Finite Group Databasebeta

← #26274503

Subgroups — #26274503

Order 12032.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248409C211yesmaximal, characteristic, complemented
2#20244762C211yesmaximal, characteristic
3#20244762C211yesmaximal, characteristic
4#20244534C211yesmaximal, characteristic
5#20244524C211yesmaximal, characteristic
6#20244345C211yesmaximal, characteristic, complemented
7#20244340C211yesmaximal, characteristic, complemented
8#20244149C211yesmaximal, characteristic, complemented
9#20244112C211yesmaximal, characteristic, complemented
10#20243973C211yesmaximal, characteristic, complemented
11#20243966C211yesmaximal, characteristic, complemented
12#20243523C211yesmaximal, characteristic, complemented
13#20243398C211yesmaximal, characteristic
14#20243213C211yesmaximal, characteristic
15C47×#2354C211yesmaximal, characteristic
16C2×#13094024C2211yescharacteristic
17C2×#13094016C2211yescharacteristic
18C2×#13093955C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093935C2211yescharacteristic
28#15689056—21no—
29#15689043—21no—
30#15689027—21no—
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689020—21no—
34#15688989C2211yescharacteristic
35C4×C4⋊Dic47C2211yescharacteristic
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C2×#117×C47—21no—
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#388—21no—
53C47×#388—21no—
54C47×#384C2211yescharacteristic
55C47×#380—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C22×Dic94—21no—
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64#13094024—22no—
65#13094024—41no—
66#13094016—22no—
67#13094016—41no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×C4×Dic47—21no—
78#13093955—22no—
79#13093955—22no—
80C4⋊(C47⋊C8)—22no—
81C4⋊(C47⋊C8)—41no—
82C4⋊(C47⋊C8)—41no—
83#13093945—22no—
84#13093945—22no—
85#13093945—41no—
86#13093945—41no—
87#13093935—22no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C22×D4×C47C2311yescharacteristic
94C23×C4×C47—21no—
95C4×D4×C47—22no—
96C4×D4×C47Q814yescomplemented
97#117×C47—44no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47D411yescharacteristic
101C2×C4⋊C4×C47D411yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115#95×C47—21no—
116#95×C47—21no—
117#95×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119C24×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47C2×Q812yes—
126C22×C4×C47—21no—
127C22×C4×C47—24no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—42no—
131C22×C4×C47—42no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C2×Dic94—42no—
144C2×Dic94—42no—
145C2×Dic94—81no—
146C4⋊C4×C47—22no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—41no—
153C4⋊C4×C47—42no—
154C4⋊C4×C47—81no—
155C4⋊C4×C47C2×Q812yes—
156C22⋊C4×C47—24no—
157C22⋊C4×C47—42no—
158C22⋊C4×C47—42no—
159C22⋊C4×C47—81no—
160C22⋊C4×C47—81no—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—21no—
164C42×C47—21no—
165C42×C47—42no—
166C42×C47—42no—
167C42×C47C2×Q812yes—
168C42×C47#4112yes—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—42no—
176C4⋊Dic47#4112yes—
177C4⋊Dic47#4112yes—
178Dic47⋊C4—42no—
179Dic47⋊C4—42no—
180Dic47⋊C4—42no—
181Dic47⋊C4—81no—
182C4×Dic47—81no—
183C2×C47⋊C8—21no—
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—
195C23×C47—22no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47C22×D411yescharacteristic
203D4×C47—22no—
204D4×C47—22no—
205D4×C47—41no—
206D4×C47—41no—
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—22no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—48no—
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×C47C22⋊Q812yes—
233C2×C4×C47C22⋊Q812yes—
234C2×C4×C47AGL(1,ℤ/8)12yes—
235C2×C4×C47C22×Q811yescharacteristic
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—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—
253Dic94—84no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258#26032—471nomaximal, Sylow
259C22×C47—42no—
260C22×C47—42no—
261C22×C47—42no—
262C22×C47—81no—
263C22×C47—81no—
264C22×C47—81no—
265C22×C47—81no—
266C22×C47C2×C22⋊Q811yescharacteristic
267C22×C47#54611yescharacteristic
268C22×C47#54811yescharacteristic
269C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C47#57511yescharacteristic
271C22×C47#57711yescharacteristic
272C22×C47#57711yescharacteristic
273C4×C47—22no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—42no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—81no—
281C4×C47—81no—
282C4×C47#53311yescharacteristic
283C4×C47#54411yescharacteristic
284C4×C47#55511yescharacteristic
285C4×C47#55611yescharacteristic
286Dic47—42no—
287Dic47—42no—
288Dic47—81no—
289Dic47—81no—
290#2550—471no—
291#2354D4711yescharacteristic
292#2065—471no—
293#2065—471no—
294#2025—471no—
295#2023—471no—
296#1989—471no—
297#1988—471no—
298#1948—471no—
299#1940—471no—
300#1920—471no—
301#1919—471no—
302#1836—471no—
303#1804—471no—
304#1762—471no—
305C2×C47—82no—
306C2×C47#243911yescharacteristic
307C2×C47#307711yescharacteristic
308C2×C47#308411yescharacteristic
309C2×C47#330611yescharacteristic
310C2×C47#332111yescharacteristic
