Subgroups — C₄⋊Dic₉₃ #13093503

Order 1488.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉₃	C₂	1	2	yes	maximal
3	C₄⋊Dic₃₁	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₃₁	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₃₁	C₄	1	2	yes	complemented
6	Dic₉₃	—	2	2	no	—
7	C₂×C₄×C₃₁	D₃	1	1	yes	characteristic
8	C₂×Dic₃₁	—	3	2	no	—
9	C₂×C₃×C₃₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₃×C₃₁	D₄	1	1	yes	characteristic
11	C₂×C₃×C₃₁	Q₈	1	1	yes	characteristic
12	C₂²×C₃₁	C₂×D₃	1	1	yes	characteristic
13	C₄×C₃₁	Dic₃	1	2	yes	complemented
14	Dic₃₁	—	6	2	no	—
15	C₃×C₃₁	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₁	Dic₆	1	1	yes	characteristic
17	C₂×C₃₁	D₁₂	1	1	yes	characteristic
18	C₂×C₃₁	C₂×Dic₃	1	1	yes	characteristic
19	C₄⋊Dic₃	—	31	1	no	maximal, Hall
20	C₃₁	C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₄	D₃₁	1	1	yes	characteristic
22	C₂×Dic₃	—	31	2	no	—
23	C₄⋊C₄	—	93	1	no	Sylow
24	C₂²×C₃	C₂×D₃₁	1	1	yes	characteristic
25	C₃×C₄	Dic₃₁	1	2	yes	complemented
26	Dic₃	—	62	2	no	—
27	C₂×C₄	—	93	2	no	—
28	C₂×C₄	D₉₃	1	1	yes	characteristic
29	C₂×C₃	Dic₆₂	1	1	yes	characteristic
30	C₂×C₃	D₁₂₄	1	1	yes	characteristic
31	C₂×C₃	C₂×Dic₃₁	1	1	yes	characteristic
32	C₂²	C₂×D₉₃	1	1	yes	characteristic
33	C₄	—	186	2	no	—
34	C₄	Dic₉₃	1	2	yes	complemented
35	C₃	C₄⋊Dic₃₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	Dic₁₈₆	1	1	yes	characteristic
37	C₂	D₃₇₂	1	1	yes	characteristic
38	C₂	C₂×Dic₉₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₃×C₄×C₃₁	C₄	semidirect
13. C₄×C₃₁	Dic₃	semidirect
15. C₃×C₃₁	C₄⋊C₄	semidirect
20. C₃₁	C₄⋊Dic₃	semidirect
25. C₃×C₄	Dic₃₁	semidirect
34. C₄	Dic₉₃	semidirect
35. 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×C₃×C₄×C₃₁	2
C₂×Dic₉₃	2
C₄⋊Dic₃₁	3
C₄⋊Dic₃	31

Subgroups — C4⋊Dic93 #13093503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊Dic₉₃ #13093503