Subgroups — #20241524

Order 6016.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688957	C₂	1	2	yes	maximal
2	C₄₇×#346	C₂	1	1	yes	maximal, characteristic
3	C₄₇⋊C₃₂	C₄	1	4	yes	complemented
4	C₂×C₁₆×C₄₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₄₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₄₇	C₈	1	1	yes	characteristic
10	C₁₆×C₄₇	C₈	1	2	yes	—
11	C₁₆×C₄₇	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₄₇	—	2	1	no	—
13	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
14	C₈×C₄₇	—	2	1	no	—
15	C₈×C₄₇	C₄²	1	1	yes	characteristic
16	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₄₇	M₃₂	1	1	yes	characteristic
18	C₄×C₄₇	—	4	1	no	—
19	C₄×C₄₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₄₇	M₃₂	1	1	yes	characteristic
21	#1398	—	47	1	no	maximal, Sylow
22	C₂×C₄₇	—	2	1	no	—
23	C₂×C₄₇	#346	1	1	yes	characteristic
24	M₆₄	—	47	2	no	—
25	#346	D₄₇	1	1	yes	characteristic
26	C₄₇	#1398	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₆	Dic₄₇	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
29	C₄×C₈	Dic₄₇	1	1	yes	characteristic
30	C₃₂	—	47	4	no	—
31	C₂×C₈	C₄₇⋊C₈	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
33	C₄²	C₄₇⋊C₈	1	1	yes	characteristic
34	C₁₆	C₄₇⋊C₈	1	2	yes	—
35	C₁₆	C₄×D₄₇	1	2	yes	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
40	C₈	C₄×Dic₄₇	1	1	yes	characteristic
41	C₂²	#13093964	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	C₄×C₄₇⋊C₈	1	1	yes	characteristic
44	C₄	#13093964	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#15688899	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₄₇
commutator	C₄×C₄₇	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄₇×#346	C₂
socle	C₂×C₄₇	#346
hypercenter	#346	D₄₇
hypocenter	C₄₇	#1398
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
3. C₄₇⋊C₃₂	C₄	semidirect
26. C₄₇	#1398	semidirect