Finite Group Databasebeta

← #26289023

Subgroups — #26289023

Order 12032.

708 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247821C211yesmaximal, characteristic
2#20246391C211yesmaximal, characteristic
3#20244798C211yesmaximal, characteristic, complemented
4#20244782C211yesmaximal, characteristic, complemented
5#20244592C211yesmaximal, characteristic
6#20244592C211yesmaximal, characteristic
7#20244147C211yesmaximal, characteristic, complemented
8#20244121C211yesmaximal, characteristic, complemented
9#20243981C211yesmaximal, characteristic, complemented
10#20243981C211yesmaximal, characteristic, complemented
11#20243645C211yesmaximal, characteristic, complemented
12#20243578C211yesmaximal, characteristic
13#20243479C211yesmaximal, characteristic
14C4×#13093949C211yesmaximal, characteristic, complemented
15C47×#1923C211yesmaximal, characteristic
16C2×#13094003C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C2×#13093958C2211yescharacteristic
20C2×#13093958C2211yescharacteristic
21C2×#13093958C2211yescharacteristic
22C2×#13093958C2211yescharacteristic
23C2×#13093949C2211yescharacteristic
24C2×#13093949C2211yescharacteristic
25C2×#13093949C2211yescharacteristic
26C2×#13093949C2211yescharacteristic
27#15689065—21no—
28#15689046—21no—
29#15689029C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689020—21no—
34#15689016—21no—
35#15689010—21no—
36#15689010—21no—
37#15688995—21no—
38#15688993C2211yescharacteristic
39#15688983C2211yescharacteristic
40#15688983C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43C22⋊C4×Dic47—21no—
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Dic94C2311yescharacteristic
60C23×Dic47—21no—
61#13094003—22no—
62#13094003—22no—
63C4×Dic94—22no—
64C4×Dic94—41no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—41no—
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88#13093958—22no—
89#13093958—22no—
90#13093958—22no—
91#13093958—41no—
92#13093949—22no—
93#13093949—22no—
94#13093949—22no—
95#13093949—41no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C23×C4×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C22×C8×C47C2311yescharacteristic
110C2×C22⋊C4×C47D411yescharacteristic
111C2×C22⋊C4×C47D411yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C4⋊C8×C47—22no—
115C22⋊C8×C47—22no—
116C22⋊C8×C47—41no—
117C4×C8×C47—41no—
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C24×C47C2×D411yescharacteristic
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×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2411yescharacteristic
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—42no—
142C22×Dic47—42no—
143C22×Dic47—81no—
144C2×Dic94—21no—
145C2×Dic94—21no—
146C2×Dic94—21no—
147C2×Dic94—21no—
148C2×Dic94—21no—
149C2×Dic94#4112yes—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47#4112yes—
162C22⋊C4×C47—41no—
163C22⋊C4×C47Q1614yes—
164C42×C47—21no—
165C42×C47—21no—
166C42×C47—21no—
167C42×C47—21no—
168C22⋊Dic47—24no—
169C22⋊Dic47—81no—
170C22⋊Dic47—81no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—42no—
184C4⋊Dic47—81no—
185C4⋊Dic47—81no—
186C4⋊Dic47#4112yes—
187C4⋊Dic47#4112yes—
188Dic47⋊C4—24no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191Dic47⋊C4—81no—
192Dic47⋊C4—81no—
193C4×Dic47—42no—
194C4×Dic47—81no—
195C4×Dic47—81no—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47—21no—
202C23×C47C2×Q1612yes—
203C23×C47C22×D411yescharacteristic
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47C2×Q1612yes—
