Subgroups — C₂×C₁₃×C₄⋊Dic₃ #11928901

Order 1248.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×C₁₃	C₂	1	2	yes	maximal
3	C₁₃×C₄⋊Dic₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₄⋊C₄	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₄	1	4	yes	complemented
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×Dic₃×C₁₃	—	2	4	no	—
9	C₂×Dic₃×C₁₃	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₃	—	3	2	no	—
11	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	—	3	4	no	—
13	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₃×C₁₃	D₄	1	2	yes	—
15	C₂²×C₃×C₁₃	Q₈	1	2	yes	—
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₁₃	C₂×C₄	1	4	yes	complemented
18	Dic₃×C₁₃	—	2	4	no	—
19	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	3	4	no	—
21	C₂×C₄×C₁₃	—	6	4	no	—
22	C₂×C₄×C₁₃	Dic₃	1	4	yes	complemented
23	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
24	C₂×C₄⋊Dic₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₁₃	C₄⋊C₄	1	4	yes	complemented
26	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₁₃	Dic₆	1	2	yes	—
30	C₂²×C₁₃	D₁₂	1	2	yes	—
31	C₂²×C₁₃	C₂×Dic₃	1	2	yes	—
32	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₃	—	6	4	no	—
34	C₄×C₁₃	C₂×Dic₃	1	4	yes	complemented
35	C₂²×C₃×C₄	C₂×C₁₃	1	1	yes	characteristic
36	C₂²×Dic₃	C₂×C₁₃	1	2	yes	—
37	C₄⋊Dic₃	C₂×C₁₃	1	4	yes	direct product factor
38	C₃×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
39	C₂×C₄⋊C₄	—	3	1	no	Sylow
40	C₂×C₁₃	C₄⋊Dic₃	1	4	yes	direct product factor
41	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
42	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
43	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
44	C₂³×C₃	C₂²×C₁₃	1	1	yes	characteristic
45	C₂×C₃×C₄	C₄×C₁₃	1	4	yes	complemented
46	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
47	C₂×Dic₃	—	2	4	no	—
48	C₂×Dic₃	C₂²×C₁₃	1	4	yes	—
49	C₂²×C₄	—	3	2	no	—
50	C₂²×C₄	D₃×C₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	3	4	no	—
52	C₁₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²×C₃	C₂×C₄×C₁₃	1	2	yes	—
54	C₂²×C₃	D₄×C₁₃	1	2	yes	—
55	C₂²×C₃	Q₈×C₁₃	1	2	yes	—
56	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
57	C₃×C₄	C₂×C₄×C₁₃	1	4	yes	complemented
58	Dic₃	—	2	4	no	—
59	C₂³	C₂×D₃×C₁₃	1	1	yes	characteristic
60	C₂×C₄	—	3	4	no	—
61	C₂×C₄	—	6	4	no	—
62	C₂×C₄	Dic₃×C₁₃	1	4	yes	complemented
63	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
64	C₂×C₃	C₁₃×C₄⋊C₄	1	4	yes	complemented
65	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
66	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
67	C₂×C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic
68	C₂²	C₁₃×Dic₆	1	2	yes	—
69	C₂²	C₁₃×D₁₂	1	2	yes	—
70	C₂²	C₂×Dic₃×C₁₃	1	2	yes	—
71	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
72	C₄	—	6	4	no	—
73	C₄	C₂×Dic₃×C₁₃	1	4	yes	complemented
74	C₃	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
75	C₂	C₁₃×C₄⋊Dic₃	1	4	yes	direct product factor
76	C₂	C₂×C₁₃×Dic₆	1	1	yes	characteristic
77	C₂	C₂×C₁₃×D₁₂	1	1	yes	characteristic
78	C₂	C₂²×Dic₃×C₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×C₄⋊Dic₃	C₂	direct (N × H)
6. C₂×C₃×C₄×C₁₃	C₄	semidirect
17. C₃×C₄×C₁₃	C₂×C₄	semidirect
22. C₂×C₄×C₁₃	Dic₃	semidirect
24. C₂×C₄⋊Dic₃	C₁₃	direct (N × H)
25. C₂×C₃×C₁₃	C₄⋊C₄	semidirect
34. C₄×C₁₃	C₂×Dic₃	semidirect
37. C₄⋊Dic₃	C₂×C₁₃	direct (N × H)
38. C₃×C₁₃	C₂×C₄⋊C₄	semidirect
40. C₂×C₁₃	C₄⋊Dic₃	direct (N × H)
45. C₂×C₃×C₄	C₄×C₁₃	semidirect
52. C₁₃	C₂×C₄⋊Dic₃	direct (N × H)
57. C₃×C₄	C₂×C₄×C₁₃	semidirect
62. C₂×C₄	Dic₃×C₁₃	semidirect
64. C₂×C₃	C₁₃×C₄⋊C₄	semidirect
73. C₄	C₂×Dic₃×C₁₃	semidirect
74. C₃	C₂×C₁₃×C₄⋊C₄	semidirect
75. C₂	C₁₃×C₄⋊Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
C₂²×Dic₃×C₁₃	2
C₁₃×C₄⋊Dic₃	2
C₂×C₁₃×C₄⋊C₄	3
C₂×C₄⋊Dic₃	13

Subgroups — C2×C13×C4⋊Dic3 #11928901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₄⋊Dic₃ #11928901