Subgroups — C₈×C₅₉⋊C₁₆ #21422011

Order 7552.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅₉⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₅₉	C₄	1	2	yes	—
5	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₅₉	C₈	1	4	yes	—
7	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
8	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
9	C₅₉⋊C₁₆	C₈	1	8	yes	direct product factor
10	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
12	C₈×C₅₉	C₁₆	1	8	yes	complemented
13	C₈×C₅₉	C₂×C₈	1	4	yes	—
14	C₂²×C₅₉	C₄×C₈	1	1	yes	characteristic
15	C₄×C₅₉	C₄×C₈	1	2	yes	—
16	C₄×C₅₉	C₂×C₁₆	1	4	yes	—
17	C₈×C₁₆	—	59	1	no	maximal, Sylow
18	C₂×C₅₉	C₈²	1	1	yes	characteristic
19	C₂×C₅₉	C₄×C₁₆	1	2	yes	—
20	C₄×C₁₆	—	59	2	no	—
21	C₈²	D₅₉	1	1	yes	characteristic
22	C₅₉	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	59	4	no	—
24	C₄×C₈	Dic₅₉	1	2	yes	—
25	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
26	C₂×C₈	C₅₉⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₅₉	1	2	yes	—
28	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
29	C₁₆	—	59	8	no	—
30	C₂×C₄	C₂×C₅₉⋊C₈	1	2	yes	—
31	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
32	C₈	C₅₉⋊C₁₆	1	8	yes	direct product factor
33	C₈	C₈×D₅₉	1	4	yes	—
34	C₂²	C₄×C₅₉⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₅₉	1	2	yes	—
36	C₄	C₂×C₅₉⋊C₁₆	1	4	yes	—
37	C₂	C₈×C₅₉⋊C₈	1	1	yes	characteristic
38	C₂	C₄×C₅₉⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₅₉
commutator, hypocenter	C₅₉	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₈²×C₅₉	C₂
socle	C₂²×C₅₉	C₄×C₈
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
9. C₅₉⋊C₁₆	C₈	direct (N × H)
12. C₈×C₅₉	C₁₆	semidirect
22. C₅₉	C₈×C₁₆	semidirect
32. C₈	C₅₉⋊C₁₆	direct (N × H)

Subgroups — C8×C59⋊C16 #21422011

Conjugacy classes of subgroups

Complements

Subgroups — C₈×C₅₉⋊C₁₆ #21422011