Subgroups — #63544

Order 288.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	#798	—	3	2	no	maximal
4	C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
5	C₃²×C₈	C₂²	1	1	yes	characteristic
6	C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
7	D₃×C₈	—	3	2	no	—
8	D₃×C₈	—	6	1	no	—
9	C₃×C₁₆	—	3	2	no	—
10	C₃⋊C₁₆	D₃	1	2	yes	complemented
11	C₂×C₃⋊D₃	C₈	1	1	yes	characteristic
12	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₃⋊Dic₃	C₈	1	1	yes	characteristic
14	M₃₂	—	9	1	no	Sylow
15	C₄×D₃	—	3	2	no	—
16	C₄×D₃	—	6	1	no	—
17	C₃×C₈	—	2	1	no	—
18	C₃×C₈	C₂×D₃	1	2	yes	—
19	C₃⋊C₈	—	3	2	no	—
20	C₃⋊C₈	—	6	1	no	—
21	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
22	C₃⋊D₃	—	2	1	no	—
23	C₂×C₈	—	9	1	no	—
24	C₁₆	—	3	2	no	—
25	C₂×D₃	—	3	2	no	—
26	C₂×D₃	—	6	1	no	—
27	C₃×C₄	—	2	1	no	—
28	C₃×C₄	C₄×D₃	1	2	yes	—
29	Dic₃	—	3	2	no	—
30	Dic₃	—	6	1	no	—
31	C₃²	M₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₄	—	9	1	no	—
33	C₈	—	9	1	no	—
34	C₈	D₃²	1	1	yes	characteristic
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	D₃×C₈	1	2	yes	—
37	D₃	—	6	2	no	—
38	D₃	—	6	2	no	—
39	C₂²	—	9	1	no	—
40	C₄	—	9	1	no	—
41	C₄	#624	1	1	yes	characteristic
42	C₃	—	2	1	no	—
43	C₃	#798	1	2	yes	complemented
44	C₂	—	18	1	no	—
45	C₂	#3710	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃²
commutator, socle	C₂×C₃²	C₂×C₈
Fitting, cosocle	C₃²×C₈	C₂²
prime radical	C₂×C₃⋊D₃	C₈
hypocenter	C₃²	M₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₈

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.