Finite Group Databasebeta

← #26284365

Subgroups — #26284365

Order 12032.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246391C211yesmaximal, characteristic, complemented
2#20244705C211yesmaximal, characteristic, complemented
3#20244584C211yesmaximal, characteristic, complemented
4#20244526C211yesmaximal, characteristic, complemented
5#20244391C211yesmaximal, characteristic
6#20244341C211yesmaximal, characteristic, complemented
7#20244074C211yesmaximal, characteristic, complemented
8#20244012C211yesmaximal, characteristic, complemented
9#20243996C211yesmaximal, characteristic, complemented
10#20243973C211yesmaximal, characteristic, complemented
11#20243746C211yesmaximal, characteristic, complemented
12#20243706C211yesmaximal, characteristic
13#20243476C211yesmaximal, characteristic, complemented
14C4×#13093947C211yesmaximal, characteristic, complemented
15C47×#2491C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×#13094003C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093947C2211yescharacteristic
23C2×#13093947C2211yescharacteristic
24C2×#13093947C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
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
48C2×C4⋊Q8×C47C2211yescharacteristic
49C2×#124×C47—21no—
50C2×#121×C47C2211yescharacteristic
51C47×#394—21no—
52C47×#393—21no—
53C47×#390C2211yescharacteristic
54C47×#390C2211yescharacteristic
55C47×#388—21no—
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×Dic94C2311yescharacteristic
60C23×Dic47—21no—
61C2×#10625335—22no—
62C2×#10625335—41no—
63C2×#10625335—41no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094003—22no—
69#13094003—22no—
70C4×Dic94—22no—
71C4×Dic94—41no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—41no—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×C22⋊Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84#13093955—22no—
85C4⋊(C47⋊C8)—41no—
86#13093947—22no—
87#13093947—22no—
88#13093947—41no—
89#13093945—22no—
90#13093945—22no—
91#13093945—41no—
92C22⋊(C47⋊C8)—41no—
93C22⋊(C47⋊C8)—41no—
94C4×C47⋊C8—41no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C22×Q8×C47—21no—
100C22×D4×C47—21no—
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C4⋊Q8×C47—22no—
104C4⋊Q8×C47—41no—
105#124×C47—44no—
106#121×C47—22no—
107#121×C47—41no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#95×C47—21no—
124#95×C47—21no—
125#95×C47D411yescharacteristic
126#95×C47D411yescharacteristic
127C24×C47—21no—
128C24×C47C2×D411yescharacteristic
129C2×Q8×C47—42no—
130C2×Q8×C47—42no—
131C2×Q8×C47—81no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—42no—
139C2×D4×C47—42no—
140C2×D4×C47—81no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2411yescharacteristic
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—42no—
161C22×Dic47—42no—
162C22×Dic47—81no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94#4112yes—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—42no—
175C4⋊C4×C47#4112yes—
176C22⋊C4×C47—41no—
177C22⋊C4×C47—42no—
178C22⋊C4×C47—42no—
179C22⋊C4×C47—42no—
180C22⋊C4×C47—42no—
181C22⋊C4×C47—42no—
182C22⋊C4×C47—81no—
183C22⋊C4×C47SD1614yescomplemented
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—42no—
189C22⋊Dic47—24no—
190#10625335—44no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—42no—
196C4⋊Dic47#4112yes—
197C4⋊Dic47#4112yes—
198Dic47⋊C4—24no—
199Dic47⋊C4—42no—
200Dic47⋊C4—81no—
201C4×Dic47—42no—
202C4×Dic47—81no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—41no—
222C23×C47—41no—
223C23×C47—41no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47C2×SD1612yes—
229C23×C47C22×D411yescharacteristic
230Q8×C47—84no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—84no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—22no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47C2×SD1612yes—
263C2×C4×C47C2×SD1612yes—
