Subgroups — (C₄₃⋊C₃)⋊#5997 #38760413

Order 25284.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#5997	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	D₇×C₄₃⋊C₃	—	14	4	no	—
7	C₇×C₄₃⋊C₃	—	2	4	no	—
8	D₇×C₄₃	—	14	4	no	—
9	C₃×#5997	—	43	1	no	maximal, Hall
10	(C₄₃⋊C₃)⋊C₄	—	49	1	no	maximal, Hall
11	C₇×C₄₃	—	2	4	no	—
12	C₃×C₇⋊D₇	—	86	1	no	—
13	C₂×C₄₃⋊C₃	—	49	1	no	—
14	#5997	—	43	1	no	Hall
15	Dic₄₃	—	49	1	no	Hall
16	C₃×C₇²	—	86	1	no	Hall
17	C₄₃⋊C₃	#5997	1	1	yes	characteristic, complemented, Hall
18	C₇⋊D₇	D₄₃⋊C₃	1	1	yes	characteristic
19	C₂×C₄₃	—	49	1	no	—
20	C₇²	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
21	C₄₃	C₃×#5997	1	1	yes	characteristic, complemented, Sylow
22	C₃×D₇	—	602	4	no	—
23	C₃×C₇	—	86	4	no	—
24	D₇	—	14	4	no	—
25	C₃×C₄	—	2107	1	no	Hall
26	C₇	—	2	4	no	—
27	C₂×C₃	—	4214	1	no	—
28	C₄	—	2107	1	no	Sylow
29	C₃	—	86	1	no	Sylow
30	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₄₃	C₃×C₄
prime radical	C₇⋊D₇×C₄₃⋊C₃	C₂
cosocle	C₄₃×C₇⋊D₇	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁

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.