Finite Group Databasebeta

← #20254930

Subgroups — #20254930

Order 6016.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094051C211yesmaximal, characteristic, complemented
2C2×#13094045C211yesmaximal, characteristic, complemented
3#15689795C211yesmaximal, characteristic, complemented
4#15689768C211yesmaximal, characteristic, complemented
5#15689512C211yesmaximal, characteristic, complemented
6#15689370C211yesmaximal, characteristic, complemented
7#15689360C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689318C211yesmaximal, characteristic, complemented
10#15689288C211yesmaximal, characteristic, complemented
11#15689271C211yesmaximal, characteristic, complemented
12#15689269C211yesmaximal, characteristic, complemented
13#15689258C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625354C2211yescharacteristic, complemented
18C2×#10625352C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094051—24no—
21#13094045—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625325C2211yescharacteristic, complemented
25C2×#10625336C2211yescharacteristic
26C2×D376C2211yescharacteristic
27C2×D376C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625334C2211yescharacteristic
30C2×#10625324C2211yescharacteristic
31C2×C8×D47C2211yescharacteristic, complemented
32#13094021—21no—
33#13094021C2211yescharacteristic, complemented
34#13094012C2211yescharacteristic
35#13094008—21no—
36#13094004C2211yescharacteristic
37#13093999—21no—
38#13093999—21no—
39#13093999C2211yescharacteristic
40#13093999C2211yescharacteristic
41#13093999C2211yescharacteristic, complemented
42#13093998—21no—
43#13093994—21no—
44C4×D188—21no—
45C4×D188C2211yescharacteristic
46C2×(C2×D47)⋊C4—21no—
47C4⋊(C47⋊C8)C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic
50#13093944C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic
57#107×C47C2211yescharacteristic, complemented
58#103×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68#10625354—22no—
69#10625354—22no—
70#10625354—41no—
71#10625354—41no—
72#10625352—22no—
73#10625352—41no—
74D4×D47—22no—
75D4×D47—41no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188D411yescharacteristic
84C2×D188C2311yescharacteristic
85C2×D188C2311yescharacteristic
86C2×D188C2311yescharacteristic
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90C2×C4×D47C2311yescharacteristic
91C2×Dic94C2311yescharacteristic
92SD16×C47D414yescomplemented
93C2×C8×C47C2311yescharacteristic
94C2×C8×C47C2311yescharacteristic
95C4⋊C4×C47—21no—
96C4⋊C4×C47C2311yescharacteristic
97C4⋊C4×C47C2311yescharacteristic
98C22⋊C4×C47—21no—
99C42×C47—21no—
100C42×C47C2311yescharacteristic
101#10625337—22no—
102#10625336—22no—
103#10625334—22no—
104#10625334—22no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47—21no—
114C4⋊Dic47D411yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117D376—22no—
118D376—41no—
119#10625325—22no—
120#10625325—41no—
121#10625324—22no—
122C8×D47—22no—
123C23×C47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130C22×D47C2×D411yescharacteristic
131C22×D47C2×D411yescharacteristic
132Q8×C47—21no—
133Q8×C47C2×D412yes—
134D4×C47—21no—
135D4×C47C2×D412yes—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—81no—
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2411yescharacteristic
143C22⋊D47—42no—
144C22⋊D47—42no—
145C2×Dic47—21no—
146C2×Dic47—42no—
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149D188—21no—
150D188—21no—
151D188—21no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188—41no—
156D188—42no—
157D188—42no—
158D188—42no—
159D188—81no—
160D188—81no—
161D188—81no—
162D188—81no—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—21no—
166C4×D47—21no—
167C4×D47—42no—
168C4×D47—42no—
169Dic94—21no—
170Dic94—21no—
171C8×C47—21no—
172C8×C47C2×D412yes—
173C47⋊C8—21no—
174C47⋊C8—21no—
175C22×C47—22no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47C22×D411yescharacteristic
179C2×D47—21no—
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—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C4×C47—22no—
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47C22×D411yescharacteristic
201C4×C47H(5,𝔽2)11yescharacteristic
202Dic47—21no—
203Dic47—21no—
204Dic47—41no—
205#3268—471nomaximal, Sylow
206C2×C47—42no—
207C2×C47D4211yescharacteristic
208C2×C47#57511yescharacteristic
209C2×C47#57611yescharacteristic
210D47—41no—
211D47—41no—
212D47—81no—
213D47—81no—
214D47—81no—
215C2×AGL(1,ℤ/8)—471no—
216C2×#135—471no—
217#550—471no—
218#546—471no—
219#496—471no—
220#468—471no—
221#466—471no—
222#464—471no—
223#459—471no—
