Subgroups — M₃₂×C₁₃⋊C₃ #11928021

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₁₃⋊C₃	C₂	1	2	yes	maximal, complemented
3	C₁₃×M₃₂	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₄×C₁₃⋊C₃	C₄	1	1	yes	characteristic
5	C₈×C₁₃⋊C₃	C₄	1	1	yes	characteristic
6	C₈×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₁₃×C₁₆	C₂×C₃	1	2	yes	complemented
9	C₂²×C₁₃⋊C₃	C₈	1	1	yes	characteristic
10	C₄×C₁₃⋊C₃	C₈	1	1	yes	characteristic
11	C₄×C₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃	C₃×C₄	1	1	yes	characteristic
13	C₈×C₁₃	C₃×C₄	1	1	yes	characteristic
14	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
15	C₃×M₃₂	—	13	1	no	maximal, Hall
16	C₂×C₁₃⋊C₃	—	2	1	no	—
17	C₂×C₁₃⋊C₃	C₂×C₈	1	1	yes	characteristic
18	C₂²×C₁₃	C₃×C₈	1	1	yes	characteristic
19	C₄×C₁₃	C₃×C₈	1	1	yes	characteristic
20	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂×C₃×C₈	—	13	1	no	—
22	C₃×C₁₆	—	13	2	no	—
23	C₁₃⋊C₃	M₃₂	1	1	yes	characteristic, direct product factor, Hall
24	M₃₂	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₃	—	2	1	no	—
26	C₂×C₁₃	C₂×C₃×C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	—	13	1	no	—
28	C₃×C₈	—	13	1	no	—
29	C₃×C₈	—	13	1	no	—
30	C₂×C₈	C₂×C₁₃⋊C₃	1	1	yes	characteristic
31	C₁₆	C₂×C₁₃⋊C₃	1	2	yes	complemented
32	C₁₃	C₃×M₃₂	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	—	13	1	no	—
34	C₃×C₄	—	13	1	no	—
35	C₃×C₄	—	13	1	no	—
36	C₂×C₄	C₄×C₁₃⋊C₃	1	1	yes	characteristic
37	C₈	C₄×C₁₃⋊C₃	1	1	yes	characteristic
38	C₈	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
39	C₂×C₃	—	13	1	no	—
40	C₂×C₃	—	26	1	no	—
41	C₂²	C₈×C₁₃⋊C₃	1	1	yes	characteristic
42	C₄	C₈×C₁₃⋊C₃	1	1	yes	characteristic
43	C₄	C₂×C₄×C₁₃⋊C₃	1	1	yes	characteristic
44	C₃	—	13	1	no	Sylow
45	C₂	—	2	1	no	—
46	C₂	C₂×C₈×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×C₁₃⋊C₃
commutator, socle	C₂×C₁₃	C₂×C₃×C₈
Fitting	C₁₃×M₃₂	C₃
prime radical	C₂²×C₁₃⋊C₃	C₈
cosocle	C₈×C₁₃	C₂²×C₃
hypercenter	M₃₂	C₁₃⋊C₃
hypocenter	C₁₃	C₃×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₁₆×C₁₃⋊C₃	C₂	semidirect
3. C₁₃×M₃₂	C₃	semidirect
8. C₁₃×C₁₆	C₂×C₃	semidirect
23. C₁₃⋊C₃	M₃₂	direct (N × H)
24. M₃₂	C₁₃⋊C₃	direct (N × H)
31. C₁₆	C₂×C₁₃⋊C₃	semidirect
32. C₁₃	C₃×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₁₃⋊C₃	2
C₁₆×C₁₃⋊C₃	2
C₁₃×M₃₂	3
C₃×M₃₂	13

Subgroups — M32×C13⋊C3 #11928021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×C₁₃⋊C₃ #11928021