Finite Group Databasebeta

← #26274337

Subgroups — #26274337

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#20247102C211yesmaximal, characteristic
2#20246267C211yesmaximal, characteristic
3#20244953C211yesmaximal, characteristic, complemented
4#20244887C211yesmaximal, characteristic, complemented
5#20244880C211yesmaximal, characteristic, complemented
6#20244724C211yesmaximal, characteristic, complemented
7#20244344C211yesmaximal, characteristic, complemented
8#20244143C211yesmaximal, characteristic, complemented
9#20243975C211yesmaximal, characteristic, complemented
10#20243964C211yesmaximal, characteristic, complemented
11#20243585C211yesmaximal, characteristic
12#20243571C211yesmaximal, characteristic
13#20243472C211yesmaximal, characteristic
14#20243108C211yesmaximal, characteristic
15C47×#1809C211yesmaximal, characteristic
16C2×#13094015C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24#15689059—21no—
25#15689046—21no—
26#15689022C2211yescharacteristic
27#15689020—21no—
28#15689019C2211yescharacteristic
29#15689019C2211yescharacteristic
30#15689019C2211yescharacteristic
31#15689010—21no—
32#15689008—21no—
33#15689008—21no—
34#15688992C2211yescharacteristic
35#15688981—21no—
36C4⋊C4×Dic47C2211yescharacteristic
37C4⋊C4×Dic47C2211yescharacteristic
38C22⋊C4×Dic47—21no—
39C4×C22⋊Dic47C2211yescharacteristic
40#15688886C2211yescharacteristic
41#15688886C2211yescharacteristic
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C22×M16×C47C2211yescharacteristic
53C2×#107×C47C2211yescharacteristic
54C2×#106×C47C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C23×Dic47—21no—
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62#13094015—22no—
63#13094015—41no—
64#13093983—22no—
65#13093983—41no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47Q814yes—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×C22⋊Dic47—21no—
82C2×C22⋊Dic47D411yescharacteristic
83C2×C22⋊Dic47D411yescharacteristic
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89#13093957—41no—
90#13093955—22no—
91Dic47⋊C8—22no—
92Dic47⋊C8—41no—
93C22⋊(C47⋊C8)—22no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95D411yescharacteristic
101C47⋊#95D411yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C2×M16×C47—22no—
104C2×M16×C47—22no—
105C2×M16×C47—41no—
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114#107×C47—41no—
115#106×C47—22no—
116#95×C47—21no—
117#95×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—21no—
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×Q812yes—
129C22×C4×C47#4112yes—
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—24no—
135C22×Dic47—21no—
136C22×Dic47—81no—
137C22×Dic47—81no—
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—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C22⋊C4×C47—42no—
158C22⋊C4×C47—81no—
159C22⋊Dic47—22no—
160C22⋊Dic47—41no—
161C22⋊Dic47—42no—
162C4⋊Dic47—24no—
163C4⋊Dic47—21no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—42no—
169C4⋊Dic47—81no—
170C4⋊Dic47C2×Q812yes—
171C4⋊Dic47C2×Q812yes—
172C4⋊Dic47#4112yes—
173Dic47⋊C4—42no—
174Dic47⋊C4—42no—
175Dic47⋊C4—42no—
176Dic47⋊C4—81no—
177Dic47⋊C4—81no—
178Dic47⋊C4—81no—
179C4×Dic47—21no—
180C4×Dic47—21no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—42no—
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—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×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47C22⋊Q812yes—
219C2×C4×C47C22×Q811yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C2×C4×C47H(5,𝔽2)11yescharacteristic
224C2×C4×C472−1+411yescharacteristic
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—22no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
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—84no—
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—81no—
271C4×C47—81no—
272C4×C47—81no—
273C4×C47—81no—
274C4×C47#53311yescharacteristic
275C4×C47#54411yescharacteristic
276C4×C47#55111yescharacteristic
277C4×C47#55211yescharacteristic
278Dic47—22no—
279Dic47—41no—
280Dic47—42no—
281Dic47—42no—
282Dic47—42no—
283Dic47—41no—
284Dic47—41no—
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#1809D4711yescharacteristic
300#1736—471no—
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×#117—471no—
