Group #36441992 — subgroups

Subgroups — #36441992

Order 22784.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₂²⋊#15667918	C₂	1	1	yes	maximal, characteristic
2	#26018346	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2216	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667948	—	2	1	no	—
5	C₂×#15667918	—	2	1	no	—
6	C₂×Q₃₂×C₈₉	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
8	#467×C₈₉	—	2	1	no	—
9	#366×C₈₉	C₄	1	1	yes	characteristic
10	#358×C₈₉	—	2	1	no	—
11	C₂×#13083558	—	4	1	no	—
12	#15667948	—	2	2	no	—
13	#15667948	—	4	1	no	—
14	#15667918	—	4	1	no	—
15	C₂×Q₁₆×C₈₉	—	2	1	no	—
16	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
17	C₂²⋊Q₈×C₈₉	—	4	1	no	—
18	Q₃₂×C₈₉	—	4	1	no	—
19	C₂×C₁₆×C₈₉	—	4	1	no	—
20	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
22	#107×C₈₉	—	2	1	no	—
23	#103×C₈₉	—	4	1	no	—
24	#13083558	—	4	2	no	—
25	#13083558	—	8	1	no	—
26	C₂×#10623494	—	8	1	no	—
27	C₂×Q₈×C₈₉	—	4	1	no	—
28	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
29	Q₁₆×C₈₉	—	4	1	no	—
30	Q₁₆×C₈₉	—	4	1	no	—
31	C₂×C₈×C₈₉	—	2	1	no	—
32	C₂×C₈×C₈₉	—	2	1	no	—
33	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
35	C₄⋊C₄×C₈₉	—	4	1	no	—
36	C₄⋊C₄×C₈₉	—	8	1	no	—
37	C₂²⋊C₄×C₈₉	—	8	1	no	—
38	C₁₆×C₈₉	—	2	1	no	—
39	C₁₆×C₈₉	—	2	1	no	—
40	C₂³×C₈₉	SD₃₂	1	1	yes	characteristic
41	Q₈×C₈₉	—	8	1	no	—
42	Q₈×C₈₉	—	8	1	no	—
43	C₂×C₄×C₈₉	—	2	1	no	—
44	C₂×C₄×C₈₉	—	2	1	no	—
45	C₂×C₄×C₈₉	—	8	1	no	—
46	C₂×C₄×C₈₉	—	8	1	no	—
47	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
48	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
49	C₈×C₈₉	—	2	1	no	—
50	C₈×C₈₉	#99	1	1	yes	characteristic
51	C₈×C₈₉	#104	1	1	yes	characteristic
52	#10623494	—	8	2	no	—
53	C₂²×C₈₉	—	2	1	no	—
54	C₂²×C₈₉	—	2	1	no	—
55	C₂²×C₈₉	—	2	1	no	—
56	C₂²×C₈₉	#357	1	1	yes	characteristic
57	C₄×C₈₉	—	2	1	no	—
58	C₄×C₈₉	—	16	1	no	—
59	C₄×C₈₉	—	16	1	no	—
60	C₄×C₈₉	#327	1	1	yes	characteristic
61	C₄×C₈₉	#360	1	1	yes	characteristic
62	#7421	—	89	1	no	maximal, Sylow
63	C₂×C₈₉	—	4	1	no	—
64	C₂×C₈₉	#1347	1	1	yes	characteristic
65	C₂×C₈₉	#1417	1	1	yes	characteristic
66	C₂×C₈₉	#1420	1	1	yes	characteristic
67	#2216	D₈₉	1	1	yes	characteristic
68	C₂²⋊C₃₂	—	89	1	no	—
69	#1381	—	89	1	no	—
70	C₈₉	#7421	1	1	yes	characteristic, complemented, Sylow
71	C₂×Q₃₂	Dic₈₉	1	1	yes	characteristic
72	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
73	#467	—	2	1	no	—
74	C₂×#108	—	178	1	no	—
75	C₂×C₃₂	—	178	1	no	—
76	#366	Dic₈₉	1	1	yes	characteristic
77	#358	—	2	1	no	—
78	C₂×Q₁₆	—	2	1	no	—
79	C₂×M₁₆	—	356	1	no	—
80	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
81	C₂²⋊Q₈	—	4	1	no	—
82	Q₃₂	—	4	1	no	—
83	C₂×C₁₆	—	4	1	no	—
84	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
85	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
86	#108	—	356	1	no	—
87	#108	—	178	2	no	—
88	#107	—	2	1	no	—
89	#103	—	4	1	no	—
90	C₃₂	—	356	1	no	—
91	C₂×Q₈	—	4	1	no	—
92	C₂²×C₄	#13083559	1	1	yes	characteristic
93	Q₁₆	—	4	1	no	—
94	Q₁₆	—	4	1	no	—
95	M₁₆	—	356	2	no	—
96	M₁₆	—	712	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	712	1	no	—
100	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
101	C₂×C₈	#13083562	1	1	yes	characteristic
102	C₄⋊C₄	—	4	1	no	—
103	C₄⋊C₄	—	8	1	no	—
104	C₂²⋊C₄	—	8	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	—	2	1	no	—
107	C₂³	#15667956	1	1	yes	characteristic
108	Q₈	—	8	1	no	—
109	Q₈	—	8	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	8	1	no	—
113	C₂×C₄	—	8	1	no	—
114	C₂×C₄	#15667933	1	1	yes	characteristic
115	C₂×C₄	#15667953	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	712	2	no	—
118	C₈	#15667927	1	1	yes	characteristic
119	C₈	#15667939	1	1	yes	characteristic
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	#19151399	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	16	1	no	—
126	C₄	—	16	1	no	—
127	C₄	#19151332	1	1	yes	characteristic
128	C₄	#19151408	1	1	yes	characteristic
129	C₂	—	4	1	no	—
130	C₂	#26018261	1	1	yes	characteristic
131	C₂	#26018436	1	1	yes	characteristic
132	C₂	#26018445	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²⋊#15667918

