Subgroups — C₂×C₃×Q₁₆ #974

Order 96.

60 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×Q₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×Q₈	—	2	2	no	—
6	C₃×Q₈	C₂²	1	4	yes	—
7	C₂×C₃×C₄	—	2	2	no	—
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₃×C₈	C₂²	1	2	yes	—
10	C₂×Q₈	C₂×C₃	1	2	yes	—
11	Q₁₆	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₈	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃	D₄	1	1	yes	characteristic
14	C₃×C₄	—	2	4	no	—
15	C₃×C₄	D₄	1	1	yes	characteristic
16	C₃×C₄	C₂³	1	1	yes	characteristic
17	Q₈	—	2	2	no	—
18	Q₈	C₂²×C₃	1	4	yes	—
19	C₂×C₄	—	2	2	no	—
20	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
21	C₈	C₂²×C₃	1	2	yes	—
22	C₂×C₃	Q₁₆	1	2	yes	direct product factor
23	C₂×C₃	C₂×D₄	1	1	yes	characteristic
24	C₂²	C₃×D₄	1	1	yes	characteristic
25	C₄	—	2	4	no	—
26	C₄	C₃×D₄	1	1	yes	characteristic
27	C₄	C₂³×C₃	1	1	yes	characteristic
28	C₃	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	C₃×Q₁₆	1	2	yes	direct product factor
30	C₂	C₂×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ 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.