Subgroups — #26018458

Order 11392.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151428	C₂	1	1	yes	maximal, characteristic
2	#19151426	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	#15667948	—	2	1	no	—
5	#15667946	—	2	1	no	—
6	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
7	C₃₂×C₈₉	C₄	1	2	yes	complemented
8	#13083558	—	4	1	no	—
9	C₄⋊Dic₈₉	—	4	1	no	—
10	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
11	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₈₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
14	C₂×Dic₈₉	—	8	1	no	—
15	C₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₈₉	Q₁₆	1	1	yes	characteristic
17	#10623494	—	8	1	no	—
18	C₂²×C₈₉	SD₃₂	1	1	yes	characteristic
19	C₄×C₈₉	#107	1	1	yes	characteristic
20	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
21	Dic₈₉	—	16	1	no	—
22	C₂×C₈₉	—	2	1	no	—
23	C₂×C₈₉	#367	1	1	yes	characteristic
24	#1426	—	89	1	no	maximal, Sylow
25	C₈₉	#1426	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	D₈₉	1	1	yes	characteristic
27	#368	—	89	1	no	—
28	#367	—	89	1	no	—
29	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
30	#108	—	178	1	no	—
31	#107	—	178	1	no	—
32	C₃₂	Dic₈₉	1	2	yes	complemented
33	M₁₆	—	356	1	no	—
34	C₂×C₈	D₃₅₆	1	1	yes	characteristic
35	C₄⋊C₄	—	356	1	no	—
36	C₁₆	Dic₁₇₈	1	1	yes	characteristic
37	C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
38	C₂×C₄	—	712	1	no	—
39	C₂×C₄	D₇₁₂	1	1	yes	characteristic
40	C₈	—	712	1	no	—
41	C₈	C₄⋊Dic₈₉	1	1	yes	characteristic
42	C₈	Dic₃₅₆	1	1	yes	characteristic
43	C₂²	#15667957	1	1	yes	characteristic
44	C₄	—	1424	1	no	—
45	C₄	#15667946	1	1	yes	characteristic
46	C₄	#15667957	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#19151426	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19151426
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	M₆₄×C₈₉	C₂
socle	C₂×C₈₉	#367
prime radical	C₂²×C₈₉	SD₃₂
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	M₆₄	D₈₉
hypocenter	C₈₉	#1426
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₈₉	C₄	semidirect
25. C₈₉	#1426	semidirect
32. C₃₂	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151428	2
#19151426	2
M₆₄×C₈₉	2
#1426	89