Subgroups — C₂²×C₃₇×C₆₇⋊C₃ #44446607

Order 29748.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×C₆₇⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃₇×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₆₇⋊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×C₆₇⋊C₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₃₇	—	67	1	no	maximal, Hall
8	C₂×C₆₇⋊C₃	C₂×C₃₇	1	3	yes	direct product factor
9	C₂²×C₆₇	C₃×C₃₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₃₇	—	67	3	no	—
11	C₆₇⋊C₃	C₂²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₃₇	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₆₇	C₂×C₃×C₃₇	1	3	yes	complemented
14	C₃×C₃₇	—	67	1	no	Hall
15	C₂×C₃₇	C₂×C₆₇⋊C₃	1	3	yes	direct product factor
16	C₆₇	C₂²×C₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	—	67	1	no	Hall
19	C₂×C₃	—	67	3	no	—
20	C₂²	C₃₇×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	67	1	no	Sylow
22	C₂	C₂×C₃₇×C₆₇⋊C₃	1	3	yes	direct product factor

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

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.