Subgroups — C₄×C₁₉₉⋊C₁₆ #27163792

Order 12736.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉₉⋊C₁₆	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉₉⋊C₁₆	C₄	1	4	yes	direct product factor
4	C₂×C₈×C₁₉₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
6	C₄²×C₁₉₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₉₉	C₈	1	2	yes	—
8	C₂×C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₉₉	C₈	1	2	yes	—
10	C₈×C₁₉₉	C₂×C₄	1	2	yes	—
11	C₂²×C₁₉₉	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₉₉	C₁₆	1	4	yes	complemented
13	C₄×C₁₉₉	C₄²	1	1	yes	characteristic
14	C₄×C₁₉₉	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₉₉	C₄×C₈	1	1	yes	characteristic
16	C₂×C₁₉₉	C₂×C₁₆	1	2	yes	—
17	C₁₉₉	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	199	1	no	maximal, Sylow
19	C₂×C₁₆	—	199	2	no	—
20	C₄×C₈	D₁₉₉	1	1	yes	characteristic
21	C₂×C₈	Dic₁₉₉	1	1	yes	characteristic
22	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
23	C₄²	Dic₁₉₉	1	1	yes	characteristic
24	C₁₆	—	199	4	no	—
25	C₂×C₄	C₁₉₉⋊C₈	1	2	yes	—
26	C₂×C₄	C₂×Dic₁₉₉	1	1	yes	characteristic
27	C₈	C₁₉₉⋊C₈	1	2	yes	—
28	C₈	C₄×D₁₉₉	1	2	yes	—
29	C₂²	C₂×C₁₉₉⋊C₈	1	1	yes	characteristic
30	C₄	C₁₉₉⋊C₁₆	1	4	yes	direct product factor
31	C₄	C₄×Dic₁₉₉	1	1	yes	characteristic
32	C₄	C₂×C₁₉₉⋊C₈	1	1	yes	characteristic
33	C₂	C₄×C₁₉₉⋊C₈	1	1	yes	characteristic
34	C₂	C₂×C₁₉₉⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₈	D₁₉₉
commutator, hypocenter	C₁₉₉	C₄×C₁₆
Frattini	C₂×C₈	C₂×D₁₉₉
Fitting	C₄×C₈×C₁₉₉	C₂
socle, prime radical	C₂²×C₁₉₉	C₂×C₈
cosocle	C₂×C₈×C₁₉₉	C₂²
LCS	G ▷ C₁₉₉
UCS	C₁ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₁₉₉⋊C₁₆	C₄	direct (N × H)
12. C₄×C₁₉₉	C₁₆	semidirect
17. C₁₉₉	C₄×C₁₆	semidirect
30. C₄	C₁₉₉⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉₉⋊C₁₆	2
C₄×C₈×C₁₉₉	2
C₄×C₁₆	199

Subgroups — C4×C199⋊C16 #27163792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉₉⋊C₁₆ #27163792