Finite Group Databasebeta

← #26289021

Subgroups — #26289021

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#20246391C211yesmaximal, characteristic
2#20244797C211yesmaximal, characteristic, complemented
3#20244780C211yesmaximal, characteristic, complemented
4#20244591C211yesmaximal, characteristic
5#20244591C211yesmaximal, characteristic
6#20244144C211yesmaximal, characteristic, complemented
7#20244118C211yesmaximal, characteristic, complemented
8#20243996C211yesmaximal, characteristic
9#20243980C211yesmaximal, characteristic, complemented
10#20243977C211yesmaximal, characteristic, complemented
11#20243641C211yesmaximal, characteristic, complemented
12#20243575C211yesmaximal, characteristic
13#20243476C211yesmaximal, characteristic
14C4×#13093947C211yesmaximal, characteristic, complemented
15C47×#2497C211yesmaximal, characteristic
16C2×#13094003C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×#13093947C2211yescharacteristic
25C2×#13093947C2211yescharacteristic
26C2×#13093947C2211yescharacteristic
27C2×#13093947C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689029C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689020—21no—
34#15689010—21no—
35#15688995—21no—
36C4×C4⋊Dic47C2211yescharacteristic
37C22⋊C4×Dic47—21no—
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C47×#400—21no—
49C47×#396—21no—
50C47×#389C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#387—21no—
54C47×#384C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×Dic94C2311yescharacteristic
60C23×Dic47—21no—
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13094003—22no—
66#13094003—22no—
67C4×Dic94—22no—
68C4×Dic94—41no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—41no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×C22⋊Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81#13093957—22no—
82#13093957—22no—
83#13093957—22no—
84#13093957—41no—
85C4⋊(C47⋊C8)—22no—
86#13093947—22no—
87#13093947—22no—
88#13093947—22no—
89#13093947—41no—
90C22⋊(C47⋊C8)—22no—
91C22⋊(C47⋊C8)—41no—
92C4×C47⋊C8—41no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C23×C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47D411yescharacteristic
109C2×C22⋊C4×C47D411yescharacteristic
110C2×C42×C47—21no—
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
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×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2411yescharacteristic
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—
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—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—42no—
159C4⋊C4×C47—81no—
160C4⋊C4×C47—81no—
161C4⋊C4×C47—81no—
162C22⋊C4×C47—41no—
163C22⋊C4×C47—81no—
164C22⋊C4×C47—81no—
165C22⋊C4×C47Q1614yes—
166C42×C47—21no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—81no—
171C22⋊Dic47—24no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—42no—
177C4⋊Dic47#4112yes—
178C4⋊Dic47#4112yes—
179Dic47⋊C4—24no—
180Dic47⋊C4—42no—
181Dic47⋊C4—81no—
182C4×Dic47—42no—
183C4×Dic47—81no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8#4112yes—
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×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47C2×Q1612yes—
234C2×C4×C47C2×Q1612yes—
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47H(5,𝔽2)11yescharacteristic
240C2×C4×C472−1+411yescharacteristic
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
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—
258C47⋊C8—22no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—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—81no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47#52911yescharacteristic
287C4×C47#53911yescharacteristic
288C4×C47#55311yescharacteristic
289C4×C47#55611yescharacteristic
290Dic47—42no—
291Dic47—42no—
292Dic47—42no—
293Dic47—81no—
294#2497D4711yescharacteristic
295#2360—471no—
296#2072—471no—
297#2068—471no—
298#2036—471no—
299#2036—471no—
300#1947—471no—
301#1942—471no—
302#1923—471no—
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⋊C8—471no—
325C2×#103—471no—
326C2×#103—471no—
327C2×#103—471no—
328C2×#103—471no—
329C2×C22⋊C8—471no—
330C2×C22⋊C8—471no—
331C2×C4×C8—471no—
332#400—21no—
333#396—21no—
334#391—471no—
335#389—471no—
336#389—941no—