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47C2×#4111yescharacteristic
266C2×C4×C47C2×#4111yescharacteristic
267C2×C4×C47C2×#4111yescharacteristic
268C2×C4×C47H(5,𝔽2)11yescharacteristic
269C2×C4×C47H(5,𝔽2)11yescharacteristic
270C2×Dic47—22no—
271C2×Dic47—22no—
272C2×Dic47—22no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—84no—
283Dic94—22no—
284Dic94—22no—
285Dic94—41no—
286Dic94—41no—
287C47⋊C8—41no—
288C47⋊C8—41no—
289C47⋊C8—41no—
290C47⋊C8—41no—
291#26724—471nomaximal, Sylow
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—22no—
295C22×C47—41no—
296C22×C47—41no—
297C22×C47—41no—
298C22×C47—41no—
299C22×C47—81no—
300C22×C47—81no—
301C22×C47—81no—
302C22×C47—81no—
303C22×C47—81no—
304C22×C47—81no—
305C22×C47—81no—
306C22×C47#52511yescharacteristic
307C22×C47#54611yescharacteristic
308C22×C47#54611yescharacteristic
309C22×C47C22×SD1611yescharacteristic
310C22×C47#57511yescharacteristic
311C22×C47#57611yescharacteristic
312C22×C47#57811yescharacteristic
313C4×C47—22no—
314C4×C47—22no—
315C4×C47—41no—
316C4×C47—42no—
317C4×C47—41no—
318C4×C47—41no—
319C4×C47—81no—
320C4×C47—81no—
321C4×C47#52911yescharacteristic
322C4×C47#53811yescharacteristic
323C4×C47#55511yescharacteristic
324C4×C47#55911yescharacteristic
325Dic47—42no—
326Dic47—42no—
327Dic47—42no—
328Dic47—81no—
329#2491D4711yescharacteristic
330#2360—471no—
331#2055—471no—
332#2035—471no—
333#2024—471no—
334#2000—471no—
335#1988—471no—
336#1934—471no—
337#1926—471no—
338#1923—471no—
339#1920—471no—
340#1880—471no—
341#1874—471no—
342#1824—471no—
343C4×#103—471no—
344C2×C47—42no—
345C2×C47—161no—
346C2×C47#245911yescharacteristic
347C2×C47#310311yescharacteristic
348C2×C47#312411yescharacteristic
349C2×C47#329511yescharacteristic
350C2×C47#329811yescharacteristic
351C2×C47#331911yescharacteristic
352C2×C47#332711yescharacteristic
353C22×SD16—471no—
354C2×C4⋊Q8C2×D4711yescharacteristic
355C2×#124—21no—
356C2×C22⋊Q8—471no—
357C2×#121C2×D4711yescharacteristic
358C2×C4×Q8—471no—
359C22×C4⋊C4—471no—
360C2×#106—471no—
361C2×C4⋊C8—471no—
362C2×#103—471no—
363C2×#103—471no—
364C2×#103—471no—
365C2×#102—471no—
366C2×#102—471no—
367C2×#102—471no—
368C2×C22⋊C8—471no—
369C2×C22⋊C8—471no—
370C2×C4×C8—471no—
371#394—21no—
372#393—21no—
373#391—471no—
374#390C2×D4711yescharacteristic
375#390C2×D4711yescharacteristic
376#389—471no—
377#389—941no—
378#388—21no—
379#387—941no—
380#385—941no—
381#380C2×D4711yescharacteristic
382C4×C4⋊C4—471no—
383C4×C4⋊C4C2×D4711yescharacteristic
384C4×C22⋊C4—941no—
385C4×C22⋊C4C2×D4711yescharacteristic
386#340—471no—
387#340—471no—
388#340—471no—
389#340—471no—
390#340—471no—
391#340—471no—
392#340—471no—
393#340—471no—
394#336—471no—
395#336—471no—
396C47#2672411yescharacteristic, complemented, Sylow
397C22×Q8—21no—
398C22×Q8—471no—
399C22×D4—21no—
400C22×D4C22×D4711yescharacteristic
401C23×C4—941no—
402C23×C4C22×D4711yescharacteristic
403C2×SD16—942no—
404C2×SD16—1881no—
405C2×SD16—1881no—
406C22×C8—471no—
407C22×C8—471no—
408C22×C8—471no—
409C22×C8—471no—
410C4⋊Q8—22no—
411C4⋊Q8—41no—
412#124—44no—
413C22⋊Q8—942no—
414C22⋊Q8—942no—
415#121—22no—
416#121—41no—
417C4×Q8—942no—
418C4×Q8—1881no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—471no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—942no—
424C2×C4⋊C4—941no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—1881no—
429C2×C4⋊C4C22×D4711yescharacteristic
430C2×C4⋊C4C22×D4711yescharacteristic
431C2×C4⋊C4C22×D4711yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—941no—
439C2×C22⋊C4C22⋊D4711yescharacteristic
440C2×C22⋊C4C22⋊D4711yescharacteristic
441C2×C42—21no—
442C2×C42—941no—
443C2×C42—941no—
444C2×C42C22×D4711yescharacteristic
445C2×C42C22×D4711yescharacteristic
446#106—942no—
447C4⋊C8—1881no—
448#103—942no—
449#103—942no—
450#103—1881no—
451#102—942no—
452#102—942no—
453#102—1881no—
454C22⋊C8—1881no—
455C22⋊C8—1881no—
456C4×C8—1881no—
457#95—21no—
