Subgroups — #20299525

Order 7232.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813691	C₂	1	2	yes	maximal
2	C₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#90673	—	2	2	no	—
4	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
5	#14268622	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#90673	—	4	2	no	—
8	C₄×D₁₁₃	D₄	1	1	yes	characteristic
9	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
10	#11744751	Q₈	1	1	yes	characteristic
11	C₂×D₁₁₃	D₈	1	1	yes	characteristic
12	#90673	—	8	2	no	—
13	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
14	Dic₁₁₃	Q₁₆	1	1	yes	characteristic
15	C₂×C₁₁₃	#107	1	1	yes	characteristic
16	D₁₁₃	SD₃₂	1	2	yes	—
17	C₁₁₃	#367	1	1	yes	characteristic, complemented, Sylow
18	#367	—	113	1	no	maximal, Sylow
19	C₂×C₁₆	—	113	1	no	—
20	#107	—	113	2	no	—
21	C₂×C₈	—	113	1	no	—
22	C₄⋊C₄	—	226	2	no	—
23	C₁₆	—	113	1	no	—
24	C₁₆	#90673	1	1	yes	characteristic, complemented
25	C₂×C₄	—	113	1	no	—
26	C₂×C₄	—	452	2	no	—
27	C₈	—	113	1	no	—
28	C₈	C₂×#90673	1	1	yes	characteristic
29	C₂²	—	113	1	no	—
30	C₄	—	113	1	no	—
31	C₄	—	904	2	no	—
32	C₄	C₄⋊#90673	1	1	yes	characteristic
33	C₂	—	113	2	no	—
34	C₂	#16813691	1	1	yes	characteristic

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