Subgroups — C₈₉×#8136 #36385984

Order 22784.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#97×C₈₉	C₂	1	3	yes	maximal
2	C₈₉×#1273	C₂	1	4	yes	maximal
3	C₂×#97×C₈₉	C₄	1	12	yes	—
4	C₂×C₄×C₈×C₈₉	C₂²	1	6	yes	—
5	C₄³×C₈₉	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₈₉	C₂×C₄	1	12	yes	—
7	C₂×C₄²×C₈₉	C₂×C₄	1	6	yes	—
8	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
9	#97×C₈₉	—	2	24	no	—
10	C₄×C₈×C₈₉	—	2	12	no	—
11	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
12	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
13	C₂×C₈×C₈₉	—	2	12	no	—
14	C₂×C₈×C₈₉	—	2	12	no	—
15	C₂×C₈×C₈₉	M₁₆	1	24	yes	—
16	C₄²×C₈₉	—	2	12	no	—
17	C₄²×C₈₉	#41	1	4	yes	—
18	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
19	C₂×C₄×C₈₉	—	2	12	no	—
20	C₂×C₄×C₈₉	#117	1	6	yes	—
21	C₂×C₄×C₈₉	C₂×M₁₆	1	12	yes	—
22	C₈×C₈₉	—	2	24	no	—
23	C₂²×C₈₉	#376	1	1	yes	characteristic
24	C₂²×C₈₉	C₄×M₁₆	1	6	yes	—
25	C₄×C₈₉	—	4	4	no	—
26	C₄×C₈₉	#432	1	12	yes	—
27	#8136	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₈₉	#1455	1	4	yes	—
29	C₂×C₈₉	#1745	1	3	yes	—
30	C₄×#97	C₂×C₈₉	1	3	yes	—
31	#1273	C₂×C₈₉	1	4	yes	—
32	C₈₉	#8136	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×#97	C₄×C₈₉	1	12	yes	—
34	C₂×C₄×C₈	C₂²×C₈₉	1	6	yes	—
35	C₄³	C₂²×C₈₉	1	1	yes	characteristic
36	C₂²×C₈	C₂×C₄×C₈₉	1	12	yes	—
37	C₂×C₄²	C₂×C₄×C₈₉	1	6	yes	—
38	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
39	#97	—	2	24	no	—
40	C₄×C₈	—	2	12	no	—
41	C₂²×C₄	C₄²×C₈₉	1	4	yes	—
42	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
43	C₂×C₈	—	2	12	no	—
44	C₂×C₈	—	2	12	no	—
45	C₂×C₈	M₁₆×C₈₉	1	24	yes	—
46	C₄²	—	2	12	no	—
47	C₄²	#41×C₈₉	1	4	yes	—
48	C₂³	C₂×C₄²×C₈₉	1	1	yes	characteristic
49	C₂×C₄	—	2	12	no	—
50	C₂×C₄	#117×C₈₉	1	6	yes	—
51	C₂×C₄	C₂×M₁₆×C₈₉	1	12	yes	—
52	C₈	—	2	24	no	—
53	C₂²	#376×C₈₉	1	1	yes	characteristic
54	C₂²	C₄×M₁₆×C₈₉	1	6	yes	—
55	C₄	—	4	4	no	—
56	C₄	#432×C₈₉	1	12	yes	—
57	C₂	C₈₉×#1455	1	4	yes	—
58	C₂	C₈₉×#1745	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₈₉	C₂³
commutator	C₂³	C₂×C₄²×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
socle, prime radical	C₂³×C₈₉	C₂×C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
27. #8136	C₈₉	direct (N × H)
32. C₈₉	#8136	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#97×C₈₉	2
C₈₉×#1273	2
#8136	89

Subgroups — C89×#8136 #36385984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#8136 #36385984