Subgroups — C₂×C₃⋊Dic₂₁ #92725

Order 504.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×Dic₂₁	—	3	4	no	maximal
4	C₂×C₃²×C₇	C₄	1	2	yes	complemented
5	C₂×C₃²×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₇	D₃	1	4	yes	—
7	Dic₂₁	—	3	8	no	—
8	C₂×C₃⋊Dic₃	—	7	1	no	maximal, Hall
9	C₃²×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×Dic₇	—	9	1	no	Hall
11	C₂×C₃×C₇	Dic₃	1	8	yes	complemented
12	C₂×C₃×C₇	C₂×D₃	1	4	yes	—
13	C₂²×C₃²	D₇	1	1	yes	characteristic
14	C₃⋊Dic₃	—	7	2	no	—
15	C₂²×C₇	C₃⋊D₃	1	1	yes	characteristic
16	Dic₇	—	9	2	no	—
17	C₂×Dic₃	—	21	4	no	—
18	C₃×C₇	C₂×Dic₃	1	4	yes	complemented
19	C₂×C₃²	Dic₇	1	2	yes	complemented
20	C₂×C₃²	C₂×D₇	1	1	yes	characteristic
21	C₂×C₇	C₃⋊Dic₃	1	2	yes	complemented
22	C₂×C₇	C₂×C₃⋊D₃	1	1	yes	characteristic
23	C₂²×C₃	D₂₁	1	4	yes	—
24	Dic₃	—	21	8	no	—
25	C₃²	C₂×Dic₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	63	1	no	Sylow
27	C₇	C₂×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	Dic₂₁	1	8	yes	complemented
29	C₂×C₃	C₂×D₂₁	1	4	yes	—
30	C₂²	C₃⋊D₂₁	1	1	yes	characteristic
31	C₄	—	63	2	no	—
32	C₃	C₂×Dic₂₁	1	4	yes	complemented
33	C₂	C₃⋊Dic₂₁	1	2	yes	direct product factor
34	C₂	C₂×C₃⋊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.