Finite Group Databasebeta

← #19144226

Subgroups — #19144226

Order 5504.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063358C211yesmaximal, characteristic, complemented
2C2×M16×D43C211yesmaximal, characteristic, complemented
3#14583411C211yesmaximal, characteristic
4C2×#13063305C211yesmaximal, characteristic, complemented
5#14583158C212yesmaximal, complemented
6#14583146C212yesmaximal, complemented
7#14583141C212yesmaximal, complemented
8#14583129C212yesmaximal, complemented
9#14582907C211yesmaximal, characteristic, complemented
10#14582898C211yesmaximal, characteristic, complemented
11C43×#428C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063358—24no—
16C2×Dic172C2212yescomplemented
17C2×#10621873C2212yescomplemented
18C2×#10621877C2211yescharacteristic
19C2×#10621872C2212yes—
20M16×D43—24no—
21C2×C8×D43C2212yes—
22#13063309—21no—
23#13063305—21no—
24#13063305—21no—
25#13063305C2212yes—
26#13063305C2211yescharacteristic
27#13063305C2212yes—
28#13063305C2211yescharacteristic
29#13063300C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063295—21no—
32C4×D172—21no—
33C4×D172—21no—
34C2×C4⋊Dic43—21no—
35C2×(C2×D43)⋊C4—21no—
36#13063248C2212yescomplemented
37#13063248C2212yescomplemented
38#13063248C2212yescomplemented
39#13063245C2212yescomplemented
40C2×M16×C43C2211yescharacteristic
41#117×C43C2211yescharacteristic
42C2×C4⋊C4×C43C2211yescharacteristic
43#107×C43C2212yescomplemented
44#106×C43C2212yescomplemented
45C23×D43D411yescharacteristic
46C22×C4×C43—21no—
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—21no—
49C22×Dic43—21no—
50C22×Dic43D411yescharacteristic
51#10621898—22no—
52#10621898—22no—
53C2×D172—21no—
54C2×D172—21no—
55C2×D172C2311yescharacteristic
56C2×C4×D43—22no—
57C2×C4×D43—22no—
58C2×C4×D43—21no—
59C2×C4×D43D411yescharacteristic
60C2×C4×D43D411yescharacteristic
61C2×C4×D43C2311yescharacteristic
62C2×C4×D43C2311yescharacteristic
63C2×Dic86—22no—
64C2×Dic86—22no—
65C2×Dic86—21no—
66C2×Dic86C2312yes—
67C2×Dic86C2311yescharacteristic
68M16×C43D414yescomplemented
69C2×C8×C43C2312yes—
70C4⋊C4×C43—21no—
71C4⋊C4×C43C2311yescharacteristic
72C4⋊C4×C43C2312yes—
73C4⋊C4×C43C2311yescharacteristic
74C22⋊C4×C43—21no—
75C42×C43—21no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4—21no—
78(C2×D43)⋊C4—22no—
79(C2×D43)⋊C4—22no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82C4⋊Dic43—22no—
83C4⋊Dic43—22no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86#10621877—22no—
87C2×C43⋊C8C2312yes—
88Dic172—24no—
89#10621873—24no—
90#10621872—24no—
91C8×D43—24no—
92C23×C43C2×D411yescharacteristic
93C22×D43—22no—
94C22×D43—22no—
95C22×D43—21no—
96C22×D43—41no—
97C22×D43C2×D411yescharacteristic
98C22×D43C2×D411yescharacteristic
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43C2×D412yes—
104C2×C4×C43C2×D411yescharacteristic
105C2×C4×C43#4112yes—
106C2×C4×C43C2411yescharacteristic
107C22⋊D43—42no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—21no—
111C2×Dic43—42no—
112C2×Dic43C2×D411yescharacteristic
113C2×Dic43C2×D411yescharacteristic
114D172—21no—
115D172—21no—
116D172—42no—
117D172—42no—
118C4×D43—22no—
119C4×D43—22no—
120C4×D43—21no—
121C4×D43—21no—
122C4×D43—21no—
123C4×D43—21no—
124C4×D43—42no—
125Dic86—22no—
126Dic86—21no—
127Dic86—22no—
128Dic86—21no—
129Dic86—42no—
130C8×C43C2×D414yes—
131C43⋊C8—22no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43#12112yes—
135C22×C43C22×D411yescharacteristic
136C2×D43—21no—
137C2×D43—21no—
138C2×D43—21no—
139C2×D43—21no—
140C2×D43—21no—
141C2×D43—44no—
142C2×D43—41no—
143C2×D43—41no—
144C2×D43—41no—
145C2×D43#13712yescomplemented
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—42no—
149C4×C43#12112yes—
150C4×C43C22×D411yescharacteristic
151C4×C43C2×#4111yescharacteristic
152Dic43—21no—
153Dic43—21no—
154Dic43—42no—
155Dic43—41no—
156#3056—431nomaximal, Sylow
157C2×C43—22no—
