Subgroups — C₃×#125 #965

Order 96.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄	C₂	1	4	yes	maximal
2	C₃×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₃×C₄²	C₂	1	1	yes	maximal, characteristic
4	#125	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×C₄	C₂²	1	2	yes	—
6	C₂×C₃×C₄	C₂²	1	4	yes	—
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₄⋊C₄	C₂×C₃	1	4	yes	—
9	C₄⋊C₄	C₂×C₃	1	2	yes	—
10	C₄²	C₂×C₃	1	1	yes	characteristic
11	C₂²×C₃	C₂³	1	1	yes	characteristic
12	C₃×C₄	—	2	2	no	—
13	C₃×C₄	—	2	4	no	—
14	C₃×C₄	Q₈	1	2	yes	—
15	C₂×C₄	C₂²×C₃	1	2	yes	—
16	C₂×C₄	C₂²×C₃	1	4	yes	—
17	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
19	C₂×C₃	#41	1	2	yes	—
20	C₂²	C₂³×C₃	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	—	2	4	no	—
23	C₄	C₃×Q₈	1	2	yes	—
24	C₃	#125	1	1	yes	characteristic, direct product factor, Sylow
25	C₂	C₂×C₃×Q₈	1	1	yes	characteristic
26	C₂	C₃×#41	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	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.

N	H ≅ G/N	type
4. #125	C₃	direct (N × H)
24. C₃	#125	direct (N × H)

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