222C2×C4×C47C2×Q1612yes—
223C2×C4×C47C2×#4111yescharacteristic
224C2×C4×C47C2×#4111yescharacteristic
225C2×C4×C47C2×#4111yescharacteristic
226C2×C4×C47C2×#4111yescharacteristic
227C2×C4×C47H(5,𝔽2)11yescharacteristic
228C2×C4×C472−1+411yescharacteristic
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—22no—
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—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—84no—
254Dic94—22no—
255Dic94—22no—
256Dic94—41no—
257Dic94—41no—
258C8×C47—22no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262#27036—471nomaximal, Sylow
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—22no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47#52511yescharacteristic
271C22×C47#54611yescharacteristic
272C22×C47#54711yescharacteristic
273C22×C47C22×Q1611yescharacteristic
274C22×C47#57511yescharacteristic
275C22×C47#57611yescharacteristic
276C22×C47#57711yescharacteristic
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47#52911yescharacteristic
283C4×C47#53911yescharacteristic
284C4×C47#55311yescharacteristic
285C4×C47#55611yescharacteristic
286Dic47—42no—
287Dic47—42no—
288Dic47—42no—
289Dic47—81no—
290Dic47—81no—
291Dic47—81no—
292Dic47—81no—
293Dic47—81no—
294#2497—471no—
295#2360—471no—
296#2072—471no—
297#2068—471no—
298#2036—471no—
299#2036—471no—
300#1947—471no—
301#1942—471no—
302#1923D4711yescharacteristic
303#1921—471no—
304#1921—471no—
305#1863—471no—
306#1852—471no—
307#1824—471no—
308C4×#103—471no—
309C2×C47—42no—
310C2×C47#246611yescharacteristic
311C2×C47#310411yescharacteristic
312C2×C47#311911yescharacteristic
313C2×C47#329911yescharacteristic
314C2×C47#331911yescharacteristic
315C2×C47#333811yescharacteristic
316C2×C47#335111yescharacteristic
317C2×C22⋊Q8—471no—
318C2×C4×Q8—471no—
319C22×C4⋊C4—471no—
320C2×#107—471no—
321C2×#107—471no—
322C2×#107—471no—
323C2×#107—471no—
324C2×C4⋊C8C2×D4711yescharacteristic
325C2×#103—471no—
326C2×#103—471no—
327C2×#103—471no—
328C2×#103—471no—
329C2×C22⋊C8C2×D4711yescharacteristic
330C2×C22⋊C8C2×D4711yescharacteristic
331C2×C4×C8C2×D4711yescharacteristic
332#400—941no—
333#396—941no—
334#391—471no—
335#389—471no—
336#389—471no—
337#389—471no—
338#389—941no—
339#388—941no—
340#387—941no—
341#387—941no—
342#385—941no—
343#384—471no—
344#380—471no—
345#380—471no—
346C4×C4⋊C4—471no—
347C4×C4⋊C4—471no—
348C4×C22⋊C4—941no—
349C4×C22⋊C4C2×D4711yescharacteristic
350#340—471no—
351#340—471no—
352#340—471no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340—471no—
358#336C2×D4711yescharacteristic
359#336C2×D4711yescharacteristic
360C47#2703611yescharacteristic, complemented, Sylow
361C22×Q8—471no—
362C23×C4—941no—
363C23×C4C22×D4711yescharacteristic
364C22×C8C22×D4711yescharacteristic
365C22×C8C22×D4711yescharacteristic
366C22×C8C22×D4711yescharacteristic
367C22×C8C22×D4711yescharacteristic
368C22⋊Q8—942no—
369C22⋊Q8—942no—
370C4×Q8—942no—
371C4×Q8—1881no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—471no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—471no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—941no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4—941no—
383C2×C4⋊C4—941no—
384C2×C4⋊C4—941no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—1881no—
389C2×C22⋊C4—941no—
390C2×C22⋊C4—941no—
391C2×C22⋊C4—941no—
392C2×C22⋊C4D18811yescharacteristic
393C2×C22⋊C4D18811yescharacteristic
394C2×C42—941no—
395C2×C42—941no—
