Finite Group Databasebeta

← #20252660

Subgroups — #20252660

Order 6016.

752 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094069C211yesmaximal, characteristic
2C2×#13094053C211yesmaximal, characteristic, complemented
3C2×SD16×D47C211yesmaximal, characteristic, complemented
4#15689696C211yesmaximal, characteristic, complemented
5#15689287C211yesmaximal, characteristic, complemented
6#15689286C211yesmaximal, characteristic, complemented
7#15689283C211yesmaximal, characteristic, complemented
8#15689282C211yesmaximal, characteristic, complemented
9#15689275C211yesmaximal, characteristic, complemented
10#15689274C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689126C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16#13094069—24no—
17#13094069—24no—
18C2×#10625350C2211yescharacteristic
19C2×#10625350C2211yescharacteristic
20C2×#10625352—21no—
21C2×#10625352C2211yescharacteristic
22C2×#10625352C2211yescharacteristic
23C2×Q8×D47C2211yescharacteristic, complemented
24C22×C22⋊D47—21no—
25C22×C22⋊D47—21no—
26C2×D4×D47—21no—
27C2×D4×D47C2211yescharacteristic
28C2×D4×D47C2211yescharacteristic
29#13094053—24no—
30C2×Dic188C2211yescharacteristic, complemented
31C2×#10625337C2211yescharacteristic, complemented
32C2×#10625325C2211yescharacteristic, complemented
33C2×#10625335C2211yescharacteristic, complemented
34C2×#10625335C2211yescharacteristic, complemented
35C2×#10625336C2211yescharacteristic, complemented
36SD16×D47—24no—
37C2×#10625324C2211yescharacteristic, complemented
38C2×C8×D47C2211yescharacteristic, complemented
39#13094023—21no—
40#13094010—21no—
41#13094009—21no—
42#13094006—21no—
43#13094004C2211yescharacteristic, complemented
44#13094003C2211yescharacteristic, complemented
45#13094000C2211yescharacteristic, complemented
46#13093982C2211yescharacteristic, complemented
47#13093949C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52#13093944C2211yescharacteristic, complemented
53C22⋊(C47⋊C8)C2211yescharacteristic, complemented
54(C2×D47)⋊C8C2211yescharacteristic, complemented
55(C2×D47)⋊C8C2211yescharacteristic, complemented
56C22×D4×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic, complemented
58C2×SD16×C47C2211yescharacteristic, complemented
59C22⋊Q8×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61#102×C47C2211yescharacteristic, complemented
62C22⋊C8×C47C2211yescharacteristic, complemented
63C24×C47—21no—
64C23×D47—21no—
65C23×D47—21no—
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47—21no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—28no—
74C2×C22⋊D47—28no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47D411yescharacteristic
81C2×C22⋊D47D411yescharacteristic
82C22×Dic47—21no—
83C22×Dic47—21no—
84Q8×D47—22no—
85Q8×D47—22no—
86#10625352—28no—
87#10625352—22no—
88#10625352—22no—
89#10625352—22no—
90#10625352D414yes—
91D4×D47—28no—
92D4×D47—22no—
93D4×D47—22no—
94D4×D47—22no—
95D4×D47D414yes—
96#10625350—22no—
97#10625350—22no—
98#10625350—22no—
99#10625350—22no—
100C2×D188D411yescharacteristic
101C2×D188C2311yescharacteristic
102C2×C4×D47—21no—
103C2×C4×D47—21no—
104C2×C4×D47C2311yescharacteristic
105C2×C4×D47C2311yescharacteristic
106C2×Dic94—21no—
107C2×Dic94D411yescharacteristic
108C2×Dic94C2311yescharacteristic
109C2×Dic94C2311yescharacteristic
110SD16×C47—22no—
111SD16×C47—22no—
112C2×C8×C47C2311yescharacteristic
113C2×C8×C47C2311yescharacteristic
114C4⋊C4×C47—21no—
115C4⋊C4×C47C2311yescharacteristic
116C22⋊C4×C47—21no—
117C22⋊Dic47—21no—
118#10625337—22no—
119#10625336—22no—
120#10625335—22no—
121#10625335—22no—
122(C2×D47)⋊C4—21no—
123(C2×D47)⋊C4—21no—
124(C2×D47)⋊C4—21no—
125C4⋊Dic47—21no—
126C4⋊Dic47C2311yescharacteristic
127Dic47⋊C4—21no—
128Dic47⋊C4—21no—
129C4×Dic47—21no—
130C2×C47⋊C8C2311yescharacteristic
