Finite Group Databasebeta

← #20255095

Subgroups — #20255095

Order 6016.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094045C211yesmaximal, characteristic, complemented
2#15689784C211yesmaximal, characteristic, complemented
3#15689767C211yesmaximal, characteristic, complemented
4#15689504C211yesmaximal, characteristic, complemented
5#15689352C211yesmaximal, characteristic, complemented
6#15689349C211yesmaximal, characteristic, complemented
7#15689343C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689282C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11#15689267C211yesmaximal, characteristic, complemented
12#15689257C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14C8×C22⋊D47C211yesmaximal, characteristic, complemented
15C22×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic, complemented
17C2×#10625352C2211yescharacteristic
18#13094045—24no—
19C2×#10625337C2211yescharacteristic, complemented
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625325C2211yescharacteristic, complemented
22C2×#10625334C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24C2×C8×D47C2211yescharacteristic, complemented
25#13094013—21no—
26#13094013C2211yescharacteristic, complemented
27#13094011C2211yescharacteristic
28#13094005—21no—
29#13094003C2211yescharacteristic
30#13094000—21no—
31#13094000C2211yescharacteristic, complemented
32#13093998—21no—
33#13093998C2211yescharacteristic
34#13093996—21no—
35#13093995C2211yescharacteristic
36#13093993—21no—
37Q8×Dic47C2211yescharacteristic, complemented
38D4×Dic47C2211yescharacteristic
39C4×C22⋊D47—21no—
40C4×C22⋊D47C2211yescharacteristic
41C2×C22⋊Dic47—21no—
42#13093956C2211yescharacteristic, complemented
43Dic47⋊C8C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50C22⋊(C47⋊C8)C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C22×Q8×C47C2211yescharacteristic
54C22×D4×C47C2211yescharacteristic
55C2×SD16×C47—24no—
56C2×SD16×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic
58C2×SD16×C47C2211yescharacteristic
59C2×SD16×C47C2211yescharacteristic
60C22×C8×C47C2211yescharacteristic
61C24×C47—21no—
62C2×Q8×C47—21no—
63C2×Q8×C47—22no—
64C2×Q8×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47D411yescharacteristic
78C22×Dic47—21no—
79C22×Dic47—21no—
80#10625354—22no—
81#10625354—41no—
82#10625352—22no—
83#10625352—41no—
84C2×D188—21no—
85C2×D188C2311yescharacteristic
86C2×C4×D47—21no—
87C2×C4×D47C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89SD16×C47—22no—
90SD16×C47—22no—
91SD16×C47—22no—
92SD16×C47D414yescomplemented
93C2×C8×C47—22no—
94C2×C8×C47C2311yescharacteristic
95C2×C8×C47C2311yescharacteristic
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47D411yescharacteristic
102#10625337—22no—
103#10625337—41no—
104#10625334—22no—
105#10625334—41no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4D411yescharacteristic
111C4⋊Dic47—21no—
112C4⋊Dic47C2311yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4D411yescharacteristic
117C4×Dic47—21no—
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122C8×D47—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—42no—
126C23×C47—42no—
127C23×C47—81no—
128C23×C47C2×D411yescharacteristic
129C22×D47—21no—
130C22×D47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—42no—
135Q8×C47C2×D412yes—
136D4×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—42no—
140D4×C47C2×D412yes—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—42no—
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C22⋊D47—22no—
149C22⋊D47—42no—
150C22⋊D47—42no—
151C22⋊D47—81no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—42no—
156C2×Dic47—81no—
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159C2×Dic47C2×D411yescharacteristic
160D188—21no—
161D188—21no—
162D188—42no—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—42no—
166Dic94—21no—
167Dic94—21no—
168C8×C47—21no—
169C8×C47C2×D412yes—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—22no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—84no—
181C22×C47#13512yescomplemented
182C22×C47C22×D411yescharacteristic
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—21no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C4×C47—22no—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47C22×D411yescharacteristic
193C4×C47H(5,𝔽2)11yescharacteristic
194Dic47—21no—
195Dic47—21no—
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200#3282—471nomaximal, Sylow
201C2×C47—22no—
