Finite Group Databasebeta

← #26233965

Subgroups — #26233965

Order 12032.

766 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
1C2×#15689158C211yesmaximal, characteristic
2#20246280C211yesmaximal, characteristic
3#20246272C211yesmaximal, characteristic
4#20244132C211yesmaximal, characteristic, complemented
5#20243983C211yesmaximal, characteristic, complemented
6#20243977C211yesmaximal, characteristic, complemented
7#20243962C211yesmaximal, characteristic, complemented
8#20243956C211yesmaximal, characteristic, complemented
9#20243482C211yesmaximal, characteristic
10#20243481C211yesmaximal, characteristic
11#20243414C211yesmaximal, characteristic
12#20243287C211yesmaximal, characteristic, complemented
13#20243285C211yesmaximal, characteristic, complemented
14#20243165C211yesmaximal, characteristic
15C47×#1944C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17C2×#13093982C2211yescharacteristic
18C2×#13093982C2211yescharacteristic
19#15689158C418yescomplemented
20C2×#13093958C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×(C2×D47)⋊C8C2211yescharacteristic
25C2×#13093934C2211yescharacteristic
26#15689022C2211yescharacteristic
27#15689022C2211yescharacteristic
28#15689015—21no—
29#15689015—21no—
30#15689013—21no—
31#15689013—21no—
32#15688990—21no—
33#15688988—21no—
34#15688980C2211yescharacteristic
35#15688980C2211yescharacteristic
36C4⋊C4×Dic47—21no—
37C4⋊C4×Dic47C2211yescharacteristic
38C4⋊C4×Dic47C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41C4×(C2×D47)⋊C4C2211yescharacteristic
42#15688968—21no—
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×#107×C47C2211yescharacteristic
54C2×#106×C47C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C22×C4×D47C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C2×C8×D47—22no—
64C2×C8×D47—22no—
65C2×C8×D47C2×C414yes—
66#13093982—22no—
67#13093982—22no—
68#13093982C2×C414yes—
69#13093982C2×C414yes—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4D411yescharacteristic
81C2×(C2×D47)⋊C4D411yescharacteristic
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47C2311yescharacteristic
89#13093958—22no—
90#13093957C2×C414yes—
91#13093957C2×C414yes—
92#13093956C2×C414yes—
93(C2×D47)⋊C8—22no—
94#13093934—22no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95D411yescharacteristic
104C47⋊#95D411yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114#107×C47—22no—
115#106×C47C2×C414yes—
116#97×C47—22no—
117#95×C47—21no—
118#95×C47—21no—
119C23×D47C2×D411yescharacteristic
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2411yescharacteristic
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47C2×D411yescharacteristic
132C22×Dic47C2×D411yescharacteristic
133C22×Dic47C2×D411yescharacteristic
134C2×C4×D47—21no—
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47C22×C412yes—
139C2×C4×D47#4112yes—
140C2×C8×C47—21no—
141C2×C8×C47—21no—
142C2×C8×C47—21no—
143C2×C8×C47C22×C412yes—
144C2×C8×C47#4112yes—
145C2×C8×C47#4112yes—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—42no—
153C4⋊C4×C47—81no—
154C4⋊C4×C47C22×C412yes—
155C4⋊C4×C47C22×C412yes—
156C42×C47—21no—
157C42×C47—21no—
158(C2×D47)⋊C4—24no—
159(C2×D47)⋊C4—24no—
160(C2×D47)⋊C4—41no—
161(C2×D47)⋊C4—41no—
162(C2×D47)⋊C4—81no—
163(C2×D47)⋊C4—81no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—42no—
171C4⋊Dic47—81no—
172C4⋊Dic47C22×C412yes—
173C4⋊Dic47C22×C412yes—
174C4×Dic47—21no—
175C4×Dic47—21no—
176C4×Dic47—24no—
177C4×Dic47—24no—
178C4×Dic47—42no—
179C4×Dic47—42no—
180C4×Dic47—81no—
181C4×Dic47—81no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8C22×C412yes—
188C8×D47—28no—
189C23×C47C22×D411yescharacteristic
190C22×D47—21no—
191C22×D47—21no—
192C22×D47—21no—
193C22×D47—21no—