311C2×C47#336811yescharacteristic
312C2×C47#337611yescharacteristic
313C2×C4⋊Q8—471no—
314C2×#125—471no—
315C2×C4×D4C2×D4711yescharacteristic
316C2×#117—21no—
317C2×#106—471no—
318C2×#106—471no—
319C2×C4⋊C8—471no—
320C2×C4⋊C8—471no—
321C2×C4⋊C8—471no—
322C2×#102—471no—
323C2×#102—471no—
324C2×#102—471no—
325C2×#102—471no—
326C2×#97—471no—
327#398—941no—
328#395—941no—
329#391—941no—
330#390C2×D4711yescharacteristic
331#390C2×D4711yescharacteristic
332#389—471no—
333#389—471no—
334#389—941no—
335#388—21no—
336#388—21no—
337#384C2×D4711yescharacteristic
338#382—471no—
339#380—21no—
340C4×C4⋊C4—471no—
341C4×C4⋊C4C2×D4711yescharacteristic
342C4×C4⋊C4C2×D4711yescharacteristic
343C4×C4⋊C4C2×D4711yescharacteristic
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#340—471no—
351#340—471no—
352#340—471no—
353#340—471no—
354#336—471no—
355#336—471no—
356C47#2603211yescharacteristic, complemented, Sylow
357C22×Q8—941no—
358C22×D4C22×D4711yescharacteristic
359C23×C4—21no—
360C22×C8—471no—
361C22×C8—471no—
362C22×C8—471no—
363C22×C8—471no—
364C4⋊Q8—942no—
365C4⋊Q8—1881no—
366#125—942no—
367#125—1881no—
368C4×D4—22no—
369C4×D4Dic9414yescomplemented
370#117—44no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—471no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4—941no—
379C2×C4⋊C4—941no—
380C2×C4⋊C4—941no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4C22⋊D4711yescharacteristic
383C2×C4⋊C4C22⋊D4711yescharacteristic
384C2×C4⋊C4C22×D4711yescharacteristic
385C2×C4⋊C4C22×D4711yescharacteristic
386C2×C4⋊C4C22×D4711yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—941no—
395C2×C42C22×D4711yescharacteristic
396C2×C42C22×D4711yescharacteristic
397C2×C42C22×D4711yescharacteristic
398#106—942no—
399#106—942no—
400C4⋊C8—942no—
401C4⋊C8—1881no—
402C4⋊C8—1881no—
403#102—942no—
404#102—942no—
405#102—1881no—
406#102—1881no—
407#97—942no—
408#95—21no—
409#95—21no—
410#95—941no—
411#95—941no—
412#95—941no—
413#95—941no—
414#95—941no—
415#95C22⋊D4711yescharacteristic
416#95C22⋊D4711yescharacteristic
417C24—21no—
418C2×Q8—3761no—
419C2×Q8—1882no—
420C2×Q8—1882no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×Dic9412yes—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4C2×C22⋊D4711yescharacteristic
438C22×C4C2×C22⋊D4711yescharacteristic
439C22×C4C2×C22⋊D4711yescharacteristic
440C22×C4C2×C22⋊D4711yescharacteristic
441C22×C4C2×C22⋊D4711yescharacteristic
442C22×C4C2×C22⋊D4711yescharacteristic
443C22×C4C23×D4711yescharacteristic
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—472no—
466C4⋊C4—472no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—3761no—
474C4⋊C4—1882no—
475C4⋊C4—1882no—
476C4⋊C4—1882no—
477C4⋊C4—1882no—
478C4⋊C4C2×Dic9412yes—
479C22⋊C4—24no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—42no—
489C42—42no—
490C42—3761no—
491C42C2×Dic9412yes—
492C42#1062535012yes—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×C22⋊D4711yescharacteristic
501Q8—3764no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—48no—
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—942no—
532C2×C4—942no—
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#1309400312yes—
544C2×C4#1309400312yes—
545C2×C4#1309405012yes—
546C2×C4C22×Dic9411yescharacteristic
547C2×C4#41×D4711yescharacteristic
548C2×C4#41×D4711yescharacteristic
549C2×C4C2×#1062535011yescharacteristic
550C2×C4#1309407011yescharacteristic
551C2×C4#1309407111yescharacteristic
552C8—1881no—
553C8—1881no—
554C8—1881no—
555C8—1881no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C2×#1309400311yescharacteristic
564C22#1568976111yescharacteristic
565C22#1568978011yescharacteristic
566C22C2×#1309405011yescharacteristic
567C22#1568992111yescharacteristic
568C22#1568993111yescharacteristic
569C22#1568993411yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—42no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—3761no—
580C4—3761no—
581C4—1882no—
582C4—1882no—
583C4#1568967611yescharacteristic
584C4#1568975111yescharacteristic
585C4#1568983611yescharacteristic
586C4#1568984111yescharacteristic
587C2—82no—
588C2#2024707311yescharacteristic
589C2#2025318511yescharacteristic
590C2#2025325011yescharacteristic
591C2#2025534311yescharacteristic
592C2#2025556811yescharacteristic
593C2#2025611311yescharacteristic
594C2#2025620911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2354C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2354D47
hypocenterC47#26032
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. #20248409C2semidirect
6. #20244345C2semidirect
7. #20244340C2semidirect
8. #20244149C2semidirect
9. #20244112C2semidirect
10. #20243973C2semidirect
11. #20243966C2semidirect
12. #20243523C2semidirect
96. C4×D4×C47Q8semidirect
356. C47#26032semidirect
369. C4×D4Dic94semidirect

Maximal subgroups

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

subgroupindex
#202484092
#202447622
#202445342
#202445242
#202443452
#202443402
#202441492
#202441122
#202439732
#202439662
#202435232
#202433982
#202432132
C47×#23542
#2603247