Subgroups — Dic₃⋊Dic₃₁ #13093451

Order 1488.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₃₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₃₁	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₃₁	C₂²	1	1	yes	characteristic
6	Dic₉₃	—	2	1	no	—
7	C₃×Dic₃₁	—	2	1	no	—
8	Dic₃×C₃₁	C₄	1	2	yes	complemented
9	C₂×C₄×C₃₁	—	3	1	no	—
10	C₂×Dic₃₁	—	3	1	no	—
11	C₂×Dic₃₁	D₃	1	1	yes	characteristic
12	C₂×C₃×C₃₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₃₁	D₄	1	1	yes	characteristic
14	C₂×C₃×C₃₁	Q₈	1	1	yes	characteristic
15	C₂²×C₃₁	C₂×D₃	1	1	yes	characteristic
16	C₄×C₃₁	—	3	2	no	—
17	Dic₃₁	—	2	1	no	—
18	Dic₃₁	—	6	1	no	—
19	C₃×C₃₁	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	Dic₆	1	1	yes	characteristic
21	C₂×C₃₁	C₄×D₃	1	1	yes	characteristic
22	C₂×C₃₁	#67	1	1	yes	characteristic
23	Dic₃⋊C₄	—	31	1	no	maximal, Hall
24	C₃₁	Dic₃⋊C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₄	—	31	1	no	—
26	C₂×Dic₃	—	31	1	no	—
27	C₂×Dic₃	D₃₁	1	1	yes	characteristic
28	C₄⋊C₄	—	93	1	no	Sylow
29	C₂²×C₃	C₂×D₃₁	1	1	yes	characteristic
30	C₃×C₄	—	62	1	no	—
31	Dic₃	—	62	1	no	—
32	Dic₃	Dic₃₁	1	2	yes	complemented
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	31	1	no	—
35	C₂×C₄	—	93	1	no	—
36	C₂×C₃	Dic₆₂	1	1	yes	characteristic
37	C₂×C₃	D₁₂₄	1	1	yes	characteristic
38	C₂×C₃	C₂×Dic₃₁	1	1	yes	characteristic
39	C₂²	D₃×D₃₁	1	1	yes	characteristic
40	C₄	—	3	2	no	—
41	C₄	—	62	1	no	—
42	C₄	—	186	1	no	—
43	C₃	C₄⋊Dic₃₁	1	1	yes	characteristic, complemented, Sylow
44	C₂	D₃×Dic₃₁	1	1	yes	characteristic
45	C₂	#10625225	1	1	yes	characteristic
46	C₂	#10625227	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×D₃₁
commutator	C₂×C₃×C₃₁	C₂×C₄
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₃₁	C₂²
hypocenter	C₃×C₃₁	C₄⋊C₄
LCS	G ▷ C₂×C₃×C₃₁ ▷ C₃×C₃₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
8. Dic₃×C₃₁	C₄	semidirect
19. C₃×C₃₁	C₄⋊C₄	semidirect
24. C₃₁	Dic₃⋊C₄	semidirect
32. Dic₃	Dic₃₁	semidirect
43. C₃	C₄⋊Dic₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₉₃	2
C₂×Dic₃×C₃₁	2
C₂×C₃×Dic₃₁	2
C₄⋊Dic₃₁	3
Dic₃⋊C₄	31

Subgroups — Dic3⋊Dic31 #13093451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃⋊Dic₃₁ #13093451