Finite Group Databasebeta

← #20257054

Subgroups — #20257054

Order 6016.

1658 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×#13094070C211yesmaximal, characteristic, complemented
2C22×#10625354C211yesmaximal, characteristic, complemented
3#15689795C211yesmaximal, characteristic, complemented
4#15689792C211yesmaximal, characteristic, complemented
5#15689784C211yesmaximal, characteristic, complemented
6#15689766C213yesmaximal, complemented
7#15689764C213yesmaximal, complemented
8D4×D188C213yesmaximal, complemented
9#15689757C213yesmaximal, complemented
10#15689703C213yesmaximal, complemented
11#15689691C213yesmaximal, complemented
12#15689632C213yesmaximal, complemented
13#121×D47C213yesmaximal, complemented
14#15689605C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16#13094070—28no—
17C2×#10625354—28no—
18C2×#10625354C2211yescharacteristic
19C2×#10625354C2213yescomplemented
20C2×#10625354C2211yescharacteristic, complemented
21C2×#10625354C2211yescharacteristic, complemented
22C2×#10625354C2213yescomplemented
23C2×#10625350C2213yescomplemented
24C22×D188C2213yescomplemented
25C22×D188C2213yescomplemented
26C2×D4×D47C2213yescomplemented
27C2×D4×D47C2213yescomplemented
28C2×D4×D47C2216yescomplemented
29C22×C4×D47C2213yescomplemented
30#13094021C2213yescomplemented
31#13094020C2213yescomplemented
32#13094013C2213yescomplemented
33#13094009C2213yescomplemented
34#13094006C2213yescomplemented
35#13094002C2213yescomplemented
36#13094001C2211yescharacteristic, complemented
37#13094000C2213yescomplemented
38#13093999C2213yescomplemented
39#13093999C2216yescomplemented
40#13093999C2213yescomplemented
41#13093998C2213yescomplemented
42#13093998C2213yescomplemented
43#13093997C2216yescomplemented
44#13093997C2216yescomplemented
45#13093997C2213yescomplemented
46#13093996C2213yescomplemented
47#13093995C2213yescomplemented
48#13093994C2216yescomplemented
49#13093994C2213yescomplemented
50#13093994C2216yescomplemented
51#13093992C2213yescomplemented
52Q8×Dic47C2211yescharacteristic, complemented
53C4×D188C2213yescomplemented
54C4×D188C2213yescomplemented
55#13093986C2213yescomplemented
56C4×C22⋊D47C2213yescomplemented
57C4×C22⋊D47C2213yescomplemented
58#13093981C2213yescomplemented
59C4⋊C4×D47C2213yescomplemented
60C22⋊C4×D47C2216yescomplemented
61C2×#41×C47C2211yescharacteristic, complemented
62C22×Q8×C47C2211yescharacteristic, complemented
63#124×C47C2213yescomplemented
64C22⋊Q8×C47C2213yescomplemented
65#121×C47C2213yescomplemented
66C4×Q8×C47C2211yescharacteristic, complemented
67C4×D4×C47C2213yescomplemented
68C23×D47C2313yes—
69C23×D47C2316yes—
70#41×C47—24no—
71C2×Q8×C47—24no—
72C2×Q8×C47C2313yes—
73C2×Q8×C47C2311yescharacteristic
74C2×D4×C47C2313yes—
75C2×D4×C47C2313yes—
76C22×C4×C47C2313yes—
77C22×C4×C47C2313yes—
78C2×C22⋊D47C2313yes—
79C2×C22⋊D47C2313yes—
80C2×C22⋊D47C2313yes—
81C2×C22⋊D47C2313yes—
82C2×C22⋊D47C2316yes—
83C22×Dic47C2311yescharacteristic
84#10625354—24no—