312C22×C4⋊C4—471no—
313C2×#107—471no—
314C2×#107C2×D4711yescharacteristic
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—471no—
326#389—941no—
327#387—941no—
328#387—941no—
329#387—941no—
330#384—471no—
331#380—941no—
332#380C2×D4711yescharacteristic
333#380C2×D4711yescharacteristic
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#340—471no—
347#340—471no—
348#340C2×D4711yescharacteristic
349#340C2×D4711yescharacteristic
350#336—471no—
351#336—471no—
352C47#2601811yescharacteristic, complemented, Sylow
353C23×C4—941no—
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—942no—
365#117—1881no—
366C2×C4⋊C4—474no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—942no—
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⋊C4—941no—
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C4⋊C4C22×D4711yescharacteristic
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C4⋊C4C22×D4711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—471no—
388C2×C22⋊C4—471no—
389C2×C22⋊C4—941no—
390C2×C42—471no—
391C2×C42—471no—
392C2×C42—941no—
393C2×C42—941no—
394C2×C42—941no—
395#107—41no—
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—
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—21no—
421C22×C4—471no—
422C22×C4—471no—
423C22×C4—471no—
424C22×C4—471no—
425C22×C4—944no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4—941no—
430C22×C4—3761no—
431C22×C4—3761no—
432C22×C4#1062535012yes—
433C22×C4D4×D4711yescharacteristic
434C22×C4Q8×D4712yes—
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#1062535212yes—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—472no—
458C4⋊C4—472no—
459C4⋊C4—472no—
460C4⋊C4—944no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—3761no—
467C4⋊C4—3761no—
468C4⋊C4—3761no—
469C4⋊C4—3761no—
470C4⋊C4—1882no—
471C4⋊C4—1882no—
472C4⋊C4—1882no—
473C4⋊C4—1882no—
474C22⋊C4—42no—
475C22⋊C4—81no—
476C22⋊C4—942no—
477C22⋊C4—1881no—
478C22⋊C4—1882no—
479C42—941no—
480C42—941no—
481C42—941no—
482C42—941no—
483C42—3761no—
484C42—3761no—
485C42—1882no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23#1309400212yes—
493C23C2×D4×D4711yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
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—41no—
512C2×C4—472no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—942no—
518C2×C4—941no—
519C2×C4—942no—
520C2×C4—942no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—3764no—
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#1309400212yes—
538C2×C4C2×Q8×D4711yescharacteristic
539C2×C4#41×D4711yescharacteristic
540C2×C4C2×#1062535211yescharacteristic
541C2×C4C2×#1062535011yescharacteristic
542C2×C4#1309406911yescharacteristic
543C2×C4#1309407111yescharacteristic
544C8—22no—
545C8—41no—
546C8—1881no—
547C8—1881no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×#1309400211yescharacteristic
556C22#1568976211yescharacteristic
557C22#1568977311yescharacteristic
558C22#137×D4711yescharacteristic
559C22#1568991911yescharacteristic
560C22#1568992711yescharacteristic
561C22#1568993211yescharacteristic
562C4—22no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—942no—
568C4—3761no—
569C4—1882no—
570C4—1882no—
571C4—1881no—
572C4—1881no—
573C4—1881no—
574C4—1882no—
575C4#1568967511yescharacteristic
576C4#1568975211yescharacteristic
577C4#1568979911yescharacteristic
578C4#1568980611yescharacteristic
579C2—42no—
580C2#2024707011yescharacteristic
581C2#2025319211yescharacteristic
582C2#2025321711yescharacteristic
583C2#2025538911yescharacteristic
584C2#2025569911yescharacteristic
585C2#2025586811yescharacteristic
586C2#2025594311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1809C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#1809D47
hypocenterC47#26018
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
3. #20244953C2semidirect
4. #20244887C2semidirect
5. #20244880C2semidirect
6. #20244724C2semidirect
7. #20244344C2semidirect
8. #20244143C2semidirect
9. #20243975C2semidirect
10. #20243964C2semidirect
352. C47#26018semidirect

Maximal subgroups

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

subgroupindex
#202471022
#202462672
#202449532
#202448872
#202448802
#202447242
#202443442
#202441432
#202439752
#202439642
#202435852
#202435712
#202434722
#202431082
C47×#18092
#2601847