Subgroups — C₃⋊((C₂²⋊C₉)⋊C₄) #88612

Order 432.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	#3757	—	3	1	no	maximal
3	(C₂²⋊C₉)⋊C₄	—	3	3	no	maximal
4	C₃×C₂²⋊C₉	C₄	1	1	yes	characteristic, complemented
5	C₃⋊Dic₉	—	4	1	no	maximal
6	C₂³×C₃²	D₃	1	1	yes	characteristic
7	C₂×C₃⋊Dic₃	—	3	1	no	—
8	C₂×C₃⋊Dic₃	—	3	1	no	—
9	C₂×C₂²⋊C₉	D₃	1	3	yes	—
10	C₂×C₃×C₉	—	4	1	no	—
11	#217	—	9	3	no	—
12	#217	—	9	1	no	—
13	C₂²×C₃²	—	3	1	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	Dic₃	1	1	yes	characteristic
16	C₃⋊Dic₃	—	6	1	no	—
17	C₃⋊Dic₃	—	6	1	no	—
18	C₂²⋊C₉	Dic₃	1	3	yes	complemented
19	Dic₉	—	12	3	no	—
20	C₃×C₉	—	4	1	no	Sylow
21	C₂³×C₃	D₉	1	3	yes	—
22	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
23	C₂×Dic₃	—	9	3	no	—
24	C₂×Dic₃	—	9	1	no	—
25	C₂×Dic₃	—	9	3	no	—
26	C₂×Dic₃	—	9	1	no	—
27	C₂×C₃²	—	3	1	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₂×C₃²	S₄	1	1	yes	characteristic
30	C₂×C₉	—	4	3	no	—
31	C₂²⋊C₄	—	27	1	no	Sylow
32	C₂²×C₃	—	3	3	no	—
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	—	3	3	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	Dic₉	1	3	yes	complemented
37	C₂²×C₃	C₃⋊Dic₃	1	1	yes	characteristic
38	Dic₃	—	18	3	no	—
39	Dic₃	—	18	1	no	—
40	Dic₃	—	18	3	no	—
41	Dic₃	—	18	1	no	—
42	C₃²	SL(2,ℤ/4)	1	1	yes	characteristic
43	C₉	—	4	3	no	—
44	C₂³	C₃⋊D₉	1	1	yes	characteristic
45	C₂×C₄	—	27	1	no	—
46	C₂×C₄	—	27	1	no	—
47	C₂×C₃	—	3	3	no	—
48	C₂×C₃	—	3	3	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂×C₃	—	3	1	no	—
51	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	3	yes	—
52	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
53	C₂²	—	3	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₃⋊Dic₉	1	1	yes	characteristic, complemented
56	C₄	—	54	1	no	—
57	C₄	—	54	1	no	—
58	C₃	(C₂²⋊C₉)⋊C₄	1	3	yes	complemented
59	C₃	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic
60	C₂	—	3	1	no	—
61	C₂	—	3	1	no	—
62	C₂	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₃⋊((C₂²⋊C₉)⋊C₂)
commutator, hypocenter	C₃×C₂²⋊C₉	C₄
Frattini	C₂×C₃	C₃⋊S₄
Fitting, socle, prime radical	C₂³×C₃²	D₃
cosocle	C₂×C₃×C₂²⋊C₉	C₂
LCS	G ▷ C₃×C₂²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
4. C₃×C₂²⋊C₉	C₄	semidirect
18. C₂²⋊C₉	Dic₃	semidirect
36. C₂²×C₃	Dic₉	semidirect
55. C₂²	C₃⋊Dic₉	semidirect
58. C₃	(C₂²⋊C₉)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂²⋊C₉	2
#3757	3
(C₂²⋊C₉)⋊C₄	3
C₃⋊Dic₉	4

Subgroups — C3⋊((C22⋊C9)⋊C4) #88612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₂²⋊C₉)⋊C₄) #88612