Subgroups — C₂×C₄⋊(C₃⋊D₉) #88735

Order 432.

270 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊D₉)	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊(C₃⋊D₃)	—	3	1	no	maximal
5	C₂×D₃₆	—	3	3	no	maximal
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊D₉	—	2	4	no	—
8	C₂×C₃⋊D₉	C₂²	1	4	yes	complemented
9	C₃×C₄×C₉	C₂²	1	2	yes	complemented
10	C₂²×C₃⋊D₃	—	3	2	no	—
11	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
12	C₄⋊(C₃⋊D₃)	—	3	4	no	—
13	C₂²×D₉	—	3	6	no	—
14	C₂×C₄×C₉	D₃	1	3	yes	complemented
15	D₃₆	—	3	12	no	—
16	C₂×C₃×C₉	D₄	1	2	yes	complemented
17	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
18	C₃⋊D₉	—	2	4	no	—
19	C₂×D₁₂	—	9	3	no	—
20	C₂×D₁₂	—	9	1	no	—
21	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
22	C₂×C₃⋊D₃	—	3	4	no	—
23	C₂×C₃⋊D₃	—	6	4	no	—
24	C₃²×C₄	C₂×D₃	1	2	yes	—
25	C₂²×C₉	C₂×D₃	1	3	yes	—
26	C₂×D₉	—	3	12	no	—
27	C₂×D₉	—	6	12	no	—
28	C₄×C₉	C₂×D₃	1	6	yes	complemented
29	C₃×C₉	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
30	C₂²×D₃	—	9	6	no	—
31	C₂²×D₃	—	9	2	no	—
32	C₂×C₃×C₄	D₉	1	3	yes	complemented
33	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
34	D₁₂	—	9	12	no	—
35	D₁₂	—	9	4	no	—
36	C₂×C₃²	D₁₂	1	2	yes	—
37	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
38	C₃⋊D₃	—	6	4	no	—
39	C₂×C₉	D₁₂	1	6	yes	complemented
40	C₂×C₉	C₂²×D₃	1	3	yes	—
41	D₉	—	6	12	no	—
42	C₂×D₄	—	27	1	no	Sylow
43	C₂²×C₃	C₂×D₉	1	3	yes	—
44	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
45	C₂×D₃	—	9	12	no	—
46	C₂×D₃	—	9	4	no	—
47	C₂×D₃	—	18	12	no	—
48	C₂×D₃	—	18	4	no	—
49	C₃×C₄	C₂×D₉	1	6	yes	complemented
50	C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
51	C₃²	C₂×D₁₂	1	1	yes	characteristic
52	C₉	C₂×D₁₂	1	3	yes	complemented
53	C₂³	—	27	2	no	—
54	D₄	—	27	4	no	—
55	C₂×C₄	C₃⋊D₉	1	1	yes	characteristic, complemented
56	C₂×C₃	D₃₆	1	6	yes	complemented
57	C₂×C₃	C₂²×D₉	1	3	yes	—
58	C₂×C₃	C₄⋊(C₃⋊D₃)	1	2	yes	—
59	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
60	D₃	—	18	12	no	—
61	D₃	—	18	4	no	—
62	C₂²	—	27	4	no	—
63	C₂²	—	54	4	no	—
64	C₂²	C₂×C₃⋊D₉	1	1	yes	characteristic
65	C₄	C₂×C₃⋊D₉	1	2	yes	complemented
66	C₃	C₂×D₃₆	1	3	yes	complemented
67	C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
68	C₂	—	54	4	no	—
69	C₂	C₄⋊(C₃⋊D₉)	1	2	yes	direct product factor
70	C₂	C₂²×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₃⋊D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle	C₂²×C₃²	C₂×D₃
hypercenter	C₂×C₄	C₃⋊D₉
hypocenter	C₃×C₉	C₂×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃⋊D₉	C₂	semidirect
2. C₂×C₃×C₄×C₉	C₂	semidirect
3. C₄⋊(C₃⋊D₉)	C₂	direct (N × H)
8. C₂×C₃⋊D₉	C₂²	semidirect
9. C₃×C₄×C₉	C₂²	semidirect
14. C₂×C₄×C₉	D₃	semidirect
16. C₂×C₃×C₉	D₄	semidirect
28. C₄×C₉	C₂×D₃	semidirect
29. C₃×C₉	C₂×D₄	semidirect
32. C₂×C₃×C₄	D₉	semidirect
39. C₂×C₉	D₁₂	semidirect
49. C₃×C₄	C₂×D₉	semidirect
52. C₉	C₂×D₁₂	semidirect
55. C₂×C₄	C₃⋊D₉	semidirect
56. C₂×C₃	D₃₆	semidirect
65. C₄	C₂×C₃⋊D₉	semidirect
66. C₃	C₂×D₃₆	semidirect
69. C₂	C₄⋊(C₃⋊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
C₂²×C₃⋊D₉	2
C₂×C₃×C₄×C₉	2
C₄⋊(C₃⋊D₉)	2
C₂×C₄⋊(C₃⋊D₃)	3
C₂×D₃₆	3

Subgroups — C2×C4⋊(C3⋊D9) #88735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊(C₃⋊D₉) #88735