Finite Group Databasebeta

← #26187419

Subgroups — #26187419

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253459C211yesmaximal, characteristic
2#20252335C211yesmaximal, characteristic, complemented
3#20242290C211yesmaximal, characteristic, complemented
4#20242276C211yesmaximal, characteristic, complemented
5#20242264C211yesmaximal, characteristic, complemented
6#20242259C211yesmaximal, characteristic, complemented
7#20242238C211yesmaximal, characteristic, complemented
8#20242229C211yesmaximal, characteristic, complemented
9#20242205C211yesmaximal, characteristic, complemented
10C8×#10625337C211yesmaximal, characteristic, complemented
11#20242174C211yesmaximal, characteristic, complemented
12#20241860C211yesmaximal, characteristic, complemented
13#20241775C211yesmaximal, characteristic
14#20241685C211yesmaximal, characteristic, complemented
15C47×#2971C211yesmaximal, characteristic
16#15689680C2211yescharacteristic
17#15689464C411yescharacteristic
18#15689464C411yescharacteristic
19#15689408C411yescharacteristic
20#15689403C411yescharacteristic
21#15689333C411yescharacteristic
22#15689328C411yescharacteristic
23#15689285C411yescharacteristic
24#15689285C411yescharacteristic
25#15689253C2211yescharacteristic
26#15689253C2211yescharacteristic
27#15689251—21no—
28#15689251—21no—
29C8×Dic94C2211yescharacteristic
30C8×Dic94C2211yescharacteristic
31C4×#10625337C2211yescharacteristic
32C4×#10625337C2211yescharacteristic
33C4×#10625335C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689176C2211yescharacteristic
36#15689176C2211yescharacteristic
37#15689151—21no—
38C2×C4⋊(C47⋊C8)C2211yescharacteristic
39#15689081—21no—
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46#15688853C2211yescharacteristic
47#15688853C2211yescharacteristic
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50D4⋊(C47⋊C8)C2211yescharacteristic
51D4⋊(C47⋊C8)C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54#15688844C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C4×#41×C47C2211yescharacteristic
57C8×Q8×C47C2211yescharacteristic
58C8×Q8×C47C2211yescharacteristic
59C47×#436—21no—
60C47×#436—21no—
61C47×#436C2211yescharacteristic
62C47×#436C2211yescharacteristic
63C47×#432—21no—
64C47×#432C2211yescharacteristic
65C4×M16×C47—21no—
66C4×M16×C47C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C22×C47⋊C8—21no—
72#13094024C2×C411yescharacteristic
73#13094024C2×C411yescharacteristic
74#13094016—21no—
75#13094003—21no—
76#13094003C2×C411yescharacteristic
77#13094003C2×C411yescharacteristic
78C4×Dic94—21no—
79C4×Dic94C2311yescharacteristic
80C4×Dic94C2311yescharacteristic
81#13093983—21no—
82#13093957C2×C411yescharacteristic
83#13093957C2×C411yescharacteristic
84#13093955C2×C411yescharacteristic
85#13093955C2×C411yescharacteristic
86C4⋊(C47⋊C8)—21no—
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—
94Dic47⋊C8—21no—
95Dic47⋊C8—21no—
96#13093948C2×C411yescharacteristic
97#13093948C2×C411yescharacteristic
98#13093947C2×C411yescharacteristic
99#13093947C2×C411yescharacteristic
100#13093947C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093945C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104C22⋊(C47⋊C8)—21no—
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106C22⋊(C47⋊C8)C2×C411yescharacteristic
107#13093934—21no—
108#13093934—21no—
109C4×C47⋊C8C2311yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C8×Dic47—21no—
114C8×Dic47—21no—
115C2×#41×C47C2×C411yescharacteristic
116C2×M16×C47—21no—
117C2×M16×C47—21no—
118C2×M16×C47D411yescharacteristic
119C2×M16×C47D411yescharacteristic
120C4×Q8×C47C2×C411yescharacteristic
121C4×Q8×C47C2311yescharacteristic
122C4×D4×C47—21no—
123C4×D4×C47—21no—
124C4×D4×C47C2×C411yescharacteristic
125C4×D4×C47C2311yescharacteristic
126#117×C47—21no—
127#117×C47C2×C411yescharacteristic
