Finite Group Databasebeta

← #20254913

Subgroups — #20254913

Order 6016.

500 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×#13094048C211yesmaximal, characteristic, complemented
2#15689772C211yesmaximal, characteristic, complemented
3#15689761C211yesmaximal, characteristic, complemented
4#15689516C211yesmaximal, characteristic, complemented
5#15689378C211yesmaximal, characteristic, complemented
6#15689352C211yesmaximal, characteristic, complemented
7#15689340C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689235C211yesmaximal, characteristic, complemented
14#15689194C211yesmaximal, characteristic, complemented
15C2×#135×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18#13094048—24no—
19C2×#10625337C2211yescharacteristic, complemented
20C2×#10625325C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24C2×#10625324C2211yescharacteristic
25#13094022C2211yescharacteristic, complemented
26#13094013C2211yescharacteristic
27#13094007—21no—
28#13094007—21no—
29#13094005—21no—
30#13094003C2211yescharacteristic, complemented
31#13094000C2211yescharacteristic
32#13094000C2211yescharacteristic
33#13093998C2211yescharacteristic
34#13093996—21no—
35#13093996—21no—
36#13093992—21no—
37D4×Dic47C2211yescharacteristic
38D4×Dic47C2211yescharacteristic, complemented
39C4×C22⋊D47C2211yescharacteristic
40C2×Dic47⋊C4—21no—
41C2×(C2×D47)⋊C4—21no—
42#13093956C2211yescharacteristic, complemented
43Dic47⋊C8C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic, complemented
50C22⋊(C47⋊C8)C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic
52#13093934C2211yescharacteristic, complemented
53C2×#41×C47C2211yescharacteristic
54C2×#41×C47C2211yescharacteristic, complemented
55#135×C47—24no—
56C2×Q16×C47C2211yescharacteristic, complemented
57C2×SD16×C47C2211yescharacteristic
58C2×SD16×C47C2211yescharacteristic, complemented
59C2×D8×C47C2211yescharacteristic
60C22×C8×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62#41×C47—22no—
63#41×C47—22no—
64#41×C47—41no—
65#41×C47—41no—
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47D411yescharacteristic
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47—21no—
82#10625352—22no—
83#10625352—41no—
84D4×D47—22no—
85D4×D47—41no—
86C2×D188C2311yescharacteristic
87C2×C4×D47C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89Q16×C47—22no—
90SD16×C47—22no—
91SD16×C47—22no—
92D8×C47D414yescomplemented
93C2×C8×C47—22no—
94C2×C8×C47C2311yescharacteristic
95C2×C8×C47C2311yescharacteristic
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47D411yescharacteristic
100#10625337—41no—
101#10625336—41no—
102#10625335—22no—
103#10625334—22no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4D411yescharacteristic
110C4⋊Dic47C2311yescharacteristic
111C4⋊Dic47C2311yescharacteristic
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117Dic47⋊C4D411yescharacteristic
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130C22×D47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—42no—
138D4×C47—42no—
139D4×C47C2×D412yes—
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×C47—42no—
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C22⋊D47—41no—
150C22⋊D47—42no—
151C22⋊D47—42no—
152C22⋊D47—81no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—42no—
157C2×Dic47—42no—
158C2×Dic47—81no—
159C2×Dic47C2×D411yescharacteristic
160C2×Dic47C2×D411yescharacteristic
161C2×Dic47C2×D411yescharacteristic
162D188—21no—
163D188—21no—
164C4×D47—21no—
165C4×D47—21no—
166Dic94—21no—
167Dic94—21no—
168C8×C47—21no—
169C8×C47C2×D412yes—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47C22×D411yescharacteristic
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—84no—
189C4×C47—21no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47C22×D411yescharacteristic
193C4×C47H(5,𝔽2)11yescharacteristic
194Dic47—21no—
195Dic47—21no—
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200#3267—471nomaximal, Sylow
201C2×C47—42no—
202C2×C47—41no—
203C2×C47—42no—
204C2×C47D4211yescharacteristic
205C2×C47#57511yescharacteristic