194C22×D47—21no—
195C22×D47—21no—
196C22×D47C4×D412yes—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47C23×C411yescharacteristic
216C2×C4×C47C2×#4111yescharacteristic
217C2×C4×C47C2×#4111yescharacteristic
218C2×C4×C47C2×#4111yescharacteristic
219C2×C4×C472−1+411yescharacteristic
220C2×C4×C472−1+411yescharacteristic
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—41no—
232C2×Dic47—41no—
233C2×Dic47—41no—
234C2×Dic47—41no—
235C2×Dic47—41no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47C4×D412yes—
242C4×D47—22no—
243C4×D47—22no—
244C4×D47—22no—
245C4×D47—22no—
246C8×C47—41no—
247C8×C47#11714yes—
248C47⋊C8—22no—
249C47⋊C8—41no—
250#22616—471nomaximal, Sylow
251C22×C47C2×C4×D411yescharacteristic
252C22×C47#54711yescharacteristic
253C22×C47#54711yescharacteristic
254C22×C47#57511yescharacteristic
255C22×C47#57511yescharacteristic
256C22×C47#57611yescharacteristic
257C22×C47#57811yescharacteristic
258C2×D47—22no—
259C2×D47—22no—
260C2×D47—22no—
261C2×D47—41no—
262C2×D47—41no—
263C2×D47—41no—
264C2×D47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—42no—
268C4×C47—42no—
269C4×C47—81no—
270C4×C47—81no—
271C4×C47C2×#11711yescharacteristic
272C4×C47#51911yescharacteristic
273C4×C47#55211yescharacteristic
274C4×C47#55211yescharacteristic
275Dic47—22no—
276Dic47—41no—
277Dic47—41no—
278Dic47—42no—
279Dic47—42no—
280Dic47—81no—
281Dic47—81no—
282C2×#427—471no—
283#2347—471no—
284#2346—471no—
285#1944—471no—
286#1944D4711yescharacteristic, complemented
287#1921—471no—
288#1921—471no—
289#1918—471no—
290#1918—471no—
291#1825—471no—
292#1825—471no—
293#1808—471no—
294#1776—471no—
295#1776—471no—
296#1752—471no—
297C2×C47#234411yescharacteristic
298C2×C47#294311yescharacteristic
299C2×C47#295111yescharacteristic
300C2×C47#334711yescharacteristic
301C2×C47#334711yescharacteristic
302C2×C47#334911yescharacteristic
303C2×C47#334911yescharacteristic
304D47—42no—
305C23×C8—471no—
306C2×#117—471no—
307C2×#117—471no—
308#427—478no—
309C2×#107—471no—
310C2×#107—471no—
311C2×#107—471no—
312C2×#107C2×D4711yescharacteristic
313C2×#106—471no—
314C2×#106C2×D4711yescharacteristic
315C2×C22⋊C8—471no—
316C2×#97—471no—
317C2×#97C2×D4711yescharacteristic
318#389—471no—
319#389—471no—
320#389C2×D4711yescharacteristic
321#389C2×D4711yescharacteristic
322#388—941no—
323#388—941no—
324#388—941no—
325#388—941no—
326#383—941no—
327#382—941no—
328#380—471no—
329#380—471no—
330C4×C4⋊C4—471no—
331C4×C4⋊C4—471no—
332C4×C4⋊C4—471no—
333C4×C4⋊C4—471no—
334C4×C4⋊C4—941no—
335C4×C22⋊C4—471no—
336#376—941no—
337#340—471no—
338#340—471no—
339#340—471no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340C2×D4711yescharacteristic
346#340C2×D4711yescharacteristic
347#336—471no—
348#336—471no—
349C47#2261611yescharacteristic, complemented, Sylow
350C23×C4—471no—
351C22×C8—471no—
352C22×C8—474no—
353C22×C8—471no—
354C22×C8—942no—
355C22×C8—942no—
356C22×C8C22×D4711yescharacteristic
357C22×C8C22×D4711yescharacteristic
358#117—474no—
359#117—474no—
360#117—942no—
361#117—942no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—471no—
365C2×C4⋊C4—471no—
366C2×C4⋊C4—471no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—941no—
369C2×C4⋊C4—941no—
370C2×C4⋊C4C22×D4711yescharacteristic
371C2×C4⋊C4C22×D4711yescharacteristic
372C2×C4⋊C4C22×D4711yescharacteristic
373C2×C4⋊C4C22×D4711yescharacteristic
374C2×C22⋊C4—471no—
375C2×C22⋊C4—471no—
376C2×C22⋊C4—941no—
377C2×C22⋊C4—941no—
378C2×C22⋊C4—941no—
379C2×C22⋊C4—941no—
380C2×C42—471no—
381C2×C42—941no—
382C2×C42—941no—
383C2×C42—941no—
384C2×C42—941no—
385C2×C42—941no—
386C2×C42—941no—
387C2×C42C22×D4711yescharacteristic
388#107—22no—
389#107—474no—
390#107—474no—
391#107—942no—
392#106—474no—
393#106C4×D4714yes—
