Subgroups — C₃×#120 #960

Order 96.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄	C₂	1	3	yes	maximal, complemented
3	C₃×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
4	#120	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃	—	2	6	no	—
6	C₂³×C₃	C₂²	1	3	yes	—
7	C₂³×C₃	C₂²	1	1	yes	characteristic, complemented
8	C₃×D₄	—	2	6	no	—
9	C₂×C₃×C₄	C₂²	1	3	yes	complemented
10	C₂⁴	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₄	C₂×C₃	1	3	yes	complemented
12	C₂²⋊C₄	C₂×C₃	1	3	yes	complemented
13	C₂²×C₃	—	2	8	no	—
14	C₂²×C₃	—	2	6	no	—
15	C₂²×C₃	—	2	3	no	—
16	C₂²×C₃	D₄	1	6	yes	complemented
17	C₂²×C₃	C₂³	1	1	yes	characteristic
18	C₃×C₄	—	2	3	no	—
19	C₂³	—	2	6	no	—
20	C₂³	C₂²×C₃	1	3	yes	—
21	C₂³	C₂²×C₃	1	1	yes	characteristic, complemented
22	D₄	—	2	6	no	—
23	C₂×C₄	C₂²×C₃	1	3	yes	complemented
24	C₂×C₃	—	2	6	no	—
25	C₂×C₃	—	4	1	no	—
26	C₂×C₃	C₂×D₄	1	3	yes	—
27	C₂²	—	2	8	no	—
28	C₂²	—	2	6	no	—
29	C₂²	—	2	3	no	—
30	C₂²	C₃×D₄	1	6	yes	complemented
31	C₂²	C₂³×C₃	1	1	yes	characteristic
32	C₄	—	2	3	no	—
33	C₃	#120	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	2	6	no	—
35	C₂	—	4	1	no	—
36	C₂	C₂×C₃×D₄	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

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.