128C2×C42×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×C47D411yescharacteristic
139#97×C47D411yescharacteristic
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—41no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×D4×C47—21no—
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C2×Dic94—21no—
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158M16×C47—22no—
159M16×C47—41no—
160M16×C47—42no—
161M16×C47—42no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47C2×D411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47C22×C411yescharacteristic
171C4⋊C4×C47C22×C411yescharacteristic
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C42×C47—21no—
176C42×C47—21no—
177C42×C47—21no—
178C42×C47C22×C411yescharacteristic
179C42×C47C2×D411yescharacteristic
180C42×C47#4111yescharacteristic
181C42×C47C2411yescharacteristic
182C22⋊Dic47—21no—
183C22⋊Dic47—21no—
184#10625337—22no—
185#10625337—22no—
186#10625335—41no—
187#10625335—41no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47C22×C411yescharacteristic
192C4⋊Dic47C22×C411yescharacteristic
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196Dic47⋊C4—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⋊C8—42no—
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C23×C47—21no—
209C23×C47C4×D411yescharacteristic
210Q8×C47—21no—
211Q8×C47#13112yes—
212D4×C47—21no—
213D4×C47—21no—
214D4×C47—42no—
215C2×C4×C47—21no—
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—41no—
223C2×C4×C47—42no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—81no—
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C23×C411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—21no—
240Dic94—21no—
241Dic94—81no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47#13712yes—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256#18013—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47C2×C4×D411yescharacteristic
264C4×C47—21no—
265C4×C47—22no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47C2×#13111yescharacteristic
272C4×C47#56811yescharacteristic
273C4×C47C2×#13711yescharacteristic
274C4×C47#57511yescharacteristic
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278Dic47—41no—
279#3107—471no—
280#2971D4711yescharacteristic
281#2962—471no—
282#1592—471no—
283#1590—471no—
284#1588—471no—
285#1587—471no—
286#1584—471no—
287#1583—471no—
288#1579—471no—
289C8×Q16—471no—
290#1573—471no—
291#1497—471no—
292#1477—471no—
293#1453—471no—
294C2×C47—41no—
295C2×C47—81no—
296C2×C47#293311yescharacteristic
297C2×C47C4×#13711yescharacteristic
298C2×C47#295711yescharacteristic
299#533—471no—
300C4×#41C2×D4711yescharacteristic
301#485—471no—
302#485—471no—
303#475—471no—
304#474—471no—
305#462—471no—
306#461—471no—
307#452—471no—
308#452—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8C2×D4711yescharacteristic
316C8×Q8C2×D4711yescharacteristic
317C4×Q16—471no—
318C4×Q16—471no—
319C4×SD16—471no—
320C4×SD16—471no—
321#436—21no—
322#436—21no—
323#436C2×D4711yescharacteristic
324#436C2×D4711yescharacteristic
325#432—21no—
326#432C2×D4711yescharacteristic
327#431—471no—
328#431—471no—
329#424—941no—
330C2×C4⋊C8—471no—
331#405—941no—
332C4×M16—21no—
333C4×M16C2×D4711yescharacteristic
334#335—471no—
335#335—471no—
336#334—471no—
337#334—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8—471no—
343Q8⋊C8—471no—
344D4⋊C8—471no—
345D4⋊C8—471no—
346#322—471no—
347#322—471no—
348#322—471no—
349C82—471no—
350C47#1801311yescharacteristic, complemented, Sylow
351C2×#41C4×D4711yescharacteristic
352C2×Q16—471no—
353C2×Q16—471no—
354C2×SD16—471no—
355C2×SD16—471no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16C22⋊D4711yescharacteristic
359C2×M16C22⋊D4711yescharacteristic
360C22×C8—941no—
361C4⋊Q8—471no—
362C4⋊Q8—471no—
363#125—941no—
364C22⋊Q8—471no—
365C22⋊Q8—471no—
