Subgroups — C₄₃⋊#10596868 #38760352

Order 25284.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#3862	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃₀₁	—	3	1	no	maximal, Hall
3	C₄₃×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₄₃	D₃	1	1	yes	characteristic
5	C₇²×C₄₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₂×ΓL(1,𝔽₈)×C₄₃	—	14	1	no	—
7	Dic₃₀₁	—	3	1	no	—
8	C₇×Dic₄₃	—	21	1	no	—
9	ΓL(1,𝔽₈)×C₄₃	—	14	1	no	—
10	C₂×C₇×C₄₃	—	2	1	no	—
11	C₂×C₇×C₄₃	—	3	1	no	—
12	C₂×C₇×C₄₃	—	6	1	no	—
13	#10596868	—	43	1	no	maximal, Hall
14	Dic₁₂₉	—	49	1	no	maximal, Hall
15	C₇×C₄₃	—	2	1	no	—
16	C₇×C₄₃	—	3	1	no	—
17	C₇×C₄₃	—	6	1	no	—
18	C₂×#3862	D₄₃	1	1	yes	characteristic
19	C₂×C₃×C₄₃	—	98	1	no	—
20	C₇×Dic₇	—	129	1	no	Hall
21	Dic₄₃	—	21	1	no	Hall
22	#3862	Dic₄₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₄₃	—	98	1	no	Hall
24	C₂×C₇²	D₁₂₉	1	1	yes	characteristic
25	C₂×C₄₃	#64418	1	1	yes	characteristic
26	C₇²	Dic₁₂₉	1	1	yes	characteristic, complemented, Sylow
27	C₄₃	#10596868	1	1	yes	characteristic, complemented, Sylow
28	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
29	C₄×C₇	—	903	1	no	—
30	Dic₇	—	129	1	no	—
31	ΓL(1,𝔽₈)	—	14	1	no	—
32	C₂×C₇	—	2	1	no	—
33	C₂×C₇	—	6	1	no	—
34	C₂×C₇	—	6	1	no	—
35	Dic₃	—	2107	1	no	Hall
36	C₇	—	2	1	no	—
37	C₇	—	6	1	no	—
38	C₇	—	6	1	no	—
39	C₂×C₃	—	98	1	no	—
40	C₄	—	903	1	no	Sylow
41	C₃	—	98	1	no	Sylow
42	C₂	C₄₃⋊#64418	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₄₃⋊#64418
commutator, hypocenter	C₄₃×#3862	C₄
Fitting, socle	C₂×C₇²×C₄₃	D₃
prime radical, cosocle	C₂×C₄₃×#3862	C₂
LCS	G ▷ C₄₃×#3862
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.