Subgroups — C₂²⋊#22547878 #44544682

Order 32004.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic
2	#22547878	—	4	1	no	maximal, Hall
3	C₂×C₃×C₇×C₁₂₇	—	3	1	no	—
4	C₂²⋊#11765917	—	7	1	no	maximal, Hall
5	C₂²×C₇×C₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×C₁₂₇	A₄	1	1	yes	characteristic
7	C₂×C₇×C₁₂₇	—	3	1	no	—
8	C₂²×C₃×C₁₂₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
9	#11765917	—	28	1	no	Hall
10	C₇×C₁₂₇	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₂₇	—	3	1	no	—
12	C₂²×C₁₂₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₂₇	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	C₁₂₇⋊C₃	1	1	yes	characteristic
18	C₇⋊C₉	—	508	1	no	Hall
19	C₂×C₃×C₇	—	3	1	no	—
20	C₂²⋊C₉	—	889	1	no	Hall
21	C₂²×C₇	#11765917	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇	C₂²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
23	C₂×C₇	—	3	1	no	—
24	C₂²×C₃	#14581888	1	1	yes	characteristic
25	C₉	—	3556	1	no	Sylow
26	C₇	C₂²⋊#11765917	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	#22547878	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₂²⋊#14581888	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂²⋊#14581888
commutator, hypocenter	C₂²×C₇×C₁₂₇	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₇×C₁₂₇	C₃
LCS	G ▷ C₂²×C₇×C₁₂₇
UCS	C₁ ◁ C₃

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.