Subgroups — C₂×#19151317 #26018461

Order 11392.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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