Subgroups — C₂²×Dic₂₁ #66733

Order 336.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₁	C₂	1	6	yes	maximal, direct product factor
3	C₂²×Dic₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₇	C₄	1	4	yes	complemented
5	C₂²×C₃×C₇	C₂²	1	3	yes	—
6	Dic₂₁	C₂²	1	4	yes	direct product factor
7	C₂³×C₇	D₃	1	1	yes	characteristic
8	C₂×Dic₇	—	3	6	no	—
9	C₂²×Dic₃	—	7	1	no	maximal, Hall
10	C₂×C₃×C₇	C₂×C₄	1	6	yes	complemented
11	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
12	C₂²×C₇	Dic₃	1	4	yes	complemented
13	C₂²×C₇	C₂×D₃	1	3	yes	—
14	Dic₇	—	3	4	no	—
15	C₂³×C₃	D₇	1	1	yes	characteristic
16	C₂×Dic₃	—	7	6	no	—
17	C₃×C₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₄	—	21	1	no	Sylow
19	C₂×C₇	C₂×Dic₃	1	6	yes	complemented
20	C₂×C₇	C₂²×D₃	1	1	yes	characteristic
21	C₂²×C₃	Dic₇	1	4	yes	complemented
22	C₂²×C₃	C₂×D₇	1	3	yes	—
23	Dic₃	—	7	4	no	—
24	C₂³	D₂₁	1	1	yes	characteristic
25	C₂×C₄	—	21	6	no	—
26	C₇	C₂²×Dic₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	C₂×Dic₇	1	6	yes	complemented
28	C₂×C₃	C₂²×D₇	1	1	yes	characteristic
29	C₂²	Dic₂₁	1	4	yes	direct product factor
30	C₂²	C₂×D₂₁	1	3	yes	—
31	C₄	—	21	4	no	—
32	C₃	C₂²×Dic₇	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₂×Dic₂₁	1	6	yes	direct product factor
34	C₂	C₂²×D₂₁	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.