Subgroups — Q₈×C₉⋊D₉ #13047455

Order 1296.

437 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₉⋊D₉	C₂	1	3	yes	maximal
3	#10619651	C₂	1	3	yes	maximal, complemented
4	Q₈×C₃⋊D₉	—	3	4	no	maximal
5	C₂×C₉⋊D₉	C₂²	1	1	yes	characteristic
6	C₄×C₉²	C₂²	1	3	yes	—
7	C₉⋊Dic₉	C₂²	1	3	yes	—
8	C₃×Q₈×C₉	D₃	1	4	yes	—
9	C₄×C₃⋊D₉	—	3	12	no	—
10	#6226	—	3	12	no	—
11	C₂×C₉²	C₂³	1	1	yes	characteristic
12	C₉⋊D₉	Q₈	1	2	yes	direct product factor
13	Q₈×C₃⋊D₃	—	9	1	no	—
14	Q₈×D₉	—	9	12	no	—
15	C₂×C₃⋊D₉	—	3	4	no	—
16	C₃×C₄×C₉	C₂×D₃	1	12	yes	—
17	C₃⋊Dic₉	—	3	12	no	—
18	C₉²	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₃²×Q₈	C₃⋊D₃	1	1	yes	characteristic
20	C₄×C₃⋊D₃	—	9	3	no	—
21	#634	—	9	3	no	—
22	Q₈×C₉	D₉	1	12	yes	complemented
23	C₄×D₉	—	9	36	no	—
24	Dic₁₈	—	9	36	no	—
25	C₂×C₃×C₉	C₂²×D₃	1	4	yes	—
26	C₃⋊D₉	—	3	8	no	—
27	D₃×Q₈	—	27	4	no	—
28	C₂×C₃⋊D₃	—	9	1	no	—
29	C₃²×C₄	C₂×C₃⋊D₃	1	3	yes	—
30	C₃⋊Dic₃	—	9	3	no	—
31	C₂×D₉	—	9	12	no	—
32	C₄×C₉	C₂×D₉	1	36	yes	—
33	Dic₉	—	9	36	no	—
34	C₃×C₉	D₃×Q₈	1	4	yes	—
35	C₃×Q₈	C₃⋊D₉	1	4	yes	—
36	C₄×D₃	—	27	12	no	—
37	Dic₆	—	27	12	no	—
38	C₂×C₃²	C₂²×C₃⋊D₃	1	1	yes	characteristic
39	C₃⋊D₃	—	9	2	no	—
40	C₂×C₉	C₂²×D₉	1	12	yes	—
41	D₉	—	9	24	no	—
42	C₂×Q₈	—	81	1	no	Sylow
43	C₂×D₃	—	27	4	no	—
44	C₃×C₄	C₂×C₃⋊D₉	1	12	yes	—
45	Dic₃	—	27	12	no	—
46	C₃²	Q₈×C₃⋊D₃	1	1	yes	characteristic
47	C₉	Q₈×D₉	1	12	yes	complemented
48	Q₈	—	81	3	no	—
49	Q₈	C₉⋊D₉	1	1	yes	characteristic, direct product factor
50	C₂×C₄	—	81	3	no	—
51	C₂×C₃	C₂²×C₃⋊D₉	1	4	yes	—
52	D₃	—	27	8	no	—
53	C₂²	—	81	1	no	—
54	C₄	—	81	3	no	—
55	C₄	C₂×C₉⋊D₉	1	3	yes	—
56	C₃	Q₈×C₃⋊D₉	1	4	yes	—
57	C₂	—	81	2	no	—
58	C₂	C₂²×C₉⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×C₉⋊D₉
commutator, cosocle	C₂×C₉²	C₂³
Frattini, socle	C₂×C₃²	C₂²×C₃⋊D₃
Fitting	Q₈×C₉²	C₂
prime radical	C₂×C₉⋊D₉	C₂²
hypercenter	Q₈	C₉⋊D₉
hypocenter	C₉²	C₂×Q₈
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
1. Q₈×C₉²	C₂	semidirect
3. #10619651	C₂	semidirect
12. C₉⋊D₉	Q₈	direct (N × H)
18. C₉²	C₂×Q₈	semidirect
22. Q₈×C₉	D₉	semidirect
47. C₉	Q₈×D₉	semidirect
49. Q₈	C₉⋊D₉	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₉²	2
C₄×C₉⋊D₉	2
#10619651	2
Q₈×C₃⋊D₉	3

Subgroups — Q8×C9⋊D9 #13047455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₉⋊D₉ #13047455