Subgroups — #20267569

Order 6592.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692961	C₂	1	2	yes	maximal
2	#97×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₁₀₃⋊C₁₆	C₄	1	4	yes	complemented
4	C₂×C₈×C₁₀₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
6	C₄²×C₁₀₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₃	—	2	1	no	—
8	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₀₃	—	2	1	no	—
10	C₈×C₁₀₃	C₂×C₄	1	2	yes	—
11	C₂²×C₁₀₃	M₁₆	1	1	yes	characteristic
12	C₄×C₁₀₃	—	4	1	no	—
13	C₄×C₁₀₃	C₄²	1	1	yes	characteristic
14	C₄×C₁₀₃	M₁₆	1	1	yes	characteristic
15	C₂×C₁₀₃	—	2	1	no	—
16	C₂×C₁₀₃	#97	1	1	yes	characteristic
17	C₁₀₃	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	103	1	no	maximal, Sylow
19	M₃₂	—	103	2	no	—
20	#97	D₁₀₃	1	1	yes	characteristic
21	C₂×C₈	Dic₁₀₃	1	1	yes	characteristic
22	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
23	C₄²	Dic₁₀₃	1	1	yes	characteristic
24	C₁₆	—	103	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₁₀₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	C₄×D₁₀₃	1	2	yes	—
29	C₂²	#13110089	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×Dic₁₀₃	1	1	yes	characteristic
32	C₄	#13110089	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#15692932	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₁₀₃⋊C₁₆	C₄	semidirect
17. C₁₀₃	#347	semidirect