Subgroups — 2₋¹⁺⁴×C₁₃⋊C₃ #11929251

Order 1248.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₁₃⋊C₃	C₂	1	10	yes	maximal, complemented
2	C₂×Q₈×C₁₃⋊C₃	C₂	1	5	yes	maximal, complemented
3	C₁₃×2₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	Q₈×C₁₃⋊C₃	C₂²	1	10	yes	—
5	D₄×C₁₃⋊C₃	C₂²	1	10	yes	—
6	C₂×C₄×C₁₃⋊C₃	C₂²	1	15	yes	—
7	C₁₃×#41	C₂×C₃	1	10	yes	complemented
8	C₂×Q₈×C₁₃	C₂×C₃	1	5	yes	complemented
9	C₂²×C₁₃⋊C₃	C₂³	1	5	yes	—
10	C₄×C₁₃⋊C₃	C₂³	1	10	yes	—
11	Q₈×C₁₃	C₂²×C₃	1	10	yes	—
12	D₄×C₁₃	C₂²×C₃	1	10	yes	—
13	C₂×C₄×C₁₃	C₂²×C₃	1	15	yes	—
14	C₃×2₋¹⁺⁴	—	13	1	no	maximal, Hall
15	C₂×C₁₃⋊C₃	—	2	5	no	—
16	C₂×C₁₃⋊C₃	C₂⁴	1	1	yes	characteristic
17	C₂²×C₁₃	C₂³×C₃	1	5	yes	—
18	C₄×C₁₃	C₂³×C₃	1	10	yes	—
19	C₃×#41	—	13	10	no	—
20	C₂×C₃×Q₈	—	13	5	no	—
21	C₁₃⋊C₃	2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Hall
22	2₋¹⁺⁴	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₁₃	—	2	5	no	—
24	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
25	C₃×Q₈	—	13	10	no	—
26	C₃×D₄	—	13	10	no	—
27	C₂×C₃×C₄	—	13	15	no	—
28	#41	C₂×C₁₃⋊C₃	1	10	yes	complemented
29	C₂×Q₈	C₂×C₁₃⋊C₃	1	5	yes	complemented
30	C₁₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₃	—	13	5	no	—
32	C₃×C₄	—	13	10	no	—
33	Q₈	C₂²×C₁₃⋊C₃	1	10	yes	—
34	D₄	C₂²×C₁₃⋊C₃	1	10	yes	—
35	C₂×C₄	C₂²×C₁₃⋊C₃	1	15	yes	—
36	C₂×C₃	—	13	1	no	—
37	C₂×C₃	—	26	5	no	—
38	C₂²	C₂³×C₁₃⋊C₃	1	5	yes	—
39	C₄	C₂³×C₁₃⋊C₃	1	10	yes	—
40	C₃	—	13	1	no	Sylow
41	C₂	—	2	5	no	—
42	C₂	C₂⁴×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂⁴×C₁₃⋊C₃
commutator, socle, cosocle	C₂×C₁₃	C₂⁴×C₃
Fitting	C₁₃×2₋¹⁺⁴	C₃
hypercenter	2₋¹⁺⁴	C₁₃⋊C₃
hypocenter	C₁₃	C₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ 2₋¹⁺⁴

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
7. C₁₃×#41	C₂×C₃	semidirect
8. C₂×Q₈×C₁₃	C₂×C₃	semidirect
21. C₁₃⋊C₃	2₋¹⁺⁴	direct (N × H)
22. 2₋¹⁺⁴	C₁₃⋊C₃	direct (N × H)
28. #41	C₂×C₁₃⋊C₃	semidirect
29. C₂×Q₈	C₂×C₁₃⋊C₃	semidirect
30. C₁₃	C₃×2₋¹⁺⁴	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
C₃×2₋¹⁺⁴	13

Subgroups — 2−1+4×C13⋊C3 #11929251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 2₋¹⁺⁴×C₁₃⋊C₃ #11929251