Subgroups — #20299485

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813695	C₂	1	1	yes	maximal, characteristic
2	C₈×#90673	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268655	C₄	1	1	yes	characteristic
5	C₄×#90673	C₄	1	1	yes	characteristic
6	#14268650	C₄	1	2	yes	complemented
7	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
8	#14268622	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
10	C₂×#90673	C₈	1	2	yes	—
11	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
12	#11744753	C₈	1	2	yes	—
13	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	#11744751	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₁₃	C₂×C₈	1	1	yes	characteristic
16	#90673	—	2	2	no	—
17	C₄×C₁₁₃	C₄²	1	1	yes	characteristic
18	Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₁₃	C₄×C₈	1	1	yes	characteristic
20	D₁₁₃	M₃₂	1	2	yes	—
21	C₁₁₃	#346	1	1	yes	characteristic, complemented, Sylow
22	#346	—	113	1	no	maximal, Sylow
23	C₂×C₁₆	—	113	1	no	—
24	C₂×C₁₆	—	113	1	no	—
25	C₄×C₈	—	113	1	no	—
26	C₂×C₈	—	113	1	no	—
27	C₂×C₈	—	113	1	no	—
28	C₄²	—	113	1	no	—
29	C₁₆	—	113	2	no	—
30	C₁₆	—	113	1	no	—
31	C₁₆	#90673	1	1	yes	characteristic, complemented
32	C₂×C₄	—	113	1	no	—
33	C₂×C₄	—	113	2	no	—
34	C₈	—	113	2	no	—
35	C₈	—	113	1	no	—
36	C₈	C₂×#90673	1	1	yes	characteristic
37	C₂²	—	113	1	no	—
38	C₄	—	113	1	no	—
39	C₄	—	226	2	no	—
40	C₄	C₄×#90673	1	1	yes	characteristic
41	C₂	—	113	2	no	—
42	C₂	C₈×#90673	1	1	yes	characteristic

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