Finite Group Databasebeta

← #26244440

Subgroups — #26244440

Order 12032.

1240 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689680C211yesmaximal, characteristic, complemented
2C2×C4×#10625335C212yesmaximal, complemented
3#20244721C211yesmaximal, characteristic, complemented
4#20244634C211yesmaximal, characteristic, complemented
5#20244584C212yesmaximal, complemented
6#20244524C211yesmaximal, characteristic, complemented
7#20244470C211yesmaximal, characteristic, complemented
8#20244391C212yesmaximal
9C4×#13093947C212yesmaximal, complemented
10C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
11C4×#121×C47C211yesmaximal, characteristic
12C22×#10625335C2212yes—
13#15689680—28no—
14C2×#13094024C2211yescharacteristic
15C2×#13094024C2211yescharacteristic
16C2×#13094016—21no—
17C2×#13094003—21no—
18C2×#13094003C2212yes—
19C2×C4×Dic94—21no—
20C2×C4×Dic94C2212yes—
21C2×#13093983—21no—
22C4×#10625335—28no—
23C2×#13093955C2212yes—
24C2×#13093947C2212yes—
25C2×#13093947C2212yes—
26C2×#13093947C2212yes—
27C2×#13093945C2212yes—
28C2×C22⋊(C47⋊C8)C2212yes—
29C2×C4×C47⋊C8C2212yes—
30#15688885C2212yes—
31#15688885C2212yes—
32#15688878C2211yescharacteristic
33#15688878C2211yescharacteristic
34C2×#121×C47C2211yescharacteristic
35C2×C4×D4×C47—21no—
36C2×C4×D4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C47×#390C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#388—21no—
41C47×#386—21no—
42C47×#380C2211yescharacteristic
43C4×C4⋊C4×C47C2211yescharacteristic
44C4×C22⋊C4×C47—21no—
45C22×Dic94—21no—
46C22×Dic94C2312yes—
47C2×#10625335—24no—
48C2×#10625335—24no—
49C2×#10625335—24no—
50C22×C47⋊C8C2312yes—
51C22×C47⋊C8C2312yes—
52#13094024—24no—
53#13094024—24no—
54#13094016—28no—
55#13094003—28no—
56#13094003—24no—
57#13094003—24no—
58C4×Dic94—28no—
59C4×Dic94—24no—
60C4×Dic94D418yescomplemented
61#13093983—28no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2312yes—
66C2×Dic47⋊C4—22no—
67C2×Dic47⋊C4—22no—
68C2×C22⋊Dic47—22no—
69C2×C4×Dic47—22no—
70#13093955—24no—
71#13093947—24no—
72#13093947—24no—
73#13093947—24no—
74#13093945—24no—
75C22⋊(C47⋊C8)—24no—
76C4×C47⋊C8—24no—
77C22×D4×C47—21no—
78C22×D4×C47C2311yescharacteristic
79C23×C4×C47—21no—
80C23×C4×C47D411yescharacteristic
81C23×C4×C47D411yescharacteristic
82C23×C4×C47C2311yescharacteristic
83#121×C47—22no—
84#121×C47—22no—
85C4×D4×C47—24no—
86C4×D4×C47—44no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C42×C47—24no—
97C2×C42×C47—21no—
98C2×C42×C47D411yescharacteristic
99C2×C42×C47D411yescharacteristic
100C2×C42×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102#95×C47—21no—
103#95×C47—21no—
104#95×C47—21no—
105C24×C47—21no—
106C24×C47C2×D411yescharacteristic
107C2×D4×C47—24no—
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—21no—
111C2×D4×C47—42no—
112C2×D4×C47—42no—
113C2×D4×C47#4112yes—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—41no—
126C22×C4×C47—42no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47SD1614yescomplemented
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2411yescharacteristic
136C22×Dic47—22no—
137C22×Dic47—22no—
138C2×Dic94—22no—
139C2×Dic94—22no—
140C2×Dic94—22no—
141C2×Dic94—22no—
142C2×Dic94—24no—
143C2×Dic94—22no—
144C2×Dic94—42no—
145C2×Dic94—42no—
146C2×Dic94C2×D414yes—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—22no—
149C4⋊C4×C47—22no—
150C4⋊C4×C47—42no—
151C4⋊C4×C47#4112yes—
152C22⋊C4×C47—24no—
153C22⋊C4×C47—42no—
154C22⋊C4×C47—42no—
155C22⋊C4×C47—42no—
156C22⋊C4×C47—42no—
157C42×C47—22no—
158C42×C47—22no—
159C42×C47—22no—
160C42×C47—42no—
161C42×C47C2×D414yes—
162C22⋊Dic47—28no—
163#10625335—216no—
164C4⋊Dic47—24no—
165C4⋊Dic47—24no—
166C4⋊Dic47—24no—
167C4⋊Dic47—22no—
168C4⋊Dic47C2×D414yes—
169Dic47⋊C4—28no—
170Dic47⋊C4—28no—
