Finite Group Databasebeta

← #20252626

Subgroups — #20252626

Order 6016.

758 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D47C211yesmaximal, characteristic, complemented
2C2×#13094053C211yesmaximal, characteristic, complemented
3C2×#13094048C211yesmaximal, characteristic, complemented
4#15689633C211yesmaximal, characteristic, complemented
5#15689288C211yesmaximal, characteristic, complemented
6#15689287C211yesmaximal, characteristic, complemented
7#15689286C211yesmaximal, characteristic, complemented
8#15689285C211yesmaximal, characteristic, complemented
9#15689267C211yesmaximal, characteristic, complemented
10#15689266C211yesmaximal, characteristic, complemented
11#15689265C211yesmaximal, characteristic, complemented
12#15689130C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#15689085C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625350—21no—
18C2×#10625350C2211yescharacteristic
19C2×#10625352—21no—
20C2×#10625352C2211yescharacteristic
21C2×#10625352C2211yescharacteristic
22#41×D47—24no—
23#41×D47—24no—
24C2×Q8×D47C2211yescharacteristic
25C2×D4×D47—21no—
26C2×D4×D47C2211yescharacteristic
27C22×C4×D47—21no—
28C22×C4×D47C2211yescharacteristic
29#13094053—24no—
30#13094048—24no—
31C2×Dic188C2211yescharacteristic, complemented
32C2×#10625337C2211yescharacteristic, complemented
33C2×#10625325C2211yescharacteristic, complemented
34C2×#10625335C2211yescharacteristic, complemented
35C2×#10625335C2211yescharacteristic, complemented
36C2×#10625334C2211yescharacteristic, complemented
37C2×#10625324C2211yescharacteristic
38C2×#10625324C2211yescharacteristic
39#13094006—21no—
40#13094004C2211yescharacteristic, complemented
41#13094003C2211yescharacteristic, complemented
42#13093995C2211yescharacteristic, complemented
43#13093992—21no—
44D4×Dic47—21no—
45(C22⋊D47)⋊C4—21no—
46#13093982C2211yescharacteristic
47#13093949C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52#13093944C2211yescharacteristic, complemented
53C22⋊(C47⋊C8)C2211yescharacteristic, complemented
54(C2×D47)⋊C8C2211yescharacteristic, complemented
55(C2×D47)⋊C8C2211yescharacteristic, complemented
56C2×#41×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic, complemented
58C2×D8×C47C2211yescharacteristic, complemented
59#121×C47C2211yescharacteristic, complemented
60#103×C47C2211yescharacteristic, complemented
61#102×C47C2211yescharacteristic, complemented
62C22⋊C8×C47C2211yescharacteristic, complemented
63C23×D47—21no—
64C23×D47D411yescharacteristic
65#41×C47—22no—
66#41×C47—22no—
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47D411yescharacteristic
82#10625354—22no—
83#10625354—22no—
84Q8×D47—22no—
85Q8×D47D414yescomplemented
86#10625352—28no—
87#10625352—22no—
88#10625352—22no—
89#10625352—22no—
90#10625352—22no—
91D4×D47—28no—
92D4×D47—22no—
93D4×D47D414yescomplemented
94#10625350—28no—
95#10625350—22no—
96#10625350—22no—
97C2×D188—21no—
98C2×D188C2311yescharacteristic
99C2×C4×D47—28no—
100C2×C4×D47—21no—
101C2×C4×D47—21no—
102C2×C4×D47—21no—
103C2×C4×D47—22no—
104C2×C4×D47—22no—
105C2×C4×D47D411yescharacteristic
106C2×C4×D47D411yescharacteristic
107C2×C4×D47C2311yescharacteristic
108C2×C4×D47C2311yescharacteristic
109C2×Dic94—21no—
110C2×Dic94C2311yescharacteristic
111C2×Dic94C2311yescharacteristic
112SD16×C47—22no—
113D8×C47—22no—
114C2×C8×C47C2311yescharacteristic
115C2×C8×C47C2311yescharacteristic
116C4⋊C4×C47C2311yescharacteristic
117C22⋊C4×C47—21no—
118C22⋊Dic47—21no—
119C22⋊Dic47—21no—
120#10625337—22no—
121#10625335—22no—
122#10625335—22no—
123#10625334—22no—
124(C2×D47)⋊C4—21no—
125(C2×D47)⋊C4—21no—
126C4⋊Dic47—21no—
127C4⋊Dic47C2311yescharacteristic
128Dic47⋊C4—21no—
129C4×Dic47—21no—
130C2×C47⋊C8C2311yescharacteristic
131C2×C47⋊C8C2311yescharacteristic
