Subgroups — C₃×C₇⋊S₄ #92749

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇⋊S₄	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂²⋊D₇	—	3	1	no	maximal
4	C₃×D₂₁	—	4	1	no	maximal
5	C₂²×C₃×C₇	D₃	1	1	yes	characteristic, complemented
6	C₂×C₃×D₇	—	3	1	no	—
7	C₇×A₄	—	2	1	no	—
8	C₇×A₄	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×Dic₇	—	3	1	no	—
10	C₃×S₄	—	7	1	no	maximal, Hall
11	C₃²×C₇	—	4	1	no	Hall
12	C₂²⋊D₇	—	3	1	no	Hall
13	C₂×C₃×C₇	—	3	1	no	—
14	D₂₁	—	4	1	no	—
15	C₃×D₇	—	6	1	no	—
16	C₃×A₄	D₇	1	1	yes	characteristic, complemented
17	C₂²×C₇	C₃×D₃	1	1	yes	characteristic, complemented
18	C₂×D₇	—	3	1	no	—
19	Dic₇	—	3	1	no	—
20	S₄	—	7	1	no	—
21	C₃×D₄	—	21	1	no	—
22	C₃×C₇	—	4	1	no	—
23	C₃×C₇	—	8	1	no	—
24	C₃×C₇	S₄	1	1	yes	characteristic, complemented
25	C₃×D₃	—	28	1	no	—
26	C₂×C₇	—	3	1	no	—
27	D₇	—	6	1	no	—
28	C₂²×C₃	—	21	1	no	—
29	C₂²×C₃	D₂₁	1	1	yes	characteristic, complemented
30	A₄	—	2	1	no	—
31	A₄	C₃×D₇	1	1	yes	characteristic, complemented
32	C₃×C₄	—	21	1	no	—
33	C₃²	—	4	1	no	Sylow
34	D₄	—	21	1	no	Sylow
35	C₇	C₃×S₄	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃	—	3	1	no	—
37	C₂×C₃	—	42	1	no	—
38	D₃	—	28	1	no	—
39	C₂²	—	21	1	no	—
40	C₂²	C₃×D₂₁	1	1	yes	characteristic, complemented
41	C₄	—	21	1	no	—
42	C₃	—	4	1	no	—
43	C₃	—	8	1	no	—
44	C₃	C₇⋊S₄	1	1	yes	characteristic, direct product factor
45	C₂	—	3	1	no	—
46	C₂	—	42	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₇⋊S₄
commutator, cosocle, hypocenter	C₇×A₄	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇	D₃
LCS	G ▷ C₇×A₄
UCS	C₁ ◁ C₃

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.