Subgroups — C₂²×C₃×Q₈ #1015

Order 96.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	12	yes	maximal, direct product factor
2	C₂²×C₃×C₄	C₂	1	3	yes	maximal
3	C₂²×Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂³×C₃	C₂²	1	1	yes	characteristic
5	C₃×Q₈	C₂²	1	16	yes	direct product factor
6	C₂×C₃×C₄	C₂²	1	18	yes	—
7	C₂×Q₈	C₂×C₃	1	12	yes	direct product factor
8	C₂²×C₄	C₂×C₃	1	3	yes	—
9	C₂²×C₃	Q₈	1	4	yes	direct product factor
10	C₂²×C₃	C₂³	1	3	yes	—
11	C₃×C₄	C₂³	1	12	yes	—
12	C₂³	C₂²×C₃	1	1	yes	characteristic
13	Q₈	C₂²×C₃	1	16	yes	direct product factor
14	C₂×C₄	C₂²×C₃	1	18	yes	—
15	C₂×C₃	C₂×Q₈	1	6	yes	direct product factor
16	C₂×C₃	C₂⁴	1	1	yes	characteristic
17	C₂²	C₃×Q₈	1	4	yes	direct product factor
18	C₂²	C₂³×C₃	1	3	yes	—
19	C₄	C₂³×C₃	1	12	yes	—
20	C₃	C₂²×Q₈	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	C₂×C₃×Q₈	1	6	yes	direct product factor
22	C₂	C₂⁴×C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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.