Subgroups — Q₈×C₃⋊Dic₃ #64154

Order 288.

210 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊Dic₃)	C₂	1	3	yes	maximal
3	C₄×C₃⋊Dic₃	C₂	1	3	yes	maximal
4	Q₈×Dic₃	—	3	4	no	maximal
5	C₃²×Q₈	C₄	1	4	yes	complemented
6	C₂×C₃²×C₄	C₂²	1	3	yes	—
7	C₂×C₃⋊Dic₃	C₂²	1	3	yes	—
8	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×Q₈	D₃	1	4	yes	—
10	C₄⋊Dic₃	—	3	12	no	—
11	C₄×Dic₃	—	3	12	no	—
12	C₂²×C₃²	C₂³	1	1	yes	characteristic
13	C₃²×C₄	C₂×C₄	1	6	yes	—
14	C₃⋊Dic₃	—	2	3	no	—
15	C₃⋊Dic₃	Q₈	1	2	yes	direct product factor
16	C₄×Q₈	—	9	1	no	Sylow
17	C₃×Q₈	Dic₃	1	16	yes	complemented
18	C₂×C₃×C₄	C₂×D₃	1	12	yes	—
19	C₂×Dic₃	—	3	4	no	—
20	C₂×Dic₃	—	3	12	no	—
21	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₃²	#41	1	1	yes	characteristic
24	C₂×Q₈	C₃⋊D₃	1	1	yes	characteristic
25	C₄⋊C₄	—	9	3	no	—
26	C₄²	—	9	3	no	—
27	C₂²×C₃	C₂²×D₃	1	4	yes	—
28	C₃×C₄	C₂×Dic₃	1	24	yes	—
29	Dic₃	—	3	8	no	—
30	Dic₃	—	6	12	no	—
31	C₃²	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈	C₃⋊Dic₃	1	4	yes	direct product factor
33	C₂×C₄	—	9	1	no	—
34	C₂×C₄	—	9	3	no	—
35	C₂×C₄	C₂×C₃⋊D₃	1	3	yes	—
36	C₂×C₃	D₃×Q₈	1	4	yes	—
37	C₂×C₃	#239	1	4	yes	—
38	C₂×C₃	C₂²×Dic₃	1	4	yes	—
39	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
40	C₄	—	9	2	no	—
41	C₄	—	18	3	no	—
42	C₄	C₂×C₃⋊Dic₃	1	6	yes	—
43	C₃	Q₈×Dic₃	1	4	yes	complemented
44	C₂	Q₈×C₃⋊D₃	1	1	yes	characteristic
45	C₂	#3832	1	1	yes	characteristic
46	C₂	C₂²×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₄
Fitting	C₂×C₃²×Q₈	C₂
socle, prime radical, cosocle	C₂²×C₃²	C₂³
hypercenter	C₂×Q₈	C₃⋊D₃
hypocenter	C₃²	C₄×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
5. C₃²×Q₈	C₄	semidirect
15. C₃⋊Dic₃	Q₈	direct (N × H)
17. C₃×Q₈	Dic₃	semidirect
31. C₃²	C₄×Q₈	semidirect
32. Q₈	C₃⋊Dic₃	direct (N × H)
43. C₃	Q₈×Dic₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×Q₈	2
C₄⋊(C₃⋊Dic₃)	2
C₄×C₃⋊Dic₃	2
Q₈×Dic₃	3

Subgroups — Q8×C3⋊Dic3 #64154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊Dic₃ #64154