Subgroups — C₂²⋊#22547884 #44544841

Order 32004.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#22547884	—	4	1	no	maximal, Hall
3	C₂×C₇×C₁₂₇⋊C₃	—	3	1	no	—
4	C₂²⋊#11765919	—	7	1	no	maximal, Hall
5	C₂²×C₇×C₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇×C₁₂₇⋊C₃	A₄	1	1	yes	characteristic
7	C₂×C₇×C₁₂₇	—	3	1	no	—
8	C₂²×C₁₂₇⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
9	#11765919	—	28	1	no	Hall
10	C₇×C₁₂₇	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₂₇⋊C₃	—	3	1	no	—
12	C₂²×C₁₂₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
13	C₁₂₇⋊C₃	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₂×C₁₂₇	—	3	1	no	—
15	C₂²⋊(C₇⋊C₉)	—	127	1	no	maximal, Hall
16	C₁₂₇	C₂²⋊(C₇⋊C₉)	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃×C₇	—	127	1	no	—
18	C₇⋊C₉	—	508	1	no	Hall
19	C₂×C₃×C₇	—	381	1	no	—
20	C₂²⋊C₉	—	889	1	no	Hall
21	C₂²×C₇	#11765919	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇	—	127	1	no	—
23	C₂×C₇	—	3	1	no	—
24	C₂²×C₃	—	127	1	no	—
25	C₉	—	3556	1	no	Sylow
26	C₇	C₂²⋊#11765919	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	381	1	no	—
28	C₂²	#22547884	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	127	1	no	—
30	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂²×C₇×C₁₂₇	C₉
prime radical, cosocle	C₂²×C₇×C₁₂₇⋊C₃	C₃
LCS	G ▷ C₂²×C₇×C₁₂₇
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.