Subgroups — Q₈×Dic₃₉ #11929004

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	C₄⋊Dic₃₉	C₂	1	3	yes	maximal
3	C₄×Dic₃₉	C₂	1	3	yes	maximal
4	Q₈×Dic₁₃	—	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×Dic₃₉	C₂²	1	3	yes	—
8	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic
10	C₄⋊Dic₁₃	—	3	3	no	—
11	C₄×Dic₁₃	—	3	3	no	—
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₃	C₂×C₄	1	6	yes	—
14	Dic₃₉	—	2	3	no	—
15	Dic₃₉	Q₈	1	2	yes	direct product factor
16	Q₈×C₁₃	Dic₃	1	4	yes	complemented
17	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
18	C₂×Dic₁₃	—	3	1	no	—
19	C₂×Dic₁₃	—	3	3	no	—
20	Q₈×Dic₃	—	13	1	no	maximal, 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	C₂×Dic₃	1	6	yes	—
26	Dic₁₃	—	3	2	no	—
27	Dic₁₃	—	6	3	no	—
28	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic
29	C₄⋊Dic₃	—	13	3	no	—
30	C₄×Dic₃	—	13	3	no	—
31	C₃×C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
32	C₄×Q₈	—	39	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	Dic₁₃	1	4	yes	complemented
37	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
38	C₂×Dic₃	—	13	1	no	—
39	C₂×Dic₃	—	13	3	no	—
40	C₂×Q₈	D₃₉	1	1	yes	characteristic
41	C₄⋊C₄	—	39	3	no	—
42	C₄²	—	39	3	no	—
43	C₁₃	Q₈×Dic₃	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
45	C₃×C₄	C₂×Dic₁₃	1	6	yes	—
46	Dic₃	—	13	2	no	—
47	Dic₃	—	26	3	no	—
48	Q₈	Dic₃₉	1	4	yes	direct product factor
49	C₂×C₄	—	39	1	no	—
50	C₂×C₄	—	39	3	no	—
51	C₂×C₄	C₂×D₃₉	1	3	yes	—
52	C₂×C₃	Q₈×D₁₃	1	1	yes	characteristic
53	C₂×C₃	#6131	1	1	yes	characteristic
54	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
55	C₂²	C₂²×D₃₉	1	1	yes	characteristic
56	C₄	—	39	2	no	—
57	C₄	—	78	3	no	—
58	C₄	C₂×Dic₃₉	1	6	yes	—
59	C₃	Q₈×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
60	C₂	Q₈×D₃₉	1	1	yes	characteristic
61	C₂	#10597794	1	1	yes	characteristic
62	C₂	C₂²×Dic₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator	C₂×C₃×C₁₃	C₂²×C₄
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle, prime radical, cosocle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×Q₈	D₃₉
hypocenter	C₃×C₁₃	C₄×Q₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
5. C₃×Q₈×C₁₃	C₄	semidirect
15. Dic₃₉	Q₈	direct (N × H)
16. Q₈×C₁₃	Dic₃	semidirect
31. C₃×C₁₃	C₄×Q₈	semidirect
36. C₃×Q₈	Dic₁₃	semidirect
43. C₁₃	Q₈×Dic₃	semidirect
48. Q₈	Dic₃₉	direct (N × H)
59. C₃	Q₈×Dic₁₃	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
C₄⋊Dic₃₉	2
C₄×Dic₃₉	2
Q₈×Dic₁₃	3
Q₈×Dic₃	13

Subgroups — Q8×Dic39 #11929004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₃₉ #11929004