Subgroups — #88943

Order 432.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6296	C₂	1	2	yes	maximal
2	C₃×#622	C₂	1	1	yes	maximal, characteristic
3	#3776	—	3	1	no	maximal
4	C₃×C₃⋊Dic₃	—	2	2	no	—
5	C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	#627	—	3	2	no	—
7	#627	—	6	2	no	—
8	#622	D₃	1	1	yes	characteristic
9	C₂×C₃³	D₄	1	1	yes	characteristic
10	Dic₁₂	—	9	1	no	maximal
11	C₃⋊Dic₃	—	2	2	no	—
12	C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
13	C₃×Dic₃	—	6	2	no	—
14	C₃×Dic₃	—	6	2	no	—
15	C₃×Dic₃	—	6	2	no	—
16	C₃×Dic₃	—	12	2	no	—
17	C₃³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	Dic₆	—	9	2	no	—
19	Dic₆	—	18	2	no	—
20	C₃×C₈	—	9	1	no	—
21	C₂×C₃²	—	2	2	no	—
22	C₂×C₃²	—	4	2	no	—
23	C₂×C₃²	D₁₂	1	1	yes	characteristic
24	Q₁₆	—	27	1	no	Sylow
25	C₃×C₄	—	9	1	no	—
26	C₃×C₄	—	18	2	no	—
27	Dic₃	—	6	2	no	—
28	Dic₃	—	6	2	no	—
29	Dic₃	—	6	2	no	—
30	Dic₃	—	12	2	no	—
31	C₃²	—	2	2	no	—
32	C₃²	—	4	2	no	—
33	C₃²	Dic₁₂	1	1	yes	characteristic, complemented
34	Q₈	—	27	2	no	—
35	C₈	—	9	1	no	—
36	C₂×C₃	—	2	2	no	—
37	C₂×C₃	—	4	2	no	—
38	C₂×C₃	GO⁺(4,𝔽₂)	1	1	yes	characteristic
39	C₄	—	9	1	no	—
40	C₄	—	18	2	no	—
41	C₃	—	2	2	no	—
42	C₃	—	4	2	no	—
43	C₃	#3776	1	1	yes	characteristic, complemented
44	C₂	#157⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#157⋊D₃
commutator, cosocle	C₃×C₃⋊Dic₃	C₂²
Fitting, socle, prime radical	C₂×C₃³	D₄
hypocenter	C₃³	Q₁₆
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.