Subgroups — Q₈×Dic₃×C₁₃ #11928918

Order 1248.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄⋊Dic₃	C₂	1	3	yes	maximal
3	C₄×Dic₃×C₁₃	C₂	1	3	yes	maximal
4	C₄×Q₈×C₁₃	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₃	C₄	1	4	yes	complemented
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂×Dic₃×C₁₃	C₂²	1	3	yes	—
8	C₂×Dic₃×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic
10	C₁₃×C₄⋊C₄	—	3	3	no	—
11	C₄²×C₁₃	—	3	3	no	—
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₃	C₂×C₄	1	6	yes	—
14	Dic₃×C₁₃	—	2	3	no	—
15	Dic₃×C₁₃	Q₈	1	2	yes	direct product factor
16	Q₈×C₁₃	Dic₃	1	4	yes	direct product factor
17	C₂×C₄×C₁₃	—	3	1	no	—
18	C₂×C₄×C₁₃	—	3	3	no	—
19	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
20	Q₈×Dic₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
24	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
25	C₄×C₁₃	—	3	2	no	—
26	C₄×C₁₃	—	6	3	no	—
27	C₄×C₁₃	C₂×Dic₃	1	6	yes	—
28	C₂×C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic
29	C₄⋊Dic₃	C₂×C₁₃	1	3	yes	—
30	C₄×Dic₃	C₂×C₁₃	1	3	yes	—
31	C₃×C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
32	C₄×Q₈	—	3	1	no	Sylow
33	C₂×C₁₃	D₃×Q₈	1	1	yes	characteristic
34	C₂×C₁₃	#239	1	1	yes	characteristic
35	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
36	C₃×Q₈	C₄×C₁₃	1	4	yes	complemented
37	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
38	C₂×Dic₃	C₂²×C₁₃	1	3	yes	—
39	C₂×Dic₃	C₂²×C₁₃	1	1	yes	characteristic
40	C₂×Q₈	D₃×C₁₃	1	1	yes	characteristic
41	C₄⋊C₄	—	3	3	no	—
42	C₄²	—	3	3	no	—
43	C₁₃	Q₈×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
45	C₃×C₄	C₂×C₄×C₁₃	1	6	yes	—
46	Dic₃	—	2	3	no	—
47	Dic₃	Q₈×C₁₃	1	2	yes	direct product factor
48	Q₈	Dic₃×C₁₃	1	4	yes	direct product factor
49	C₂×C₄	—	3	1	no	—
50	C₂×C₄	—	3	3	no	—
51	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
52	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
53	C₂×C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic
54	C₂×C₃	C₁₃×#41	1	1	yes	characteristic
55	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
56	C₄	—	3	2	no	—
57	C₄	—	6	3	no	—
58	C₄	C₂×Dic₃×C₁₃	1	6	yes	—
59	C₃	C₄×Q₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
60	C₂	D₃×Q₈×C₁₃	1	1	yes	characteristic
61	C₂	C₁₃×#239	1	1	yes	characteristic
62	C₂	C₂²×Dic₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
cosocle	C₂²×C₃	C₂³×C₁₃
hypercenter	C₂×Q₈×C₁₃	D₃
hypocenter	C₃	C₄×Q₈×C₁₃
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
5. C₃×Q₈×C₁₃	C₄	semidirect
15. Dic₃×C₁₃	Q₈	direct (N × H)
16. Q₈×C₁₃	Dic₃	direct (N × H)
20. Q₈×Dic₃	C₁₃	direct (N × H)
31. C₃×C₁₃	C₄×Q₈	semidirect
36. C₃×Q₈	C₄×C₁₃	semidirect
43. C₁₃	Q₈×Dic₃	direct (N × H)
47. Dic₃	Q₈×C₁₃	direct (N × H)
48. Q₈	Dic₃×C₁₃	direct (N × H)
59. C₃	C₄×Q₈×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₃	2
C₁₃×C₄⋊Dic₃	2
C₄×Dic₃×C₁₃	2
C₄×Q₈×C₁₃	3
Q₈×Dic₃	13

Subgroups — Q8×Dic3×C13 #11928918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₃×C₁₃ #11928918