Subgroups — #63555

Order 288.

95 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃⋊C₈	C₂	1	2	yes	maximal
3	#815	—	3	2	no	maximal
4	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
5	C₂×C₃⋊Dic₃	C₄	1	2	yes	—
6	C₃×C₃⋊C₈	C₄	1	4	yes	complemented
7	C₂×C₃×C₈	—	3	2	no	—
8	C₄×Dic₃	—	3	2	no	—
9	C₄×Dic₃	—	6	1	no	—
10	C₂×C₃⋊C₈	D₃	1	2	yes	—
11	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₃²×C₄	C₂×C₄	1	2	yes	—
13	C₃⋊Dic₃	—	2	2	no	—
14	#97	—	9	1	no	Sylow
15	C₂×C₃×C₄	—	2	1	no	—
16	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
17	C₂×Dic₃	—	3	4	no	—
18	C₂×Dic₃	—	6	2	no	—
19	C₃×C₈	—	3	4	no	—
20	C₃⋊C₈	Dic₃	1	4	yes	complemented
21	C₂×C₃²	C₄²	1	1	yes	characteristic
22	C₂×C₃²	M₁₆	1	2	yes	—
23	C₂×C₈	—	3	2	no	—
24	C₄²	—	9	1	no	—
25	C₂²×C₃	—	2	1	no	—
26	C₂²×C₃	C₄×D₃	1	2	yes	—
27	C₃×C₄	—	2	2	no	—
28	C₃×C₄	C₄×D₃	1	2	yes	—
29	C₃×C₄	C₂×Dic₃	1	2	yes	—
30	Dic₃	—	6	4	no	—
31	Dic₃	—	6	4	no	—
32	C₃²	#97	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄	—	9	2	no	—
34	C₂×C₄	D₃²	1	1	yes	characteristic
35	C₈	—	3	4	no	—
36	C₂×C₃	—	2	2	no	—
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	ΓL(1,𝔽₂₅)	1	4	yes	—
39	C₂×C₃	C₄×Dic₃	1	2	yes	—
40	C₂²	#624	1	1	yes	characteristic
41	C₄	—	18	2	no	—
42	C₄	D₃×Dic₃	1	2	yes	—
43	C₃	—	2	1	no	—
44	C₃	#815	1	2	yes	complemented
45	C₂	#3712	1	2	yes	—
46	C₂	Dic₃²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃²
commutator	C₂×C₃²	C₄²
Fitting, cosocle	C₂×C₃²×C₄	C₂²
socle, prime radical	C₂²×C₃²	C₂×C₄
hypocenter	C₃²	#97
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×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.