Subgroups — Q₈×C₁₃×D₇ #13089898

Order 1456.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×D₇	C₂	1	3	yes	maximal
3	C₁₃×Dic₁₄	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₃×D₇	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₁₃	C₂²	1	3	yes	—
6	C₁₃×Dic₇	C₂²	1	3	yes	—
7	C₂×Q₈×C₁₃	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
9	C₁₃×D₇	Q₈	1	2	yes	direct product factor
10	Q₈×D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	Q₈×C₁₃	—	7	3	no	—
12	Q₈×C₁₃	D₇	1	1	yes	characteristic, direct product factor
13	C₂×C₄×C₁₃	—	7	3	no	—
14	C₇×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
15	C₇×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
16	C₄×D₇	C₂×C₁₃	1	3	yes	—
17	Dic₁₄	C₂×C₁₃	1	3	yes	complemented
18	C₂²×C₁₃	—	7	1	no	—
19	C₄×C₁₃	—	7	3	no	—
20	C₄×C₁₃	C₂×D₇	1	3	yes	—
21	C₂×D₇	C₂²×C₁₃	1	1	yes	characteristic
22	C₄×C₇	C₂²×C₁₃	1	3	yes	—
23	Dic₇	C₂²×C₁₃	1	3	yes	—
24	C₂×C₁₃	—	7	2	no	—
25	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
26	C₂×Q₈	—	7	1	no	Sylow
27	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
28	D₇	Q₈×C₁₃	1	2	yes	direct product factor
29	C₁₃	Q₈×D₇	1	1	yes	characteristic, direct product factor, Sylow
30	Q₈	—	7	3	no	—
31	Q₈	C₁₃×D₇	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	7	3	no	—
33	C₇	C₂×Q₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	7	1	no	—
35	C₄	—	7	3	no	—
36	C₄	C₂×C₁₃×D₇	1	3	yes	—
37	C₂	—	7	2	no	—
38	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	C₂²×D₇
commutator, cosocle	C₂×C₇	C₂³×C₁₃
Frattini	C₂	C₂²×C₁₃×D₇
Fitting	C₇×Q₈×C₁₃	C₂
socle	C₂×C₇×C₁₃	C₂³
prime radical	C₂×C₁₃×D₇	C₂²
hypercenter	Q₈×C₁₃	D₇
hypocenter	C₇	C₂×Q₈×C₁₃
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₁₃ ◁ Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×Q₈×C₁₃	C₂	semidirect
3. C₁₃×Dic₁₄	C₂	semidirect
9. C₁₃×D₇	Q₈	direct (N × H)
10. Q₈×D₇	C₁₃	direct (N × H)
12. Q₈×C₁₃	D₇	direct (N × H)
14. C₇×C₁₃	C₂×Q₈	semidirect
15. C₇×Q₈	C₂×C₁₃	semidirect
17. Dic₁₄	C₂×C₁₃	semidirect
28. D₇	Q₈×C₁₃	direct (N × H)
29. C₁₃	Q₈×D₇	direct (N × H)
31. Q₈	C₁₃×D₇	direct (N × H)
33. C₇	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
C₇×Q₈×C₁₃	2
C₄×C₁₃×D₇	2
C₁₃×Dic₁₄	2
C₂×Q₈×C₁₃	7
Q₈×D₇	13

Subgroups — Q8×C13×D7 #13089898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₃×D₇ #13089898