394C22⋊C8—942no—
395#97—22no—
396#97—942no—
397#95—21no—
398#95—21no—
399#95—471no—
400#95—471no—
401#95—941no—
402#95—941no—
403#95—941no—
404#95—941no—
405#95—941no—
406#95—941no—
407#95—941no—
408#95—941no—
409C24—471no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—471no—
415C22×C4—472no—
416C22×C4—472no—
417C22×C4—471no—
418C22×C4—471no—
419C22×C4—941no—
420C22×C4—941no—
421C22×C4—941no—
422C22×C4—941no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4D4×D4711yescharacteristic
428C22×C4D4×D4711yescharacteristic
429C22×C4C23×D4711yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—472no—
434C2×C8—941no—
435C2×C8—941no—
436C2×C8—948no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8C2×C4×D4712yes—
441C2×C8#1062535212yes—
442C2×C8#1062535412yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—42no—
450C4⋊C4—81no—
451C4⋊C4—472no—
452C4⋊C4—472no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—3761no—
460C4⋊C4—1882no—
461C4⋊C4C2×C4×D4712yes—
462C4⋊C4C2×C4×D4712yes—
463C22⋊C4—944no—
464C22⋊C4—944no—
465C22⋊C4—3761no—
466C22⋊C4—3761no—
467C22⋊C4—1881no—
468C22⋊C4—1881no—
469C42—21no—
470C42—21no—
471C42—944no—
472C42—944no—
473C42—941no—
474C42—941no—
475C42—3761no—
476C42—3761no—
477C42—1882no—
478C42—1882no—
479C23—472no—
480C23—941no—
481C23—941no—
482C23—941no—
483C23—941no—
484C23—941no—
485C23—941no—
486C23C2×D4×D4711yescharacteristic
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—472no—
506C2×C4—941no—
507C2×C4—941no—
508C2×C4—942no—
509C2×C4—942no—
510C2×C4—942no—
511C2×C4—942no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—942no—
515C2×C4—942no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—1881no—
521C2×C4—1881no—
522C2×C4—1881no—
523C2×C4—1881no—
524C2×C4—1881no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4C22×C4×D4711yescharacteristic
531C2×C4#41×D4711yescharacteristic
532C2×C4C2×#1062535211yescharacteristic
533C2×C4C2×#1062535411yescharacteristic
534C2×C4#1309407111yescharacteristic
535C2×C4#1309407211yescharacteristic
536C8—41no—
537C8—942no—
538C8—1881no—
539C8#1309398214yes—
540C22—942no—
541C22—942no—
542C22—942no—
543C22—1881no—
544C22—1881no—
545C22—1881no—
546C22—1881no—
547C22C4×D4×D4711yescharacteristic
548C22#1568977311yescharacteristic
549C22#1568977611yescharacteristic
550C22#1568991911yescharacteristic
551C22#1568992211yescharacteristic
552C22#1568992711yescharacteristic
553C22#1568993911yescharacteristic
554C4—42no—
555C4—42no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—942no—
561C4—3761no—
562C4—3761no—
563C4—1882no—
564C4—1882no—
565C4—1881no—
566C4—1881no—
567C4C2×#1309398211yescharacteristic
568C4#1568959911yescharacteristic
569C4#1568980711yescharacteristic
570C4#1568981111yescharacteristic
571C2—1882no—
572C2#2024625611yescharacteristic
573C2#2025218311yescharacteristic
574C2#2025226011yescharacteristic
575C2#2025588311yescharacteristic
576C2#2025588711yescharacteristic
577C2#2025591311yescharacteristic
578C2#2025591711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1944C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1944D47
hypocenterC47#22616
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
4. #20244132C2semidirect
5. #20243983C2semidirect
6. #20243977C2semidirect
7. #20243962C2semidirect
8. #20243956C2semidirect
12. #20243287C2semidirect
13. #20243285C2semidirect
15. C47×#1944C2semidirect
19. #15689158C4semidirect
286. #1944D47semidirect
349. C47#22616semidirect

Maximal subgroups

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

subgroupindex
C2×#156891582
#202462802
#202462722
#202441322
#202439832
#202439772
#202439622
#202439562
#202434822
#202434812
#202434142
#202432872
#202432852
#202431652
C47×#19442
#2261647