Subgroups — D₃²×D₁₃ #11745596

Order 936.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃⋊D₃)⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×D₃₉	C₂	1	2	yes	maximal, complemented
3	D₃²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃⋊D₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₃×D₁₃	C₂	1	2	yes	maximal, complemented
6	C₂×D₃×D₁₃	—	3	2	no	maximal
7	C₃⋊D₃₉	C₂²	1	1	yes	characteristic, complemented
8	C₁₃×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
9	C₃×D₃₉	C₂²	1	2	yes	complemented
10	C₃×D₃×C₁₃	C₂²	1	2	yes	complemented
11	C₃²×D₁₃	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₃₉	—	3	2	no	—
13	C₂×D₃×C₁₃	—	3	2	no	—
14	C₂×C₃×D₁₃	—	3	2	no	—
15	D₃×D₁₃	—	3	2	no	—
16	D₃×D₁₃	—	3	2	no	—
17	D₃×D₁₃	—	3	2	no	—
18	D₃×D₁₃	—	6	1	no	—
19	D₃×D₁₃	D₃	1	2	yes	direct product factor
20	C₃²×C₁₃	C₂³	1	1	yes	characteristic, complemented, Hall
21	C₂²×D₁₃	—	9	1	no	Hall
22	C₂×C₃×C₁₃	—	3	2	no	—
23	D₃₉	—	3	2	no	—
24	D₃₉	—	6	1	no	—
25	D₃₉	C₂×D₃	1	2	yes	complemented
26	C₃×D₁₃	—	2	1	no	—
27	C₃×D₁₃	—	3	2	no	—
28	C₃×D₁₃	C₂×D₃	1	2	yes	complemented
29	D₃×C₁₃	—	3	2	no	—
30	D₃×C₁₃	—	6	1	no	—
31	D₃×C₁₃	C₂×D₃	1	2	yes	complemented
32	C₂×D₃²	—	13	1	no	maximal, Hall
33	C₂²×C₁₃	—	9	1	no	—
34	C₂×D₁₃	—	3	2	no	—
35	C₂×D₁₃	—	9	1	no	—
36	C₂×D₁₃	—	9	2	no	—
37	C₂×D₁₃	—	9	1	no	—
38	C₃×C₁₃	—	2	1	no	—
39	C₃×C₁₃	C₂²×D₃	1	2	yes	complemented
40	C₂×C₃⋊D₃	—	13	1	no	—
41	C₂×C₃×D₃	—	13	2	no	—
42	D₃²	—	13	1	no	—
43	D₃²	—	13	2	no	—
44	D₃²	D₁₃	1	1	yes	characteristic, direct product factor
45	C₂×C₁₃	—	3	2	no	—
46	C₂×C₁₃	—	9	1	no	—
47	D₁₃	—	3	2	no	—
48	D₁₃	—	9	1	no	—
49	D₁₃	D₃²	1	1	yes	characteristic, direct product factor
50	C₂²×D₃	—	39	2	no	—
51	C₂×C₃²	—	13	1	no	—
52	C₃⋊D₃	—	13	1	no	—
53	C₃⋊D₃	C₂×D₁₃	1	1	yes	characteristic, complemented
54	C₃×D₃	—	13	2	no	—
55	C₃×D₃	C₂×D₁₃	1	2	yes	complemented
56	C₁₃	C₂×D₃²	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	39	2	no	—
58	C₂×D₃	—	3	2	no	—
59	C₂×D₃	—	13	2	no	—
60	C₂×D₃	—	39	2	no	—
61	C₂×D₃	—	39	2	no	—
62	C₂×D₃	—	39	2	no	—
63	C₂×D₃	—	39	2	no	—
64	C₂×D₃	—	78	1	no	—
65	C₃²	C₂²×D₁₃	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	117	1	no	Sylow
67	C₂×C₃	—	3	2	no	—
68	C₂×C₃	—	13	2	no	—
69	C₂×C₃	—	26	1	no	—
70	C₂×C₃	—	39	2	no	—
71	D₃	—	3	2	no	—
72	D₃	—	6	1	no	—
73	D₃	—	13	2	no	—
74	D₃	—	39	2	no	—
75	D₃	—	78	1	no	—
76	D₃	D₃×D₁₃	1	2	yes	direct product factor
77	C₂²	—	9	1	no	—
78	C₂²	—	39	2	no	—
79	C₂²	—	117	2	no	—
80	C₂²	—	117	1	no	—
81	C₂²	—	117	1	no	—
82	C₃	—	2	1	no	—
83	C₃	C₂×D₃×D₁₃	1	2	yes	complemented
84	C₂	—	3	2	no	—
85	C₂	—	9	1	no	—
86	C₂	—	13	1	no	—
87	C₂	—	39	2	no	—
88	C₂	—	117	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃	C₂³
LCS	G ▷ C₃²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. (C₃⋊D₃)⋊D₁₃	C₂	semidirect
2. D₃×D₃₉	C₂	semidirect
3. D₃²×C₁₃	C₂	semidirect
4. C₃⋊D₃×D₁₃	C₂	semidirect
5. C₃×D₃×D₁₃	C₂	semidirect
7. C₃⋊D₃₉	C₂²	semidirect
8. C₁₃×C₃⋊D₃	C₂²	semidirect
9. C₃×D₃₉	C₂²	semidirect
10. C₃×D₃×C₁₃	C₂²	semidirect
11. C₃²×D₁₃	C₂²	semidirect
19. D₃×D₁₃	D₃	direct (N × H)
20. C₃²×C₁₃	C₂³	semidirect
25. D₃₉	C₂×D₃	semidirect
28. C₃×D₁₃	C₂×D₃	semidirect
31. D₃×C₁₃	C₂×D₃	semidirect
39. C₃×C₁₃	C₂²×D₃	semidirect
44. D₃²	D₁₃	direct (N × H)
49. D₁₃	D₃²	direct (N × H)
53. C₃⋊D₃	C₂×D₁₃	semidirect
55. C₃×D₃	C₂×D₁₃	semidirect
56. C₁₃	C₂×D₃²	semidirect
65. C₃²	C₂²×D₁₃	semidirect
76. D₃	D₃×D₁₃	direct (N × H)
83. C₃	C₂×D₃×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
(C₃⋊D₃)⋊D₁₃	2
D₃×D₃₉	2
D₃²×C₁₃	2
C₃⋊D₃×D₁₃	2
C₃×D₃×D₁₃	2
C₂×D₃×D₁₃	3
C₂×D₃²	13

Subgroups — D32×D13 #11745596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃²×D₁₃ #11745596