202C2×C47—42no—
203C2×C47—81no—
204C2×C47D4211yescharacteristic
205C2×C47C2×#13511yescharacteristic
206C2×C47#57711yescharacteristic
207D47—41no—
208D47—81no—
209C2×#135—471no—
210C22×SD16D4711yescharacteristic, complemented
211#548—471no—
212#546—471no—
213#495—471no—
214#465—471no—
215#465—471no—
216#464—471no—
217#463—471no—
218#452—471no—
219#451—471no—
220#449—471no—
221#447—471no—
222C4×SD16—471no—
223C8×D4—471no—
224C47#328211yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41—471no—
227C22×Q8C2×D4711yescharacteristic
228C22×D4C2×D4711yescharacteristic
229#135—944no—
230C2×Q16—471no—
231C2×Q16—471no—
232C2×SD16—24no—
233C2×SD16—471no—
234C2×SD16C2×D4711yescharacteristic
235C2×SD16C2×D4711yescharacteristic
236C2×SD16C2×D4711yescharacteristic
237C2×SD16C2×D4711yescharacteristic
238C2×D8—471no—
239C2×D8—471no—
240C22×C8—471no—
241C22×C8C2×D4711yescharacteristic
242#124—471no—
243#124—471no—
244#124—941no—
245#123—941no—
246C22⋊Q8—471no—
247C22⋊Q8—471no—
248C22⋊Q8—941no—
249#121—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#120—941no—
254C4×Q8—471no—
255C4×D4—471no—
256C4×D4—471no—
257C4×D4—941no—
258C2×C22⋊C4—941no—
259#106—471no—
260C4⋊C8—471no—
261#103—471no—
262#103—471no—
263#103—471no—
264#102—471no—
265#102—471no—
266#102—471no—
267C22⋊C8—471no—
268C22⋊C8—471no—
269C4×C8—471no—
270C24—21no—
271#41—942no—
272#41—942no—
273#41—1881no—
274#41—1881no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—471no—
279C2×Q8C22×D4711yescharacteristic
280C2×Q8C22×D4711yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—471no—
285C2×D4—471no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4C22×D4711yescharacteristic
291C2×D4C22×D4711yescharacteristic
292C22×C4—21no—
293C22×C4—471no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4C22×D4711yescharacteristic
298Q16—942no—
299Q16—1881no—
300SD16—22no—
301SD16—22no—
302SD16—22no—
303SD16—942no—
304SD16C22⋊D4714yescomplemented
305D8—942no—
306D8—1881no—
307C2×C8—22no—
308C2×C8—471no—
309C2×C8—471no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C22⋊C4—471no—
320C22⋊C4—471no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C42—471no—
331C42—941no—
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—471no—
338C23—941no—
339C23D4×D4711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—941no—
345Q8—941no—
346Q8C2×C22⋊D4712yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—942no—
352D4—941no—
353D4—941no—
354D4—3761no—
355D4—1882no—
356D4—1882no—
357D4—1882no—
358D4C2×C22⋊D4712yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—471no—
365C2×C4—471no—
366C2×C4—471no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—3761no—
373C2×C4—1882no—
374C2×C4—1882no—
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—941no—
379C8—941no—
380C8C2×C22⋊D4712yes—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—84no—
390C22—941no—
391C22—941no—
392C22—941no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22#1309404512yescomplemented
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—941no—
402C4—941no—
403C4—941no—
404C4—1881no—
405C4—1881no—
406C4—1881no—
407C4C22×C22⋊D4711yescharacteristic
408C4#1309406911yescharacteristic
409C2—22no—
410C2—42no—
411C2—81no—
412C2—3761no—
413C2—1881no—
414C2D4×C22⋊D4711yescharacteristic
415C2C2×#1309404511yescharacteristic
416C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×SD16×C47C2
socleC22×C47C22×D4
hypercenterC22×SD16D47
hypocenterC47#3282
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13094045C2semidirect
2. #15689784C2semidirect
3. #15689767C2semidirect
4. #15689504C2semidirect
5. #15689352C2semidirect
6. #15689349C2semidirect
7. #15689343C2semidirect
8. #15689340C2semidirect
9. #15689282C2semidirect
10. #15689279C2semidirect
11. #15689267C2semidirect
12. #15689257C2semidirect
13. SD16×Dic47C2semidirect
14. C8×C22⋊D47C2semidirect
15. C22×SD16×C47C2semidirect
16. C2×#10625354C22semidirect
19. C2×#10625337C22semidirect
20. C2×#10625337C22semidirect
21. C2×#10625325C22semidirect
24. C2×C8×D47C22semidirect
26. #13094013C22semidirect
31. #13094000C22semidirect
37. Q8×Dic47C22semidirect
42. #13093956C22semidirect
43. Dic47⋊C8C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
47. #13093946C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. C8×Dic47C22semidirect
92. SD16×C47D4semidirect
181. C22×C47#135semidirect
210. C22×SD16D47semidirect
224. C47#3282semidirect
304. SD16C22⋊D47semidirect
396. C22#13094045semidirect