Subgroups — C₃×C₄⋊Q₈ #968

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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