Finite Group Databasebeta

← #19135036

Subgroups — #19135036

Order 5504.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583410C211yesmaximal, characteristic
2C22×C4×Dic43C211yesmaximal, characteristic, complemented
3C2×#13063251C212yesmaximal, complemented
4#14582660C212yesmaximal, complemented
5C43×#407C211yesmaximal, characteristic, complemented
6C2×#10621898C2211yescharacteristic
7C23×Dic43—21no—
8#13063308—21no—
9#13063304C412yescomplemented
10#13063299C412yescomplemented
11#13063294—21no—
12C4×C22⋊D43—22no—
13#13063284C2211yescharacteristic
14C2×C4×Dic43—21no—
15C2×C4×Dic43—24no—
16C2×C4×Dic43C2212yes—
17#13063251—24no—
18C23×C4×C43C2211yescharacteristic
19C2×M16×C43C2212yes—
20C22⋊C8×C43—22no—
21C24×C43D411yescharacteristic
22C22×C4×C43—22no—
23C22×C4×C43—22no—
24C22×C4×C43C2×C412yes—
25C22×C4×C43D412yes—
26C22×C4×C43D411yescharacteristic
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—22no—
29C2×C22⋊D43—21no—
30C22×Dic43—24no—
31C22×Dic43—28no—
32C22×Dic43—22no—
33#10621898—22no—
34#10621898—22no—
35C2×D172C2×C411yescharacteristic, complemented
36C2×C4×D43—21no—
37C2×Dic86C2×C411yescharacteristic, complemented
38M16×C43—22no—
39M16×C43—22no—
40C2×C8×C43—22no—
41C22⋊Dic43—22no—
42C22⋊Dic43—21no—
43(C2×D43)⋊C4—22no—
44C4⋊Dic43C2×C412yescomplemented
45Dic43⋊C4—22no—
46C4×Dic43—24no—
47C4×Dic43—22no—
48C4×Dic43—21no—
49C4×Dic43D414yescomplemented
50C23×C43—24no—
51C23×C43—21no—
52C23×C43—21no—
53C23×C43C22⋊C412yes—
54C23×C43C2×D411yescharacteristic
55C22×D43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—24no—
59C2×C4×C43—24no—
60C2×C4×C43C22⋊C412yes—
61C2×C4×C43C22×C411yescharacteristic
62C2×C4×C43C2×D412yes—
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43#4112yes—
65C22⋊D43—44no—
66C22⋊D43—41no—
67C22⋊D43—41no—
68C2×Dic43—216no—
69C2×Dic43—28no—
70C2×Dic43—24no—
71C2×Dic43—22no—
72C2×Dic43—21no—
73D172—22no—
74C4×D43—42no—
75Dic86—22no—
76C8×C43—42no—
77C22×C43—24no—
78C22×C43—24no—
79C22×C43—22no—
80C22×C43—22no—
81C22×C43—22no—
82C22×C43#10414yescomplemented
83C22×C43C2×C22⋊C411yescharacteristic
84C22×C43#12011yescharacteristic
85C22×C43#12311yescharacteristic
86C2×D43—41no—
87C2×D43—42no—
88C4×C43—22no—
89C4×C43C4×D412yes—
90C4×C43#12112yes—
91Dic43—28no—
92Dic43—41no—
93Dic43—42no—
94#1896—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—24no—
97C2×C43—21no—
98C2×C43#38611yescharacteristic
99C2×C43C2×#10412yes—
100D43—81no—
101#525—431no—
102C22×C42—431no—
103C2×#104—432no—
104#407D4311yescharacteristic, complemented
105#339—432no—
106C43#189611yescharacteristic, complemented, Sylow
107C2×#41—431no—
108C23×C4—861no—
109C23×C4C2×D4311yescharacteristic
110C2×M16C2×D4312yes—
111#123—861no—
112C22⋊Q8—432no—
113#121—432no—
114#120—861no—
115C4×D4—862no—
116#117—431no—
117C2×C42—432no—
118C2×C42—864no—
119C2×C42—861no—
120#104—864no—
121C22⋊C8—22no—
122C24D17211yescharacteristic
123#41—862no—
124#41—862no—
125C2×Q8—431no—
126C2×D4—431no—
127C2×D4—862no—
128C2×D4—861no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—864no—
132C22×C4—868no—
133C22×C4—862no—
134C22×C4—861no—
135C22×C4C4×D4312yes—
136C22×C4D17211yescharacteristic
137C22×C4C22⋊D4312yes—
138C22×C4C22×D4311yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—432no—
143C4⋊C4—862no—
144C22⋊C4—862no—
145C22⋊C4—861no—
146C22⋊C4—862no—
147C42—434no—
148C42—864no—
149C42—862no—
150C42—861no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—861no—
155C23(C2×D43)⋊C412yes—
156C23C2×D17211yescharacteristic
157Q8—862no—
158D4—862no—
159D4—1724no—
160D4—1721no—
161D4—1721no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—8616no—
167C2×C4—868no—
168C2×C4—864no—
169C2×C4—862no—
170C2×C4—861no—
171C2×C4—1722no—
172C2×C4(C2×D43)⋊C412yes—
173C2×C4C2×C4×D4311yescharacteristic
174C2×C4D4×D4312yes—
175C2×C4#1062190012yes—
176C2×C4C2×C22⋊D4311yescharacteristic
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—1722no—
184C22—1721no—
185C22#1306325114yescomplemented
186C22C2×(C2×D43)⋊C411yescharacteristic
187C22#1306329511yescharacteristic
188C22#1306330911yescharacteristic
189C4—22no—
190C4—868no—
191C4—1722no—
192C4—1721no—
193C4(C22⋊D43)⋊C412yes—
194C4#1306329712yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—3441no—
199C2#1458277611yescharacteristic
200C2C2×#1306325112yes—
subgroupG/H
centerC2×C4C2×C22⋊D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#407C2
socleC22×C43C2×C22⋊C4
hypercenter#407D43
hypocenterC43#1896
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic43C2semidirect
3. C2×#13063251C2semidirect
4. #14582660C2semidirect
5. C43×#407C2semidirect
9. #13063304C4semidirect
10. #13063299C4semidirect
35. C2×D172C2×C4semidirect
37. C2×Dic86C2×C4semidirect
44. C4⋊Dic43C2×C4semidirect
49. C4×Dic43D4semidirect
82. C22×C43#104semidirect
104. #407D43semidirect
106. C43#1896semidirect
185. C22#13063251semidirect