Finite Group Databasebeta

← #26187440

Subgroups — #26187440

Order 12032.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253431C211yesmaximal, characteristic
2#20252548C211yesmaximal, characteristic, complemented
3#20252425C211yesmaximal, characteristic, complemented
4#20242275C211yesmaximal, characteristic, complemented
5#20242270C211yesmaximal, characteristic, complemented
6#20242263C211yesmaximal, characteristic, complemented
7#20242255C211yesmaximal, characteristic, complemented
8#20242249C211yesmaximal, characteristic, complemented
9#20242248C211yesmaximal, characteristic, complemented
10#20242185C211yesmaximal, characteristic, complemented
11#20242180C211yesmaximal, characteristic, complemented
12#20242174C211yesmaximal, characteristic, complemented
13C2×#15688852C211yesmaximal, characteristic, complemented
14#20241671C211yesmaximal, characteristic, complemented
15C47×#1494C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17#15689456C411yescharacteristic
18#15689439C411yescharacteristic
19#15689420C411yescharacteristic
20#15689420C411yescharacteristic
21#15689335C411yescharacteristic
22#15689335C411yescharacteristic
23#15689273C411yescharacteristic
24#15689256C411yescharacteristic
25#15689254C2211yescharacteristic, complemented
26Q8×C47⋊C8C2211yescharacteristic, complemented
27C4×#10625336C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689201C2211yescharacteristic, complemented
32#15689200C2211yescharacteristic
33#15689200C2211yescharacteristic
34#15689196—21no—
35#15689196—21no—
36#15689195—21no—
37D4×C47⋊C8—21no—
38D4×C47⋊C8C2211yescharacteristic, complemented
39#15689188C2211yescharacteristic
40#15689188C2211yescharacteristic
41#15689184—21no—
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689150—21no—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46#15689085—21no—
47C22⋊C8×D47—21no—
48#15688875C2211yescharacteristic, complemented
49#15688875C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688873C2211yescharacteristic, complemented
52#15688852C2211yescharacteristic
53#15688852C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688844C2211yescharacteristic, complemented
57#15688844C2211yescharacteristic, complemented
58C8×C47⋊C8C2211yescharacteristic, complemented
59C8×C47⋊C8C2211yescharacteristic, complemented
60C47×#529C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic, complemented
66C47×D4⋊C8C2211yescharacteristic, complemented
67C22×D188C2×C411yescharacteristic
68C22×C4×D47—21no—
69C2×#10625336C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625334C2×C411yescharacteristic
73C2×#10625329—21no—
74C2×#10625324—21no—
75C2×#10625324—21no—
76C22×C47⋊C8—21no—
77C22×C47⋊C8—21no—
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80C4×D188—21no—
81C4×D188—21no—
82C4×D188C2×C411yescharacteristic
83C4×D188C2×C411yescharacteristic
84C4×D188C2311yescharacteristic
85C4×D188C2311yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
87C2×(C2×D47)⋊C4—21no—
88#13093957C2×C411yescharacteristic
89#13093957C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)—21no—
95C4⋊(C47⋊C8)C2×C411yescharacteristic
96C4⋊(C47⋊C8)C2×C411yescharacteristic
97C4⋊(C47⋊C8)D411yescharacteristic
98C4⋊(C47⋊C8)D411yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107#13093944C2×C411yescharacteristic
108#13093944C2×C411yescharacteristic
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112C22⋊(C47⋊C8)C2×C411yescharacteristic
113C22⋊(C47⋊C8)D411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119#13093935—21no—
120C4×C47⋊C8—21no—
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C22×C8×C47—21no—
126#126×C47—21no—
127#125×C47C2×C411yescharacteristic
128#124×C47C2×C411yescharacteristic
129#123×C47—21no—
130C22⋊Q8×C47C2×C411yescharacteristic
131#121×C47C2×C411yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47—21no—
134C4×D4×C47C2311yescharacteristic
135#117×C47—21no—
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C23×D47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47—21no—
147C2×D4×C47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×Dic47—21no—
153C2×D188—22no—
154C2×D188—21no—
155C2×D188—41no—
156C2×D188C22×C411yescharacteristic
157C2×D188C22×C411yescharacteristic
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—81no—
163C2×C4×D47—81no—
