Subgroups — C₈×C₂₃⋊C₁₆ #15671312

Order 2944.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₂₃	C₄	1	2	yes	—
4	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₂₃⋊C₁₆	C₄	1	4	yes	—
6	C₂×C₈×C₂₃	C₈	1	4	yes	—
7	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
8	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂₃⋊C₁₆	C₈	1	8	yes	direct product factor
10	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₂₃	C₂×C₈	1	2	yes	—
12	C₈×C₂₃	C₁₆	1	8	yes	complemented
13	C₈×C₂₃	C₂×C₈	1	4	yes	—
14	C₈×C₁₆	—	23	1	no	maximal, Sylow
15	C₂²×C₂₃	C₄×C₈	1	1	yes	characteristic
16	C₄×C₂₃	C₄×C₈	1	2	yes	—
17	C₄×C₂₃	C₂×C₁₆	1	4	yes	—
18	C₄×C₁₆	—	23	2	no	—
19	C₈²	D₂₃	1	1	yes	characteristic
20	C₂×C₂₃	C₈²	1	1	yes	characteristic
21	C₂×C₂₃	C₄×C₁₆	1	2	yes	—
22	C₂×C₁₆	—	23	4	no	—
23	C₄×C₈	Dic₂₃	1	2	yes	—
24	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
25	C₂₃	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₈	C₂₃⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₂₃	1	2	yes	—
28	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
29	C₁₆	—	23	8	no	—
30	C₂×C₄	C₂×C₂₃⋊C₈	1	2	yes	—
31	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
32	C₈	C₂₃⋊C₁₆	1	8	yes	direct product factor
33	C₈	C₈×D₂₃	1	4	yes	—
34	C₂²	C₄×C₂₃⋊C₈	1	1	yes	characteristic
35	C₄	C₂×C₂₃⋊C₁₆	1	4	yes	—
36	C₄	C₈×Dic₂₃	1	2	yes	—
37	C₂	C₈×C₂₃⋊C₈	1	1	yes	characteristic
38	C₂	C₄×C₂₃⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₂₃
commutator, hypocenter	C₂₃	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₈²×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₄×C₈
cosocle	C₄×C₈×C₂₃	C₂²
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
9. C₂₃⋊C₁₆	C₈	direct (N × H)
12. C₈×C₂₃	C₁₆	semidirect
25. C₂₃	C₈×C₁₆	semidirect
32. C₈	C₂₃⋊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
C₄×C₂₃⋊C₁₆	2
C₈²×C₂₃	2
C₈×C₁₆	23

Subgroups — C8×C23⋊C16 #15671312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂₃⋊C₁₆ #15671312