85#10625354—24no—
86#10625354—212no—
87#10625354—212no—
88#10625354D418yescomplemented
89D4×D47—212no—
90D4×D47—212no—
91D4×D47—412no—
92#10625350—212no—
93C2×D188—212no—
94C2×D188—212no—
95C2×D188C2316yes—
96C2×D188C2313yes—
97C2×D188C2313yes—
98C2×D188C2313yes—
99C2×D188C2313yes—
100C2×D188C2316yes—
101C2×D188C2313yes—
102C2×C4×D47—212no—
103C2×C4×D47C2313yes—
104C2×C4×D47C2313yes—
105C2×C4×D47C2313yes—
106C2×C4×D47C2313yes—
107C2×C4×D47C2316yes—
108C2×C4×D47C2313yes—
109C2×Dic94C2311yescharacteristic
110C4⋊C4×C47C2313yes—
111C4⋊C4×C47C2313yes—
112C22⋊C4×C47C2311yescharacteristic
113C22⋊C4×C47C2313yes—
114C22⋊C4×C47C2316yes—
115C42×C47C2313yes—
116C22⋊Dic47C2313yes—
117C22⋊Dic47C2311yescharacteristic
118(C2×D47)⋊C4C2313yes—
119(C2×D47)⋊C4C2316yes—
120(C2×D47)⋊C4C2313yes—
121(C2×D47)⋊C4C2313yes—
122(C2×D47)⋊C4C2313yes—
123(C2×D47)⋊C4C2313yes—
124(C2×D47)⋊C4C2313yes—
125C4⋊Dic47C2313yes—
126C4⋊Dic47C2311yescharacteristic
127Dic47⋊C4C2313yes—
128Dic47⋊C4C2311yescharacteristic
129Dic47⋊C4C2311yescharacteristic
130Dic47⋊C4C2313yes—
131C4×Dic47C2313yes—
132C23×C47C2413yes—
133C23×C47C2411yescharacteristic
134C22×D47—26no—
135C22×D47—26no—
136C22×D47—212no—
137C22×D47—43no—
138C22×D47—46no—
139C22×D47—46no—
140C22×D47C2413yes—
141C22×D47C2413yes—
142C22×D47C2413yes—
143Q8×C47—26no—
144Q8×C47C2×D414yescomplemented
145D4×C47—26no—
146D4×C47—26no—
147C2×C4×C47—26no—
148C2×C4×C47—26no—
149C2×C4×C47C2411yescharacteristic
150C2×C4×C47C2413yes—
151C2×C4×C47C2413yes—
152C2×C4×C47C2411yescharacteristic
153C2×C4×C47C2413yes—
154C22⋊D47—26no—
155C22⋊D47—26no—
156C22⋊D47—26no—
157C22⋊D47—46no—
158C22⋊D47—43no—
159C2×Dic47—22no—
160C2×Dic47C2411yescharacteristic
161C2×Dic47C2413yes—
162C2×Dic47C2411yescharacteristic
163C2×Dic47C2411yescharacteristic
164C2×Dic47C2411yescharacteristic
165D188—26no—
166D188—212no—
167D188—26no—
168D188—26no—
169D188—43no—
170D188—46no—
171D188C2×D4112yescomplemented
172C4×D47—26no—
173C4×D47—26no—
174C4×D47—26no—
175C4×D47—26no—
176C4×D47—46no—
177C4×D47C2×D4112yescomplemented
178Dic94—22no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—23no—
182C22×C47—23no—
183C22×C47—23no—
184C22×C47H(5,𝔽2)12yescomplemented
185C22×C47C2511yescharacteristic
186C2×D47—23no—
187C2×D47—23no—
188C2×D47—23no—
189C2×D47—23no—
190C2×D47—23no—
191C2×D47—23no—
192C2×D47—23no—
193C2×D47—23no—
194C2×D47—412no—
195C2×D47—812no—
196C2×D47C22×D416yes—
197C4×C47—21no—
198C4×C47—23no—
199C4×C47—23no—
200C4×C47—21no—
201C4×C47C22×D416yes—
202Dic47—21no—
203Dic47—21no—
204Dic47—23no—
205Dic47—21no—
206Dic47C22×D412yes—
207#3488—471nomaximal, Sylow
208C2×C47—22no—
209C2×C47—43no—
210C2×C47C23×D411yescharacteristic
211C2×C47C2×H(5,𝔽2)11yescharacteristic
212C2×C47#58511yescharacteristic
213D47—26no—
214D47—43no—
215D47—43no—
216C2×H(5,𝔽2)—471no—
217C22×#41—471no—
218#550—471no—
219#550—471no—
220#548—471no—
221#548D4711yescharacteristic, complemented
222#546—473no—
223#546—473no—
224D42—473no—
