Subgroups — #20298418

Order 7232.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813562	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11744751	C₄	1	1	yes	characteristic
5	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
6	#14268622	—	2	1	no	—
7	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₁₃	—	2	1	no	—
9	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₁₃	—	2	1	no	—
11	C₈×C₁₁₃	D₄	1	1	yes	characteristic
12	C₈×C₁₁₃	Q₈	1	1	yes	characteristic
13	#11744751	C₈	1	2	yes	—
14	C₂²×C₁₁₃	M₁₆	1	1	yes	characteristic
15	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
17	Dic₁₁₃	—	2	2	no	—
18	C₂×C₁₁₃	—	2	1	no	—
19	C₂×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
20	C₁₁₃	#364	1	1	yes	characteristic, complemented, Sylow
21	#364	—	113	1	no	maximal, Sylow
22	M₃₂	—	113	1	no	—
23	M₃₂	D₁₁₃	1	1	yes	characteristic
24	C₄×C₈	—	113	1	no	—
25	C₂×C₈	—	113	1	no	—
26	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
27	C₄²	—	113	1	no	—
28	C₁₆	—	2	1	no	—
29	C₁₆	—	226	1	no	—
30	C₂×C₄	—	226	1	no	—
31	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
32	C₈	—	113	2	no	—
33	C₈	Dic₂₂₆	1	1	yes	characteristic
34	C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
35	C₂²	#14268630	1	1	yes	characteristic
36	C₄	—	226	2	no	—
37	C₄	#14268626	1	1	yes	characteristic
38	C₄	C₈×D₁₁₃	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#16813551	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₁₁₃	#364	semidirect