Subgroups — #38760339

Order 25284.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263480	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20263480	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	#16813400	—	7	8	no	maximal
6	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×#11744748	—	7	8	no	—
8	C₇×Dic₄₃	ΓL(1,𝔽₈)	1	8	yes	complemented
9	#11744748	—	7	8	no	—
10	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
11	C₄×#3861	—	43	1	no	maximal, Hall
12	(C₄₃⋊C₃)⋊C₄	—	49	1	no	Hall
13	C₇×C₄₃	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
14	C₂×#3861	—	43	1	no	—
15	C₂×C₄₃⋊C₃	—	49	1	no	—
16	C₄×C₇²	—	43	1	no	Hall
17	Dic₄₃	#3861	1	1	yes	characteristic, complemented, Hall
18	#3861	—	43	1	no	Hall
19	C₄₃⋊C₃	—	49	1	no	Hall
20	C₂×C₇²	D₄₃⋊C₃	1	1	yes	characteristic
21	C₂×C₄₃	C₂×#3861	1	1	yes	characteristic
22	C₄×ΓL(1,𝔽₈)	—	301	8	no	—
23	C₇²	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
24	C₄₃	C₄×#3861	1	1	yes	characteristic, complemented, Sylow
25	C₂×ΓL(1,𝔽₈)	—	301	8	no	—
26	C₄×C₇	—	43	8	no	—
27	ΓL(1,𝔽₈)	—	301	8	no	—
28	C₂×C₇	#14268587	1	8	yes	—
29	C₃×C₄	—	2107	1	no	Hall
30	C₇	#16813400	1	8	yes	complemented
31	C₂×C₃	—	2107	1	no	—
32	C₄	—	43	1	no	Sylow
33	C₃	—	2107	1	no	Sylow
34	C₂	#27162432	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#27162432
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×#20263480	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.