Subgroups — C₂×C₁₀₉×#3862 #44545261

Order 32046.

40 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, direct product factor, Hall
2	C₂×C₇²×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×ΓL(1,𝔽₈)×C₁₀₉	—	7	2	no	maximal
5	ΓL(1,𝔽₈)×C₁₀₉	—	7	2	no	—
6	C₂×C₇×C₁₀₉	—	3	2	no	—
7	C₂×C₇×C₁₀₉	ΓL(1,𝔽₈)	1	2	yes	complemented
8	C₇×C₁₀₉	—	3	2	no	—
9	C₇×C₁₀₉	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
10	C₂×C₃×C₁₀₉	—	49	1	no	Hall
11	C₃×C₁₀₉	—	49	1	no	Hall
12	C₂×#3862	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₀₉	#3862	1	1	yes	characteristic, direct product factor, Hall
14	#3862	C₂×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
15	C₁₀₉	C₂×#3862	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₇²	C₃×C₁₀₉	1	1	yes	characteristic, complemented, Hall
17	C₇²	C₂×C₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
19	ΓL(1,𝔽₈)	—	7	2	no	—
20	C₂×C₇	—	3	2	no	—
21	C₂×C₇	ΓL(1,𝔽₈)×C₁₀₉	1	2	yes	complemented
22	C₇	—	3	2	no	—
23	C₇	C₂×ΓL(1,𝔽₈)×C₁₀₉	1	2	yes	complemented
24	C₂×C₃	—	49	1	no	Hall
25	C₃	—	49	1	no	Sylow
26	C₂	C₁₀₉×#3862	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₀₉	#3862
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₀₉	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×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.