Subgroups — C₈₉×#7330 #36385178

Order 22784.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#1397	C₂	1	2	yes	maximal
2	C₈₉×#1311	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₈₉	C₄	1	4	yes	—
4	C₄×C₁₆×C₈₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
6	C₈²×C₈₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₈₉	C₈	1	2	yes	—
8	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₈₉	C₈	1	2	yes	—
10	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
11	C₃₂×C₈₉	C₈	1	8	yes	complemented
12	C₂×C₈×C₈₉	—	2	2	no	—
13	C₂×C₈×C₈₉	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
16	C₁₆×C₈₉	—	2	2	no	—
17	C₁₆×C₈₉	C₂×C₈	1	4	yes	—
18	C₂×C₄×C₈₉	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄×C₈₉	M₃₂	1	2	yes	—
20	C₈×C₈₉	—	4	2	no	—
21	C₈×C₈₉	C₄×C₈	1	2	yes	—
22	C₈×C₈₉	M₃₂	1	2	yes	—
23	C₂²×C₈₉	#346	1	1	yes	characteristic
24	C₄×C₈₉	—	2	2	no	—
25	C₄×C₈₉	C₈²	1	1	yes	characteristic
26	C₄×C₈₉	#346	1	1	yes	characteristic
27	#7330	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₈₉	#1311	1	1	yes	characteristic
29	C₂×C₈₉	#1398	1	2	yes	—
30	#1397	C₂×C₈₉	1	2	yes	—
31	#1311	C₂×C₈₉	1	1	yes	characteristic
32	C₈₉	#7330	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃₂	C₄×C₈₉	1	4	yes	—
34	C₄×C₁₆	C₄×C₈₉	1	1	yes	characteristic
35	C₄×C₁₆	C₂²×C₈₉	1	1	yes	characteristic
36	C₈²	C₄×C₈₉	1	1	yes	characteristic
37	C₂×C₁₆	C₈×C₈₉	1	2	yes	—
38	C₂×C₁₆	C₂×C₄×C₈₉	1	2	yes	—
39	C₄×C₈	C₈×C₈₉	1	2	yes	—
40	C₄×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
41	C₃₂	C₈×C₈₉	1	8	yes	complemented
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	C₄²×C₈₉	1	1	yes	characteristic
44	C₂×C₈	C₂×C₈×C₈₉	1	1	yes	characteristic
45	C₄²	C₂×C₈×C₈₉	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	C₂×C₈×C₈₉	1	4	yes	—
48	C₂×C₄	C₄×C₈×C₈₉	1	1	yes	characteristic
49	C₂×C₄	M₃₂×C₈₉	1	2	yes	—
50	C₈	—	4	2	no	—
51	C₈	C₄×C₈×C₈₉	1	2	yes	—
52	C₈	M₃₂×C₈₉	1	2	yes	—
53	C₂²	#346×C₈₉	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₈²×C₈₉	1	1	yes	characteristic
56	C₄	#346×C₈₉	1	1	yes	characteristic
57	C₂	C₈₉×#1311	1	1	yes	characteristic
58	C₂	C₈₉×#1398	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₈₉	C₄²
commutator	C₄	C₈²×C₈₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₈₉
socle, prime radical	C₂²×C₈₉	#346
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₃₂×C₈₉	C₈	semidirect
27. #7330	C₈₉	direct (N × H)
32. C₈₉	#7330	direct (N × H)
41. C₃₂	C₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#1397	2
C₈₉×#1311	2
#7330	89

Subgroups — C89×#7330 #36385178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7330 #36385178