Finite Group Databasebeta

← #26186231

Subgroups — #26186231

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253400C211yesmaximal, characteristic
2C8×#10625350C211yesmaximal, characteristic, complemented
3#20242264C211yesmaximal, characteristic, complemented
4#20242257C211yesmaximal, characteristic, complemented
5#20242250C211yesmaximal, characteristic, complemented
6#20242243C211yesmaximal, characteristic, complemented
7#20242210C211yesmaximal, characteristic, complemented
8#20242205C211yesmaximal, characteristic, complemented
9#20242200C211yesmaximal, characteristic, complemented
10#20242198C211yesmaximal, characteristic, complemented
11#20242169C211yesmaximal, characteristic, complemented
12#20241820C211yesmaximal, characteristic, complemented
13#20241796C211yesmaximal, characteristic, complemented
14#20241680C211yesmaximal, characteristic, complemented
15C47×#2966C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689461C411yescharacteristic
18#15689444C411yescharacteristic
19#15689427C411yescharacteristic
20#15689420C411yescharacteristic
21#15689342C411yescharacteristic
22#15689335C411yescharacteristic
23#15689283C411yescharacteristic
24#15689266C411yescharacteristic
25C8×Dic94C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625337C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625335C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31C8×D188C2211yescharacteristic
32C8×D188C2211yescharacteristic
33C8×C22⋊D47—21no—
34C8×C22⋊D47—21no—
35#15689176C2211yescharacteristic
36#15689176C2211yescharacteristic
37#15689176C2211yescharacteristic
38#15689174—21no—
39C4×C8×D47—21no—
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46#15688853C2211yescharacteristic
47#15688853C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54#15688845C2211yescharacteristic
55#15688845C2211yescharacteristic
56C47×#529C2211yescharacteristic
57C47×#446C2211yescharacteristic
58C8×Q8×C47C2211yescharacteristic
59C47×#436C2211yescharacteristic
60C47×#435—21no—
61C8×D4×C47—21no—
62C8×D4×C47C2211yescharacteristic
63C47×#433—21no—
64C47×#432C2211yescharacteristic
65C47×#405—21no—
66C2×C4×C8×C47C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×C8×D47—21no—
73C2×C8×D47—21no—
74C4×Dic94C2×C411yescharacteristic
75C4×Dic94C2311yescharacteristic
76C4×D188C2×C411yescharacteristic
77C4×D188C2311yescharacteristic
78C4×C22⋊D47—21no—
79C4×C22⋊D47—21no—
80#13093983C2×C411yescharacteristic
81#13093981—21no—
82C42×D47—21no—
83#13093957C2×C411yescharacteristic
84#13093957C2×C411yescharacteristic
85#13093955C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)C2×C411yescharacteristic
89C4⋊(C47⋊C8)C2×C411yescharacteristic
90C4⋊(C47⋊C8)C2311yescharacteristic
91C4⋊(C47⋊C8)C2311yescharacteristic
92Dic47⋊C8—21no—
93Dic47⋊C8—21no—
94#13093948C2×C411yescharacteristic
95#13093948C2×C411yescharacteristic
96#13093947C2×C411yescharacteristic
97#13093947C2×C411yescharacteristic
98#13093945C2×C411yescharacteristic
99#13093945C2×C411yescharacteristic
100#13093944C2×C411yescharacteristic
101#13093944C2×C411yescharacteristic
102C22⋊(C47⋊C8)—21no—
103C22⋊(C47⋊C8)—21no—
104C22⋊(C47⋊C8)C2×C411yescharacteristic
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106(C2×D47)⋊C8—21no—
107(C2×D47)⋊C8—21no—
108C4×C47⋊C8—21no—
109C4×C47⋊C8C2311yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C8×Dic47—21no—
114C8×Dic47—21no—
115C2×M16×C47—21no—
116C22×C8×C47—21no—
117C22×C8×C47D411yescharacteristic
118C22×C8×C47D411yescharacteristic
119#126×C47—21no—
120#125×C47C2×C411yescharacteristic
121#124×C47C2×C411yescharacteristic
122#123×C47—21no—
123C22⋊Q8×C47C2×C411yescharacteristic
124#121×C47C2×C411yescharacteristic
125C4×Q8×C47C2311yescharacteristic
126C4×D4×C47—21no—
127C4×D4×C47C2311yescharacteristic
128#117×C47—21no—
129C2×C42×C47C2311yescharacteristic
130C4⋊C8×C47—21no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47—21no—
137#97×C47—21no—
