Subgroups — D₈×D₃₉ #11928972

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₃₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597667	C₂	1	2	yes	maximal, complemented
4	D₃₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₁₃	—	3	1	no	maximal, Hall
7	C₂²×D₃₉	—	2	2	no	—
8	C₃×D₄×C₁₃	C₂²	1	2	yes	complemented
9	#64625	—	2	2	no	—
10	D₁₅₆	C₂²	1	2	yes	complemented
11	C₄×D₃₉	C₂²	1	1	yes	characteristic
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₃⋊#1055	C₂²	1	1	yes	characteristic, complemented
14	D₄×D₁₃	—	3	2	no	—
15	C₁₃×D₈	D₃	1	1	yes	characteristic, complemented
16	#6104	—	3	2	no	—
17	D₁₀₄	—	3	1	no	—
18	C₈×D₁₃	—	3	1	no	—
19	C₂²×C₃×C₁₃	—	2	2	no	—
20	C₂×D₃₉	—	2	2	no	—
21	C₂×D₃₉	—	4	4	no	—
22	C₂×D₃₉	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	Dic₃₉	D₄	1	1	yes	characteristic
25	C₂²×D₁₃	—	6	2	no	—
26	D₄×C₁₃	C₂×D₃	1	2	yes	complemented
27	C₂²⋊D₁₃	—	6	2	no	—
28	D₅₂	—	3	2	no	—
29	C₄×D₁₃	—	3	1	no	—
30	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
31	#1055	—	3	1	no	—
32	D₃×D₈	—	13	1	no	maximal, Hall
33	C₂×C₃×C₁₃	—	4	2	no	—
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	D₃₉	—	4	2	no	—
36	D₃₉	D₈	1	2	yes	direct product factor
37	C₂²×C₁₃	—	2	2	no	—
38	C₂×D₁₃	—	3	1	no	—
39	C₂×D₁₃	—	6	2	no	—
40	C₂×D₁₃	—	12	4	no	—
41	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
42	Dic₁₃	—	3	1	no	—
43	D₃×D₄	—	13	2	no	—
44	C₃×D₈	D₁₃	1	1	yes	characteristic, complemented
45	#213	—	13	2	no	—
46	D₂₄	—	13	1	no	—
47	D₃×C₈	—	13	1	no	—
48	C₃×C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Hall
49	C₂×D₈	—	39	1	no	Sylow
50	C₂×C₁₃	—	4	2	no	—
51	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
52	D₁₃	—	3	2	no	—
53	D₁₃	—	12	2	no	—
54	C₂²×D₃	—	26	2	no	—
55	C₃×D₄	C₂×D₁₃	1	2	yes	complemented
56	#67	—	26	2	no	—
57	D₁₂	—	13	2	no	—
58	C₄×D₃	—	13	1	no	—
59	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
60	C₃⋊C₈	—	13	1	no	—
61	C₂×D₄	—	39	2	no	—
62	D₈	—	39	2	no	—
63	D₈	—	39	1	no	—
64	D₈	D₃₉	1	1	yes	characteristic, direct product factor
65	C₂×C₈	—	39	1	no	—
66	C₁₃	D₃×D₈	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₃	—	2	2	no	—
68	C₂×D₃	—	13	1	no	—
69	C₂×D₃	—	26	2	no	—
70	C₂×D₃	—	52	4	no	—
71	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
72	Dic₃	—	13	1	no	—
73	C₂³	—	78	2	no	—
74	D₄	—	39	2	no	—
75	D₄	—	78	2	no	—
76	D₄	C₂×D₃₉	1	2	yes	complemented
77	C₂×C₄	—	39	1	no	—
78	C₈	—	39	1	no	—
79	C₈	C₂×D₃₉	1	1	yes	characteristic, complemented
80	C₂×C₃	—	4	2	no	—
81	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
82	D₃	—	13	2	no	—
83	D₃	—	52	2	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	39	1	no	—
86	C₂²	—	78	2	no	—
87	C₂²	—	156	4	no	—
88	C₄	—	39	1	no	—
89	C₄	C₂²×D₃₉	1	1	yes	characteristic
90	C₃	D₈×D₁₃	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	4	2	no	—
92	C₂	—	39	2	no	—
93	C₂	—	156	2	no	—
94	C₂	D₄×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₉
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₃₉
Fitting	C₃×C₁₃×D₈	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	D₈	D₃₉
hypocenter	C₃×C₁₃	C₂×D₈
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₃₉	C₂	semidirect
2. C₃×C₁₃×D₈	C₂	semidirect
3. #10597667	C₂	semidirect
4. D₃₁₂	C₂	semidirect
5. C₈×D₃₉	C₂	semidirect
8. C₃×D₄×C₁₃	C₂²	semidirect
10. D₁₅₆	C₂²	semidirect
12. C₃×C₈×C₁₃	C₂²	semidirect
13. C₃⋊#1055	C₂²	semidirect
15. C₁₃×D₈	D₃	semidirect
26. D₄×C₁₃	C₂×D₃	semidirect
30. C₈×C₁₃	C₂×D₃	semidirect
36. D₃₉	D₈	direct (N × H)
44. C₃×D₈	D₁₃	semidirect
48. C₃×C₁₃	C₂×D₈	semidirect
55. C₃×D₄	C₂×D₁₃	semidirect
59. C₃×C₈	C₂×D₁₃	semidirect
64. D₈	D₃₉	direct (N × H)
66. C₁₃	D₃×D₈	semidirect
76. D₄	C₂×D₃₉	semidirect
79. C₈	C₂×D₃₉	semidirect
90. C₃	D₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₃₉	2
C₃×C₁₃×D₈	2
#10597667	2
D₃₁₂	2
C₈×D₃₉	2
D₈×D₁₃	3
D₃×D₈	13

Subgroups — D8×D39 #11928972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₃₉ #11928972