Finite Group Databasebeta

← #26275328

Subgroups — #26275328

Order 12032.

678 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
1#20248620C211yesmaximal, characteristic, complemented
2#20246360C211yesmaximal, characteristic
3#20244914C211yesmaximal, characteristic
4#20244762C211yesmaximal, characteristic
5#20244758C211yesmaximal, characteristic
6#20244157C211yesmaximal, characteristic, complemented
7#20244154C211yesmaximal, characteristic, complemented
8#20244148C211yesmaximal, characteristic, complemented
9#20244105C211yesmaximal, characteristic, complemented
10#20243982C211yesmaximal, characteristic, complemented
11#20243960C211yesmaximal, characteristic, complemented
12#20243551C211yesmaximal, characteristic, complemented
13#20243396C211yesmaximal, characteristic
14#102×Dic47C211yesmaximal, characteristic
15C47×#2092C211yesmaximal, characteristic
16C2×D4×Dic47C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×C8×Dic47C2211yescharacteristic
27#15689064—21no—
28#15689057—21no—
29#15689026C2211yescharacteristic
30#15689022C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689017—21no—
33#15689011—21no—
34#15689008—21no—
35#15689005—21no—
36#15688992C2211yescharacteristic
37#15688988C2211yescharacteristic
38#15688988C2211yescharacteristic
39#15688984—21no—
40C4⋊C4×Dic47C2211yescharacteristic
41C4⋊C4×Dic47C2211yescharacteristic
42C4×Dic47⋊C4C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C22⋊C4×Dic47—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×#107×C47C2211yescharacteristic
53C2×#106×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#102×C47C2211yescharacteristic
56C47×#390C2211yescharacteristic
57C47×#382C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C23×Dic47—21no—
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62D4×Dic47—22no—
63D4×Dic47Q814yes—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2311yescharacteristic
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4D411yescharacteristic
73C2×Dic47⋊C4D411yescharacteristic
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47C2311yescharacteristic
81C2×C4×Dic47C2311yescharacteristic
82#13093958—22no—
83#13093957—41no—
84#13093955—41no—
85#13093955—41no—
86C4⋊(C47⋊C8)—22no—
87Dic47⋊C8—22no—
88Dic47⋊C8—22no—
89#13093945—22no—
90#13093945—41no—
91C8×Dic47—22no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95D411yescharacteristic
102C47⋊#95D411yescharacteristic
103C22×D4×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C42×C47C2311yescharacteristic
112#107×C47—22no—
113#106×C47—41no—
114#102×C47—22no—
115#102×C47—41no—
116#95×C47—21no—
117#95×C47—21no—
118C24×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47C2×Q812yes—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—21no—
132C22×Dic47—24no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—81no—
137C22×Dic47—81no—
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47#4112yes—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C22⋊C4×C47—42no—
155C22⋊C4×C47—81no—
156C42×C47—21no—
157C42×C47—21no—
158C22⋊Dic47—24no—
159C22⋊Dic47—42no—
160C22⋊Dic47—81no—
161C4⋊Dic47—21no—
162C4⋊Dic47—21no—
163C4⋊Dic47—21no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—42no—
169C4⋊Dic47C2×Q812yes—
170Dic47⋊C4—22no—
171Dic47⋊C4—41no—
172Dic47⋊C4—42no—
173Dic47⋊C4—81no—
174Dic47⋊C4—81no—
175C4×Dic47—21no—
176C4×Dic47—21no—
177C4×Dic47—81no—
178C4×Dic47—81no—
179C4×Dic47—81no—
180C4×Dic47C2×Q812yes—
181C4×Dic47#4112yes—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8#4112yes—
