Finite Group Databasebeta

← #20254996

Subgroups — #20254996

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094052C211yesmaximal, characteristic, complemented
2C2×#13094051C211yesmaximal, characteristic, complemented
3#15689770C211yesmaximal, characteristic, complemented
4#15689764C211yesmaximal, characteristic, complemented
5#15689504C211yesmaximal, characteristic, complemented
6#15689370C211yesmaximal, characteristic, complemented
7#15689341C211yesmaximal, characteristic, complemented
8#15689337C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic, complemented
10#15689283C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689256C211yesmaximal, characteristic, complemented
13#15689205C211yesmaximal, characteristic, complemented
14#15689199C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18C22×D188C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic, complemented
20#13094052—24no—
21#13094051—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625325C2211yescharacteristic, complemented
25C2×#10625336C2211yescharacteristic, complemented
26C2×D376C2211yescharacteristic
27C2×D376C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625334C2211yescharacteristic
30C2×#10625324C2211yescharacteristic, complemented
31#13094013C2211yescharacteristic, complemented
32#13094011C2211yescharacteristic, complemented
33#13094009—21no—
34#13094006—21no—
35#13094004C2211yescharacteristic, complemented
36#13093999—21no—
37#13093999C2211yescharacteristic
38#13093995—21no—
39#13093994—21no—
40#13093992—21no—
41#13093986C2211yescharacteristic, complemented
42#13093986C2211yescharacteristic, complemented
43C4×C22⋊D47C2211yescharacteristic
44C22⋊C4×D47—21no—
45C22⋊C4×D47—21no—
46Dic47⋊C8C2211yescharacteristic, complemented
47#13093947C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic, complemented
51C22⋊(C47⋊C8)C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×M16×C47C2211yescharacteristic, complemented
56C22⋊Q8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#107×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47D411yescharacteristic
70#10625354—22no—
71#10625354—41no—
72D4×D47—22no—
73D4×D47—41no—
74#10625350—22no—
75#10625350—41no—
76C2×D188—22no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—41no—
81C2×D188C2311yescharacteristic
82C2×D188C2311yescharacteristic
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47C2311yescharacteristic
89C2×Dic94C2311yescharacteristic
90SD16×C47—22no—
91M16×C47—22no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C4⋊C4×C47—21no—
95C4⋊C4×C47C2311yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47D411yescharacteristic
102#10625337—41no—
103#10625336—22no—
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)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47—21no—
114Dic47⋊C4D411yescharacteristic
115C4×Dic47C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117C2×C47⋊C8C2311yescharacteristic
118D376—22no—
119D376D414yescomplemented
120#10625325—22no—
121#10625325—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—81no—
133C22×D47—81no—
134C22×D47C2×D411yescharacteristic
135Q8×C47—21no—
136Q8×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—81no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2411yescharacteristic
147C22⋊D47—41no—
148C22⋊D47—42no—
149C22⋊D47—42no—
150C2×Dic47—21no—
151C2×Dic47C2×D411yescharacteristic
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154D188—21no—
155D188—21no—
156D188—21no—
157D188—21no—
158D188—42no—
159D188—42no—
160D188—81no—
161D188C2×D412yes—
162D188C2×D412yes—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—42no—
166C4×D47—42no—
167C4×D47—81no—
168C4×D47—81no—
169Dic94—21no—
170Dic94—21no—
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×C47C22×D411yescharacteristic
182C2×D47—21no—
183C2×D47—22no—
184C2×D47—22no—
185C2×D47—21no—
186C2×D47—21no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C2×D47—84no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47C22×D411yescharacteristic
201C4×C47H(5,𝔽2)11yescharacteristic
202Dic47—21no—
203Dic47—21no—
204Dic47—21no—
205Dic47—41no—
206#3273—471nomaximal, Sylow
207C2×C47—41no—
208C2×C47—81no—
209C2×C47D4211yescharacteristic
210C2×C47#57511yescharacteristic
211C2×C47#57611yescharacteristic
212D47—41no—
213D47—42no—
214D47—42no—
215D47—81no—
216C2×AGL(1,ℤ/8)—471no—
217C2×AGL(1,ℤ/8)—471no—
218#546—471no—
219#546—471no—
220#495—471no—
221#468—471no—
222#468D4711yescharacteristic, complemented
223#463—471no—
224#463—471no—
225#452—471no—
226#452—471no—
227#447—471no—
228#447—471no—
229C4×D8—471no—
230#436—471no—
231C47#327311yescharacteristic, complemented, Sylow
