Finite Group Databasebeta

← #26274336

Subgroups — #26274336

Order 12032.

704 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247099C211yesmaximal, characteristic
2#20246261C211yesmaximal, characteristic
3#20244952C211yesmaximal, characteristic, complemented
4#20244889C211yesmaximal, characteristic, complemented
5#20244880C211yesmaximal, characteristic, complemented
6#20244728C211yesmaximal, characteristic, complemented
7#20244342C211yesmaximal, characteristic, complemented
8#20244146C211yesmaximal, characteristic, complemented
9#20243976C211yesmaximal, characteristic, complemented
10#20243586C211yesmaximal, characteristic
11#20243572C211yesmaximal, characteristic
12#20243473C211yesmaximal, characteristic
13#20243420C211yesmaximal, characteristic
14#20243106C211yesmaximal, characteristic
15C47×#1919C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C2×#13094015C2211yescharacteristic
18C2×#13093982C2211yescharacteristic
19C2×C4⋊C4×D47C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×(C2×D47)⋊C8C2211yescharacteristic
26#15689060—21no—
27#15689045—21no—
28#15689022—21no—
29#15689022C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689019C2211yescharacteristic
32#15689008—21no—
33#15689007—21no—
34#15689005—21no—
35#15688993C2211yescharacteristic
36#15688982—21no—
37#15688980C2211yescharacteristic
38#15688980C2211yescharacteristic
39C4⋊C4×Dic47C2211yescharacteristic
40C4×(C2×D47)⋊C4—21no—
41C4×(C2×D47)⋊C4C2211yescharacteristic
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×#106×C47C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×C4×D47—21no—
60C22×C4×D47C2311yescharacteristic
61C2×#10625324—22no—
62C2×#10625324—22no—
63C2×#10625324—41no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13094015—22no—
67#13094015—41no—
68#13093982—22no—
69#13093982—41no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C4⋊C4×D47—22no—
83C4⋊C4×D47Q814yes—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4D411yescharacteristic
88C2×(C2×D47)⋊C4D411yescharacteristic
89C2×C4×Dic47—21no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47C2311yescharacteristic
92#13093957—41no—
93#13093957—41no—
94#13093955—22no—
95C4⋊(C47⋊C8)—22no—
96Dic47⋊C8—41no—
97(C2×D47)⋊C8—22no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95D411yescharacteristic
105C47⋊#95D411yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115#106×C47—22no—
116#95×C47—21no—
117#95×C47—21no—
118C23×D47C2×D411yescharacteristic
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47C2×D411yescharacteristic
131C22×Dic47C2×D411yescharacteristic
132C22×Dic47C2×D411yescharacteristic
133C2×C4×D47—21no—
134C2×C4×D47—21no—
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—24no—
138C2×C4×D47—81no—
139C2×C4×D47—81no—
140C2×C4×D47C2×Q812yes—
141C2×C4×D47#4112yes—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—42no—
155C4⋊C4×C47C2×Q812yes—
156C4⋊C4×C47#4112yes—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—81no—
160(C2×D47)⋊C4—22no—
161(C2×D47)⋊C4—41no—
162(C2×D47)⋊C4—42no—
163(C2×D47)⋊C4—42no—
164(C2×D47)⋊C4—81no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—42no—
173C4⋊Dic47—42no—
174C4⋊Dic47—81no—
175C4⋊Dic47—81no—
176C4⋊Dic47C2×Q812yes—
177Dic47⋊C4—24no—
178Dic47⋊C4—42no—
179Dic47⋊C4—81no—
180Dic47⋊C4—81no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—42no—
184C4×Dic47—81no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8#4112yes—
191#10625324—44no—
192C23×C47C22×D411yescharacteristic
193C22×D47—21no—
194C22×D47—21no—
195C22×D47—21no—
196C22×D47—21no—
197C22×D47—21no—
198C22×D47—21no—
