Subgroups — D₃×Q₈×C₁₃ #10597783

Order 624.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₃×C₁₃	C₂	1	3	yes	maximal
3	C₁₃×Dic₆	C₂	1	3	yes	maximal, complemented
4	C₂×Q₈×C₁₃	—	3	1	no	maximal, Hall
5	C₂×D₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	Dic₃×C₁₃	C₂²	1	3	yes	—
8	Q₈×C₁₃	—	3	3	no	—
9	Q₈×C₁₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₄×C₁₃	—	3	3	no	—
11	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	D₃×C₁₃	Q₈	1	2	yes	direct product factor
13	C₂²×C₁₃	—	3	1	no	—
14	C₄×C₁₃	—	3	3	no	—
15	C₄×C₁₃	C₂×D₃	1	3	yes	—
16	D₃×Q₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃	—	3	2	no	—
19	C₂×C₁₃	C₂²×D₃	1	1	yes	characteristic
20	C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₄×D₃	C₂×C₁₃	1	3	yes	—
22	Dic₆	C₂×C₁₃	1	3	yes	complemented
23	C₂×Q₈	—	3	1	no	Sylow
24	C₁₃	D₃×Q₈	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×D₃	C₂²×C₁₃	1	1	yes	characteristic
26	C₃×C₄	C₂²×C₁₃	1	3	yes	—
27	Dic₃	C₂²×C₁₃	1	3	yes	—
28	Q₈	—	3	3	no	—
29	Q₈	D₃×C₁₃	1	1	yes	characteristic, direct product factor
30	C₂×C₄	—	3	3	no	—
31	C₂×C₃	C₂³×C₁₃	1	1	yes	characteristic
32	D₃	Q₈×C₁₃	1	2	yes	direct product factor
33	C₂²	—	3	1	no	—
34	C₄	—	3	3	no	—
35	C₄	C₂×D₃×C₁₃	1	3	yes	—
36	C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	3	2	no	—
38	C₂	C₂²×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₁₃
Frattini	C₂	C₂²×D₃×C₁₃
Fitting	C₃×Q₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂³
prime radical	C₂×D₃×C₁₃	C₂²
hypercenter	Q₈×C₁₃	D₃
hypocenter	C₃	C₂×Q₈×C₁₃
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₁₃	C₂	semidirect
3. C₁₃×Dic₆	C₂	semidirect
9. Q₈×C₁₃	D₃	direct (N × H)
12. D₃×C₁₃	Q₈	direct (N × H)
16. D₃×Q₈	C₁₃	direct (N × H)
17. C₃×C₁₃	C₂×Q₈	semidirect
20. C₃×Q₈	C₂×C₁₃	semidirect
22. Dic₆	C₂×C₁₃	semidirect
24. C₁₃	D₃×Q₈	direct (N × H)
29. Q₈	D₃×C₁₃	direct (N × H)
32. D₃	Q₈×C₁₃	direct (N × H)
36. C₃	C₂×Q₈×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₁₃	2
C₄×D₃×C₁₃	2
C₁₃×Dic₆	2
C₂×Q₈×C₁₃	3
D₃×Q₈	13

Subgroups — D3×Q8×C13 #10597783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Q₈×C₁₃ #10597783