Finite Group Databasebeta

← #20246928

Subgroups — #20246928

Order 6016.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093996C211yesmaximal, characteristic, complemented
2C2×#13093996C211yesmaximal, characteristic, complemented
3C2×#13093993C211yesmaximal, characteristic, complemented
4C2×D4×Dic47C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic47C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689039C211yesmaximal, characteristic, complemented
8#15689037C211yesmaximal, characteristic, complemented
9#15689031C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15689017C211yesmaximal, characteristic, complemented
12#15689003C211yesmaximal, characteristic, complemented
13#15689000C211yesmaximal, characteristic, complemented
14#15688995C211yesmaximal, characteristic, complemented
15C2×#120×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic, complemented
20C23×Dic47C2211yescharacteristic
21C23×Dic47C2211yescharacteristic
22C23×Dic47C2211yescharacteristic, complemented
23#13093996—24no—
24#13093996—24no—
25#13093993—24no—
26D4×Dic47—24no—
27C2×C4⋊Dic47C2211yescharacteristic, complemented
28C2×Dic47⋊C4C2211yescharacteristic, complemented
29C2×Dic47⋊C4C2211yescharacteristic, complemented
30C2×Dic47⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic47—24no—
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×C22⋊Dic47C2211yescharacteristic, complemented
40C2×C22⋊Dic47C2211yescharacteristic, complemented
41C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic47C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C25×C47C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51C22×D4×C47C2211yescharacteristic
52C22×D4×C47C2211yescharacteristic
53#120×C47—24no—
54C2×C22⋊C4×C47C2211yescharacteristic
55C2×C22⋊C4×C47C2211yescharacteristic
56C2×C22⋊C4×C47C2211yescharacteristic
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—22no—
60C24×C47—22no—
61C24×C47—22no—
62C24×C47—41no—
63C24×C47—41no—
64C24×C47C2311yescharacteristic
65C24×C47C2311yescharacteristic
66C24×C47C2311yescharacteristic
67C24×C47C2311yescharacteristic
68C23×D47C2311yescharacteristic
69C2×D4×C47—22no—
70C2×D4×C47—22no—
71C2×D4×C47—22no—
72C2×D4×C47—22no—
73C2×D4×C47—22no—
74C2×D4×C47—22no—
75C2×D4×C47—41no—
76C2×D4×C47—41no—
77C2×D4×C47D414yescomplemented
78C22×C4×C47C2311yescharacteristic
79C22×C4×C47C2311yescharacteristic
80C22×C4×C47C2311yescharacteristic
81C2×C22⋊D47—22no—
82C2×C22⋊D47—22no—
83C2×C22⋊D47—22no—
84C2×C22⋊D47—22no—
85C2×C22⋊D47—22no—
86C2×C22⋊D47—22no—
87C2×C22⋊D47—22no—
88C2×C22⋊D47—22no—
89C2×C22⋊D47—22no—
90C2×C22⋊D47—41no—
91C2×C22⋊D47—41no—
92C2×C22⋊D47—41no—
93C22×Dic47—22no—
94C22×Dic47—22no—
95C22×Dic47—22no—
96C22×Dic47—22no—
97C22×Dic47—22no—
98C22×Dic47—22no—
99C22×Dic47—41no—
100C22×Dic47—41no—
101C22×Dic47—41no—
102C22×Dic47C2311yescharacteristic
103C22×Dic47C2311yescharacteristic
104C22×Dic47C2311yescharacteristic
