Finite Group Databasebeta

← #19135042

Subgroups — #19135042

Order 5504.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#14583411C211yesmaximal, characteristic
2C2×#13063282C211yesmaximal, characteristic, complemented
3C2×#13063253C211yesmaximal, characteristic, complemented
4C2×#13063251C211yesmaximal, characteristic, complemented
5#14582862C211yesmaximal, characteristic, complemented
6#14582658C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×C4×D43C2211yescharacteristic
10C2×#10621877C2211yescharacteristic
11#13063309—21no—
12#13063305C412yescomplemented
13#13063300C412yescomplemented
14#13063295—21no—
15C4×D172—22no—
16#13063282—22no—
17#13063282—22no—
18C2×Dic43⋊C4—21no—
19C2×(C2×D43)⋊C4—21no—
20C2×C4×Dic43C2211yescharacteristic
21#13063253—22no—
22#13063251—22no—
23(C2×D43)⋊C8—22no—
24C2×M16×C43C2211yescharacteristic
25#117×C43C2211yescharacteristic
26C2×C42×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C22×Dic43—21no—
32C22×Dic43D411yescharacteristic
33#10621898—21no—
34#10621898—21no—
35#10621898—21no—
36#10621898—21no—
37C2×D172—22no—
38C2×D172C2×C411yescharacteristic
39C2×C4×D43—21no—
40C2×C4×D43—21no—
41C2×C4×D43—21no—
42C2×C4×D43—21no—
43C2×C4×D43—21no—
44C2×C4×D43C2×C412yes—
45C2×C4×D43D412yes—
46C2×Dic86C2×C411yescharacteristic
47M16×C43—21no—
48M16×C43—21no—
49C2×C8×C43—21no—
50C4⋊C4×C43C2×C412yes—
51C22⋊C4×C43—21no—
52C42×C43—21no—
53C42×C43—21no—
54C42×C43D412yescomplemented
55(C2×D43)⋊C4—24no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—22no—
59Dic43⋊C4—24no—
60C4×Dic43—21no—
61C4×Dic43D412yescomplemented
62#10621877—21no—
63#10621877—21no—
64C2×C43⋊C8—21no—
65C23×C43C2×D411yescharacteristic
66C22×D43—21no—
67C22×D43—21no—
68C22×D43—21no—
69C22×D43—42no—
70C22×D43C22⋊C412yes—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—42no—
74C2×C4×C43C22×C411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43#4111yescharacteristic
79C2×C4×C43#4111yescharacteristic
80C22⋊D43—41no—
81C22⋊D43—41no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43—42no—
87C2×Dic43C22⋊C412yes—
88D172—21no—
89D172—21no—
90D172—44no—
91C4×D43—22no—
92C4×D43—22no—
93C4×D43—22no—
94C4×D43—22no—
95C4×D43—41no—
96C4×D43—41no—
97Dic86—21no—
98Dic86—21no—
99C8×C43—41no—
100C43⋊C8—41no—
101C22×C43—22no—
102C22×C43C2×C22⋊C411yescharacteristic
103C22×C43#12011yescharacteristic
104C22×C43#12311yescharacteristic
105C2×D43—22no—
106C2×D43—22no—
107C2×D43—22no—
108C2×D43—42no—
109C2×D43—42no—
110C2×D43—41no—
111C2×D43—42no—
112C4×C43—42no—
113C4×C43—42no—
114C4×C43C4×D411yescharacteristic
115C4×C43C4×D411yescharacteristic
116C4×C43#12111yescharacteristic
117C4×C43#12111yescharacteristic
118Dic43—22no—
119Dic43—42no—
120Dic43—41no—
121#1897—431nomaximal, Sylow
122C2×C43—21no—
123C2×C43—21no—
124C2×C43#38611yescharacteristic
125C2×C43#42112yes—
126D43—42no—
127D43—81no—
128#525—431no—
129C2×#117—431no—
130C2×#104—431no—
131C2×#104—431no—
132#407—431no—
133#339—431no—
134#339D4311yescharacteristic, complemented
135C43#189711yescharacteristic, complemented, Sylow
136C2×#41—431no—
137C23×C4—431no—
138C2×M16—431no—
139C2×M16C2×D4311yescharacteristic
140#123—861no—
141C22⋊Q8—432no—
142#121—432no—
143#120—861no—
144C4×D4—862no—
145#117—862no—
146#117—862no—
147#117C2×D4311yescharacteristic
148C2×C4⋊C4—861no—
149C2×C22⋊C4—861no—
150C2×C42—431no—
151C2×C42C2×D4311yescharacteristic
152#104—862no—
153#104—862no—
154C22⋊C8—862no—
155C24—431no—
156#41—861no—
157#41—861no—
158#41—861no—
159#41—861no—
160C2×Q8—431no—
161C2×D4—431no—
162C2×D4—862no—
163C2×D4—861no—
164C22×C4—21no—
165C22×C4—431no—
166C22×C4—432no—
167C22×C4—432no—
168C22×C4—861no—
169C22×C4—861no—
170C22×C4—861no—
171C22×C4—861no—
172C22×C4—861no—
173C22×C4—861no—
174C22×C4C22×D4311yescharacteristic
175M16—21no—
176M16—21no—
177M16—861no—
178M16—861no—
179C2×C8—21no—
180C2×C8—861no—
181C4⋊C4—862no—
182C4⋊C4—864no—
183C4⋊C4C4×D4312yes—
184C22⋊C4—21no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—864no—
188C42—21no—
189C42—21no—
190C42—432no—
191C42—861no—
192C42D17212yescomplemented
193C23—432no—
194C23—861no—
195C23—861no—
196C23—861no—
197C23—1722no—
198C23D4×D4311yescharacteristic
199Q8—861no—
200Q8—861no—
201D4—861no—
202D4—861no—
203D4—1724no—
204D4—1721no—
205D4—1721no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—432no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—1722no—
219C2×C4—1721no—
220C2×C4—1721no—
221C2×C4C2×C4×D4311yescharacteristic
222C2×C4C2×D17211yescharacteristic
223C2×C4#1062189811yescharacteristic
224C2×C4D4×D4311yescharacteristic
225C2×C4D4×D4311yescharacteristic
226C2×C4#1062190211yescharacteristic
227C8—41no—
228C8—1721no—
229C22—22no—
230C22—862no—
231C22—862no—
232C22—862no—
233C22—1722no—
234C22—1722no—
235C22—1722no—
236C22—1721no—
237C22C22⋊C4×D4311yescharacteristic
238C22#1306329511yescharacteristic
239C22#1306331011yescharacteristic
240C4—42no—
241C4—42no—
242C4—862no—
243C4—1722no—
244C4—1721no—
245C4#1306328711yescharacteristic
246C4C4×D17211yescharacteristic
247C4#1306329811yescharacteristic
248C4#1306330011yescharacteristic
249C2—21no—
250C2—21no—
251C2—3441no—
252C2—1722no—
253C2#1458277711yescharacteristic
254C2#1458291412yes—
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC22×C43C2×C22⋊C4
hypercenter#339D43
hypocenterC43#1897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#13063282C2semidirect
3. C2×#13063253C2semidirect
4. C2×#13063251C2semidirect
5. #14582862C2semidirect
6. #14582658C2semidirect
7. C43×#339C2semidirect
12. #13063305C4semidirect
13. #13063300C4semidirect
54. C42×C43D4semidirect
61. C4×Dic43D4semidirect
134. #339D43semidirect
135. C43#1897semidirect
192. C42D172semidirect