Subgroups — C₃⋊((C₆₁⋊C₃)⋊D₃₁) #46801421

Order 34038.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₆₁⋊C₃)⋊D₃₁	—	3	1	no	maximal
3	D₅₆₇₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₃₁×C₆₁⋊C₃	—	2	1	no	—
6	C₃₁×C₆₁⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₁₈₉₁	—	3	1	no	Hall
8	C₃₁×C₆₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₆₁⋊C₃)	—	31	1	no	maximal, Hall
10	C₃×D₉₃	—	61	1	no	maximal, Hall
11	C₃×C₆₁⋊C₃	D₃₁	1	1	yes	characteristic, complemented, Hall
12	D₁₈₃	—	31	1	no	—
13	D₆₁⋊C₃	—	93	1	no	—
14	C₃²×C₃₁	—	61	1	no	Hall
15	D₉₃	—	61	1	no	—
16	C₃×D₃₁	—	183	1	no	—
17	C₃×C₆₁	C₃×D₃₁	1	1	yes	characteristic, complemented
18	C₆₁⋊C₃	—	2	1	no	—
19	C₆₁⋊C₃	D₉₃	1	1	yes	characteristic, complemented
20	D₆₁	—	93	1	no	Hall
21	C₃×C₃₁	—	61	1	no	—
22	C₃×C₃₁	—	122	1	no	—
23	C₃×C₃₁	D₆₁⋊C₃	1	1	yes	characteristic, complemented
24	D₃₁	—	183	1	no	Hall
25	C₆₁	C₃×D₉₃	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	C₃⋊(D₆₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1891	1	no	Hall
28	C₃²	—	61	1	no	Sylow
29	C₂×C₃	—	5673	1	no	—
30	D₃	—	1891	1	no	—
31	C₃	—	61	1	no	—
32	C₃	—	122	1	no	—
33	C₃	(C₆₁⋊C₃)⋊D₃₁	1	1	yes	characteristic, complemented
34	C₂	—	5673	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₆₁	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₆₁
UCS	C₁

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.