132Dic188—22no—
133#10625325—22no—
134#10625324—22no—
135#10625324—22no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47C2×D411yescharacteristic
139C22×D47—21no—
140C22×D47—22no—
141C22×D47—24no—
142C22×D47—41no—
143C22×D47—41no—
144C22×D47—42no—
145C22×D47—42no—
146C22×D47C2×D411yescharacteristic
147C22×D47C2×D411yescharacteristic
148Q8×C47—21no—
149Q8×C47C2×D412yes—
150D4×C47—24no—
151D4×C47—21no—
152D4×C47—21no—
153D4×C47—21no—
154D4×C47—42no—
155D4×C47C2×D412yes—
156C2×C4×C47—24no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47C2×D411yescharacteristic
162C2×C4×C47C2411yescharacteristic
163C22⋊D47—24no—
164C22⋊D47—24no—
165C22⋊D47—24no—
166C22⋊D47—42no—
167C22⋊D47—42no—
168C2×Dic47—24no—
169C2×Dic47—21no—
170C2×Dic47—22no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—42no—
174C2×Dic47C2×D411yescharacteristic
175C2×Dic47C2×D411yescharacteristic
176D188—24no—
177D188—21no—
178D188C2×D412yes—
179C4×D47—24no—
180C4×D47—24no—
181C4×D47—22no—
182C4×D47—24no—
183C4×D47—21no—
184C4×D47—21no—
185C4×D47—22no—
186C4×D47C2×D412yes—
187C4×D47C2×D412yes—
188Dic94—21no—
189Dic94—24no—
190Dic94—21no—
191Dic94—21no—
192Dic94C2×D412yes—
193C8×C47—21no—
194C8×C47—21no—
195C47⋊C8—21no—
196C47⋊C8—21no—
197C22×C47—21no—
198C22×C47—22no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47C22×D411yescharacteristic
207C2×D47—21no—
208C2×D47—21no—
209C2×D47—21no—
210C2×D47—22no—
211C2×D47—21no—
212C2×D47—21no—
213C2×D47—44no—
214C2×D47—48no—
215C2×D47—41no—
216C2×D47—41no—
217C2×D47#12012yes—
218C4×C47—22no—
219C4×C47—21no—
220C4×C47—41no—
221C4×C47C22×D411yescharacteristic
222C4×C47C22×D411yescharacteristic
223Dic47—22no—
224Dic47—21no—
225Dic47—41no—
226Dic47—41no—
227Dic47#12012yes—
228#3005—471nomaximal, Sylow
229C2×C47—41no—
230C2×C47—42no—
231C2×C47—81no—
232C2×C47C2×#12011yescharacteristic
233C2×C47#57511yescharacteristic
234C2×C47#57511yescharacteristic
235D47—22no—
236D47—41no—
237D47—42no—
238C22×#41—471no—
239C2×#137—471no—
240C2×AGL(1,ℤ/8)—471no—
241#525—471no—
242#452—471no—
243#452—471no—
244#452—471no—
245#452—471no—
246#449—471no—
247#449—471no—
248#449—471no—
249#449D4711yescharacteristic, complemented
250#419—471no—
251#418—471no—
252#407—471no—
253C47#300511yescharacteristic, complemented, Sylow
254C2×#41—471no—
255C2×#41—471no—
256C2×#41—471no—
257C2×#41—471no—
258C2×#41—941no—
259C2×#41—941no—
260C2×#41—944no—
261C2×#41—944no—
262C2×#41C2×D4711yescharacteristic
263C22×Q8—471no—
264C22×D4—471no—
265C22×D4—941no—
266C23×C4—471no—
267C23×C4—941no—
268#137—944no—
269AGL(1,ℤ/8)—944no—
270C2×Q16—471no—
271C2×Q16—471no—
272C2×SD16—471no—
273C2×SD16—471no—
274C2×SD16—471no—
275C2×SD16C2×D4711yescharacteristic, complemented
276C2×D8—471no—
277C2×D8C2×D4711yescharacteristic, complemented
278C2×M16—471no—
279C2×M16—471no—
280#123—941no—
281C22⋊Q8—471no—
282C22⋊Q8—471no—
283#121—471no—
284#121C2×D4711yescharacteristic, complemented
285#120—941no—
286C4×D4—941no—
287C4×D4—941no—
288#117—471no—
289#103—471no—
290#103—471no—
291#103—471no—
292#103C2×D4711yescharacteristic, complemented
293#102—471no—
294#102—471no—
295#102—471no—
296#102C2×D4711yescharacteristic, complemented
297C22⋊C8—471no—
298C22⋊C8—471no—
299C22⋊C8—471no—
300C22⋊C8C2×D4711yescharacteristic, complemented
301C24—471no—
302C24—941no—
303#41—22no—
304#41—22no—
305#41—942no—
306#41—942no—
307#41—948no—
308#41—942no—
309#41—942no—
310#41—942no—
311#41—948no—
312#41—942no—
313#41—942no—
314#41—942no—
315C2×Q8—474no—
316C2×Q8—471no—
317C2×Q8—471no—
318C2×Q8—941no—
319C2×Q8—942no—
320C2×Q8C22×D4711yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—474no—
324C2×D4—471no—
325C2×D4—941no—
326C2×D4—942no—
327C2×D4—941no—
328C2×D4—948no—
329C2×D4—941no—
330C2×D4—941no—
