Finite Group Databasebeta

← #20247510

Subgroups — #20247510

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×#13094000C211yesmaximal, characteristic, complemented
2C2×#13093992C211yesmaximal, characteristic
3C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689051C211yesmaximal, characteristic, complemented
5#15689039C211yesmaximal, characteristic, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689034C211yesmaximal, characteristic, complemented
8#15689023C211yesmaximal, characteristic, complemented
9#15689016C211yesmaximal, characteristic, complemented
10#15689014C211yesmaximal, characteristic, complemented
11#15688999C211yesmaximal, characteristic, complemented
12#15688999C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×#124×C47C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13094000—24no—
22#13093992—24no—
23C2×C4⋊Dic47C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic, complemented
30C2×C22⋊Dic47C2211yescharacteristic, complemented
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C22⋊C4×D47—24no—
40C2×C4×Dic47C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C22×Q8×C47C2211yescharacteristic, complemented
48C22×D4×C47C2211yescharacteristic
49#124×C47—24no—
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic, complemented
53C2×C22⋊C4×C47C2211yescharacteristic, complemented
54C2×C42×C47C2211yescharacteristic, complemented
55C24×C47C2311yescharacteristic
56C24×C47C2311yescharacteristic
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—22no—
62C23×D47—41no—
63C23×D47—41no—
64C23×D47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C2×Q8×C47—22no—
67C2×Q8×C47—22no—
68C2×Q8×C47—41no—
69C2×D4×C47—22no—
70C2×D4×C47—22no—
71C2×D4×C47—41no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—41no—
83C22×Dic47C2311yescharacteristic
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C2×C4×D47—22no—
90C2×C4×D47—22no—
91C2×C4×D47—22no—
92C2×C4×D47—22no—
93C2×C4×D47—41no—
94C2×C4×D47—41no—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47—22no—
98C22⋊C4×C47D414yescomplemented
99C42×C47—22no—
100C22⋊Dic47—22no—
101C22⋊Dic47—22no—
102C22⋊Dic47—41no—
103C22⋊Dic47—41no—
104C22⋊Dic47—41no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—41no—
112(C2×D47)⋊C4D414yes—
113C4⋊Dic47—22no—
114Dic47⋊C4—22no—
115Dic47⋊C4—22no—
116C4×Dic47—41no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
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×C47C2×D412yes—
131C23×C47C2411yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—28no—
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—44no—
144C22×D47—44no—
145C22×D47—44no—
146C22×D47—44no—
147C22×D47—44no—
148C22×D47—44no—
149C22×D47C2×D412yes—
150C22×D47#4112yes—
151C22×D47#4112yes—
152C22×D47#4112yes—
153Q8×C47—44no—
154D4×C47—44no—
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—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47C2×D412yes—
168C2×C4×C47C2×D412yes—
169C2×C4×C47C2×D412yes—
170C22⋊D47—44no—
171C22⋊D47—44no—
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—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47C2×D412yes—
190C4×D47—44no—
191C4×D47—44no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47C22×D411yescharacteristic
207C22×C47C22×D411yescharacteristic
208C22×C47C2×#4111yescharacteristic
209C22×C47C2×#4111yescharacteristic
210C22×C47C2×#4111yescharacteristic
211C22×C47H(5,𝔽2)11yescharacteristic
212C22×C47H(5,𝔽2)11yescharacteristic
213C2×D47—22no—
214C2×D47—22no—
215C2×D47—22no—
216C2×D47—22no—
217C2×D47—22no—
218C2×D47—22no—
219C2×D47—22no—
220C2×D47—22no—
221C2×D47—22no—
222C2×D47—416no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47#12414yescomplemented
228C4×C47—22no—
229C4×C47—22no—
230C4×C47—22no—
231C4×C47—41no—
232C4×C47—41no—
233Dic47—22no—
234Dic47—41no—
235Dic47—41no—
236Dic47—41no—
237Dic47—41no—
238Dic47—41no—
239#2472—471nomaximal, Sylow
240C2×C47—42no—
241C2×C47—81no—
242C2×C47#52511yescharacteristic
243C2×C47C2×#12411yescharacteristic
244C2×C47#53811yescharacteristic
245C2×C47D4211yescharacteristic
246C2×C47#54611yescharacteristic
247C2×C47#54611yescharacteristic
248C2×C47#55111yescharacteristic
249D47—24no—
250D47—42no—
251C2×#124D4711yescharacteristic, complemented
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#379—471no—
