Finite Group Databasebeta

← #26219359

Subgroups — #26219359

Order 12032.

890 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689220C211yesmaximal, characteristic
2#20246035C211yesmaximal, characteristic, complemented
3#20245749C211yesmaximal, characteristic
4#20244030C211yesmaximal, characteristic, complemented
5#20244021C211yesmaximal, characteristic, complemented
6#20243983C211yesmaximal, characteristic, complemented
7#20243956C211yesmaximal, characteristic, complemented
8#20243722C211yesmaximal, characteristic
9#20243720C211yesmaximal, characteristic
10#20243637C211yesmaximal, characteristic
11#20243288C211yesmaximal, characteristic, complemented
12#20243207C211yesmaximal, characteristic, complemented
13#102×Dic47C211yesmaximal, characteristic
14#20243138C211yesmaximal, characteristic, complemented
15C47×#1864C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×#13093989C2211yescharacteristic
18C2×D4×Dic47C2211yescharacteristic
19C2×D4×Dic47C2211yescharacteristic
20#15689220C418yescomplemented
21C2×#13093958C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093949C2211yescharacteristic
24C2×#13093949C2211yescharacteristic
25C2×#13093947C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093934C2211yescharacteristic
28C2×C8×Dic47C2211yescharacteristic
29#15689029C2211yescharacteristic
30#15689028C2211yescharacteristic
31#15689022C2211yescharacteristic
32#15689010—21no—
33#15689004—21no—
34#15688990—21no—
35#15688988—21no—
36C4⋊C4×Dic47C2211yescharacteristic
37C4⋊C4×Dic47C2211yescharacteristic
38C4⋊C4×Dic47C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C22⋊C4×Dic47—21no—
41C22⋊C4×Dic47—21no—
42C4×C22⋊Dic47—21no—
43#15688969C2211yescharacteristic
44C2×C47⋊#95—21no—
45#15688886C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C2×#106×C47C2211yescharacteristic
55C2×#102×C47C2211yescharacteristic
56C2×#102×C47C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×Dic94C2311yescharacteristic
61C23×Dic47—21no—
62C23×Dic47—21no—
63C2×#10625335—22no—
64C2×#10625335—22no—
65C2×#10625335C2×C414yes—
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13093989—22no—
69#13093989C2×C414yescomplemented
70D4×Dic47—22no—
71D4×Dic47—22no—
72D4×Dic47—22no—
73D4×Dic47C2×C414yes—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88#13093958—22no—
89#13093957C2×C414yescomplemented
90#13093949—22no—
91#13093949C2×C414yescomplemented
92#13093947—22no—
93#13093945—22no—
94#13093934C2×C414yescomplemented
95C8×Dic47—22no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95D411yescharacteristic
106C47⋊#95D411yescharacteristic
107C47⋊#95D411yescharacteristic
108C47⋊#95D411yescharacteristic
109C22×D4×C47C2311yescharacteristic
110C23×C4×C47—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C4×D4×C47—22no—
114C4×D4×C47—22no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C42×C47C2311yescharacteristic
121#106×C47—22no—
122#102×C47—22no—
123#102×C47C2×C414yes—
124#95×C47—21no—
125C24×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47C22×C412yes—
130C2×D4×C47#4112yes—
131C2×D4×C47#4112yes—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—24no—
135C22×C4×C47—21no—
136C22×C4×C47—81no—
137C22×C4×C47—81no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2411yescharacteristic
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—24no—
145C22×Dic47—24no—
146C22×Dic47—21no—
147C22×Dic47—81no—
148C22×Dic47—81no—
149C22×Dic47—81no—
150C22×Dic47—81no—
151C22×Dic47C2×D411yescharacteristic
152C22×Dic47C2×D411yescharacteristic
153C22×Dic47C2×D411yescharacteristic
154C22×Dic47C2×D411yescharacteristic
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94C22×C412yes—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47C22×C412yes—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—81no—
172C4⋊C4×C47C22×C412yes—
173C4⋊C4×C47#4112yes—
174C22⋊C4×C47—24no—
175C42×C47—21no—
