Subgroups — #127⋊(C₁₃⋊C₃) #11928755

Order 1248.

56 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×#127	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₂²⋊(C₁₃⋊C₃)	—	4	1	no	maximal
4	C₂×D₄×C₁₃	—	3	1	no	—
5	C₂×D₄×C₁₃	—	3	1	no	—
6	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²⋊(C₁₃⋊C₃)	—	4	1	no	—
8	C₂³×C₁₃	—	3	1	no	—
9	C₂³×C₁₃	A₄	1	1	yes	characteristic
10	D₄×C₁₃	—	6	2	no	—
11	D₄×C₁₃	—	6	2	no	—
12	C₂×C₄×C₁₃	—	3	1	no	—
13	#127⋊C₃	—	13	1	no	maximal, Hall
14	C₂×C₁₃⋊C₃	—	16	1	no	—
15	C₂²×C₁₃	—	6	1	no	—
16	C₂²×C₁₃	—	6	1	no	—
17	C₂²×C₁₃	—	6	2	no	—
18	C₂²×C₁₃	C₂×A₄	1	1	yes	characteristic
19	C₄×C₁₃	—	3	2	no	—
20	C₄²⋊C₃	—	13	1	no	—
21	C₁₃⋊C₃	—	16	1	no	Hall
22	#127	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₃	—	3	1	no	—
24	C₂×C₁₃	—	4	1	no	—
25	C₂×C₁₃	—	12	1	no	—
26	C₂×A₄	—	52	1	no	—
27	C₂×D₄	—	3	1	no	—
28	C₂×D₄	—	3	1	no	—
29	C₄²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
30	C₁₃	#127⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	A₄	—	52	1	no	—
32	C₂³	—	3	1	no	—
33	C₂³	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
34	D₄	—	6	2	no	—
35	D₄	—	6	2	no	—
36	C₂×C₄	—	3	1	no	—
37	C₂×C₃	—	208	1	no	—
38	C₂²	—	6	1	no	—
39	C₂²	—	6	1	no	—
40	C₂²	—	6	2	no	—
41	C₂²	C₂×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
42	C₄	—	3	2	no	—
43	C₃	—	208	1	no	Sylow
44	C₂	—	3	1	no	—
45	C₂	—	4	1	no	—
46	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₄²×C₁₃	C₂×C₃
Frattini	C₂²	C₂×C₂²⋊(C₁₃⋊C₃)
Fitting	C₁₃×#127	C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ C₄²×C₁₃
UCS	C₁

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.