Subgroups — #3712

Order 144.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	ΓL(1,𝔽₂₅)	—	3	2	no	maximal
4	C₂×C₃⋊D₃	C₄	1	1	yes	characteristic
5	C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₃⋊Dic₃	C₄	1	1	yes	characteristic
7	C₄×D₃	—	3	2	no	—
8	C₄×D₃	—	6	1	no	—
9	C₃×C₈	—	3	2	no	—
10	C₃⋊C₈	D₃	1	2	yes	complemented
11	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₃⋊D₃	—	2	1	no	—
13	M₁₆	—	9	1	no	Sylow
14	C₂×D₃	—	3	2	no	—
15	C₂×D₃	—	6	1	no	—
16	C₃×C₄	—	2	1	no	—
17	C₃×C₄	C₂×D₃	1	2	yes	—
18	Dic₃	—	3	2	no	—
19	Dic₃	—	6	1	no	—
20	C₃²	M₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₄	—	9	1	no	—
22	C₈	—	3	2	no	—
23	C₂×C₃	—	2	1	no	—
24	C₂×C₃	C₄×D₃	1	2	yes	—
25	D₃	—	6	2	no	—
26	D₃	—	6	2	no	—
27	C₂²	—	9	1	no	—
28	C₄	—	9	1	no	—
29	C₄	D₃²	1	1	yes	characteristic
30	C₃	—	2	1	no	—
31	C₃	ΓL(1,𝔽₂₅)	1	2	yes	complemented
32	C₂	—	18	1	no	—
33	C₂	#624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃²
commutator, socle	C₂×C₃²	C₂×C₄
Fitting, cosocle	C₃²×C₄	C₂²
prime radical	C₂×C₃⋊D₃	C₄
hypocenter	C₃²	M₁₆
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄

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.