Subgroups — C₂²×C₆₇×C₃₇⋊C₃ #44446608

Order 29748.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₇×C₃₇⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃₇×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₇×C₃₇⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃₇×C₆₇	C₂×C₃	1	3	yes	complemented
5	C₃₇×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃×C₆₇	—	37	1	no	maximal, Hall
7	C₂²×C₃₇⋊C₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₆₇	—	37	3	no	—
9	C₂²×C₆₇	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₇⋊C₃	C₂×C₆₇	1	3	yes	direct product factor
11	C₃×C₆₇	—	37	1	no	Hall
12	C₂²×C₃₇	C₃×C₆₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₆₇	C₂×C₃₇⋊C₃	1	3	yes	direct product factor
14	C₃₇⋊C₃	C₂²×C₆₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃₇	C₂×C₃×C₆₇	1	3	yes	complemented
16	C₆₇	C₂²×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₂²×C₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃	—	37	1	no	Hall
19	C₂×C₃	—	37	3	no	—
20	C₂²	C₆₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	C₂×C₆₇×C₃₇⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₆₇	C₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₂²×C₃×C₆₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃₇×C₆₇	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂²×C₆₇

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.