Finite Group Databasebeta

← #20246920

Subgroups — #20246920

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×#13093995C211yesmaximal, characteristic, complemented
3C2×#13093993C211yesmaximal, characteristic, complemented
4C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic47C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689039C211yesmaximal, characteristic, complemented
8#15689037C211yesmaximal, characteristic, complemented
9#15689031C211yesmaximal, characteristic, complemented
10#15689026C211yesmaximal, characteristic, complemented
11#15689011C211yesmaximal, characteristic, complemented
12#15689003C211yesmaximal, characteristic, complemented
13#15688999C211yesmaximal, characteristic, complemented
14#15688998C211yesmaximal, characteristic, complemented
15C2×#120×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic, complemented
20C23×Dic47C2211yescharacteristic
21C23×Dic47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic, complemented
23#13093996—24no—
24#13093995—24no—
25#13093993—24no—
26(C22⋊D47)⋊C4—24no—
27C2×C4⋊Dic47C2211yescharacteristic, complemented
28C2×C4⋊Dic47C2211yescharacteristic, 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×C22⋊Dic47C2211yescharacteristic, 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—22no—
76C2×D4×C47—41no—
77C2×D4×C47—41no—
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—41no—
90C2×C22⋊D47—41no—
91C2×C22⋊D47—41no—
92C2×C22⋊D47D414yescomplemented
93C22×Dic47—22no—
94C22×Dic47—22no—
95C22×Dic47—22no—
96C22×Dic47—22no—
97C22×Dic47—41no—
98C22×Dic47—41no—
99C22×Dic47C2311yescharacteristic
100C22×Dic47C2311yescharacteristic
101C22×Dic47C2311yescharacteristic
102C22×Dic47C2311yescharacteristic
103C22×Dic47C2311yescharacteristic
104C22×Dic47C2311yescharacteristic
105C22×Dic47C2311yescharacteristic
106C2×C4×D47—22no—
107C2×C4×D47—22no—
108C2×C4×D47—41no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C22⋊C4×C47D414yescomplemented
112C22⋊Dic47—22no—
113C22⋊Dic47—22no—
114C22⋊Dic47—22no—
115C22⋊Dic47—22no—
116C22⋊Dic47—22no—
117C22⋊Dic47—22no—
118C22⋊Dic47—22no—
119C22⋊Dic47—22no—
120C22⋊Dic47—41no—
121C22⋊Dic47D414yescomplemented
122(C2×D47)⋊C4—22no—
123(C2×D47)⋊C4—22no—
124C4⋊Dic47—22no—
125C4⋊Dic47—41no—
126Dic47⋊C4—22no—
127Dic47⋊C4—22no—
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—21no—
153C23×C47—44no—
154C23×C47—44no—
155C23×C47—44no—
156C23×C47—44no—
157C23×C47—44no—
158C23×C47—44no—
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×D47C2×D412yes—
172D4×C47—44no—
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×C47C2×D412yes—
183C2×C4×C47C2×D412yes—
184C22⋊D47—28no—
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—21no—
206C2×Dic47—44no—
207C2×Dic47—44no—
208C2×Dic47C2×D412yes—
209C2×Dic47C2×D412yes—
210C2×Dic47C2×D412yes—
211C4×D47—44no—
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—416no—
225C22×C47—41no—
226C22×C47—41no—
227C22×C47—41no—
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—22no—
249C2×D47—22no—
250C2×D47—22no—
251C2×D47—41no—
252C2×D47—41no—
253C2×D47—41no—
254C2×D47—41no—
255C4×C47—22no—
256C4×C47—22no—
257C4×C47—41no—
258Dic47—22no—
259Dic47—22no—
260Dic47—22no—
261Dic47—41no—
262Dic47—41no—
263Dic47—41no—
264Dic47—41no—
265#2424—471nomaximal, Sylow
266C2×C47—24no—
267C2×C47—42no—
268C2×C47—42no—
269C2×C47—81no—
270C2×C47C2×#12111yescharacteristic
271C2×C47#52511yescharacteristic
272C2×C47#53811yescharacteristic
273C2×C47D4211yescharacteristic
274C2×C47D4211yescharacteristic
275C2×C47#54611yescharacteristic
276C2×C47#54611yescharacteristic
277D47—42no—
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—22no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—474no—
357C2×D4—942no—
358C2×D4—942no—
359C2×D4—942no—
360C2×D4—942no—
361C2×D4—942no—
362C2×D4—942no—
363C2×D4—942no—
364C2×D4—942no—
365C2×D4—1881no—
366C2×D4—1881no—
367C2×D4—1881no—
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—474no—
394C22⋊C4—942no—
395C22⋊C4—942no—
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—1881no—
405C22⋊C4C22⋊D4714yescomplemented
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—21no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—472no—
438C23—941no—
439C23—941no—
440C23—941no—
441C23—941no—
442C23—941no—
443C23—941no—
444C23D4×D4712yes—
445C23D4×D4712yes—
446C23#1062535212yes—
447C23#1062535212yes—
448C23C2×C22⋊D4712yes—
449C23C23×D4711yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—948no—
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—472no—
465C2×C4—472no—
466C2×C4—472no—
467C2×C4—941no—
468C2×C4—941no—
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—1884no—
486C2×C4—1884no—
487C2×C4—1884no—
488C2×C4C2×C22⋊D4712yes—
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—416no—
503C22—41no—
504C22—41no—
505C22—41no—
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—942no—
519C22—942no—
520C22—942no—
521C22—1881no—
522C22—1881no—
523C22—1881no—
524C22—1881no—
525C22#1309399514yescomplemented
526C22C2×D4×D4711yescharacteristic
527C22C2×D4×D4711yescharacteristic
528C22C22×C22⋊D4711yescharacteristic
529C22C2×#1062535211yescharacteristic
530C22C2×#1062535211yescharacteristic
531C22#1309406911yescharacteristic
532C22#1309406911yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—942no—
537C4—942no—
538C4—942no—
539C4—1881no—
540C4—1881no—
541C4—1881no—
542C4—1881no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—81no—
547C2—1882no—
548C2C2×#1309399511yescharacteristic
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×#13093995C2semidirect
3. C2×#13093993C2semidirect
4. C2×(C22⋊D47)⋊C4C2semidirect
5. C22×C22⋊Dic47C2semidirect
6. #15689046C2semidirect
7. #15689039C2semidirect
8. #15689037C2semidirect
9. #15689031C2semidirect
10. #15689026C2semidirect
11. #15689011C2semidirect
12. #15689003C2semidirect
13. #15688999C2semidirect
14. #15688998C2semidirect
15. C2×#120×C47C2semidirect
19. C22×C22⋊D47C22semidirect
22. C22×C4×D47C22semidirect
27. C2×C4⋊Dic47C22semidirect
28. C2×C4⋊Dic47C22semidirect
29. C2×Dic47⋊C4C22semidirect
30. C2×Dic47⋊C4C22semidirect
39. C2×C22⋊Dic47C22semidirect
40. C2×C22⋊Dic47C22semidirect
41. C2×C22⋊Dic47C22semidirect
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
92. C2×C22⋊D47D4semidirect
111. C22⋊C4×C47D4semidirect
121. C22⋊Dic47D4semidirect
240. C22×C47#121semidirect
281. C2×#120D47semidirect
293. C47#2424semidirect
405. C22⋊C4C22⋊D47semidirect
525. C22#13093995semidirect