Subgroups — C₉×C₄⋊Q₈ #63530

Order 288.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	2	yes	maximal
2	C₉×C₄⋊C₄	C₂	1	4	yes	maximal
3	C₄²×C₉	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄⋊Q₈	C₃	1	1	yes	maximal, characteristic
5	Q₈×C₉	—	2	4	no	—
6	C₂×C₄×C₉	C₂²	1	4	yes	—
7	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₉	C₂²	1	2	yes	—
9	C₂×C₃×Q₈	C₂×C₃	1	2	yes	—
10	C₃×C₄⋊C₄	C₂×C₃	1	4	yes	—
11	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₉	C₂³	1	1	yes	characteristic
13	C₄×C₉	—	2	4	no	—
14	C₄×C₉	D₄	1	2	yes	—
15	C₄×C₉	Q₈	1	4	yes	complemented
16	C₄⋊Q₈	C₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×Q₈	—	2	4	no	—
18	C₂×C₃×C₄	C₂²×C₃	1	4	yes	—
19	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
21	C₂×C₉	C₂×D₄	1	1	yes	characteristic
22	C₂×C₉	C₂×Q₈	1	2	yes	—
23	C₂×Q₈	C₂×C₉	1	2	yes	—
24	C₄⋊C₄	C₂×C₉	1	4	yes	—
25	C₄²	C₂×C₉	1	1	yes	characteristic
26	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
27	C₃×C₄	—	2	4	no	—
28	C₃×C₄	C₃×D₄	1	2	yes	—
29	C₃×C₄	C₃×Q₈	1	4	yes	—
30	C₉	C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
31	Q₈	—	2	4	no	—
32	C₂×C₄	C₂²×C₉	1	4	yes	—
33	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
34	C₂×C₄	C₂²×C₉	1	2	yes	—
35	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
36	C₂×C₃	C₂×C₃×Q₈	1	2	yes	—
37	C₂²	C₂³×C₉	1	1	yes	characteristic
38	C₄	—	2	4	no	—
39	C₄	D₄×C₉	1	2	yes	—
40	C₄	Q₈×C₉	1	4	yes	complemented
41	C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic
42	C₂	C₂×D₄×C₉	1	1	yes	characteristic
43	C₂	C₂×Q₈×C₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³
commutator	C₂²	C₂³×C₉
Frattini, socle, prime radical, cosocle	C₂²×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄×C₉	Q₈	semidirect
16. C₄⋊Q₈	C₉	direct (N × H)
30. C₉	C₄⋊Q₈	direct (N × H)
40. C₄	Q₈×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₉	2
C₉×C₄⋊C₄	2
C₄²×C₉	2
C₃×C₄⋊Q₈	3

Subgroups — C9×C4⋊Q8 #63530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄⋊Q₈ #63530