Subgroups — C₈×C₇₁⋊C₁₆ #22586255

Order 9088.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇₁⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇₁⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₇₁	C₄	1	2	yes	—
5	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
6	C₇₁⋊C₁₆	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₇₁	C₈	1	4	yes	—
8	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
9	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₇₁	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₇₁	C₂×C₈	1	2	yes	—
12	C₈×C₇₁	C₁₆	1	8	yes	complemented
13	C₈×C₇₁	C₂×C₈	1	4	yes	—
14	C₂²×C₇₁	C₄×C₈	1	1	yes	characteristic
15	C₄×C₇₁	C₄×C₈	1	2	yes	—
16	C₄×C₇₁	C₂×C₁₆	1	4	yes	—
17	C₂×C₇₁	C₈²	1	1	yes	characteristic
18	C₂×C₇₁	C₄×C₁₆	1	2	yes	—
19	C₈×C₁₆	—	71	1	no	maximal, Sylow
20	C₇₁	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	71	2	no	—
22	C₈²	D₇₁	1	1	yes	characteristic
23	C₂×C₁₆	—	71	4	no	—
24	C₄×C₈	Dic₇₁	1	2	yes	—
25	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
26	C₂×C₈	C₇₁⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₇₁	1	2	yes	—
28	C₄²	C₂×Dic₇₁	1	1	yes	characteristic
29	C₁₆	—	71	8	no	—
30	C₂×C₄	C₄×Dic₇₁	1	1	yes	characteristic
31	C₂×C₄	C₂×C₇₁⋊C₈	1	2	yes	—
32	C₈	C₇₁⋊C₁₆	1	8	yes	direct product factor
33	C₈	C₈×D₇₁	1	4	yes	—
34	C₂²	C₄×C₇₁⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₇₁	1	2	yes	—
36	C₄	C₂×C₇₁⋊C₁₆	1	4	yes	—
37	C₂	C₈×C₇₁⋊C₈	1	1	yes	characteristic
38	C₂	C₄×C₇₁⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₇₁
commutator, hypocenter	C₇₁	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₇₁
Fitting	C₈²×C₇₁	C₂
socle	C₂²×C₇₁	C₄×C₈
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. C₇₁⋊C₁₆	C₈	direct (N × H)
12. C₈×C₇₁	C₁₆	semidirect
20. C₇₁	C₈×C₁₆	semidirect
32. C₈	C₇₁⋊C₁₆	direct (N × H)

Subgroups — C8×C71⋊C16 #22586255

Conjugacy classes of subgroups

Complements

Subgroups — C₈×C₇₁⋊C₁₆ #22586255