Finite Group Databasebeta

← #26187006

Subgroups — #26187006

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253952C211yesmaximal, characteristic
2#20252363C211yesmaximal, characteristic, complemented
3#20242238C211yesmaximal, characteristic, complemented
4#20242236C211yesmaximal, characteristic, complemented
5#20242231C211yesmaximal, characteristic, complemented
6#20242229C211yesmaximal, characteristic, complemented
7#20242224C211yesmaximal, characteristic, complemented
8#20242222C211yesmaximal, characteristic, complemented
9#20242217C211yesmaximal, characteristic, complemented
10#20242215C211yesmaximal, characteristic, complemented
11#20242149C211yesmaximal, characteristic, complemented
12#20241848C211yesmaximal, characteristic, complemented
13#20241846C211yesmaximal, characteristic, complemented
14C2×#15688844C211yesmaximal, characteristic, complemented
15C47×#2966C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689522C411yescharacteristic
18#15689505C411yescharacteristic
19#15689480C411yescharacteristic
20#15689477C411yescharacteristic
21#15689362C411yescharacteristic
22#15689357C411yescharacteristic
23#15689354C411yescharacteristic
24#15689350C411yescharacteristic
25#15689253C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625337C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625335C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689202C2211yescharacteristic
32#15689194—21no—
33C8×D188C2211yescharacteristic
34C8×C22⋊D47—21no—
35#15689182—21no—
36#15689180C2211yescharacteristic
37#15689077—21no—
38C2×C4×C47⋊C8C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
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#15688844C2211yescharacteristic
53#15688844C2211yescharacteristic
54#15688844C2211yescharacteristic
55#15688844C2211yescharacteristic
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×#10625337C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625324—21no—
72C22×C47⋊C8—21no—
73C22×C47⋊C8C2×C411yescharacteristic
74C22×C47⋊C8C2×C411yescharacteristic
75C2×C8×D47—21no—
76#13094018—21no—
77#13094016C2×C411yescharacteristic
78#13094012C2×C411yescharacteristic
79#13094007—21no—
80#13094003C2×C411yescharacteristic
81#13093998C2×C411yescharacteristic
82C4×Dic94C2311yescharacteristic
83C4×D188C2311yescharacteristic
84C4×C22⋊D47—21no—
85#13093981—21no—
86#13093957C2×C411yescharacteristic
87#13093957C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
89#13093955C2×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—
103(C2×D47)⋊C8—21no—
104(C2×D47)⋊C8—21no—
105#13093935—21no—
106#13093934—21no—
107C4×C47⋊C8—21no—
108C4×C47⋊C8C2×C411yescharacteristic
109C4×C47⋊C8C2×C411yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
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—
152C2×D188C22×C411yescharacteristic
153C2×C4×D47—21no—
154C2×Dic94C22×C411yescharacteristic
155M16×C47—42no—
156C2×C8×C47—22no—
157C2×C8×C47—22no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—42no—
161C2×C8×C47C2×D411yescharacteristic
162C2×C8×C47C2×D411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C22⋊C4×C47—21no—
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C42×C47—21no—
177C42×C47C22×C411yescharacteristic
178C42×C47C2×D411yescharacteristic
179C42×C47#4111yescharacteristic
180C42×C47C2411yescharacteristic
181C22⋊Dic47—21no—
182#10625337—41no—
183#10625336—41no—
184#10625335—41no—
185#10625334—41no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189(C2×D47)⋊C4—21no—
190C4⋊Dic47C22×C411yescharacteristic
