Finite Group Databasebeta

← #20246918

Subgroups — #20246918

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×#13093998C211yesmaximal, characteristic, complemented
2C2×#13093996C211yesmaximal, characteristic, complemented
3C2×#13093994C211yesmaximal, characteristic, complemented
4C2×#13093992C211yesmaximal, characteristic, complemented
5C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689040C211yesmaximal, characteristic, complemented
8#15689039C211yesmaximal, characteristic, complemented
9#15689032C211yesmaximal, characteristic, complemented
10#15689025C211yesmaximal, characteristic, complemented
11#15689014C211yesmaximal, characteristic, complemented
12#15689002C211yesmaximal, characteristic, complemented
13#15689002C211yesmaximal, characteristic, complemented
14#15688998C211yesmaximal, characteristic, complemented
15C2×C4×D4×C47C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C22×C22⋊D47C2211yescharacteristic
22C22×C22⋊D47C2211yescharacteristic, complemented
23C23×Dic47C2211yescharacteristic
24#13093998—24no—
25#13093996—24no—
26#13093994—24no—
27#13093992—24no—
28C2×C4⋊Dic47C2211yescharacteristic, complemented
29C2×C4⋊Dic47C2211yescharacteristic, complemented
30C2×Dic47⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic, complemented
33C2×(C2×D47)⋊C4—24no—
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C22×D4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51C23×C4×C47C2211yescharacteristic, complemented
52C4×D4×C47—24no—
53C2×C4⋊C4×C47C2211yescharacteristic, complemented
54C2×C22⋊C4×C47C2211yescharacteristic
55C2×C22⋊C4×C47C2211yescharacteristic, complemented
56C2×C42×C47C2211yescharacteristic, complemented
57C24×C47C2311yescharacteristic
58C24×C47C2311yescharacteristic
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—22no—
62C23×D47—22no—
63C23×D47—22no—
64C23×D47—41no—
65C23×D47—41no—
66C23×D47C2311yescharacteristic
67C23×D47C2311yescharacteristic
68C23×D47C2311yescharacteristic
69C2×D4×C47—22no—
70C2×D4×C47—22no—
71C2×D4×C47D414yescomplemented
72C22×C4×C47—22no—
73C22×C4×C47—22no—
74C22×C4×C47—22no—
75C22×C4×C47—22no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47C2311yescharacteristic
79C22×C4×C47C2311yescharacteristic
80C22×C4×C47C2311yescharacteristic
81C22×C4×C47C2311yescharacteristic
82C22×C4×C47C2311yescharacteristic
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—22no—
91C2×C22⋊D47—22no—
92C2×C22⋊D47—41no—
93C2×C22⋊D47—41no—
94C2×C22⋊D47—41no—
95C22×Dic47—22no—
96C22×Dic47—22no—
97C22×Dic47—41no—
98C22×Dic47C2311yescharacteristic
99C22×Dic47C2311yescharacteristic
100C22×Dic47C2311yescharacteristic
101C22×Dic47C2311yescharacteristic
102C22×Dic47C2311yescharacteristic
103C2×D188—22no—
104C2×D188—22no—
105C2×D188—22no—
106C2×D188—22no—
107C2×D188—41no—
108C2×D188—41no—
109C4⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C22⋊C4×C47D414yescomplemented
112C42×C47—22no—
113C22⋊Dic47—22no—
114C22⋊Dic47—22no—
115(C2×D47)⋊C4—22no—
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—22no—
118(C2×D47)⋊C4—22no—
119(C2×D47)⋊C4—22no—
120(C2×D47)⋊C4—22no—
121(C2×D47)⋊C4—22no—
122(C2×D47)⋊C4—22no—
123(C2×D47)⋊C4—22no—
124(C2×D47)⋊C4—41no—
125(C2×D47)⋊C4D414yescomplemented
126C4⋊Dic47—22no—
127C4⋊Dic47—41no—
128Dic47⋊C4—22no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47C2×D412yes—
140C23×C47C2×D412yes—
141C23×C47C2×D412yes—
142C23×C47#4112yes—
143C23×C47C2411yescharacteristic
144C22×D47—28no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47—21no—
152C22×D47—21no—
153C22×D47—21no—
