Subgroups — #64079

Order 288.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊Dic₃)	C₂	1	2	yes	maximal
3	#3750	C₂	1	4	yes	maximal
4	#870	—	3	4	no	maximal
5	C₂×C₃²×C₄	C₂²	1	2	yes	—
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊Dic₃	C₂²	1	4	yes	—
8	C₃×C₄²	D₃	1	4	yes	—
9	C₄⋊Dic₃	—	3	8	no	—
10	Dic₃⋊C₄	—	3	16	no	—
11	C₂²×C₃²	C₂³	1	1	yes	characteristic
12	C₃²×C₄	—	2	2	no	—
13	C₃²×C₄	Q₈	1	2	yes	—
14	C₃⋊Dic₃	—	2	4	no	—
15	#125	—	9	1	no	Sylow
16	C₂×C₃×C₄	C₂×D₃	1	8	yes	—
17	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
18	C₂×Dic₃	—	3	16	no	—
19	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₃²	#41	1	2	yes	—
21	C₄⋊C₄	—	9	4	no	—
22	C₄⋊C₄	—	9	2	no	—
23	C₄²	C₃⋊D₃	1	1	yes	characteristic
24	C₂²×C₃	C₂²×D₃	1	4	yes	—
25	C₃×C₄	—	2	8	no	—
26	C₃×C₄	Dic₆	1	8	yes	—
27	Dic₃	—	6	16	no	—
28	C₃²	#125	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₄	—	9	4	no	—
30	C₂×C₄	C₂×C₃⋊D₃	1	2	yes	—
31	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
32	C₂×C₃	C₂×Dic₆	1	4	yes	—
33	C₂×C₃	#235	1	8	yes	—
34	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	18	4	no	—
37	C₄	#634	1	2	yes	—
38	C₃	#870	1	4	yes	complemented
39	C₂	C₂×#634	1	1	yes	characteristic
40	C₂	#3828	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₃
commutator, socle, prime radical, cosocle	C₂²×C₃²	C₂³
Fitting	C₃²×C₄²	C₂
hypercenter	C₄²	C₃⋊D₃
hypocenter	C₃²	#125
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄²

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
28. C₃²	#125	semidirect
38. C₃	#870	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.