458#95—21no—
459#95—941no—
460#95—941no—
461#95—941no—
462#95—941no—
463#95C22⋊D4711yescharacteristic
464#95C22⋊D4711yescharacteristic
465C24—21no—
466C24C2×C22⋊D4711yescharacteristic
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—81no—
470C2×Q8—472no—
471C2×Q8—941no—
472C2×Q8—941no—
473C2×Q8—941no—
474C2×Q8—941no—
475C2×Q8—941no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—81no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—941no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—941no—
498C22×C4—3761no—
499C22×C4—1882no—
500C22×C4—1882no—
501C22×C4C2×C22⋊D4711yescharacteristic
502C22×C4C2×C22⋊D4711yescharacteristic
503C22×C4C2×C22⋊D4711yescharacteristic
504C22×C4C2×C22⋊D4711yescharacteristic
505C22×C4C2×C22⋊D4711yescharacteristic
506C22×C4C23×D4711yescharacteristic
507SD16—1884no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—941no—
519C2×C8—941no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—472no—
527C4⋊C4—472no—
528C4⋊C4—944no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4—941no—
532C4⋊C4—941no—
533C4⋊C4—3761no—
534C4⋊C4—1882no—
535C4⋊C4—1882no—
536C4⋊C4#1062535212yes—
537C22⋊C4—41no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—944no—
545C22⋊C4#1062533514yescomplemented
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—3761no—
552C42—1882no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×#1062533512yes—
567C23C22×C22⋊D4711yescharacteristic
568Q8—84no—
569Q8—942no—
570Q8—942no—
571Q8—1881no—
572Q8—1881no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—84no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—942no—
605C2×C4—942no—
606C2×C4—942no—
607C2×C4—3764no—
608C2×C4—1881no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4—1881no—
612C2×C4—1881no—
613C2×C4—1881no—
614C2×C4—1881no—
615C2×C4—1881no—
616C2×C4—1881no—
617C2×C4C2×#1062533512yes—
618C2×C4C2×#1062533512yes—
619C2×C4#41×D4711yescharacteristic
620C2×C4#41×D4711yescharacteristic
621C2×C4#41×D4711yescharacteristic
622C2×C4C2×#1062535211yescharacteristic
623C2×C4#1309406911yescharacteristic
624C2×C4#1309407011yescharacteristic
625C8—1881no—
626C8—1881no—
627C8—1881no—
628C8—1881no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22#1568963011yescharacteristic
644C22#1568976111yescharacteristic
645C22#1568976711yescharacteristic
646C22C22×#1062533511yescharacteristic
647C22#1568992111yescharacteristic
648C22#1568992611yescharacteristic
649C22#1568993811yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—3761no—
659C4—1882no—
660C4—1882no—
661C4—1882no—
662C4#1568965211yescharacteristic
663C4#1568970711yescharacteristic
664C4#1568983511yescharacteristic
665C4#1568985511yescharacteristic
666C2—42no—
667C2—161no—
668C2#2024732111yescharacteristic
669C2#2025341511yescharacteristic
670C2#2025364411yescharacteristic
671C2#2025521211yescharacteristic
672C2#2025524711yescharacteristic
673C2#2025553811yescharacteristic
674C2#2025565611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2491C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenter#2491D47
hypocenterC47#26724
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2491

Complements

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

NH ≅ G/Ntype
1. #20246391C2semidirect
2. #20244705C2semidirect
3. #20244584C2semidirect
4. #20244526C2semidirect
6. #20244341C2semidirect
7. #20244074C2semidirect
8. #20244012C2semidirect
9. #20243996C2semidirect
10. #20243973C2semidirect
11. #20243746C2semidirect
13. #20243476C2semidirect
14. C4×#13093947C2semidirect
183. C22⋊C4×C47SD16semidirect
396. C47#26724semidirect
545. C22⋊C4#10625335semidirect

Maximal subgroups

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

subgroupindex
#202463912
#202447052
#202445842
#202445262
#202443912
#202443412
#202440742
#202440122
#202439962
#202439732
#202437462
#202437062
#202434762
C4×#130939472
C47×#24912
#2672447