158C2×C43C2×#12111yescharacteristic
159C2×C43C2×#13711yescharacteristic
160C2×C43#57511yescharacteristic
161D43—22no—
162D43—41no—
163D43—81no—
164C2×#137—431no—
165C22×M16—431no—
166#525—431no—
167C2×C22⋊Q8—431no—
168#470—432no—
169#468—432no—
170#467—432no—
171#465—432no—
172#428D4311yescharacteristic, complemented
173#419—431no—
174#417—431no—
175C43#305611yescharacteristic, complemented, Sylow
176C2×#41—431no—
177C22×Q8—431no—
178C23×C4—431no—
179#137—864no—
180C2×Q16—432no—
181C2×SD16—432no—
182C2×M16—431no—
183C2×M16—432no—
184C2×M16—864no—
185C2×M16C2×D4311yescharacteristic
186C22×C8—432no—
187#123—861no—
188C22⋊Q8—432no—
189C22⋊Q8—432no—
190C22⋊Q8—431no—
191C22⋊Q8—431no—
192C22⋊Q8—861no—
193C22⋊Q8—861no—
194#121—431no—
195#121—431no—
196#120—861no—
197C4×D4—861no—
198C4×D4—861no—
199#117C2×D4311yescharacteristic
200C2×C4⋊C4—861no—
201C2×C4⋊C4C2×D4311yescharacteristic
202C2×C22⋊C4—861no—
203#107C2×D4312yescomplemented
204#106C2×D4312yescomplemented
205#103—432no—
206#103—432no—
207#103—432no—
208#102—432no—
209C24—431no—
210#41—862no—
211#41—862no—
212C2×Q8—432no—
213C2×Q8—431no—
214C2×Q8—861no—
215C2×Q8—862no—
216C2×Q8—862no—
217C2×D4—431no—
218C2×D4—861no—
219C2×D4—861no—
220C2×D4—861no—
221C22×C4—21no—
222C22×C4—431no—
223C22×C4—431no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—431no—
227C22×C4—862no—
228C22×C4—862no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4C22×D4311yescharacteristic
232Q16—864no—
233SD16—864no—
234M16—862no—
235M16—864no—
236M16D17214yescomplemented
237C2×C8—432no—
238C2×C8—864no—
239C2×C8C22×D4312yes—
240C4⋊C4—21no—
241C4⋊C4—862no—
242C4⋊C4—862no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4C22×D4312yes—
246C4⋊C4C22×D4311yescharacteristic
247C4⋊C4C22×D4311yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—861no—
250C22⋊C4—861no—
251C22⋊C4—862no—
252C22⋊C4—862no—
253C22⋊C4—861no—
254C22⋊C4—861no—
255C42—21no—
256C23—431no—
257C23—431no—
258C23—862no—
259C23—862no—
260C23—861no—
261C23—1721no—
262C23D4×D4311yescharacteristic
263Q8—862no—
264Q8—861no—
265Q8—862no—
266Q8—861no—
267Q8—1722no—
268D4—861no—
269D4—861no—
270D4—1722no—
271D4—1722no—
272D4—1722no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—431no—
278C2×C4—431no—
279C2×C4—862no—
280C2×C4—862no—
281C2×C4—862no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4—861no—
286C2×C4—861no—
287C2×C4—862no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4C2×D17212yes—
291C2×C4D4×D4311yescharacteristic
292C2×C4#1062190212yes—
293C2×C4C23×D4311yescharacteristic
294C8—862no—
295C8C2×D17214yes—
296C22—21no—
297C22—21no—
298C22—432no—
299C22—861no—
300C22—861no—
301C22—861no—
302C22—861no—
303C22—861no—
304C22—1724no—
305C22—1721no—
306C22—1721no—
307C22—1721no—
308C22#1306330012yes—
309C22C2×D4×D4311yescharacteristic
310C4—41no—
311C4—42no—
312C4—41no—
313C4—861no—
314C4—861no—
315C4—1721no—
316C4—1722no—
317C4#1306330012yes—
318C4C22×D17211yescharacteristic
319C4C2×#1062190211yescharacteristic
320C2—22no—
321C2—862no—
322C2—3441no—
323C2—1721no—
324C2C2×#1306330011yescharacteristic
325C2#137×D4311yescharacteristic
326C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3056
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
1. C2×#13063358C2semidirect
2. C2×M16×D43C2semidirect
4. C2×#13063305C2semidirect
5. #14583158C2semidirect
6. #14583146C2semidirect
7. #14583141C2semidirect
8. #14583129C2semidirect
9. #14582907C2semidirect
10. #14582898C2semidirect
11. C43×#428C2semidirect
16. C2×Dic172C22semidirect
17. C2×#10621873C22semidirect
36. #13063248C22semidirect
37. #13063248C22semidirect
38. #13063248C22semidirect
39. #13063245C22semidirect
43. #107×C43C22semidirect
44. #106×C43C22semidirect
68. M16×C43D4semidirect
145. C2×D43#137semidirect
172. #428D43semidirect
175. C43#3056semidirect
203. #107C2×D43semidirect
204. #106C2×D43semidirect
236. M16D172semidirect