Subgroups — #26018452

Order 11392.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151424	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
3	#15667946	—	2	2	no	—
4	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
5	C₃₂×C₈₉	C₄	1	2	yes	complemented
6	C₄⋊Dic₈₉	—	4	2	no	—
7	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
8	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₈₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
11	C₂×Dic₈₉	—	8	2	no	—
12	C₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₈₉	Q₁₆	1	1	yes	characteristic
14	C₂²×C₈₉	D₁₆	1	1	yes	characteristic
15	C₄×C₈₉	#107	1	1	yes	characteristic
16	C₄×C₈₉	Q₃₂	1	1	yes	characteristic
17	Dic₈₉	—	16	2	no	—
18	C₂×C₈₉	#366	1	1	yes	characteristic
19	C₂×C₈₉	D₃₂	1	1	yes	characteristic
20	C₂×C₈₉	Q₆₄	1	1	yes	characteristic
21	#1423	—	89	1	no	maximal, Sylow
22	C₈₉	#1423	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃₂	D₈₉	1	1	yes	characteristic
24	#366	—	89	2	no	—
25	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
26	#107	—	178	2	no	—
27	C₃₂	Dic₈₉	1	2	yes	complemented
28	C₂×C₈	D₃₅₆	1	1	yes	characteristic
29	C₄⋊C₄	—	356	2	no	—
30	C₁₆	Dic₁₇₈	1	1	yes	characteristic
31	C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
32	C₂×C₄	—	712	2	no	—
33	C₂×C₄	D₇₁₂	1	1	yes	characteristic
34	C₈	C₄⋊Dic₈₉	1	1	yes	characteristic
35	C₈	Dic₃₅₆	1	1	yes	characteristic
36	C₂²	D₁₄₂₄	1	1	yes	characteristic
37	C₄	—	1424	2	no	—
38	C₄	#15667946	1	1	yes	characteristic
39	C₄	Dic₇₁₂	1	1	yes	characteristic
40	C₂	#19151424	1	1	yes	characteristic
41	C₂	D₂₈₄₈	1	1	yes	characteristic
42	C₂	Dic₁₄₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₄₂₄
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	C₂×C₃₂×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	D₁₆
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	C₂×C₃₂	D₈₉
hypocenter	C₈₉	#1423
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₈₉	C₄	semidirect
22. C₈₉	#1423	semidirect
27. C₃₂	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151424	2
C₂×C₃₂×C₈₉	2
#1423	89