Finite Group Databasebeta

← #26219517

Subgroups — #26219517

Order 12032.

780 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252184C211yesmaximal, characteristic
2#20252038C211yesmaximal, characteristic, complemented
3#20251814C211yesmaximal, characteristic, complemented
4#20244037C211yesmaximal, characteristic, complemented
5#20244035C211yesmaximal, characteristic, complemented
6#20243990C211yesmaximal, characteristic, complemented
7#20243984C211yesmaximal, characteristic, complemented
8#20243715C211yesmaximal, characteristic
9#20243713C211yesmaximal, characteristic
10#20243665C211yesmaximal, characteristic, complemented
11#20243296C211yesmaximal, characteristic, complemented
12#104×Dic47C211yesmaximal, characteristic, complemented
13#20243192C211yesmaximal, characteristic, complemented
14#20243135C211yesmaximal, characteristic, complemented
15C47×#1866C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18#41×Dic47C2211yescharacteristic
19#15689591C2211yescharacteristic
20#15689232C411yescharacteristic, complemented
21#15689232C411yescharacteristic, complemented
22#15689227C411yescharacteristic, complemented
23#15689227C411yescharacteristic, complemented
24#15689226C411yescharacteristic, complemented
25#15689226C411yescharacteristic, complemented
26#15689220C411yescharacteristic, complemented
27#15689220C411yescharacteristic, complemented
28#15689183—21no—
29#15689183—21no—
30#15689179—21no—
31#15689179—21no—
32C2×#13093960C2211yescharacteristic
33#15689159C2211yescharacteristic
34#15689150C2211yescharacteristic
35C2×#13093952C2211yescharacteristic
36C2×#13093951C2211yescharacteristic
37C2×#13093950C2211yescharacteristic
38#15689120C2211yescharacteristic
39#15689091C2211yescharacteristic
40#15689089C2211yescharacteristic
41#15689081—21no—
42#15689081C2211yescharacteristic
43#15689078—21no—
44#15689078C2211yescharacteristic
45M16×Dic47—21no—
46M16×Dic47C2211yescharacteristic
47M16×Dic47C2211yescharacteristic
48C2×#13093934—21no—
49C2×#13093934C2211yescharacteristic
50C2×#13093934C2211yescharacteristic
51C42×Dic47C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688887C2211yescharacteristic
54#15688884C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688882C2211yescharacteristic
57#15688878C2211yescharacteristic
58#15688877C2211yescharacteristic
59#15688877C2211yescharacteristic
60C2×#131×C47C2211yescharacteristic
61C2×#108×C47C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C2×#104×C47C2211yescharacteristic
64C47×#416C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094044—22no—
69#13094044—22no—
70C2×#10625337C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C2×#10625336C2×C411yescharacteristic
73C2×#10625334C2×C411yescharacteristic
74#13094031—22no—
75#13094031—22no—
76C2×#10625329—21no—
77C2×#10625329C2311yescharacteristic
78C2×#10625329C2311yescharacteristic
79C22×C47⋊C8—21no—
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82Q8×Dic47C2×C411yescharacteristic
83Q8×Dic47C2×C411yescharacteristic
84#13093989C2×C411yescharacteristic
85#13093989C2×C411yescharacteristic
86D4×Dic47—21no—
87D4×Dic47—21no—
88D4×Dic47C2×C411yescharacteristic
