Finite Group Databasebeta

← #20254934

Subgroups — #20254934

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×#13094043C211yesmaximal, characteristic, complemented
3#15689793C211yesmaximal, characteristic, complemented
4#15689768C211yesmaximal, characteristic, complemented
5#15689510C211yesmaximal, characteristic, complemented
6#15689368C211yesmaximal, characteristic, complemented
7#15689358C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689286C211yesmaximal, characteristic, complemented
10#15689269C211yesmaximal, characteristic, complemented
11#15689265C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689193C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×#10625352C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic
20#13094048—24no—
21#13094043—24no—
22C2×Dic188C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic, complemented
26C2×#10625335C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625324C2211yescharacteristic
30C2×C8×D47C2211yescharacteristic, complemented
31#13094020—21no—
32#13094012C2211yescharacteristic
33#13094008—21no—
34#13094004C2211yescharacteristic
35#13093999C2211yescharacteristic
36#13093998—21no—
37#13093996—21no—
38#13093996—21no—
39#13093995C2211yescharacteristic
40#13093995C2211yescharacteristic, complemented
41#13093994—21no—
42C4×Dic94C2211yescharacteristic, complemented
43C4×D188C2211yescharacteristic
44D4×Dic47—21no—
45C2×(C2×D47)⋊C4—21no—
46#13093957C2211yescharacteristic, complemented
47#13093949C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic
50#13093945C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093935C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic
56#127×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic
58C4⋊C8×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77#10625352—22no—
78#10625352—22no—
79#10625352—22no—
80#10625352—41no—
81#10625352—41no—
82#10625352—41no—
83D4×D47—22no—
84D4×D47—41no—
85C2×D188—21no—
86C2×D188D411yescharacteristic
87C2×D188C2311yescharacteristic
88C2×C4×D47C2311yescharacteristic
89C2×C4×D47C2311yescharacteristic
90C2×Dic94C2311yescharacteristic
91C2×Dic94C2311yescharacteristic
92D8×C47—22no—
93D8×C47—22no—
94C2×C8×C47C2311yescharacteristic
95C2×C8×C47C2311yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C22⋊C4×C47—21no—
98C42×C47C2311yescharacteristic
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101#10625335—22no—
102#10625335—41no—
103#10625335D414yescomplemented
104#10625334—22no—
105#10625334—41no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4D411yescharacteristic
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47—21no—
113C4⋊Dic47D411yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116C4×Dic47—21no—
117C2×C47⋊C8C2311yescharacteristic
118C2×C47⋊C8C2311yescharacteristic
119Dic188—22no—
120#10625325—22no—
121#10625324—22no—
122C8×D47—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130C22×D47C2×D411yescharacteristic
131C22×D47C2×D411yescharacteristic
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—42no—
138D4×C47—81no—
139D4×C47C2×D412yes—
140C2×C4×C47—21no—
141C2×C4×C47—81no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2411yescharacteristic
145C22⋊D47—42no—
146C22⋊D47—42no—
147C22⋊D47—42no—
148C22⋊D47—42no—
149C22⋊D47—81no—
150C22⋊D47—81no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—42no—
155C2×Dic47—42no—
156C2×Dic47—42no—
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159D188—21no—
160D188—21no—
161D188—41no—
162D188—81no—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—21no—
166C4×D47—21no—
167Dic94—21no—
168Dic94—21no—
169Dic94—21no—
170Dic94C2×D412yes—
171C8×C47—21no—
172C8×C47—21no—
173C47⋊C8—21no—
174C47⋊C8C2×D412yes—
175C22×C47—22no—
176C22×C47—41no—
177C22×C47—41no—
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—21no—
187C2×D47—21no—
188C2×D47—21no—
189C2×D47—21no—
