Subgroups — #92693

Order 504.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₁	C₂	1	2	yes	maximal, complemented
3	D₃×Dic₇	—	3	2	no	maximal
4	C₂×C₃²×C₇	C₂²	1	1	yes	characteristic
5	C₇×C₃⋊D₃	C₄	1	2	yes	complemented
6	C₂×D₃×C₇	—	3	2	no	—
7	C₂×D₃×C₇	—	6	1	no	—
8	Dic₂₁	D₃	1	2	yes	complemented
9	C₃×Dic₇	—	3	2	no	—
10	#624	—	7	1	no	maximal, Hall
11	C₃²×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×Dic₇	—	9	1	no	Hall
13	C₂×C₃×C₇	—	2	1	no	—
14	C₂×C₃×C₇	C₂×D₃	1	2	yes	—
15	D₃×C₇	—	3	4	no	—
16	D₃×C₇	—	6	2	no	—
17	C₂×C₃⋊D₃	D₇	1	1	yes	characteristic
18	C₃×Dic₃	—	7	2	no	—
19	C₂²×C₇	—	9	1	no	—
20	Dic₇	—	3	2	no	—
21	C₄×D₃	—	21	2	no	—
22	C₃×C₇	—	2	1	no	—
23	C₃×C₇	C₄×D₃	1	2	yes	complemented
24	C₂×C₃²	C₂×D₇	1	1	yes	characteristic
25	C₃⋊D₃	Dic₇	1	2	yes	complemented
26	C₂×C₇	—	9	2	no	—
27	C₂×C₇	D₃²	1	1	yes	characteristic
28	C₂×D₃	—	3	2	no	—
29	C₂×D₃	—	6	1	no	—
30	C₃×C₄	—	21	2	no	—
31	Dic₃	—	7	2	no	—
32	C₃²	C₂×Dic₇	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄	—	63	1	no	Sylow
34	C₇	#624	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	D₃×D₇	1	2	yes	—
37	D₃	—	3	4	no	—
38	D₃	—	6	2	no	—
39	C₂²	—	9	1	no	—
40	C₄	—	21	2	no	—
41	C₃	—	2	1	no	—
42	C₃	D₃×Dic₇	1	2	yes	complemented
43	C₂	—	9	2	no	—
44	C₂	(C₃⋊D₃)⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₃⋊D₃)⋊D₇
commutator, hypocenter	C₃²×C₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₇	C₂²
prime radical	C₂×C₇×C₃⋊D₃	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂

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.