Subgroups — #44545239

Order 32046.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₆₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₈)⋊D₁₀₉	—	7	1	no	maximal
5	ΓL(1,𝔽₈)×D₁₀₉	—	7	1	no	maximal
6	ΓL(1,𝔽₈)×C₁₀₉	—	7	1	no	—
7	ΓL(1,𝔽₈)×C₁₀₉	—	7	1	no	—
8	ΓL(1,𝔽₈)×C₁₀₉	—	14	3	no	—
9	D₇₆₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
10	C₇×D₁₀₉	—	7	1	no	—
11	C₇×C₁₀₉	—	2	3	no	—
12	C₇×C₁₀₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
13	C₇×C₁₀₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₃×D₁₀₉	—	49	1	no	Hall
15	C₃×C₁₀₉	—	49	1	no	Hall
16	#64423	—	109	1	no	maximal, Hall
17	D₁₀₉	—	7	1	no	Hall
18	#3861	D₁₀₉	1	1	yes	characteristic, complemented, Hall
19	C₁₀₉	#64423	1	1	yes	characteristic, complemented, Sylow
20	C₇×D₇	—	109	1	no	Hall
21	C₇²	C₃×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
22	C₂×ΓL(1,𝔽₈)	—	763	1	no	—
23	AGL(1,𝔽₇)	—	763	1	no	—
24	ΓL(1,𝔽₈)	—	7	1	no	—
25	ΓL(1,𝔽₈)	—	7	1	no	—
26	ΓL(1,𝔽₈)	—	14	3	no	—
27	C₂×C₇	—	763	1	no	—
28	D₇	—	109	1	no	—
29	C₇	—	2	3	no	—
30	C₇	ΓL(1,𝔽₈)×D₁₀₉	1	1	yes	characteristic, complemented
31	C₇	ΓL(1,𝔽₈)⋊D₁₀₉	1	1	yes	characteristic, complemented
32	C₂×C₃	—	5341	1	no	Hall
33	C₃	—	49	1	no	Sylow
34	C₂	—	763	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₀₉	C₂×C₃
LCS	G ▷ C₇²×C₁₀₉
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.