Subgroups — #26018449

Order 11392.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151432	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#13083549	C₄	1	1	yes	characteristic
5	C₈×Dic₈₉	C₄	1	1	yes	characteristic
6	#15667918	—	2	1	no	—
7	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
8	C₃₂×C₈₉	—	2	1	no	—
9	C₂×#10623494	C₈	1	1	yes	characteristic
10	C₄×Dic₈₉	C₈	1	1	yes	characteristic
11	#13083549	—	2	1	no	—
12	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₈₉	D₄	1	1	yes	characteristic
14	C₁₆×C₈₉	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₈₉	—	2	1	no	—
17	C₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₈₉	M₁₆	1	1	yes	characteristic
19	#10623494	C₁₆	1	2	yes	—
20	C₂²×C₈₉	M₃₂	1	1	yes	characteristic
21	C₄×C₈₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
23	Dic₈₉	—	2	2	no	—
24	C₂×C₈₉	—	2	1	no	—
25	C₂×C₈₉	C₄⋊C₁₆	1	1	yes	characteristic
26	#1422	—	89	1	no	maximal, Sylow
27	C₈₉	#1422	1	1	yes	characteristic, complemented, Sylow
28	M₆₄	—	89	1	no	—
29	M₆₄	D₈₉	1	1	yes	characteristic
30	C₄×C₁₆	—	89	1	no	—
31	C₂×C₁₆	—	89	1	no	—
32	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
33	C₄×C₈	—	89	1	no	—
34	C₃₂	—	2	1	no	—
35	C₃₂	—	178	1	no	—
36	C₂×C₈	—	89	1	no	—
37	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
38	C₄²	—	89	1	no	—
39	C₁₆	—	178	1	no	—
40	C₁₆	Dic₁₇₈	1	1	yes	characteristic
41	C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
42	C₂×C₄	—	178	1	no	—
43	C₂×C₄	C₈×D₈₉	1	1	yes	characteristic
44	C₈	—	89	2	no	—
45	C₈	#13083553	1	1	yes	characteristic
46	C₈	#13083557	1	1	yes	characteristic
47	C₂²	#15667951	1	1	yes	characteristic
48	C₄	—	178	2	no	—
49	C₄	#15667941	1	1	yes	characteristic
50	C₄	C₁₆×D₈₉	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#19151416	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₈₉
commutator	C₄×C₈₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	M₆₄×C₈₉	C₂
socle	C₂×C₈₉	C₄⋊C₁₆
prime radical	C₂²×C₈₉	M₃₂
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	M₆₄	D₈₉
hypocenter	C₈₉	#1422
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
27. C₈₉	#1422	semidirect

Maximal subgroups

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

subgroup	index
#19151432	2
C₁₆×Dic₈₉	2
M₆₄×C₈₉	2
#1422	89