Finite Group Databasebeta

← #19144201

Subgroups — #19144201

Order 5504.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#13063345C211yesmaximal, characteristic, complemented
2C22×#10621877C211yesmaximal, characteristic, complemented
3#14583410C211yesmaximal, characteristic, complemented
4#14583155C212yesmaximal, complemented
5#14583150C212yesmaximal, complemented
6#14583147C212yesmaximal, complemented
7#14583143C212yesmaximal, complemented
8#14582935C211yesmaximal, characteristic, complemented
9#14582895C211yesmaximal, characteristic, complemented
10#14582893C211yesmaximal, characteristic, complemented
11C43×#525C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13#13063345—24no—
14C2×#10621885C2211yescharacteristic, complemented
15C2×#10621883C2211yescharacteristic, complemented
16C2×#10621884C2211yescharacteristic, complemented
17C2×#10621882C2211yescharacteristic, complemented
18C2×#10621877—24no—
19C2×#10621877C2212yes—
20C2×#10621877C2212yes—
21C22×C43⋊C8C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063308—21no—
24#13063304C2212yes—
25#13063299C2212yes—
26#13063294—21no—
27C4×C22⋊D43—22no—
28#13063284C2211yescharacteristic
29#13063258C2212yescomplemented
30#13063256C2212yescomplemented
31#13063249C2212yescomplemented
32#13063248C2212yescomplemented
33#13063246C2212yescomplemented
34#13063245C2212yescomplemented
35C2×#41×C43C2211yescharacteristic
36C23×C4×C43C2211yescharacteristic
37#123×C43—21no—
38C22⋊Q8×C43C2212yes—
39#121×C43C2212yes—
40#120×C43—21no—
41C4×D4×C43—22no—
42#117×C43C2211yescharacteristic
43C24×C43D411yescharacteristic
44#41×C43—22no—
45#41×C43—22no—
46C2×Q8×C43C2311yescharacteristic
47C2×D4×C43—22no—
48C2×D4×C43—21no—
49C2×D4×C43C2311yescharacteristic
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—21no—
53C22×C4×C43D412yes—
54C22×C4×C43D411yescharacteristic
55C22×C4×C43C2312yes—
56C22×C4×C43C2311yescharacteristic
57C2×C22⋊D43—22no—
58C2×C22⋊D43—21no—
59#10621898—22no—
60#10621898—22no—
61C2×D172C2311yescharacteristic
62C2×C4×D43—21no—
63C2×Dic86C2311yescharacteristic
64C4⋊C4×C43—22no—
65C4⋊C4×C43C2312yes—
66C22⋊C4×C43—22no—
67C22⋊C4×C43—21no—
68C22⋊C4×C43—22no—
69C42×C43—21no—
70C22⋊Dic43—21no—
71C22⋊Dic43—22no—
72#10621885—22no—
73#10621884—22no—
74#10621883—22no—
75#10621882—22no—
76(C2×D43)⋊C4—22no—
77C4⋊Dic43C2312yes—
78Dic43⋊C4—22no—
79C4×Dic43—21no—
80#10621877—24no—
81#10621877—24no—
82C2×C43⋊C8—22no—
83C2×C43⋊C8D414yescomplemented
84C2×C43⋊C8C2312yes—
85C2×C43⋊C8C2311yescharacteristic
86C2×C43⋊C8C2311yescharacteristic
87C23×C43—22no—
88C23×C43—21no—
89C23×C43—42no—
90C23×C43C2×D412yes—
91C23×C43C2×D411yescharacteristic
92C22×D43—21no—
93Q8×C43—21no—
94Q8×C43—21no—
95D4×C43—21no—
96D4×C43—21no—
97D4×C43—44no—
98D4×C43—42no—
99C2×C4×C43—22no—
100C2×C4×C43—24no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43—42no—
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D412yes—
108C2×C4×C43C2×D411yescharacteristic
109C2×C4×C43#4112yes—
110C2×C4×C43C2411yescharacteristic
111C22⋊D43—44no—
112C22⋊D43—42no—
113C2×Dic43—22no—
114C2×Dic43—21no—
115D172—21no—
116D172—21no—
117C4×D43—42no—
118Dic86—21no—
119Dic86—21no—
120C43⋊C8—22no—
121C43⋊C8C2×D412yes—
122C43⋊C8C2×D412yes—
123C22×C43—22no—
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—22no—
127C22×C43—44no—
128C22×C43—41no—
129C22×C43—42no—
130C22×C43#12112yes—
131C22×C43C22×D411yescharacteristic
132C2×D43—41no—
133C2×D43—42no—
134C4×C43—22no—
135C4×C43—41no—
136C4×C43—42no—
137C4×C43#12112yes—
138C4×C43C22×D411yescharacteristic
139C4×C43C2×#4111yescharacteristic
140Dic43—41no—
