Subgroups — C₂²×Q₈×C₁₃⋊C₃ #11929248

Order 1248.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂²×C₁₃⋊C₃
commutator, cosocle	C₂×C₁₃	C₂⁴×C₃
Frattini	C₂	C₂⁴×C₁₃⋊C₃
Fitting	C₂²×Q₈×C₁₃	C₃
socle	C₂³×C₁₃	C₂²×C₃
prime radical	C₂³×C₁₃⋊C₃	C₂²
hypercenter	C₂²×Q₈	C₁₃⋊C₃
hypocenter	C₁₃	C₂²×C₃×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₁₃⋊C₃	C₂	direct (N × H)
3. C₂²×Q₈×C₁₃	C₃	semidirect
5. Q₈×C₁₃⋊C₃	C₂²	direct (N × H)
7. C₂×Q₈×C₁₃	C₂×C₃	semidirect
9. C₂²×C₁₃⋊C₃	Q₈	direct (N × H)
13. Q₈×C₁₃	C₂²×C₃	semidirect
16. C₂×C₁₃⋊C₃	C₂×Q₈	direct (N × H)
18. C₂²×C₁₃	C₃×Q₈	semidirect
23. C₁₃⋊C₃	C₂²×Q₈	direct (N × H)
24. C₂²×Q₈	C₁₃⋊C₃	direct (N × H)
25. C₂×C₁₃	C₂×C₃×Q₈	semidirect
30. C₂×Q₈	C₂×C₁₃⋊C₃	direct (N × H)
32. C₁₃	C₂²×C₃×Q₈	semidirect
37. Q₈	C₂²×C₁₃⋊C₃	direct (N × H)
41. C₂²	Q₈×C₁₃⋊C₃	direct (N × H)
45. C₂	C₂×Q₈×C₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₃⋊C₃	2
C₂²×C₄×C₁₃⋊C₃	2
C₂²×Q₈×C₁₃	3
C₂²×C₃×Q₈	13

Subgroups — C22×Q8×C13⋊C3 #11929248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Q₈×C₁₃⋊C₃ #11929248