199C22×D47C22⋊Q812yes—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
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×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47#13712yes—
218C2×C4×C47C22×Q811yescharacteristic
219C2×C4×C47C2×#4111yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47H(5,𝔽2)11yescharacteristic
223C2×C4×C472−1+411yescharacteristic
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—22no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
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×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47C22⋊Q812yes—
245C4×D47—22no—
246C4×D47—22no—
247C4×D47—22no—
248C4×D47—22no—
249C4×D47—84no—
250C8×C47—41no—
251C8×C47—41no—
252C47⋊C8—22no—
253C47⋊C8—41no—
254#26018—471nomaximal, Sylow
255C22×C47C2×C22⋊Q811yescharacteristic
256C22×C47#54611yescharacteristic
257C22×C47#54711yescharacteristic
258C22×C47C2×#13711yescharacteristic
259C22×C47#57511yescharacteristic
260C22×C47#57611yescharacteristic
261C22×C47#57711yescharacteristic
262C2×D47—22no—
263C2×D47—22no—
264C2×D47—22no—
265C2×D47—41no—
266C2×D47—41no—
267C2×D47—41no—
268C2×D47—41no—
269C4×C47—22no—
270C4×C47—42no—
271C4×C47—42no—
272C4×C47—41no—
273C4×C47—81no—
274C4×C47—81no—
275C4×C47#53311yescharacteristic
276C4×C47#54411yescharacteristic
277C4×C47#55111yescharacteristic
278C4×C47#55211yescharacteristic
279Dic47—22no—
280Dic47—41no—
281Dic47—42no—
282Dic47—41no—
283Dic47—81no—
284Dic47—81no—
285Dic47—81no—
286#2441—471no—
287#2345—471no—
288#2100—471no—
289#2088—471no—
290#2086—471no—
291#2059—471no—
292#1989—471no—
293#1947—471no—
294#1920—471no—
295#1919D4711yescharacteristic, complemented
296#1854—471no—
297#1851—471no—
298#1823—471no—
299#1809—471no—
300#1736—471no—
301C2×C47#243811yescharacteristic
302C2×C47#307811yescharacteristic
303C2×C47#308111yescharacteristic
304C2×C47#330911yescharacteristic
305C2×C47#333111yescharacteristic
306C2×C47#334611yescharacteristic
307C2×C47#335111yescharacteristic
308D47—42no—
309C22×M16—471no—
310C2×#125—471no—
311C2×#117—471no—
312C22×C4⋊C4—471no—
313C2×#107—471no—
314C2×#107—471no—
315C2×#106—471no—
316C2×#106C2×D4711yescharacteristic
317C2×C4⋊C8—471no—
318C2×C4⋊C8—471no—
319C2×C22⋊C8—471no—
320#399—941no—
321#396—941no—
322#389—471no—
323#389—471no—
324#389—471no—
325#389—941no—
326#389C2×D4711yescharacteristic
327#387—941no—
328#387—941no—
329#387—941no—
330#384—471no—
331#380—471no—
332#380—471no—
333#380—941no—
334C4×C4⋊C4—471no—
335C4×C4⋊C4C2×D4711yescharacteristic
336C4×C22⋊C4—471no—
337C4×C22⋊C4—941no—
338#340—471no—
339#340—471no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340C2×D4711yescharacteristic
348#340C2×D4711yescharacteristic
349#340C2×D4711yescharacteristic
350#336—471no—
351#336C2×D4711yescharacteristic
352C47#2601811yescharacteristic, complemented, Sylow
353C23×C4—471no—
354C23×C4—941no—
355C2×M16—942no—
356C2×M16—942no—
357C2×M16—1881no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8C22×D4711yescharacteristic
361C22×C8C22×D4711yescharacteristic
362#125—942no—
363#125—1881no—
364#117—942no—
365#117—1881no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—474no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—942no—
373C2×C4⋊C4—941no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4—941no—
379C2×C4⋊C4—941no—
380C2×C4⋊C4—941no—
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C4⋊C4C22×D4711yescharacteristic
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C4⋊C4C22×D4711yescharacteristic
385C2×C22⋊C4—471no—
386C2×C22⋊C4—471no—
387C2×C22⋊C4—941no—
388C2×C22⋊C4—941no—
389C2×C22⋊C4—941no—
