Finite Group Databasebeta

← #26187465

Subgroups — #26187465

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253468C211yesmaximal, characteristic
2#20252544C211yesmaximal, characteristic
3#20252477C211yesmaximal, characteristic, complemented
4#20242282C211yesmaximal, characteristic, complemented
5#20242275C211yesmaximal, characteristic, complemented
6#20242263C211yesmaximal, characteristic, complemented
7#20242262C211yesmaximal, characteristic, complemented
8#20242256C211yesmaximal, characteristic, complemented
9#20242248C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242185C211yesmaximal, characteristic, complemented
12#20242171C211yesmaximal, characteristic, complemented
13#20241849C211yesmaximal, characteristic
14#20241671C211yesmaximal, characteristic, complemented
15C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689453C411yescharacteristic
18#15689436C411yescharacteristic
19#15689430C411yescharacteristic
20#15689430C411yescharacteristic
21#15689345C411yescharacteristic
22#15689345C411yescharacteristic
23#15689279C411yescharacteristic
24#15689262C411yescharacteristic
25#15689254—21no—
26#15689254—21no—
27#15689254C2211yescharacteristic
28#15689254C2211yescharacteristic
29#15689250C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31Q8×C47⋊C8C2211yescharacteristic
32#15689247C2211yescharacteristic
33C4×#10625337C2211yescharacteristic
34C4×#10625337C2211yescharacteristic
35C4×#10625336C2211yescharacteristic
36C4×#10625336C2211yescharacteristic
37#15689200C2211yescharacteristic
38#15689194—21no—
39#15689188C2211yescharacteristic
40C8×C22⋊D47—21no—
41#15689183—21no—
42#15689180—21no—
43#15689180C2211yescharacteristic
44#15689176—21no—
45#15689176C2211yescharacteristic
46#15689176C2211yescharacteristic
47#15689148—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688844C2211yescharacteristic
57#15688844C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C2×C4×Q8×C47C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×C8×D47—21no—
73#13094018—21no—
74#13094016C2×C411yescharacteristic
75#13094012C2×C411yescharacteristic
76#13094007—21no—
77#13094003C2×C411yescharacteristic
78#13093998C2×C411yescharacteristic
79C4×Dic94C2311yescharacteristic
80C4×D188C2311yescharacteristic
81C4×C22⋊D47—21no—
82#13093981—21no—
83#13093957C2×C411yescharacteristic
84#13093957C2×C411yescharacteristic
85#13093955C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)—21no—
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2×C411yescharacteristic
93C4⋊(C47⋊C8)D411yescharacteristic
94C4⋊(C47⋊C8)D411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093947C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)C2×C411yescharacteristic
109C22⋊(C47⋊C8)C2×C411yescharacteristic
110C22⋊(C47⋊C8)D411yescharacteristic
111C22⋊(C47⋊C8)D411yescharacteristic
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114#13093935—21no—
115#13093935—21no—
116#13093935—21no—
117#13093934—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8—21no—
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C22×Q8×C47C2×C411yescharacteristic
126C22×C8×C47—21no—
127C22×C8×C47—21no—
128C4×Q8×C47—21no—
129C4×Q8×C47—21no—
130C4×Q8×C47C2×C411yescharacteristic
131C4×Q8×C47C2×C411yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133C4×Q8×C47C2311yescharacteristic
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47C2×C411yescharacteristic
136C2×C42×C47—21no—
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—21no—
139C4⋊C8×C47C2311yescharacteristic
140C4⋊C8×C47C2311yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—22no—
146C2×Q8×C47—41no—
147C2×Q8×C47C22×C411yescharacteristic
148C2×Q8×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C2×C22⋊D47—21no—
155C2×D188C22×C411yescharacteristic
156C2×C4×D47—21no—
157C2×Dic94C22×C411yescharacteristic
158C2×C8×C47—24no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—81no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47C22×C411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47#4111yescharacteristic
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180#10625337—22no—
181#10625337—41no—
182#10625336—22no—
183#10625336—41no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194C4×Dic47—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205#10625324—81no—
206C8×D47—81no—
207C23×C47C4×D411yescharacteristic
208C22×D47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—42no—
213Q8×C47#13112yes—
214C2×C4×C47—21no—
215C2×C4×C47—22no—
216C2×C4×C47—21no—
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—42no—
224C2×C4×C47—42no—
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C22⋊D47—42no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235D188—21no—
236D188—21no—
237C4×D47—41no—
238C4×D47—41no—
239Dic94—21no—
240Dic94—21no—
241C8×C47—22no—
242C8×C47—22no—
243C8×C47—41no—
244C8×C47—41no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#18017—471nomaximal, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47#44312yes—
259C22×C47C2×C4×D411yescharacteristic
260C2×D47—41no—
261C2×D47—41no—
262C2×D47—41no—
263C4×C47—21no—
264C4×C47—22no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47C2×#13111yescharacteristic
272C4×C47#56811yescharacteristic
273C4×C47#57711yescharacteristic