141Dic43—42no—
142#3054—431nomaximal, Sylow
143C2×C43—22no—
144C2×C43—42no—
145C2×C43—81no—
146C2×C43C2×#12111yescharacteristic
147C2×C43#57512yes—
148D43—81no—
149C2×#135—431no—
150C22×M16—431no—
151#525—431no—
152#525D4311yescharacteristic, complemented
153#470—432no—
154#469—432no—
155#468—432no—
156#468—432no—
157#427—431no—
158#416—431no—
159#416—431no—
160C43#305411yescharacteristic, complemented, Sylow
161C2×#41—431no—
162C2×#41C2×D4311yescharacteristic
163C23×C4C2×D4311yescharacteristic
164#135—864no—
165C2×Q16—431no—
166C2×SD16—431no—
167C2×SD16—431no—
168C2×D8—431no—
169C2×M16—432no—
170C2×M16—432no—
171C2×M16—864no—
172C22×C8—431no—
173C22×C8—431no—
174#123—21no—
175#123—861no—
176C22⋊Q8—432no—
177C22⋊Q8C2×D4312yes—
178#121—432no—
179#121C2×D4312yes—
180#120—21no—
181#120—861no—
182C4×D4—22no—
183C4×D4—862no—
184#117—431no—
185#117C2×D4311yescharacteristic
186#107—432no—
187#106—432no—
188#103—432no—
189#103—432no—
190#102—432no—
191#102—432no—
192C24C22⋊D4311yescharacteristic
193#41—22no—
194#41—22no—
195#41—862no—
196#41—862no—
197C2×Q8—431no—
198C2×Q8C22×D4311yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—431no—
202C2×D4—862no—
203C2×D4—861no—
204C2×D4C22×D4311yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—861no—
209C22×C4C22⋊D4311yescharacteristic
210C22×C4C22⋊D4312yes—
211C22×C4C22×D4312yes—
212C22×C4C22×D4311yescharacteristic
213Q16—862no—
214SD16—862no—
215SD16—862no—
216D8—862no—
217M16—864no—
218M16—864no—
219C2×C8—434no—
220C2×C8—431no—
221C2×C8—431no—
222C2×C8—432no—
223C2×C8—862no—
224C4⋊C4—22no—
225C4⋊C4—432no—
226C4⋊C4—862no—
227C4⋊C4C22×D4312yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—861no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C42—21no—
235C42—861no—
236C23—22no—
237C23—21no—
238C23—42no—
239C23—861no—
240C23C2×C22⋊D4312yes—
241C23C2×C22⋊D4311yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—861no—
245Q8—861no—
246D4—21no—
247D4—21no—
248D4—44no—
249D4—42no—
250D4—861no—
251D4—861no—
252D4—1724no—
253D4—1722no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—862no—
262C2×C4—861no—
263C2×C4—1722no—
264C2×C4D4×D4312yes—
265C2×C4#1062190012yes—
266C2×C4C2×C22⋊D4312yes—
267C2×C4C2×C22⋊D4311yescharacteristic
268C2×C4C23×D4311yescharacteristic
269C8—432no—
270C8—432no—
271C8—862no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—44no—
277C22—41no—
278C22—42no—
279C22—1721no—
280C22—1722no—
281C22#1306329712yes—
282C22C22×C22⋊D4311yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—1721no—
287C4—1722no—
288C4#1306329712yes—
289C4C2×D4×D4311yescharacteristic
290C4C2×#1062190011yescharacteristic
291C2—22no—
292C2—42no—
293C2—81no—
294C2—3441no—
295C2C2×#1306329711yescharacteristic
296C2#1458369712yes—
subgroupG/H
centerC2×C4C2×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#525C2
socleC22×C43C22×D4
hypercenter#525D43
hypocenterC43#3054
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#13063345C2semidirect
2. C22×#10621877C2semidirect
3. #14583410C2semidirect
4. #14583155C2semidirect
5. #14583150C2semidirect
6. #14583147C2semidirect
7. #14583143C2semidirect
8. #14582935C2semidirect
9. #14582895C2semidirect
10. #14582893C2semidirect
11. C43×#525C2semidirect
14. C2×#10621885C22semidirect
15. C2×#10621883C22semidirect
16. C2×#10621884C22semidirect
17. C2×#10621882C22semidirect
29. #13063258C22semidirect
30. #13063256C22semidirect
31. #13063249C22semidirect
32. #13063248C22semidirect
33. #13063246C22semidirect
34. #13063245C22semidirect
83. C2×C43⋊C8D4semidirect
152. #525D43semidirect
160. C43#3054semidirect