138#97×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47D411yescharacteristic
141C4×C8×C47D411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47—21no—
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C2×C22⋊D47—21no—
152#10625350—22no—
153#10625350—22no—
154C2×D188C22×C411yescharacteristic
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×Dic94C22×C411yescharacteristic
159M16×C47—42no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—41no—
163C2×C8×C47—41no—
164C2×C8×C47—42no—
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C2×C8×C47C2×D411yescharacteristic
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C42×C47—21no—
181C42×C47C22×C411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47#4111yescharacteristic
184C42×C47C2411yescharacteristic
185C22⋊Dic47—21no—
186#10625337—22no—
187#10625336—22no—
188#10625335—22no—
189#10625334—22no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192C4⋊Dic47C22×C411yescharacteristic
193C4⋊Dic47C22×C411yescharacteristic
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C8×D47—42no—
208C8×D47—42no—
209C23×C47—21no—
210C23×C47C4×D411yescharacteristic
211C22×D47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214D4×C47—21no—
215D4×C47—21no—
216D4×C47—42no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C23×C411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C22⋊D47—24no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237D188—21no—
238D188#13112yes—
239C4×D47—24no—
240C4×D47—42no—
241C4×D47—41no—
242C4×D47—41no—
243Dic94—21no—
244Dic94#13112yes—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—41no—
250C8×C47—41no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259#17909—471nomaximal, Sylow
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47C2×C4×D411yescharacteristic
267C2×D47—22no—
268C2×D47—41no—
269C2×D47—41no—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47C2×#13111yescharacteristic
278C4×C47C2×#13111yescharacteristic
279C4×C47#57511yescharacteristic
280C4×C47#57511yescharacteristic
281Dic47—22no—
282Dic47—41no—
283Dic47—41no—
284#3102—471no—
285#2966D4711yescharacteristic, complemented
286C8×#41—471no—
287#1588—471no—
288#1587—471no—
289#1586—471no—
290#1585—471no—
291#1580—471no—
292#1579—471no—
293SD16⋊C8—471no—
294SD16⋊C8—471no—
295#1572—471no—
296#1488—471no—
297#1482—471no—
298#1452—471no—
299C2×C47—41no—
300C2×C47—81no—
301C2×C47#292911yescharacteristic
302C2×C47#294311yescharacteristic
303C2×C47#295511yescharacteristic
304D47—42no—
305#529C2×D4711yescharacteristic
306C4×#41—471no—
307#485—471no—
308#482—471no—
309#479—471no—
310#478—471no—
311#464—471no—
312#463—471no—
313#452—471no—
314#449—471no—
315#446C2×D4711yescharacteristic
316C8×Q8—471no—
317C8×Q8—471no—
318C8×Q8C2×D4711yescharacteristic
319C4×Q16—471no—
320C4×SD16—471no—
321C4×SD16—471no—
322C4×D8—471no—
323#436C2×D4711yescharacteristic
324#435—21no—
325C8×D4—21no—
326C8×D4—471no—
327C8×D4—471no—
328C8×D4—941no—
329C8×D4—941no—
330C8×D4C2×D4711yescharacteristic
331#433—21no—
332#432C2×D4711yescharacteristic
333#431—471no—
334#431—471no—
335#431—471no—
336#431—941no—
337#405—21no—
338C2×C4×C8—941no—
339C2×C4×C8C2×D4711yescharacteristic
340#335—471no—
341#335—471no—
342#334—471no—
343#334—471no—
344Q8⋊C8—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348D4⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8—471no—
352#322—471no—
353#322—471no—
354#322—471no—
355#322—471no—
356C47#1790911yescharacteristic, complemented, Sylow
357C2×#41—471no—
358C2×Q16—471no—
359C2×SD16—471no—
360C2×SD16—471no—
361C2×D8—471no—
362C2×M16—21no—
363C22×C8—21no—
364C22×C8—941no—
365C22×C8—941no—
366C22×C8C22⋊D4711yescharacteristic
367C22×C8C22⋊D4711yescharacteristic
368#126—21no—
369#125C4×D4711yescharacteristic
370#124C4×D4711yescharacteristic
371#123—21no—
372C22⋊Q8C4×D4711yescharacteristic
373#121C4×D4711yescharacteristic
374C4×Q8—471no—
375C4×Q8—471no—
376C4×Q8C22×D4711yescharacteristic