191C4⋊Dic47C22×C411yescharacteristic
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196C4×Dic47—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—41no—
202C2×C47⋊C8—41no—
203C2×C47⋊C8—42no—
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208#10625324—42no—
209C8×D47—42no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212C22×D47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—42no—
218C2×C4×C47—22no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C22⋊D47—42no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238D188—21no—
239D188—21no—
240C4×D47—41no—
241C4×D47—41no—
242Dic94—21no—
243Dic94—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47#13512yes—
249C8×C47#13512yes—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258#17978—471nomaximal, Sylow
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47#44412yes—
265C22×C47C2×C4×D411yescharacteristic
266C2×D47—41no—
267C2×D47—41no—
268C2×D47—41no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47#56811yescharacteristic
277C4×C47#56811yescharacteristic
278C4×C47C2×#13511yescharacteristic
279C4×C47C2×#13511yescharacteristic
280Dic47—41no—
281Dic47—41no—
282Dic47—41no—
283#3168—471no—
284#2966—471no—
285#2966D4711yescharacteristic, complemented
286#1584—471no—
287#1584—471no—
288#1583—471no—
289#1583—471no—
290#1582—471no—
291#1582—471no—
292#1581—471no—
293#1581—471no—
294#1568—471no—
295#1494—471no—
296#1494—471no—
297C2×#322—471no—
298C2×C47—22no—
299C2×C47—81no—
300C2×C47#293211yescharacteristic
301C2×C47C4×#13511yescharacteristic
302C2×C47C2×#44411yescharacteristic
303D47—81no—
304#529—471no—
305#529C2×D4711yescharacteristic
306#499—471no—
307#495—471no—
308#488—471no—
309#488—471no—
310#467—471no—
311#466—471no—
312#465—471no—
313#465—471no—
314#446—471no—
315#446C2×D4711yescharacteristic
316C8×Q8—471no—
317C8×Q8C2×D4711yescharacteristic
318C4×Q16—471no—
319C4×SD16—471no—
320C4×SD16—471no—
321C4×D8—471no—
322#436—471no—
323#436C2×D4711yescharacteristic
324#435—21no—
325#435—941no—
326C8×D4—21no—
327C8×D4—471no—
328C8×D4—941no—
329C8×D4C2×D4711yescharacteristic
330#433—21no—
331#433—941no—
332#432—471no—
333#432C2×D4711yescharacteristic
334#405—21no—
335#405—941no—
336C2×C4×C8—471no—
337C2×C4×C8—471no—
338C2×C4×C8C2×D4711yescharacteristic
339#335—471no—
340#335—471no—
341#334—471no—
342#334—471no—
343Q8⋊C8—471no—
344Q8⋊C8—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347D4⋊C8—471no—
348D4⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8—471no—
351#322—471no—
352#322—471no—
353#322—471no—
354#322—471no—
355C47#1797811yescharacteristic, complemented, Sylow
356C2×Q16—471no—
357C2×SD16—471no—
358C2×SD16—471no—
359C2×D8—471no—
360C2×M16—21no—
361C2×M16—941no—
362C22×C8—21no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—941no—
366C22×C8—941no—
367C22×C8C22⋊D4711yescharacteristic
368C22×C8C22⋊D4711yescharacteristic
369#126—21no—
370#126—941no—
371#125—471no—
372#125C4×D4711yescharacteristic
373#124—471no—
374#124C4×D4711yescharacteristic
375#123—21no—
376#123—941no—
377C22⋊Q8—471no—
378C22⋊Q8C4×D4711yescharacteristic
379#121—471no—
380#121C4×D4711yescharacteristic
381C4×Q8—471no—
382C4×Q8C22×D4711yescharacteristic
383C4×D4—21no—
384C4×D4—471no—
385C4×D4—941no—
386C4×D4C22×D4711yescharacteristic
387#117—21no—
388#117—941no—
389C2×C42C22×D4711yescharacteristic
390#107—471no—
391#107—471no—
392#106—471no—
393#106—471no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8C22×D4711yescharacteristic
401C4⋊C8C22×D4711yescharacteristic
402#103—471no—
