Group #36554673 — subgroups

Subgroups — #1840×D₈₉ #36554673

Order 22784.

894 conjugacy classes of subgroups; only the 283 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 283 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	#376×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#26020397	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020396	C₂	1	6	yes	maximal, complemented
4	#336×D₈₉	C₂	1	6	yes	maximal
5	C₈₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₈₉	C₂²	1	4	yes	—
7	C₂×C₄²×D₈₉	C₂²	1	3	yes	—
8	#19151444	C₂²	1	3	yes	—
9	#19151443	C₄	1	4	yes	—
10	#95×D₈₉	C₄	1	4	yes	—
11	#19151353	C₂²	1	6	yes	—
12	#19151352	C₂²	1	12	yes	—
13	#376×C₈₉	C₂²	1	1	yes	characteristic
14	#336×C₈₉	C₂²	1	6	yes	—
15	C₂²×C₄×D₈₉	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
17	C₂²×#10623494	C₂³	1	4	yes	—
18	C₂×C₈×D₈₉	—	2	24	no	—
19	C₂×C₄×Dic₈₉	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₈₉	C₂³	1	3	yes	—
21	C₄²×D₈₉	—	2	12	no	—
22	#15667919	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
24	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
25	#95×C₈₉	C₂×C₄	1	4	yes	—
26	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
27	C₂²×Dic₈₉	C₂²×C₄	1	6	yes	—
28	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×D₈₉	—	2	12	no	—
30	C₂×C₄×D₈₉	—	2	24	no	—
31	C₂×C₄×D₈₉	#41	1	12	yes	—
32	C₂×#10623494	—	2	12	no	—
33	C₈×D₈₉	—	4	16	no	—
34	C₄×Dic₈₉	—	2	6	no	—
35	C₄×Dic₈₉	—	2	12	no	—
36	C₂²×C₄×C₈₉	C₂²×C₄	1	6	yes	—
37	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
38	C₂×C₈×C₈₉	—	2	12	no	—
39	C₄²×C₈₉	—	2	6	no	—
40	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
41	C₂²×D₈₉	#117	1	6	yes	—
42	C₂²×D₈₉	#131	1	8	yes	—
43	C₂×C₄×C₈₉	—	2	6	no	—
44	C₂×C₄×C₈₉	—	2	12	no	—
45	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
46	C₂×Dic₈₉	—	2	6	no	—
47	C₂×Dic₈₉	—	2	12	no	—
48	C₂×Dic₈₉	#117	1	6	yes	—
49	C₄×D₈₉	—	4	24	no	—
50	C₄×D₈₉	#126	1	16	yes	—
51	C₈×C₈₉	—	4	4	no	—
52	#10623494	—	4	4	no	—
53	C₂²×C₈₉	C₂×#117	1	3	yes	—
54	C₂²×C₈₉	C₂×#131	1	4	yes	—
55	C₂×D₈₉	#383	1	4	yes	—
56	C₂×D₈₉	#433	1	24	yes	—
57	C₄×C₈₉	—	4	6	no	—
58	C₄×C₈₉	C₂×#126	1	4	yes	—
59	Dic₈₉	—	4	6	no	—
60	Dic₈₉	#383	1	4	yes	—
61	C₂×#1840	—	89	1	no	maximal, Sylow
62	C₂×C₈₉	C₂×#383	1	1	yes	characteristic
63	C₂×C₈₉	C₂×#433	1	6	yes	—
64	D₈₉	#1840	1	8	yes	direct product factor
65	C₂×#376	—	89	1	no	—
66	#1840	—	89	1	no	—
67	#1840	—	89	6	no	—
68	#1840	D₈₉	1	1	yes	characteristic, direct product factor
69	C₂×#336	—	89	6	no	—
70	C₈₉	C₂×#1840	1	1	yes	characteristic, complemented, Sylow
71	C₂³×C₈	—	89	4	no	—
72	C₂²×C₄²	—	89	3	no	—
73	#376	—	89	3	no	—
74	#376	—	89	4	no	—
75	#376	C₂×D₈₉	1	1	yes	characteristic
76	C₂×#95	—	89	4	no	—
77	#336	—	89	12	no	—
78	#336	—	89	6	no	—
79	#336	C₂×D₈₉	1	6	yes	—
80	C₂³×C₄	—	89	1	no	—
81	C₂³×C₄	—	89	6	no	—
82	C₂²×C₈	—	89	4	no	—
83	C₂²×C₈	—	178	24	no	—
84	C₂²×C₈	C₂²×D₈₉	1	4	yes	—
85	C₂×C₄²	—	89	6	no	—
86	C₂×C₄²	—	89	3	no	—
87	C₂×C₄²	—	178	12	no	—
88	C₂×C₄²	C₂²×D₈₉	1	3	yes	—
89	#95	—	89	12	no	—
90	#95	C₄×D₈₉	1	4	yes	—
91	C₂⁴	—	89	1	no	—
92	C₂²×C₄	—	89	1	no	—
93	C₂²×C₄	—	89	12	no	—
94	C₂²×C₄	—	89	6	no	—
95	C₂²×C₄	—	178	12	no	—
96	C₂²×C₄	—	178	24	no	—
97	C₂²×C₄	C₂×C₄×D₈₉	1	6	yes	—
98	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
99	C₂×C₈	—	2	12	no	—
100	C₂×C₈	—	356	16	no	—
101	C₂×C₈	—	178	12	no	—
102	C₄²	—	2	6	no	—
103	C₄²	—	178	12	no	—
104	C₄²	—	178	6	no	—
105	C₂³	—	89	6	no	—
106	C₂³	—	89	8	no	—
107	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
108	C₂×C₄	—	2	6	no	—
109	C₂×C₄	—	2	12	no	—
110	C₂×C₄	—	89	6	no	—
111	C₂×C₄	—	89	16	no	—
112	C₂×C₄	—	356	24	no	—
113	C₂×C₄	—	178	6	no	—
114	C₂×C₄	—	178	12	no	—
115	C₂×C₄	#41×D₈₉	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	356	4	no	—
118	C₂²	—	89	24	no	—
119	C₂²	—	89	4	no	—
120	C₂²	#117×D₈₉	1	3	yes	—
121	C₂²	#131×D₈₉	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	89	4	no	—
124	C₄	—	356	6	no	—
125	C₄	#126×D₈₉	1	4	yes	—
126	C₂	—	89	8	no	—
127	C₂	#383×D₈₉	1	1	yes	characteristic
128	C₂	#433×D₈₉	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#376×D₈₉

