Subgroups — #28388786

Order 14464.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₆₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#20298317	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₈₀₈	—	2	1	no	—
5	D₁₆×C₁₁₃	—	2	1	no	—
6	C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
7	D₉₀₄	—	4	1	no	—
8	D₈×C₁₁₃	—	4	1	no	—
9	C₁₆×C₁₁₃	D₄	1	1	yes	characteristic
10	D₄×C₁₁₃	—	8	1	no	—
11	D₄₅₂	—	8	1	no	—
12	C₈×C₁₁₃	D₈	1	1	yes	characteristic
13	C₂²×C₁₁₃	—	16	1	no	—
14	C₂×D₁₁₃	—	16	1	no	—
15	C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
16	C₂×C₁₁₃	—	32	1	no	—
17	C₂×C₁₁₃	D₃₂	1	1	yes	characteristic
18	D₁₁₃	—	32	1	no	—
19	D₆₄	—	113	1	no	maximal, Sylow
20	C₁₁₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
21	D₃₂	—	113	1	no	—
22	D₃₂	D₁₁₃	1	1	yes	characteristic, complemented
23	C₆₄	—	113	1	no	—
24	D₁₆	—	2	1	no	—
25	D₁₆	—	226	1	no	—
26	C₃₂	C₂×D₁₁₃	1	1	yes	characteristic
27	D₈	—	4	1	no	—
28	D₈	—	452	1	no	—
29	C₁₆	C₂²⋊D₁₁₃	1	1	yes	characteristic
30	D₄	—	8	1	no	—
31	D₄	—	904	1	no	—
32	C₈	#14268632	1	1	yes	characteristic
33	C₂²	—	16	1	no	—
34	C₂²	—	1808	1	no	—
35	C₄	#16813563	1	1	yes	characteristic
36	C₂	—	32	1	no	—
37	C₂	—	3616	1	no	—
38	C₂	#20298433	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.