89D4×Dic47C2×C411yescharacteristic
90#13093986C2×C411yescharacteristic
91#13093986C2×C411yescharacteristic
92(C22⋊D47)⋊C4—21no—
93(C22⋊D47)⋊C4—21no—
94#13093983—21no—
95#13093983C2311yescharacteristic
96#13093981—21no—
97C2×C4×Dic47—21no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47—21no—
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102C42×D47—21no—
103#13093960—22no—
104#13093957C2×C411yescharacteristic
105#13093957C2×C411yescharacteristic
106#13093955C2×C411yescharacteristic
107#13093955C2×C411yescharacteristic
108C4⋊(C47⋊C8)—21no—
109C4⋊(C47⋊C8)—21no—
110#13093952—22no—
111#13093951—22no—
112#13093950—22no—
113#13093949C2×C411yescharacteristic
114#13093949C2×C411yescharacteristic
115#13093946C2×C411yescharacteristic
116#13093946C2×C411yescharacteristic
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121#13093934—21no—
122#13093934—21no—
123#13093934—21no—
124#13093934—21no—
125#13093934C2×C411yescharacteristic
126#13093934C2×C411yescharacteristic
127#13093934C2×C411yescharacteristic
128#13093934C2×C411yescharacteristic
129#13093934D411yescharacteristic
130#13093934D411yescharacteristic
131#13093934D411yescharacteristic
132#13093934D411yescharacteristic
133C8×Dic47—21no—
134C8×Dic47—21no—
135C8×Dic47—21no—
136C8×Dic47—21no—
137C2×#41×C47C2311yescharacteristic
138#131×C47—22no—
139#131×C47—22no—
140C2×M16×C47—21no—
141C2×M16×C47C2311yescharacteristic
142C2×M16×C47C2311yescharacteristic
143C22×C8×C47—21no—
144C22×C8×C47C2311yescharacteristic
145C22×C8×C47C2311yescharacteristic
146#117×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148#108×C47—22no—
149C4⋊C8×C47—21no—
150C4⋊C8×C47—21no—
151#104×C47—22no—
152#103×C47C2×C411yescharacteristic
153#103×C47C2×C411yescharacteristic
154#102×C47C2×C411yescharacteristic
155#102×C47C2×C411yescharacteristic
156#41×C47—21no—
157#41×C47—21no—
158#41×C47#4112yes—
159#41×C47#4112yes—
160C2×Q8×C47C22×C411yescharacteristic
161C2×D4×C47—21no—
162C2×D4×C47C22×C411yescharacteristic
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47C2411yescharacteristic
166C2×C22⋊D47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47#4111yescharacteristic
171C22×Dic47#4111yescharacteristic
172#10625350—21no—
173#10625350—21no—
174#10625350—21no—
175#10625350—21no—
176C2×D188C22×C411yescharacteristic
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×Dic94C22×C411yescharacteristic
181M16×C47—24no—
182M16×C47—21no—
183M16×C47—21no—
184M16×C47—21no—
185M16×C47#4112yes—
186C2×C8×C47—24no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47C22×C411yescharacteristic
194C2×C8×C47C22×C411yescharacteristic
195C2×C8×C47C2×D411yescharacteristic
196C2×C8×C47C2×D411yescharacteristic
197C4⋊C4×C47C22×C411yescharacteristic
198C4⋊C4×C47C22×C411yescharacteristic
199C22⋊C4×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C22⋊Dic47—21no—
204C22⋊Dic47—21no—
205C22⋊Dic47—21no—
206#10625337—22no—
207#10625336—22no—
208#10625335—22no—
209#10625334—22no—
210(C2×D47)⋊C4—21no—
211(C2×D47)⋊C4—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47C22×C411yescharacteristic
215C4⋊Dic47C22×C411yescharacteristic
216Dic47⋊C4—21no—
