Finite Group Databasebeta

← #19144545

Subgroups — #19144545

Order 5504.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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×#13063305C211yesmaximal, characteristic
2#117×D43C211yesmaximal, characteristic
3#14583243C212yesmaximal, complemented
4#14583242C212yesmaximal, complemented
5#14583236C212yesmaximal, complemented
6#14583231C212yesmaximal, complemented
7#14582939C211yesmaximal, characteristic, complemented
8#14582909C211yesmaximal, characteristic, complemented
9#14582907C211yesmaximal, characteristic, complemented
10#14582862C211yesmaximal, characteristic
11C43×#428C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C2×#10621877C2211yescharacteristic
15#13063305—21no—
16#13063305—21no—
17#13063305C2212yes—
18#13063305C2212yes—
19#13063284C2211yescharacteristic
20#13063283C2211yescharacteristic
21#13063283C2211yescharacteristic
22#13063282—21no—
23#13063281—21no—
24C2×C4⋊Dic43—21no—
25C4⋊C4×D43C2211yescharacteristic
26C4⋊C4×D43C2211yescharacteristic
27C2×(C2×D43)⋊C4—21no—
28C22⋊C4×D43—21no—
29C42×D43—21no—
30#13063258C2212yescomplemented
31#13063256C2212yescomplemented
32#13063250C2212yescomplemented
33#13063250C2212yescomplemented
34#13063248C2212yescomplemented
35#13063248C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37(C2×D43)⋊C8C2212yes—
38C2×M16×C43C2211yescharacteristic
39#117×C43C2211yescharacteristic
40C2×C4⋊C4×C43C2211yescharacteristic
41#107×C43C2212yescomplemented
42#106×C43C2212yescomplemented
43C23×D43D411yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43C2311yescharacteristic
46C22×Dic43—21no—
47C22×Dic43D411yescharacteristic
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×C4×D43—21no—
51C2×C4×D43—21no—
52C2×C4×D43D411yescharacteristic
53C2×C4×D43D411yescharacteristic
54C2×C4×D43C2311yescharacteristic
55C2×C4×D43C2311yescharacteristic
56C2×Dic86—22no—
57C2×Dic86—22no—
58C2×Dic86—21no—
59C2×Dic86C2312yes—
60M16×C43—22no—
61C2×C8×C43C2312yes—
62C4⋊C4×C43—21no—
63C4⋊C4×C43C2311yescharacteristic
64C4⋊C4×C43C2312yes—
65C4⋊C4×C43C2311yescharacteristic
66C22⋊C4×C43—21no—
67C42×C43—21no—
68C22⋊Dic43—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43C2311yescharacteristic
76C4⋊Dic43C2311yescharacteristic
77Dic43⋊C4—21no—
78Dic43⋊C4—21no—
79C4×Dic43—21no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82#10621877—22no—
83C2×C43⋊C8C2312yes—
84C23×C43C2×D411yescharacteristic
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—41no—
88C22×D43C2×D411yescharacteristic
89C22×D43C2×D411yescharacteristic
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—42no—
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43#4112yes—
96C2×C4×C43#4112yes—
97C2×C4×C43C2411yescharacteristic
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—42no—
103C2×Dic43C2×D411yescharacteristic
104C2×Dic43C2×D411yescharacteristic
105C4×D43—22no—
106C4×D43—22no—
107C4×D43—21no—
108C4×D43—21no—
109C4×D43—21no—
110C4×D43—21no—
111C4×D43—42no—
112C4×D43—42no—
113Dic86—22no—
114Dic86—22no—
115Dic86—42no—
116C8×C43—22no—
117C43⋊C8—22no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43#12312yes—
121C22×C43C22×D411yescharacteristic
122C2×D43—21no—
123C2×D43—21no—
124C2×D43—21no—
125C2×D43—21no—
126C2×D43—21no—
127C2×D43—44no—
128C2×D43#13712yes—
129C4×C43—41no—
130C4×C43—41no—
131C4×C43—42no—
132C4×C43#12312yes—
133C4×C43C2×#4111yescharacteristic
134C4×C43C2×#4111yescharacteristic
135Dic43—21no—
136Dic43—21no—
137Dic43—42no—
138Dic43—41no—
