Subgroups — #49093519

Order 35968.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₄₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈₉₉₂	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₂₂₄₈	—	2	1	no	—
5	D₄₄₉₆	—	2	1	no	—
6	C₃₂×C₂₈₁	C₂²	1	1	yes	characteristic
7	Dic₁₁₂₄	—	4	1	no	—
8	D₂₂₄₈	—	4	1	no	—
9	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
10	Dic₅₆₂	—	8	1	no	—
11	D₁₁₂₄	—	8	1	no	—
12	C₈×C₂₈₁	D₈	1	1	yes	characteristic
13	C₂×D₂₈₁	—	16	1	no	—
14	C₄×C₂₈₁	D₁₆	1	1	yes	characteristic
15	Dic₂₈₁	—	16	1	no	—
16	C₂×C₂₈₁	D₃₂	1	1	yes	characteristic
17	D₂₈₁	—	32	1	no	—
18	C₂₈₁	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	SD₁₂₈	—	281	1	no	maximal, Sylow
20	Q₆₄	—	281	1	no	—
21	D₃₂	—	281	1	no	—
22	C₆₄	D₂₈₁	1	1	yes	characteristic, complemented
23	Q₃₂	—	562	1	no	—
24	D₁₆	—	562	1	no	—
25	C₃₂	C₂×D₂₈₁	1	1	yes	characteristic
26	Q₁₆	—	1124	1	no	—
27	D₈	—	1124	1	no	—
28	C₁₆	D₁₁₂₄	1	1	yes	characteristic
29	Q₈	—	2248	1	no	—
30	D₄	—	2248	1	no	—
31	C₈	D₂₂₄₈	1	1	yes	characteristic
32	C₂²	—	4496	1	no	—
33	C₄	—	4496	1	no	—
34	C₄	D₄₄₉₆	1	1	yes	characteristic
35	C₂	—	8992	1	no	—
36	C₂	D₈₉₉₂	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.