224#452—471no—
225#449—471no—
226#449—471no—
227#447—471no—
228#440D4711yescharacteristic, complemented
229#435—471no—
230C47#326811yescharacteristic, complemented, Sylow
231C2×#41—471no—
232C2×#41—471no—
233C2×#41—471no—
234C22×D4—471no—
235AGL(1,ℤ/8)—944no—
236#135—944no—
237C2×Q16—471no—
238C2×SD16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16C2×D4711yescharacteristic
242C2×D8—471no—
243C2×D8—471no—
244C2×D8—471no—
245C2×D8—471no—
246C2×M16—471no—
247C22×C8—471no—
248#127—471no—
249#127—941no—
250#124—471no—
251#123—941no—
252C22⋊Q8—471no—
253#121—471no—
254#121—471no—
255#121—471no—
256#121—941no—
257#121—941no—
258#121—941no—
259#120—941no—
260C4×Q8C2×D4711yescharacteristic, complemented
261C4×D4—471no—
262C4×D4—941no—
263C4×D4C2×D4711yescharacteristic
264C2×C22⋊C4—941no—
265#107C2×D4711yescharacteristic, complemented
266C4⋊C8—471no—
267#103—471no—
268#103C2×D4711yescharacteristic, complemented
269#102—471no—
270#102—471no—
271#102—471no—
272#102C2×D4711yescharacteristic
273C22⋊C8—471no—
274C22⋊C8—471no—
275#97C2×D4711yescharacteristic, complemented
276C24—941no—
277#41—942no—
278#41—942no—
279#41—942no—
280#41—1881no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8C22×D4711yescharacteristic
285C2×D4—471no—
286C2×D4—471no—
287C2×D4—471no—
288C2×D4—471no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—942no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—1881no—
300C2×D4C22×D4711yescharacteristic
301C22×C4—21no—
302C22×C4—471no—
303C22×C4—471no—
304C22×C4—941no—
305C22×C4—941no—
306C22×C4—941no—
307Q16—942no—
308SD16—942no—
309SD16—942no—
310SD16—1881no—
311SD16D18814yescomplemented
312D8—942no—
313D8—942no—
314D8—942no—
315D8—1881no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8—942no—
320C2×C8C22×D4711yescharacteristic
321C2×C8C22×D4711yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4C22×D4711yescharacteristic
326C4⋊C4C22×D4711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—471no—
329C22⋊C4—471no—
330C22⋊C4—941no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C42—21no—
337C42C22×D4711yescharacteristic
338C23—21no—
339C23—471no—
340C23—471no—
341C23—941no—
342C23—941no—
343C23—941no—
344C23—3761no—
345C23—1882no—
346C23—1882no—
347Q8—21no—
348Q8—941no—
349Q8—941no—
350Q8C2×D18812yes—
351D4—21no—
352D4—941no—
353D4—941no—
354D4—941no—
355D4—941no—
356D4—941no—
357D4—941no—
358D4—3761no—
359D4—3761no—
360D4—3761no—
361D4—3761no—
362D4—1881no—
363D4—1882no—
364D4—1882no—
365D4—1882no—
366D4—1882no—
367D4—1882no—
368D4C2×D18812yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—471no—
374C2×C4—471no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—1882no—
381C2×C4—1882no—
382C2×C4—1882no—
383C2×C4D4×D4711yescharacteristic
384C2×C4D4×D4711yescharacteristic
385C2×C4C23×D4711yescharacteristic
386C8—21no—
387C8—941no—
388C8—941no—
389C8C2×D18812yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—941no—
394C22—941no—
395C22—941no—
396C22—941no—
397C22—941no—
398C22—941no—
399C22—3764no—
400C22—1881no—
401C22—1881no—
402C22—1881no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22C2×D4×D4711yescharacteristic
410C4—22no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—941no—
416C4—941no—
417C4—1881no—
418C4C22×D18811yescharacteristic
419C4#1309407011yescharacteristic
420C2—42no—
421C2—3761no—
422C2—3761no—
423C2—3761no—
424C2—1881no—
425C2—1881no—
426C2D4×D18811yescharacteristic
427C2#1568992211yescharacteristic
428C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3268
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×#13094045C2semidirect
3. #15689795C2semidirect
4. #15689768C2semidirect
5. #15689512C2semidirect
6. #15689370C2semidirect
7. #15689360C2semidirect
8. #15689345C2semidirect
9. #15689318C2semidirect
10. #15689288C2semidirect
11. #15689271C2semidirect
12. #15689269C2semidirect
13. #15689258C2semidirect
14. #15689196C2semidirect
15. C47×#440C2semidirect
17. C2×#10625354C22semidirect
22. C2×#10625337C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625325C22semidirect
31. C2×C8×D47C22semidirect
33. #13094021C22semidirect
41. #13093999C22semidirect
47. C4⋊(C47⋊C8)C22semidirect
48. #13093947C22semidirect
50. #13093944C22semidirect
51. #13093944C22semidirect
53. (C2×D47)⋊C8C22semidirect
55. C4×Q8×C47C22semidirect
57. #107×C47C22semidirect
58. #103×C47C22semidirect
60. #97×C47C22semidirect
92. SD16×C47D4semidirect
228. #440D47semidirect
230. C47#3268semidirect
260. C4×Q8C2×D47semidirect
265. #107C2×D47semidirect
268. #103C2×D47semidirect
275. #97C2×D47semidirect
311. SD16D188semidirect