Finite Group Databasebeta

← #20253067

Subgroups — #20253067

Order 6016.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic, complemented
2C2×#13094030C211yesmaximal, characteristic, complemented
3#15689702C211yesmaximal, characteristic, complemented
4#15689689C211yesmaximal, characteristic, complemented
5#15689374C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic, complemented
7#15689370C211yesmaximal, characteristic, complemented
8#15689367C211yesmaximal, characteristic, complemented
9#15689358C211yesmaximal, characteristic, complemented
10#15689352C211yesmaximal, characteristic, complemented
11#15689351C211yesmaximal, characteristic, complemented
12#15689164C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#466C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094048—24no—
20C2×#10625325C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23#13094030—24no—
24C2×#10625329C2211yescharacteristic, complemented
25C2×#10625324C2211yescharacteristic
26C2×#10625324C2211yescharacteristic, complemented
27C2×C8×D47C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic, complemented
29#13094020—21no—
30#13094010—21no—
31#13094004C2211yescharacteristic, complemented
32#13094003C2211yescharacteristic, complemented
33#13094001—21no—
34#13093999C2211yescharacteristic
35#13093998C2211yescharacteristic
36#13093997—21no—
37#13093996—21no—
38#13093995—21no—
39#13093995C2211yescharacteristic
40#13093995C2211yescharacteristic, complemented
41#13093994—21no—
42#13093992—21no—
43#13093982C2211yescharacteristic
44C4⋊C4×D47C2211yescharacteristic
45#13093957C2211yescharacteristic, complemented
46#13093956C2211yescharacteristic, complemented
47#13093955C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic
51#13093945C2211yescharacteristic
52#13093945C2211yescharacteristic, complemented
53#13093944C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55C22×C8×C47C2211yescharacteristic, complemented
56#121×C47C2211yescharacteristic
57#121×C47C2211yescharacteristic, complemented
58#107×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47D411yescharacteristic
73C2×C22⋊D47D411yescharacteristic
74C22×Dic47—21no—
75#10625352—22no—
76#10625352—22no—
77D4×D47—22no—
78D4×D47—22no—
79#10625350—22no—
80#10625350—22no—
81C2×D188—21no—
82C2×D188D411yescharacteristic
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×C4×D47C2311yescharacteristic
87C2×Dic94D411yescharacteristic
88C2×Dic94C2311yescharacteristic
89D8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100#10625335—22no—
101#10625334—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47C2311yescharacteristic
108C4⋊Dic47C2311yescharacteristic
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111C4×Dic47—21no—
112#10625329—22no—
113C2×C47⋊C8C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115#10625325—22no—
116#10625324—22no—
117#10625324D414yescomplemented
118C8×D47—22no—
119C8×D47—22no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47C2×D411yescharacteristic
123C22×D47—21no—
124C22×D47—42no—
125C22×D47—81no—
126C22×D47—81no—
127C22×D47C2×D411yescharacteristic
128C22×D47C2×D411yescharacteristic
129D4×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—21no—
133D4×C47—81no—
134D4×C47—81no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2411yescharacteristic
141C22⋊D47—22no—
142C22⋊D47—22no—
143C22⋊D47—42no—
144C22⋊D47—42no—
145C22⋊D47—81no—
146C22⋊D47—81no—
147C22⋊D47—81no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—42no—
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154D188—22no—
155D188—21no—
156D188—21no—
157D188—81no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—81no—
161C4×D47C2×D412yes—
162C4×D47#4112yes—
163Dic94—22no—
164Dic94—21no—
165Dic94—21no—
166C8×C47—21no—
167C8×C47C2×D412yes—
168C47⋊C8—21no—
169C47⋊C8C2×D412yes—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47C22×D411yescharacteristic
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—84no—
189C2×D47#12112yes—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47C22×D411yescharacteristic
194C4×C47C2×#4111yescharacteristic
195Dic47—21no—
196Dic47—41no—
197Dic47—41no—
198Dic47—41no—
199Dic47#12112yes—
200#3062—471nomaximal, Sylow
201C2×C47—41no—
202C2×C47—81no—
203C2×C47—81no—
204C2×C47C2×#12111yescharacteristic
205C2×C47#57611yescharacteristic
206C2×C47#57711yescharacteristic
207D47—22no—
208D47—41no—