331C2×D4—941no—
332C2×D4—941no—
333C2×D4C22×D4711yescharacteristic
334C2×D4C22×D4711yescharacteristic
335C22×C4—21no—
336C22×C4—471no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—471no—
341C22×C4—942no—
342C22×C4—942no—
343C22×C4—941no—
344C22×C4—941no—
345C22×C4—948no—
346C22×C4—941no—
347C22×C4—941no—
348C22×C4—941no—
349C22×C4C22×D4711yescharacteristic
350Q16—942no—
351Q16—942no—
352SD16—22no—
353SD16—942no—
354SD16—942no—
355SD16—942no—
356D8—22no—
357D8—942no—
358M16—942no—
359M16—942no—
360C2×C8—471no—
361C2×C8—471no—
362C2×C8C22×D4711yescharacteristic
363C2×C8C22×D4711yescharacteristic
364C4⋊C4—471no—
365C4⋊C4—941no—
366C4⋊C4—941no—
367C4⋊C4C22×D4711yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—941no—
370C22⋊C4—941no—
371C22⋊C4—941no—
372C22⋊C4—941no—
373C42—941no—
374C23—21no—
375C23—21no—
376C23—471no—
377C23—471no—
378C23—944no—
379C23—942no—
380C23—941no—
381C23—1881no—
382C23—1881no—
383C23—1882no—
384C23—1882no—
385C23D4×D4711yescharacteristic
386Q8—21no—
387Q8—472no—
388Q8—944no—
389Q8—941no—
390Q8—941no—
391Q8—941no—
392Q8D4×D4712yes—
393D4—24no—
394D4—21no—
395D4—21no—
396D4—21no—
397D4—42no—
398D4—472no—
399D4—944no—
400D4—944no—
401D4—944no—
402D4—944no—
403D4—941no—
404D4—1882no—
405D4—1882no—
406D4D4×D4712yes—
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—471no—
413C2×C4—472no—
414C2×C4—472no—
415C2×C4—471no—
416C2×C4—942no—
417C2×C4—942no—
418C2×C4—944no—
419C2×C4—944no—
420C2×C4—944no—
421C2×C4—942no—
422C2×C4—944no—
423C2×C4—941no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—1882no—
429C2×C4D4×D4711yescharacteristic
430C2×C4C23×D4711yescharacteristic
431C8—21no—
432C8—21no—
433C8—941no—
434C8—941no—
435C22—21no—
436C22—22no—
437C22—21no—
438C22—21no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—472no—
445C22—941no—
446C22—941no—
447C22—942no—
448C22—941no—
449C22—941no—
450C22—941no—
451C22—1884no—
452C22—1888no—
453C22—1881no—
454C22—1881no—
455C22C2×D4×D4711yescharacteristic
456C4—21no—
457C4—22no—
458C4—41no—
459C4—472no—
460C4—941no—
461C4—942no—
462C4—1881no—
463C4—1881no—
464C4C2×D4×D4711yescharacteristic
465C4C2×D4×D4711yescharacteristic
466C2—41no—
467C2—42no—
468C2—81no—
469C2—942no—
470C2—1881no—
471C2—1882no—
472C2#120×D4711yescharacteristic
473C2#1568991911yescharacteristic
474C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3005
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#41×D47C2semidirect
2. C2×#13094053C2semidirect
3. C2×#13094048C2semidirect
4. #15689633C2semidirect
5. #15689288C2semidirect
6. #15689287C2semidirect
7. #15689286C2semidirect
8. #15689285C2semidirect
9. #15689267C2semidirect
10. #15689266C2semidirect
11. #15689265C2semidirect
12. #15689130C2semidirect
13. #15689126C2semidirect
14. #15689085C2semidirect
15. C47×#449C2semidirect
31. C2×Dic188C22semidirect
32. C2×#10625337C22semidirect
33. C2×#10625325C22semidirect
34. C2×#10625335C22semidirect
35. C2×#10625335C22semidirect
36. C2×#10625334C22semidirect
40. #13094004C22semidirect
41. #13094003C22semidirect
42. #13093995C22semidirect
47. #13093949C22semidirect
48. #13093948C22semidirect
49. #13093947C22semidirect
50. #13093946C22semidirect
51. #13093945C22semidirect
52. #13093944C22semidirect
53. C22⋊(C47⋊C8)C22semidirect
54. (C2×D47)⋊C8C22semidirect
55. (C2×D47)⋊C8C22semidirect
57. C2×SD16×C47C22semidirect
58. C2×D8×C47C22semidirect
59. #121×C47C22semidirect
60. #103×C47C22semidirect
61. #102×C47C22semidirect
62. C22⋊C8×C47C22semidirect
85. Q8×D47D4semidirect
93. D4×D47D4semidirect
249. #449D47semidirect
253. C47#3005semidirect
275. C2×SD16C2×D47semidirect
277. C2×D8C2×D47semidirect
284. #121C2×D47semidirect
292. #103C2×D47semidirect
296. #102C2×D47semidirect
300. C22⋊C8C2×D47semidirect