Finite Group Databasebeta

← #20254929

Subgroups — #20254929

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×#13094049C211yesmaximal, characteristic, complemented
2C2×#13094044C211yesmaximal, characteristic, complemented
3#15689769C211yesmaximal, characteristic, complemented
4#15689510C211yesmaximal, characteristic, complemented
5#15689367C211yesmaximal, characteristic, complemented
6#15689357C211yesmaximal, characteristic, complemented
7#15689345C211yesmaximal, characteristic, complemented
8#15689315C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689268C211yesmaximal, characteristic, complemented
11#15689266C211yesmaximal, characteristic, complemented
12#15689256C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15C47×#550C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18#13094049—24no—
19#13094044—24no—
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625335C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic
24C2×#10625336C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625329C2211yescharacteristic
30C22×C47⋊C8C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic
32#13094009—21no—
33#13094003C2211yescharacteristic
34#13093998C2211yescharacteristic
35#13093997—21no—
36#13093992—21no—
37C4×D188C2211yescharacteristic
38C22⋊C4×D47—21no—
39#13093957C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50C2×#41×C47C2211yescharacteristic
51C2×#41×C47C2211yescharacteristic, complemented
52#127×C47—21no—
53#127×C47C2211yescharacteristic, complemented
54#121×C47—21no—
55#121×C47—21no—
56#121×C47C2211yescharacteristic
57#121×C47C2211yescharacteristic, complemented
58C4×Q8×C47C2211yescharacteristic, complemented
59C4×D4×C47—21no—
60C4×D4×C47C2211yescharacteristic
61C23×D47—21no—
62#41×C47—22no—
63#41×C47—22no—
64#41×C47—41no—
65#41×C47—41no—
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47D411yescharacteristic
74C2×D4×C47C2311yescharacteristic
75C2×D4×C47C2311yescharacteristic
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47C2311yescharacteristic
79C22×C4×C47C2311yescharacteristic
80C2×C22⋊D47—21no—
81C2×C22⋊D47—21no—
82#10625350—22no—
83#10625350—41no—
84C2×D188—22no—
85C2×D188—21no—
86C2×D188—41no—
87C2×D188C2311yescharacteristic
88C2×D188C2311yescharacteristic
89C2×C4×D47—21no—
90C2×C4×D47—21no—
91C2×Dic94C2311yescharacteristic
92C4⋊C4×C47—21no—
93C4⋊C4×C47D411yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47D411yescharacteristic
98C22⋊C4×C47D411yescharacteristic
99C42×C47—21no—
100C42×C47C2311yescharacteristic
101C22⋊Dic47—21no—
102#10625337—22no—
103#10625336—22no—
104#10625336D414yescomplemented
105#10625335—22no—
106#10625335—41no—
107#10625334—22no—
108#10625334—22no—
109#10625334—22no—
110#10625334—41no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4—21no—
114(C2×D47)⋊C4—21no—
115C4⋊Dic47C2311yescharacteristic
116Dic47⋊C4—21no—
117#10625329—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C23×C47—21no—
124C23×C47—21no—
125C23×C47C2×D411yescharacteristic
126C23×C47C2×D411yescharacteristic
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—81no—
132Q8×C47—21no—
133Q8×C47C2×D412yes—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—21no—
138D4×C47—41no—
139D4×C47—42no—
140D4×C47—42no—
141D4×C47—42no—
142D4×C47—81no—
143D4×C47—81no—
144D4×C47—81no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47C2×D411yescharacteristic
154C2×C4×C47C2×D411yescharacteristic
155C2×C4×C47C2×D411yescharacteristic
156C2×C4×C47C2×D411yescharacteristic
157C2×C4×C47C2411yescharacteristic
158C22⋊D47—42no—
159C22⋊D47—81no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162D188—21no—
163D188—21no—
164D188—21no—
165D188—42no—
166D188C2×D412yes—
167C4×D47—42no—
168C4×D47—81no—
169Dic94—21no—
170Dic94—21no—
171C47⋊C8—21no—
172C47⋊C8—21no—
173C47⋊C8—21no—
174C47⋊C8C2×D412yes—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47C22×D411yescharacteristic
188C2×D47—22no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—22no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—41no—
201C4×C47C22×D411yescharacteristic
202C4×C47H(5,𝔽2)11yescharacteristic
203Dic47—41no—
204Dic47—41no—
205#3268—471nomaximal, Sylow
206C2×C47—41no—
207C2×C47—41no—
208C2×C47—81no—
209C2×C47—81no—
210C2×C47D4211yescharacteristic
211C2×C47#57511yescharacteristic
212C2×C47#57611yescharacteristic
213D47—42no—
214D47—81no—
215C2×AGL(1,ℤ/8)—471no—
