Finite Group Databasebeta

← #20247511

Subgroups — #20247511

Order 6016.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3C2×#13093993C211yesmaximal, characteristic
4C22×C22⋊Dic47C211yesmaximal, characteristic, complemented
5#15689051C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic, complemented
7#15689038C211yesmaximal, characteristic, complemented
8#15689035C211yesmaximal, characteristic, complemented
9#15689023C211yesmaximal, characteristic, complemented
10#15689016C211yesmaximal, characteristic, complemented
11#15689011C211yesmaximal, characteristic, complemented
12#15689000C211yesmaximal, characteristic, complemented
13#15689000C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C47×#379C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic, complemented
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic
21C23×Dic47C2211yescharacteristic
22#13094010—24no—
23#13094001—24no—
24#13093993—24no—
25C2×C4⋊Dic47C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic47—24no—
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C2×C4×Dic47C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C25×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C24×C47—22no—
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—22no—
60C24×C47—41no—
61C24×C47—41no—
62C24×C47C2311yescharacteristic
63C24×C47C2311yescharacteristic
64C24×C47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—22no—
75C2×C22⋊D47—22no—
76C2×C22⋊D47—22no—
77C2×C22⋊D47—41no—
78C2×C22⋊D47—41no—
79C22×Dic47—22no—
80C22×Dic47—22no—
81C22×Dic47—22no—
82C22×Dic47—22no—
83C22×Dic47—41no—
84C22×Dic47—41no—
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C2×Dic94—22no—
93C2×Dic94—22no—
94C2×Dic94—41no—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47—22no—
98C22⋊C4×C47—22no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊Dic47—22no—
102C22⋊Dic47—22no—
103C22⋊Dic47—22no—
104C22⋊Dic47—22no—
105C22⋊Dic47—22no—
106C22⋊Dic47D414yes—
107C22⋊Dic47D414yescomplemented
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—41no—
111(C2×D47)⋊C4—41no—
112C4⋊Dic47—22no—
113Dic47⋊C4—22no—
114Dic47⋊C4—22no—
115C4×Dic47—22no—
116C4×Dic47—41no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—28no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—44no—
135C23×C47—44no—
136C23×C47—44no—
137C23×C47—44no—
138C23×C47—44no—
139C23×C47—44no—
140C23×C47C2×D412yes—
141C23×C47C2×D412yes—
142C23×C47#4112yes—
143C23×C47#4112yes—
144C23×C47#4112yes—
145C23×C47C2411yescharacteristic
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47—21no—
152C22×D47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C22⋊D47—44no—
166C22⋊D47—44no—
167C22⋊D47—44no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—44no—
186C2×Dic47—44no—
187C2×Dic47C2×D412yes—
188C2×Dic47C2×D412yes—
189C2×Dic47C2×D412yes—
190C2×Dic47C2×D412yes—
191Dic94—44no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—22no—
203C22×C47—22no—
204C22×C47—416no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47—41no—
212C22×C47—41no—
213C22×C47#12414yescomplemented
214C22×C47C22×D411yescharacteristic
215C22×C47C22×D411yescharacteristic
216C22×C47C2×#4111yescharacteristic
217C22×C47C2×#4111yescharacteristic
218C22×C47C2×#4111yescharacteristic
219C22×C47H(5,𝔽2)11yescharacteristic
220C22×C47H(5,𝔽2)11yescharacteristic
221C2×D47—41no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C4×C47—41no—
229C4×C47—41no—
230C4×C47—41no—
231C4×C47—41no—
232Dic47—22no—
233Dic47—22no—
234Dic47—22no—
235Dic47—22no—
236Dic47—41no—
237Dic47—41no—
238Dic47—41no—
239#2472—471nomaximal, Sylow
240C2×C47—24no—
241C2×C47—42no—
242C2×C47—42no—
243C2×C47#52511yescharacteristic
244C2×C47C2×#12411yescharacteristic
245C2×C47#53811yescharacteristic
246C2×C47D4211yescharacteristic
247C2×C47#54611yescharacteristic
248C2×C47#54611yescharacteristic
249C2×C47#55111yescharacteristic
250D47—81no—
251C2×#124—471no—
252C2×C22⋊Q8—471no—
253C2×#120—471no—
254C22×C22⋊C4—471no—
255#397—471no—
256#394—471no—
257#394—471no—
258#393—471no—
259#390—471no—
260#388—471no—
261#388—471no—
262#386—471no—
263#386—471no—