225D42—473no—
226#537—473no—
227#535—473no—
228#525—473no—
229C2×#121—473no—
230#520—471no—
231C47#348811yescharacteristic, complemented, Sylow
232H(5,𝔽2)—948no—
233C2×#41—471no—
234C2×#41—473no—
235C2×#41—473no—
236C2×#41—471no—
237C2×#41—471no—
238C2×#41—473no—
239C2×#41—948no—
240C2×#41C2×D4711yescharacteristic, complemented
241C22×Q8C2×D4711yescharacteristic, complemented
242C22×D4—473no—
243C22×D4—473no—
244C22×D4—476no—
245C22×D4—473no—
246C22×D4—473no—
247C23×C4—473no—
248#127—473no—
249#127—473no—
250#124—473no—
251#124C2×D4713yescomplemented
252#123—473no—
253#123—473no—
254C22⋊Q8—473no—
255C22⋊Q8—473no—
256C22⋊Q8—471no—
257C22⋊Q8C2×D4713yescomplemented
258#121—473no—
259#121—473no—
260#121—473no—
261#121—473no—
262#121—473no—
263#121—476no—
264#121—473no—
265#121—476no—
266#121—473no—
267#121—476no—
268#121C2×D4713yescomplemented
269#120—473no—
270#120—473no—
271#120—476no—
272#120—476no—
273C4×Q8—471no—
274C4×Q8C2×D4711yescharacteristic, complemented
275C4×D4—473no—
276C4×D4—473no—
277C4×D4—473no—
278C4×D4—473no—
279C4×D4—473no—
280C4×D4C2×D4713yescomplemented
281#117—473no—
282C2×C4⋊C4—473no—
283C2×C22⋊C4—476no—
284C24—473no—
285C24—476no—
286#41—24no—
287#41—478no—
288#41—9412no—
289#41—9412no—
290#41—9412no—
291#41—944no—
292#41—944no—
293C2×Q8—24no—
294C2×Q8—471no—
295C2×Q8C22×D4713yes—
296C2×Q8C22×D4711yescharacteristic
297C2×D4—473no—
298C2×D4—473no—
299C2×D4—473no—
300C2×D4—473no—
301C2×D4—476no—
302C2×D4—473no—
303C2×D4—476no—
304C2×D4—473no—
305C2×D4—473no—
306C2×D4—473no—
307C2×D4—473no—
308C2×D4—476no—
309C2×D4—9412no—
310C2×D4—9412no—
311C2×D4—9412no—
312C2×D4—9412no—
313C2×D4—18812no—
314C2×D4C22×D4713yes—
315C2×D4C22×D4713yes—
316C22×C4—473no—
317C22×C4—471no—
318C22×C4—473no—
319C22×C4—473no—
320C22×C4—473no—
321C22×C4—473no—
322C22×C4—476no—
323C22×C4—9412no—
324C22×C4C22×D4713yes—
325C22×C4C22×D4713yes—
326C4⋊C4—473no—
327C4⋊C4—471no—
328C4⋊C4—471no—
329C4⋊C4—473no—
330C4⋊C4—473no—
331C4⋊C4—471no—
332C4⋊C4C22×D4713yes—
333C4⋊C4C22×D4713yes—
334C22⋊C4—473no—
335C22⋊C4—471no—
336C22⋊C4—473no—
337C22⋊C4—476no—
338C22⋊C4—473no—
339C22⋊C4—473no—
340C22⋊C4—473no—
341C22⋊C4—473no—
342C22⋊C4—473no—
343C22⋊C4C22×D4716yes—
344C22⋊C4C22×D4711yescharacteristic
345C22⋊C4C22×D4713yes—
346C42—473no—
347C42C22×D4713yes—
348C23—473no—
349C23—473no—
350C23—473no—
351C23—9412no—
352C23—946no—
353C23—946no—
354C23—1886no—
355C23—1886no—
356C23—1883no—
357C23C23×D4713yes—
358C23C23×D4711yescharacteristic
359Q8—26no—
360Q8—942no—
361Q8D4×D4714yescomplemented
362D4—26no—
363D4—26no—
364D4—4712no—
365D4—946no—
366D4—9412no—
367D4—946no—
368D4—946no—
369D4—946no—
370D4—946no—
371D4—946no—
372D4—1883no—
373D4—1886no—
374D4—1883no—
375D4—1886no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—471no—
379C2×C4—4712no—
380C2×C4—471no—
381C2×C4—473no—
382C2×C4—471no—
383C2×C4—471no—
384C2×C4—946no—
385C2×C4—946no—
386C2×C4—942no—
387C2×C4—946no—
388C2×C4—946no—
389C2×C4—1886no—
