Subgroups — #13093509

Order 1488.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₃₁	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₃₁	—	2	2	no	—
5	C₂²×C₃×C₃₁	C₄	1	2	yes	complemented
6	C₂²×C₃×C₃₁	C₂²	1	1	yes	characteristic
7	Dic₉₃	—	2	2	no	—
8	C₂³×C₃₁	D₃	1	1	yes	characteristic
9	C₂×Dic₃₁	—	3	2	no	—
10	C₂×C₃×C₃₁	—	2	2	no	—
11	C₂×C₃×C₃₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₃₁	D₄	1	2	yes	—
13	C₂²×C₃₁	—	2	2	no	—
14	C₂²×C₃₁	Dic₃	1	2	yes	complemented
15	C₂²×C₃₁	C₂×D₃	1	1	yes	characteristic
16	Dic₃₁	—	6	2	no	—
17	C₃×C₃₁	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃₁	—	2	2	no	—
19	C₂×C₃₁	C₂×Dic₃	1	1	yes	characteristic
20	C₂×C₃₁	#67	1	2	yes	—
21	#217	—	31	1	no	maximal, Hall
22	C₃₁	#217	1	1	yes	characteristic, complemented, Sylow
23	C₂³×C₃	D₃₁	1	1	yes	characteristic
24	C₂×Dic₃	—	31	2	no	—
25	C₂²⋊C₄	—	93	1	no	Sylow
26	C₂²×C₃	—	2	2	no	—
27	C₂²×C₃	Dic₃₁	1	2	yes	complemented
28	C₂²×C₃	C₂×D₃₁	1	1	yes	characteristic
29	Dic₃	—	62	2	no	—
30	C₂³	D₉₃	1	1	yes	characteristic
31	C₂×C₄	—	93	2	no	—
32	C₂×C₃	—	2	2	no	—
33	C₂×C₃	C₂×Dic₃₁	1	1	yes	characteristic
34	C₂×C₃	C₂²⋊D₃₁	1	2	yes	—
35	C₂²	—	2	2	no	—
36	C₂²	Dic₉₃	1	2	yes	complemented
37	C₂²	C₂×D₉₃	1	1	yes	characteristic
38	C₄	—	186	2	no	—
39	C₃	C₂²⋊Dic₃₁	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	2	2	no	—
41	C₂	C₂×Dic₉₃	1	1	yes	characteristic
42	C₂	#10625247	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂×D₉₃
commutator	C₂×C₃×C₃₁	C₂×C₄
Fitting, prime radical	C₂³×C₃×C₃₁	C₂
socle, cosocle	C₂²×C₃×C₃₁	C₂²
hypercenter	C₂³	D₉₃
hypocenter	C₃×C₃₁	C₂²⋊C₄
LCS	G ▷ C₂×C₃×C₃₁ ▷ C₃×C₃₁
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×Dic₉₃	C₂	semidirect
5. C₂²×C₃×C₃₁	C₄	semidirect
14. C₂²×C₃₁	Dic₃	semidirect
17. C₃×C₃₁	C₂²⋊C₄	semidirect
22. C₃₁	#217	semidirect
27. C₂²×C₃	Dic₃₁	semidirect
36. C₂²	Dic₉₃	semidirect
39. C₃	C₂²⋊Dic₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₃₁	2
C₂×Dic₉₃	2
C₂²⋊Dic₃₁	3
#217	31