Subgroups — C₄⋊Dic₂₁ #66630

Order 336.

52 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	C₂×Dic₂₁	C₂	1	2	yes	maximal
3	C₄⋊Dic₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₇	C₄	1	2	yes	complemented
6	Dic₂₁	—	2	2	no	—
7	C₂×C₄×C₇	D₃	1	1	yes	characteristic
8	C₂×Dic₇	—	3	2	no	—
9	C₄⋊Dic₃	—	7	1	no	maximal, Hall
10	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₇	D₄	1	1	yes	characteristic
12	C₂×C₃×C₇	Q₈	1	1	yes	characteristic
13	C₂²×C₇	C₂×D₃	1	1	yes	characteristic
14	C₄×C₇	Dic₃	1	2	yes	complemented
15	Dic₇	—	6	2	no	—
16	C₂×C₃×C₄	D₇	1	1	yes	characteristic
17	C₂×Dic₃	—	7	2	no	—
18	C₃×C₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
19	C₄⋊C₄	—	21	1	no	Sylow
20	C₂×C₇	Dic₆	1	1	yes	characteristic
21	C₂×C₇	D₁₂	1	1	yes	characteristic
22	C₂×C₇	C₂×Dic₃	1	1	yes	characteristic
23	C₂²×C₃	C₂×D₇	1	1	yes	characteristic
24	C₃×C₄	Dic₇	1	2	yes	complemented
25	Dic₃	—	14	2	no	—
26	C₂×C₄	—	21	2	no	—
27	C₂×C₄	D₂₁	1	1	yes	characteristic
28	C₇	C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	Dic₁₄	1	1	yes	characteristic
30	C₂×C₃	D₂₈	1	1	yes	characteristic
31	C₂×C₃	C₂×Dic₇	1	1	yes	characteristic
32	C₂²	C₂×D₂₁	1	1	yes	characteristic
33	C₄	—	42	2	no	—
34	C₄	Dic₂₁	1	2	yes	complemented
35	C₃	C₄⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	Dic₄₂	1	1	yes	characteristic
37	C₂	D₈₄	1	1	yes	characteristic
38	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.