396C2×C42—941no—
397C2×C42C22×D4711yescharacteristic
398C2×C42C22×D4711yescharacteristic
399#107—942no—
400#107—942no—
401#107—942no—
402#107—1881no—
403C4⋊C8—22no—
404#103—942no—
405#103—942no—
406#103—942no—
407#103—1881no—
408C22⋊C8—22no—
409C22⋊C8—41no—
410C4×C8—41no—
411#95—941no—
412#95—941no—
413#95—941no—
414#95—941no—
415#95—941no—
416#95—941no—
417#95—941no—
418#95—941no—
419#95—941no—
420#95D18811yescharacteristic
421#95D18811yescharacteristic
422C24C2×D18811yescharacteristic
423C2×Q8—472no—
424C2×Q8—941no—
425C2×Q8—941no—
426C2×Q8—941no—
427C2×Q8—941no—
428C2×Q8—941no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—3761no—
444C22×C4—1882no—
445C22×C4—1882no—
446C22×C4C2×D18811yescharacteristic
447C22×C4C2×D18811yescharacteristic
448C22×C4C2×D18811yescharacteristic
449C22×C4C2×D18811yescharacteristic
450C22×C4C2×D18811yescharacteristic
451C22×C4C23×D4711yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8#1062535212yes—
464C4⋊C4—472no—
465C4⋊C4—472no—
466C4⋊C4—944no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—3761no—
480C4⋊C4—3761no—
481C4⋊C4—3761no—
482C4⋊C4—3761no—
483C4⋊C4—1882no—
484C4⋊C4—1882no—
485C4⋊C4—1882no—
486C22⋊C4—41no—
487C22⋊C4—944no—
488C22⋊C4—3761no—
489C22⋊C4—3761no—
490C22⋊C4Dic18814yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—3761no—
496C42—3761no—
497C42—1882no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×Dic18812yes—
505C23C22×D18811yescharacteristic
506Q8—942no—
507Q8—942no—
508Q8—1881no—
509Q8—1881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—942no—
528C2×C4—942no—
529C2×C4—942no—
530C2×C4—3764no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4—1881no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4C2×Dic18812yes—
553C2×C4C2×Dic18812yes—
554C2×C4#41×D4711yescharacteristic
555C2×C4#41×D4711yescharacteristic
556C2×C4#41×D4711yescharacteristic
557C2×C4C2×#1062535211yescharacteristic
558C2×C4#1309406911yescharacteristic
559C2×C4#1309407111yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22#1568963511yescharacteristic
572C22#1568976811yescharacteristic
573C22#1568977711yescharacteristic
574C22C22×Dic18811yescharacteristic
575C22#1568992311yescharacteristic
576C22#1568992811yescharacteristic
577C22#1568993511yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—3761no—
584C4—3761no—
585C4—3761no—
586C4—3761no—
587C4—3761no—
588C4—1882no—
589C4—1882no—
590C4—1882no—
591C4#1568965211yescharacteristic
592C4#1568971611yescharacteristic
593C4#1568981611yescharacteristic
594C4#1568984011yescharacteristic
595C2—42no—
596C2#2024742211yescharacteristic
597C2#2025342811yescharacteristic
598C2#2025358911yescharacteristic
599C2#2025526511yescharacteristic
600C2#2025554611yescharacteristic
601C2#2025578111yescharacteristic
602C2#2025595011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1923C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#1923D47
hypocenterC47#27036
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #20244798C2semidirect
4. #20244782C2semidirect
7. #20244147C2semidirect
8. #20244121C2semidirect
9. #20243981C2semidirect
10. #20243981C2semidirect
11. #20243645C2semidirect
14. C4×#13093949C2semidirect
360. C47#27036semidirect

Maximal subgroups

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

subgroupindex
#202478212
#202463912
#202447982
#202447822
#202445922
#202441472
#202441212
#202439812
#202436452
#202435782
#202434792
C4×#130939492
C47×#19232
#2703647