Subgroups — #26020008

Order 11392.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151556	C₂	1	3	yes	maximal
2	#19151355	C₂	1	3	yes	maximal
3	#338×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10623494	C₂²	1	1	yes	characteristic
5	#15667971	C₂²	1	3	yes	—
6	#15667922	C₄	1	6	yes	complemented
7	C₈×Dic₈₉	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₈₉	C₂²	1	3	yes	—
9	C₂×#10623494	C₂×C₄	1	3	yes	—
10	C₂×#10623494	C₂×C₄	1	3	yes	—
11	C₄⋊Dic₈₉	—	2	3	no	—
12	C₂²⋊Dic₈₉	—	2	3	no	—
13	C₄×Dic₈₉	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
15	M₁₆×C₈₉	—	2	6	no	—
16	C₂×C₈×C₈₉	C₂×C₄	1	6	yes	—
17	C₂³×C₈₉	#41	1	1	yes	characteristic
18	C₂×C₄×C₈₉	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₈₉	#41	1	3	yes	—
20	C₂×Dic₈₉	—	2	6	no	—
21	C₈×C₈₉	—	2	6	no	—
22	#10623494	C₄²	1	1	yes	characteristic
23	#10623494	C₄²	1	3	yes	—
24	C₂²×C₈₉	—	4	1	no	—
25	C₂²×C₈₉	#117	1	3	yes	—
26	C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₈₉	#117	1	3	yes	—
28	Dic₈₉	—	4	6	no	—
29	C₂×C₈₉	—	2	3	no	—
30	C₂×C₈₉	#376	1	1	yes	characteristic
31	#1747	—	89	1	no	maximal, Sylow
32	C₈₉	#1747	1	1	yes	characteristic, complemented, Sylow
33	#405	—	89	3	no	—
34	#338	D₈₉	1	1	yes	characteristic
35	H(3,ℤ/4)	—	89	3	no	—
36	C₂×M₁₆	C₂×D₈₉	1	3	yes	—
37	C₂²×C₈	—	89	1	no	—
38	#117	—	89	3	no	—
39	#97	—	89	6	no	—
40	C₄×C₈	—	89	6	no	—
41	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	89	3	no	—
44	C₂×C₈	—	89	3	no	—
45	C₂×C₈	C₄×D₈₉	1	6	yes	—
46	C₄⋊C₄	—	178	3	no	—
47	C₂²⋊C₄	—	178	3	no	—
48	C₄²	—	89	6	no	—
49	C₂³	#13083575	1	1	yes	characteristic
50	C₂×C₄	—	178	6	no	—
51	C₂×C₄	C₂×C₄×D₈₉	1	3	yes	—
52	C₂×C₄	#13083573	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	89	1	no	—
55	C₈	—	89	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#15667970	1	3	yes	—
58	C₄	—	356	6	no	—
59	C₄	C₄²×D₈₉	1	1	yes	characteristic
60	C₄	#15667968	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#19151443	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₈₉
commutator	C₄×C₈₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₈₉
Fitting	#338×C₈₉	C₂
socle	C₂×C₈₉	#376
prime radical	C₂³×C₈₉	#41
cosocle	C₂²×C₄×C₈₉	C₂³
hypercenter	#338	D₈₉
hypocenter	C₈₉	#1747
LCS	G ▷ C₄×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #15667922	C₄	semidirect
7. C₈×Dic₈₉	C₄	semidirect
32. C₈₉	#1747	semidirect

Maximal subgroups

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

subgroup	index
#19151556	2
#19151355	2
#338×C₈₉	2
#1747	89