Subgroups — #26018469

Order 11392.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₄₂₄	C₂	1	1	yes	maximal, characteristic
2	#19151317	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	Dic₇₁₂	—	2	1	no	—
5	Q₃₂×C₈₉	—	2	1	no	—
6	C₃₂×C₈₉	C₂²	1	1	yes	characteristic
7	Dic₃₅₆	—	4	1	no	—
8	Q₁₆×C₈₉	—	4	1	no	—
9	C₁₆×C₈₉	D₄	1	1	yes	characteristic
10	Q₈×C₈₉	—	8	1	no	—
11	Dic₁₇₈	—	8	1	no	—
12	C₈×C₈₉	D₈	1	1	yes	characteristic
13	C₄×C₈₉	—	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	Q₁₂₈	—	89	1	no	maximal, Sylow
18	C₈₉	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	89	1	no	—
20	Q₆₄	D₈₉	1	1	yes	characteristic
21	C₆₄	—	89	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	178	1	no	—
24	C₃₂	C₂×D₈₉	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	356	1	no	—
27	C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	712	1	no	—
30	C₈	#13083559	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1424	1	no	—
33	C₄	#15667953	1	1	yes	characteristic
34	C₂	#19151433	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₈₉	Q₁₂₈	semidirect

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