Subgroups — #26018455

Order 11392.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15667918	C₂	1	1	yes	maximal, characteristic
2	#19151428	C₂	1	1	yes	maximal, characteristic
3	#368×C₈₉	C₂	1	1	yes	maximal, characteristic
4	#15667948	—	2	1	no	—
5	#15667918	C₄	1	2	yes	—
6	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
7	#108×C₈₉	—	2	1	no	—
8	#13083558	—	4	1	no	—
9	M₁₆×C₈₉	—	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	C₈×C₈₉	—	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	Q₃₂	1	1	yes	characteristic
19	C₄×C₈₉	#107	1	1	yes	characteristic
20	C₄×C₈₉	D₁₆	1	1	yes	characteristic
21	C₂×C₈₉	—	2	1	no	—
22	C₂×C₈₉	#366	1	1	yes	characteristic
23	#1425	—	89	1	no	maximal, Sylow
24	C₈₉	#1425	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	89	1	no	—
26	#368	—	89	1	no	—
27	#368	D₈₉	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	178	1	no	—
31	C₃₂	—	89	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	356	1	no	—
34	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
35	C₁₆	Dic₁₇₈	1	1	yes	characteristic
36	C₁₆	C₄×D₈₉	1	1	yes	characteristic
37	C₂×C₄	#13083559	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	712	1	no	—
40	C₈	#13083553	1	1	yes	characteristic
41	C₈	#13083564	1	1	yes	characteristic
42	C₂²	#15667958	1	1	yes	characteristic
43	C₄	#15667945	1	1	yes	characteristic
44	C₄	#15667953	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#19151423	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15667953
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	#368×C₈₉	C₂
socle	C₂×C₈₉	#366
prime radical	C₂²×C₈₉	Q₃₂
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	#368	D₈₉
hypocenter	C₈₉	#1425
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
24. C₈₉	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15667918	2
#19151428	2
#368×C₈₉	2
#1425	89