Subgroups — #22553135

Order 8384.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862182	C₂	1	1	yes	maximal, characteristic
2	#16862178	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#14523497	—	2	1	no	—
5	C₄⋊Dic₁₃₁	—	2	1	no	—
6	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
7	C₁₆×C₁₃₁	C₄	1	2	yes	complemented
8	C₂×Dic₁₃₁	—	4	1	no	—
9	C₁₃₁⋊C₈	—	4	1	no	—
10	C₂×C₄×C₁₃₁	D₄	1	1	yes	characteristic
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	D₁₃₁	1	1	yes	characteristic
22	#108	—	131	1	no	—
23	#106	—	131	1	no	—
24	M₁₆	—	262	1	no	—
25	C₂×C₈	C₂×D₁₃₁	1	1	yes	characteristic
26	C₄⋊C₄	—	262	1	no	—
27	C₁₆	Dic₁₃₁	1	2	yes	complemented
28	C₂×C₄	—	524	1	no	—
29	C₂×C₄	D₅₂₄	1	1	yes	characteristic
30	C₈	—	524	1	no	—
31	C₈	C₂×Dic₁₃₁	1	1	yes	characteristic
32	C₈	Dic₂₆₂	1	1	yes	characteristic
33	C₂²	#14523502	1	1	yes	characteristic
34	C₄	—	1048	1	no	—
35	C₄	C₄⋊Dic₁₃₁	1	1	yes	characteristic
36	C₄	#14523502	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#16862178	1	1	yes	characteristic

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