Subgroups — C₂×C₃²×Q₈ #3837

Order 144.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₃²×C₄	C₂	1	3	yes	maximal
3	C₂×C₃×Q₈	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²	C₂²	1	1	yes	characteristic
5	C₃²×C₄	C₂²	1	6	yes	—
6	C₃×Q₈	C₂×C₃	1	16	yes	direct product factor
7	C₂×C₃×C₄	C₂×C₃	1	12	yes	—
8	C₂×C₃²	Q₈	1	2	yes	direct product factor
9	C₂×C₃²	C₂³	1	1	yes	characteristic
10	C₂×Q₈	C₃²	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₃	C₂²×C₃	1	4	yes	—
12	C₃×C₄	C₂²×C₃	1	24	yes	—
13	C₃²	C₂×Q₈	1	1	yes	characteristic, direct product factor, Sylow
14	Q₈	C₂×C₃²	1	4	yes	direct product factor
15	C₂×C₄	C₂×C₃²	1	3	yes	—
16	C₂×C₃	C₃×Q₈	1	8	yes	direct product factor
17	C₂×C₃	C₂³×C₃	1	4	yes	—
18	C₂²	C₂²×C₃²	1	1	yes	characteristic
19	C₄	C₂²×C₃²	1	6	yes	—
20	C₃	C₂×C₃×Q₈	1	4	yes	direct product factor
21	C₂	C₃²×Q₈	1	2	yes	direct product factor
22	C₂	C₂³×C₃²	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃²	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ 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.