Subgroups — D₃×(C₄₃⋊C₃)⋊C₇ #19129355

Order 5418.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₄₃⋊C₃)⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₄₃⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₄₃⋊C₃)⋊C₇	—	3	1	no	maximal
4	C₃×C₄₃⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented
5	(C₄₃⋊C₃)⋊C₇	—	2	1	no	—
6	(C₄₃⋊C₃)⋊C₇	D₃	1	1	yes	characteristic, direct product factor
7	D₃×C₄₃⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
8	C₂×C₄₃⋊C₇	—	3	1	no	Hall
9	C₃×C₄₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₄₃⋊C₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented
12	C₂×C₄₃⋊C₃	—	3	1	no	—
13	C₃×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	C₄₃⋊C₃	—	2	1	no	—
15	C₄₃⋊C₃	D₃×C₇	1	1	yes	characteristic, complemented
16	C₃×D₃×C₇	—	43	1	no	maximal, Hall
17	C₂×C₄₃	—	3	1	no	Hall
18	C₃²×C₇	—	43	1	no	Hall
19	C₄₃	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₇	—	129	1	no	—
21	D₃×C₇	—	43	1	no	—
22	C₃×C₇	—	43	1	no	—
23	C₃×C₇	—	43	1	no	—
24	C₃×C₇	—	86	1	no	—
25	C₃×D₃	—	43	1	no	Hall
26	C₂×C₇	—	129	1	no	Hall
27	C₃²	—	43	1	no	Sylow
28	C₇	—	43	1	no	Sylow
29	C₂×C₃	—	129	1	no	—
30	D₃	(C₄₃⋊C₃)⋊C₇	1	1	yes	characteristic, direct product factor
31	C₃	—	43	1	no	—
32	C₃	—	86	1	no	—
33	C₃	C₂×(C₄₃⋊C₃)⋊C₇	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₄₃	C₂×C₃×C₇
LCS	G ▷ C₃×C₄₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.