Subgroups — (C₄₃⋊C₃)⋊(C₇⋊Dic₇) #38760349

Order 25284.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇⋊Dic₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	(C₄₃⋊C₃)⋊Dic₇	—	7	8	no	maximal
6	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₄₃⋊C₃	D₇	1	8	yes	—
8	Dic₃₀₁	—	7	8	no	—
9	C₇×C₄₃⋊C₃	Dic₇	1	8	yes	complemented
10	C₂×C₇×C₄₃	C₃×D₇	1	8	yes	—
11	C₃×C₇⋊Dic₇	—	43	1	no	maximal, Hall
12	(C₄₃⋊C₃)⋊C₄	—	49	1	no	Hall
13	C₇×C₄₃	C₃×Dic₇	1	8	yes	complemented
14	C₂×C₃×C₇²	—	86	1	no	—
15	C₂×C₄₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic
16	C₇⋊Dic₇	—	43	1	no	Hall
17	Dic₄₃	—	49	1	no	Hall
18	C₃×C₇²	—	86	1	no	Hall
19	C₄₃⋊C₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇²	D₄₃⋊C₃	1	1	yes	characteristic
21	C₂×C₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic
22	C₃×Dic₇	—	301	8	no	—
23	C₇²	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
24	C₄₃	C₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	—	86	8	no	—
26	Dic₇	—	301	8	no	—
27	C₃×C₇	—	86	8	no	—
28	C₂×C₇	(C₄₃⋊C₃)⋊D₇	1	8	yes	—
29	C₃×C₄	—	2107	1	no	Hall
30	C₇	(C₄₃⋊C₃)⋊Dic₇	1	8	yes	complemented
31	C₂×C₃	—	86	1	no	—
32	C₄	—	2107	1	no	Sylow
33	C₃	—	86	1	no	Sylow
34	C₂	(C₄₃⋊C₃)⋊(C₇⋊D₇)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₄₃⋊C₃)⋊(C₇⋊D₇)
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×C₇²×C₄₃⋊C₃	C₂
LCS	G ▷ C₇²×C₄₃
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.