Subgroups — #14580740

Order 2624.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050163	C₂	1	2	yes	maximal
2	#13050098	C₂	1	1	yes	maximal, characteristic
3	#13050097	C₂	1	2	yes	maximal
4	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
5	#107×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₂	—	2	2	no	—
7	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
9	C₄⋊Dic₄₁	C₂²	1	2	yes	—
10	#10620279	—	2	2	no	—
11	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
12	C₂×#66491	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₁	—	2	2	no	—
14	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
15	C₂×Dic₄₁	—	2	2	no	—
16	C₂×Dic₄₁	D₄	1	1	yes	characteristic
17	C₂×Dic₄₁	D₄	1	1	yes	characteristic
18	Dic₈₂	—	4	4	no	—
19	C₈×C₄₁	Q₈	1	2	yes	complemented
20	#66491	Q₈	1	2	yes	complemented
21	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
22	C₄×C₄₁	—	4	2	no	—
23	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
25	Dic₄₁	—	4	2	no	—
26	Dic₄₁	D₈	1	2	yes	—
27	Dic₄₁	Q₁₆	1	2	yes	—
28	C₂×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
30	C₂×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
31	#500	—	41	1	no	maximal, Sylow
32	C₄₁	#500	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊Q₈	—	41	2	no	—
34	#107	—	41	1	no	—
35	#107	—	41	2	no	—
36	#107	D₄₁	1	1	yes	characteristic
37	C₄×C₈	—	41	1	no	—
38	C₂×Q₈	—	82	2	no	—
39	C₂×C₈	—	41	1	no	—
40	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
41	C₄⋊C₄	—	41	2	no	—
42	C₄⋊C₄	—	82	2	no	—
43	C₄⋊C₄	C₂×D₄₁	1	2	yes	—
44	C₄²	—	41	1	no	—
45	Q₈	—	164	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	41	1	no	—
48	C₂×C₄	—	41	1	no	—
49	C₂×C₄	—	82	2	no	—
50	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
51	C₈	—	41	2	no	—
52	C₈	Dic₈₂	1	2	yes	complemented
53	C₂²	D₄×D₄₁	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	41	2	no	—
56	C₄	—	41	2	no	—
57	C₄	—	164	2	no	—
58	C₄	C₂×Dic₈₂	1	1	yes	characteristic
59	C₄	Q₈×D₄₁	1	1	yes	characteristic
60	C₂	#13050163	1	1	yes	characteristic
61	C₂	D₈×D₄₁	1	1	yes	characteristic
62	C₂	Q₁₆×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#107×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
hypercenter	#107	D₄₁
hypocenter	C₄₁	#500
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₄₁	Q₈	semidirect
20. #66491	Q₈	semidirect
32. C₄₁	#500	semidirect
52. C₈	Dic₈₂	semidirect

Maximal subgroups

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

subgroup	index
#13050163	2
#13050098	2
#13050097	2
C₈×Dic₄₁	2
#107×C₄₁	2
#500	41