Subgroups — (C₂×D₄₉₉)⋊C₈ #30630263

Order 15968.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄₉₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₉₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₄₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄₉₉	C₄	1	1	yes	characteristic
5	C₂×Dic₄₉₉	C₄	1	1	yes	characteristic
6	C₄×D₄₉₉	—	2	1	no	—
7	C₄×D₄₉₉	—	2	1	no	—
8	C₄₉₉⋊C₈	—	2	1	no	—
9	C₂×C₄×C₄₉₉	C₂²	1	1	yes	characteristic
10	C₈×C₄₉₉	—	2	1	no	—
11	C₂²×C₄₉₉	C₂×C₄	1	1	yes	characteristic
12	C₂×D₄₉₉	—	2	1	no	—
13	C₂×D₄₉₉	—	2	1	no	—
14	C₂×D₄₉₉	C₈	1	2	yes	complemented
15	C₄×C₄₉₉	D₄	1	1	yes	characteristic
16	C₄×C₄₉₉	D₄	1	1	yes	characteristic
17	Dic₄₉₉	—	2	1	no	—
18	C₂×C₄₉₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄₉₉	C₂×C₈	1	1	yes	characteristic
20	C₂×C₄₉₉	M₁₆	1	1	yes	characteristic
21	D₄₉₉	—	2	2	no	—
22	C₄₉₉	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
23	C₂²⋊C₈	—	499	1	no	maximal, Sylow
24	C₂²×C₄	—	499	1	no	—
25	C₂×C₈	—	499	1	no	—
26	C₂×C₈	D₄₉₉	1	1	yes	characteristic, complemented
27	C₂³	—	499	1	no	—
28	C₂×C₄	—	998	1	no	—
29	C₂×C₄	—	998	1	no	—
30	C₂×C₄	—	499	1	no	—
31	C₂×C₄	C₂×D₄₉₉	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	998	1	no	—
34	C₂²	—	998	1	no	—
35	C₂²	—	998	1	no	—
36	C₂²	—	499	2	no	—
37	C₂²	C₄×D₄₉₉	1	1	yes	characteristic
38	C₄	—	998	1	no	—
39	C₄	C₂²⋊D₄₉₉	1	1	yes	characteristic
40	C₄	D₁₉₉₆	1	1	yes	characteristic
41	C₂	—	998	2	no	—
42	C₂	(C₂×D₄₉₉)⋊C₄	1	1	yes	characteristic
43	C₂	C₈×D₄₉₉	1	1	yes	characteristic
44	C₂	#22547794	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₄₉₉
commutator	C₂×C₄₉₉	C₂×C₈
Fitting	C₂×C₈×C₄₉₉	C₂
socle	C₂²×C₄₉₉	C₂×C₄
prime radical	C₂²×D₄₉₉	C₄
cosocle	C₂×C₄×C₄₉₉	C₂²
hypercenter	C₂×C₈	D₄₉₉
hypocenter	C₄₉₉	C₂²⋊C₈
LCS	G ▷ C₂×C₄₉₉ ▷ C₄₉₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₉₉⋊C₈	C₂	semidirect
3. C₂×C₈×C₄₉₉	C₂	semidirect
14. C₂×D₄₉₉	C₈	semidirect
22. C₄₉₉	C₂²⋊C₈	semidirect
26. C₂×C₈	D₄₉₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄₉₉	2
C₂×C₄₉₉⋊C₈	2
C₂×C₈×C₄₉₉	2
C₂²⋊C₈	499

Subgroups — (C2×D499)⋊C8 #30630263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₄₉₉)⋊C₈ #30630263