Subgroups — (C₄₃⋊C₉)⋊(C₇⋊D₇) #49181592

Order 37926.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₄₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	(C₄₃⋊C₉)⋊D₇	—	7	8	no	maximal
5	C₇⋊D₃₀₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇×C₄₃⋊C₉	D₇	1	8	yes	complemented
7	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₃₀₁	—	7	8	no	—
9	C₃×C₇×C₄₃	C₃×D₇	1	8	yes	—
10	C₉×C₇⋊D₇	—	43	1	no	maximal, Hall
11	D₄₃⋊C₉	—	49	1	no	Hall
12	D₃₀₁	—	7	8	no	—
13	C₇²×C₉	—	43	1	no	Hall
14	C₄₃⋊C₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
15	C₇×C₄₃	C₉×D₇	1	8	yes	complemented
16	C₃×C₇⋊D₇	—	43	1	no	—
17	C₃×D₄₃	—	49	1	no	—
18	C₃×C₇²	D₄₃⋊C₃	1	1	yes	characteristic
19	C₃×C₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic
20	C₉×D₇	—	301	8	no	—
21	C₇⋊D₇	—	43	1	no	Hall
22	D₄₃	—	49	1	no	Hall
23	C₇×C₉	—	43	8	no	—
24	C₇²	D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
25	C₄₃	C₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
26	C₃×D₇	—	301	8	no	—
27	C₃×C₇	(C₄₃⋊C₃)⋊D₇	1	8	yes	—
28	C₂×C₉	—	2107	1	no	Hall
29	D₇	—	301	8	no	—
30	C₉	—	43	1	no	Sylow
31	C₇	(C₄₃⋊C₉)⋊D₇	1	8	yes	complemented
32	C₂×C₃	—	2107	1	no	—
33	C₃	(C₄₃⋊C₃)⋊(C₇⋊D₇)	1	1	yes	characteristic
34	C₂	—	2107	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	(C₄₃⋊C₃)⋊(C₇⋊D₇)
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇⋊D₃₀₁	C₃
LCS	G ▷ C₇²×C₄₃
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.