Subgroups — #20299702

Order 7232.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813719	C₂	1	2	yes	maximal
2	C₈×#90673	C₂	1	1	yes	maximal, characteristic
3	#14268659	—	2	2	no	—
4	#14268655	C₂²	1	1	yes	characteristic
5	C₄×#90673	C₄	1	1	yes	characteristic
6	C₈×D₁₁₃	C₄	1	1	yes	characteristic
7	C₂×#90673	—	2	1	no	—
8	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
9	#11744753	D₄	1	1	yes	characteristic
10	#11744753	Q₈	1	1	yes	characteristic
11	C₈×C₁₁₃	C₈	1	1	yes	characteristic
12	#11744751	C₈	1	1	yes	characteristic
13	C₂×D₁₁₃	M₁₆	1	1	yes	characteristic
14	#90673	—	2	2	no	—
15	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	Dic₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
18	D₁₁₃	—	2	1	no	—
19	C₁₁₃	#364	1	1	yes	characteristic, complemented, Sylow
20	#364	—	113	1	no	maximal, Sylow
21	M₃₂	—	113	2	no	—
22	C₄×C₈	—	113	1	no	—
23	C₂×C₈	—	113	1	no	—
24	C₂×C₈	—	113	1	no	—
25	C₄²	—	113	1	no	—
26	C₁₆	—	226	2	no	—
27	C₂×C₄	—	113	1	no	—
28	C₂×C₄	—	226	1	no	—
29	C₈	—	113	1	no	—
30	C₈	—	113	1	no	—
31	C₈	—	113	1	no	—
32	C₈	#11744762	1	1	yes	characteristic
33	C₂²	—	113	1	no	—
34	C₄	—	113	1	no	—
35	C₄	—	226	2	no	—
36	C₄	C₂×#11744762	1	1	yes	characteristic
37	C₂	—	226	1	no	—
38	C₂	C₄⋊#11744762	1	1	yes	characteristic

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

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