Subgroups — C₂×Dic₁₃⋊A₄ #11929165

Order 1248.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²	D₁₃⋊A₄
commutator, hypocenter	C₂²×C₁₃	C₂×C₃×C₄
Frattini	C₂	C₂×D₁₃⋊A₄
Fitting, socle	C₂⁴×C₁₃	C₂×C₃
prime radical	C₂²×C₂²⋊(C₁₃⋊C₃)	C₂
cosocle	C₂³×C₁₃	C₂²×C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. Dic₁₃⋊A₄	C₂	direct (N × H)
3. C₂³×Dic₁₃	C₃	semidirect
4. C₂×C₂²⋊(C₁₃⋊C₃)	C₄	semidirect
11. C₂²×Dic₁₃	C₂×C₃	semidirect
12. C₂²⋊(C₁₃⋊C₃)	C₂×C₄	semidirect
18. C₂³×C₁₃	C₃×C₄	semidirect
25. C₂×Dic₁₃	A₄	semidirect
36. C₂²×C₁₃	C₂×C₃×C₄	semidirect
39. Dic₁₃	C₂×A₄	semidirect
47. C₂×C₁₃	C₄×A₄	semidirect
57. C₁₃	C₂×C₄×A₄	semidirect
64. C₂³	Dic₁₃⋊C₃	semidirect
81. C₂²	C₂×Dic₁₃⋊C₃	semidirect
89. C₂	Dic₁₃⋊A₄	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×C₂²⋊(C₁₃⋊C₃)	2
Dic₁₃⋊A₄	2
C₂³×Dic₁₃	3
C₂×Dic₁₃⋊C₃	4
C₂×C₄×A₄	13

Subgroups — C2×Dic13⋊A4 #11929165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₁₃⋊A₄ #11929165