Subgroups — #26018462

Order 11392.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#19151317	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₈₉	C₄	1	1	yes	characteristic
5	#15667918	C₄	1	1	yes	characteristic
6	C₃₂×C₈₉	C₂²	1	1	yes	characteristic
7	C₈×D₈₉	C₈	1	1	yes	characteristic
8	#13083549	C₈	1	1	yes	characteristic
9	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
10	C₄×D₈₉	C₁₆	1	1	yes	characteristic
11	C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
12	#10623494	C₁₆	1	1	yes	characteristic
13	C₂×D₈₉	C₃₂	1	1	yes	characteristic
14	C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
15	Dic₈₉	C₃₂	1	1	yes	characteristic
16	C₂×C₈₉	C₂×C₃₂	1	1	yes	characteristic
17	D₈₉	—	2	1	no	—
18	M₁₂₈	—	89	1	no	maximal, Sylow
19	C₈₉	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃₂	—	89	1	no	—
21	C₆₄	—	89	1	no	—
22	C₆₄	D₈₉	1	1	yes	characteristic, complemented
23	C₂×C₁₆	—	89	1	no	—
24	C₃₂	—	89	1	no	—
25	C₃₂	C₂×D₈₉	1	1	yes	characteristic
26	C₂×C₈	—	89	1	no	—
27	C₁₆	—	89	1	no	—
28	C₁₆	C₄×D₈₉	1	1	yes	characteristic
29	C₂×C₄	—	89	1	no	—
30	C₈	—	89	1	no	—
31	C₈	C₈×D₈₉	1	1	yes	characteristic
32	C₂²	—	89	1	no	—
33	C₄	—	89	1	no	—
34	C₄	C₁₆×D₈₉	1	1	yes	characteristic
35	C₂	—	178	1	no	—
36	C₂	C₃₂×D₈₉	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.