217Dic47⋊C4—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—21no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—42no—
226C4×Dic47—42no—
227C4×Dic47C22×C411yescharacteristic
228C4×Dic47C22×C411yescharacteristic
229C4×Dic47C2×D411yescharacteristic
230C4×Dic47C2×D411yescharacteristic
231#10625329—24no—
232#10625329—21no—
233#10625329—21no—
234#10625329—21no—
235#10625329#4112yes—
236C2×C47⋊C8—24no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8C22×C411yescharacteristic
244C2×C47⋊C8C22×C411yescharacteristic
245C2×C47⋊C8C2×D411yescharacteristic
246C2×C47⋊C8C2×D411yescharacteristic
247C23×C47—21no—
248C23×C47C2×#4111yescharacteristic
249C22×D47—21no—
250Q8×C47—21no—
251Q8×C47#11712yes—
252D4×C47—22no—
253D4×C47—22no—
254D4×C47—21no—
255D4×C47#11712yes—
256C2×C4×C47—21no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47C23×C411yescharacteristic
265C2×C4×C47C22×D411yescharacteristic
266C2×C4×C47C2×#4111yescharacteristic
267C2×C4×C47C2×#4111yescharacteristic
268C2×C4×C47C2×#4111yescharacteristic
269C2×C4×C47C2×#4111yescharacteristic
270C22⋊D47—41no—
271C22⋊D47—41no—
272C2×Dic47—22no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—81no—
281C2×Dic47—81no—
282C2×Dic47C4×D411yescharacteristic
283C2×Dic47C4×D411yescharacteristic
284C2×Dic47C4×D411yescharacteristic
285C2×Dic47C4×D411yescharacteristic
286D188—21no—
287D188—21no—
288C4×D47—41no—
289C4×D47—41no—
290C4×D47—81no—
291C4×D47—81no—
292Dic94—21no—
293Dic94—21no—
294C8×C47—21no—
295C8×C47—21no—
296C8×C47—21no—
297C8×C47—22no—
298C8×C47—21no—
299C8×C47—41no—
300C47⋊C8—21no—
301C47⋊C8—21no—
302C47⋊C8—21no—
303C47⋊C8—22no—
304C47⋊C8—21no—
305C47⋊C8—41no—
306#21139—471nomaximal, Sylow
307C22×C47—21no—
308C22×C47—21no—
309C22×C47—22no—
310C22×C47—41no—
311C22×C47—41no—
312C22×C47C2×C4×D411yescharacteristic
313C22×C47#52911yescharacteristic
314C22×C47#52911yescharacteristic
315C2×D47—41no—
316C2×D47—41no—
317C2×D47—41no—
318C4×C47—22no—
319C4×C47—42no—
320C4×C47—41no—
321C4×C47—41no—
322C4×C47C2×#11711yescharacteristic
323C4×C47C4×#4111yescharacteristic
324C4×C47#52511yescharacteristic
325C4×C47#52511yescharacteristic
326Dic47—21no—
327Dic47—21no—
328Dic47—21no—
329Dic47—21no—
330Dic47—42no—
331Dic47—41no—
332Dic47—41no—
333Dic47—41no—
334#2943—471no—
335#2923—471no—
336#2875—471no—
337#1929—471no—
338#1929—471no—
339#1922—471no—
340#1922—471no—
341#1876—471no—
342#1876—471no—
343#1866—471no—
344#1866D4711yescharacteristic, complemented
345#1778—471no—
346C4×#104—471no—
347C4×#104—471no—
348#1745—471no—
349C2×C47—21no—
350C2×C47—21no—
351C2×C47—42no—
352C2×C47#229011yescharacteristic
353C2×C47#295611yescharacteristic
354C2×C47#295611yescharacteristic
355D47—81no—
356C2×#135—471no—
357C2×#131—471no—
358C2×#131C2×D4711yescharacteristic
359C4×#41—471no—
360C4×#41—471no—
361#442—471no—
362#442—471no—
363#441—471no—
364#441—471no—
365#440—471no—
366#440—471no—
367#440—471no—
368#440—471no—
369#433—941no—
370#433—941no—
371#432—941no—
372#432—941no—
373C2×#108—471no—
374C2×#108C2×D4711yescharacteristic
375#427—471no—
376#424—471no—
377#424C2×D4711yescharacteristic
378C2×#104—471no—
379C2×#104—471no—
380C2×#104—471no—
