Subgroups — C₂×#26018071 #36442337

Order 22784.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26018071	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₈₉	C₄	1	1	yes	characteristic
4	C₆₄×C₈₉	C₄	1	1	yes	characteristic
5	C₆₄×C₈₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₈₉	C₈	1	1	yes	characteristic
7	C₃₂×C₈₉	C₈	1	1	yes	characteristic
8	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₈₉	C₁₆	1	1	yes	characteristic
10	C₁₆×C₈₉	C₁₆	1	1	yes	characteristic
11	C₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
12	C₂×C₄×C₈₉	C₃₂	1	1	yes	characteristic
13	C₈×C₈₉	C₃₂	1	1	yes	characteristic
14	C₈×C₈₉	C₂×C₁₆	1	1	yes	characteristic
15	C₂²×C₈₉	C₆₄	1	1	yes	characteristic
16	C₄×C₈₉	C₆₄	1	1	yes	characteristic
17	C₄×C₈₉	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₁₂₈	—	89	1	no	maximal, Sylow
19	C₂×C₈₉	C₁₂₈	1	2	yes	complemented
20	C₂×C₈₉	C₂×C₆₄	1	1	yes	characteristic
21	C₂×C₆₄	D₈₉	1	1	yes	characteristic
22	C₁₂₈	—	89	2	no	—
23	C₈₉	C₂×C₁₂₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	Dic₈₉	1	1	yes	characteristic
25	C₆₄	Dic₈₉	1	1	yes	characteristic
26	C₆₄	C₂×D₈₉	1	1	yes	characteristic
27	C₂×C₁₆	#10623494	1	1	yes	characteristic
28	C₃₂	#10623494	1	1	yes	characteristic
29	C₃₂	C₂×Dic₈₉	1	1	yes	characteristic
30	C₂×C₈	#13083549	1	1	yes	characteristic
31	C₁₆	#13083549	1	1	yes	characteristic
32	C₁₆	C₂×#10623494	1	1	yes	characteristic
33	C₂×C₄	#15667918	1	1	yes	characteristic
34	C₈	#15667918	1	1	yes	characteristic
35	C₈	C₂×#13083549	1	1	yes	characteristic
36	C₂²	#19151317	1	1	yes	characteristic
37	C₄	#19151317	1	1	yes	characteristic
38	C₄	C₂×#15667918	1	1	yes	characteristic
39	C₂	#26018071	1	2	yes	direct product factor
40	C₂	C₂×#19151317	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₆₄	D₈₉
commutator, hypocenter	C₈₉	C₂×C₁₂₈
Frattini	C₆₄	C₂×D₈₉
Fitting	C₂×C₆₄×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	C₆₄
cosocle	C₆₄×C₈₉	C₂²
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. #26018071	C₂	direct (N × H)
19. C₂×C₈₉	C₁₂₈	semidirect
23. C₈₉	C₂×C₁₂₈	semidirect
39. C₂	#26018071	direct (N × H)

Maximal subgroups

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

subgroup	index
#26018071	2
C₂×C₆₄×C₈₉	2
C₂×C₁₂₈	89

Subgroups — C2×#26018071 #36442337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26018071 #36442337