232C2×#41—471no—
233C2×#41—471no—
234C22×D4—471no—
235C22×D4—471no—
236AGL(1,ℤ/8)—944no—
237AGL(1,ℤ/8)—944no—
238C2×Q16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×SD16C2×D4711yescharacteristic, complemented
243C2×D8—471no—
244C2×D8—471no—
245C2×D8—471no—
246C2×D8—471no—
247C2×M16—471no—
248C2×M16C2×D4711yescharacteristic, complemented
249#124—471no—
250#124—471no—
251#123—941no—
252#123—941no—
253C22⋊Q8—471no—
254C22⋊Q8C2×D4711yescharacteristic, complemented
255#121—471no—
256#121—941no—
257#121—941no—
258#121C2×D4711yescharacteristic
259#120—941no—
260#120—941no—
261C4×D4—471no—
262C4×D4—471no—
263C4×D4—471no—
264C2×C22⋊C4—941no—
265C2×C22⋊C4—941no—
266#107C2×D4711yescharacteristic, complemented
267C4⋊C8—471no—
268#103—471no—
269#103C2×D4711yescharacteristic, complemented
270#102—471no—
271#102—471no—
272#102—471no—
273#102C2×D4711yescharacteristic, complemented
274C22⋊C8—471no—
275C22⋊C8—471no—
276C4×C8—471no—
277C24—941no—
278C24—941no—
279#41—942no—
280#41—942no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8C22×D4711yescharacteristic
285C2×D4—21no—
286C2×D4—471no—
287C2×D4—471no—
288C2×D4—471no—
289C2×D4—471no—
290C2×D4—942no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—942no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—1881no—
298C2×D4—1881no—
299C2×D4C22×D4711yescharacteristic
300C22×C4—471no—
301C22×C4—941no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4C22×D4711yescharacteristic
306Q16—1881no—
307SD16—22no—
308SD16—942no—
309SD16—942no—
310SD16—942no—
311D8—474no—
312D8—942no—
313D8—942no—
314D8—1881no—
315M16—22no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8C22×D4711yescharacteristic
320C2×C8C22×D4711yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—471no—
323C4⋊C4—941no—
324C4⋊C4C22×D4711yescharacteristic
325C4⋊C4C22×D4711yescharacteristic
326C22⋊C4—21no—
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—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C42—471no—
339C23—21no—
340C23—471no—
341C23—941no—
342C23—941no—
343C23—941no—
344C23—3761no—
345C23—3761no—
346C23—1882no—
347C23—1882no—
348C23—1882no—
349C23—1882no—
350C23D4×D4711yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—941no—
354Q8—941no—
355D4—21no—
356D4—21no—
357D4—81no—
358D4—472no—
359D4—472no—
360D4—941no—
361D4—941no—
362D4—941no—
363D4—941no—
364D4—3761no—
365D4—1882no—
366D4—1882no—
367D4—1881no—
368D4—1882no—
369D4—1882no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—471no—
376C2×C4—471no—
377C2×C4—471no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—3761no—
382C2×C4—3761no—
383C2×C4—1882no—
384C2×C4—1882no—
385C2×C4D4×D4711yescharacteristic
386C2×C4C23×D4711yescharacteristic
387C8—21no—
388C8—941no—
389C8—941no—
390C8D4×D4712yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—941no—
398C22—942no—
399C22—942no—
400C22—941no—
401C22—941no—
402C22—3764no—
403C22—3764no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22—1881no—
410C22—1881no—
411C22C2×D4×D4711yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—941no—
417C4—941no—
418C4—941no—
419C4—1881no—
420C4C2×D4×D4711yescharacteristic
421C4#1309407011yescharacteristic
422C2—41no—
423C2—81no—
424C2—3761no—
425C2—1881no—
426C2—1882no—
427C2—1882no—
428C2#1568975711yescharacteristic
429C2#1568992211yescharacteristic
430C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. C2×#13094051C2semidirect
3. #15689770C2semidirect
4. #15689764C2semidirect
5. #15689504C2semidirect
6. #15689370C2semidirect
7. #15689341C2semidirect
8. #15689337C2semidirect
9. #15689288C2semidirect
10. #15689283C2semidirect
11. #15689258C2semidirect
12. #15689256C2semidirect
13. #15689205C2semidirect
14. #15689199C2semidirect
15. C47×#468C2semidirect
18. C22×D188C22semidirect
19. C2×D4×D47C22semidirect
22. C2×#10625337C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625325C22semidirect
25. C2×#10625336C22semidirect
30. C2×#10625324C22semidirect
31. #13094013C22semidirect
32. #13094011C22semidirect
35. #13094004C22semidirect
41. #13093986C22semidirect
42. #13093986C22semidirect
46. Dic47⋊C8C22semidirect
47. #13093947C22semidirect
48. #13093944C22semidirect
49. #13093944C22semidirect
50. #13093944C22semidirect
51. C22⋊(C47⋊C8)C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
54. C2×SD16×C47C22semidirect
55. C2×M16×C47C22semidirect
56. C22⋊Q8×C47C22semidirect
58. #107×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
119. D376D4semidirect
222. #468D47semidirect
231. C47#3273semidirect
242. C2×SD16C2×D47semidirect
248. C2×M16C2×D47semidirect
254. C22⋊Q8C2×D47semidirect
266. #107C2×D47semidirect
269. #103C2×D47semidirect
273. #102C2×D47semidirect