Subgroups — D₇×C₃⋊C₈ #66554

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₇	—	3	1	no	maximal, Hall
5	C₂×C₃×D₇	C₄	1	1	yes	characteristic
6	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₃×Dic₇	C₄	1	1	yes	characteristic
8	C₄×D₇	D₃	1	1	yes	characteristic
9	C₇×C₈	—	3	1	no	—
10	C₇⋊C₈	—	3	1	no	—
11	C₂×C₃⋊C₈	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
13	C₃×D₇	C₈	1	2	yes	complemented
14	C₂×D₇	Dic₃	1	1	yes	characteristic
15	C₄×C₇	C₂×D₃	1	1	yes	characteristic
16	Dic₇	Dic₃	1	1	yes	characteristic
17	C₂×C₃×C₄	—	7	1	no	—
18	C₃⋊C₈	—	7	1	no	—
19	C₃⋊C₈	D₇	1	1	yes	characteristic, direct product factor
20	C₃×C₇	C₂×C₈	1	1	yes	characteristic, complemented, Hall
21	C₂×C₈	—	21	1	no	Sylow
22	C₂×C₇	C₂×Dic₃	1	1	yes	characteristic
23	D₇	C₃⋊C₈	1	2	yes	direct product factor
24	C₂²×C₃	—	7	1	no	—
25	C₃×C₄	—	7	1	no	—
26	C₃×C₄	C₂×D₇	1	1	yes	characteristic
27	C₂×C₄	—	7	1	no	—
28	C₈	—	3	1	no	—
29	C₈	—	21	1	no	—
30	C₇	C₂×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	7	2	no	—
32	C₂×C₃	C₄×D₇	1	1	yes	characteristic
33	C₂²	—	7	1	no	—
34	C₄	—	7	1	no	—
35	C₄	D₃×D₇	1	1	yes	characteristic
36	C₃	C₈×D₇	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	7	2	no	—
38	C₂	Dic₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂×C₈
Fitting, cosocle	C₃×C₄×C₇	C₂²
socle	C₂×C₃×C₇	C₂×C₄
prime radical	C₂×C₃×D₇	C₄
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₄

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.