164C2×C8×C47—24no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C42×C47—21no—
181C42×C47C22×C411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47#4111yescharacteristic
184C42×C47C2411yescharacteristic
185#10625336—22no—
186#10625336—41no—
187#10625334—22no—
188#10625334—41no—
189(C2×D47)⋊C4—21no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192(C2×D47)⋊C4—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47C22×C411yescharacteristic
195C4⋊Dic47C22×C411yescharacteristic
196#10625329—81no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—81no—
200C2×C47⋊C8—81no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209#10625324—81no—
210#10625324—81no—
211C8×D47—81no—
212C8×D47—81no—
213C23×C47—21no—
214C23×C47C4×D411yescharacteristic
215C22×D47—21no—
216C22×D47—21no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—81no—
220Q8×C47—21no—
221Q8×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—42no—
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C23×C411yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—81no—
244D188—21no—
245D188—21no—
246D188—21no—
247D188—42no—
248D188#13112yes—
249C4×D47—41no—
250C4×D47—41no—
251C4×D47—41no—
252C4×D47—41no—
253C4×D47—81no—
254C4×D47—81no—
255C8×C47—22no—
256C8×C47—22no—
257C8×C47—41no—
258C8×C47—41no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—21no—
267C47⋊C8—41no—
268C47⋊C8—41no—
269#18014—471nomaximal, Sylow
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47#44312yes—
276C22×C47C2×C4×D411yescharacteristic
277C2×D47—22no—
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C2×D47—41no—
282C2×D47—41no—
283C2×D47—84no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47C2×#13111yescharacteristic
292C4×C47#56811yescharacteristic
293C4×C47#57611yescharacteristic
294C4×C47#57711yescharacteristic
295Dic47—41no—
296Dic47—41no—
297#3105—471no—
298#2994—471no—
299#2974—471no—
300#1590—471no—
301#1589—471no—
302#1588—471no—
303#1586—471no—
304#1586—471no—
305#1585—471no—
306C8×SD16—471no—
307C8×D8—471no—
308#1573—471no—
309#1494D4711yescharacteristic, complemented
310C2×D4⋊C8—471no—
311#1450—471no—
312C2×C47—22no—
313C2×C47—81no—
314C2×C47#293311yescharacteristic
315C2×C47#294611yescharacteristic
316C2×C47C2×#44311yescharacteristic
317D47—42no—
318D47—81no—
319#529C2×D4711yescharacteristic
320C2×C4×D4—471no—
321#484—471no—
322#481—471no—
323#478—471no—
324#478—471no—
325#463—471no—
326#463—471no—
327#450—471no—
328#447—471no—
329#446—471no—
330C8×Q8—471no—
331C4×SD16—471no—
332C4×SD16—471no—
333C4×D8—471no—
334C4×D8—471no—
335#436—471no—
336#436—471no—
337#436—471no—
338#435—941no—
339#435—941no—
340#435—941no—
341C8×D4—471no—
342C8×D4—471no—
343C8×D4—471no—
344C8×D4—941no—
345#433—941no—
346#432C2×D4711yescharacteristic
347#431—471no—
348#431—471no—
349#424—941no—
350C2×C4⋊C8—471no—
351#407—941no—
352C2×C22⋊C8—941no—
353C2×C4×C8C2×D4711yescharacteristic
354#335—471no—
355#335—471no—
356#334—471no—
357#334—471no—
358Q8⋊C8C2×D4711yescharacteristic, complemented
359Q8⋊C8C2×D4711yescharacteristic, complemented
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364D4⋊C8C2×D4711yescharacteristic, complemented
365D4⋊C8C2×D4711yescharacteristic, complemented
366#322—471no—
367#322—471no—
368C82—471no—
369C82—471no—
370C47#1801411yescharacteristic, complemented, Sylow
371C22×D4—471no—
372C23×C4—941no—
373C2×SD16—471no—
374C2×SD16—471no—
375C2×D8—471no—
376C2×D8—471no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C22×C8—21no—
381C22×C8—941no—
382C22×C8—941no—
383C22×C8—941no—
384C22×C8—941no—
385#126—21no—
386#125C4×D4711yescharacteristic
387#124C4×D4711yescharacteristic
388#123—21no—
389C22⋊Q8C4×D4711yescharacteristic
390#121C4×D4711yescharacteristic
391C4×Q8C22×D4711yescharacteristic
392C4×D4—21no—
393C4×D4—471no—
394C4×D4—471no—
395C4×D4—471no—
396C4×D4—471no—
397C4×D4—941no—
398C4×D4—941no—
399C4×D4C22×D4711yescharacteristic
400#117—21no—
401C2×C4⋊C4—471no—
402C2×C22⋊C4—941no—
403C2×C42C22×D4711yescharacteristic
404#107—471no—
405#107—471no—
406#106—471no—
407#106—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—471no—
412C4⋊C8—471no—
413C4⋊C8—471no—
414C4⋊C8—941no—
415C4⋊C8—941no—
416C4⋊C8—941no—
417C4⋊C8C22×D4711yescharacteristic
418C4⋊C8C22×D4711yescharacteristic
419#103—471no—
