Subgroups — ΓL(1,𝔽₈)×D₇₃₇ #44526261

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×ΓL(1,𝔽₈)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₃₇	—	7	1	no	maximal, Hall
5	ΓL(1,𝔽₈)×D₆₇	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₆₇	—	7	1	no	Hall
7	D₇₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
8	ΓL(1,𝔽₈)×C₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₇×D₆₇	—	11	1	no	Hall
10	C₁₁×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	ΓL(1,𝔽₈)×D₁₁	—	67	1	no	maximal, Hall
13	C₃×D₆₇	—	77	1	no	Hall
14	C₁₁×ΓL(1,𝔽₈)	D₆₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₇	—	7	1	no	Hall
16	C₇×D₁₁	—	67	1	no	Hall
17	D₆₇	—	11	1	no	Hall
18	C₇×C₁₁	C₃×D₆₇	1	1	yes	characteristic, complemented, Hall
19	C₆₇	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₁₁	—	469	1	no	Hall
21	C₂×ΓL(1,𝔽₈)	—	737	1	no	Hall
22	C₃×C₁₁	—	7	1	no	Hall
23	D₁₁	—	67	1	no	Hall
24	ΓL(1,𝔽₈)	D₇₃₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	737	1	no	Hall
26	C₁₁	ΓL(1,𝔽₈)×D₆₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₇₃₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	5159	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	—	737	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₆₇
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.