Group #36385293 — subgroups

Subgroups — C₈₉×#7445 #36385293

Order 22784.

132 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2247	C₂	1	1	yes	maximal, characteristic
2	C₈₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1371	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₈₉	—	2	1	no	—
5	C₂×Q₃₂×C₈₉	C₄	1	2	yes	—
6	#494×C₈₉	—	2	1	no	—
7	C₂×C₃₂×C₈₉	—	2	1	no	—
8	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
9	#335×C₈₉	—	2	1	no	—
10	C₂×Q₁₆×C₈₉	—	2	2	no	—
11	C₂×Q₁₆×C₈₉	—	4	1	no	—
12	C₄⋊Q₈×C₈₉	—	4	1	no	—
13	Q₃₂×C₈₉	—	4	2	no	—
14	Q₃₂×C₈₉	—	4	1	no	—
15	Q₃₂×C₈₉	—	4	1	no	—
16	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
18	C₄⋊C₈×C₈₉	—	4	1	no	—
19	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
20	C₃₂×C₈₉	—	4	1	no	—
21	C₂×Q₈×C₈₉	—	4	2	no	—
22	Q₁₆×C₈₉	—	4	2	no	—
23	Q₁₆×C₈₉	—	4	2	no	—
24	Q₁₆×C₈₉	—	8	2	no	—
25	C₂×C₈×C₈₉	—	8	1	no	—
26	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
28	C₄⋊C₄×C₈₉	—	8	1	no	—
29	C₄⋊C₄×C₈₉	—	8	1	no	—
30	C₄²×C₈₉	D₈	1	1	yes	characteristic
31	C₁₆×C₈₉	—	2	1	no	—
32	C₁₆×C₈₉	D₈	1	1	yes	characteristic
33	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
34	Q₈×C₈₉	—	8	2	no	—
35	Q₈×C₈₉	—	8	2	no	—
36	C₂×C₄×C₈₉	—	8	2	no	—
37	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
38	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
39	C₂×C₄×C₈₉	SD₃₂	1	1	yes	characteristic
40	C₈×C₈₉	—	2	1	no	—
41	C₈×C₈₉	—	16	1	no	—
42	C₈×C₈₉	#100	1	1	yes	characteristic
43	C₈×C₈₉	#102	1	1	yes	characteristic
44	C₂²×C₈₉	#357	1	1	yes	characteristic
45	C₄×C₈₉	—	2	1	no	—
46	C₄×C₈₉	—	16	2	no	—
47	C₄×C₈₉	#331	1	1	yes	characteristic
48	C₄×C₈₉	#361	1	1	yes	characteristic
49	C₄×C₈₉	SD₆₄	1	1	yes	characteristic
50	C₄×C₈₉	Q₆₄	1	1	yes	characteristic
51	#7445	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂×C₈₉	#1361	1	1	yes	characteristic
53	C₂×C₈₉	#1416	1	1	yes	characteristic
54	C₂×C₈₉	#1420	1	1	yes	characteristic
55	#2247	C₂×C₈₉	1	1	yes	characteristic
56	C₄⋊C₃₂	C₂×C₈₉	1	1	yes	characteristic
57	#1371	C₂×C₈₉	1	1	yes	characteristic
58	C₈₉	#7445	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×Q₃₂	—	2	1	no	—
60	C₂×Q₃₂	C₄×C₈₉	1	2	yes	—
61	#494	—	2	1	no	—
62	C₂×C₃₂	—	2	1	no	—
63	C₄×C₁₆	C₂²×C₈₉	1	1	yes	characteristic
64	#335	—	2	1	no	—
65	C₂×Q₁₆	—	2	2	no	—
66	C₂×Q₁₆	—	4	1	no	—
67	C₄⋊Q₈	—	4	1	no	—
68	Q₃₂	—	4	2	no	—
69	Q₃₂	—	4	1	no	—
70	Q₃₂	—	4	1	no	—
71	C₂×C₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
72	C₂×C₁₆	D₄×C₈₉	1	1	yes	characteristic
73	C₄⋊C₈	—	4	1	no	—
74	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
75	C₃₂	—	4	1	no	—
76	C₂×Q₈	—	4	2	no	—
77	Q₁₆	—	4	2	no	—
78	Q₁₆	—	4	2	no	—
79	Q₁₆	—	8	2	no	—
80	C₂×C₈	—	8	1	no	—
81	C₂×C₈	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
82	C₂×C₈	SD₁₆×C₈₉	1	1	yes	characteristic
83	C₄⋊C₄	—	8	1	no	—
84	C₄⋊C₄	—	8	1	no	—
85	C₄²	D₈×C₈₉	1	1	yes	characteristic
86	C₁₆	—	2	1	no	—
87	C₁₆	D₈×C₈₉	1	1	yes	characteristic
88	C₁₆	SD₁₆×C₈₉	1	1	yes	characteristic
89	Q₈	—	8	2	no	—
90	Q₈	—	8	2	no	—
91	C₂×C₄	—	8	2	no	—
92	C₂×C₄	#102×C₈₉	1	1	yes	characteristic
93	C₂×C₄	D₁₆×C₈₉	1	1	yes	characteristic
94	C₂×C₄	SD₃₂×C₈₉	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	16	1	no	—
97	C₈	#100×C₈₉	1	1	yes	characteristic
98	C₈	#102×C₈₉	1	1	yes	characteristic
99	C₂²	#357×C₈₉	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	16	2	no	—
102	C₄	#331×C₈₉	1	1	yes	characteristic
103	C₄	#361×C₈₉	1	1	yes	characteristic
104	C₄	SD₆₄×C₈₉	1	1	yes	characteristic
105	C₄	Q₆₄×C₈₉	1	1	yes	characteristic
106	C₂	C₈₉×#1361	1	1	yes	characteristic
107	C₂	C₈₉×#1416	1	1	yes	characteristic
108	C₂	C₈₉×#1420	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2247