209D47—81no—
210C2×AGL(1,ℤ/8)—471no—
211C2×#131—471no—
212#537—471no—
213#535—471no—
214#469—471no—
215#469—471no—
216#468—471no—
217#468—471no—
218#466—471no—
219#466D4711yescharacteristic, complemented
220#465—471no—
221#465—471no—
222#428—471no—
223#416—471no—
224C2×#102—471no—
225C47#306211yescharacteristic, complemented, Sylow
226C2×#41—471no—
227C2×#41—471no—
228C22×D4—471no—
229AGL(1,ℤ/8)—944no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×D8—471no—
233C2×D8C2×D4711yescharacteristic
234#131—944no—
235C2×M16—471no—
236C2×M16—471no—
237C2×M16—471no—
238C22×C8—471no—
239C22×C8—471no—
240C22×C8C2×D4711yescharacteristic, complemented
241#127—941no—
242#124—941no—
243C22⋊Q8—471no—
244C22⋊Q8—471no—
245C22⋊Q8—941no—
246#121—471no—
247#121—471no—
248#121—471no—
249#121—471no—
250#121—941no—
251#121—941no—
252#121—941no—
253#121C2×D4711yescharacteristic
254#121C2×D4711yescharacteristic, complemented
255#120—941no—
256#120—941no—
257#117—471no—
258C2×C4⋊C4—471no—
259#107—471no—
260#107C2×D4711yescharacteristic, complemented
261#106—471no—
262#106—471no—
263#103—471no—
264#103—471no—
265#102—471no—
266#102—471no—
267#102—471no—
268#102—471no—
269#102C2×D4711yescharacteristic
270#102C2×D4711yescharacteristic, complemented
271C24—941no—
272#41—942no—
273#41—942no—
274#41—942no—
275#41—942no—
276C2×Q8—471no—
277C2×Q8—471no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—471no—
284C2×D4—941no—
285C2×D4—942no—
286C2×D4—942no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4C22×D4711yescharacteristic
293C2×D4C22×D4711yescharacteristic
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—941no—
297C22×C4—941no—
298C22×C4C22×D4711yescharacteristic
299SD16—942no—
300SD16—942no—
301D8—22no—
302D8—942no—
303M16—474no—
304M16—942no—
305M16—942no—
306C2×C8—22no—
307C2×C8—471no—
308C2×C8—471no—
309C2×C8—942no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—471no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4C22×D4711yescharacteristic
319C4⋊C4C22×D4711yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C42—941no—
330C23—21no—
331C23—21no—
332C23—471no—
333C23—471no—
334C23—941no—
335C23—3761no—
336C23—3761no—
337C23—1882no—
338C23D4×D4711yescharacteristic
339Q8—942no—
340Q8—941no—
341Q8—941no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—81no—
347D4—81no—
348D4—942no—
349D4—942no—
350D4—942no—
351D4—941no—
352D4—941no—
353D4—3761no—
354D4—3761no—
355D4—3761no—
356D4—3761no—
357D4—1882no—
358D4—1882no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—471no—
364C2×C4—472no—
365C2×C4—472no—
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×C4D4×D4711yescharacteristic
375C2×C4C23×D4711yescharacteristic
376C8—21no—
377C8—472no—
378C8—941no—
379C8D4×D4712yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—472no—
390C22—941no—
391C22—941no—
392C22—941no—
393C22—941no—
394C22—941no—
395C22—3764no—
396C22—1881no—
397C22—1881no—
398C22—1881no—
399C22C2×D4×D4711yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—472no—
404C4—941no—
405C4—1881no—
406C4—1881no—
407C4—1881no—
408C4C2×D4×D4711yescharacteristic
409C4#41×D4711yescharacteristic
410C2—41no—
411C2—81no—
412C2—81no—
413C2—942no—
414C2—3761no—
415C2—1881no—
416C2#121×D4711yescharacteristic
417C2#1568992411yescharacteristic
418C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3062
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×#13094030C2semidirect
3. #15689702C2semidirect
4. #15689689C2semidirect
5. #15689374C2semidirect
6. #15689373C2semidirect
7. #15689370C2semidirect
8. #15689367C2semidirect
9. #15689358C2semidirect
10. #15689352C2semidirect
11. #15689351C2semidirect
12. #15689164C2semidirect
13. #15689116C2semidirect
14. #102×D47C2semidirect
15. C47×#466C2semidirect
24. C2×#10625329C22semidirect
26. C2×#10625324C22semidirect
28. C2×C8×D47C22semidirect
31. #13094004C22semidirect
32. #13094003C22semidirect
40. #13093995C22semidirect
45. #13093957C22semidirect
46. #13093956C22semidirect
47. #13093955C22semidirect
48. #13093949C22semidirect
49. #13093947C22semidirect
52. #13093945C22semidirect
55. C22×C8×C47C22semidirect
57. #121×C47C22semidirect
58. #107×C47C22semidirect
60. #102×C47C22semidirect
117. #10625324D4semidirect
219. #466D47semidirect
225. C47#3062semidirect
240. C22×C8C2×D47semidirect
254. #121C2×D47semidirect
260. #107C2×D47semidirect
270. #102C2×D47semidirect