Group #36470811 — subgroups

Subgroups — #36470811

Order 22784.

310 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 163 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	#26020416	C₂	1	2	yes	maximal
2	#26018344	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667946	C₂²	1	4	yes	—
5	C₂×#15667944	—	2	2	no	—
6	#19151464	—	2	2	no	—
7	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
9	C₄×C₁₆×C₈₉	C₄	1	4	yes	complemented
10	C₂×C₄⋊Dic₈₉	—	2	4	no	—
11	#15667946	—	2	8	no	—
12	#15667944	—	4	4	no	—
13	#15667919	—	4	4	no	—
14	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
17	C₂×C₁₆×C₈₉	—	2	4	no	—
18	C₂×C₁₆×C₈₉	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₈₉	Q₈	1	2	yes	—
21	C₂²×Dic₈₉	—	4	4	no	—
22	C₄⋊Dic₈₉	—	4	4	no	—
23	C₄⋊Dic₈₉	—	4	4	no	—
24	C₂²×C₄×C₈₉	D₈	1	2	yes	—
25	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
26	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₈₉	SD₁₆	1	4	yes	—
28	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₈×C₈₉	#41	1	4	yes	—
31	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
32	C₄²×C₈₉	Q₁₆	1	2	yes	—
33	C₁₆×C₈₉	—	2	4	no	—
34	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
35	C₂×C₄×C₈₉	—	2	4	no	—
36	C₂×C₄×C₈₉	#107	1	4	yes	—
37	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₈₉	#124	1	2	yes	—
39	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
40	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
41	C₂×Dic₈₉	—	8	4	no	—
42	C₂×Dic₈₉	—	8	8	no	—
43	C₈×C₈₉	#106	1	4	yes	—
44	C₈×C₈₉	#117	1	2	yes	—
45	C₈×C₈₉	#125	1	2	yes	—
46	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
47	C₂²×C₈₉	#486	1	2	yes	—
48	C₂²×C₈₉	#508	1	4	yes	—
49	C₄×C₈₉	—	2	4	no	—
50	C₄×C₈₉	#382	1	1	yes	characteristic
51	C₄×C₈₉	C₂×#106	1	1	yes	characteristic
52	C₄×C₈₉	#487	1	2	yes	—
53	Dic₈₉	—	16	4	no	—
54	#12889	—	89	1	no	maximal, Sylow
55	C₂×C₈₉	#1834	1	1	yes	characteristic
56	C₂×C₈₉	#2158	1	2	yes	—
57	C₂×C₈₉	#2242	1	4	yes	—
58	C₂×C₄×C₁₆	D₈₉	1	1	yes	characteristic
59	#1846	—	89	2	no	—
60	#1380	—	89	4	no	—
61	C₈₉	#12889	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
63	C₂×#107	—	89	4	no	—
64	C₂×#106	—	178	2	no	—
65	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
66	#382	—	178	2	no	—
67	C₄×C₁₆	Dic₈₉	1	4	yes	complemented
68	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
69	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
70	C₂×C₄⋊C₄	—	178	4	no	—
71	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
72	C₂×C₁₆	—	2	4	no	—
73	C₂×C₁₆	C₂×Dic₈₉	1	4	yes	—
74	#107	—	178	8	no	—
75	#106	—	356	4	no	—
76	C₄×C₈	Dic₁₇₈	1	2	yes	—
77	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
78	#95	—	356	4	no	—
79	C₂²×C₄	—	356	4	no	—
80	C₂²×C₄	D₇₁₂	1	2	yes	—
81	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
82	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
83	C₂×C₈	#13083563	1	4	yes	—
84	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
85	C₂×C₈	C₂×Dic₁₇₈	1	1	yes	characteristic
86	C₂×C₈	#13083574	1	4	yes	—
87	C₄⋊C₄	—	356	4	no	—
88	C₄⋊C₄	—	356	4	no	—
89	C₄²	C₄⋊Dic₈₉	1	2	yes	—
90	C₄²	Dic₃₅₆	1	2	yes	—
91	C₁₆	—	2	4	no	—
92	C₂³	C₂×D₇₁₂	1	1	yes	characteristic
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	712	4	no	—
95	C₂×C₄	—	712	8	no	—
96	C₂×C₄	#15667946	1	4	yes	—
97	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
98	C₂×C₄	#15668000	1	2	yes	—
99	C₂×C₄	C₂×#13083563	1	2	yes	—
100	C₂×C₄	C₂×Dic₃₅₆	1	1	yes	characteristic
101	C₈	#15667944	1	4	yes	—
102	C₈	#15667971	1	2	yes	—
103	C₈	#15668004	1	2	yes	—
104	C₂²	C₂×#15667946	1	1	yes	characteristic
105	C₂²	#19151945	1	2	yes	—
106	C₂²	#19152030	1	4	yes	—
107	C₄	—	2	4	no	—
108	C₄	—	1424	4	no	—
109	C₄	#19151464	1	1	yes	characteristic
110	C₄	C₂×#15667944	1	1	yes	characteristic
111	C₄	#19151949	1	2	yes	—
112	C₂	#26020380	1	1	yes	characteristic
113	C₂	#26022036	1	2	yes	—
114	C₂	#26022484	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26020416

