Subgroups — C₂×C₃⋊(C₇⋊C₈) #66626

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊C₈)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊C₈	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₇	C₄	1	1	yes	characteristic
5	C₃×C₄×C₇	C₄	1	1	yes	characteristic
6	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₇	D₃	1	1	yes	characteristic
8	C₇⋊C₈	—	3	2	no	—
9	C₂×C₃⋊C₈	—	7	1	no	maximal, Hall
10	C₂×C₃×C₇	C₈	1	2	yes	complemented
11	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₇	Dic₃	1	1	yes	characteristic
13	C₄×C₇	Dic₃	1	1	yes	characteristic
14	C₄×C₇	C₂×D₃	1	1	yes	characteristic
15	C₂×C₃×C₄	D₇	1	1	yes	characteristic
16	C₃⋊C₈	—	7	2	no	—
17	C₃×C₇	C₂×C₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₈	—	21	1	no	Sylow
19	C₂×C₇	C₃⋊C₈	1	2	yes	complemented
20	C₂×C₇	C₂×Dic₃	1	1	yes	characteristic
21	C₂²×C₃	Dic₇	1	1	yes	characteristic
22	C₃×C₄	Dic₇	1	1	yes	characteristic
23	C₃×C₄	C₂×D₇	1	1	yes	characteristic
24	C₂×C₄	D₂₁	1	1	yes	characteristic
25	C₈	—	21	2	no	—
26	C₇	C₂×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	C₇⋊C₈	1	2	yes	complemented
28	C₂×C₃	C₂×Dic₇	1	1	yes	characteristic
29	C₂²	Dic₂₁	1	1	yes	characteristic
30	C₄	Dic₂₁	1	1	yes	characteristic
31	C₄	C₂×D₂₁	1	1	yes	characteristic
32	C₃	C₂×C₇⋊C₈	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₃⋊(C₇⋊C₈)	1	2	yes	direct product factor
34	C₂	C₂×Dic₂₁	1	1	yes	characteristic

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.