C₂

yes

maximal, characteristic

#26018346

C₂

yes

maximal, characteristic

C₈₉×#2216

C₂

yes

maximal, characteristic

C₂×#15667948

—

C₂×#15667918

—

C₂×Q₃₂×C₈₉

C₄

yes

characteristic

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

#467×C₈₉

—

#366×C₈₉

C₄

yes

characteristic

#358×C₈₉

—

—

—

—

—

C₂×Q₁₆×C₈₉

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²⋊Q₈×C₈₉

—

Q₃₂×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

#107×C₈₉

—

#103×C₈₉

—

#13083558

—

#13083558

—

C₂×#10623494

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

D₈

yes

characteristic

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₁₆×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

SD₃₂

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

characteristic

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#357

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

D₈₉

yes

characteristic

C₂²⋊C₃₂

—

#1381

—

C₈₉

#7421

yes

characteristic, complemented, Sylow

C₂×Q₃₂

Dic₈₉

yes

characteristic

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

#467

—

C₂×#108

—

178

—

C₂×C₃₂

—

178

—

#366

Dic₈₉

yes

characteristic

#358

—

C₂×Q₁₆

—

C₂×M₁₆

—

356

—

C₂²×C₈

C₂²⋊D₈₉

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₈₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

#108

—

356

—

#108

—

178

—

#107

—

#103

—

C₃₂

—

356

—

C₂×Q₈

—

C₂²×C₄

#13083559

yes

characteristic

Q₁₆

—

Q₁₆

—

M₁₆

—

356

—

M₁₆

—

712

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

712

—

100

C₂×C₈

C₂²⋊Dic₈₉

yes

characteristic

101

C₂×C₈

#13083562

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₁₆

—

106

C₁₆

—

107

C₂³

#15667956

yes

characteristic

108

Q₈

—

109

Q₈

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#15667933

yes

characteristic

115

C₂×C₄

#15667953

yes

characteristic

116

C₈

—

117

C₈

—

712

—

118

C₈

#15667927

yes

characteristic

119

C₈

#15667939

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#19151399

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

#19151332

yes

characteristic

128

C₄

#19151408

yes

characteristic

129

C₂

—

130

C₂

#26018261

yes

characteristic

131

C₂

#26018436

yes

characteristic

132

C₂

#26018445

yes

characteristic

	subgroup	G/H
center	C₂²	#19151399
commutator	C₂×C₁₆×C₈₉	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₈₉
Fitting	C₈₉×#2216	C₂
socle	C₂²×C₈₉	#357
prime radical	C₂³×C₈₉	SD₃₂
cosocle	C₂²×C₁₆×C₈₉	C₂²
hypercenter	#2216	D₈₉
hypocenter	C₈₉	#7421
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #2216

subgroup

G/H

center

C₂²

#19151399

commutator

C₂×C₁₆×C₈₉

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₈₉

Fitting

C₈₉×#2216

C₂

socle

C₂²×C₈₉

#357

prime radical

C₂³×C₈₉

SD₃₂

cosocle

C₂²×C₁₆×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂×C₁₆×C₈₉ ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #2216

N	H ≅ G/N	type
70. C₈₉	#7421	semidirect

H ≅ G/N

type

70. C₈₉

#7421

semidirect

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

subgroup	index
C₂²⋊#15667918	2
#26018346	2
C₈₉×#2216	2
#7421	89

subgroup

index

C₂²⋊#15667918

#26018346

C₈₉×#2216

#7421

Subgroups — #36441992

Conjugacy classes of subgroups

Complements

Maximal subgroups