264#379D4711yescharacteristic, complemented
265C4×C22⋊C4—471no—
266C47#247211yescharacteristic, complemented, Sylow
267C25C2×D4711yescharacteristic
268C22×Q8—471no—
269C22×D4—471no—
270C22×D4—471no—
271C22×D4—471no—
272C23×C4—471no—
273C23×C4—471no—
274#124—944no—
275C22⋊Q8—944no—
276#120—944no—
277C2×C4⋊C4—471no—
278C2×C4⋊C4—471no—
279C2×C4⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—471no—
282C2×C22⋊C4—471no—
283C2×C22⋊C4—471no—
284C2×C22⋊C4—471no—
285C2×C22⋊C4—471no—
286C2×C22⋊C4—471no—
287C2×C22⋊C4—471no—
288C2×C22⋊C4—471no—
289C2×C22⋊C4—471no—
290C2×C22⋊C4—471no—
291C2×C22⋊C4—944no—
292C2×C22⋊C4C2×D4711yescharacteristic
293C2×C22⋊C4C2×D4711yescharacteristic
294C2×C22⋊C4C2×D4711yescharacteristic
295C2×C22⋊C4C2×D4711yescharacteristic
296C2×C22⋊C4C2×D4711yescharacteristic
297C2×C22⋊C4C2×D4711yescharacteristic
298C2×C42—471no—
299C2×C42—471no—
300#95—471no—
301#95—471no—
302#95—471no—
303#95—471no—
304#95—471no—
305#95—471no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—471no—
314C24C22×D4711yescharacteristic
315C24C22×D4711yescharacteristic
316C24C22×D4711yescharacteristic
317C2×Q8—942no—
318C2×Q8—942no—
319C2×Q8—1881no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—942no—
323C2×D4—942no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—1881no—
328C2×D4—1881no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—471no—
332C22×C4—471no—
333C22×C4—471no—
334C22×C4—471no—
335C22×C4—471no—
336C22×C4—942no—
337C22×C4—942no—
338C22×C4—942no—
339C22×C4—942no—
340C22×C4—1881no—
341C22×C4—1881no—
342C22×C4C22×D4711yescharacteristic
343C22×C4C22×D4711yescharacteristic
344C22×C4C22×D4711yescharacteristic
345C22×C4C22×D4711yescharacteristic
346C4⋊C4—942no—
347C4⋊C4—942no—
348C4⋊C4—942no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—474no—
356C22⋊C4—474no—
357C22⋊C4—942no—
358C22⋊C4—942no—
359C22⋊C4—942no—
360C22⋊C4—942no—
361C22⋊C4—942no—
362C22⋊C4—942no—
363C22⋊C4—942no—
364C22⋊C4—1881no—
365C22⋊C4—1881no—
366C42—942no—
367C42—1881no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23#1062535012yes—
399C23D4×D4712yes—
400C23D4×D4712yes—
401C23#1062535212yes—
402C23#1062535212yes—
403C23C23×D4711yescharacteristic
404Q8—1884no—
405D4—1884no—
406D4—1884no—
407D4—1884no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—472no—
421C2×C4—472no—
422C2×C4—472no—
423C2×C4—472no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—1884no—
442C2×C4—1884no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22#1309401014yescomplemented
472C22C2×D4×D4711yescharacteristic
473C22C2×D4×D4711yescharacteristic
474C22C2×#1062535211yescharacteristic
475C22C2×#1062535211yescharacteristic
476C22C2×#1062535011yescharacteristic
477C22#1309406911yescharacteristic
478C22#1309406911yescharacteristic
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—942no—
484C4—942no—
485C4—942no—
486C4—942no—
487C4—1881no—
488C4—1881no—
489C4—1881no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—3761no—
494C2#1568962911yescharacteristic
495C2C2×#1309401011yescharacteristic
496C2#1568970811yescharacteristic
497C2#1568975511yescharacteristic
498C2#1568976011yescharacteristic
499C2#1568976311yescharacteristic
500C2#1568979911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#379C2
hypercenter#379D47
hypocenterC47#2472
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. C2×#13094001C2semidirect
4. C22×C22⋊Dic47C2semidirect
5. #15689051C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689035C2semidirect
9. #15689023C2semidirect
10. #15689016C2semidirect
11. #15689011C2semidirect
12. #15689000C2semidirect
13. #15689000C2semidirect
14. C22⋊C4×Dic47C2semidirect
15. C47×#379C2semidirect
16. C22×Dic94C22semidirect
25. C2×C4⋊Dic47C22semidirect
26. C2×Dic47⋊C4C22semidirect
27. C2×Dic47⋊C4C22semidirect
36. C2×(C2×D47)⋊C4C22semidirect
37. C2×(C2×D47)⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
40. C2×C4×Dic47C22semidirect
41. C2×C4×Dic47C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
107. C22⋊Dic47D4semidirect
213. C22×C47#124semidirect
264. #379D47semidirect
266. C47#2472semidirect
471. C22#13094010semidirect