Finite Group Databasebeta

← #26274331

Subgroups — #26274331

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#20247095C211yesmaximal, characteristic
2#20246265C211yesmaximal, characteristic
3#20244954C211yesmaximal, characteristic, complemented
4#20244888C211yesmaximal, characteristic, complemented
5#20244880C211yesmaximal, characteristic, complemented
6#20244729C211yesmaximal, characteristic, complemented
7#20244342C211yesmaximal, characteristic, complemented
8#20244145C211yesmaximal, characteristic, complemented
9#20243972C211yesmaximal, characteristic, complemented
10#20243969C211yesmaximal, characteristic, complemented
11#20243587C211yesmaximal, characteristic
12#20243571C211yesmaximal, characteristic
13#20243474C211yesmaximal, characteristic
14#20243421C211yesmaximal, characteristic
15C47×#1736C211yesmaximal, characteristic
16C2×#13094015C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093956C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24#15689059—21no—
25#15689046—21no—
26#15689022C2211yescharacteristic
27#15689022C2211yescharacteristic
28#15689022C2211yescharacteristic
29#15689021—21no—
30#15689019C2211yescharacteristic
31#15689009—21no—
32#15689009—21no—
33#15689007—21no—
34#15688992C2211yescharacteristic
35#15688983—21no—
36#15688983C2211yescharacteristic
37#15688983C2211yescharacteristic
38C4⋊C4×Dic47C2211yescharacteristic
39C4⋊C4×Dic47C2211yescharacteristic
40C4×C22⋊Dic47—21no—
41C4×C22⋊Dic47C2211yescharacteristic
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C22×M16×C47C2211yescharacteristic
53C2×#117×C47C2211yescharacteristic
54C22×C4⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61#13094015—22no—
62#13094015—41no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47D411yescharacteristic
78C2×C22⋊Dic47D411yescharacteristic
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47C2311yescharacteristic
82C2×C4×Dic47C2311yescharacteristic
83#13093958—41no—
84#13093957—41no—
85#13093956—22no—
86#13093955—22no—
87Dic47⋊C8—22no—
88Dic47⋊C8—41no—
89C22⋊(C47⋊C8)—22no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95D411yescharacteristic
99C47⋊#95D411yescharacteristic
100C23×C4×C47—21no—
101C23×C4×C47C2311yescharacteristic
102C2×M16×C47—22no—
103C2×M16×C47—22no—
104C2×M16×C47—41no—
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107#117×C47—22no—
108#117×C47—41no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47Q814yes—
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
117C2×C42×C47—21no—
118C24×C47C2×D411yescharacteristic
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—24no—
127C22×C4×C47—21no—
128C22×C4×C47—81no—
129C22×C4×C47—81no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×Q812yes—
132C22×C4×C47#4112yes—
133C22×C4×C47C2411yescharacteristic
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142M16×C47—44no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47#4112yes—
149C4⋊C4×C47—24no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47C2×Q812yes—
156C4⋊C4×C47C2×Q812yes—
157C4⋊C4×C47#4112yes—
158C22⋊C4×C47—42no—
159C42×C47—42no—
160C22⋊Dic47—22no—
161C22⋊Dic47—41no—
162C22⋊Dic47—42no—
163C22⋊Dic47—81no—
164C4⋊Dic47—21no—
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—
176Dic47⋊C4—42no—
177Dic47⋊C4—42no—
178Dic47⋊C4—81no—
179Dic47⋊C4—81no—
180C4×Dic47—21no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—21no—
184C4×Dic47—81no—
185C4×Dic47—81no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47C22⋊Q812yes—
199C23×C47C22×D411yescharacteristic
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
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—41no—
218C2×C4×C47—84no—
219C2×C4×C47C22⋊Q812yes—
220C2×C4×C47C22×Q811yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C2×C4×C47C2×#4111yescharacteristic
224C2×C4×C47H(5,𝔽2)11yescharacteristic
225C2×C4×C472−1+411yescharacteristic
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47#13712yes—
250C8×C47—22no—
251C8×C47—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254#26018—471nomaximal, Sylow
255C22×C47—22no—
256C22×C47—22no—
257C22×C47—22no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47C2×C22⋊Q811yescharacteristic
263C22×C47#54611yescharacteristic
264C22×C47#54711yescharacteristic
265C22×C47C2×#13711yescharacteristic
266C22×C47#57511yescharacteristic
267C22×C47#57611yescharacteristic
268C22×C47#57711yescharacteristic
269C4×C47—22no—
270C4×C47—42no—
271C4×C47—42no—
272C4×C47—42no—
273C4×C47—81no—
274C4×C47#53311yescharacteristic
275C4×C47#54411yescharacteristic
276C4×C47#55111yescharacteristic
277C4×C47#55211yescharacteristic
278Dic47—22no—
279Dic47—41no—
280Dic47—41no—
281Dic47—41no—
282Dic47—81no—
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#1919—471no—
296#1854—471no—
297#1851—471no—
298#1823—471no—
299#1809—471no—
300#1736D4711yescharacteristic
301C2×C47—42no—
302C2×C47#243811yescharacteristic
