Subgroups — SD₃₂×C₁₃⋊C₃ #11928023

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₁₆×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×SD₃₂	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	Q₈×C₁₃⋊C₃	—	2	1	no	—
6	D₄×C₁₃⋊C₃	—	2	1	no	—
7	C₈×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
8	C₁₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃×D₈	C₂×C₃	1	1	yes	characteristic
10	C₁₃×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₁₃⋊C₃	—	4	1	no	—
12	C₄×C₁₃⋊C₃	—	4	1	no	—
13	C₄×C₁₃⋊C₃	D₄	1	1	yes	characteristic
14	Q₈×C₁₃	—	2	1	no	—
15	D₄×C₁₃	—	2	1	no	—
16	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
17	C₃×SD₃₂	—	13	1	no	maximal, Hall
18	C₂×C₁₃⋊C₃	—	8	1	no	—
19	C₂×C₁₃⋊C₃	D₈	1	1	yes	characteristic
20	C₂²×C₁₃	—	4	1	no	—
21	C₄×C₁₃	—	4	1	no	—
22	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
23	C₃×Q₁₆	—	13	1	no	—
24	C₃×D₈	—	13	1	no	—
25	C₃×C₁₆	—	13	1	no	—
26	C₁₃⋊C₃	SD₃₂	1	1	yes	characteristic, direct product factor, Hall
27	SD₃₂	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₃	—	8	1	no	—
29	C₂×C₁₃	C₃×D₈	1	1	yes	characteristic
30	C₃×Q₈	—	26	1	no	—
31	C₃×D₄	—	26	1	no	—
32	C₃×C₈	—	13	1	no	—
33	Q₁₆	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
34	D₈	C₂×C₁₃⋊C₃	1	1	yes	characteristic
35	C₁₆	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
36	C₁₃	C₃×SD₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	52	1	no	—
38	C₃×C₄	—	13	1	no	—
39	C₃×C₄	—	52	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	2	1	no	—
42	C₈	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
43	C₂×C₃	—	13	1	no	—
44	C₂×C₃	—	104	1	no	—
45	C₂²	—	4	1	no	—
46	C₄	—	4	1	no	—
47	C₄	D₄×C₁₃⋊C₃	1	1	yes	characteristic
48	C₃	—	13	1	no	Sylow
49	C₂	—	8	1	no	—
50	C₂	D₈×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×C₁₃⋊C₃
commutator, cosocle	C₈×C₁₃	C₂²×C₃
Frattini	C₈	C₂²×C₁₃⋊C₃
Fitting	C₁₃×SD₃₂	C₃
socle	C₂×C₁₃	C₃×D₈
prime radical	D₈×C₁₃⋊C₃	C₂
hypercenter	SD₃₂	C₁₃⋊C₃
hypocenter	C₁₃	C₃×SD₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×C₁₃⋊C₃	C₂	semidirect
3. C₁₆×C₁₃⋊C₃	C₂	semidirect
4. C₁₃×SD₃₂	C₃	semidirect
8. C₁₃×Q₁₆	C₂×C₃	semidirect
10. C₁₃×C₁₆	C₂×C₃	semidirect
26. C₁₃⋊C₃	SD₃₂	direct (N × H)
27. SD₃₂	C₁₃⋊C₃	direct (N × H)
33. Q₁₆	C₂×C₁₃⋊C₃	semidirect
35. C₁₆	C₂×C₁₃⋊C₃	semidirect
36. C₁₃	C₃×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×C₁₃⋊C₃	2
D₈×C₁₃⋊C₃	2
C₁₆×C₁₃⋊C₃	2
C₁₃×SD₃₂	3
C₃×SD₃₂	13

Subgroups — SD32×C13⋊C3 #11928023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₃₂×C₁₃⋊C₃ #11928023