Subgroups — #44544713

Order 32004.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22547884	C₂	1	1	yes	maximal, characteristic
2	C₇×(C₁₂₇⋊C₃)⋊C₄	C₃	1	1	yes	maximal, characteristic
3	#22547884	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
5	#11765919⋊C₄	—	7	1	no	maximal, Hall
6	C₇×Dic₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₂₇⋊C₃	C₃×C₄	1	1	yes	characteristic
8	C₂×#11765919	—	7	1	no	—
9	C₂×C₇×C₁₂₇	C₂×C₉	1	1	yes	characteristic
10	(C₁₂₇⋊C₃)⋊C₄	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	#11765919	—	7	1	no	Hall
12	C₇×C₁₂₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₂₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	Dic₁₂₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
15	C₁₂₇⋊C₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₂×C₁₂₇	C₂×C₇⋊C₉	1	1	yes	characteristic
17	C₄×C₇⋊C₉	—	127	1	no	maximal, Hall
18	C₁₂₇	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇⋊C₉	—	127	1	no	—
20	C₃×C₄×C₇	—	127	1	no	—
21	C₇⋊C₉	—	127	1	no	Hall
22	C₂×C₃×C₇	—	127	1	no	—
23	C₄×C₉	—	889	1	no	Hall
24	C₄×C₇	—	127	1	no	Hall
25	C₃×C₇	—	127	1	no	—
26	C₂×C₉	—	889	1	no	—
27	C₂×C₇	#11765919⋊C₂	1	1	yes	characteristic
28	C₃×C₄	—	127	1	no	—
29	C₉	—	889	1	no	Sylow
30	C₇	#11765919⋊C₄	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	127	1	no	—
32	C₄	—	127	1	no	Sylow
33	C₃	—	127	1	no	—
34	C₂	#30630689	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#30630689
commutator, hypocenter	C₇×C₁₂₇	C₄×C₉
Fitting, socle	C₂×C₇×C₁₂₇	C₂×C₉
prime radical, cosocle	C₂×C₇×C₁₂₇⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₁₂₇
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.