265C4×C22⋊C4—471no—
266C47#247211yescharacteristic, complemented, Sylow
267C25—471no—
268C22×Q8C2×D4711yescharacteristic, complemented
269C22×D4—471no—
270C22×D4—471no—
271C22×D4C2×D4711yescharacteristic
272C23×C4—471no—
273C23×C4—471no—
274#124—24no—
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—471no—
292C2×C22⋊C4—471no—
293C2×C22⋊C4—944no—
294C2×C22⋊C4C2×D4711yescharacteristic
295C2×C22⋊C4C2×D4711yescharacteristic
296C2×C22⋊C4C2×D4711yescharacteristic, complemented
297C2×C22⋊C4C2×D4711yescharacteristic, complemented
298C2×C42—471no—
299C2×C42C2×D4711yescharacteristic, complemented
300#95—471no—
301#95—471no—
302#95—471no—
303#95—471no—
304#95—471no—
305#95—471no—
306C24—471no—
307C24—471no—
308C24—942no—
309C24—942no—
310C24—942no—
311C24—942no—
312C24—942no—
313C24—1881no—
314C24—1881no—
315C24C22×D4711yescharacteristic
316C24C22×D4711yescharacteristic
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—41no—
323C2×D4—942no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—942no—
328C2×D4—1881no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—471no—
332C22×C4—471no—
333C22×C4—471no—
334C22×C4—471no—
335C22×C4—942no—
336C22×C4—942no—
337C22×C4—942no—
338C22×C4—942no—
339C22×C4—1881no—
340C22×C4—1881no—
341C22×C4C22×D4711yescharacteristic
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—474no—
353C22⋊C4—942no—
354C22⋊C4—942no—
355C22⋊C4—942no—
356C22⋊C4—942no—
357C22⋊C4—942no—
358C22⋊C4—942no—
359C22⋊C4—942no—
360C22⋊C4—942no—
361C22⋊C4—1881no—
362C22⋊C4—1881no—
363C22⋊C4—1881no—
364C22⋊C4—1881no—
365C22⋊C4C22⋊D4714yescomplemented
366C42—22no—
367C42—1881no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—472no—
382C23—472no—
383C23—472no—
384C23—472no—
385C23—948no—
386C23—941no—
387C23—941no—
388C23—941no—
389C23—941no—
390C23—941no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—1884no—
397C23—1884no—
398C23—1884no—
399C23—1884no—
400C23—1884no—
401C23—1884no—
402C23C2×C22⋊D4712yes—
403C23C23×D4711yescharacteristic
404Q8—44no—
405D4—44no—
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—941no—
422C2×C4—941no—
423C2×C4—941no—
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—1884no—
439C2×C4—1884no—
440C2×C4D4×D4712yes—
441C2×C4C2×C22⋊D4712yes—
442C2×C4C2×C22⋊D4712yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—474no—
458C22—942no—
459C22—942no—
460C22—942no—
461C22—942no—
462C22—942no—
463C22—942no—
464C22—942no—
465C22—942no—
466C22—942no—
467C22—18816no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22C2×D4×D4711yescharacteristic
473C22C22×C22⋊D4711yescharacteristic
474C22#41×D4711yescharacteristic
475C22#41×D4711yescharacteristic
476C22#41×D4711yescharacteristic
477C22#1309406911yescharacteristic
478C22#1309407011yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—942no—
485C4—1881no—
486C4—1881no—
487C4—1881no—
488C4—1881no—
489C4—1881no—
490C2—42no—
491C2—81no—
492C2—944no—
493C2—1882no—
494C2#1568963011yescharacteristic
495C2#124×D4711yescharacteristic
496C2#1568970711yescharacteristic
497C2D4×C22⋊D4711yescharacteristic
498C2#1568976111yescharacteristic
499C2#1568976611yescharacteristic
500C2#1568980311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#124×C47C2
hypercenterC2×#124D47
hypocenterC47#2472
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13094000C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689051C2semidirect
5. #15689039C2semidirect
6. #15689037C2semidirect
7. #15689034C2semidirect
8. #15689023C2semidirect
9. #15689016C2semidirect
10. #15689014C2semidirect
11. #15688999C2semidirect
12. #15688999C2semidirect
13. #15688978C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C2×#124×C47C2semidirect
23. C2×C4⋊Dic47C22semidirect
24. C2×Dic47⋊C4C22semidirect
25. C2×Dic47⋊C4C22semidirect
29. C2×C22⋊Dic47C22semidirect
30. C2×C22⋊Dic47C22semidirect
40. C2×C4×Dic47C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C22×Q8×C47C22semidirect
52. C2×C22⋊C4×C47C22semidirect
53. C2×C22⋊C4×C47C22semidirect
54. C2×C42×C47C22semidirect
98. C22⋊C4×C47D4semidirect
227. C2×D47#124semidirect
251. C2×#124D47semidirect
266. C47#2472semidirect
268. C22×Q8C2×D47semidirect
296. C2×C22⋊C4C2×D47semidirect
297. C2×C22⋊C4C2×D47semidirect
299. C2×C42C2×D47semidirect
365. C22⋊C4C22⋊D47semidirect