171C4×Dic47—28no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—22no—
177C2×C47⋊C8#4114yes—
178C23×C47—21no—
179C23×C47—21no—
180C23×C47—21no—
181C23×C47—21no—
182C23×C47—21no—
183C23×C47—21no—
184C23×C47—22no—
185C23×C47—41no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47C2×SD1612yes—
192C23×C47C22×D411yescharacteristic
193D4×C47—24no—
194D4×C47—48no—
195D4×C47—42no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—28no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—22no—
206C2×C4×C47—21no—
207C2×C4×C47—44no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—84no—
219C2×C4×C47#12012yes—
220C2×C4×C47#12012yes—
221C2×C4×C47C2×SD1612yes—
222C2×C4×C47C2×SD1612yes—
223C2×C4×C47#13512yes—
224C2×C4×C47#13712yes—
225C2×C4×C47C22×D412yes—
226C2×C4×C47C2×#4112yes—
227C2×C4×C47C2×#4111yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C2×Dic47—24no—
230C2×Dic47—24no—
231C2×Dic47—42no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235Dic94—24no—
236Dic94—24no—
237Dic94—48no—
238Dic94—42no—
239Dic94—42no—
240C47⋊C8—24no—
241C47⋊C8—42no—
242#23568—471nomaximal, Sylow
243C22×C47—22no—
244C22×C47—22no—
245C22×C47—22no—
246C22×C47—41no—
247C22×C47—41no—
248C22×C47—41no—
249C22×C47—41no—
250C22×C47—42no—
251C22×C47—42no—
252C22×C47—42no—
253C22×C47—81no—
254C22×C47—81no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47C2×#12011yescharacteristic
258C22×C47#52511yescharacteristic
259C22×C47#53211yescharacteristic
260C22×C47C22×SD1611yescharacteristic
261C22×C47C2×#13511yescharacteristic
262C22×C47C2×#13711yescharacteristic
263C22×C47#57511yescharacteristic
264C4×C47—22no—
265C4×C47—22no—
266C4×C47—22no—
267C4×C47—42no—
268C4×C47—41no—
269C4×C47—81no—
270C4×C47—81no—
271C4×C47#44814yes—
272C4×C47#52512yes—
273C4×C47#53212yes—
274Dic47—44no—
275Dic47—44no—
276C2×#533—471no—
277C2×C4×SD16—472no—
278C4×#121D4711yescharacteristic
279#2058—471no—
280#2043—471no—
281#2035—472no—
282#2023—471no—
283#2013—471no—
284#2000—472no—
285C4×#103—472no—
286C4×C22⋊C8—471no—
287C2×C47—42no—
288C2×C47—82no—
289C2×C47#238811yescharacteristic
290C2×C47C2×#44811yescharacteristic
291C2×C47#300211yescharacteristic
292C2×C47#310111yescharacteristic
293C2×C47#310711yescharacteristic
294C2×C47#316711yescharacteristic
295C2×C47#317211yescharacteristic
296C22×SD16—472no—
297#533—948no—
298C2×C4⋊Q8—471no—
299C2×C4⋊Q8—471no—
300C2×#125—941no—
301C2×C22⋊Q8—472no—
302C2×C22⋊Q8—941no—
303C2×#121C2×D4711yescharacteristic
304C2×C4×Q8—472no—
305C2×C4×Q8—941no—
306C2×C4×D4—21no—
307C2×C4×D4C2×D4711yescharacteristic
308C2×#117—941no—
309C22×C42C2×D4711yescharacteristic
310C4×SD16—948no—
311C2×#106—472no—
312C2×#103—472no—
313C2×#103—472no—
314C2×#103—472no—
315C2×#102—472no—
316C2×C22⋊C8—472no—
317C2×C4×C8—472no—
318#390C2×D4711yescharacteristic
319#389C2×D4711yescharacteristic
320#388—21no—
321#386—21no—
322#380C2×D4711yescharacteristic
323C4×C4⋊C4C2×D4711yescharacteristic
324C4×C22⋊C4—21no—
325#340—472no—
326#340—472no—
327#336—471no—
328#336—471no—
329C47#2356811yescharacteristic, complemented, Sylow
330C22×Q8—472no—
331C22×Q8—941no—
332C22×D4—21no—
333C22×D4C22×D4711yescharacteristic
334C23×C4—21no—
335C23×C4C22⋊D4711yescharacteristic
336C23×C4C22⋊D4711yescharacteristic
337C23×C4C22×D4711yescharacteristic
338C2×SD16—944no—
339C2×SD16—944no—
340C2×SD16—944no—
341C22×C8—472no—
342C22×C8—472no—
343C4⋊Q8—944no—
344C4⋊Q8—944no—
345#125—948no—
346C22⋊Q8—944no—
347C22⋊Q8—944no—
348C22⋊Q8—948no—
349#121—22no—
350#121—22no—
351C4×Q8—478no—
352C4×Q8—948no—
353C4×Q8—944no—
354C4×D4—24no—
355C4×D4—44no—
356#117—948no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—472no—
359C2×C4⋊C4—941no—
360C2×C4⋊C4—941no—
361C2×C4⋊C4—942no—
362C2×C4⋊C4—942no—
363C2×C4⋊C4—941no—
364C2×C4⋊C4C22×D4711yescharacteristic
365C2×C4⋊C4C22×D4711yescharacteristic
