Finite Group Databasebeta

← #20254925

Subgroups — #20254925

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×#13094048C211yesmaximal, characteristic, complemented
2C2×#13094046C211yesmaximal, characteristic, complemented
3#15689791C211yesmaximal, characteristic, complemented
4#15689770C211yesmaximal, characteristic, complemented
5#15689511C211yesmaximal, characteristic, complemented
6#15689370C211yesmaximal, characteristic, complemented
7#15689344C211yesmaximal, characteristic, complemented
8#15689317C211yesmaximal, characteristic, complemented
9#15689286C211yesmaximal, characteristic, complemented
10#15689266C211yesmaximal, characteristic, complemented
11#15689266C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689222C211yesmaximal, characteristic, complemented
14#15689194C211yesmaximal, characteristic, complemented
15C47×#466C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic, complemented
18C2×#10625352C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094048—24no—
21#13094046—24no—
22C2×Dic188C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625325C2211yescharacteristic, complemented
25C2×#10625335C2211yescharacteristic
26C2×#10625335C2211yescharacteristic, complemented
27C2×D376C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625334C2211yescharacteristic
30C2×#10625324C2211yescharacteristic
31#13094020—21no—
32#13094020C2211yescharacteristic, complemented
33#13094011C2211yescharacteristic
34#13094006—21no—
35#13094004C2211yescharacteristic
36#13093999C2211yescharacteristic
37#13093997—21no—
38#13093996—21no—
39#13093995—21no—
40#13093992—21no—
41#13093989C2211yescharacteristic, complemented
42#13093986C2211yescharacteristic
43C4×C22⋊D47C2211yescharacteristic
44(C22⋊D47)⋊C4—21no—
45C22⋊C4×D47—21no—
46Dic47⋊C8C2211yescharacteristic, complemented
47#13093947C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic
50#13093944C2211yescharacteristic, complemented
51C22⋊(C47⋊C8)C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic
53#13093934C2211yescharacteristic, complemented
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⋊D47—21no—
73C2×C22⋊D47D411yescharacteristic
74C22×Dic47—21no—
75#10625352—22no—
76#10625352—41no—
77D4×D47—22no—
78D4×D47—41no—
79#10625350—22no—
80#10625350—22no—
81#10625350—41no—
82#10625350—41no—
83C2×D188—21no—
84C2×D188C2311yescharacteristic
85C2×D188C2311yescharacteristic
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90C2×Dic94C2311yescharacteristic
91C2×Dic94C2311yescharacteristic
92D8×C47—22no—
93C2×C8×C47—22no—
94C2×C8×C47C2311yescharacteristic
95C2×C8×C47C2311yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C4⋊C4×C47C2311yescharacteristic
98C22⋊C4×C47—21no—
99C22⋊C4×C47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47D411yescharacteristic
103#10625335—22no—
104#10625335—41no—
105#10625334—22no—
106#10625334—41no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4D411yescharacteristic
111C4⋊Dic47—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4D411yescharacteristic
114C4×Dic47—21no—
115C4×Dic47C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117C2×C47⋊C8C2311yescharacteristic
118Dic188—22no—
119D376—22no—
120#10625325—22no—
121#10625325D414yescomplemented
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—81no—
131C22×D47C2×D411yescharacteristic
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—81no—
137D4×C47—81no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—41no—
145C22⋊D47—42no—
146C22⋊D47—42no—
147C22⋊D47—42no—
148C22⋊D47—42no—
149C22⋊D47—42no—
150C22⋊D47—81no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—42no—
154C2×Dic47C2×D411yescharacteristic
155C2×Dic47C2×D411yescharacteristic
156C2×Dic47C2×D411yescharacteristic
157D188—21no—
158D188—21no—
159D188—21no—
160D188—81no—
161D188C2×D412yes—
162C4×D47—21no—
163C4×D47—21no—
164C4×D47—42no—
165C4×D47—42no—
166C4×D47—81no—
167Dic94—21no—
168Dic94—21no—
169Dic94—21no—
170Dic94C2×D412yes—
171C8×C47—21no—
172C8×C47C2×D412yes—
173C47⋊C8—21no—
174C47⋊C8—21no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47C22×D411yescharacteristic
185C2×D47—21no—
186C2×D47—22no—
187C2×D47—21no—
188C2×D47—21no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C4×C47—21no—
196C4×C47—41no—
197C4×C47—41no—
198C4×C47C22×D411yescharacteristic
199C4×C47H(5,𝔽2)11yescharacteristic
200Dic47—22no—
201Dic47—21no—
202Dic47—21no—
203Dic47—21no—
204Dic47—41no—
205#3268—471nomaximal, Sylow
206C2×C47—41no—
207C2×C47—81no—
208C2×C47—81no—
209C2×C47D4211yescharacteristic