390C2×C42—21no—
391C2×C42—471no—
392C2×C42—941no—
393C2×C42—941no—
394C2×C42C22×D4711yescharacteristic
395#107—1881no—
396#107—1881no—
397#106—22no—
398#106—942no—
399C4⋊C8—942no—
400C4⋊C8—1881no—
401C22⋊C8—942no—
402#95—21no—
403#95—21no—
404#95—471no—
405#95—471no—
406#95—941no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95—941no—
412C24—471no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—471no—
418C22×C4—472no—
419C22×C4—472no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—944no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—3761no—
432C22×C4—3761no—
433C22×C4D4×D4711yescharacteristic
434C22×C4D4×D4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436M16—1884no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—472no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—42no—
456C4⋊C4—472no—
457C4⋊C4—944no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—3761no—
466C4⋊C4—3761no—
467C4⋊C4—3761no—
468C4⋊C4—3761no—
469C4⋊C4—1882no—
470C4⋊C4—1882no—
471C4⋊C4—1882no—
472C4⋊C4#1062535012yes—
473C4⋊C4Q8×D4712yes—
474C22⋊C4—942no—
475C22⋊C4—3761no—
476C22⋊C4—1881no—
477C22⋊C4—1882no—
478C22⋊C4—1882no—
479C42—21no—
480C42—21no—
481C42—81no—
482C42—941no—
483C42—941no—
484C42—3761no—
485C42—1882no—
486C23—472no—
487C23—941no—
488C23—941no—
489C23—941no—
490C23—941no—
491C23—941no—
492C23—941no—
493C23C2×D4×D4711yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—472no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—942no—
515C2×C4—942no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—942no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—3764no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4#1309405312yes—
538C2×C4C2×Q8×D4711yescharacteristic
539C2×C4#41×D4711yescharacteristic
540C2×C4#41×D4711yescharacteristic
541C2×C4C2×#1062535011yescharacteristic
542C2×C4#1309407011yescharacteristic
543C2×C4#1309407111yescharacteristic
544C8—41no—
545C8—41no—
546C8—942no—
547C8—1881no—
548C22—942no—
549C22—942no—
550C22—942no—
551C22—1881no—
552C22—1881no—
553C22—1881no—
554C22—1881no—
555C22C22⋊Q8×D4711yescharacteristic
556C22#1568976911yescharacteristic
557C22#1568977111yescharacteristic
558C22C2×#1309405311yescharacteristic
559C22#1568992211yescharacteristic
560C22#1568992711yescharacteristic
561C22#1568993011yescharacteristic
562C4—22no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—81no—
567C4—81no—
568C4—942no—
569C4—3761no—
570C4—3761no—
571C4—3761no—
572C4—1882no—
573C4—1881no—
574C4—1881no—
575C4#1568967711yescharacteristic
576C4#1568975311yescharacteristic
577C4#1568979811yescharacteristic
578C4#1568981211yescharacteristic
579C2—1882no—
580C2#2024706911yescharacteristic
581C2#2025318811yescharacteristic
582C2#2025321811yescharacteristic
583C2#2025539911yescharacteristic
584C2#2025570611yescharacteristic
585C2#2025587111yescharacteristic
586C2#2025594611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1919C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#1919D47
hypocenterC47#26018
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
3. #20244952C2semidirect
4. #20244889C2semidirect
5. #20244880C2semidirect
6. #20244728C2semidirect
7. #20244342C2semidirect
8. #20244146C2semidirect
9. #20243976C2semidirect
15. C47×#1919C2semidirect
295. #1919D47semidirect
352. C47#26018semidirect

Maximal subgroups

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

subgroupindex
#202470992
#202462612
#202449522
#202448892
#202448802
#202447282
#202443422
#202441462
#202439762
#202435862
#202435722
#202434732
#202434202
#202431062
C47×#19192
#2601847