Subgroups — C₄⋊#14519683 #21444015

Order 7808.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519683	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
3	#14519683	—	2	2	no	—
4	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₆₁	C₈	1	1	yes	characteristic
10	C₁₆×C₆₁	—	2	1	no	—
11	C₁₆×C₆₁	D₄	1	1	yes	characteristic
12	C₁₆×C₆₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₆₁	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₆₁	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
16	C₈×C₆₁	—	2	1	no	—
17	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₆₁	M₁₆	1	1	yes	characteristic
19	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₆₁	—	2	1	no	—
21	C₄×C₆₁	C₃₂	1	2	yes	complemented
22	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₆₁	M₃₂	1	1	yes	characteristic
24	C₄⋊C₃₂	—	61	1	no	maximal, Sylow
25	C₂×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
26	C₂×C₆₁	C₂×C₃₂	1	1	yes	characteristic
27	C₂×C₆₁	M₆₄	1	1	yes	characteristic
28	C₂×C₃₂	—	61	2	no	—
29	C₄×C₁₆	D₆₁	1	1	yes	characteristic
30	C₆₁	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	Dic₆₁	1	1	yes	characteristic
32	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
33	C₄×C₈	Dic₆₁	1	1	yes	characteristic
34	C₃₂	—	122	2	no	—
35	C₂×C₈	#92418	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
37	C₄²	#92418	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	Dic₁₂₂	1	1	yes	characteristic
40	C₁₆	D₂₄₄	1	1	yes	characteristic
41	C₂×C₄	#11758185	1	1	yes	characteristic
42	C₂×C₄	#11758185	1	1	yes	characteristic
43	C₂×C₄	C₂×#92418	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	#11758194	1	1	yes	characteristic
46	C₈	C₄⋊Dic₆₁	1	1	yes	characteristic
47	C₂²	C₂×#11758185	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	#14519683	1	2	yes	complemented
50	C₄	C₄⋊#92418	1	1	yes	characteristic
51	C₄	#14519717	1	1	yes	characteristic
52	C₂	C₄⋊#11758185	1	1	yes	characteristic
53	C₂	C₂×#14519683	1	1	yes	characteristic
54	C₂	#16839596	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₆₁
commutator	C₂×C₆₁	C₂×C₃₂
Fitting	C₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₁₆
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	C₄⋊C₃₂
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
21. C₄×C₆₁	C₃₂	semidirect
30. C₆₁	C₄⋊C₃₂	semidirect
49. C₄	#14519683	semidirect

Subgroups — C4⋊#14519683 #21444015

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊#14519683 #21444015