Subgroups — C₈₉×#7548 #36385396

Order 22784.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1425	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1424	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
5	#368×C₈₉	—	2	1	no	—
6	#366×C₈₉	—	2	1	no	—
7	C₆₄×C₈₉	C₄	1	2	yes	complemented
8	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
9	#108×C₈₉	—	4	1	no	—
10	#107×C₈₉	—	4	1	no	—
11	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₈₉	Q₈	1	1	yes	characteristic
13	M₁₆×C₈₉	—	8	1	no	—
14	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
15	C₄⋊C₄×C₈₉	—	8	1	no	—
16	C₁₆×C₈₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₈₉	—	16	1	no	—
19	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
20	C₈×C₈₉	—	16	1	no	—
21	C₈×C₈₉	#107	1	1	yes	characteristic
22	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
23	C₂²×C₈₉	SD₆₄	1	1	yes	characteristic
24	C₄×C₈₉	—	32	1	no	—
25	C₄×C₈₉	#366	1	1	yes	characteristic
26	C₄×C₈₉	SD₆₄	1	1	yes	characteristic
27	#7548	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₈₉	—	2	1	no	—
29	C₂×C₈₉	#1424	1	1	yes	characteristic
30	M₁₂₈	C₂×C₈₉	1	1	yes	characteristic
31	#1425	C₂×C₈₉	1	1	yes	characteristic
32	#1424	C₂×C₈₉	1	1	yes	characteristic
33	C₈₉	#7548	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃₂	C₂²×C₈₉	1	1	yes	characteristic
35	#368	—	2	1	no	—
36	#366	—	2	1	no	—
37	C₆₄	C₄×C₈₉	1	2	yes	complemented
38	C₂×C₁₆	D₄×C₈₉	1	1	yes	characteristic
39	#108	—	4	1	no	—
40	#107	—	4	1	no	—
41	C₃₂	C₂×C₄×C₈₉	1	1	yes	characteristic
42	C₃₂	Q₈×C₈₉	1	1	yes	characteristic
43	M₁₆	—	8	1	no	—
44	C₂×C₈	D₈×C₈₉	1	1	yes	characteristic
45	C₄⋊C₄	—	8	1	no	—
46	C₁₆	C₄⋊C₄×C₈₉	1	1	yes	characteristic
47	C₁₆	Q₁₆×C₈₉	1	1	yes	characteristic
48	C₂×C₄	—	16	1	no	—
49	C₂×C₄	D₁₆×C₈₉	1	1	yes	characteristic
50	C₈	—	16	1	no	—
51	C₈	#107×C₈₉	1	1	yes	characteristic
52	C₈	Q₃₂×C₈₉	1	1	yes	characteristic
53	C₂²	SD₆₄×C₈₉	1	1	yes	characteristic
54	C₄	—	32	1	no	—
55	C₄	#366×C₈₉	1	1	yes	characteristic
56	C₄	SD₆₄×C₈₉	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	C₈₉×#1424	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	#1424
commutator	C₃₂	C₂×C₄×C₈₉
Frattini, cosocle	C₂×C₃₂	C₂²×C₈₉
prime radical	C₂²×C₈₉	SD₆₄
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₂×C₄×C₈₉ ◁ C₂×C₈×C₈₉ ◁ C₂×C₁₆×C₈₉ ◁ C₂×C₃₂×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₆₄×C₈₉	C₄	semidirect
27. #7548	C₈₉	direct (N × H)
33. C₈₉	#7548	direct (N × H)
37. C₆₄	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×M₁₂₈	2
C₈₉×#1425	2
C₈₉×#1424	2
#7548	89

Subgroups — C89×#7548 #36385396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7548 #36385396