Subgroups — C₈×C₁₉₉⋊C₈ #27163738

Order 12736.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉₉⋊C₈	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉₉⋊C₈	C₄	1	4	yes	—
4	C₂×C₈×C₁₉₉	C₄	1	2	yes	—
5	C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
6	C₁₉₉⋊C₈	C₈	1	8	yes	direct product factor
7	C₂×C₄×C₁₉₉	C₂×C₄	1	2	yes	—
8	C₂×C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₉₉	C₈	1	4	yes	complemented
10	C₂²×C₁₉₉	C₄²	1	1	yes	characteristic
11	C₄×C₁₉₉	C₂×C₈	1	4	yes	—
12	C₄×C₁₉₉	C₂×C₈	1	2	yes	—
13	C₂×C₁₉₉	C₄×C₈	1	2	yes	—
14	C₂×C₁₉₉	C₄×C₈	1	1	yes	characteristic
15	C₁₉₉	C₈²	1	1	yes	characteristic, complemented, Sylow
16	C₈²	—	199	1	no	maximal, Sylow
17	C₄×C₈	—	199	2	no	—
18	C₄×C₈	D₁₉₉	1	1	yes	characteristic
19	C₂×C₈	—	199	4	no	—
20	C₂×C₈	Dic₁₉₉	1	2	yes	—
21	C₄²	C₂×D₁₉₉	1	1	yes	characteristic
22	C₂×C₄	C₄×D₁₉₉	1	2	yes	—
23	C₂×C₄	C₂×Dic₁₉₉	1	1	yes	characteristic
24	C₈	—	199	8	no	—
25	C₈	C₁₉₉⋊C₈	1	4	yes	direct product factor
26	C₂²	C₄×Dic₁₉₉	1	1	yes	characteristic
27	C₄	C₈×D₁₉₉	1	4	yes	—
28	C₄	C₂×C₁₉₉⋊C₈	1	2	yes	—
29	C₂	C₈×Dic₁₉₉	1	2	yes	—
30	C₂	C₄×C₁₉₉⋊C₈	1	1	yes	characteristic

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

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