Subgroups — C₃⁵×C₃₇⋊C₃ #41008262

Order 26973.

113264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₃₇⋊C₃	C₃	1	363	yes	maximal, direct product factor
2	C₃⁵×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₃₇⋊C₃	C₃²	1	10890	yes	direct product factor
4	C₃⁴×C₃₇	C₃²	1	121	yes	complemented
5	C₃³×C₃₇	C₃³	1	1210	yes	complemented
6	C₃²×C₃₇⋊C₃	C₃³	1	32670	yes	direct product factor
7	C₃⁶	—	37	1	no	maximal, Sylow
8	C₃²×C₃₇	C₃⁴	1	1210	yes	complemented
9	C₃×C₃₇⋊C₃	C₃⁴	1	9801	yes	direct product factor
10	C₃⁵	—	37	363	no	—
11	C₃⁵	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃×C₃₇	C₃⁵	1	121	yes	complemented
13	C₃₇⋊C₃	C₃⁵	1	243	yes	direct product factor
14	C₃⁴	—	37	10890	no	—
15	C₃⁴	C₃×C₃₇⋊C₃	1	121	yes	direct product factor
16	C₃₇	C₃⁶	1	1	yes	characteristic, complemented, Sylow
17	C₃³	—	37	32670	no	—
18	C₃³	C₃²×C₃₇⋊C₃	1	1210	yes	direct product factor
19	C₃²	—	37	9801	no	—
20	C₃²	C₃³×C₃₇⋊C₃	1	1210	yes	direct product factor
21	C₃	—	37	243	no	—
22	C₃	C₃⁴×C₃₇⋊C₃	1	121	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃⁵	C₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₃⁶
Frattini	C₁	G
Fitting, socle	C₃⁵×C₃₇	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃⁵

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.