Subgroups — C₂²×(C₃₃₇⋊C₃)⋊C₇ #43246742

Order 28308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₃₃₇⋊C₃)⋊C₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃₃₇⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	(C₃₃₇⋊C₃)⋊C₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃₃₇⋊C₇	C₂×C₃	1	3	yes	complemented
5	C₂²×C₃₃₇⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃₃₇⋊C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃₃₇⋊C₃	C₂×C₇	1	3	yes	complemented
8	C₂²×C₃₃₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃₃₇⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₃₇	C₂×C₃×C₇	1	3	yes	complemented
11	C₃₃₇	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃×C₇	—	337	1	no	maximal, Hall
13	C₂×C₃×C₇	—	337	3	no	—
14	C₂²×C₇	—	337	1	no	Hall
15	C₃×C₇	—	337	1	no	Hall
16	C₂×C₇	—	337	3	no	—
17	C₂²×C₃	—	2359	1	no	Hall
18	C₇	—	337	1	no	Sylow
19	C₂×C₃	—	2359	3	no	—
20	C₂²	(C₃₃₇⋊C₃)⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	2359	1	no	Sylow
22	C₂	C₂×(C₃₃₇⋊C₃)⋊C₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	(C₃₃₇⋊C₃)⋊C₇
commutator, cosocle, hypocenter	C₃₃₇	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃₃₇	C₃×C₇
LCS	G ▷ C₃₃₇
UCS	C₁ ◁ C₂²

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.