105C22×Dic47C2311yescharacteristic
106C22×Dic47C2311yescharacteristic
107C22×Dic47C2311yescharacteristic
108C22×Dic47C2311yescharacteristic
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C22⋊C4×C47—22no—
112C22⋊Dic47—22no—
113C22⋊Dic47—22no—
114C22⋊Dic47—22no—
115C22⋊Dic47—22no—
116C22⋊Dic47—22no—
117C22⋊Dic47—22no—
118C22⋊Dic47—22no—
119C22⋊Dic47D414yescomplemented
120C22⋊Dic47D414yescomplemented
121(C2×D47)⋊C4—22no—
122(C2×D47)⋊C4—22no—
123(C2×D47)⋊C4—41no—
124C4⋊Dic47—22no—
125Dic47⋊C4—22no—
126Dic47⋊C4—22no—
127Dic47⋊C4—41no—
128C4×Dic47—22no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—28no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—21no—
140C23×C47—21no—
141C23×C47—21no—
142C23×C47—21no—
143C23×C47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C23×C47—21no—
147C23×C47—21no—
148C23×C47—21no—
149C23×C47—21no—
150C23×C47—21no—
151C23×C47—21no—
152C23×C47—44no—
153C23×C47—44no—
154C23×C47—44no—
155C23×C47—44no—
156C23×C47—44no—
157C23×C47—44no—
158C23×C47C2×D412yes—
159C23×C47C2×D412yes—
160C23×C47C2×D412yes—
161C23×C47C2×D412yes—
162C23×C47#4112yes—
163C23×C47#4112yes—
164C23×C47C2411yescharacteristic
165C22×D47—21no—
166C22×D47—21no—
167C22×D47—21no—
168C22×D47—21no—
169C22×D47—21no—
170C22×D47—21no—
171C22×D47—21no—
172D4×C47—28no—
173D4×C47—44no—
174D4×C47—44no—
175C2×C4×C47—21no—
176C2×C4×C47—21no—
177C2×C4×C47—21no—
178C2×C4×C47—21no—
179C2×C4×C47—21no—
180C2×C4×C47—21no—
181C2×C4×C47—21no—
182C2×C4×C47—21no—
183C2×C4×C47C2×D412yes—
184C22⋊D47—44no—
185C22⋊D47—44no—
186C22⋊D47—44no—
187C22⋊D47—44no—
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—21no—
193C2×Dic47—21no—
194C2×Dic47—21no—
195C2×Dic47—21no—
196C2×Dic47—21no—
197C2×Dic47—21no—
198C2×Dic47—21no—
199C2×Dic47—21no—
200C2×Dic47—21no—
201C2×Dic47—21no—
202C2×Dic47—21no—
203C2×Dic47—21no—
204C2×Dic47—21no—
205C2×Dic47—44no—
206C2×Dic47—44no—
207C2×Dic47—44no—
208C2×Dic47C2×D412yes—
209C2×Dic47C2×D412yes—
210C2×Dic47C2×D412yes—
211C2×Dic47C2×D412yes—
212C22×C47—22no—
213C22×C47—22no—
214C22×C47—22no—
215C22×C47—22no—
216C22×C47—22no—
217C22×C47—22no—
218C22×C47—22no—
219C22×C47—22no—
220C22×C47—22no—
221C22×C47—22no—
222C22×C47—22no—
223C22×C47—22no—
224C22×C47—22no—
225C22×C47—22no—
226C22×C47—22no—
227C22×C47—416no—
228C22×C47—41no—
229C22×C47—41no—
230C22×C47—41no—
231C22×C47—41no—
232C22×C47—41no—
233C22×C47—41no—
234C22×C47—41no—
235C22×C47—41no—
236C22×C47—41no—
237C22×C47—41no—
238C22×C47—41no—
239C22×C47—41no—
240C22×C47#12114yescomplemented
241C22×C47C22×D411yescharacteristic
242C22×C47C22×D411yescharacteristic
243C22×C47C22×D411yescharacteristic
244C22×C47C2×#4111yescharacteristic
245C22×C47C2×#4111yescharacteristic
246C22×C47H(5,𝔽2)11yescharacteristic
247C22×C47H(5,𝔽2)11yescharacteristic
248C2×D47—41no—
249C2×D47—41no—
250C2×D47—41no—
251C2×D47—41no—
252C2×D47—41no—
253C2×D47—41no—
254C2×D47—41no—
255C4×C47—22no—
256C4×C47—41no—
257C4×C47—41no—