188C23×C47—22no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47C22×D411yescharacteristic
196D4×C47—22no—
197D4×C47—22no—
198D4×C47—41no—
199D4×C47—41no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
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×C47C22×Q811yescharacteristic
216C2×C4×C47C2×#4111yescharacteristic
217C2×C4×C47C2×#4111yescharacteristic
218C2×C4×C47C2×#4111yescharacteristic
219C2×C4×C47H(5,𝔽2)11yescharacteristic
220C2×C4×C472−1+411yescharacteristic
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—22no—
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×Dic47—41no—
242C2×Dic47—84no—
243C2×Dic47C22⋊Q812yes—
244C2×Dic47C22⋊Q812yes—
245C2×Dic47#13512yes—
246C8×C47—22no—
247C8×C47—41no—
248C47⋊C8—22no—
249C47⋊C8—41no—
250#26094—471nomaximal, Sylow
251C22×C47—42no—
252C22×C47—42no—
253C22×C47—42no—
254C22×C47—81no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47C2×C22⋊Q811yescharacteristic
259C22×C47#54711yescharacteristic
260C22×C47#55011yescharacteristic
261C22×C47C2×#13511yescharacteristic
262C22×C47#57511yescharacteristic
263C22×C47#57611yescharacteristic
264C22×C47#57711yescharacteristic
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—81no—
268C4×C47—81no—
269C4×C47—81no—
270C4×C47#53311yescharacteristic
271C4×C47#54411yescharacteristic
272C4×C47#55211yescharacteristic
273C4×C47#55311yescharacteristic
274Dic47—22no—
275Dic47—22no—
276Dic47—22no—
277Dic47—42no—
278Dic47—41no—
279Dic47—81no—
280Dic47—81no—
281Dic47—81no—
282#2570—471no—
283#2357—471no—
284#2093—471no—
285#2092D4711yescharacteristic
286#2065—471no—
287#2065—471no—
288#1949—471no—
289#1949—471no—
290#1948—471no—
291#1939—471no—
292#1921—471no—
293#1918—471no—
294#1846—471no—
295#1804—471no—
296C4×#102—471no—
297C2×C47—82no—
298C2×C47#244111yescharacteristic
299C2×C47#307611yescharacteristic
300C2×C47#308111yescharacteristic
301C2×C47#333711yescharacteristic
302C2×C47#335511yescharacteristic
303C2×C47#339611yescharacteristic
304C2×C47#340111yescharacteristic
305C2×C4×D4—471no—
306C2×#107—471no—
307C2×#107—471no—
308C2×#107C2×D4711yescharacteristic
309C2×#106—471no—
310C2×#106—471no—
311C2×#106C2×D4711yescharacteristic
312C2×C4⋊C8—471no—
313C2×C4⋊C8—471no—
314C2×C4⋊C8—471no—
315C2×#102—471no—
316C2×#102—471no—
317C2×#102C2×D4711yescharacteristic
318C2×#102C2×D4711yescharacteristic
319C2×C4×C8—471no—
320#400—941no—
321#398—941no—
322#390—471no—
323#390C2×D4711yescharacteristic
324#389—471no—
325#389—471no—
326#388—941no—
327#388—941no—
328#387—941no—
329#387—941no—
330#384—471no—
331#382—471no—
332#382—471no—
333#382C2×D4711yescharacteristic
334#381—941no—
335C4×C4⋊C4—471no—
336C4×C4⋊C4—471no—
337C4×C4⋊C4—471no—
338C4×C4⋊C4—471no—
339C4×C22⋊C4—941no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#336—471no—
347#336C2×D4711yescharacteristic
348C47#2609411yescharacteristic, complemented, Sylow
349C22×D4C22×D4711yescharacteristic
350C23×C4—941no—
351C22×C8—471no—
352C22×C8—471no—
353C22×C8C22×D4711yescharacteristic
354C22×C8C22×D4711yescharacteristic
355C4×D4—474no—
356C4×D4—942no—
357C2×C4⋊C4—471no—
358C2×C4⋊C4—471no—
359C2×C4⋊C4—471no—
360C2×C4⋊C4—471no—
361C2×C4⋊C4—471no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—941no—
364C2×C4⋊C4—941no—
365C2×C4⋊C4—941no—
366C2×C4⋊C4—941no—
367C2×C4⋊C4C22×D4711yescharacteristic
368C2×C4⋊C4C22×D4711yescharacteristic
369C2×C4⋊C4C22×D4711yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—941no—
373C2×C22⋊C4—941no—
374C2×C22⋊C4—941no—
375C2×C42—471no—
376C2×C42—471no—
377C2×C42—941no—
378C2×C42—941no—
379C2×C42—941no—
