Subgroups — C₃₇×C₇⋊D₆₃ #45657371

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₃⋊(C₇⋊D₇)	—	3	1	no	maximal
3	C₃×C₇²×C₃₇	D₃	1	1	yes	characteristic
4	C₃₇×D₆₃	—	7	8	no	maximal
5	C₃₇×C₇⋊D₇	—	9	1	no	Hall
6	C₇×C₉×C₃₇	D₇	1	8	yes	complemented
7	C₇²×C₃₇	D₉	1	1	yes	characteristic, complemented, Hall
8	C₃₇×D₂₁	—	21	8	no	—
9	C₇⋊D₆₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇×C₃₇	D₂₁	1	8	yes	—
11	D₉×C₃₇	—	49	1	no	Hall
12	D₇×C₃₇	—	63	8	no	—
13	C₇²×C₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
14	C₉×C₃₇	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₇⋊D₇)	—	3	1	no	—
16	C₇×C₃₇	D₆₃	1	8	yes	complemented
17	D₃×C₃₇	—	147	1	no	—
18	C₃×C₇²	D₃×C₃₇	1	1	yes	characteristic
19	D₆₃	—	7	8	no	—
20	C₃×C₃₇	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
21	C₇⋊D₇	—	9	1	no	Hall
22	C₂×C₃₇	—	441	1	no	Hall
23	C₇×C₉	D₇×C₃₇	1	8	yes	complemented
24	C₇²	D₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
25	D₂₁	—	21	8	no	—
26	C₃₇	C₇⋊D₆₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×C₇	C₃₇×D₂₁	1	8	yes	—
28	D₉	—	49	1	no	Hall
29	D₇	—	63	8	no	—
30	C₉	C₃₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₃₇×D₆₃	1	8	yes	complemented
32	D₃	—	147	1	no	—
33	C₃	C₃₇×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
34	C₂	—	441	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	C₇⋊D₆₃
commutator, cosocle, hypocenter	C₇²×C₉	C₂×C₃₇
Frattini	C₃	C₃₇×C₃⋊(C₇⋊D₇)
Fitting	C₇²×C₉×C₃₇	C₂
socle	C₃×C₇²×C₃₇	D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ 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.