Subgroups — #26018174

Order 11392.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151374	C₂	1	1	yes	maximal, characteristic
2	#19151319	C₂	1	1	yes	maximal, characteristic
3	#346×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#13083549	C₄	1	2	yes	—
5	C₄×#10623494	C₄	1	2	yes	—
6	C₂×C₁₆×C₈₉	C₄	1	2	yes	—
7	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
8	C₂×#10623494	—	2	2	no	—
9	#13083549	C₈	1	4	yes	complemented
10	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₈₉	—	2	2	no	—
14	C₂×C₄×C₈₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₈₉	M₁₆	1	2	yes	—
16	C₈×C₈₉	C₂×C₈	1	2	yes	—
17	C₈×C₈₉	M₁₆	1	2	yes	—
18	#10623494	—	4	2	no	—
19	C₂²×C₈₉	#97	1	1	yes	characteristic
20	C₄×C₈₉	—	2	2	no	—
21	C₄×C₈₉	C₄×C₈	1	1	yes	characteristic
22	C₄×C₈₉	#97	1	1	yes	characteristic
23	C₂×C₈₉	#322	1	1	yes	characteristic
24	C₂×C₈₉	#347	1	2	yes	—
25	#1313	—	89	1	no	maximal, Sylow
26	C₈₉	#1313	1	1	yes	characteristic, complemented, Sylow
27	#346	—	89	1	no	—
28	#346	D₈₉	1	1	yes	characteristic
29	#322	—	89	1	no	—
30	C₂×C₁₆	—	89	2	no	—
31	C₂×C₁₆	Dic₈₉	1	2	yes	—
32	C₄×C₈	—	89	2	no	—
33	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
34	C₂×C₈	—	178	2	no	—
35	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₈₉	1	1	yes	characteristic
37	C₄²	C₄×D₈₉	1	1	yes	characteristic
38	C₁₆	—	2	2	no	—
39	C₁₆	—	89	4	no	—
40	C₂×C₄	C₄×Dic₈₉	1	1	yes	characteristic
41	C₂×C₄	#13083557	1	2	yes	—
42	C₈	—	356	2	no	—
43	C₈	C₈×D₈₉	1	2	yes	—
44	C₈	#13083558	1	2	yes	—
45	C₂²	#15667922	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₈×Dic₈₉	1	1	yes	characteristic
48	C₄	#15667923	1	1	yes	characteristic
49	C₂	#19151320	1	1	yes	characteristic
50	C₂	#19151375	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₈₉
commutator	C₄×C₈₉	C₄×C₈
Frattini	C₄×C₈	C₂×D₈₉
Fitting	#346×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	#97
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	#346	D₈₉
hypocenter	C₈₉	#1313
LCS	G ▷ C₄×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #346

Complements

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

N	H ≅ G/N	type
9. #13083549	C₈	semidirect
26. C₈₉	#1313	semidirect

Maximal subgroups

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

subgroup	index
#19151374	2
#19151319	2
#346×C₈₉	2
#1313	89