258Dic47—22no—
259Dic47—22no—
260Dic47—22no—
261Dic47—22no—
262Dic47—41no—
263Dic47—41no—
264Dic47—41no—
265#2424—471nomaximal, Sylow
266C2×C47—24no—
267C2×C47—42no—
268C2×C47—42no—
269C2×C47—42no—
270C2×C47C2×#12111yescharacteristic
271C2×C47#52511yescharacteristic
272C2×C47#53811yescharacteristic
273C2×C47D4211yescharacteristic
274C2×C47D4211yescharacteristic
275C2×C47#54611yescharacteristic
276C2×C47#54611yescharacteristic
277D47—81no—
278C2×#121—471no—
279C2×#121—471no—
280C2×#120—471no—
281C2×#120D4711yescharacteristic, complemented
282C2×C4×D4—471no—
283C22×C22⋊C4—471no—
284#396—471no—
285#394—471no—
286#394—471no—
287#392—471no—
288#390—471no—
289#388—471no—
290#386—471no—
291#386—471no—
292#385—471no—
293C47#242411yescharacteristic, complemented, Sylow
294C25C2×D4711yescharacteristic
295C22×D4—471no—
296C22×D4—471no—
297C22×D4—471no—
298C22×D4—471no—
299C22×D4C2×D4711yescharacteristic
300C22×D4C2×D4711yescharacteristic
301C22×D4C2×D4711yescharacteristic
302C23×C4—471no—
303C23×C4—471no—
304C23×C4—471no—
305#121—944no—
306#121—944no—
307#120—24no—
308#120—944no—
309C4×D4—944no—
310C2×C4⋊C4—471no—
311C2×C4⋊C4—471no—
312C2×C4⋊C4—471no—
313C2×C4⋊C4—471no—
314C2×C22⋊C4—471no—
315C2×C22⋊C4—471no—
316C2×C22⋊C4—471no—
317C2×C22⋊C4—471no—
318C2×C22⋊C4—471no—
319C2×C22⋊C4—471no—
320C2×C22⋊C4—471no—
321C2×C22⋊C4—471no—
322C2×C22⋊C4—471no—
323C2×C22⋊C4—471no—
324C2×C22⋊C4—471no—
325C2×C22⋊C4—471no—
326C2×C22⋊C4—944no—
327C2×C22⋊C4C2×D4711yescharacteristic
328C2×C22⋊C4C2×D4711yescharacteristic
329C2×C22⋊C4C2×D4711yescharacteristic
330C2×C42—471no—
331#95—471no—
332#95—471no—
333#95—471no—
334#95—471no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—41no—
341C24—41no—
342C24—471no—
343C24C22×D4711yescharacteristic
344C24C22×D4711yescharacteristic
345C24C22×D4711yescharacteristic
346C24C22×D4711yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—942no—
356C2×D4—942no—
357C2×D4—942no—
358C2×D4—942no—
359C2×D4—942no—
360C2×D4—942no—
361C2×D4—942no—
362C2×D4—942no—
363C2×D4—942no—
364C2×D4—1881no—
365C2×D4—1881no—
366C2×D4—1881no—
367C2×D4C22⋊D4714yescomplemented
368C22×C4—471no—
369C22×C4—471no—
370C22×C4—471no—
371C22×C4—471no—
372C22×C4—471no—
373C22×C4—471no—
374C22×C4—471no—
375C22×C4—942no—
376C22×C4—942no—
377C22×C4—942no—
378C22×C4—942no—
379C22×C4—942no—
380C22×C4—942no—
381C22×C4—1881no—
382C22×C4—1881no—
383C22×C4—1881no—
384C22×C4C22×D4711yescharacteristic
385C22×C4C22×D4711yescharacteristic
386C22×C4C22×D4711yescharacteristic
387C4⋊C4—942no—
388C4⋊C4—942no—
389C4⋊C4—942no—
390C4⋊C4—1881no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—474no—
395C22⋊C4—474no—
396C22⋊C4—942no—
397C22⋊C4—942no—
398C22⋊C4—942no—
399C22⋊C4—942no—
400C22⋊C4—942no—
401C22⋊C4—942no—
402C22⋊C4—942no—
403C22⋊C4—942no—
404C22⋊C4—942no—
405C22⋊C4—1881no—
406C42—942no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—28no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—941no—
