Subgroups — Q₈×C₂₃⋊C₈ #13092543

Order 1472.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₂₃⋊C₈)	C₂	1	3	yes	maximal
3	C₄×C₂₃⋊C₈	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₃	C₄	1	1	yes	characteristic
5	C₄⋊C₄×C₂₃	C₄	1	3	yes	—
6	C₄²×C₂₃	C₂²	1	3	yes	—
7	C₂×C₂₃⋊C₈	C₂²	1	3	yes	—
8	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
9	Q₈×C₂₃	C₈	1	4	yes	complemented
10	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
13	C₂₃⋊C₈	—	2	3	no	—
14	C₂₃⋊C₈	Q₈	1	2	yes	direct product factor
15	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₂₃	—	2	3	no	—
17	C₄×C₂₃	C₂×C₈	1	6	yes	—
18	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₂₃	#41	1	1	yes	characteristic
20	C₈×Q₈	—	23	1	no	maximal, Sylow
21	C₂×C₂₃	C₄×Q₈	1	1	yes	characteristic
22	C₂×C₂₃	C₂²×C₈	1	1	yes	characteristic
23	C₂×C₂₃	#131	1	1	yes	characteristic
24	C₄×Q₈	D₂₃	1	1	yes	characteristic
25	C₄⋊C₈	—	23	3	no	—
26	C₄×C₈	—	23	3	no	—
27	C₂₃	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	Dic₂₃	1	1	yes	characteristic
29	C₂×C₈	—	23	1	no	—
30	C₂×C₈	—	23	3	no	—
31	C₄⋊C₄	Dic₂₃	1	3	yes	—
32	C₄²	C₂×D₂₃	1	3	yes	—
33	Q₈	C₂₃⋊C₈	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₂₃	1	3	yes	—
35	C₂×C₄	C₂×Dic₂₃	1	3	yes	—
36	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
37	C₈	—	23	2	no	—
38	C₈	—	46	3	no	—
39	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×C₂₃⋊C₈	1	6	yes	—
42	C₄	Q₈×D₂₃	1	1	yes	characteristic
43	C₄	#67292	1	1	yes	characteristic
44	C₂	C₂²×C₂₃⋊C₈	1	1	yes	characteristic
45	C₂	Q₈×Dic₂₃	1	1	yes	characteristic
46	C₂	#10625119	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂²×C₈
Fitting	C₄×Q₈×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂²×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₄×Q₈	D₂₃
hypocenter	C₂₃	C₈×Q₈
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₂₃	C₈	semidirect
14. C₂₃⋊C₈	Q₈	direct (N × H)
27. C₂₃	C₈×Q₈	semidirect
33. Q₈	C₂₃⋊C₈	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×Q₈×C₂₃	2
C₄⋊(C₂₃⋊C₈)	2
C₄×C₂₃⋊C₈	2
C₈×Q₈	23

Subgroups — Q8×C23⋊C8 #13092543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₂₃⋊C₈ #13092543