420#103—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425#102—471no—
426#102—471no—
427C22⋊C8—21no—
428C22⋊C8—471no—
429C22⋊C8—471no—
430C22⋊C8—471no—
431C22⋊C8—471no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437C22⋊C8—941no—
438#97—21no—
439#97—941no—
440C4×C8—21no—
441C4×C8—471no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—471no—
445C4×C8—941no—
446C4×C8C22×D4711yescharacteristic
447C4×C8C22×D4711yescharacteristic
448C24—941no—
449C2×Q8C2×C4×D4711yescharacteristic
450C2×D4—21no—
451C2×D4—471no—
452C2×D4—471no—
453C2×D4—942no—
454C2×D4—941no—
455C2×D4—1881no—
456C2×D4C2×C4×D4711yescharacteristic
457C22×C4—21no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—3761no—
464C22×C4—3761no—
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4#1062535211yescharacteristic
468SD16—942no—
469SD16—1881no—
470D8—942no—
471D8—1881no—
472M16—3761no—
473M16—3761no—
474M16—3761no—
475C2×C8—24no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—471no—
481C2×C8—471no—
482C2×C8—471no—
483C2×C8—471no—
484C2×C8—471no—
485C2×C8—471no—
486C2×C8—471no—
487C2×C8—471no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—3761no—
491C2×C8—3761no—
492C2×C8—3761no—
493C2×C8—3761no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—471no—
499C4⋊C4—471no—
500C4⋊C4—941no—
501C4⋊C4C2×C4×D4711yescharacteristic
502C4⋊C4C2×C4×D4711yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—941no—
509C22⋊C4—941no—
510C22⋊C4—941no—
511C22⋊C4—941no—
512C42—21no—
513C42C2×C4×D4711yescharacteristic
514C42D4×D4711yescharacteristic
515C42#1062535211yescharacteristic
516C42C23×D4711yescharacteristic
517C23—21no—
518C23—941no—
519C23—941no—
520C23—3761no—
521C23—1882no—
522C23—1882no—
523C23(C22⋊D47)⋊C411yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—472no—
530D4—941no—
531D4—941no—
532D4—941no—
533D4—1882no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—3761no—
547C2×C4—3761no—
548C2×C4—3761no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4(C22⋊D47)⋊C411yescharacteristic
554C2×C4(C22⋊D47)⋊C411yescharacteristic
555C2×C4(C22⋊D47)⋊C411yescharacteristic
556C2×C4C22×C4×D4711yescharacteristic
557C2×C4C2×D4×D4711yescharacteristic
558C2×C4C2×#1062535211yescharacteristic
559C8—22no—
560C8—22no—
561C8—41no—
562C8—41no—
563C8—941no—
564C8—941no—
565C8—941no—
566C8—941no—
567C8—941no—
568C8—941no—
569C8—941no—
570C8—941no—
571C8—1881no—
572C8—1881no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—942no—
579C22—3764no—
580C22—1881no—
581C22—1881no—
582C22—1881no—
583C22—1881no—
584C22—1881no—
585C22#1568923712yes—
586C22C2×(C22⋊D47)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—1881no—
595C4—1881no—
596C4#131×D4711yescharacteristic
597C4#1568988811yescharacteristic
598C4#1568992511yescharacteristic
599C4#1568993011yescharacteristic
600C2—22no—
601C2—81no—
602C2—3761no—
603C2—1882no—
604C2#2025211811yescharacteristic
605C2#2025222311yescharacteristic
606C2C2×#1568923711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1494C2
socleC22×C47C2×C4×D4
prime radical#15689256C4
cosocleC42×C47C24
hypercenter#1494D47
hypocenterC47#18014
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #20252548C2semidirect
3. #20252425C2semidirect
4. #20242275C2semidirect
5. #20242270C2semidirect
6. #20242263C2semidirect
7. #20242255C2semidirect
8. #20242249C2semidirect
9. #20242248C2semidirect
10. #20242185C2semidirect
11. #20242180C2semidirect
12. #20242174C2semidirect
13. C2×#15688852C2semidirect
14. #20241671C2semidirect
15. C47×#1494C2semidirect
25. #15689254C22semidirect
26. Q8×C47⋊C8C22semidirect
31. #15689201C22semidirect
38. D4×C47⋊C8C22semidirect
48. #15688875C22semidirect
49. #15688875C22semidirect
50. #15688873C22semidirect
51. #15688873C22semidirect
56. #15688844C22semidirect
57. #15688844C22semidirect
58. C8×C47⋊C8C22semidirect
59. C8×C47⋊C8C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×D4⋊C8C22semidirect
309. #1494D47semidirect
358. Q8⋊C8C2×D47semidirect
359. Q8⋊C8C2×D47semidirect
364. D4⋊C8C2×D47semidirect
365. D4⋊C8C2×D47semidirect
370. C47#18014semidirect

Maximal subgroups

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

subgroupindex
#202534312
#202525482
#202524252
#202422752
#202422702
#202422632
#202422552
#202422492
#202422482
#202421852
#202421802
#202421742
C2×#156888522
#202416712
C47×#14942
#1801447