Subgroups — C₂×C₃₇⋊C₃² #37590243

Order 24642.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#16861552	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#16861551	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×C₃₇⋊C₃	C₃	1	2	yes	maximal, complemented
5	#16861552	C₂×C₃	1	1	yes	characteristic, complemented
6	#16861551	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₇×C₃₇⋊C₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₃₇²	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₃×C₃₇⋊C₃	—	37	2	no	maximal
11	C₃×C₃₇⋊C₃	—	37	2	no	—
12	C₂×C₃×C₃₇	—	37	2	no	—
13	C₂×C₃₇⋊C₃	—	37	2	no	—
14	C₂×C₃₇⋊C₃	—	37	2	no	—
15	C₂×C₃₇⋊C₃	—	111	12	no	—
16	C₂×C₃₇⋊C₃	C₃₇⋊C₃	1	2	yes	direct product factor
17	C₃×C₃₇	—	37	2	no	—
18	C₃₇⋊C₃	—	37	2	no	—
19	C₃₇⋊C₃	—	37	2	no	—
20	C₃₇⋊C₃	—	111	12	no	—
21	C₃₇⋊C₃	C₂×C₃₇⋊C₃	1	2	yes	direct product factor
22	C₂×C₃₇	—	3	12	no	—
23	C₂×C₃₇	C₃×C₃₇⋊C₃	1	2	yes	complemented
24	C₃₇	—	3	12	no	—
25	C₃₇	C₂×C₃×C₃₇⋊C₃	1	2	yes	complemented
26	C₂×C₃²	—	1369	1	no	Hall
27	C₃²	—	1369	1	no	Sylow
28	C₂×C₃	—	37	2	no	—
29	C₂×C₃	—	1369	1	no	—
30	C₂×C₃	—	1369	1	no	—
31	C₃	—	37	2	no	—
32	C₃	—	1369	1	no	—
33	C₃	—	1369	1	no	—
34	C₂	C₃₇⋊C₃²	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₃₇⋊C₃²
commutator, cosocle, hypocenter	C₃₇²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃₇²	C₃²
LCS	G ▷ C₃₇²
UCS	C₁ ◁ C₂

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.