Subgroups — #22553133

Order 8384.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862186	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₁₃₁⋊C₁₆	—	2	2	no	—
4	C₂×C₈×C₁₃₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
6	C₄²×C₁₃₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₃₁	—	2	1	no	—
8	C₂×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₃₁	C₈	1	2	yes	—
10	C₈×C₁₃₁	D₄	1	1	yes	characteristic
11	C₈×C₁₃₁	Q₈	1	1	yes	characteristic
12	C₂²×C₁₃₁	M₁₆	1	1	yes	characteristic
13	C₄×C₁₃₁	—	2	2	no	—
14	C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₃₁	—	2	1	no	—
17	C₂×C₁₃₁	C₄⋊C₈	1	1	yes	characteristic
18	C₁₃₁	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	131	1	no	maximal, Sylow
20	M₃₂	—	131	2	no	—
21	C₄×C₈	D₁₃₁	1	1	yes	characteristic
22	C₂×C₈	Dic₁₃₁	1	1	yes	characteristic
23	C₂×C₈	C₂×D₁₃₁	1	1	yes	characteristic
24	C₄²	Dic₁₃₁	1	1	yes	characteristic
25	C₁₆	—	262	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×Dic₁₃₁	1	1	yes	characteristic
28	C₈	C₁₃₁⋊C₈	1	2	yes	—
29	C₈	D₅₂₄	1	1	yes	characteristic
30	C₈	Dic₂₆₂	1	1	yes	characteristic
31	C₂²	#14523497	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊Dic₁₃₁	1	1	yes	characteristic
34	C₄	C₂×C₁₃₁⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₁₃₁⋊C₈)	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₃₁	#364	semidirect