381C2×#104C2×D4711yescharacteristic
382#416—471no—
383#416C2×D4711yescharacteristic
384#408—471no—
385#408—471no—
386#405—471no—
387#405—471no—
388#405—941no—
389#405—941no—
390C4×M16—471no—
391C4×M16—471no—
392C4×M16—941no—
393C2×#97—471no—
394C2×#97—471no—
395C2×#97—941no—
396C43—471no—
397#341—471no—
398#341—471no—
399#339—471no—
400#339—471no—
401#339—471no—
402#339C2×D4711yescharacteristic
403#336—471no—
404#336—471no—
405#336—471no—
406#336C2×D4711yescharacteristic
407C47#2113911yescharacteristic, complemented, Sylow
408C2×#41—471no—
409C2×#41C22×D4711yescharacteristic
410#135—942no—
411#135—942no—
412C2×Q16—471no—
413C2×SD16—471no—
414C2×SD16—471no—
415C2×D8—471no—
416#131—22no—
417#131—22no—
418#131—942no—
419#131—942no—
420C2×M16—21no—
421C2×M16—471no—
422C2×M16—471no—
423C2×M16—941no—
424C2×M16C22×D4711yescharacteristic
425C2×M16C22×D4711yescharacteristic
426C22×C8—21no—
427C22×C8—471no—
428C22×C8—471no—
429C22×C8—941no—
430C22×C8C22×D4711yescharacteristic
431C22×C8C22×D4711yescharacteristic
432C4×Q8—471no—
433C4×Q8—471no—
434C4×Q8—471no—
435C4×Q8—471no—
436C4×D4—471no—
437C4×D4—471no—
438C4×D4—471no—
439C4×D4—471no—
440C4×D4—941no—
441C4×D4—941no—
442C4×D4—941no—
443C4×D4—941no—
444#117—471no—
445#117—941no—
446#117—941no—
447#117C22×D4711yescharacteristic
448C2×C42—471no—
449C2×C42—471no—
450C2×C42—941no—
451C2×C42—941no—
452C2×C42—941no—
453C2×C42—941no—
454C2×C42C22×D4711yescharacteristic
455#108—22no—
456#108—942no—
457#107—471no—
458#107—471no—
459#106—471no—
460#106—471no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—941no—
464C4⋊C8—941no—
465#104—22no—
466#104—942no—
467#104—942no—
468#104—942no—
469#103—471no—
470#103—471no—
471#103C4×D4711yescharacteristic
472#103C4×D4711yescharacteristic
473#102—471no—
474#102—471no—
475#102C4×D4711yescharacteristic
476#102C4×D4711yescharacteristic
477C22⋊C8—941no—
478C22⋊C8—941no—
479C22⋊C8—941no—
480C22⋊C8—941no—
481#97—471no—
482#97—471no—
483#97—471no—
484#97—471no—
485#97—471no—
486#97—471no—
487#97—471no—
488#97—471no—
489#97—941no—
490#97—941no—
491#97—941no—
492#97—941no—
493C4×C8—941no—
494C4×C8—941no—
495C4×C8—941no—
496C4×C8—941no—
497#41—21no—
498#41—21no—
499#41—941no—
500#41—941no—
501#41—941no—
502#41—941no—
503#41#1062535212yes—
504#41#1062535412yes—
505C2×Q8—471no—
506C2×Q8C2×C4×D4711yescharacteristic
507C2×D4—21no—
508C2×D4—471no—
509C2×D4—941no—
510C2×D4C2×C4×D4711yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—471no—
514C22×C4—471no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—941no—
521C22×C4C23×D4711yescharacteristic
522Q16—942no—
523SD16—942no—
524SD16—942no—
525D8—942no—
526M16—24no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—472no—
531M16—944no—
532M16—941no—
533M16—941no—
534M16—941no—
535M16#1062535212yes—
536C2×C8—24no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—471no—
544C2×C8—471no—
545C2×C8—471no—
546C2×C8—471no—
547C2×C8—944no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8C2×C4×D4711yescharacteristic
555C2×C8C2×C4×D4711yescharacteristic
556C2×C8D4×D4711yescharacteristic
557C2×C8D4×D4711yescharacteristic
558C4⋊C4—471no—
559C4⋊C4—471no—
