Subgroups — C₂²×A₄⋊D₁₃ #11929329

Order 1248.

262 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, complemented
2	C₂×A₄⋊D₁₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₂²⋊D₁₃	—	3	1	no	maximal, Hall
4	C₂²×D₃₉	—	4	1	no	maximal
5	C₂×A₄×C₁₃	C₂²	1	3	yes	complemented
6	A₄⋊D₁₃	C₂²	1	4	yes	direct product factor
7	C₂⁴×C₁₃	D₃	1	1	yes	characteristic, complemented
8	C₂³×D₁₃	—	3	1	no	—
9	C₂×C₂²⋊D₁₃	—	3	6	no	—
10	C₂×C₂²⋊D₁₃	—	3	6	no	—
11	C₂²×Dic₁₃	—	3	1	no	—
12	C₂²×C₃×C₁₃	—	4	1	no	—
13	C₂×D₃₉	—	4	6	no	—
14	A₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
15	C₂³×C₁₃	—	3	1	no	—
16	C₂³×C₁₃	—	3	3	no	—
17	C₂³×C₁₃	C₂×D₃	1	3	yes	complemented
18	C₂²×D₁₃	—	3	6	no	—
19	C₂²×D₁₃	—	6	3	no	—
20	C₂²×D₁₃	—	6	1	no	—
21	C₂²⋊D₁₃	—	3	12	no	—
22	C₂²⋊D₁₃	—	3	4	no	—
23	C₂×Dic₁₃	—	3	6	no	—
24	C₂²×S₄	—	13	1	no	maximal, Hall
25	C₂×C₃×C₁₃	—	4	3	no	—
26	D₃₉	—	4	4	no	—
27	C₂²×C₁₃	—	3	3	no	—
28	C₂²×C₁₃	—	3	3	no	—
29	C₂²×C₁₃	—	3	3	no	—
30	C₂²×C₁₃	—	6	1	no	—
31	C₂²×C₁₃	S₄	1	1	yes	characteristic, complemented
32	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic, complemented
33	C₂×D₁₃	—	3	4	no	—
34	C₂×D₁₃	—	6	6	no	—
35	C₂×D₁₃	—	6	6	no	—
36	Dic₁₃	—	3	4	no	—
37	C₂²×A₄	D₁₃	1	1	yes	characteristic, complemented
38	C₂×S₄	—	13	6	no	—
39	C₃×C₁₃	—	4	1	no	Hall
40	C₂²×D₄	—	39	1	no	Sylow
41	C₂×C₁₃	—	3	1	no	—
42	C₂×C₁₃	—	3	3	no	—
43	C₂×C₁₃	C₂×S₄	1	3	yes	complemented
44	D₁₃	—	6	4	no	—
45	C₂²×D₃	—	52	1	no	—
46	C₂×A₄	C₂×D₁₃	1	3	yes	complemented
47	S₄	—	13	4	no	—
48	C₂⁴	—	39	1	no	—
49	C₂⁴	D₃₉	1	1	yes	characteristic, complemented
50	C₂×D₄	—	39	6	no	—
51	C₂×D₄	—	39	6	no	—
52	C₂²×C₄	—	39	1	no	—
53	C₁₃	C₂²×S₄	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₃	—	4	1	no	—
55	C₂×D₃	—	52	6	no	—
56	A₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
57	C₂³	—	3	1	no	—
58	C₂³	—	3	3	no	—
59	C₂³	—	39	6	no	—
60	C₂³	—	78	3	no	—
61	C₂³	—	78	1	no	—
62	C₂³	C₂×D₃₉	1	3	yes	complemented
63	D₄	—	39	12	no	—
64	D₄	—	39	4	no	—
65	C₂×C₄	—	39	6	no	—
66	C₂×C₃	—	4	3	no	—
67	D₃	—	52	4	no	—
68	C₂²	—	3	3	no	—
69	C₂²	—	3	3	no	—
70	C₂²	—	3	3	no	—
71	C₂²	—	6	1	no	—
72	C₂²	—	39	4	no	—
73	C₂²	—	78	6	no	—
74	C₂²	—	78	6	no	—
75	C₂²	A₄⋊D₁₃	1	1	yes	characteristic, direct product factor
76	C₂²	C₂²×D₃₉	1	1	yes	characteristic, complemented
77	C₄	—	39	4	no	—
78	C₃	—	4	1	no	Sylow
79	C₂	—	3	1	no	—
80	C₂	—	3	3	no	—
81	C₂	—	78	4	no	—
82	C₂	C₂×A₄⋊D₁₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	A₄⋊D₁₃
commutator, cosocle, hypocenter	A₄×C₁₃	C₂³
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₃	D₃
LCS	G ▷ A₄×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×A₄×C₁₃	C₂	semidirect
2. C₂×A₄⋊D₁₃	C₂	direct (N × H)
5. C₂×A₄×C₁₃	C₂²	semidirect
6. A₄⋊D₁₃	C₂²	direct (N × H)
7. C₂⁴×C₁₃	D₃	semidirect
14. A₄×C₁₃	C₂³	semidirect
17. C₂³×C₁₃	C₂×D₃	semidirect
31. C₂²×C₁₃	S₄	semidirect
32. C₂²×C₁₃	C₂²×D₃	semidirect
37. C₂²×A₄	D₁₃	semidirect
43. C₂×C₁₃	C₂×S₄	semidirect
46. C₂×A₄	C₂×D₁₃	semidirect
49. C₂⁴	D₃₉	semidirect
53. C₁₃	C₂²×S₄	semidirect
56. A₄	C₂²×D₁₃	semidirect
62. C₂³	C₂×D₃₉	semidirect
75. C₂²	A₄⋊D₁₃	direct (N × H)
76. C₂²	C₂²×D₃₉	semidirect
82. C₂	C₂×A₄⋊D₁₃	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
C₂×A₄⋊D₁₃	2
C₂²×C₂²⋊D₁₃	3
C₂²×D₃₉	4
C₂²×S₄	13

Subgroups — C22×A4⋊D13 #11929329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×A₄⋊D₁₃ #11929329