Subgroups — #14580711

Order 2624.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10620282	C₂	1	2	yes	maximal, complemented
3	#13050160	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₄₁	C₂²	1	2	yes	—
7	C₂×C₂²⋊D₄₁	—	2	4	no	—
8	C₂×D₁₆₄	C₂²	1	2	yes	—
9	D₈×C₄₁	—	2	2	no	—
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	#10620282	—	2	4	no	—
12	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
13	C₂×#66491	C₂²	1	1	yes	characteristic
14	D₃₂₈	—	2	2	no	—
15	C₂³×C₄₁	—	2	2	no	—
16	C₂²×D₄₁	—	2	2	no	—
17	D₄×C₄₁	—	2	2	no	—
18	D₄×C₄₁	—	2	2	no	—
19	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
20	C₂²⋊D₄₁	—	4	8	no	—
21	C₂×Dic₄₁	D₄	1	2	yes	—
22	D₁₆₄	—	2	2	no	—
23	D₁₆₄	—	2	2	no	—
24	C₈×C₄₁	D₄	1	2	yes	complemented
25	#66491	D₄	1	2	yes	complemented
26	C₂²×C₄₁	—	4	2	no	—
27	C₂²×C₄₁	—	4	4	no	—
28	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
29	C₂×D₄₁	—	4	2	no	—
30	C₂×D₄₁	—	4	4	no	—
31	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
33	Dic₄₁	D₈	1	4	yes	complemented
34	C₂×C₄₁	—	8	2	no	—
35	C₂×C₄₁	#127	1	1	yes	characteristic
36	C₂×C₄₁	C₂×D₈	1	2	yes	—
37	D₄₁	—	8	2	no	—
38	#493	—	41	1	no	maximal, Sylow
39	C₄₁	#493	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₈	—	41	2	no	—
41	C₂×D₈	—	41	1	no	—
42	C₂×D₈	D₄₁	1	1	yes	characteristic, complemented
43	#127	—	41	2	no	—
44	C₄×C₈	—	41	1	no	—
45	C₂×D₄	—	41	2	no	—
46	C₂×D₄	—	82	4	no	—
47	C₂×D₄	C₂×D₄₁	1	2	yes	—
48	D₈	—	2	2	no	—
49	D₈	—	82	4	no	—
50	D₈	—	82	2	no	—
51	C₂×C₈	—	41	1	no	—
52	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
53	C₄²	—	41	1	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	82	2	no	—
56	D₄	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	82	2	no	—
59	D₄	—	82	2	no	—
60	D₄	—	164	8	no	—
61	C₂×C₄	—	41	2	no	—
62	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
63	C₈	—	41	2	no	—
64	C₈	C₂²⋊D₄₁	1	2	yes	complemented
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	164	2	no	—
68	C₂²	—	164	4	no	—
69	C₂²	D₄×D₄₁	1	1	yes	characteristic
70	C₄	—	41	4	no	—
71	C₄	D₄×D₄₁	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
73	C₂	—	8	2	no	—
74	C₂	—	328	2	no	—
75	C₂	#13050160	1	1	yes	characteristic
76	C₂	D₈×D₄₁	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₂×D₈×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
hypercenter	C₂×D₈	D₄₁
hypocenter	C₄₁	#493
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
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×D₃₂₈	C₂	semidirect
2. C₂×#10620282	C₂	semidirect
3. #13050160	C₂	semidirect
4. C₈×Dic₄₁	C₂	semidirect
5. C₂×D₈×C₄₁	C₂	semidirect
24. C₈×C₄₁	D₄	semidirect
25. #66491	D₄	semidirect
33. Dic₄₁	D₈	semidirect
39. C₄₁	#493	semidirect
42. C₂×D₈	D₄₁	semidirect
64. C₈	C₂²⋊D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₂₈	2
C₂×#10620282	2
#13050160	2
C₈×Dic₄₁	2
C₂×D₈×C₄₁	2
#493	41