366C22⋊Q8—941no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—941no—
370C4×Q8C4×D4711yescharacteristic
371C4×Q8C22×D4711yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C4×D4711yescharacteristic
375C4×D4C22×D4711yescharacteristic
376#117—21no—
377#117—941no—
378#117C4×D4711yescharacteristic
379C2×C42—21no—
380C2×C42C22×D4711yescharacteristic
381#107—471no—
382#107—471no—
383#106—471no—
384#106—471no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—471no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8—941no—
397C4⋊C8C22×D4711yescharacteristic
398C4⋊C8C22×D4711yescharacteristic
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#103—471no—
405#102—471no—
406#102—471no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—471no—
411C22⋊C8—471no—
412C22⋊C8—941no—
413#97—21no—
414#97—941no—
415#97—941no—
416#97C22⋊D4711yescharacteristic
417#97C22⋊D4711yescharacteristic
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—941no—
425C4×C8—941no—
426C4×C8C22×D4711yescharacteristic
427C4×C8C22×D4711yescharacteristic
428#41—22no—
429#41—41no—
430C2×Q8—471no—
431C2×Q8—471no—
432C2×Q8—941no—
433C2×Q8C2×C4×D4711yescharacteristic
434C2×D4—21no—
435C2×D4C2×C4×D4711yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4#1062535011yescharacteristic
441C22×C4C2×C22⋊D4711yescharacteristic
442Q16—942no—
443Q16—942no—
444SD16—1881no—
445SD16—1881no—
446M16—22no—
447M16—41no—
448M16—42no—
449M16—42no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—1882no—
461C2×C8C2×C22⋊D4711yescharacteristic
462C2×C8C2×C22⋊D4711yescharacteristic
463C2×C8C2×C22⋊D4711yescharacteristic
464C2×C8C2×C22⋊D4711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—471no—
468C4⋊C4—471no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4C2×C4×D4711yescharacteristic
477C4⋊C4C2×C4×D4711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—941no—
482C22⋊C4—941no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—941no—
487C42—941no—
488C42C2×C4×D4711yescharacteristic
489C42#1062535011yescharacteristic
490C42C2×C22⋊D4711yescharacteristic
491C42C23×D4711yescharacteristic
492C23—21no—
493C23C4×C22⋊D4711yescharacteristic
494Q8—21no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—941no—
499Q8—3761no—
500Q8#1309403212yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4C4×C22⋊D4711yescharacteristic
521C2×C4C4×C22⋊D4711yescharacteristic
522C2×C4C4×C22⋊D4711yescharacteristic
523C2×C4C22×C4×D4711yescharacteristic
524C2×C4C22×C22⋊D4711yescharacteristic
525C2×C4C2×#1062535011yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—1881no—
536C8—1881no—
537C8—1881no—
538C8—1881no—
539C8#1309405412yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D4711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—1881no—
555C4—1881no—
556C4—1881no—
557C4—1881no—
558C4C2×#1309403211yescharacteristic
559C4#1568988911yescharacteristic
560C4C2×#1309405411yescharacteristic
561C4#1568992111yescharacteristic
562C2—41no—
563C2—81no—
564C2#2025211311yescharacteristic
565C2C4×#1309405411yescharacteristic
566C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2971C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×C47C2×C4
cosocleC42×C47C24
hypercenter#2971D47
hypocenterC47#18013
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #20252335C2semidirect
3. #20242290C2semidirect
4. #20242276C2semidirect
5. #20242264C2semidirect
6. #20242259C2semidirect
7. #20242238C2semidirect
8. #20242229C2semidirect
9. #20242205C2semidirect
10. C8×#10625337C2semidirect
11. #20242174C2semidirect
12. #20241860C2semidirect
14. #20241685C2semidirect
350. C47#18013semidirect

Maximal subgroups

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

subgroupindex
#202534592
#202523352
#202422902
#202422762
#202422642
#202422592
#202422382
#202422292
#202422052
C8×#106253372
#202421742
#202418602
#202417752
#202416852
C47×#29712
#1801347