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47—21no—
158C22×D47—21no—
159C22×D47—21no—
160C22×D47—21no—
161C22×D47—21no—
162C22×D47—21no—
163C22×D47—21no—
164C22×D47—44no—
165C22×D47—44no—
166C22×D47—44no—
167C22×D47—44no—
168C22×D47—44no—
169C22×D47—44no—
170C22×D47C2×D412yes—
171C22×D47#4112yes—
172D4×C47—28no—
173C2×C4×C47—21no—
174C2×C4×C47—21no—
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×C47—21no—
184C2×C4×C47—44no—
185C2×C4×C47—44no—
186C2×C4×C47C2×D412yes—
187C2×C4×C47C2×D412yes—
188C2×C4×C47C2×D412yes—
189C2×C4×C47C2×D412yes—
190C22⋊D47—44no—
191C22⋊D47—44no—
192C22⋊D47—44no—
193C22⋊D47—44no—
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—21no—
207C2×Dic47—21no—
208C2×Dic47—44no—
209C2×Dic47C2×D412yes—
210D188—44no—
211D188—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—41no—
222C22×C47—41no—
223C22×C47—41no—
224C22×C47—41no—
225C22×C47#12114yescomplemented
226C22×C47C22×D411yescharacteristic
227C22×C47C22×D411yescharacteristic
228C22×C47C22×D411yescharacteristic
229C22×C47C2×#4111yescharacteristic
230C22×C47C2×#4111yescharacteristic
231C22×C47H(5,𝔽2)11yescharacteristic
232C22×C47H(5,𝔽2)11yescharacteristic
233C2×D47—22no—
234C2×D47—22no—
235C2×D47—22no—
236C2×D47—22no—
237C2×D47—22no—
238C2×D47—22no—
239C2×D47—416no—
240C2×D47—41no—
241C2×D47—41no—
242C2×D47—41no—
243C2×D47—41no—
244C2×D47—41no—
245C2×D47—41no—
246C2×D47—41no—
247C2×D47—41no—
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—22no—
257C4×C47—22no—
258C4×C47—22no—
259C4×C47—41no—
260Dic47—22no—
261Dic47—41no—
262Dic47—41no—
263Dic47—41no—
264Dic47—41no—
265#2424—471nomaximal, Sylow
266C2×C47—24no—
267C2×C47—42no—
268C2×C47C2×#12111yescharacteristic
269C2×C47#52511yescharacteristic
270C2×C47#53811yescharacteristic
271C2×C47D4211yescharacteristic
272C2×C47D4211yescharacteristic
273C2×C47#54611yescharacteristic
274C2×C47#54611yescharacteristic
275D47—42no—
276D47—42no—
277D47—81no—
278C2×#121—471no—
279C2×#121—471no—
280C2×#120—471no—
281C2×#120—471no—
282C2×C4×D4D4711yescharacteristic, complemented
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
294C25—471no—
295C22×D4—471no—
296C22×D4—471no—
297C22×D4—471no—
298C22×D4—471no—
299C22×D4—471no—
300C22×D4—471no—
301C22×D4C2×D4711yescharacteristic
302C23×C4—471no—
303C23×C4C2×D4711yescharacteristic
304C23×C4C2×D4711yescharacteristic, complemented
305#121—944no—
306#121—944no—
307#120—944no—
308#120—944no—
309C4×D4—24no—
310C2×C4⋊C4—471no—
311C2×C4⋊C4—471no—
312C2×C4⋊C4—471no—
313C2×C4⋊C4C2×D4711yescharacteristic, complemented
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—471no—
327C2×C22⋊C4—944no—
328C2×C22⋊C4C2×D4711yescharacteristic
329C2×C22⋊C4C2×D4711yescharacteristic, complemented
330C2×C42C2×D4711yescharacteristic, complemented
331#95—471no—
332#95—471no—
333#95—471no—
334#95—471no—
335C24—471no—
336C24—471no—
337C24—471no—
338C24—942no—
339C24—942no—
340C24—942no—
341C24—942no—
342C24—942no—
343C24—1881no—
344C24—1881no—
345C24C22×D4711yescharacteristic
346C24C22×D4711yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—942no—
350C2×D4—942no—
351C2×D4—942no—
352C2×D4—942no—
353C2×D4—942no—
354C2×D4—942no—
355C2×D4—942no—
356C2×D4—942no—
357C2×D4—942no—
358C2×D4—942no—
359C2×D4—942no—
360C2×D4—942no—
361C2×D4—942no—
362C2×D4—1881no—
363C2×D4—1881no—
364C2×D4—1881no—
365C2×D4—1881no—
366C2×D4—1881no—
367C2×D4D18814yescomplemented
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—471no—
375C22×C4—471no—
376C22×C4—471no—
377C22×C4—471no—
378C22×C4—471no—
379C22×C4—942no—
380C22×C4—942no—
381C22×C4—1881no—
382C22×C4C22×D4711yescharacteristic
