Subgroups — #22553136

Order 8384.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862186	C₂	1	1	yes	maximal, characteristic
2	#16862178	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₃₁	—	2	1	no	—
5	C₁₃₁⋊C₁₆	C₄	1	2	yes	complemented
6	M₁₆×C₁₃₁	—	2	1	no	—
7	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₃₁	—	4	1	no	—
9	C₂×C₄×C₁₃₁	D₄	1	1	yes	characteristic
10	C₈×C₁₃₁	—	4	1	no	—
11	C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₃₁	Q₈	1	1	yes	characteristic
13	C₂²×C₁₃₁	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₃₁	SD₁₆	1	1	yes	characteristic
16	Dic₁₃₁	—	8	1	no	—
17	C₂×C₁₃₁	—	2	1	no	—
18	C₂×C₁₃₁	#106	1	1	yes	characteristic
19	C₁₃₁	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	131	1	no	maximal, Sylow
21	M₃₂	—	131	1	no	—
22	#108	D₁₃₁	1	1	yes	characteristic
23	#106	—	131	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₁₃₁	1	1	yes	characteristic
26	C₄⋊C₄	—	262	1	no	—
27	C₁₆	—	131	2	no	—
28	C₂×C₄	—	524	1	no	—
29	C₂×C₄	C₂²⋊D₁₃₁	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	C₄×D₁₃₁	1	1	yes	characteristic
32	C₈	Dic₂₆₂	1	1	yes	characteristic
33	C₂²	#14523500	1	1	yes	characteristic
34	C₄	—	1048	1	no	—
35	C₄	Dic₁₃₁⋊C₄	1	1	yes	characteristic
36	C₄	#14523501	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#16862177	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₁₃₁⋊C₁₆	C₄	semidirect
19. C₁₃₁	#365	semidirect