274C4×C47#57811yescharacteristic
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278#3108—471no—
279#2994—471no—
280#2984—471no—
281#1591—471no—
282#1590—471no—
283#1588—471no—
284#1587—471no—
285#1587—471no—
286#1585—471no—
287C8×Q16—471no—
288C8×SD16—471no—
289#1573—471no—
290#1494—471no—
291C2×Q8⋊C8D4711yescharacteristic, complemented
292#1450—471no—
293C2×C47—22no—
294C2×C47#293311yescharacteristic
295C2×C47#294711yescharacteristic
296C2×C47C2×#44311yescharacteristic
297D47—81no—
298#529—471no—
299C2×C4×Q8C2×D4711yescharacteristic
300#483—471no—
301#480—471no—
302#479—471no—
303#479—471no—
304#464—471no—
305#464—471no—
306#451—471no—
307#448—471no—
308#446—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8—471no—
316C4×Q16—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16—471no—
320#436—471no—
321#435—941no—
322C8×D4—471no—
323C8×D4—941no—
324#433—941no—
325#432—471no—
326#432—941no—
327#431—471no—
328#431—471no—
329#431—941no—
330#424—941no—
331C2×C4⋊C8C2×D4711yescharacteristic
332C2×C4×C8C2×D4711yescharacteristic
333#335—471no—
334#335—471no—
335#334—471no—
336#334—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8C2×D4711yescharacteristic
340Q8⋊C8C2×D4711yescharacteristic
341Q8⋊C8C2×D4711yescharacteristic
342Q8⋊C8C2×D4711yescharacteristic
343D4⋊C8—471no—
344D4⋊C8—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C82—471no—
349C47#1801711yescharacteristic, complemented, Sylow
350C22×Q8C4×D4711yescharacteristic
351C2×Q16—471no—
352C2×Q16—471no—
353C2×SD16—471no—
354C2×SD16—471no—
355C2×M16—941no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—941no—
359#126—941no—
360#125—471no—
361#124—471no—
362#123—941no—
363C22⋊Q8—471no—
364#121—471no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—471no—
368C4×Q8C4×D4711yescharacteristic
369C4×Q8C4×D4711yescharacteristic
370C4×Q8C22×D4711yescharacteristic
371C4×Q8C22×D4711yescharacteristic
372C4×D4—471no—
373C4×D4—941no—
374#117—941no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C4×D4711yescharacteristic
377C2×C42—21no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—21no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8C22×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#102—471no—
405#102—471no—
406C22⋊C8—471no—
407C22⋊C8—471no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—941no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413#97—941no—
414#97—941no—
415#97—941no—
416#97—941no—
417C4×C8—21no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—471no—
431C2×Q8C2×C4×D4711yescharacteristic
432C2×Q8C2×C4×D4711yescharacteristic
433C2×D4—471no—
434C2×D4—941no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—941no—
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4D4×D4711yescharacteristic
440C22×C4#1062535211yescharacteristic
441Q16—942no—
442Q16—1881no—
443SD16—942no—
444SD16—1881no—
445M16—3761no—
446C2×C8—24no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—81no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—3761no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—471no—
469C4⋊C4—471no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4C2×C4×D4711yescharacteristic
475C4⋊C4C2×C4×D4711yescharacteristic
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—941no—
486C42C2×C4×D4711yescharacteristic
487C42D4×D4711yescharacteristic
488C42#1062535211yescharacteristic
489C42C23×D4711yescharacteristic
490C23—941no—
491C23(C22⋊D47)⋊C411yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—941no—
497Q8—941no—
498Q8#1309403012yes—
499D4—941no—
500D4—941no—
501D4—1882no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—1881no—
517C2×C4—1881no—
518C2×C4(C22⋊D47)⋊C411yescharacteristic
519C2×C4(C22⋊D47)⋊C411yescharacteristic
520C2×C4(C22⋊D47)⋊C411yescharacteristic
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4C2×#1062535211yescharacteristic
524C8—22no—
525C8—22no—
526C8—41no—
527C8—41no—
528C8—941no—
529C8—941no—
530C8—941no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—1881no—
537C8—1881no—
538C22—21no—
539C22—21no—
540C22—1881no—
541C22—1881no—
542C22—1881no—
543C22#1568923712yes—
544C22C2×(C22⋊D47)⋊C411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4C2×#1309403011yescharacteristic
557C4#1568988911yescharacteristic
558C4#1568992911yescharacteristic
559C4#1568993611yescharacteristic
560C2—22no—
561C2—3761no—
562C2#2025210911yescharacteristic
563C2#2025222511yescharacteristic
564C2C2×#1568923711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×Q8⋊C8C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenterC2×Q8⋊C8D47
hypocenterC47#18017
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #20252477C2semidirect
4. #20242282C2semidirect
5. #20242275C2semidirect
6. #20242263C2semidirect
7. #20242262C2semidirect
8. #20242256C2semidirect
9. #20242248C2semidirect
10. #20242192C2semidirect
11. #20242185C2semidirect
12. #20242171C2semidirect
14. #20241671C2semidirect
15. C2×C47×Q8⋊C8C2semidirect
291. C2×Q8⋊C8D47semidirect
349. C47#18017semidirect

Maximal subgroups

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

subgroupindex
#202534682
#202525442
#202524772
#202422822
#202422752
#202422632
#202422622
#202422562
#202422482
#202421922
#202421852
#202421712
#202418492
#202416712
C2×C47×Q8⋊C82
#1801747