Subgroups — C₂×C₈×D₁₉₉ #20263956

Order 6368.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₉₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₁₉₉	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₉₉	C₄	1	1	yes	characteristic
6	C₂×Dic₁₉₉	C₄	1	1	yes	characteristic
7	C₄×D₁₉₉	C₄	1	2	yes	—
8	C₄×D₁₉₉	C₂²	1	2	yes	—
9	C₁₉₉⋊C₈	C₂²	1	2	yes	complemented
10	C₂×C₄×C₁₉₉	C₂²	1	1	yes	characteristic
11	C₈×C₁₉₉	C₂²	1	2	yes	complemented
12	C₂²×C₁₉₉	C₂×C₄	1	1	yes	characteristic
13	C₂×D₁₉₉	C₈	1	4	yes	direct product factor
14	C₂×D₁₉₉	C₂×C₄	1	2	yes	—
15	C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₉₉	C₂³	1	1	yes	characteristic
17	Dic₁₉₉	C₂×C₄	1	2	yes	—
18	C₂×C₁₉₉	C₂×C₈	1	2	yes	complemented
19	C₂×C₁₉₉	C₂²×C₄	1	1	yes	characteristic
20	D₁₉₉	C₂×C₈	1	4	yes	direct product factor
21	C₁₉₉	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₈	—	199	1	no	maximal, Sylow
23	C₂²×C₄	—	199	1	no	—
24	C₂×C₈	—	199	1	no	—
25	C₂×C₈	—	199	4	no	—
26	C₂×C₈	D₁₉₉	1	1	yes	characteristic, direct product factor
27	C₂³	—	199	1	no	—
28	C₂×C₄	—	199	1	no	—
29	C₂×C₄	—	199	2	no	—
30	C₂×C₄	—	199	2	no	—
31	C₂×C₄	C₂×D₁₉₉	1	1	yes	characteristic
32	C₈	—	199	2	no	—
33	C₈	C₂×D₁₉₉	1	2	yes	direct product factor
34	C₂²	—	199	4	no	—
35	C₂²	—	199	2	no	—
36	C₂²	C₄×D₁₉₉	1	1	yes	characteristic
37	C₄	—	199	2	no	—
38	C₄	C₄×D₁₉₉	1	1	yes	characteristic
39	C₄	C₂²×D₁₉₉	1	1	yes	characteristic
40	C₂	—	199	4	no	—
41	C₂	C₈×D₁₉₉	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₁₉₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉₉⋊C₈	C₂	semidirect
3. C₈×D₁₉₉	C₂	direct (N × H)
4. C₂×C₈×C₁₉₉	C₂	semidirect
9. C₁₉₉⋊C₈	C₂²	semidirect
11. C₈×C₁₉₉	C₂²	semidirect
13. C₂×D₁₉₉	C₈	direct (N × H)
18. C₂×C₁₉₉	C₂×C₈	semidirect
20. D₁₉₉	C₂×C₈	direct (N × H)
21. C₁₉₉	C₂²×C₈	semidirect
26. C₂×C₈	D₁₉₉	direct (N × H)
33. C₈	C₂×D₁₉₉	direct (N × H)
41. C₂	C₈×D₁₉₉	direct (N × H)

Subgroups — C2×C8×D199 #20263956

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₈×D₁₉₉ #20263956