560C4⋊C4—941no—
561C4⋊C4—941no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4C2×C4×D4711yescharacteristic
565C4⋊C4C2×C4×D4711yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—941no—
568C22⋊C4—941no—
569C22⋊C4—941no—
570C22⋊C4—941no—
571C22⋊C4—941no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—471no—
576C42—471no—
577C42—471no—
578C42—471no—
579C42—941no—
580C42—941no—
581C42—941no—
582C42—941no—
583C42—941no—
584C42—941no—
585C42—941no—
586C42—1882no—
587C42—1882no—
588C23—21no—
589C23—941no—
590C23#41×D4711yescharacteristic
591Q8—21no—
592Q8—941no—
593Q8—941no—
594Q8#1309398212yes—
595D4—22no—
596D4—22no—
597D4—21no—
598D4—941no—
599D4—941no—
600D4—1881no—
601D4—1881no—
602D4#1309398212yes—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—471no—
612C2×C4—471no—
613C2×C4—471no—
614C2×C4—471no—
615C2×C4—942no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—941no—
619C2×C4—3761no—
620C2×C4—3761no—
621C2×C4—3761no—
622C2×C4—3761no—
623C2×C4—1881no—
624C2×C4—1881no—
625C2×C4—1881no—
626C2×C4—1881no—
627C2×C4—1881no—
628C2×C4—1881no—
629C2×C4C22×C4×D4711yescharacteristic
630C2×C4C2×D4×D4711yescharacteristic
631C2×C4#41×D4711yescharacteristic
632C2×C4C2×#1062535211yescharacteristic
633C2×C4C2×#1062535211yescharacteristic
634C2×C4C2×#1062535411yescharacteristic
635C8—21no—
636C8—21no—
637C8—21no—
638C8—22no—
639C8—21no—
640C8—41no—
641C8—941no—
642C8—941no—
643C8—941no—
644C8—941no—
645C8—942no—
646C8—1881no—
647C22—21no—
648C22—21no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—1881no—
653C22—1881no—
654C22—1881no—
655C22C4×D4×D4711yescharacteristic
656C22#1568965011yescharacteristic
657C22#1568965911yescharacteristic
658C4—22no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—941no—
663C4—941no—
664C4—941no—
665C4—941no—
666C4—1882no—
667C4—1881no—
668C4—1881no—
669C4—1881no—
670C4C2×#1309398211yescharacteristic
671C4C4×#1062535211yescharacteristic
672C4#1568962911yescharacteristic
673C4#1568963611yescharacteristic
674C2—21no—
675C2—21no—
676C2—42no—
677C2—3761no—
678C2#2024582411yescharacteristic
679C2#2025229311yescharacteristic
680C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1866C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenter#1866D47
hypocenterC47#21139
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #20252038C2semidirect
3. #20251814C2semidirect
4. #20244037C2semidirect
5. #20244035C2semidirect
6. #20243990C2semidirect
7. #20243984C2semidirect
10. #20243665C2semidirect
11. #20243296C2semidirect
12. #104×Dic47C2semidirect
13. #20243192C2semidirect
14. #20243135C2semidirect
15. C47×#1866C2semidirect
20. #15689232C4semidirect
21. #15689232C4semidirect
22. #15689227C4semidirect
23. #15689227C4semidirect
24. #15689226C4semidirect
25. #15689226C4semidirect
26. #15689220C4semidirect
27. #15689220C4semidirect
344. #1866D47semidirect
407. C47#21139semidirect

Maximal subgroups

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

subgroupindex
#202521842
#202520382
#202518142
#202440372
#202440352
#202439902
#202439842
#202437152
#202437132
#202436652
#202432962
#104×Dic472
#202431922
#202431352
C47×#18662
#2113947