437C23—941no—
438C23—941no—
439C23—941no—
440C23—941no—
441C23—941no—
442C23—941no—
443C23D4×D4712yes—
444C23D4×D4712yes—
445C23#1062535212yes—
446C23#1062535212yes—
447C23C2×C22⋊D4712yes—
448C23C2×C22⋊D4712yes—
449C23C23×D4711yescharacteristic
450D4—28no—
451D4—44no—
452D4—44no—
453D4—1884no—
454D4—1884no—
455D4—1884no—
456D4—1884no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—472no—
466C2×C4—472no—
467C2×C4—472no—
468C2×C4—472no—
469C2×C4—941no—
470C2×C4—941no—
471C2×C4—941no—
472C2×C4—941no—
473C2×C4—941no—
474C2×C4—941no—
475C2×C4—941no—
476C2×C4—941no—
477C2×C4—941no—
478C2×C4—941no—
479C2×C4—941no—
480C2×C4—941no—
481C2×C4—941no—
482C2×C4—941no—
483C2×C4—941no—
484C2×C4—941no—
485C2×C4—941no—
486C2×C4—1884no—
487C2×C4—1884no—
488C2×C4—1884no—
489C2×C4C2×C22⋊D4712yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—416no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—1881no—
519C22—1881no—
520C22—1881no—
521C22—1881no—
522C22—1881no—
523C22—1881no—
524C22—1881no—
525C22#1309399614yescomplemented
526C22C2×D4×D4711yescharacteristic
527C22C2×D4×D4711yescharacteristic
528C22C22×C22⋊D4711yescharacteristic
529C22C2×#1062535211yescharacteristic
530C22C2×#1062535211yescharacteristic
531C22#1309406911yescharacteristic
532C22#1309406911yescharacteristic
533C4—22no—
534C4—41no—
535C4—41no—
536C4—942no—
537C4—942no—
538C4—942no—
539C4—942no—
540C4—1881no—
541C4—1881no—
542C4—1881no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—42no—
547C2—3761no—
548C2C2×#1309399611yescharacteristic
549C2#1568962911yescharacteristic
550C2#1568970811yescharacteristic
551C2#1568975511yescharacteristic
552C2D4×C22⋊D4711yescharacteristic
553C2#1568976011yescharacteristic
554C2#1568976711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#120×C47C2
hypercenterC2×#120D47
hypocenterC47#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13093996C2semidirect
2. C2×#13093996C2semidirect
3. C2×#13093993C2semidirect
4. C2×D4×Dic47C2semidirect
5. C22×C22⋊Dic47C2semidirect
6. #15689046C2semidirect
7. #15689039C2semidirect
8. #15689037C2semidirect
9. #15689031C2semidirect
10. #15689023C2semidirect
11. #15689017C2semidirect
12. #15689003C2semidirect
13. #15689000C2semidirect
14. #15688995C2semidirect
15. C2×#120×C47C2semidirect
19. C22×C22⋊D47C22semidirect
22. C23×Dic47C22semidirect
27. C2×C4⋊Dic47C22semidirect
28. C2×Dic47⋊C4C22semidirect
29. C2×Dic47⋊C4C22semidirect
30. C2×Dic47⋊C4C22semidirect
39. C2×C22⋊Dic47C22semidirect
40. C2×C22⋊Dic47C22semidirect
41. C2×(C2×D47)⋊C4C22semidirect
42. C2×(C2×D47)⋊C4C22semidirect
43. C2×(C2×D47)⋊C4C22semidirect
44. C2×C4×Dic47C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
77. C2×D4×C47D4semidirect
119. C22⋊Dic47D4semidirect
120. C22⋊Dic47D4semidirect
240. C22×C47#121semidirect
281. C2×#120D47semidirect
293. C47#2424semidirect
367. C2×D4C22⋊D47semidirect
525. C22#13093996semidirect