Subgroups — D₃²⋊C₄ #3772

Order 144.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²	C₂	1	1	yes	maximal, characteristic
2	C₂×#157	C₂	1	1	yes	maximal, characteristic, complemented
3	#624	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₂×C₃×D₃	—	2	1	no	—
6	D₃²	—	2	1	no	—
7	D₃²	C₄	1	2	yes	complemented
8	#157	—	2	1	no	—
9	C₃×Dic₃	—	2	1	no	—
10	C₂²×D₃	—	6	1	no	—
11	C₄×D₃	—	6	1	no	—
12	C₂×C₃²	D₄	1	1	yes	characteristic
13	C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
14	C₃⋊D₃	D₄	1	1	yes	characteristic
15	C₃×D₃	—	2	2	no	—
16	C₂²⋊C₄	—	9	1	no	maximal, Sylow
17	C₂²×C₃	—	6	1	no	—
18	C₂×D₃	—	2	1	no	—
19	C₂×D₃	—	6	2	no	—
20	C₂×D₃	—	6	1	no	—
21	C₂×D₃	—	6	1	no	—
22	C₂×D₃	—	6	2	no	—
23	C₃×C₄	—	6	1	no	—
24	Dic₃	—	2	1	no	—
25	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	9	1	no	—
27	C₂×C₄	—	9	1	no	—
28	C₂×C₄	—	9	1	no	—
29	C₂×C₃	—	2	1	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	—	6	2	no	—
32	D₃	—	2	2	no	—
33	D₃	—	6	1	no	—
34	D₃	—	6	1	no	—
35	D₃	—	6	1	no	—
36	D₃	—	6	1	no	—
37	C₂²	—	6	1	no	—
38	C₂²	—	9	2	no	—
39	C₂²	—	9	1	no	—
40	C₂²	—	18	1	no	—
41	C₄	—	6	1	no	—
42	C₄	—	18	1	no	—
43	C₃	—	2	1	no	—
44	C₃	—	2	1	no	—
45	C₂	—	6	2	no	—
46	C₂	—	9	1	no	—
47	C₂	—	9	1	no	—
48	C₂	GO⁺(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	GO⁺(4,𝔽₂)
commutator	C₃⋊D₃	C₂×C₄
Fitting, socle	C₂×C₃²	D₄
prime radical	C₂×D₃²	C₂
cosocle	C₂×C₃⋊D₃	C₂²
hypocenter	C₃²	C₂²⋊C₄
LCS	G ▷ C₃⋊D₃ ▷ 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.