216C2×#135—471no—
217#550D4711yescharacteristic, complemented
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#440—471no—
229#435—471no—
230C47#326811yescharacteristic, complemented, Sylow
231C2×#41—471no—
232C2×#41C2×D4711yescharacteristic
233C2×#41C2×D4711yescharacteristic, complemented
234C22×D4—471no—
235AGL(1,ℤ/8)—944no—
236#135—944no—
237C2×Q16—471no—
238C2×SD16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×D8—471no—
243C2×D8—471no—
244C2×D8—471no—
245C2×D8—471no—
246C2×M16—471no—
247C22×C8—471no—
248#127—21no—
249#127C2×D4711yescharacteristic, complemented
250#124—471no—
251#123—941no—
252C22⋊Q8—471no—
253#121—21no—
254#121—21no—
255#121—471no—
256#121—941no—
257#121C2×D4711yescharacteristic
258#121C2×D4711yescharacteristic, complemented
259#120—941no—
260C4×Q8C2×D4711yescharacteristic, complemented
261C4×D4—21no—
262C4×D4—471no—
263C4×D4C2×D4711yescharacteristic
264C2×C22⋊C4—941no—
265#107—471no—
266C4⋊C8—471no—
267#103—471no—
268#103—471no—
269#102—471no—
270#102—471no—
271#102—471no—
272#102—471no—
273C22⋊C8—471no—
274C22⋊C8—471no—
275#97—471no—
276C24—941no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—942no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8C22×D4711yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—471no—
292C2×D4—471no—
293C2×D4—942no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—1881no—
298C2×D4C22⋊D4711yescharacteristic
299C2×D4C22×D4711yescharacteristic
300C2×D4C22×D4711yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4C22×D4711yescharacteristic
306C22×C4C22×D4711yescharacteristic
307Q16—942no—
308SD16—474no—
309SD16—942no—
310SD16—942no—
311SD16—1881no—
312D8—942no—
313D8—942no—
314D8—942no—
315D8—1881no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8—471no—
320C2×C8—471no—
321C2×C8—942no—
322C4⋊C4—21no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4C22⋊D4711yescharacteristic
326C4⋊C4C22×D4711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4C22⋊D4711yescharacteristic
335C22⋊C4C22⋊D4711yescharacteristic
336C42—21no—
337C42C22×D4711yescharacteristic
338C23—21no—
339C23—21no—
340C23—941no—
341C23—941no—
342C23—3761no—
343C23—1882no—
344C23—1882no—
345C23C2×C22⋊D4711yescharacteristic
346C23C2×C22⋊D4711yescharacteristic
347Q8—21no—
348Q8—941no—
349Q8—941no—
350Q8D4×D4712yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—472no—
363D4—941no—
364D4—941no—
365D4—941no—
366D4—3761no—
367D4—1882no—
368D4—1882no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—3761no—
380C2×C4—1882no—
381C2×C4C2×C22⋊D4711yescharacteristic
382C2×C4C2×C22⋊D4711yescharacteristic
383C2×C4C2×C22⋊D4711yescharacteristic
384C2×C4C2×C22⋊D4711yescharacteristic
385C2×C4C23×D4711yescharacteristic
386C8—472no—
387C8—941no—
388C8—941no—
389C8—941no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—942no—
403C22—3764no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22C22×C22⋊D4711yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—1881no—
417C4—1881no—
418C4C2×D4×D4711yescharacteristic
419C4#1309406911yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—3761no—
425C2—1882no—
426C2D4×C22⋊D4711yescharacteristic
427C2#1568992111yescharacteristic
428C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#550C2
socleC22×C47C22×D4
hypercenter#550D47
hypocenterC47#3268
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#13094049C2semidirect
2. C2×#13094044C2semidirect
3. #15689769C2semidirect
4. #15689510C2semidirect
5. #15689367C2semidirect
6. #15689357C2semidirect
7. #15689345C2semidirect
8. #15689315C2semidirect
9. #15689285C2semidirect
10. #15689268C2semidirect
11. #15689266C2semidirect
12. #15689256C2semidirect
13. #15689221C2semidirect
14. #15689195C2semidirect
15. C47×#550C2semidirect
20. C2×#10625337C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625335C22semidirect
30. C22×C47⋊C8C22semidirect
39. #13093957C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093948C22semidirect
42. #13093947C22semidirect
43. #13093945C22semidirect
44. #13093945C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. #13093935C22semidirect
51. C2×#41×C47C22semidirect
53. #127×C47C22semidirect
57. #121×C47C22semidirect
58. C4×Q8×C47C22semidirect
104. #10625336D4semidirect
217. #550D47semidirect
230. C47#3268semidirect
233. C2×#41C2×D47semidirect
249. #127C2×D47semidirect
258. #121C2×D47semidirect
260. C4×Q8C2×D47semidirect