383C22×C4C22×D4711yescharacteristic
384C22×C4C22×D4711yescharacteristic
385C22×C4C22×D4711yescharacteristic
386C22×C4C22×D4711yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—942no—
389C4⋊C4—942no—
390C4⋊C4—1881no—
391C22⋊C4—22no—
392C22⋊C4—474no—
393C22⋊C4—942no—
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—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—472no—
418C23—472no—
419C23—948no—
420C23—941no—
421C23—941no—
422C23—941no—
423C23—941no—
424C23—941no—
425C23—941no—
426C23—941no—
427C23—941no—
428C23—941no—
429C23—941no—
430C23—941no—
431C23—941no—
432C23—941no—
433C23—941no—
434C23—941no—
435C23—941no—
436C23—941no—
437C23—941no—
438C23—941no—
439C23—1884no—
440C23—1884no—
441C23—1884no—
442C23—1884no—
443C23—1884no—
444C23—1884no—
445C23C2×D18812yes—
446C23C2×D18812yes—
447C23#1062535012yes—
448C23C2×C22⋊D4712yes—
449C23C23×D4711yescharacteristic
450D4—28no—
451D4—1884no—
452D4—1884no—
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—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—472no—
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×C4C2×D18812yes—
487C2×C4D4×D4712yes—
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—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—942no—
504C22—942no—
505C22—942no—
506C22—942no—
507C22—942no—
508C22—942no—
509C22—18816no—
510C22—1881no—
511C22—1881no—
512C22—1881no—
513C22—1881no—
514C22—1881no—
515C22—1881no—
516C22—1881no—
517C22—1881no—
518C22—1881no—
519C22—1881no—
520C22—1881no—
521C22—1881no—
522C22—1881no—
523C22—1881no—
524C22—1881no—
525C22#1309399814yescomplemented
526C22C2×D4×D4711yescharacteristic
527C22C22×C22⋊D4711yescharacteristic
528C22C22×D18811yescharacteristic
529C22#41×D4711yescharacteristic
530C22C2×#1062535011yescharacteristic
531C22#1309406911yescharacteristic
532C22#1309407011yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—942no—
539C4—1881no—
540C4—1881no—
541C4—1881no—
542C4—1881no—
543C2—24no—
544C2—42no—
545C2—3761no—
546C2—1882no—
547C2—1882no—
548C2C2×#1309399811yescharacteristic
549C2#1568963211yescharacteristic
550C2#1568970611yescharacteristic
551C2D4×C22⋊D4711yescharacteristic
552C2D4×D18811yescharacteristic
553C2#1568976111yescharacteristic
554C2#1568976811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×D4×C47C2
hypercenterC2×C4×D4D47
hypocenterC47#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13093998C2semidirect
2. C2×#13093996C2semidirect
3. C2×#13093994C2semidirect
4. C2×#13093992C2semidirect
5. C22×(C2×D47)⋊C4C2semidirect
6. #15689045C2semidirect
7. #15689040C2semidirect
8. #15689039C2semidirect
9. #15689032C2semidirect
10. #15689025C2semidirect
11. #15689014C2semidirect
12. #15689002C2semidirect
13. #15689002C2semidirect
14. #15688998C2semidirect
15. C2×C4×D4×C47C2semidirect
22. C22×C22⋊D47C22semidirect
28. C2×C4⋊Dic47C22semidirect
29. C2×C4⋊Dic47C22semidirect
30. C2×Dic47⋊C4C22semidirect
32. C2×C22⋊Dic47C22semidirect
42. C2×(C2×D47)⋊C4C22semidirect
43. C2×(C2×D47)⋊C4C22semidirect
44. C2×(C2×D47)⋊C4C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
51. C23×C4×C47C22semidirect
53. C2×C4⋊C4×C47C22semidirect
55. C2×C22⋊C4×C47C22semidirect
56. C2×C42×C47C22semidirect
71. C2×D4×C47D4semidirect
111. C22⋊C4×C47D4semidirect
125. (C2×D47)⋊C4D4semidirect
225. C22×C47#121semidirect
282. C2×C4×D4D47semidirect
293. C47#2424semidirect
304. C23×C4C2×D47semidirect
313. C2×C4⋊C4C2×D47semidirect
329. C2×C22⋊C4C2×D47semidirect
330. C2×C42C2×D47semidirect
367. C2×D4D188semidirect
405. C22⋊C4C22⋊D47semidirect
525. C22#13093998semidirect