377C4×D4—21no—
378C4×D4—471no—
379C4×D4—471no—
380C4×D4—941no—
381C4×D4—941no—
382C4×D4C22×D4711yescharacteristic
383#117—21no—
384#117—471no—
385#117—941no—
386C2×C42—941no—
387C2×C42C22×D4711yescharacteristic
388#107—471no—
389#107—471no—
390#106—471no—
391#106—471no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8C22×D4711yescharacteristic
402C4⋊C8C22×D4711yescharacteristic
403#103—471no—
404#103—471no—
405#103—471no—
406#103—471no—
407#102—471no—
408#102—471no—
409#102—471no—
410#102—471no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—471no—
415C22⋊C8—471no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—941no—
428C4×C8—941no—
429C4×C8—941no—
430C4×C8C22⋊D4711yescharacteristic
431C4×C8C22⋊D4711yescharacteristic
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434#41—942no—
435#41—942no—
436C2×Q8—471no—
437C2×Q8C2×C4×D4711yescharacteristic
438C2×D4—21no—
439C2×D4—471no—
440C2×D4—941no—
441C2×D4C2×C4×D4711yescharacteristic
442C22×C4—21no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4C2×C4×D4711yescharacteristic
447C22×C4#1062535011yescharacteristic
448C22×C4C2×C22⋊D4711yescharacteristic
449Q16—942no—
450SD16—942no—
451SD16—942no—
452D8—942no—
453M16—42no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—42no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—1882no—
468C2×C8—1882no—
469C2×C8C2×C22⋊D4711yescharacteristic
470C2×C8C2×C22⋊D4711yescharacteristic
471C2×C8C2×C22⋊D4711yescharacteristic
472C2×C8C2×C22⋊D4711yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—471no—
478C4⋊C4—471no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4C2×C4×D4711yescharacteristic
482C4⋊C4C2×C4×D4711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C42—21no—
492C42—941no—
493C42—941no—
494C42—941no—
495C42C2×C4×D4711yescharacteristic
496C42#1062535011yescharacteristic
497C42C2×C22⋊D4711yescharacteristic
498C42C23×D4711yescharacteristic
499C23—21no—
500C23—941no—
501C23C4×C22⋊D4711yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—472no—
505Q8—941no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—472no—
510D4—944no—
511D4—941no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—944no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—1882no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4C4×C22⋊D4711yescharacteristic
530C2×C4C4×C22⋊D4711yescharacteristic
531C2×C4C4×C22⋊D4711yescharacteristic
532C2×C4C22×C4×D4711yescharacteristic
533C2×C4C22×C22⋊D4711yescharacteristic
534C2×C4C2×#1062535011yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—941no—
542C8—941no—
543C8—941no—
544C8—941no—
545C8—1881no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—942no—
556C22—1881no—
557C22—1881no—
558C22C2×C4×C22⋊D4711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—942no—
567C4—1881no—
568C4—1881no—
569C4#131×D4711yescharacteristic
570C4#131×D4711yescharacteristic
571C4#1568992111yescharacteristic
572C4#1568992111yescharacteristic
573C2—41no—
574C2—81no—
575C2—1882no—
576C2#2025208011yescharacteristic
577C2#2025218611yescharacteristic
578C2#2025228911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2966C2
socleC22×C47C2×C4×D4
prime radical#15689266C4
cosocleC42×C47C24
hypercenter#2966D47
hypocenterC47#17909
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. C8×#10625350C2semidirect
3. #20242264C2semidirect
4. #20242257C2semidirect
5. #20242250C2semidirect
6. #20242243C2semidirect
7. #20242210C2semidirect
8. #20242205C2semidirect
9. #20242200C2semidirect
10. #20242198C2semidirect
11. #20242169C2semidirect
12. #20241820C2semidirect
13. #20241796C2semidirect
14. #20241680C2semidirect
15. C47×#2966C2semidirect
285. #2966D47semidirect
356. C47#17909semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202534002
C8×#106253502
#202422642
#202422572
#202422502
#202422432
#202422102
#202422052
#202422002
#202421982
#202421692
#202418202
#202417962
#202416802
C47×#29662
#1790947