Subgroups — C₂×A₄⋊Dic₁₃ #11929128

Order 1248.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×A₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	A₄⋊Dic₁₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂²⋊Dic₁₃	—	3	1	no	maximal, Hall
4	C₂×A₄×C₁₃	C₄	1	2	yes	complemented
5	C₂×A₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₃₉	—	4	1	no	maximal
7	C₂⁴×C₁₃	D₃	1	1	yes	characteristic
8	C₂²×Dic₁₃	—	3	1	no	—
9	C₂²×Dic₁₃	—	3	1	no	—
10	C₂²⋊Dic₁₃	—	3	2	no	—
11	C₂²⋊Dic₁₃	—	3	2	no	—
12	C₂²×C₃×C₁₃	—	4	1	no	—
13	A₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
14	Dic₃₉	—	4	2	no	—
15	C₂³×C₁₃	—	3	1	no	—
16	C₂³×C₁₃	—	3	1	no	—
17	C₂³×C₁₃	—	3	2	no	—
18	C₂³×C₁₃	Dic₃	1	2	yes	complemented
19	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
20	C₂×Dic₁₃	—	3	2	no	—
21	C₂×Dic₁₃	—	3	2	no	—
22	C₂×Dic₁₃	—	6	2	no	—
23	C₂×Dic₁₃	—	6	1	no	—
24	C₂×Dic₁₃	—	6	1	no	—
25	C₂×SL(2,ℤ/4)	—	13	1	no	maximal, Hall
26	C₂×C₃×C₁₃	—	4	2	no	—
27	C₂×C₃×C₁₃	—	4	1	no	—
28	C₂²×C₁₃	—	3	2	no	—
29	C₂²×C₁₃	—	3	1	no	—
30	C₂²×C₁₃	—	3	2	no	—
31	C₂²×C₁₃	—	3	2	no	—
32	C₂²×C₁₃	—	3	1	no	—
33	C₂²×C₁₃	—	3	1	no	—
34	C₂²×C₁₃	—	6	1	no	—
35	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic, complemented
36	C₂²×C₁₃	S₄	1	1	yes	characteristic
37	Dic₁₃	—	6	2	no	—
38	Dic₁₃	—	6	2	no	—
39	C₂²×A₄	D₁₃	1	1	yes	characteristic
40	SL(2,ℤ/4)	—	13	2	no	—
41	C₃×C₁₃	—	4	1	no	Hall
42	C₂×C₂²⋊C₄	—	39	1	no	Sylow
43	C₂×C₁₃	—	3	1	no	—
44	C₂×C₁₃	—	3	1	no	—
45	C₂×C₁₃	—	3	2	no	—
46	C₂×C₁₃	SL(2,ℤ/4)	1	2	yes	complemented
47	C₂×C₁₃	C₂×S₄	1	1	yes	characteristic
48	C₂×A₄	Dic₁₃	1	2	yes	complemented
49	C₂×A₄	C₂×D₁₃	1	1	yes	characteristic
50	C₂×Dic₃	—	52	1	no	—
51	C₂⁴	D₃₉	1	1	yes	characteristic
52	C₂²×C₄	—	39	1	no	—
53	C₂²×C₄	—	39	1	no	—
54	C₂²⋊C₄	—	39	2	no	—
55	C₂²⋊C₄	—	39	2	no	—
56	C₁₃	C₂×SL(2,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	4	1	no	—
58	A₄	C₂×Dic₁₃	1	1	yes	characteristic, complemented
59	Dic₃	—	52	2	no	—
60	C₂³	—	3	1	no	—
61	C₂³	—	3	1	no	—
62	C₂³	—	3	2	no	—
63	C₂³	Dic₃₉	1	2	yes	complemented
64	C₂³	C₂×D₃₉	1	1	yes	characteristic
65	C₂×C₄	—	39	2	no	—
66	C₂×C₄	—	39	2	no	—
67	C₂×C₄	—	78	2	no	—
68	C₂×C₄	—	78	1	no	—
69	C₂×C₄	—	78	1	no	—
70	C₂×C₃	—	4	2	no	—
71	C₂×C₃	—	4	1	no	—
72	C₂²	—	3	2	no	—
73	C₂²	—	3	1	no	—
74	C₂²	—	3	2	no	—
75	C₂²	—	3	2	no	—
76	C₂²	—	3	1	no	—
77	C₂²	—	3	1	no	—
78	C₂²	—	6	1	no	—
79	C₂²	C₂×Dic₃₉	1	1	yes	characteristic, complemented
80	C₂²	A₄⋊D₁₃	1	1	yes	characteristic
81	C₄	—	78	2	no	—
82	C₄	—	78	2	no	—
83	C₃	—	4	1	no	Sylow
84	C₂	—	3	1	no	—
85	C₂	—	3	1	no	—
86	C₂	—	3	2	no	—
87	C₂	A₄⋊Dic₁₃	1	2	yes	direct product factor
88	C₂	C₂×A₄⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	A₄⋊D₁₃
commutator, hypocenter	A₄×C₁₃	C₂×C₄
Frattini	C₂	C₂×A₄⋊D₁₃
Fitting, socle	C₂⁴×C₁₃	D₃
prime radical	C₂²×A₄×C₁₃	C₂
cosocle	C₂×A₄×C₁₃	C₂²
LCS	G ▷ A₄×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. A₄⋊Dic₁₃	C₂	direct (N × H)
4. C₂×A₄×C₁₃	C₄	semidirect
13. A₄×C₁₃	C₂×C₄	semidirect
18. C₂³×C₁₃	Dic₃	semidirect
35. C₂²×C₁₃	C₂×Dic₃	semidirect
46. C₂×C₁₃	SL(2,ℤ/4)	semidirect
48. C₂×A₄	Dic₁₃	semidirect
56. C₁₃	C₂×SL(2,ℤ/4)	semidirect
58. A₄	C₂×Dic₁₃	semidirect
63. C₂³	Dic₃₉	semidirect
79. C₂²	C₂×Dic₃₉	semidirect
87. C₂	A₄⋊Dic₁₃	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×A₄×C₁₃	2
A₄⋊Dic₁₃	2
C₂×C₂²⋊Dic₁₃	3
C₂×Dic₃₉	4
C₂×SL(2,ℤ/4)	13

Subgroups — C2×A4⋊Dic13 #11929128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×A₄⋊Dic₁₃ #11929128