Subgroups — #20299522

Order 7232.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813692	C₂	1	1	yes	maximal, characteristic
2	#16813690	C₂	1	1	yes	maximal, characteristic
3	#16813561	C₂	1	1	yes	maximal, characteristic
4	#14268657	—	2	1	no	—
5	C₄⋊#90673	—	2	1	no	—
6	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
7	#14268622	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
9	C₂×#90673	—	4	1	no	—
10	C₄×D₁₁₃	D₄	1	1	yes	characteristic
11	#11744753	—	4	1	no	—
12	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
13	#11744751	Q₈	1	1	yes	characteristic
14	C₂×D₁₁₃	SD₁₆	1	1	yes	characteristic
15	#90673	—	8	1	no	—
16	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	Dic₁₁₃	SD₁₆	1	1	yes	characteristic
18	C₂×C₁₁₃	#106	1	1	yes	characteristic
19	D₁₁₃	—	2	1	no	—
20	C₁₁₃	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	113	1	no	maximal, Sylow
22	M₃₂	—	113	1	no	—
23	#108	—	113	1	no	—
24	#106	—	113	1	no	—
25	M₁₆	—	226	1	no	—
26	C₂×C₈	—	113	1	no	—
27	C₄⋊C₄	—	226	1	no	—
28	C₁₆	—	113	1	no	—
29	C₁₆	#90673	1	1	yes	characteristic, complemented
30	C₂×C₄	—	113	1	no	—
31	C₂×C₄	—	452	1	no	—
32	C₈	—	113	1	no	—
33	C₈	—	452	1	no	—
34	C₈	C₂×#90673	1	1	yes	characteristic
35	C₂²	—	113	1	no	—
36	C₄	—	113	1	no	—
37	C₄	—	904	1	no	—
38	C₄	C₄⋊#90673	1	1	yes	characteristic
39	C₂	—	226	1	no	—
40	C₂	#16813690	1	1	yes	characteristic

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