Subgroups — C₂×ΓL(1,𝔽₈)⋊D₁₉₇ #30658447

Order 16548.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)⋊D₁₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×ΓL(1,𝔽₈)×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	ΓL(1,𝔽₈)×C₁₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₉₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₃₇₉	C₂×C₃	1	2	yes	complemented
7	C₂×C₃×D₁₉₇	—	7	1	no	maximal, Hall
8	C₇×C₁₉₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₉₇	—	14	1	no	—
10	C₃×D₁₉₇	—	7	2	no	—
11	C₂×D₁₉₇	—	7	1	no	Hall
12	C₃×C₁₉₇	—	14	1	no	Hall
13	C₂×C₁₉₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
14	D₁₉₇	—	7	2	no	—
15	C₁₉₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
16	C₂×AGL(1,𝔽₇)	—	197	1	no	maximal, Hall
17	C₂×ΓL(1,𝔽₈)	D₁₉₇	1	1	yes	characteristic, complemented
18	AGL(1,𝔽₇)	—	197	2	no	—
19	C₂×D₇	—	197	1	no	Hall
20	ΓL(1,𝔽₈)	C₂×D₁₉₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇	C₃×D₁₉₇	1	1	yes	characteristic, complemented
22	D₇	—	197	2	no	—
23	C₂²×C₃	—	1379	1	no	Hall
24	C₇	C₂×C₃×D₁₉₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	14	1	no	—
26	C₂×C₃	—	1379	2	no	—
27	C₂²	—	1379	1	no	Sylow
28	C₃	—	14	1	no	Sylow
29	C₂	—	1379	2	no	—
30	C₂	ΓL(1,𝔽₈)⋊D₁₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	ΓL(1,𝔽₈)⋊D₁₉₇
commutator, cosocle, hypocenter	C₇×C₁₉₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉₇	C₂×C₃
LCS	G ▷ C₇×C₁₉₇
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.