131C2×C47⋊C8C2311yescharacteristic
132Dic188—22no—
133#10625325—22no—
134#10625324—22no—
135C8×D47—22no—
136C23×C47—24no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—81no—
140C23×C47—81no—
141C23×C47C2×D411yescharacteristic
142C22×D47—21no—
143C22×D47—24no—
144C22×D47—24no—
145C22×D47—81no—
146C22×D47—81no—
147C22×D47—81no—
148C22×D47—81no—
149C22×D47C2×D411yescharacteristic
150C22×D47C2×D411yescharacteristic
151Q8×C47—21no—
152Q8×C47—21no—
153D4×C47—24no—
154D4×C47—21no—
155D4×C47—21no—
156D4×C47C2×D412yes—
157D4×C47C2×D412yes—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47C2×D411yescharacteristic
163C2×C4×C47C2411yescharacteristic
164C22⋊D47—24no—
165C22⋊D47—24no—
166C22⋊D47—24no—
167C22⋊D47—22no—
168C22⋊D47—24no—
169C22⋊D47—22no—
170C22⋊D47—24no—
171C2×Dic47—24no—
172C2×Dic47—21no—
173C2×Dic47—24no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47C2×D411yescharacteristic
177C2×Dic47C2×D411yescharacteristic
178D188—22no—
179D188—21no—
180D188C2×D412yes—
181C4×D47—24no—
182C4×D47—21no—
183C4×D47—21no—
184C4×D47—42no—
185C4×D47C2×D412yes—
186C4×D47C2×D412yes—
187Dic94—21no—
188Dic94—22no—
189Dic94—21no—
190Dic94—21no—
191Dic94—42no—
192Dic94C2×D412yes—
193C8×C47—21no—
194C8×C47—21no—
195C47⋊C8—21no—
196C47⋊C8—21no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—21no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—84no—
207C22×C47C22×D411yescharacteristic
208C2×D47—21no—
209C2×D47—21no—
210C2×D47—21no—
211C2×D47—22no—
212C2×D47—21no—
213C2×D47—21no—
214C2×D47—41no—
215C2×D47—41no—
216C2×D47—84no—
217C2×D47—84no—
218C2×D47#12012yes—
219C4×C47—21no—
220C4×C47—41no—
221C4×C47—41no—
222C4×C47C22×D411yescharacteristic
223C4×C47C22×D411yescharacteristic
224Dic47—21no—
225Dic47—22no—
226Dic47—41no—
227Dic47—41no—
228Dic47#12012yes—
229#3009—471nomaximal, Sylow
230C2×C47—42no—
231C2×C47—42no—
232C2×C47—41no—
233C2×C47C2×#12011yescharacteristic
234C2×C47#57711yescharacteristic
235C2×C47#57711yescharacteristic
236D47—22no—
237D47—41no—
238D47—42no—
239C2×H(5,𝔽2)—471no—
240C2×#137—471no—
241C22×SD16—471no—
242#536—471no—
243#452—471no—
244#452—471no—
245#452—471no—
246#452—471no—
247#450—471no—
248#450—471no—
249#450—471no—
250#450D4711yescharacteristic, complemented
251#418—471no—
252#416—471no—
253#408—471no—
254C47#300911yescharacteristic, complemented, Sylow
255H(5,𝔽2)—944no—
256H(5,𝔽2)—944no—
257C2×#41—471no—
258C2×#41—471no—
259C2×#41—471no—
260C2×#41—471no—
261C2×#41—941no—
262C22×Q8—471no—
263C22×D4—471no—
264C22×D4—471no—
265C22×D4—941no—
266C22×D4—941no—
267C22×D4—941no—
268C22×D4C2×D4711yescharacteristic
269#137—944no—
270C2×Q16—471no—
271C2×Q16—471no—
272C2×SD16—471no—
273C2×SD16—471no—
274C2×SD16—471no—
275C2×SD16—471no—
276C2×SD16—944no—
277C2×SD16C2×D4711yescharacteristic, complemented
278C2×SD16C2×D4711yescharacteristic, complemented
279C2×M16—471no—
280C22×C8—471no—
281C4⋊Q8—941no—
282#124—941no—
283#123—941no—
284#123—941no—
285C22⋊Q8—471no—
286C22⋊Q8—471no—
287C22⋊Q8—471no—
288C22⋊Q8C2×D4711yescharacteristic, complemented
289#117—471no—
290#103—471no—
291#103—471no—
292#102—471no—
293#102—471no—
294#102—471no—
295#102—471no—
296#102C2×D4711yescharacteristic, complemented
297#102C2×D4711yescharacteristic, complemented
298C22⋊C8—471no—
299C22⋊C8—471no—
300C22⋊C8—471no—
301C22⋊C8C2×D4711yescharacteristic, complemented
302C24—21no—
303C24—941no—
304C24—941no—
305#41—474no—
306#41—942no—
307#41—942no—
308#41—942no—
309#41—942no—
310#41—942no—
311#41—942no—
312#41—948no—
313#41—942no—
314C2×Q8—471no—
315C2×Q8—471no—
316C2×Q8—471no—
317C2×Q8—941no—
318C2×Q8—942no—
319C2×Q8—942no—
320C2×Q8C22×D4711yescharacteristic
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—21no—
324C2×D4—474no—
325C2×D4—471no—
326C2×D4—471no—
327C2×D4—471no—
328C2×D4—471no—
329C2×D4—942no—