366C2×C4⋊C4C22×D4711yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—942no—
373C2×C42—24no—
374C2×C42—21no—
375C2×C42—942no—
376C2×C42C22⋊D4711yescharacteristic
377C2×C42C22⋊D4711yescharacteristic
378C2×C42C22×D4711yescharacteristic
379C2×C42C22×D4711yescharacteristic
380#106—944no—
381#103—944no—
382#103—944no—
383#103—944no—
384#102—944no—
385C22⋊C8—944no—
386C4×C8—944no—
387#95—21no—
388#95—21no—
389#95—21no—
390C24—21no—
391C24C2×C22⋊D4711yescharacteristic
392C2×Q8—474no—
393C2×Q8—944no—
394C2×Q8—942no—
395C2×Q8—942no—
396C2×Q8—942no—
397C2×Q8—942no—
398C2×Q8—942no—
399C2×Q8—1882no—
400C2×Q8—1882no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4#1062535012yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—41no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—942no—
424C22×C4—942no—
425C22×C4#1062533514yescomplemented
426C22×C4C2×C22⋊D4711yescharacteristic
427C22×C4C2×C22⋊D4711yescharacteristic
428C22×C4C2×C22⋊D4711yescharacteristic
429C22×C4C2×C22⋊D4711yescharacteristic
430C22×C4C2×C22⋊D4711yescharacteristic
431C22×C4C23×D4711yescharacteristic
432SD16—9416no—
433C2×C8—474no—
434C2×C8—942no—
435C2×C8—942no—
436C2×C8—942no—
437C2×C8—942no—
438C2×C8—942no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4—474no—
444C4⋊C4—948no—
445C4⋊C4—944no—
446C4⋊C4—944no—
447C4⋊C4—944no—
448C4⋊C4—948no—
449C4⋊C4—942no—
450C4⋊C4#1062535012yes—
451C22⋊C4—24no—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—948no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—42no—
461C42—948no—
462C42D4×D4714yes—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C2×#1062533512yes—
477C23C22×C22⋊D4711yescharacteristic
478Q8—944no—
479Q8—944no—
480Q8—1888no—
481Q8—1882no—
482Q8—1882no—
483D4—24no—
484D4—48no—
485D4—42no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—28no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—84no—
509C2×C4—944no—
510C2×C4—944no—
511C2×C4—1882no—
512C2×C4—1882no—
513C2×C4—1882no—
514C2×C4—1882no—
515C2×C4#1309399212yes—
516C2×C4#1309399212yes—
517C2×C4C2×#1062533512yes—
518C2×C4C2×#1062533512yes—
519C2×C4#1309404412yes—
520C2×C4#1309405412yes—
521C2×C4C2×D4×D4712yes—
522C2×C4#41×D4712yes—
523C2×C4C2×#1062535011yescharacteristic
524C2×C4C2×#1062535011yescharacteristic
525C8—944no—
526C8—1882no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C2×#1309399211yescharacteristic
542C22#1568963411yescharacteristic
543C22#1568966911yescharacteristic
544C22C22×#1062533511yescharacteristic
545C22C2×#1309404411yescharacteristic
546C22C2×#1309405411yescharacteristic
547C22#1568992111yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—1884no—
556C4—1884no—
557C4#1568926114yes—
558C4#1568963212yes—
559C4#1568967012yes—
560C2—42no—
561C2—82no—
562C2#2024660311yescharacteristic
563C2C2×#1568926111yescharacteristic
564C2#2025260411yescharacteristic
565C2#2025339611yescharacteristic
566C2#2025345911yescharacteristic
567C2#2025394311yescharacteristic
568C2#2025399511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×#121×C47C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenterC4×#121D47
hypocenterC47#23568
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#15689680C2semidirect
2. C2×C4×#10625335C2semidirect
3. #20244721C2semidirect
4. #20244634C2semidirect
5. #20244584C2semidirect
6. #20244524C2semidirect
7. #20244470C2semidirect
9. C4×#13093947C2semidirect
10. C4×C22⋊(C47⋊C8)C2semidirect
60. C4×Dic94D4semidirect
129. C22×C4×C47SD16semidirect
329. C47#23568semidirect
425. C22×C4#10625335semidirect

Maximal subgroups

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

subgroupindex
C2×#156896802
C2×C4×#106253352
#202447212
#202446342
#202445842
#202445242
#202444702
#202443912
C4×#130939472
C4×C22⋊(C47⋊C8)2
C4×#121×C472
#2356847