Subgroups — A₄×Dic₂₆ #11929145

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×A₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	A₄×Dic₁₃	C₂	1	2	yes	maximal
3	C₂²×Dic₂₆	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×A₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₃×Dic₂₆	—	4	1	no	maximal
6	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂²×Dic₁₃	C₂×C₃	1	2	yes	—
8	C₂×Dic₂₆	—	3	1	no	—
9	C₂×Dic₂₆	—	3	1	no	—
10	C₂×Dic₂₆	—	3	2	no	—
11	A₄×C₁₃	Q₈	1	1	yes	characteristic, complemented
12	C₃×C₄×C₁₃	—	4	1	no	—
13	C₃×Dic₁₃	—	4	2	no	—
14	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₄×C₁₃	—	3	1	no	—
16	C₂×C₄×C₁₃	—	3	1	no	—
17	C₂×Dic₁₃	—	3	2	no	—
18	C₂×Dic₁₃	—	3	2	no	—
19	Dic₂₆	—	3	2	no	—
20	Dic₂₆	—	3	1	no	—
21	Dic₂₆	—	3	2	no	—
22	Dic₂₆	A₄	1	1	yes	characteristic, direct product factor
23	Q₈×A₄	—	13	1	no	maximal, Hall
24	C₂×C₃×C₁₃	—	4	1	no	—
25	C₂²×C₁₃	—	3	1	no	—
26	C₂²×C₁₃	—	3	1	no	—
27	C₂²×C₁₃	C₃×Q₈	1	1	yes	characteristic, complemented
28	C₄×C₁₃	—	3	1	no	—
29	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic
30	Dic₁₃	—	3	2	no	—
31	Dic₁₃	C₂×A₄	1	2	yes	—
32	C₄×A₄	—	13	2	no	—
33	C₄×A₄	D₁₃	1	1	yes	characteristic
34	C₃×C₁₃	—	4	1	no	Hall
35	C₂²×Q₈	—	13	1	no	Sylow
36	C₂×C₁₃	—	3	1	no	—
37	C₂×C₁₃	—	3	1	no	—
38	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
39	C₂×A₄	C₂×D₁₃	1	1	yes	characteristic
40	C₃×Q₈	—	52	1	no	—
41	C₂×Q₈	—	39	1	no	—
42	C₂×Q₈	—	39	1	no	—
43	C₂×Q₈	—	39	2	no	—
44	C₂²×C₄	—	13	2	no	—
45	C₂²×C₄	C₃×D₁₃	1	1	yes	characteristic
46	C₁₃	Q₈×A₄	1	1	yes	characteristic, complemented, Sylow
47	A₄	Dic₂₆	1	1	yes	characteristic, direct product factor
48	C₃×C₄	—	4	1	no	—
49	C₃×C₄	—	52	2	no	—
50	C₂³	C₂×C₃×D₁₃	1	1	yes	characteristic
51	Q₈	—	13	1	no	—
52	Q₈	—	39	2	no	—
53	Q₈	—	39	2	no	—
54	Q₈	—	39	1	no	—
55	C₂×C₄	—	3	1	no	—
56	C₂×C₄	—	3	1	no	—
57	C₂×C₄	—	39	2	no	—
58	C₂×C₄	—	39	2	no	—
59	C₂×C₃	—	4	1	no	—
60	C₂²	—	3	1	no	—
61	C₂²	—	3	1	no	—
62	C₂²	C₃×Dic₂₆	1	1	yes	characteristic, complemented
63	C₄	—	3	1	no	—
64	C₄	—	13	2	no	—
65	C₄	—	39	2	no	—
66	C₄	A₄×D₁₃	1	1	yes	characteristic
67	C₃	—	4	1	no	Sylow
68	C₂	—	3	1	no	—
69	C₂	—	3	1	no	—
70	C₂	C₂×A₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×A₄×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂²×C₃
Fitting	C₂²×C₄×C₁₃	C₂×C₃
prime radical	C₂×A₄×C₁₃	C₂²
hypercenter	C₄	A₄×D₁₃
hypocenter	C₂²×C₁₃	C₃×Q₈
LCS	G ▷ C₂³×C₁₃ ▷ C₂²×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. C₂²×Dic₂₆	C₃	semidirect
11. A₄×C₁₃	Q₈	semidirect
22. Dic₂₆	A₄	direct (N × H)
27. C₂²×C₁₃	C₃×Q₈	semidirect
46. C₁₃	Q₈×A₄	semidirect
47. A₄	Dic₂₆	direct (N × H)
62. C₂²	C₃×Dic₂₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×A₄×C₁₃	2
A₄×Dic₁₃	2
C₂²×Dic₂₆	3
C₃×Dic₂₆	4
Q₈×A₄	13

Subgroups — A4×Dic26 #11929145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×Dic₂₆ #11929145