Subgroups — SD₁₆×C₃₁⋊C₃ #13093458

Order 1488.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₈×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂²×C₃₁⋊C₃	—	2	1	no	—
6	C₄×C₃₁⋊C₃	—	2	1	no	—
7	C₄×C₃₁⋊C₃	C₂²	1	1	yes	characteristic
8	Q₈×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₄×C₃₁	C₂×C₃	1	1	yes	characteristic
10	C₈×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃₁⋊C₃	—	4	1	no	—
12	C₂×C₃₁⋊C₃	D₄	1	1	yes	characteristic
13	C₂²×C₃₁	—	2	1	no	—
14	C₄×C₃₁	—	2	1	no	—
15	C₄×C₃₁	C₂²×C₃	1	1	yes	characteristic
16	C₃₁⋊C₃	SD₁₆	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃₁	—	4	1	no	—
18	C₂×C₃₁	C₃×D₄	1	1	yes	characteristic
19	C₃×SD₁₆	—	31	1	no	maximal, Hall
20	C₃₁	C₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₃×Q₈	—	31	1	no	—
22	C₃×D₄	—	31	1	no	—
23	C₃×C₈	—	31	1	no	—
24	SD₁₆	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	—	62	1	no	—
26	C₃×C₄	—	31	1	no	—
27	C₃×C₄	—	62	1	no	—
28	Q₈	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
29	D₄	C₂×C₃₁⋊C₃	1	1	yes	characteristic
30	C₈	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₃	—	31	1	no	—
32	C₂×C₃	—	124	1	no	—
33	C₂²	—	2	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂²×C₃₁⋊C₃	1	1	yes	characteristic
36	C₃	—	31	1	no	Sylow
37	C₂	—	4	1	no	—
38	C₂	D₄×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₃₁⋊C₃
commutator, cosocle	C₄×C₃₁	C₂²×C₃
Frattini	C₄	C₂²×C₃₁⋊C₃
Fitting	SD₁₆×C₃₁	C₃
socle	C₂×C₃₁	C₃×D₄
prime radical	D₄×C₃₁⋊C₃	C₂
hypercenter	SD₁₆	C₃₁⋊C₃
hypocenter	C₃₁	C₃×SD₁₆
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×C₃₁⋊C₃	C₂	semidirect
3. C₈×C₃₁⋊C₃	C₂	semidirect
4. SD₁₆×C₃₁	C₃	semidirect
8. Q₈×C₃₁	C₂×C₃	semidirect
10. C₈×C₃₁	C₂×C₃	semidirect
16. C₃₁⋊C₃	SD₁₆	direct (N × H)
20. C₃₁	C₃×SD₁₆	semidirect
24. SD₁₆	C₃₁⋊C₃	direct (N × H)
28. Q₈	C₂×C₃₁⋊C₃	semidirect
30. C₈	C₂×C₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₃₁⋊C₃	2
D₄×C₃₁⋊C₃	2
C₈×C₃₁⋊C₃	2
SD₁₆×C₃₁	3
C₃×SD₁₆	31

Subgroups — SD16×C31⋊C3 #13093458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×C₃₁⋊C₃ #13093458