Subgroups — Q₈×C₃⋊C₈ #5023

Order 192.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊C₈)	C₂	1	3	yes	maximal
3	C₄×C₃⋊C₈	C₂	1	3	yes	maximal
4	C₈×Q₈	—	3	1	no	maximal, Sylow
5	C₂×C₃×Q₈	C₄	1	1	yes	characteristic
6	C₃×C₄⋊C₄	C₄	1	3	yes	—
7	C₃×C₄²	C₂²	1	3	yes	—
8	C₂×C₃⋊C₈	C₂²	1	3	yes	—
9	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×Q₈	D₃	1	1	yes	characteristic
11	C₄⋊C₈	—	3	3	no	—
12	C₄×C₈	—	3	3	no	—
13	C₃×Q₈	C₈	1	4	yes	complemented
14	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
15	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
16	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
17	C₃⋊C₈	—	2	3	no	—
18	C₃⋊C₈	Q₈	1	2	yes	direct product factor
19	C₂×Q₈	Dic₃	1	1	yes	characteristic
20	C₂×C₈	—	3	1	no	—
21	C₂×C₈	—	3	3	no	—
22	C₄⋊C₄	Dic₃	1	3	yes	—
23	C₄²	C₂×D₃	1	3	yes	—
24	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
25	C₃×C₄	—	2	3	no	—
26	C₃×C₄	C₂×C₈	1	6	yes	—
27	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
28	C₃×C₄	#41	1	1	yes	characteristic
29	Q₈	C₃⋊C₈	1	4	yes	direct product factor
30	C₂×C₄	C₂×Dic₃	1	3	yes	—
31	C₂×C₄	C₂×Dic₃	1	3	yes	—
32	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
33	C₈	—	3	2	no	—
34	C₈	—	6	3	no	—
35	C₂×C₃	C₄×Q₈	1	1	yes	characteristic
36	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₃	#131	1	1	yes	characteristic
38	C₂²	C₂²×Dic₃	1	1	yes	characteristic
39	C₄	—	2	3	no	—
40	C₄	C₂×C₃⋊C₈	1	6	yes	—
41	C₄	D₃×Q₈	1	1	yes	characteristic
42	C₄	#239	1	1	yes	characteristic
43	C₃	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
44	C₂	C₂²×C₃⋊C₈	1	1	yes	characteristic
45	C₂	Q₈×Dic₃	1	1	yes	characteristic
46	C₂	#948	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃
commutator	C₂×C₃	C₂²×C₈
Fitting	C₃×C₄×Q₈	C₂
socle, prime radical	C₂²×C₃	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₄×Q₈	D₃
hypocenter	C₃	C₈×Q₈
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
13. C₃×Q₈	C₈	semidirect
18. C₃⋊C₈	Q₈	direct (N × H)
29. Q₈	C₃⋊C₈	direct (N × H)
43. C₃	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈	2
C₄⋊(C₃⋊C₈)	2
C₄×C₃⋊C₈	2
C₈×Q₈	3

Subgroups — Q8×C3⋊C8 #5023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊C₈ #5023