Subgroups — #14580460

Order 2624.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₈₂	C₂	1	1	yes	maximal, characteristic
2	#13050093	C₂	1	2	yes	maximal
3	C₄×#66491	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₄₁	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₂	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₁	C₂²	1	2	yes	—
8	C₄²×C₄₁	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₄₁	C₄	1	1	yes	characteristic
10	#10620279	C₄	1	2	yes	—
11	C₄×Dic₄₁	C₂²	1	2	yes	—
12	C₂×#66491	C₂²	1	1	yes	characteristic
13	C₂×#66491	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
19	Dic₈₂	C₈	1	4	yes	complemented
20	C₈×C₄₁	—	2	2	no	—
21	#66491	—	2	1	no	—
22	#66491	Q₈	1	2	yes	complemented
23	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₄₁	—	2	1	no	—
25	C₄×C₄₁	C₂×C₈	1	2	yes	—
26	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₄₁	#41	1	1	yes	characteristic
28	Dic₄₁	—	2	2	no	—
29	Dic₄₁	C₂×C₈	1	4	yes	—
30	C₂×C₄₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₄₁	#131	1	1	yes	characteristic
33	C₈×Q₈	—	41	1	no	maximal, Sylow
34	C₄₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₄×Q₈	—	41	1	no	—
36	C₄⋊C₈	—	41	2	no	—
37	C₄⋊C₈	D₄₁	1	1	yes	characteristic
38	C₄×C₈	—	41	2	no	—
39	C₄×C₈	—	41	1	no	—
40	C₂×Q₈	—	41	1	no	—
41	C₂×C₈	—	41	1	no	—
42	C₂×C₈	—	41	1	no	—
43	C₂×C₈	C₂×D₄₁	1	2	yes	—
44	C₄⋊C₄	—	41	2	no	—
45	C₄⋊C₄	—	41	1	no	—
46	C₄²	—	41	2	no	—
47	C₄²	C₂×D₄₁	1	1	yes	characteristic
48	Q₈	—	41	4	no	—
49	C₂×C₄	—	41	2	no	—
50	C₂×C₄	—	41	2	no	—
51	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
52	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	41	2	no	—
56	C₈	—	82	1	no	—
57	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	41	4	no	—
60	C₄	—	82	2	no	—
61	C₄	C₈×D₄₁	1	2	yes	—
62	C₄	#10620308	1	1	yes	characteristic
63	C₄	Q₈×D₄₁	1	1	yes	characteristic
64	C₂	#13050129	1	1	yes	characteristic
65	C₂	C₂×C₈×D₄₁	1	1	yes	characteristic
66	C₂	#13050172	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator	C₂×C₄₁	C₂²×C₈
Fitting	C₄⋊C₈×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂²×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄⋊C₈	D₄₁
hypocenter	C₄₁	C₈×Q₈
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
19. Dic₈₂	C₈	semidirect
22. #66491	Q₈	semidirect
34. C₄₁	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₈₂	2
#13050093	2
C₄×#66491	2
C₈×Dic₄₁	2
C₄⋊C₈×C₄₁	2
C₈×Q₈	41