Finite Group Databasebeta

← #19144696

Subgroups — #19144696

Order 5504.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583454C211yesmaximal, characteristic, complemented
2C4×D4×D43C211yesmaximal, characteristic
3#14583236C212yesmaximal, complemented
4#14583176C211yesmaximal, characteristic, complemented
5#14583105C211yesmaximal, characteristic, complemented
6#14583104C211yesmaximal, characteristic, complemented
7#14583051C212yesmaximal
8#14582998C212yesmaximal, complemented
9#14582996C212yesmaximal, complemented
10#14582955C211yesmaximal, characteristic, complemented
11C43×#474C211yesmaximal, characteristic, complemented
12C2×D4×D43C2211yescharacteristic
13C22×C4×D43—21no—
14C2×#10621873C2212yes—
15C2×#10621883C2212yes—
16#13063325C2211yescharacteristic, complemented
17#13063316—21no—
18#13063305C2212yes—
19#13063301—21no—
20Q8×Dic43—21no—
21#13063290C2212yescomplemented
22C4×D172C2211yescharacteristic
23D4×Dic43C2211yescharacteristic
24#13063287C2211yescharacteristic
25C4×C22⋊D43—21no—
26(C22⋊D43)⋊C4—21no—
27#13063283—21no—
28C4⋊C4×D43C2211yescharacteristic
29C22⋊C4×D43—21no—
30C42×D43C2211yescharacteristic
31#13063258C2212yescomplemented
32C4⋊(C43⋊C8)C2211yescharacteristic, complemented
33#13063250C2212yescomplemented
34#13063248C2212yescomplemented
35#13063245C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063235C2212yescomplemented
38C4⋊Q8×C43C2211yescharacteristic, complemented
39C4×D4×C43C2211yescharacteristic
40#107×C43C2212yescomplemented
41C4⋊C8×C43C2211yescharacteristic, complemented
42#102×C43C2212yes—
43C23×D43—21no—
44C2×Q8×C43—21no—
45C2×D4×C43C2311yescharacteristic
46C22×C4×C43—21no—
47C2×C22⋊D43—21no—
48C22×Dic43—21no—
49D4×D43—22no—
50D4×D43—22no—
51C2×D172C2311yescharacteristic
52C2×C4×D43—21no—
53C2×C4×D43—21no—
54C2×C4×D43—21no—
55C2×C4×D43—44no—
56C2×C4×D43D411yescharacteristic
57C2×C4×D43D411yescharacteristic
58C2×C4×D43C2311yescharacteristic
59C2×Dic86C2312yes—
60C2×C8×C43C2312yes—
61C4⋊C4×C43—21no—
62C4⋊C4×C43C2312yes—
63C4⋊C4×C43C2311yescharacteristic
64C22⋊C4×C43—21no—
65C42×C43C2311yescharacteristic
66C22⋊Dic43—21no—
67#10621883—24no—
68(C2×D43)⋊C4—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—22no—
71C4⋊Dic43—21no—
72C4⋊Dic43—21no—
73C4⋊Dic43—22no—
74C4⋊Dic43C2311yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—22no—
77C4×Dic43—22no—
78C4×Dic43D411yescharacteristic
79C4×Dic43D411yescharacteristic
80C4×Dic43C2311yescharacteristic
81C2×C43⋊C8C2312yes—
82#10621873—24no—
83C23×C43—21no—
84C22×D43—24no—
85C22×D43—21no—
86C22×D43—42no—
87C22×D43—42no—
88C22×D43C2×D411yescharacteristic
89Q8×C43—42no—
90D4×C43—21no—
91D4×C43#4112yes—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—42no—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2411yescharacteristic
98C22⋊D43—24no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—42no—
102C2×Dic43C2×D411yescharacteristic
103C2×Dic43C2×D411yescharacteristic
104C2×Dic43C2×D411yescharacteristic
105D172—21no—
106D172#4112yes—
107C4×D43—22no—
108C4×D43—22no—
109C4×D43—21no—
110C4×D43—21no—
111C4×D43—42no—
112C4×D43—42no—
113C4×D43—42no—
114Dic86—22no—
115Dic86—22no—
116C8×C43—22no—
117C43⋊C8—22no—
118C22×C43—22no—
119C22×C43—41no—
120C22×C43—41no—
121C22×C43C22×D411yescharacteristic
122C2×D43—21no—
123C2×D43—21no—
124C2×D43—22no—
125C2×D43—48no—
126C2×D43—41no—
127C2×D43—41no—
128C2×D43#13712yes—
129C4×C43—21no—
130C4×C43—41no—
131C4×C43—42no—
132C4×C43AGL(1,ℤ/8)12yes—
133C4×C43C2×#4111yescharacteristic
134C4×C43C2×#4111yescharacteristic
135Dic43—21no—
136Dic43—21no—
137Dic43—21no—
