Subgroups — (C₂×D₉)⋊C₈ #63379

Order 288.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊C₈	—	3	1	no	maximal
5	C₂²×D₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₉	C₄	1	1	yes	characteristic
8	C₄×D₉	—	2	1	no	—
9	C₄×D₉	—	2	1	no	—
10	C₈×C₉	—	2	1	no	—
11	C₉⋊C₈	—	2	1	no	—
12	C₂×C₄×D₃	—	3	1	no	—
13	C₂×C₃×C₈	D₃	1	1	yes	characteristic
14	C₂×C₃⋊C₈	—	3	1	no	—
15	C₂²×C₉	C₂×C₄	1	1	yes	characteristic
16	C₂×D₉	—	2	1	no	—
17	C₂×D₉	—	2	1	no	—
18	C₂×D₉	C₈	1	2	yes	complemented
19	C₄×C₉	D₄	1	1	yes	characteristic
20	C₄×C₉	D₄	1	1	yes	characteristic
21	Dic₉	—	2	1	no	—
22	C₂²⋊C₈	—	9	1	no	Sylow
23	C₂²×D₃	—	3	1	no	—
24	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₃	—	3	1	no	—
26	C₄×D₃	—	6	1	no	—
27	C₄×D₃	—	6	1	no	—
28	C₃×C₈	—	2	1	no	—
29	C₃⋊C₈	—	6	1	no	—
30	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₉	M₁₆	1	1	yes	characteristic
33	D₉	—	2	2	no	—
34	C₂²×C₄	—	9	1	no	—
35	C₂×C₈	—	9	1	no	—
36	C₂×C₈	D₉	1	1	yes	characteristic, complemented
37	C₂²×C₃	C₄×D₃	1	1	yes	characteristic
38	C₂×D₃	—	3	2	no	—
39	C₂×D₃	—	6	1	no	—
40	C₂×D₃	—	6	1	no	—
41	C₃×C₄	D₁₂	1	1	yes	characteristic
42	C₃×C₄	#67	1	1	yes	characteristic
43	Dic₃	—	6	1	no	—
44	C₉	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
45	C₂³	—	9	1	no	—
46	C₂×C₄	—	9	1	no	—
47	C₂×C₄	—	18	1	no	—
48	C₂×C₄	—	18	1	no	—
49	C₂×C₄	C₂×D₉	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	—	18	1	no	—
52	C₂×C₃	D₃×C₈	1	1	yes	characteristic
53	C₂×C₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
54	C₂×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
55	D₃	—	6	2	no	—
56	C₂²	—	9	2	no	—
57	C₂²	—	18	1	no	—
58	C₂²	—	18	1	no	—
59	C₂²	C₄×D₉	1	1	yes	characteristic
60	C₄	—	18	1	no	—
61	C₄	D₃₆	1	1	yes	characteristic
62	C₄	#611	1	1	yes	characteristic
63	C₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
64	C₂	—	18	2	no	—
65	C₂	C₈×D₉	1	1	yes	characteristic
66	C₂	#3663	1	1	yes	characteristic
67	C₂	(C₂×D₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₉
commutator	C₂×C₉	C₂×C₈
Frattini	C₂×C₃×C₄	C₂×D₃
Fitting	C₂×C₈×C₉	C₂
socle	C₂²×C₃	C₄×D₃
prime radical	C₂²×D₉	C₄
cosocle	C₂×C₄×C₉	C₂²
hypercenter	C₂×C₈	D₉
hypocenter	C₉	C₂²⋊C₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×C₉	C₂	semidirect
3. C₂×C₉⋊C₈	C₂	semidirect
18. C₂×D₉	C₈	semidirect
36. C₂×C₈	D₉	semidirect
44. C₉	C₂²⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₉	2
C₂×C₈×C₉	2
C₂×C₉⋊C₈	2
(C₂×D₃)⋊C₈	3

Subgroups — (C2×D9)⋊C8 #63379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₉)⋊C₈ #63379