C₂

yes

maximal, characteristic

C₈₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic

C₈₉×#1371

C₂

yes

maximal, characteristic

C₂×Q₃₂×C₈₉

—

C₂×Q₃₂×C₈₉

C₄

yes

—

#494×C₈₉

—

C₂×C₃₂×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₄⋊Q₈×C₈₉

—

Q₃₂×C₈₉

—

Q₃₂×C₈₉

—

Q₃₂×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₃₂×C₈₉

—

C₂×Q₈×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

SD₁₆

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

characteristic

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

SD₃₂

yes

characteristic

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

SD₆₄

yes

characteristic

C₄×C₈₉

Q₆₄

yes

characteristic

#7445

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

characteristic

C₄⋊C₃₂

C₂×C₈₉

yes

characteristic

#1371

C₂×C₈₉

yes

characteristic

C₈₉

#7445

yes

characteristic, direct product factor, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

C₄×C₈₉

yes

—

#494

—

C₂×C₃₂

—

C₄×C₁₆

C₂²×C₈₉

yes

characteristic

#335

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₂×C₄×C₈₉

yes

characteristic

C₂×C₁₆

D₄×C₈₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

D₄×C₈₉

yes

characteristic

C₃₂

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₈₉

yes

characteristic

C₂×C₈

SD₁₆×C₈₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₈×C₈₉

yes

characteristic

C₁₆

—

C₁₆

D₈×C₈₉

yes

characteristic

C₁₆

SD₁₆×C₈₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

#102×C₈₉

yes

characteristic

C₂×C₄

D₁₆×C₈₉

yes

characteristic

C₂×C₄

SD₃₂×C₈₉

yes

characteristic

C₈

—

C₈

—

C₈

#100×C₈₉

yes

characteristic

C₈

#102×C₈₉

yes

characteristic

C₂²

#357×C₈₉

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

#331×C₈₉

yes

characteristic

103

C₄

#361×C₈₉

yes

characteristic

104

C₄

SD₆₄×C₈₉

yes

characteristic

105

C₄

Q₆₄×C₈₉

yes

characteristic

106

C₂

C₈₉×#1361

yes

characteristic

107

C₂

C₈₉×#1416

yes

characteristic

108

C₂

C₈₉×#1420

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₈₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₈₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₈₉
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄²×C₈₉ ◁ C₄×C₈×C₈₉ ◁ C₄×C₁₆×C₈₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₈₉

#357

commutator

C₂×C₁₆

C₂×C₄×C₈₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₈₉

LCS

G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₈₉ ◁ C₄²×C₈₉ ◁ C₄×C₈×C₈₉ ◁ C₄×C₁₆×C₈₉ ◁ G

N	H ≅ G/N	type
51. #7445	C₈₉	direct (N × H)
58. C₈₉	#7445	direct (N × H)

H ≅ G/N

type

51. #7445

C₈₉

direct (N × H)

58. C₈₉

#7445

direct (N × H)

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

subgroup	index
C₈₉×#2247	2
C₈₉×C₄⋊C₃₂	2
C₈₉×#1371	2
#7445	89

subgroup

index

C₈₉×#2247

C₈₉×C₄⋊C₃₂

C₈₉×#1371

#7445

Subgroups — C₈₉×#7445 #36385293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#7445 #36385293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7445 #36385293