337#389C2×D4711yescharacteristic
338#389C2×D4711yescharacteristic
339#388—21no—
340#387—21no—
341#387—941no—
342#385—941no—
343#384C2×D4711yescharacteristic
344#380C2×D4711yescharacteristic
345#380C2×D4711yescharacteristic
346C4×C4⋊C4—471no—
347C4×C4⋊C4C2×D4711yescharacteristic
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#336—471no—
359#336—471no—
360C47#2703611yescharacteristic, complemented, Sylow
361C22×Q8—471no—
362C23×C4—941no—
363C23×C4C22×D4711yescharacteristic
364C22×C8—471no—
365C22×C8—471no—
366C22×C8—471no—
367C22×C8—471no—
368C22⋊Q8—942no—
369C22⋊Q8—942no—
370C4×Q8—942no—
371C4×Q8—1881no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
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—1881no—
385C2×C4⋊C4C22×D4711yescharacteristic
386C2×C4⋊C4C22×D4711yescharacteristic
387C2×C4⋊C4C22×D4711yescharacteristic
388C2×C4⋊C4C22×D4711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—941no—
392C2×C22⋊C4C22⋊D4711yescharacteristic
393C2×C22⋊C4C22⋊D4711yescharacteristic
394C2×C42—21no—
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—942no—
404#103—942no—
405#103—942no—
406#103—942no—
407#103—1881no—
408C22⋊C8—942no—
409C22⋊C8—1881no—
410C4×C8—1881no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—941no—
417#95—941no—
418#95—941no—
419#95—941no—
420#95C22⋊D4711yescharacteristic
421#95C22⋊D4711yescharacteristic
422C24C2×C22⋊D4711yescharacteristic
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—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—3761no—
444C22×C4—1882no—
445C22×C4—1882no—
446C22×C4C2×C22⋊D4711yescharacteristic
447C22×C4C2×C22⋊D4711yescharacteristic
448C22×C4C2×C22⋊D4711yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450C22×C4C2×C22⋊D4711yescharacteristic
451C22×C4C23×D4711yescharacteristic
452C2×C8—472no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—472no—
477C4⋊C4—472no—
478C4⋊C4—944no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—3761no—
484C4⋊C4—1882no—
485C4⋊C4—1882no—
486C22⋊C4—41no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—944no—
490C22⋊C4#1062533714yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—81no—
496C42—3761no—
497C42—1882no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×#1062533712yes—
505C23C22×C22⋊D4711yescharacteristic
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—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—3764no—
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×#1062533712yes—
553C2×C4C2×#1062533712yes—
554C2×C4#41×D4711yescharacteristic
555C2×C4#41×D4711yescharacteristic
556C2×C4#41×D4711yescharacteristic
557C2×C4#41×D4711yescharacteristic
558C2×C4#1309407011yescharacteristic
559C2×C4#1309407111yescharacteristic
560C8—942no—
561C8—1881no—
562C8—1881no—
563C8—1881no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22#1568963011yescharacteristic
572C22#1568976111yescharacteristic
573C22#1568977211yescharacteristic
574C22C22×#1062533711yescharacteristic
575C22#1568992111yescharacteristic
576C22#1568992611yescharacteristic
577C22#1568993411yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—3761no—
588C4—1882no—
589C4—1882no—
590C4—1882no—
591C4#1568965611yescharacteristic
592C4#1568971411yescharacteristic
593C4#1568982411yescharacteristic
594C4#1568984011yescharacteristic
595C2—42no—
596C2#2024742011yescharacteristic
597C2#2025342311yescharacteristic
598C2#2025358111yescharacteristic
599C2#2025525811yescharacteristic
600C2#2025553811yescharacteristic
601C2#2025577611yescharacteristic
602C2#2025594211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2497C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2497D47
hypocenterC47#27036
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2497

Complements

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

NH ≅ G/Ntype
2. #20244797C2semidirect
3. #20244780C2semidirect
6. #20244144C2semidirect
7. #20244118C2semidirect
9. #20243980C2semidirect
10. #20243977C2semidirect
11. #20243641C2semidirect
14. C4×#13093947C2semidirect
360. C47#27036semidirect

Maximal subgroups

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

subgroupindex
#202463912
#202447972
#202447802
#202445912
#202441442
#202441182
#202439962
#202439802
#202439772
#202436412
#202435752
#202434762
C4×#130939472
C47×#24972
#2703647