Subgroups — C₃×#124 #964

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
5	#124	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂³×C₃	C₂²	1	2	yes	—
7	C₃×Q₈	—	2	2	no	—
8	C₃×D₄	—	2	2	no	—
9	C₂×C₃×C₄	C₂²	1	2	yes	—
10	C₂×C₃×C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₂×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×D₄	C₂×C₃	1	1	yes	characteristic
14	C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
15	C₄²	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃	—	2	2	no	—
17	C₂²×C₃	—	2	4	no	—
18	C₂²×C₃	C₂³	1	1	yes	characteristic
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	—	2	2	no	—
21	C₃×C₄	D₄	1	2	yes	—
22	C₂³	C₂²×C₃	1	2	yes	—
23	Q₈	—	2	2	no	—
24	D₄	—	2	2	no	—
25	C₂×C₄	C₂²×C₃	1	2	yes	—
26	C₂×C₄	C₂²×C₃	1	2	yes	—
27	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₃	—	4	2	no	—
29	C₂×C₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃	#41	1	2	yes	—
31	C₂²	—	2	2	no	—
32	C₂²	—	2	4	no	—
33	C₂²	C₂³×C₃	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	2	2	no	—
36	C₄	C₃×D₄	1	2	yes	—
37	C₃	#124	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	—	4	2	no	—
39	C₂	C₂×C₃×D₄	1	1	yes	characteristic
40	C₂	C₃×#41	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂
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.