Subgroups — #3775

Order 144.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#627	C₂	1	1	yes	maximal, characteristic, complemented
2	#625	C₂	1	1	yes	maximal, characteristic
3	#622	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃	—	2	1	no	—
5	C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₃×Dic₃	—	2	1	no	—
7	#67	—	6	1	no	—
8	Dic₆	—	6	1	no	—
9	C₂×C₃²	D₄	1	1	yes	characteristic
10	C₃×D₃	—	4	1	no	—
11	SD₁₆	—	9	1	no	maximal, Sylow
12	C₂²×C₃	—	6	1	no	—
13	C₂×D₃	—	2	1	no	—
14	C₃×C₄	—	6	1	no	—
15	Dic₃	—	2	1	no	—
16	Dic₃	—	6	1	no	—
17	Dic₃	—	6	1	no	—
18	C₃²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	Q₈	—	9	1	no	—
20	D₄	—	9	1	no	—
21	C₈	—	9	1	no	—
22	C₂×C₃	—	2	1	no	—
23	C₂×C₃	—	2	1	no	—
24	C₂×C₃	—	12	1	no	—
25	D₃	—	4	1	no	—
26	C₂²	—	6	1	no	—
27	C₄	—	6	1	no	—
28	C₄	—	9	1	no	—
29	C₃	—	2	1	no	—
30	C₃	—	2	1	no	—
31	C₂	—	12	1	no	—
32	C₂	GO⁺(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	GO⁺(4,𝔽₂)
commutator, cosocle	C₃⋊Dic₃	C₂²
Fitting, socle	C₂×C₃²	D₄
prime radical	#625	C₂
hypocenter	C₃²	SD₁₆
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
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.