303C2×C47#307811yescharacteristic
304C2×C47#308111yescharacteristic
305C2×C47#330911yescharacteristic
306C2×C47#333111yescharacteristic
307C2×C47#334611yescharacteristic
308C2×C47#335111yescharacteristic
309C22×M16C2×D4711yescharacteristic
310C2×#125—471no—
311C2×#117C2×D4711yescharacteristic
312C22×C4⋊C4C2×D4711yescharacteristic
313C2×#107—471no—
314C2×#107—471no—
315C2×#106—471no—
316C2×#106—471no—
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—471no—
326#389—941no—
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⋊C4—471no—
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#340C2×D4711yescharacteristic
347#340C2×D4711yescharacteristic
348#340C2×D4711yescharacteristic
349#340C2×D4711yescharacteristic
350#336—471no—
351#336—471no—
352C47#2601811yescharacteristic, complemented, Sylow
353C23×C4—21no—
354C23×C4C22×D4711yescharacteristic
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—41no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8C22×D4711yescharacteristic
361C22×C8C22×D4711yescharacteristic
362#125—942no—
363#125—1881no—
364#117—22no—
365#117—41no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—941no—
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⋊C4Dic9414yes—
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C4⋊C4C22×D4711yescharacteristic
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C4⋊C4C22×D4711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—471no—
387C2×C22⋊C4—471no—
388C2×C22⋊C4—941no—
389C2×C22⋊C4—941no—
390C2×C42—21no—
391C2×C42—471no—
392C2×C42—471no—
393C2×C42—941no—
394C2×C42—941no—
395#107—1881no—
396#107—1881no—
397#106—942no—
398#106—942no—
399C4⋊C8—942no—
400C4⋊C8—1881no—
401C22⋊C8—942no—
402#95—471no—
403#95—471no—
404#95—941no—
405#95—941no—
406#95—941no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95—941no—
412C24D4×D4711yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4—471no—
425C22×C4—471no—
426C22×C4—471no—
427C22×C4—471no—
428C22×C4—941no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4C2×Dic9412yes—
433C22×C4D4×D4711yescharacteristic
434C22×C4#1062535212yes—
435C22×C4C23×D4711yescharacteristic
436M16—44no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8#1062535012yes—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—3761no—
464C4⋊C4—3761no—
465C4⋊C4—3761no—
466C4⋊C4—3761no—
467C4⋊C4—1882no—
468C4⋊C4—1882no—
469C4⋊C4—1882no—
470C4⋊C4—1882no—
471C4⋊C4C2×Dic9412yes—
472C4⋊C4C2×Dic9412yes—
473C4⋊C4#1062535012yes—
474C22⋊C4—42no—
475C22⋊C4—942no—
476C22⋊C4—3761no—
477C22⋊C4—1881no—
478C22⋊C4—1882no—
479C42—42no—
480C42—941no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42—3761no—
485C42—3761no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23#1309400112yes—
493C23C2×D4×D4711yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
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—41no—
512C2×C4—84no—
513C2×C4—472no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—941no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—1881no—
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#1309400112yes—
538C2×C4C22×Dic9411yescharacteristic
539C2×C4C2×#1062535211yescharacteristic
540C2×C4C2×#1062535011yescharacteristic
541C2×C4C2×#1062535011yescharacteristic
542C2×C4#1309406911yescharacteristic
543C2×C4#1309407211yescharacteristic
544C8—22no—
545C8—41no—
546C8—1881no—
547C8—1881no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×#1309400111yescharacteristic
556C22#1568976311yescharacteristic
557C22#1568977411yescharacteristic
558C22#137×D4711yescharacteristic
559C22#1568992211yescharacteristic
560C22#1568992711yescharacteristic
561C22#1568993311yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—81no—
567C4—942no—
568C4—3761no—
569C4—3761no—
570C4—3761no—
571C4—3761no—
572C4—1881no—
573C4—1881no—
574C4—1881no—
575C4#1568968011yescharacteristic
576C4#1568975411yescharacteristic
577C4#1568979911yescharacteristic
578C4#1568980811yescharacteristic
579C2—42no—
580C2#2024706411yescharacteristic
581C2#2025319011yescharacteristic
582C2#2025322111yescharacteristic
583C2#2025539511yescharacteristic
584C2#2025570011yescharacteristic
585C2#2025587411yescharacteristic
586C2#2025594911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1736C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#1736D47
hypocenterC47#26018
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #20244954C2semidirect
4. #20244888C2semidirect
5. #20244880C2semidirect
6. #20244729C2semidirect
7. #20244342C2semidirect
8. #20244145C2semidirect
9. #20243972C2semidirect
10. #20243969C2semidirect
352. C47#26018semidirect

Maximal subgroups

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

subgroupindex
#202470952
#202462652
#202449542
#202448882
#202448802
#202447292
#202443422
#202441452
#202439722
#202439692
#202435872
#202435712
#202434742
#202434212
C47×#17362
#2601847