Subgroups — Q₈×C₃⋊D₉ #88745

Order 432.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₃⋊D₉	C₂	1	3	yes	maximal
3	#6226	C₂	1	3	yes	maximal, complemented
4	Q₈×C₃⋊D₃	—	3	1	no	maximal
5	Q₈×D₉	—	3	3	no	maximal
6	C₂×C₃⋊D₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	3	yes	—
8	C₃⋊Dic₉	C₂²	1	3	yes	—
9	C₃²×Q₈	D₃	1	1	yes	characteristic
10	C₄×C₃⋊D₃	—	3	3	no	—
11	#634	—	3	3	no	—
12	Q₈×C₉	D₃	1	3	yes	complemented
13	C₄×D₉	—	3	9	no	—
14	Dic₁₈	—	3	9	no	—
15	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
16	C₃⋊D₉	Q₈	1	2	yes	direct product factor
17	D₃×Q₈	—	9	3	no	—
18	D₃×Q₈	—	9	1	no	—
19	C₂×C₃⋊D₃	—	3	1	no	—
20	C₃²×C₄	C₂×D₃	1	3	yes	—
21	C₃⋊Dic₃	—	3	3	no	—
22	C₂×D₉	—	3	3	no	—
23	C₄×C₉	C₂×D₃	1	9	yes	—
24	Dic₉	—	3	9	no	—
25	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₃×Q₈	D₉	1	3	yes	complemented
27	C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
28	C₄×D₃	—	9	9	no	—
29	C₄×D₃	—	9	3	no	—
30	Dic₆	—	9	9	no	—
31	Dic₆	—	9	3	no	—
32	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
33	C₃⋊D₃	—	3	2	no	—
34	C₂×C₉	C₂²×D₃	1	3	yes	—
35	D₉	—	3	6	no	—
36	C₂×Q₈	—	27	1	no	Sylow
37	C₂×D₃	—	9	3	no	—
38	C₂×D₃	—	9	1	no	—
39	C₃×C₄	C₂×D₉	1	9	yes	—
40	C₃×C₄	C₂×C₃⋊D₃	1	3	yes	—
41	Dic₃	—	9	9	no	—
42	Dic₃	—	9	3	no	—
43	C₃²	D₃×Q₈	1	1	yes	characteristic
44	C₉	D₃×Q₈	1	3	yes	complemented
45	Q₈	—	27	3	no	—
46	Q₈	C₃⋊D₉	1	1	yes	characteristic, direct product factor
47	C₂×C₄	—	27	3	no	—
48	C₂×C₃	C₂²×D₉	1	3	yes	—
49	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
50	D₃	—	9	6	no	—
51	D₃	—	9	2	no	—
52	C₂²	—	27	1	no	—
53	C₄	—	27	3	no	—
54	C₄	C₂×C₃⋊D₉	1	3	yes	—
55	C₃	Q₈×D₉	1	3	yes	complemented
56	C₃	Q₈×C₃⋊D₃	1	1	yes	characteristic
57	C₂	—	27	2	no	—
58	C₂	C₂²×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×C₃⋊D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊D₃
Fitting	C₃×Q₈×C₉	C₂
socle	C₂×C₃²	C₂²×D₃
prime radical	C₂×C₃⋊D₉	C₂²
hypercenter	Q₈	C₃⋊D₉
hypocenter	C₃×C₉	C₂×Q₈
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₉	C₂	semidirect
3. #6226	C₂	semidirect
12. Q₈×C₉	D₃	semidirect
16. C₃⋊D₉	Q₈	direct (N × H)
25. C₃×C₉	C₂×Q₈	semidirect
26. C₃×Q₈	D₉	semidirect
44. C₉	D₃×Q₈	semidirect
46. Q₈	C₃⋊D₉	direct (N × H)
55. C₃	Q₈×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₉	2
C₄×C₃⋊D₉	2
#6226	2
Q₈×C₃⋊D₃	3
Q₈×D₉	3

Subgroups — Q8×C3⋊D9 #88745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊D₉ #88745