Subgroups — #16840811

Order 3904.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519844	C₂	1	2	yes	maximal
2	C₄⋊#92420	C₂	1	1	yes	maximal, characteristic
3	C₄×#92420	C₂	1	1	yes	maximal, characteristic
4	C₄×#92420	C₂	1	2	yes	maximal
5	#14519742	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₂₂	C₄	1	1	yes	characteristic
7	C₂×#92420	C₂²	1	2	yes	—
8	C₂×#92420	C₂²	1	1	yes	characteristic
9	C₂×#92420	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
11	#11758196	C₄	1	2	yes	—
12	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₄×Dic₆₁	C₂²	1	2	yes	—
14	C₂×C₄×C₆₁	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₆₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₆₁	C₂³	1	1	yes	characteristic
19	Dic₁₂₂	C₈	1	4	yes	complemented
20	#92420	—	2	2	no	—
21	#92420	—	2	1	no	—
22	#92420	Q₈	1	2	yes	complemented
23	C₂²×C₆₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₆₁	—	2	2	no	—
25	C₄×C₆₁	C₂×C₈	1	2	yes	—
26	Dic₆₁	—	2	1	no	—
27	Dic₆₁	C₂×C₈	1	4	yes	—
28	Dic₆₁	C₂×Q₈	1	1	yes	characteristic
29	Dic₆₁	#41	1	1	yes	characteristic
30	C₂×C₆₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₆₁	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₆₁	#131	1	1	yes	characteristic
33	C₈×Q₈	—	61	1	no	maximal, Sylow
34	C₆₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₄×Q₈	—	61	1	no	—
36	C₄⋊C₈	—	61	1	no	—
37	C₄⋊C₈	—	61	2	no	—
38	C₄×C₈	—	61	2	no	—
39	C₄×C₈	—	61	1	no	—
40	C₂×Q₈	—	61	1	no	—
41	C₂×C₈	—	61	1	no	—
42	C₂×C₈	—	61	2	no	—
43	C₂×C₈	—	61	1	no	—
44	C₄⋊C₄	—	61	2	no	—
45	C₄⋊C₄	#6923	1	1	yes	characteristic
46	C₄²	—	61	2	no	—
47	C₄²	—	61	1	no	—
48	Q₈	—	61	4	no	—
49	C₂×C₄	—	61	2	no	—
50	C₂×C₄	—	61	1	no	—
51	C₂×C₄	—	61	1	no	—
52	C₂×C₄	C₂×#6923	1	2	yes	—
53	C₂×C₄	C₂×#6923	1	1	yes	characteristic
54	C₈	—	61	2	no	—
55	C₈	—	122	2	no	—
56	C₈	—	122	1	no	—
57	C₂²	C₂²×#6923	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	61	1	no	—
60	C₄	—	61	1	no	—
61	C₄	—	61	4	no	—
62	C₄	—	122	1	no	—
63	C₄	D₆₁⋊C₈	1	2	yes	—
64	C₂	Q₈×#6923	1	1	yes	characteristic
65	C₂	C₂×D₆₁⋊C₈	1	1	yes	characteristic
66	C₂	#14519864	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#6923
commutator	C₂×C₆₁	C₂²×C₈
Fitting	C₄⋊C₄×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	C₂²×C₄
cosocle	C₂×Dic₆₁	C₂³
hypercenter	C₄⋊C₄	#6923
hypocenter	C₆₁	C₈×Q₈
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
19. Dic₁₂₂	C₈	semidirect
22. #92420	Q₈	semidirect
34. C₆₁	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
#14519844	2
C₄⋊#92420	2
C₄×#92420	2
#14519742	2
C₈×Q₈	61