76	C₂	D₈×D₅₄₁	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₅₄₁
commutator, cosocle	C₂×C₄×C₅₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₅₄₁
Fitting	C₂×D₈×C₅₄₁	C₂
socle	C₂²×C₅₄₁	C₂×D₄
hypercenter	C₂×D₈	D₅₄₁
hypocenter	C₅₄₁	#493
LCS	G ▷ C₂×C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₄₃₂₈	C₂	semidirect
2. C₂×#22575821	C₂	semidirect
3. #31772624	C₂	semidirect
4. C₈×Dic₅₄₁	C₂	semidirect
5. C₂×D₈×C₅₄₁	C₂	semidirect
20. #16864513	D₄	semidirect
25. C₈×C₅₄₁	D₄	semidirect
33. Dic₅₄₁	D₈	semidirect
38. C₅₄₁	#493	semidirect
42. C₂×D₈	D₅₄₁	semidirect
64. C₈	C₂²⋊D₅₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₃₂₈	2
C₂×#22575821	2
#31772624	2
C₈×Dic₅₄₁	2
C₂×D₈×C₅₄₁	2
#493	541