C₂

yes

maximal

#26018344

C₂

yes

maximal

C₂×C₄×C₁₆×C₈₉

C₂

yes

maximal, characteristic

C₂×#15667946

C₂²

yes

—

C₂×#15667944

—

#19151464

—

C₂²×C₁₆×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₄×C₁₆×C₈₉

C₄

yes

complemented

C₂×C₄⋊Dic₈₉

—

#15667946

—

#15667944

—

#15667919

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

Q₈

yes

—

C₂²×Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂²×C₄×C₈₉

D₈

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₄⋊C₄

yes

—

C₂×C₈×C₈₉

SD₁₆

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₄²×C₈₉

C₄⋊C₄

yes

—

C₄²×C₈₉

Q₁₆

yes

—

C₁₆×C₈₉

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#107

yes

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₉

#124

yes

—

C₂×C₄×C₈₉

C₂×SD₁₆

yes

—

C₂×C₄×C₈₉

C₂×Q₁₆

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

#106

yes

—

C₈×C₈₉

#117

yes

—

C₈×C₈₉

#125

yes

—

C₂²×C₈₉

C₂×#107

yes

characteristic

C₂²×C₈₉

#486

yes

—

C₂²×C₈₉

#508

yes

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#2242

yes

—

C₂×C₄×C₁₆

D₈₉

yes

characteristic

#1846

—

#1380

—

C₈₉

#12889

yes

characteristic, complemented, Sylow

C₂²×C₁₆

C₂×D₈₉

yes

—

C₂×#107

—

C₂×#106

—

178

—

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

#382

—

178

—

C₄×C₁₆

Dic₈₉

yes

complemented

C₂²×C₈

D₃₅₆

yes

characteristic

C₂²×C₈

C₂²×D₈₉

yes

characteristic

C₂×C₄⋊C₄

—

178

—

C₂×C₄²

D₃₅₆

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₈₉

yes

—

#107

—

178

—

#106

—

356

—

C₄×C₈

Dic₁₇₈

yes

—

C₄×C₈

C₂×Dic₈₉

yes

—

#95

—

356

—

C₂²×C₄

—

356

—

C₂²×C₄

D₇₁₂

yes

—

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

C₂×C₈

C₄⋊Dic₈₉

yes

—

C₂×C₈

#13083563

yes

—

C₂×C₈

C₂²×Dic₈₉

yes

characteristic

C₂×C₈

C₂×Dic₁₇₈

yes

characteristic

C₂×C₈

#13083574

yes

—

C₄⋊C₄

—

356

—

C₄⋊C₄

—

356

—

C₄²

C₄⋊Dic₈₉

yes

—

C₄²

Dic₃₅₆

yes

—

C₁₆

—

C₂³

C₂×D₇₁₂

yes

characteristic

C₂×C₄

—

C₂×C₄

—

712

—

C₂×C₄

—

712

—

C₂×C₄

#15667946

yes

—

C₂×C₄

C₂×C₄⋊Dic₈₉

yes

characteristic

C₂×C₄

#15668000

yes

—

C₂×C₄

C₂×#13083563

yes

—

100

C₂×C₄

C₂×Dic₃₅₆

yes

characteristic

101

C₈

#15667944

yes

—

102

C₈

#15667971

yes

—

103

C₈

#15668004

yes

—

104

C₂²

C₂×#15667946

yes

characteristic

105

C₂²

#19151945

yes

—

106

C₂²

#19152030

yes

—

107

C₄

—

108

C₄

—

1424

—

109

C₄

#19151464

yes

characteristic

110

C₄

C₂×#15667944

yes

characteristic

111

C₄

#19151949

yes

—

112

C₂

#26020380

yes

characteristic

113

C₂

#26022036

yes

—

114

C₂

#26022484

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₁₂
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×C₄×C₁₆×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×D₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×C₄×C₁₆	D₈₉
hypocenter	C₈₉	#12889
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂³

C₂×D₇₁₂

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂×C₄×C₁₆×C₈₉

C₂

socle, prime radical

C₂³×C₈₉

C₂×D₈

cosocle

C₂²×C₈×C₈₉

C₂³

hypercenter

C₂×C₄×C₁₆

D₈₉

hypocenter

C₈₉

#12889

LCS

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
9. C₄×C₁₆×C₈₉	C₄	semidirect
61. C₈₉	#12889	semidirect
67. C₄×C₁₆	Dic₈₉	semidirect

H ≅ G/N

type

9. C₄×C₁₆×C₈₉

C₄

semidirect

61. C₈₉

#12889

semidirect

67. C₄×C₁₆

Dic₈₉

semidirect

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

subgroup	index
#26020416	2
#26018344	2
C₂×C₄×C₁₆×C₈₉	2
#12889	89

subgroup

index

#26020416

#26018344

C₂×C₄×C₁₆×C₈₉

#12889

Subgroups — #36470811

Conjugacy classes of subgroups

Complements

Maximal subgroups