176C42×C47—21no—
177C22⋊Dic47—24no—
178C22⋊Dic47—24no—
179#10625335—28no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—81no—
185C4⋊Dic47C22×C412yes—
186C4⋊Dic47#4112yes—
187Dic47⋊C4—24no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47—24no—
191C4×Dic47—81no—
192C4×Dic47—81no—
193C4×Dic47—81no—
194C4×Dic47—81no—
195C4×Dic47C22×C412yes—
196C4×Dic47#4112yes—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8C22×C412yes—
203C23×C47—22no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47C22×D411yescharacteristic
211D4×C47—22no—
212D4×C47—22no—
213D4×C47—22no—
214D4×C47#11714yes—
215C2×C4×C47—22no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
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—84no—
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—22no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—84no—
260C2×Dic47—84no—
261C2×Dic47C4×D412yes—
262C2×Dic47C4×D412yes—
263Dic94—22no—
264Dic94—22no—
265Dic94—41no—
266Dic94—41no—
267C8×C47—22no—
268C8×C47—41no—
269C47⋊C8—22no—
270C47⋊C8—41no—
271#21125—471nomaximal, Sylow
272C22×C47—24no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—42no—
277C22×C47—42no—
278C22×C47—42no—
279C22×C47C2×C4×D411yescharacteristic
280C22×C47#52511yescharacteristic
281C22×C47#52511yescharacteristic
282C22×C47#57611yescharacteristic
283C22×C47#57711yescharacteristic
284C22×C47#57711yescharacteristic
285C22×C47#57811yescharacteristic
286C4×C47—41no—
287C4×C47—42no—
288C4×C47—41no—
289C4×C47—42no—
290C4×C47—81no—
291C4×C47C2×#11711yescharacteristic
292C4×C47C4×#4111yescharacteristic
293C4×C47#52911yescharacteristic
294C4×C47#52911yescharacteristic
295Dic47—22no—
296Dic47—22no—
297Dic47—41no—
298Dic47—42no—
299Dic47—41no—
300Dic47—42no—
301Dic47—42no—
302Dic47—81no—
303C2×#440—471no—
304#2320—471no—
305#2275—471no—
306#1928—471no—
307#1927—471no—
308#1921—471no—
309#1918—471no—
310#1877—471no—
311#1877—471no—
312#1864D4711yescharacteristic
313#1862—471no—
314#1776—471no—
315C4×#103—471no—
316C4×#102—471no—
317#1746—471no—
318C2×C47—44no—
319C2×C47#229011yescharacteristic
320C2×C47#294611yescharacteristic
321C2×C47#294711yescharacteristic
322C2×C47#311811yescharacteristic
323C2×C47#312011yescharacteristic
324C2×C47#312311yescharacteristic
325C2×C47#312411yescharacteristic
326C22×SD16—471no—
327C2×C4×Q8—471no—
328C2×C4×D4—471no—
329C2×C4×D4—471no—
330C2×C4×D4C2×D4711yescharacteristic
331#440—478no—
332C2×#107—471no—
333C2×#107—471no—
334C2×#106C2×D4711yescharacteristic
335C2×#103—471no—
336C2×#103—471no—
337C2×#103—471no—
338C2×#102—471no—
339C2×#102C2×D4711yescharacteristic
340C2×#102C2×D4711yescharacteristic
341C2×#97—471no—
342C2×C4×C8—471no—
343#391—471no—
344#391—471no—
345#389—471no—
346#389C2×D4711yescharacteristic
347#387—941no—
348#387—941no—
349#383—941no—
350#382—941no—
351C4×C4⋊C4—471no—
352C4×C4⋊C4—471no—
353C4×C4⋊C4—471no—
354C4×C4⋊C4—471no—
355C4×C22⋊C4—941no—
356C4×C22⋊C4—941no—
357C4×C22⋊C4—941no—
358#376—471no—
359C2×#95—941no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340C2×D4711yescharacteristic
366#336—471no—
367#336—471no—
368#336—471no—
369#336C2×D4711yescharacteristic
370C47#2112511yescharacteristic, complemented, Sylow
371C22×Q8—471no—
372C22×D4C22×D4711yescharacteristic
373C23×C4—21no—
374C23×C4—941no—
375C23×C4—941no—
376C2×SD16—474no—
377C2×SD16—942no—
378C2×SD16—942no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8C22×D4711yescharacteristic
382C22×C8C22×D4711yescharacteristic
383C4×Q8—474no—
384C4×Q8—942no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—474no—
388C4×D4—942no—
389C4×D4—942no—
390C4×D4—942no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C4⋊C4C22×D4711yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C42—471no—
404C2×C42—471no—
405C2×C42—941no—
406C2×C42—941no—
407C2×C42—941no—
408C2×C42—941no—
409C2×C42—941no—
410C2×C42C22×D4711yescharacteristic
411#107—474no—
