Subgroups — C₃×C₇×D₈ #66642

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₄	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₇	—	2	2	no	—
5	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₇×D₄	C₂×C₃	1	2	yes	complemented
7	C₇×C₈	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇	—	4	2	no	—
10	C₂×C₃×C₇	D₄	1	1	yes	characteristic
11	C₂²×C₇	—	2	2	no	—
12	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₃×D₄	C₂×C₇	1	2	yes	complemented
14	C₃×C₈	C₂×C₇	1	1	yes	characteristic, complemented
15	C₃×C₇	D₈	1	1	yes	characteristic, direct product factor, Hall
16	D₈	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₇	—	4	2	no	—
18	C₂×C₇	C₃×D₄	1	1	yes	characteristic
19	C₂²×C₃	—	2	2	no	—
20	C₃×C₄	C₂²×C₇	1	1	yes	characteristic
21	D₄	C₂×C₃×C₇	1	2	yes	complemented
22	C₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₇	C₃×D₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃	—	4	2	no	—
25	C₂×C₃	C₇×D₄	1	1	yes	characteristic
26	C₂²	—	2	2	no	—
27	C₄	C₂²×C₃×C₇	1	1	yes	characteristic
28	C₃	C₇×D₈	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	4	2	no	—
30	C₂	C₃×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	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.