206C2×C47#57711yescharacteristic
207D47—41no—
208D47—81no—
209C2×AGL(1,ℤ/8)—471no—
210C2×#135D4711yescharacteristic, complemented
211#547—471no—
212#546—471no—
213#497—471no—
214#470—471no—
215#465—471no—
216#463—471no—
217#461—471no—
218#452—471no—
219#452—471no—
220#450—471no—
221#449—471no—
222#442—471no—
223#435—471no—
224C47#326711yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41C2×D4711yescharacteristic
227C2×#41C2×D4711yescharacteristic, complemented
228C22×D4—471no—
229AGL(1,ℤ/8)—944no—
230#135—24no—
231C2×Q16—471no—
232C2×Q16C2×D4711yescharacteristic, complemented
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—471no—
236C2×SD16C2×D4711yescharacteristic
237C2×SD16C2×D4711yescharacteristic, complemented
238C2×D8—471no—
239C2×D8C2×D4711yescharacteristic
240C2×M16—471no—
241C22×C8C2×D4711yescharacteristic, complemented
242C4⋊Q8—471no—
243#124—471no—
244#123—941no—
245#123—941no—
246#123—941no—
247C22⋊Q8—471no—
248C22⋊Q8—471no—
249C22⋊Q8—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#120—941no—
254C4×D4—471no—
255C4×D4—471no—
256C4×D4—471no—
257C2×C4⋊C4—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—
269#97—471no—
270C24—941no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—942no—
276#41—1881no—
277C2×Q8—471no—
278C2×Q8C22×D4711yescharacteristic
279C2×Q8C22×D4711yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—471no—
283C2×D4—471no—
284C2×D4—941no—
285C2×D4—942no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—1881no—
289C2×D4C22×D4711yescharacteristic
290C2×D4C22×D4711yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—471no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4C22×D4711yescharacteristic
298Q16—22no—
299Q16—1881no—
300SD16—22no—
301SD16—22no—
302SD16—942no—
303SD16—942no—
304SD16—1881no—
305D8—942no—
306D8C22⋊D4714yescomplemented
307M16—942no—
308C2×C8—22no—
309C2×C8—471no—
310C2×C8—471no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C4⋊C4—941no—
320C4⋊C4—941no—
321C22⋊C4—471no—
322C22⋊C4—471no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C42—471no—
332C23—21no—
333C23—21no—
334C23—471no—
335C23—941no—
336C23—3761no—
337C23—1882no—
338C23—1882no—
339C23D4×D4711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—941no—
345Q8—941no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—42no—
350D4—941no—
351D4—941no—
352D4—3761no—
353D4—1881no—
354D4—1882no—
355D4—1882no—
356D4C2×C22⋊D4712yes—
357D4C2×C22⋊D4712yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
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—22no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—941no—
391C22—941no—
392C22—941no—
393C22—3764no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—941no—
402C4—941no—
403C4—941no—
404C4—1881no—
405C4—1881no—
406C4—1881no—
407C4C22×C22⋊D4711yescharacteristic
408C4#1309406911yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—3761no—
413C2—1881no—
414C2D4×C22⋊D4711yescharacteristic
415C2#1568992011yescharacteristic
416C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. #15689772C2semidirect
3. #15689761C2semidirect
4. #15689516C2semidirect
5. #15689378C2semidirect
6. #15689352C2semidirect
7. #15689340C2semidirect
8. #15689326C2semidirect
9. #15689285C2semidirect
10. #15689282C2semidirect
11. #15689272C2semidirect
12. #15689268C2semidirect
13. #15689235C2semidirect
14. #15689194C2semidirect
15. C2×#135×C47C2semidirect
19. C2×#10625337C22semidirect
25. #13094022C22semidirect
30. #13094003C22semidirect
38. D4×Dic47C22semidirect
42. #13093956C22semidirect
43. Dic47⋊C8C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
49. #13093945C22semidirect
50. C22⋊(C47⋊C8)C22semidirect
52. #13093934C22semidirect
54. C2×#41×C47C22semidirect
56. C2×Q16×C47C22semidirect
58. C2×SD16×C47C22semidirect
60. C22×C8×C47C22semidirect
92. D8×C47D4semidirect
210. C2×#135D47semidirect
224. C47#3267semidirect
227. C2×#41C2×D47semidirect
232. C2×Q16C2×D47semidirect
237. C2×SD16C2×D47semidirect
241. C22×C8C2×D47semidirect
306. D8C22⋊D47semidirect