403#103—471no—
404#103—471no—
405#103—471no—
406#102—471no—
407#102—471no—
408#102—471no—
409#102—471no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—941no—
414C22⋊C8—941no—
415C22⋊C8—941no—
416#97—21no—
417#97—21no—
418#97—941no—
419#97—941no—
420C4×C8—21no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—941no—
428C4×C8—941no—
429C4×C8C22⋊D4711yescharacteristic
430C4×C8C22⋊D4711yescharacteristic
431C4×C8C22×D4711yescharacteristic
432C4×C8C22×D4711yescharacteristic
433C2×Q8—471no—
434C2×Q8C2×C4×D4711yescharacteristic
435C2×D4—21no—
436C2×D4—471no—
437C2×D4—941no—
438C2×D4C2×C4×D4711yescharacteristic
439C22×C4—21no—
440C22×C4—941no—
441C22×C4C2×C4×D4711yescharacteristic
442C22×C4#1062535011yescharacteristic
443C22×C4C2×C22⋊D4711yescharacteristic
444Q16—1881no—
445SD16—1881no—
446SD16—1881no—
447D8—1881no—
448M16—42no—
449M16—1882no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—1881no—
464C2×C8—1881no—
465C2×C8—1882no—
466C2×C8—1882no—
467C2×C8C2×C22⋊D4711yescharacteristic
468C2×C8C2×C22⋊D4711yescharacteristic
469C2×C8C2×C22⋊D4711yescharacteristic
470C2×C8C2×C22⋊D4711yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—471no—
476C4⋊C4—471no—
477C4⋊C4—941no—
478C4⋊C4—941no—
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—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—941no—
495C42C2×C4×D4711yescharacteristic
496C42#1062535011yescharacteristic
497C42C2×C22⋊D4711yescharacteristic
498C42C23×D4711yescharacteristic
499C23—21no—
500C23—941no—
501C23C4×C22⋊D4711yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—941no—
505Q8—941no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—941no—
510D4—941no—
511D4—1882no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4C4×C22⋊D4711yescharacteristic
528C2×C4C4×C22⋊D4711yescharacteristic
529C2×C4C4×C22⋊D4711yescharacteristic
530C2×C4C22×C4×D4711yescharacteristic
531C2×C4C22×C22⋊D4711yescharacteristic
532C2×C4C2×#1062535011yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—941no—
538C8—941no—
539C8—941no—
540C8—941no—
541C8—1881no—
542C8—1881no—
543C8—1881no—
544C8—1881no—
545C8#1309404412yes—
546C8#1309404412yes—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—1881no—
553C22—1881no—
554C22—1881no—
555C22#1568924312yes—
556C22C2×C4×C22⋊D4711yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—1881no—
565C4—1881no—
566C4—1881no—
567C4#1568988811yescharacteristic
568C4#1568988811yescharacteristic
569C4C2×#1309404411yescharacteristic
570C4C2×#1309404411yescharacteristic
571C2—22no—
572C2—81no—
573C2—3761no—
574C2#2025210411yescharacteristic
575C2C4×#1309404411yescharacteristic
576C2C2×#1568924311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2966C2
socleC22×C47C2×C4×D4
prime radical#15689357C4
cosocleC42×C47C24
hypercenter#2966D47
hypocenterC47#17978
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. #20252363C2semidirect
3. #20242238C2semidirect
4. #20242236C2semidirect
5. #20242231C2semidirect
6. #20242229C2semidirect
7. #20242224C2semidirect
8. #20242222C2semidirect
9. #20242217C2semidirect
10. #20242215C2semidirect
11. #20242149C2semidirect
12. #20241848C2semidirect
13. #20241846C2semidirect
14. C2×#15688844C2semidirect
15. C47×#2966C2semidirect
285. #2966D47semidirect
355. C47#17978semidirect

Maximal subgroups

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

subgroupindex
#202539522
#202523632
#202422382
#202422362
#202422312
#202422292
#202422242
#202422222
#202422172
#202422152
#202421492
#202418482
#202418462
C2×#156888442
C47×#29662
#1797847