190C2×D47—21no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47C22×D411yescharacteristic
199C4×C47H(5,𝔽2)11yescharacteristic
200Dic47—22no—
201Dic47—21no—
202Dic47—21no—
203Dic47—41no—
204Dic47—41no—
205#3268—471nomaximal, Sylow
206C2×C47—42no—
207C2×C47—81no—
208C2×C47—81no—
209C2×C47D4211yescharacteristic
210C2×C47#57511yescharacteristic
211C2×C47#57611yescharacteristic
212D47—41no—
213D47—41no—
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#459D4711yescharacteristic, complemented
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×D8C2×D4711yescharacteristic
245C2×D8C2×D4711yescharacteristic
246C2×M16—471no—
247C22×C8—471no—
248#127—941no—
249#127C2×D4711yescharacteristic, complemented
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×Q8—471no—
261C4×D4—471no—
262C4×D4—941no—
263C4×D4C2×D4711yescharacteristic
264C2×C22⋊C4—941no—
265#107—471no—
266C4⋊C8C2×D4711yescharacteristic, complemented
267#103—471no—
268#103—471no—
269#102—471no—
270#102—471no—
271#102C2×D4711yescharacteristic, complemented
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—941no—
290C2×D4—941no—
291C2×D4—942no—
292C2×D4—941no—
293C2×D4—941no—
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—471no—
303C22×C4—471no—
304C22×C4—941no—
305C22×C4—941no—
306C22×C4—941no—
307Q16—942no—
308SD16—474no—
309SD16—942no—
310SD16—942no—
311SD16—1881no—
312D8—22no—
313D8—22no—
314D8—942no—
315D8—1881no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8—942no—
320C2×C8C22×D4711yescharacteristic
321C2×C8C22×D4711yescharacteristic
322C4⋊C4—471no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4—941no—
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—941no—
337C42C22×D4711yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—471no—
342C23—471no—
343C23—941no—
344C23—3761no—
345C23—1882no—
346C23—1882no—
347Q8—472no—
348Q8—941no—
349Q8—941no—
350Q8—941no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—941no—
359D4—941no—
360D4—3761no—
361D4—3761no—
362D4—3761no—
363D4—1881no—
364D4—1882no—
365D4—1882no—
366D4—1882no—
367D4—1882no—
368D4D4×D4712yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—471no—
372C2×C4—471no—
373C2×C4—941no—
374C2×C4—941no—
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—21no—
388C8—472no—
389C8—941no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—941no—
400C22—941no—
401C22—941no—
402C22—941no—
403C22—941no—
404C22—941no—
405C22—3764no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22C2×D4×D4711yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—941no—
414C4—941no—
415C4—942no—
416C4—1881no—
417C4—1881no—
418C4C2×D4×D4711yescharacteristic
419C4#1309407011yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—3761no—
424C2—1881no—
425C2—1881no—
426C2#1568975711yescharacteristic
427C2#1568991911yescharacteristic
428C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3268
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×#13094043C2semidirect
3. #15689793C2semidirect
4. #15689768C2semidirect
5. #15689510C2semidirect
6. #15689368C2semidirect
7. #15689358C2semidirect
8. #15689346C2semidirect
9. #15689286C2semidirect
10. #15689269C2semidirect
11. #15689265C2semidirect
12. #15689255C2semidirect
13. #15689223C2semidirect
14. #15689193C2semidirect
15. C47×#459C2semidirect
18. C2×#10625352C22semidirect
22. C2×Dic188C22semidirect
25. C2×#10625335C22semidirect
26. C2×#10625335C22semidirect
30. C2×C8×D47C22semidirect
40. #13093995C22semidirect
42. C4×Dic94C22semidirect
46. #13093957C22semidirect
47. #13093949C22semidirect
48. #13093947C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093935C22semidirect
56. #127×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #102×C47C22semidirect
60. #102×C47C22semidirect
103. #10625335D4semidirect
223. #459D47semidirect
230. C47#3268semidirect
249. #127C2×D47semidirect
266. C4⋊C8C2×D47semidirect
271. #102C2×D47semidirect
272. #102C2×D47semidirect