330C2×D4—941no—
331C2×D4—941no—
332C2×D4—942no—
333C2×D4—948no—
334C2×D4—941no—
335C2×D4—941no—
336C2×D4—948no—
337C2×D4—948no—
338C2×D4—941no—
339C2×D4—942no—
340C2×D4C22×D4711yescharacteristic
341C2×D4C22×D4711yescharacteristic
342C22×C4—471no—
343C22×C4—471no—
344C22×C4—941no—
345C22×C4—941no—
346C22×C4—941no—
347C22×C4—941no—
348C22×C4C22×D4711yescharacteristic
349Q16—942no—
350Q16—942no—
351SD16—22no—
352SD16—22no—
353SD16—942no—
354SD16—942no—
355SD16—942no—
356SD16—942no—
357M16—942no—
358C2×C8—471no—
359C2×C8—471no—
360C2×C8—942no—
361C2×C8C22×D4711yescharacteristic
362C2×C8C22×D4711yescharacteristic
363C4⋊C4—21no—
364C4⋊C4—471no—
365C4⋊C4—941no—
366C4⋊C4—941no—
367C4⋊C4—941no—
368C4⋊C4C22×D4711yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—941no—
371C22⋊C4—941no—
372C22⋊C4—941no—
373C22⋊C4—941no—
374C42—941no—
375C23—24no—
376C23—21no—
377C23—21no—
378C23—81no—
379C23—81no—
380C23—471no—
381C23—471no—
382C23—944no—
383C23—944no—
384C23—941no—
385C23—3761no—
386C23—3761no—
387C23—3761no—
388C23—3761no—
389C23D4×D4711yescharacteristic
390Q8—21no—
391Q8—21no—
392Q8—472no—
393Q8—942no—
394Q8—941no—
395Q8—941no—
396Q8—941no—
397Q8—1882no—
398D4—24no—
399D4—21no—
400D4—21no—
401D4—472no—
402D4—942no—
403D4—942no—
404D4—944no—
405D4—942no—
406D4—944no—
407D4—944no—
408D4—944no—
409D4—944no—
410D4—941no—
411D4D4×D4712yes—
412D4D4×D4712yes—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—471no—
418C2×C4—472no—
419C2×C4—472no—
420C2×C4—471no—
421C2×C4—944no—
422C2×C4—944no—
423C2×C4—944no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—1882no—
430C2×C4D4×D4711yescharacteristic
431C2×C4C23×D4711yescharacteristic
432C8—21no—
433C8—21no—
434C8—941no—
435C8—941no—
436C22—21no—
437C22—22no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—84no—
446C22—472no—
447C22—941no—
448C22—941no—
449C22—942no—
450C22—941no—
451C22—941no—
452C22—941no—
453C22—3764no—
454C22—3764no—
455C22—1881no—
456C22—1881no—
457C22C2×D4×D4711yescharacteristic
458C4—21no—
459C4—41no—
460C4—41no—
461C4—472no—
462C4—941no—
463C4—942no—
464C4—1881no—
465C4—1881no—
466C4C2×D4×D4711yescharacteristic
467C4C2×D4×D4711yescharacteristic
468C2—41no—
469C2—42no—
470C2—42no—
471C2—942no—
472C2—1881no—
473C2—1882no—
474C2#120×D4711yescharacteristic
475C2#1568992911yescharacteristic
476C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3009
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×#13094053C2semidirect
3. C2×SD16×D47C2semidirect
4. #15689696C2semidirect
5. #15689287C2semidirect
6. #15689286C2semidirect
7. #15689283C2semidirect
8. #15689282C2semidirect
9. #15689275C2semidirect
10. #15689274C2semidirect
11. #15689272C2semidirect
12. #15689126C2semidirect
13. #15689116C2semidirect
14. #15689088C2semidirect
15. C47×#450C2semidirect
23. C2×Q8×D47C22semidirect
30. C2×Dic188C22semidirect
31. C2×#10625337C22semidirect
32. C2×#10625325C22semidirect
33. C2×#10625335C22semidirect
34. C2×#10625335C22semidirect
35. C2×#10625336C22semidirect
37. C2×#10625324C22semidirect
38. C2×C8×D47C22semidirect
43. #13094004C22semidirect
44. #13094003C22semidirect
45. #13094000C22semidirect
46. #13093982C22semidirect
47. #13093949C22semidirect
48. #13093947C22semidirect
49. #13093946C22semidirect
50. #13093945C22semidirect
51. #13093945C22semidirect
52. #13093944C22semidirect
53. C22⋊(C47⋊C8)C22semidirect
54. (C2×D47)⋊C8C22semidirect
55. (C2×D47)⋊C8C22semidirect
57. C2×SD16×C47C22semidirect
58. C2×SD16×C47C22semidirect
59. C22⋊Q8×C47C22semidirect
60. #102×C47C22semidirect
61. #102×C47C22semidirect
62. C22⋊C8×C47C22semidirect
250. #450D47semidirect
254. C47#3009semidirect
277. C2×SD16C2×D47semidirect
278. C2×SD16C2×D47semidirect
288. C22⋊Q8C2×D47semidirect
296. #102C2×D47semidirect
297. #102C2×D47semidirect
301. C22⋊C8C2×D47semidirect