390C2×C4C23×D4711yescharacteristic
391C2×C4C23×D4713yes—
392C2×C4C23×D4713yes—
393C2×C4C23×D4711yescharacteristic
394C2×C4C23×D4713yes—
395C22—21no—
396C22—21no—
397C22—23no—
398C22—23no—
399C22—23no—
400C22—476no—
401C22—943no—
402C22—943no—
403C22—943no—
404C22—943no—
405C22—943no—
406C22—943no—
407C22—943no—
408C22—943no—
409C22—37612no—
410C22—18812no—
411C22#1309407012yescomplemented
412C22C24×D4711yescharacteristic
413C4—21no—
414C4—23no—
415C4—23no—
416C4—21no—
417C4—472no—
418C4—941no—
419C4—941no—
420C4—943no—
421C4—941no—
422C4C2×D4×D4716yes—
423C2—22no—
424C2—43no—
425C2—946no—
426C2—1883no—
427C2—1883no—
428C2C22×D4×D4711yescharacteristic
429C2C2×#1309407011yescharacteristic
430C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3488
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C22×#10625354C2semidirect
3. #15689795C2semidirect
4. #15689792C2semidirect
5. #15689784C2semidirect
6. #15689766C2semidirect
7. #15689764C2semidirect
8. D4×D188C2semidirect
9. #15689757C2semidirect
10. #15689703C2semidirect
11. #15689691C2semidirect
12. #15689632C2semidirect
13. #121×D47C2semidirect
14. #15689605C2semidirect
15. C47×#548C2semidirect
19. C2×#10625354C22semidirect
20. C2×#10625354C22semidirect
21. C2×#10625354C22semidirect
22. C2×#10625354C22semidirect
23. C2×#10625350C22semidirect
24. C22×D188C22semidirect
25. C22×D188C22semidirect
26. C2×D4×D47C22semidirect
27. C2×D4×D47C22semidirect
28. C2×D4×D47C22semidirect
29. C22×C4×D47C22semidirect
30. #13094021C22semidirect
31. #13094020C22semidirect
32. #13094013C22semidirect
33. #13094009C22semidirect
34. #13094006C22semidirect
35. #13094002C22semidirect
36. #13094001C22semidirect
37. #13094000C22semidirect
38. #13093999C22semidirect
39. #13093999C22semidirect
40. #13093999C22semidirect
41. #13093998C22semidirect
42. #13093998C22semidirect
43. #13093997C22semidirect
44. #13093997C22semidirect
45. #13093997C22semidirect
46. #13093996C22semidirect
47. #13093995C22semidirect
48. #13093994C22semidirect
49. #13093994C22semidirect
50. #13093994C22semidirect
51. #13093992C22semidirect
52. Q8×Dic47C22semidirect
53. C4×D188C22semidirect
54. C4×D188C22semidirect
55. #13093986C22semidirect
56. C4×C22⋊D47C22semidirect
57. C4×C22⋊D47C22semidirect
58. #13093981C22semidirect
59. C4⋊C4×D47C22semidirect
60. C22⋊C4×D47C22semidirect
61. C2×#41×C47C22semidirect
62. C22×Q8×C47C22semidirect
63. #124×C47C22semidirect
64. C22⋊Q8×C47C22semidirect
65. #121×C47C22semidirect
66. C4×Q8×C47C22semidirect
67. C4×D4×C47C22semidirect
88. #10625354D4semidirect
144. Q8×C47C2×D4semidirect
171. D188C2×D4semidirect
177. C4×D47C2×D4semidirect
184. C22×C47H(5,𝔽2)semidirect
221. #548D47semidirect
231. C47#3488semidirect
240. C2×#41C2×D47semidirect
241. C22×Q8C2×D47semidirect
251. #124C2×D47semidirect
257. C22⋊Q8C2×D47semidirect
268. #121C2×D47semidirect
274. C4×Q8C2×D47semidirect
280. C4×D4C2×D47semidirect
361. Q8D4×D47semidirect
411. C22#13094070semidirect