139Dic43—41no—
140#3095—431nomaximal, Sylow
141C2×C43—22no—
142C2×C43C2×#12311yescharacteristic
143C2×C43C2×#13711yescharacteristic
144C2×C43#57511yescharacteristic
145D43—22no—
146D43—41no—
147C2×C22⋊Q8—431no—
148C2×#117—431no—
149#485—432no—
150#485—432no—
151#484—432no—
152#483—432no—
153#428—431no—
154#428D4311yescharacteristic, complemented
155#419—431no—
156#419—431no—
157#407—431no—
158C43#309511yescharacteristic, complemented, Sylow
159C22×Q8—431no—
160C23×C4—431no—
161C2×M16—431no—
162C2×M16C2×D4311yescharacteristic
163C22⋊Q8—432no—
164C22⋊Q8—432no—
165C22⋊Q8—861no—
166C22⋊Q8—861no—
167#117—431no—
168#117—431no—
169#117—431no—
170#117—861no—
171#117—861no—
172#117C2×D4311yescharacteristic
173C2×C4⋊C4—431no—
174C2×C4⋊C4—431no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4C2×D4311yescharacteristic
177C2×C22⋊C4—861no—
178C2×C22⋊C4—861no—
179C2×C42—861no—
180#107—432no—
181#107C2×D4312yescomplemented
182#106—432no—
183#106C2×D4312yescomplemented
184#103—432no—
185#103—432no—
186#103—432no—
187#103—432no—
188C22⋊C8—432no—
189C22⋊C8—432no—
190C24—431no—
191C2×Q8—432no—
192C2×Q8—861no—
193C2×Q8—862no—
194C2×Q8—862no—
195C22×C4—21no—
196C22×C4—431no—
197C22×C4—431no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—861no—
202C22×C4—861no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4—861no—
206C22×C4C22×D4311yescharacteristic
207M16—22no—
208M16—862no—
209C2×C8—432no—
210C2×C8C22×D4312yes—
211C4⋊C4—21no—
212C4⋊C4—431no—
213C4⋊C4—431no—
214C4⋊C4—861no—
215C4⋊C4—861no—
216C4⋊C4—862no—
217C4⋊C4—862no—
218C4⋊C4C22×D4311yescharacteristic
219C4⋊C4C22×D4311yescharacteristic
220C4⋊C4C22×D4312yes—
221C22⋊C4—21no—
222C22⋊C4—861no—
223C22⋊C4—861no—
224C22⋊C4—862no—
225C22⋊C4—862no—
226C22⋊C4—861no—
227C42—21no—
228C42—861no—
229C42—861no—
230C42—861no—
231C23—431no—
232C23—431no—
233C23—862no—
234C23—862no—
235C23—1721no—
236C23D4×D4311yescharacteristic
237Q8—862no—
238Q8—862no—
239Q8—1722no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—431no—
245C2×C4—431no—
246C2×C4—862no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—861no—
250C2×C4—861no—
251C2×C4—861no—
252C2×C4—861no—
253C2×C4—861no—
254C2×C4—861no—
255C2×C4—862no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4#1062189812yes—
260C2×C4D4×D4311yescharacteristic
261C2×C4#1062190212yes—
262C2×C4C23×D4311yescharacteristic
263C8—22no—
264C8—862no—
265C22—21no—
266C22—21no—
267C22—432no—
268C22—861no—
269C22—861no—
270C22—861no—
271C22—861no—
272C22—861no—
273C22—1724no—
274C22#1306331012yes—
275C22C2×D4×D4311yescharacteristic
276C4—41no—
277C4—42no—
278C4—41no—
279C4—861no—
280C4—861no—
281C4—1722no—
282C4—1721no—
283C4—1721no—
284C4#1306331012yes—
285C4C2×#1062189811yescharacteristic
286C4C2×#1062190211yescharacteristic
287C2—22no—
288C2—862no—
289C2—1721no—
290C2C2×#1306331011yescharacteristic
291C2#137×D4311yescharacteristic
292C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3095
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #14583243C2semidirect
4. #14583242C2semidirect
5. #14583236C2semidirect
6. #14583231C2semidirect
7. #14582939C2semidirect
8. #14582909C2semidirect
9. #14582907C2semidirect
11. C43×#428C2semidirect
30. #13063258C22semidirect
31. #13063256C22semidirect
32. #13063250C22semidirect
33. #13063250C22semidirect
34. #13063248C22semidirect
35. #13063248C22semidirect
41. #107×C43C22semidirect
42. #106×C43C22semidirect
154. #428D43semidirect
158. C43#3095semidirect
181. #107C2×D43semidirect
183. #106C2×D43semidirect