Subgroups — C₃×C₇×Q₁₆ #66644

Order 336.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₈	C₂	1	2	yes	maximal
2	C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₇×Q₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×C₇	—	2	2	no	—
5	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₇×Q₈	C₂×C₃	1	2	yes	—
7	C₇×C₈	C₂×C₃	1	1	yes	characteristic
8	C₃×Q₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇	D₄	1	1	yes	characteristic
10	C₄×C₇	—	2	2	no	—
11	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
12	C₃×Q₈	C₂×C₇	1	2	yes	—
13	C₃×C₈	C₂×C₇	1	1	yes	characteristic
14	C₃×C₇	Q₁₆	1	1	yes	characteristic, direct product factor, Hall
15	Q₁₆	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₇	C₃×D₄	1	1	yes	characteristic
17	C₃×C₄	—	2	2	no	—
18	C₃×C₄	C₂²×C₇	1	1	yes	characteristic
19	Q₈	C₂×C₃×C₇	1	2	yes	—
20	C₈	C₂×C₃×C₇	1	1	yes	characteristic
21	C₇	C₃×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃	C₇×D₄	1	1	yes	characteristic
23	C₄	—	2	2	no	—
24	C₄	C₂²×C₃×C₇	1	1	yes	characteristic
25	C₃	C₇×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₃×C₇	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃×C₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₇ ◁ C₃×C₄×C₇ ◁ 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.