Subgroups — C₃×Q₁₆×C₁₉ #11744902

Order 912.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₉	C₂	1	2	yes	maximal
2	C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×C₁₉	—	2	2	no	—
5	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	Q₈×C₁₉	C₂×C₃	1	2	yes	—
7	C₈×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×C₁₉	D₄	1	1	yes	characteristic
9	C₄×C₁₉	—	2	2	no	—
10	C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
11	C₃×C₁₉	Q₁₆	1	1	yes	characteristic, direct product factor, Hall
12	C₃×Q₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₉	C₃×D₄	1	1	yes	characteristic
14	C₃×Q₈	C₂×C₁₉	1	2	yes	—
15	C₃×C₈	C₂×C₁₉	1	1	yes	characteristic
16	C₁₉	C₃×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
17	Q₁₆	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	2	2	no	—
19	C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
20	Q₈	C₂×C₃×C₁₉	1	2	yes	—
21	C₈	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₂×C₃	D₄×C₁₉	1	1	yes	characteristic
23	C₄	—	2	2	no	—
24	C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
25	C₃	Q₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×D₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₃×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₁₉ ◁ C₃×C₄×C₁₉ ◁ 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.