Subgroups — C₁₃×#126⋊C₃ #11928746

Order 1248.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#126	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×A₄×C₁₃	—	4	1	no	maximal
4	C₁₃×C₄⋊C₄	—	3	1	no	—
5	C₁₃×C₂²⋊C₄	—	3	1	no	—
6	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	A₄×C₁₃	—	4	1	no	—
8	C₂³×C₁₃	A₄	1	1	yes	characteristic
9	C₂×C₄×C₁₃	—	3	1	no	—
10	C₂×C₄×C₁₃	—	3	1	no	—
11	#126⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₁₃	—	16	1	no	—
13	C₂²×C₁₃	—	6	1	no	—
14	C₂²×C₁₃	C₂×A₄	1	1	yes	characteristic
15	C₄×C₁₃	—	6	1	no	—
16	C₄×C₁₃	—	6	1	no	—
17	C₄²⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃×C₁₃	—	16	1	no	Hall
19	#126	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₃	—	3	1	no	—
21	C₂×C₁₃	—	4	1	no	—
22	C₂×A₄	—	4	1	no	—
23	C₄⋊C₄	—	3	1	no	—
24	C₂²⋊C₄	—	3	1	no	—
25	C₄²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
26	C₁₃	#126⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	A₄	—	4	1	no	—
28	C₂³	A₄×C₁₃	1	1	yes	characteristic
29	C₂×C₄	—	3	1	no	—
30	C₂×C₄	—	3	1	no	—
31	C₂×C₃	—	16	1	no	—
32	C₂²	—	6	1	no	—
33	C₂²	C₂×A₄×C₁₃	1	1	yes	characteristic
34	C₄	—	6	1	no	—
35	C₄	—	6	1	no	—
36	C₃	—	16	1	no	Sylow
37	C₂	—	3	1	no	—
38	C₂	—	4	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#126⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₁₃
Frattini	C₂²	C₂×A₄×C₁₃
Fitting	C₁₃×#126	C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₁₃

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

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