Subgroups — #26018468

Order 11392.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₈₄₈	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇₁₂	—	2	1	no	—
5	D₁₄₂₄	—	2	1	no	—
6	C₃₂×C₈₉	C₂²	1	1	yes	characteristic
7	Dic₃₅₆	—	4	1	no	—
8	D₇₁₂	—	4	1	no	—
9	C₁₆×C₈₉	D₄	1	1	yes	characteristic
10	D₃₅₆	—	8	1	no	—
11	Dic₁₇₈	—	8	1	no	—
12	C₈×C₈₉	D₈	1	1	yes	characteristic
13	C₂×D₈₉	—	16	1	no	—
14	C₄×C₈₉	D₁₆	1	1	yes	characteristic
15	Dic₈₉	—	16	1	no	—
16	C₂×C₈₉	D₃₂	1	1	yes	characteristic
17	D₈₉	—	32	1	no	—
18	SD₁₂₈	—	89	1	no	maximal, Sylow
19	C₈₉	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	—	89	1	no	—
21	D₃₂	—	89	1	no	—
22	C₆₄	D₈₉	1	1	yes	characteristic, complemented
23	Q₃₂	—	178	1	no	—
24	D₁₆	—	178	1	no	—
25	C₃₂	C₂×D₈₉	1	1	yes	characteristic
26	Q₁₆	—	356	1	no	—
27	D₈	—	356	1	no	—
28	C₁₆	D₃₅₆	1	1	yes	characteristic
29	Q₈	—	712	1	no	—
30	D₄	—	712	1	no	—
31	C₈	D₇₁₂	1	1	yes	characteristic
32	C₂²	—	1424	1	no	—
33	C₄	—	1424	1	no	—
34	C₄	D₁₄₂₄	1	1	yes	characteristic
35	C₂	—	2848	1	no	—
36	C₂	D₂₈₄₈	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.