C₂

yes

maximal, characteristic

#26020397

C₂

yes

maximal, characteristic, complemented

#26020396

C₂

yes

maximal, complemented

#336×D₈₉

C₂

yes

maximal

C₈₉×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₉

C₂²

yes

—

C₂×C₄²×D₈₉

C₂²

yes

—

#19151444

C₂²

yes

—

#19151443

C₄

yes

—

#95×D₈₉

C₄

yes

—

#19151353

C₂²

yes

—

#19151352

C₂²

yes

—

#376×C₈₉

C₂²

yes

characteristic

#336×C₈₉

C₂²

yes

—

C₂²×C₄×D₈₉

C₂×C₄

yes

—

C₂²×C₄×D₈₉

C₂³

yes

characteristic

C₂²×#10623494

C₂³

yes

—

C₂×C₈×D₈₉

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂³

yes

—

C₄²×D₈₉

—

#15667919

C₂×C₄

yes

—

C₂²×C₈×C₈₉

C₂³

yes

—

C₂×C₄²×C₈₉

C₂³

yes

—

#95×C₈₉

C₂×C₄

yes

—

C₂³×D₈₉

C₂²×C₄

yes

characteristic

C₂²×Dic₈₉

C₂²×C₄

yes

—

C₂²×Dic₈₉

C₂²×C₄

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

#41

yes

—

C₂×#10623494

—

C₈×D₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂²×C₄×C₈₉

C₂⁴

yes

characteristic

C₂×C₈×C₈₉

—

C₄²×C₈₉

—

C₂³×C₈₉

C₂³×C₄

yes

characteristic

C₂²×D₈₉

#117

yes

—

C₂²×D₈₉

#131

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×#41

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#117

yes

—

C₄×D₈₉

—

C₄×D₈₉

#126

yes

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

C₂×#117

yes

—

C₂²×C₈₉

C₂×#131

yes

—

C₂×D₈₉

#383

yes

—

C₂×D₈₉

#433

yes

—

C₄×C₈₉

—

C₄×C₈₉

C₂×#126

yes

—

Dic₈₉

—

Dic₈₉

#383

yes

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

D₈₉

#1840

yes

direct product factor

—

—

—

D₈₉

yes

characteristic, direct product factor

C₂×#336

—

C₈₉

C₂×#1840

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₈₉

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₈₉

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

178

—

C₂²×C₈

C₂²×D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

178

—

C₂×C₄²

C₂²×D₈₉

yes

—

#95

—

#95

C₄×D₈₉

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

178

—

C₂²×C₄

—

178

—

C₂²×C₄

C₂×C₄×D₈₉

yes

—

C₂²×C₄

C₂³×D₈₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

356

—

101

C₂×C₈

—

178

—

102

C₄²

—

103

C₄²

—

178

—

104

C₄²

—

178

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×C₄×D₈₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

356

—

113

C₂×C₄

—

178

—

114

C₂×C₄

—

178

—

115

C₂×C₄

#41×D₈₉

yes

—

116

C₈

—

117

C₈

—

356

—

118

C₂²

—

119

C₂²

—

120

C₂²

#117×D₈₉

yes

—

121

C₂²

#131×D₈₉

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

356

—

125

C₄

#126×D₈₉

yes

—

126

C₂

—

127

C₂

#383×D₈₉

yes

characteristic

128

C₂

#433×D₈₉

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1840	C₂
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1840	D₈₉
hypocenter	C₈₉	C₂×#1840
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₈₉

commutator, socle

C₂³×C₈₉

C₂³×C₄

Fitting

C₈₉×#1840

C₂

prime radical

C₂³×D₈₉

C₂²×C₄

cosocle

C₂²×C₄×C₈₉

C₂⁴

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #26020397	C₂	semidirect
3. #26020396	C₂	semidirect
5. C₈₉×#1840	C₂	semidirect
64. D₈₉	#1840	direct (N × H)
68. #1840	D₈₉	direct (N × H)
70. C₈₉	C₂×#1840	semidirect

H ≅ G/N

type

2. #26020397

C₂

semidirect

3. #26020396

C₂

semidirect

5. C₈₉×#1840

C₂

semidirect

64. D₈₉

#1840

direct (N × H)

68. #1840

D₈₉

direct (N × H)

70. C₈₉

C₂×#1840

semidirect

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

subgroup	index
#376×D₈₉	2
#26020397	2
#26020396	2
#336×D₈₉	2
C₈₉×#1840	2
C₂×#1840	89

subgroup

index

#376×D₈₉

#26020397

#26020396

#336×D₈₉

C₈₉×#1840

C₂×#1840

Subgroups — #1840×D₈₉ #36554673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1840×D89 #36554673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1840×D₈₉ #36554673