412#107—942no—
413#106—22no—
414#103—474no—
415#103—942no—
416#103—942no—
417#102—22no—
418#102—942no—
419#102C4×D4714yes—
420#97—474no—
421C4×C8—942no—
422#95—21no—
423#95—471no—
424#95—471no—
425#95—471no—
426#95—471no—
427#95—941no—
428#95—941no—
429#95—941no—
430#95—941no—
431#95—941no—
432#95—941no—
433#95—941no—
434#95—941no—
435#95—941no—
436C24—21no—
437C2×Q8—472no—
438C2×Q8—941no—
439C2×Q8—941no—
440C2×Q8—941no—
441C2×Q8—941no—
442C2×Q8—941no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×C4×D4712yes—
447C2×D4#1062535212yes—
448C2×D4#1062535412yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—944no—
460C22×C4—944no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—3761no—
466C22×C4—3761no—
467C22×C4—3761no—
468C22×C4—3761no—
469C22×C4D4×D4711yescharacteristic
470C22×C4D4×D4711yescharacteristic
471C22×C4C23×D4711yescharacteristic
472SD16—948no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—472no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8C2×C4×D4712yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—472no—
491C4⋊C4—472no—
492C4⋊C4—944no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—3761no—
498C4⋊C4C2×C4×D4712yes—
499C4⋊C4#1062535212yes—
500C22⋊C4—24no—
501C22⋊C4—944no—
502C22⋊C4—944no—
503C42—21no—
504C42—21no—
505C42—472no—
506C42—472no—
507C42—944no—
508C42—941no—
509C42—941no—
510C42—3761no—
511C42—3761no—
512C42—3761no—
513C42—3761no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D4711yescharacteristic
522Q8—942no—
523Q8—942no—
524Q8—1881no—
525Q8—1881no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4#1309398214yes—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—472no—
547C2×C4—472no—
548C2×C4—941no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—942no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—3764no—
562C2×C4—3764no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4—1881no—
572C2×C4C22×C4×D4711yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#41×D4711yescharacteristic
575C2×C4C2×#1062535211yescharacteristic
576C2×C4C2×#1062535211yescharacteristic
577C2×C4C2×#1062535411yescharacteristic
578C8—22no—
579C8—41no—
580C8—942no—
581C8—1881no—
582C22—24no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C4×D4×D4711yescharacteristic
590C22#1568962911yescharacteristic
591C22#1568963611yescharacteristic
592C22#1568992711yescharacteristic
593C22#1568992911yescharacteristic
594C22#1568993311yescharacteristic
595C22#1568993711yescharacteristic
596C4—42no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—81no—
601C4—942no—
602C4—942no—
603C4—3761no—
604C4—1882no—
605C4—1882no—
606C4—1881no—
607C4—1882no—
608C4—1881no—
609C4C2×#1309398211yescharacteristic
610C4C4×#1062535211yescharacteristic
611C4#1568965011yescharacteristic
612C4#1568965911yescharacteristic
613C2—44no—
614C2#2024582411yescharacteristic
615C2#2025221711yescharacteristic
616C2#2025222411yescharacteristic
617C2#2025357711yescharacteristic
618C2#2025360711yescharacteristic
619C2#2025363411yescharacteristic
620C2#2025364311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1864C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenter#1864D47
hypocenterC47#21125
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #20246035C2semidirect
4. #20244030C2semidirect
5. #20244021C2semidirect
6. #20243983C2semidirect
7. #20243956C2semidirect
11. #20243288C2semidirect
12. #20243207C2semidirect
14. #20243138C2semidirect
20. #15689220C4semidirect
69. #13093989C2×C4semidirect
89. #13093957C2×C4semidirect
91. #13093949C2×C4semidirect
94. #13093934C2×C4semidirect
370. C47#21125semidirect

Maximal subgroups

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

subgroupindex
C2×#156892202
#202460352
#202457492
#202440302
#202440212
#202439832
#202439562
#202437222
#202437202
#202436372
#202432882
#202432072
#102×Dic472
#202431382
C47×#18642
#2112547