380C2×C42C22×D4711yescharacteristic
381#107—22no—
382#107—942no—
383#107—1881no—
384#106—41no—
385#106—1881no—
386#106—1881no—
387C4⋊C8—942no—
388C4⋊C8—942no—
389C4⋊C8—942no—
390#102—22no—
391#102—41no—
392#102—942no—
393#102—1881no—
394C4×C8—942no—
395#95—21no—
396#95—21no—
397#95—471no—
398#95—471no—
399#95—941no—
400#95—941no—
401#95—941no—
402#95—941no—
403#95—941no—
404#95—941no—
405#95—941no—
406#95—941no—
407#95—941no—
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4Q8×D4712yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—471no—
419C22×C4—471no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—944no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—3761no—
428C22×C4—3761no—
429C22×C4D4×D4711yescharacteristic
430C22×C4D4×D4711yescharacteristic
431C22×C4C23×D4711yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—472no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8#1062535212yes—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—472no—
451C4⋊C4—942no—
452C4⋊C4—941no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—3761no—
460C4⋊C4—3761no—
461C4⋊C4—1881no—
462C4⋊C4—1882no—
463C4⋊C4—1882no—
464C22⋊C4—42no—
465C22⋊C4—81no—
466C22⋊C4—944no—
467C22⋊C4—3761no—
468C22⋊C4—1882no—
469C42—21no—
470C42—21no—
471C42—472no—
472C42—472no—
473C42—941no—
474C42—941no—
475C42—3761no—
476C42—3761no—
477C42—3761no—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C2×D4×D4711yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
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—472no—
507C2×C4—472no—
508C2×C4—941no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—942no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—3764no—
519C2×C4—1881no—
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×C4C2×Q8×D4711yescharacteristic
531C2×C4#41×D4711yescharacteristic
532C2×C4#41×D4711yescharacteristic
533C2×C4C2×#1062535211yescharacteristic
534C2×C4#1309406911yescharacteristic
535C2×C4#1309407111yescharacteristic
536C8—22no—
537C8—41no—
538C8—942no—
539C8—1881no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C22⋊Q8×D4711yescharacteristic
548C22#1568977111yescharacteristic
549C22#1568979311yescharacteristic
550C22#135×D4711yescharacteristic
551C22#1568991911yescharacteristic
552C22#1568992511yescharacteristic
553C22#1568993311yescharacteristic
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—942no—
560C4—942no—
561C4—942no—
562C4—3761no—
563C4—3761no—
564C4—3761no—
565C4—1882no—
566C4—1881no—
567C4#1568967511yescharacteristic
568C4#1568975211yescharacteristic
569C4#1568981011yescharacteristic
570C4#1568981811yescharacteristic
571C2—82no—
572C2#2024709411yescharacteristic
573C2#2025317311yescharacteristic
574C2#2025321611yescharacteristic
575C2#2025576011yescharacteristic
576C2#2025598711yescharacteristic
577C2#2025639711yescharacteristic
578C2#2025644911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2092C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2092D47
hypocenterC47#26094
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. #20248620C2semidirect
6. #20244157C2semidirect
7. #20244154C2semidirect
8. #20244148C2semidirect
9. #20244105C2semidirect
10. #20243982C2semidirect
11. #20243960C2semidirect
12. #20243551C2semidirect
348. C47#26094semidirect

Maximal subgroups

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

subgroupindex
#202486202
#202463602
#202449142
#202447622
#202447582
#202441572
#202441542
#202441482
#202441052
#202439822
#202439602
#202435512
#202433962
#102×Dic472
C47×#20922
#2609447