Subgroups — 2₋¹⁺⁴⋊(C₁₃⋊C₃) #11929265

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₈⋊(C₁₃⋊C₃)	C₂	1	2	yes	maximal, complemented
3	C₁₃×2₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	Q₈⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic
5	D₄×C₁₃⋊C₃	—	4	1	no	maximal
6	C₁₃×#41	—	3	1	no	—
7	C₁₃×#41	—	3	2	no	—
8	C₁₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×Q₈×C₁₃	—	3	1	no	—
10	C₂×Q₈×C₁₃	C₂×C₃	1	2	yes	complemented
11	C₂²×C₁₃⋊C₃	—	4	2	no	—
12	C₄×C₁₃⋊C₃	—	4	1	no	—
13	Q₈×C₁₃	—	3	1	no	—
14	Q₈×C₁₃	—	3	2	no	—
15	Q₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
16	D₄×C₁₃	—	3	2	no	—
17	D₄×C₁₃	—	3	1	no	—
18	D₄×C₁₃	A₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	3	2	no	—
20	C₂×C₄×C₁₃	—	3	2	no	—
21	C₂×C₄×C₁₃	—	3	1	no	—
22	2₋¹⁺⁴⋊C₃	—	13	1	no	maximal, Hall
23	C₂×C₁₃⋊C₃	—	4	1	no	—
24	C₂×C₁₃⋊C₃	—	8	2	no	—
25	C₂²×C₁₃	—	3	1	no	—
26	C₂²×C₁₃	C₂×A₄	1	2	yes	—
27	C₄×C₁₃	—	3	2	no	—
28	C₄×C₁₃	—	3	1	no	—
29	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic
30	#41⋊C₃	—	13	1	no	—
31	C₂×SL(2,𝔽₃)	—	13	2	no	—
32	C₁₃⋊C₃	—	4	1	no	Hall
33	2₋¹⁺⁴	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₃	—	2	2	no	—
35	C₂×C₁₃	—	6	1	no	—
36	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
37	C₃×D₄	—	52	1	no	—
38	SL(2,𝔽₃)	—	13	1	no	—
39	#41	—	3	1	no	—
40	#41	—	3	2	no	—
41	#41	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	3	1	no	—
43	C₂×Q₈	C₂×C₁₃⋊C₃	1	2	yes	complemented
44	C₁₃	2₋¹⁺⁴⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₃	—	52	2	no	—
46	C₃×C₄	—	52	1	no	—
47	Q₈	—	3	2	no	—
48	Q₈	—	3	1	no	—
49	Q₈	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
50	D₄	—	3	1	no	—
51	D₄	—	3	2	no	—
52	D₄	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
53	C₂×C₄	—	3	2	no	—
54	C₂×C₄	—	3	2	no	—
55	C₂×C₄	—	3	1	no	—
56	C₂×C₃	—	52	1	no	—
57	C₂×C₃	—	104	2	no	—
58	C₂²	—	3	1	no	—
59	C₂²	C₂×C₂²⋊(C₁₃⋊C₃)	1	2	yes	—
60	C₄	—	3	2	no	—
61	C₄	—	3	1	no	—
62	C₄	C₂×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
63	C₃	—	52	1	no	Sylow
64	C₂	—	2	2	no	—
65	C₂	—	6	1	no	—
66	C₂	C₂²×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	Q₈×C₁₃	C₂²×C₃
Fitting	C₁₃×2₋¹⁺⁴	C₃
socle	C₂×C₁₃	C₂²×A₄
hypercenter	D₄	C₂²⋊(C₁₃⋊C₃)
LCS	G ▷ Q₈×C₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #41⋊(C₁₃⋊C₃)	C₂	semidirect
2. C₂×Q₈⋊(C₁₃⋊C₃)	C₂	semidirect
3. C₁₃×2₋¹⁺⁴	C₃	semidirect
8. C₁₃×#41	C₂×C₃	semidirect
10. C₂×Q₈×C₁₃	C₂×C₃	semidirect
33. 2₋¹⁺⁴	C₁₃⋊C₃	semidirect
41. #41	C₂×C₁₃⋊C₃	semidirect
43. C₂×Q₈	C₂×C₁₃⋊C₃	semidirect
44. C₁₃	2₋¹⁺⁴⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#41⋊(C₁₃⋊C₃)	2
C₂×Q₈⋊(C₁₃⋊C₃)	2
C₁₃×2₋¹⁺⁴	3
D₄×C₁₃⋊C₃	4
2₋¹⁺⁴⋊C₃	13

Subgroups — 2−1+4⋊(C13⋊C3) #11929265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 2₋¹⁺⁴⋊(C₁₃⋊C₃) #11929265