Subgroups — C₁₀₉×#64418 #44545199

Order 32046.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇×C₁₀₉	—	3	1	no	maximal, Hall
3	C₇²×C₁₀₉	D₃	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₈)×C₁₀₉	—	14	1	no	—
5	C₂×C₇×C₁₀₉	—	21	1	no	—
6	D₇×C₁₀₉	—	3	1	no	—
7	C₇×C₁₀₉	—	2	1	no	—
8	C₇×C₁₀₉	—	3	1	no	—
9	C₇×C₁₀₉	—	3	1	no	—
10	D₃×C₁₀₉	—	49	1	no	maximal, Hall
11	C₃×C₁₀₉	—	49	1	no	Hall
12	#64418	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₀₉	—	21	1	no	Hall
14	#3862	C₂×C₁₀₉	1	1	yes	characteristic, complemented, Hall
15	C₁₀₉	#64418	1	1	yes	characteristic, direct product factor, Sylow
16	C₇×D₇	—	3	1	no	Hall
17	C₇²	D₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
18	ΓL(1,𝔽₈)	—	14	1	no	—
19	C₂×C₇	—	21	1	no	—
20	D₇	—	3	1	no	—
21	C₇	—	2	1	no	—
22	C₇	—	3	1	no	—
23	C₇	—	3	1	no	—
24	D₃	—	49	1	no	Hall
25	C₃	—	49	1	no	Sylow
26	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₉	#64418
commutator, cosocle, hypocenter	#3862	C₂×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₀₉	D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₁₀₉

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.