Subgroups — #88941

Order 432.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6295	C₂	1	2	yes	maximal, complemented
2	C₃×#622	C₂	1	1	yes	maximal, characteristic, complemented
3	#3774	—	3	1	no	maximal
4	C₂×C₃×C₃⋊D₃	—	2	2	no	—
5	C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	#626	—	6	2	no	—
7	#625	—	3	2	no	—
8	#622	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃³	D₄	1	1	yes	characteristic
10	C₃×C₃⋊D₃	—	4	2	no	—
11	D₂₄	—	9	1	no	maximal
12	C₂×C₃⋊D₃	—	2	2	no	—
13	C₂×C₃×D₃	—	6	2	no	—
14	C₂×C₃×D₃	—	6	2	no	—
15	C₂×C₃×D₃	—	12	2	no	—
16	C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
17	C₃×Dic₃	—	6	2	no	—
18	C₃³	D₈	1	1	yes	characteristic, complemented, Sylow
19	#67	—	18	2	no	—
20	D₁₂	—	9	2	no	—
21	C₃×C₈	—	9	1	no	—
22	C₂×C₃²	—	2	2	no	—
23	C₂×C₃²	—	4	2	no	—
24	C₂×C₃²	D₁₂	1	1	yes	characteristic
25	C₃⋊D₃	—	4	2	no	—
26	C₃×D₃	—	12	2	no	—
27	C₃×D₃	—	12	4	no	—
28	C₃×D₃	—	12	2	no	—
29	D₈	—	27	1	no	Sylow
30	C₂²×C₃	—	18	2	no	—
31	C₂×D₃	—	6	2	no	—
32	C₂×D₃	—	6	2	no	—
33	C₂×D₃	—	12	2	no	—
34	C₃×C₄	—	9	1	no	—
35	Dic₃	—	6	2	no	—
36	C₃²	—	2	2	no	—
37	C₃²	—	4	2	no	—
38	C₃²	D₂₄	1	1	yes	characteristic, complemented
39	D₄	—	27	2	no	—
40	C₈	—	9	1	no	—
41	C₂×C₃	—	2	2	no	—
42	C₂×C₃	—	4	2	no	—
43	C₂×C₃	—	36	2	no	—
44	C₂×C₃	GO⁺(4,𝔽₂)	1	1	yes	characteristic
45	D₃	—	12	2	no	—
46	D₃	—	12	4	no	—
47	D₃	—	12	2	no	—
48	C₂²	—	18	2	no	—
49	C₄	—	9	1	no	—
50	C₃	—	2	2	no	—
51	C₃	—	4	2	no	—
52	C₃	#3774	1	1	yes	characteristic, complemented
53	C₂	—	36	2	no	—
54	C₂	#157⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#157⋊D₃
commutator, cosocle	C₃×C₃⋊Dic₃	C₂²
Fitting, socle	C₂×C₃³	D₄
hypocenter	C₃³	D₈
LCS	G ▷ C₃×C₃⋊Dic₃ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂

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.