138Dic43—42no—
139Dic43—41no—
140#3110—431nomaximal, Sylow
141C2×C43—42no—
142C2×C43#52511yescharacteristic
143C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C43C2×#13711yescharacteristic
145D43—22no—
146D43—42no—
147#533—431no—
148C2×C4×D4—431no—
149#484—432no—
150#474—431no—
151#474D4311yescharacteristic, complemented
152#461—431no—
153#461—431no—
154#450—432no—
155#440—432no—
156#440—432no—
157#432—431no—
158C43#311011yescharacteristic, complemented, Sylow
159C22×D4—431no—
160C23×C4—861no—
161C2×SD16—432no—
162C2×SD16—432no—
163C4⋊Q8—431no—
164C4⋊Q8C2×D4311yescharacteristic, complemented
165#125—861no—
166C22⋊Q8—432no—
167C22⋊Q8—861no—
168C4×Q8—432no—
169C4×Q8—861no—
170C4×D4—431no—
171C4×D4—431no—
172C4×D4—431no—
173C4×D4—861no—
174C4×D4—861no—
175C4×D4C2×D4311yescharacteristic
176#117—861no—
177C2×C4⋊C4—431no—
178C2×C22⋊C4—861no—
179C2×C42—431no—
180#107—432no—
181#107C2×D4312yescomplemented
182C4⋊C8—431no—
183C4⋊C8C2×D4311yescharacteristic, complemented
184#103—432no—
185#103—432no—
186#102—432no—
187#102C2×D4312yes—
188C22⋊C8—432no—
189#97—432no—
190C24—861no—
191C2×Q8—21no—
192C2×Q8—432no—
193C2×D4—431no—
194C2×D4—861no—
195C2×D4—862no—
196C2×D4—862no—
197C2×D4C22×D4311yescharacteristic
198C22×C4—21no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—431no—
202C22×C4—861no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—861no—
206C22×C4—1724no—
207SD16—864no—
208SD16—864no—
209C2×C8—432no—
210C2×C8C22×D4312yes—
211C4⋊C4—21no—
212C4⋊C4—431no—
213C4⋊C4—861no—
214C4⋊C4—862no—
215C4⋊C4—862no—
216C4⋊C4—861no—
217C4⋊C4—861no—
218C4⋊C4C22×D4312yes—
219C4⋊C4C22×D4311yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—861no—
222C22⋊C4—862no—
223C22⋊C4—861no—
224C22⋊C4—861no—
225C42—431no—
226C42—431no—
227C42—431no—
228C42—862no—
229C42C22×D4311yescharacteristic
230C23—21no—
231C23—431no—
232C23—864no—
233C23—861no—
234C23—1722no—
235C23—1722no—
236Q8—42no—
237Q8—862no—
238Q8—862no—
239D4—21no—
240D4—432no—
241D4—864no—
242D4—861no—
243D4#1062190212yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—431no—
248C2×C4—431no—
249C2×C4—431no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—861no—
254C2×C4—862no—
255C2×C4—861no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4D4×D4311yescharacteristic
261C2×C4D4×D4311yescharacteristic
262C2×C4C23×D4311yescharacteristic
263C8—22no—
264C8—862no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—432no—
269C22—861no—
270C22—861no—
271C22—862no—
272C22—1728no—
273C22—1721no—
274C22—1721no—
275C22C2×D4×D4311yescharacteristic
276C4—21no—
277C4—41no—
278C4—42no—
279C4—861no—
280C4—861no—
281C4—861no—
282C4—1722no—
283C4—1721no—
284C4#1306334912yes—
285C4#41×D4311yescharacteristic
286C4C2×#1062190211yescharacteristic
287C2—42no—
288C2—862no—
289C2—1722no—
290C2#1458341211yescharacteristic
291C2C2×#1306334911yescharacteristic
292C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3110
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583236C2semidirect
4. #14583176C2semidirect
5. #14583105C2semidirect
6. #14583104C2semidirect
8. #14582998C2semidirect
9. #14582996C2semidirect
10. #14582955C2semidirect
11. C43×#474C2semidirect
16. #13063325C22semidirect
21. #13063290C22semidirect
31. #13063258C22semidirect
32. C4⋊(C43⋊C8)C22semidirect
33. #13063250C22semidirect
34. #13063248C22semidirect
37. #13063235C22semidirect
38. C4⋊Q8×C43C22semidirect
40. #107×C43C22semidirect
41. C4⋊C8×C43C22semidirect
151. #474D43semidirect
158. C43#3110semidirect
164. C4⋊Q8C2×D43semidirect
181. #107C2×D43semidirect
183. C4⋊C8C2×D43semidirect