Subgroups — Q₈×Dic₉ #63507

Order 288.

105 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₉	C₂	1	3	yes	maximal
3	C₄×Dic₉	C₂	1	3	yes	maximal
4	Q₈×Dic₃	—	3	1	no	maximal
5	Q₈×C₉	C₄	1	4	yes	complemented
6	C₂×C₄×C₉	C₂²	1	3	yes	—
7	C₂×Dic₉	C₂²	1	3	yes	—
8	C₂×Dic₉	C₂²	1	1	yes	characteristic
9	C₂×C₃×Q₈	D₃	1	1	yes	characteristic
10	C₄⋊Dic₃	—	3	3	no	—
11	C₄×Dic₃	—	3	3	no	—
12	C₂²×C₉	C₂³	1	1	yes	characteristic
13	C₄×C₉	C₂×C₄	1	6	yes	—
14	Dic₉	—	2	3	no	—
15	Dic₉	Q₈	1	2	yes	direct product factor
16	C₄×Q₈	—	9	1	no	Sylow
17	C₃×Q₈	Dic₃	1	4	yes	—
18	C₂×C₃×C₄	C₂×D₃	1	3	yes	—
19	C₂×Dic₃	—	3	1	no	—
20	C₂×Dic₃	—	3	3	no	—
21	C₂×C₉	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₉	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₉	#41	1	1	yes	characteristic
24	C₂×Q₈	D₉	1	1	yes	characteristic
25	C₄⋊C₄	—	9	3	no	—
26	C₄²	—	9	3	no	—
27	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
28	C₃×C₄	C₂×Dic₃	1	6	yes	—
29	Dic₃	—	3	2	no	—
30	Dic₃	—	6	3	no	—
31	C₉	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈	Dic₉	1	4	yes	direct product factor
33	C₂×C₄	—	9	1	no	—
34	C₂×C₄	—	9	3	no	—
35	C₂×C₄	C₂×D₉	1	3	yes	—
36	C₂×C₃	D₃×Q₈	1	1	yes	characteristic
37	C₂×C₃	#239	1	1	yes	characteristic
38	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
39	C₂²	C₂²×D₉	1	1	yes	characteristic
40	C₄	—	9	2	no	—
41	C₄	—	18	3	no	—
42	C₄	C₂×Dic₉	1	6	yes	—
43	C₃	Q₈×Dic₃	1	1	yes	characteristic
44	C₂	Q₈×D₉	1	1	yes	characteristic
45	C₂	#3701	1	1	yes	characteristic
46	C₂	C₂²×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₉
commutator	C₂×C₉	C₂²×C₄
Frattini, socle, prime radical	C₂²×C₃	C₂²×D₃
Fitting	C₂×Q₈×C₉	C₂
cosocle	C₂²×C₉	C₂³
hypercenter	C₂×Q₈	D₉
hypocenter	C₉	C₄×Q₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

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

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