Subgroups — #88993

Order 432.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#622	C₂	1	2	yes	maximal, complemented
3	#3792	—	3	1	no	maximal
4	C₂²×C₃³	C₄	1	1	yes	characteristic
5	C₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
6	C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊Dic₃	D₃	1	1	yes	characteristic
8	C₂×C₃×Dic₃	—	6	2	no	—
9	#622	—	3	2	no	—
10	C₂×C₃³	—	2	1	no	—
11	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
12	#208	—	9	1	no	maximal
13	C₂²×C₃²	—	2	2	no	—
14	C₂²×C₃²	—	4	2	no	—
15	C₂²×C₃²	Dic₃	1	1	yes	characteristic
16	C₃⋊Dic₃	Dic₃	1	1	yes	characteristic
17	C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
18	C₃×Dic₃	—	6	2	no	—
19	C₃×Dic₃	—	6	2	no	—
20	C₃³	M₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₄	—	9	1	no	—
22	C₂×Dic₃	—	6	2	no	—
23	C₃⋊C₈	—	9	2	no	—
24	C₂×C₃²	—	2	1	no	—
25	C₂×C₃²	—	2	4	no	—
26	C₂×C₃²	—	2	2	no	—
27	C₂×C₃²	—	4	4	no	—
28	C₂×C₃²	—	4	2	no	—
29	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
30	M₁₆	—	27	1	no	Sylow
31	C₂²×C₃	—	2	2	no	—
32	C₂²×C₃	—	4	2	no	—
33	C₂²×C₃	#157	1	1	yes	characteristic
34	C₃×C₄	—	9	1	no	—
35	C₃×C₄	—	9	1	no	—
36	Dic₃	—	6	2	no	—
37	Dic₃	—	6	2	no	—
38	C₃²	—	2	2	no	—
39	C₃²	—	4	2	no	—
40	C₃²	#208	1	1	yes	characteristic, complemented
41	C₂×C₄	—	9	1	no	—
42	C₈	—	27	2	no	—
43	C₂×C₃	—	2	4	no	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	—	2	2	no	—
46	C₂×C₃	—	4	4	no	—
47	C₂×C₃	—	4	2	no	—
48	C₂×C₃	C₂×#157	1	1	yes	characteristic
49	C₂²	C₃⋊#157	1	1	yes	characteristic
50	C₄	—	9	1	no	—
51	C₄	—	9	1	no	—
52	C₃	—	2	2	no	—
53	C₃	—	4	2	no	—
54	C₃	#3792	1	1	yes	characteristic, complemented
55	C₂	—	2	1	no	—
56	C₂	C₂×C₃⋊#157	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊#157
commutator, socle	C₂×C₃³	C₂×C₄
Fitting, prime radical	C₂²×C₃³	C₄
cosocle	C₃×C₃⋊Dic₃	C₂²
hypercenter	C₂²	C₃⋊#157
hypocenter	C₃³	M₁₆
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₃⋊#622	C₂	semidirect
20. C₃³	M₁₆	semidirect
40. C₃²	#208	semidirect
54. C₃	#3792	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₃⋊Dic₃	2
C₃⋊#622	2
#3792	3
#208	9