210C2×C47#57511yescharacteristic
211C2×C47#57611yescharacteristic
212D47—41no—
213D47—42no—
214D47—81no—
215C2×AGL(1,ℤ/8)—471no—
216C2×#135—471no—
217#550—471no—
218#546—471no—
219#496—471no—
220#468—471no—
221#466D4711yescharacteristic, complemented
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×#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×SD16—471no—
242C2×D8—471no—
243C2×D8—471no—
244C2×D8—471no—
245C2×D8C2×D4711yescharacteristic
246C2×M16—471no—
247C22×C8C2×D4711yescharacteristic, complemented
248#127—471no—
249#127—941no—
250#124—471no—
251#123—941no—
252C22⋊Q8—471no—
253#121—471no—
254#121—941no—
255#121—941no—
256#121—941no—
257#121C2×D4711yescharacteristic
258#121C2×D4711yescharacteristic, complemented
259#120—941no—
260C4×Q8—471no—
261C4×D4—471no—
262C4×D4—471no—
263C4×D4—941no—
264C2×C22⋊C4—941no—
265#107C2×D4711yescharacteristic, complemented
266C4⋊C8—471no—
267#103—471no—
268#103—471no—
269#102—471no—
270#102—471no—
271#102C2×D4711yescharacteristic
272#102C2×D4711yescharacteristic, complemented
273C22⋊C8—471no—
274C22⋊C8—471no—
275#97—471no—
276C24—941no—
277#41—942no—
278#41—942no—
279#41—942no—
280#41—1881no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8—471no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—471no—
288C2×D4—471no—
289C2×D4—471no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—942no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—1881no—
299C2×D4C22×D4711yescharacteristic
300C2×D4C22×D4711yescharacteristic
301C22×C4—471no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4—941no—
306C22×C4C22×D4711yescharacteristic
307Q16—942no—
308SD16—474no—
309SD16—942no—
310SD16—942no—
311SD16—1881no—
312D8—22no—
313D8—942no—
314D8—942no—
315D8—1881no—
316M16—942no—
317C2×C8—22no—
318C2×C8—471no—
319C2×C8—471no—
320C2×C8C22×D4711yescharacteristic
321C2×C8C22×D4711yescharacteristic
322C4⋊C4—471no—
323C4⋊C4—941no—
324C4⋊C4—941no—
325C4⋊C4C22×D4711yescharacteristic
326C4⋊C4C22×D4711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—471no—
330C22⋊C4—471no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C42—471no—
337C42—941no—
338C23—21no—
339C23—21no—
340C23—471no—
341C23—941no—
342C23—941no—
343C23—3761no—
344C23—1882no—
345C23—1882no—
346C23D4×D4711yescharacteristic
347Q8—472no—
348Q8—941no—
349Q8—941no—
350Q8—941no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—81no—
356D4—81no—
357D4—472no—
358D4—941no—
359D4—941no—
360D4—941no—
361D4—3761no—
362D4—3761no—
363D4—1881no—
364D4—1882no—
365D4—1882no—
366D4—1882no—
367D4—1882no—
368D4—1882no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—471no—
374C2×C4—471no—
375C2×C4—471no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—3761no—
381C2×C4—1882no—
382C2×C4—1882no—
383C2×C4—1882no—
384C2×C4D4×D4711yescharacteristic
385C2×C4C23×D4711yescharacteristic
386C8—21no—
387C8—941no—
388C8—941no—
389C8D4×D4712yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—941no—
400C22—942no—
401C22—941no—
402C22—941no—
403C22—3764no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22C2×D4×D4711yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—941no—
414C4—942no—
415C4—941no—
416C4—941no—
417C4—1881no—
418C4C2×D4×D4711yescharacteristic
419C4#1309407011yescharacteristic
420C2—41no—
421C2—81no—
422C2—81no—
423C2—3761no—
424C2—1881no—
425C2—1882no—
426C2#1568975711yescharacteristic
427C2#1568992011yescharacteristic
428C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3268
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×#13094046C2semidirect
3. #15689791C2semidirect
4. #15689770C2semidirect
5. #15689511C2semidirect
6. #15689370C2semidirect
7. #15689344C2semidirect
8. #15689317C2semidirect
9. #15689286C2semidirect
10. #15689266C2semidirect
11. #15689266C2semidirect
12. #15689258C2semidirect
13. #15689222C2semidirect
14. #15689194C2semidirect
15. C47×#466C2semidirect
17. C2×#10625350C22semidirect
22. C2×Dic188C22semidirect
24. C2×#10625325C22semidirect
26. C2×#10625335C22semidirect
32. #13094020C22semidirect
41. #13093989C22semidirect
46. Dic47⋊C8C22semidirect
47. #13093947C22semidirect
48. #13093947C22semidirect
50. #13093944C22semidirect
51. C22⋊(C47⋊C8)C22semidirect
53. #13093934C22semidirect
55. C22×C8×C47C22semidirect
57. #121×C47C22semidirect
58. #107×C47C22semidirect
60. #102×C47C22semidirect
121. #10625325D4semidirect
221. #466D47semidirect
230. C47#3268semidirect
247. C22×C8C2×D47semidirect
258. #121C2×D47semidirect
265. #107C2×D47semidirect
272. #102C2×D47semidirect