Subgroups — D₄×C₂²⋊(C₁₃⋊C₃) #11929260

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	2	yes	maximal, complemented
2	C₄×C₂²⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₂²⋊(C₁₃⋊C₃)	—	2	2	no	—
5	C₂×C₂²⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic
6	D₄×C₁₃⋊C₃	—	4	1	no	maximal
7	C₂⁴×C₁₃	C₂×C₃	1	2	yes	complemented
8	C₂×D₄×C₁₃	—	3	1	no	—
9	C₂×D₄×C₁₃	—	3	1	no	—
10	C₂×D₄×C₁₃	—	3	2	no	—
11	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²⋊(C₁₃⋊C₃)	D₄	1	1	yes	characteristic, direct product factor
13	C₂²×C₁₃⋊C₃	—	4	2	no	—
14	C₄×C₁₃⋊C₃	—	4	1	no	—
15	C₂³×C₁₃	—	2	2	no	—
16	C₂³×C₁₃	—	3	2	no	—
17	C₂³×C₁₃	—	3	2	no	—
18	C₂³×C₁₃	—	6	2	no	—
19	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
20	D₄×C₁₃	—	3	2	no	—
21	D₄×C₁₃	—	3	2	no	—
22	D₄×C₁₃	—	3	1	no	—
23	D₄×C₁₃	A₄	1	1	yes	characteristic, complemented
24	C₂×C₄×C₁₃	—	3	1	no	—
25	C₂×C₄×C₁₃	—	3	1	no	—
26	D₄×A₄	—	13	1	no	maximal, Hall
27	C₂×C₁₃⋊C₃	—	4	1	no	—
28	C₂×C₁₃⋊C₃	—	8	2	no	—
29	C₂²×C₁₃	—	3	1	no	—
30	C₂²×C₁₃	—	3	1	no	—
31	C₂²×C₁₃	—	3	2	no	—
32	C₂²×C₁₃	—	6	2	no	—
33	C₂²×C₁₃	—	6	2	no	—
34	C₂²×C₁₃	—	6	2	no	—
35	C₂²×C₁₃	—	6	2	no	—
36	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic, complemented
37	C₂²×C₁₃	C₂×A₄	1	2	yes	complemented
38	C₄×C₁₃	—	3	1	no	—
39	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic, complemented
40	C₂²×A₄	—	13	2	no	—
41	C₄×A₄	—	13	1	no	—
42	C₁₃⋊C₃	—	4	1	no	Hall
43	C₂²×D₄	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₁₃	—	2	2	no	—
45	C₂×C₁₃	—	3	1	no	—
46	C₂×C₁₃	—	3	1	no	—
47	C₂×C₁₃	—	6	2	no	—
48	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
49	C₂×A₄	—	13	1	no	—
50	C₂×A₄	—	26	2	no	—
51	C₃×D₄	—	52	1	no	—
52	C₂⁴	C₂×C₁₃⋊C₃	1	2	yes	complemented
53	C₂×D₄	—	3	1	no	—
54	C₂×D₄	—	3	1	no	—
55	C₂×D₄	—	3	2	no	—
56	C₂²×C₄	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
57	C₁₃	D₄×A₄	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	52	2	no	—
59	A₄	—	13	1	no	—
60	C₃×C₄	—	52	1	no	—
61	C₂³	—	2	2	no	—
62	C₂³	—	3	2	no	—
63	C₂³	—	3	2	no	—
64	C₂³	—	6	2	no	—
65	C₂³	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
66	D₄	—	3	2	no	—
67	D₄	—	3	2	no	—
68	D₄	—	3	1	no	—
69	D₄	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₃	—	52	1	no	—
73	C₂×C₃	—	104	2	no	—
74	C₂²	—	3	1	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	3	2	no	—
77	C₂²	—	6	2	no	—
78	C₂²	—	6	2	no	—
79	C₂²	—	6	2	no	—
80	C₂²	—	6	2	no	—
81	C₂²	D₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
82	C₂²	C₂×C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
83	C₄	—	3	1	no	—
84	C₄	C₂×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented
85	C₃	—	52	1	no	Sylow
86	C₂	—	2	2	no	—
87	C₂	—	3	1	no	—
88	C₂	—	3	1	no	—
89	C₂	—	6	2	no	—
90	C₂	C₂²×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×C₂²⋊(C₁₃⋊C₃)
commutator, socle, cosocle	C₂³×C₁₃	C₂²×C₃
Fitting	C₂²×D₄×C₁₃	C₃
hypercenter	D₄	C₂²⋊(C₁₃⋊C₃)
hypocenter	C₂²×C₁₃	C₃×D₄
LCS	G ▷ C₂³×C₁₃ ▷ C₂²×C₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊(C₁₃⋊C₃)	C₂	semidirect
2. C₄×C₂²⋊(C₁₃⋊C₃)	C₂	semidirect
3. C₂²×D₄×C₁₃	C₃	semidirect
7. C₂⁴×C₁₃	C₂×C₃	semidirect
11. C₂²×C₄×C₁₃	C₂×C₃	semidirect
12. C₂²⋊(C₁₃⋊C₃)	D₄	direct (N × H)
23. D₄×C₁₃	A₄	semidirect
36. C₂²×C₁₃	C₃×D₄	semidirect
37. C₂²×C₁₃	C₂×A₄	semidirect
39. C₄×C₁₃	C₂×A₄	semidirect
43. C₂²×D₄	C₁₃⋊C₃	semidirect
52. C₂⁴	C₂×C₁₃⋊C₃	semidirect
56. C₂²×C₄	C₂×C₁₃⋊C₃	semidirect
57. C₁₃	D₄×A₄	semidirect
69. D₄	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
81. C₂²	D₄×C₁₃⋊C₃	semidirect
82. C₂²	C₂×C₂²⋊(C₁₃⋊C₃)	semidirect
84. C₄	C₂×C₂²⋊(C₁₃⋊C₃)	semidirect

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
C₄×C₂²⋊(C₁₃⋊C₃)	2
C₂²×D₄×C₁₃	3
D₄×C₁₃⋊C₃	4
D₄×A₄	13

Subgroups — D4×C22⋊(C13⋊C3) #11929260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₂²⋊(C₁₃⋊C₃) #11929260