Finite Group Databasebeta

← #26223960

Subgroups — #26223960

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689424C211yesmaximal, characteristic
2C4×#13094016C211yesmaximal, characteristic, complemented
3C42×D188C211yesmaximal, characteristic
4#20244343C211yesmaximal, characteristic, complemented
5#20244158C211yesmaximal, characteristic, complemented
6#20243974C211yesmaximal, characteristic, complemented
7#20243960C211yesmaximal, characteristic, complemented
8#20243652C211yesmaximal, characteristic
9#20243638C211yesmaximal, characteristic
10#20243399C211yesmaximal, characteristic
11#20243285C211yesmaximal, characteristic, complemented
12#20243285C211yesmaximal, characteristic, complemented
13#20243214C211yesmaximal, characteristic
14#20243214C211yesmaximal, characteristic
15C47×#1767C211yesmaximal, characteristic, complemented
16C2×#13094016C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20C2×C42×D47—21no—
21#15689424C418yescomplemented
22C2×#13093958C2211yescharacteristic
23C2×#13093958C2211yescharacteristic
24C2×#13093956C2211yescharacteristic
25C2×#13093956C2211yescharacteristic
26C2×#13093946C2211yescharacteristic
27C2×#13093946C2211yescharacteristic
28C2×#13093946C2211yescharacteristic
29C2×#13093946C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689007—21no—
33#15689007—21no—
34#15688989C2211yescharacteristic
35C4×Dic47⋊C4—21no—
36C4×Dic47⋊C4—21no—
37C4×C4⋊Dic47C2211yescharacteristic
38C4×C4⋊Dic47C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42C4×(C2×D47)⋊C4—21no—
43C4×(C2×D47)⋊C4—21no—
44C4×(C2×D47)⋊C4—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53C2×C4⋊C8×C47C2211yescharacteristic
54C2×C4⋊C8×C47C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic
57C43×C47C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47—21no—
63C22×C4×D47—21no—
64#13094016—22no—
65#13094016C2×C414yescomplemented
66C4×D188—22no—
67C4×D188—22no—
68C4×D188—22no—
69C4×D188—22no—
70C4×D188C2×C414yes—
71C4×D188Q814yes—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47—21no—
91C42×D47—44no—
92#13093958—22no—
93#13093958C2×C414yescomplemented
94#13093956—22no—
95#13093956C2×C414yescomplemented
96#13093946—22no—
97#13093946—22no—
98#13093946C2×C414yes—
99#13093946C2×C414yes—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C2×C42×C47D411yescharacteristic
114C2×C42×C47D411yescharacteristic
115C2×C42×C47D411yescharacteristic
116C2×C42×C47D411yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—22no—
121C4⋊C8×C47C2×C414yescomplemented
122#97×C47—22no—
123#97×C47—22no—
124C23×D47—21no—
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2411yescharacteristic
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188C22×C412yes—
143C2×D188C2×Q812yes—
144C2×D188#4112yes—
145C2×C4×D47—24no—
146C2×C4×D47—24no—
147C2×C4×D47—24no—
148C2×C4×D47—42no—
149C2×C4×D47—42no—
150C2×C4×D47—42no—
151C2×C4×D47—42no—
152C2×C4×D47—42no—
153C2×C4×D47—42no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47C22×C412yes—
165C2×C8×C47C22×C412yes—
166C42×C47—22no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—41no—
170C42×C47—41no—
171C42×C47—41no—
172C42×C47C22×C412yes—
173C42×C47C2×Q812yes—
174C42×C47#4112yes—
175C42×C47#4112yes—
176(C2×D47)⋊C4—24no—
177(C2×D47)⋊C4—24no—
178(C2×D47)⋊C4—24no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47C22×C412yes—
189C4⋊Dic47C22×C412yes—
190C4⋊Dic47C22×C412yes—
191C4⋊Dic47C2×Q812yes—
192C4⋊Dic47#4112yes—
193Dic47⋊C4—24no—
194Dic47⋊C4—24no—
195Dic47⋊C4—42no—
196Dic47⋊C4—42no—
197C4×Dic47—42no—
198C4×Dic47—42no—
199C4×Dic47—42no—
200C4×Dic47—42no—
201C4×Dic47—42no—
202C23×C47C22×D411yescharacteristic
203C22×D47—22no—
204C22×D47—22no—
205C22×D47—22no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
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×C47C4×D412yes—
224C2×C4×C47C4×D412yes—
225C2×C4×C47C22⋊Q812yes—
226C2×C4×C47C22⋊Q812yes—
227C2×C4×C47AGL(1,ℤ/8)12yes—
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×Q811yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
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—
253C2×Dic47—41no—
254C2×Dic47—41no—
255D188—22no—
256D188—22no—
257D188—22no—
258D188C4×Q814yes—
259C4×D47—48no—
260C4×D47—48no—
261C4×D47—48no—
262C8×C47—22no—
263C8×C47—22no—
264C8×C47—41no—
265C8×C47—41no—
266#21617—471nomaximal, Sylow
267C22×C47C2×C4×D411yescharacteristic
268C22×C47C2×C22⋊Q811yescharacteristic
269C22×C47#52511yescharacteristic
270C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C47#57511yescharacteristic
272C22×C47#57511yescharacteristic
273C22×C47#57511yescharacteristic
274C2×D47—24no—
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—42no—
279C2×D47—42no—
280C2×D47—42no—
281C4×C47—22no—
282C4×C47—22no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—41no—
287C4×C47C2×C4×Q811yescharacteristic
288C4×C47C4×#4111yescharacteristic
289C4×C47#52911yescharacteristic
290C4×C47#53311yescharacteristic
291Dic47—42no—
292Dic47—42no—
293Dic47—42no—
294Dic47—42no—
295Dic47—42no—
296Dic47—81no—
297Dic47—81no—
298C2×#478—471no—
299C4×#125—471no—
300C42×D4—471no—
301#1989—471no—
302#1949—471no—
303#1920—471no—
304#1918—471no—
305#1864—471no—
306#1862—471no—
307#1804—471no—
308#1776—471no—
309#1776—471no—
310#1767D4711yescharacteristic, complemented
311#1762—471no—
312#1762—471no—
313C2×C47C4×C22⋊Q811yescharacteristic
314C2×C47#294311yescharacteristic
315C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
316C2×C47#307711yescharacteristic
317C2×C47#308011yescharacteristic
318C2×C47#311111yescharacteristic
319C2×C47#311411yescharacteristic
320D47—44no—
321C2×#125—471no—
322C2×C4×D4—471no—
323C2×C4×D4—471no—
324C2×C4×D4—471no—
325C22×C42—941no—
326#478—478no—
327C2×#107—471no—
328C2×#107—471no—
329C2×#106—471no—
330C2×#106—471no—
331C2×C4⋊C8C2×D4711yescharacteristic
332C2×C4⋊C8C2×D4711yescharacteristic
333C2×#102—471no—
334C2×#102—471no—
335C2×#102—471no—
336C2×#102—471no—
337C2×#97C2×D4711yescharacteristic
338C2×#97C2×D4711yescharacteristic
339#389—471no—
340#389—471no—
341#387—941no—
342#387—941no—
343#382—471no—
344C4×C4⋊C4—471no—
345C4×C4⋊C4—471no—
346C4×C4⋊C4—471no—
347C4×C4⋊C4—471no—
348C4×C4⋊C4—471no—
349C4×C4⋊C4—941no—
350C4×C4⋊C4—941no—
351C4×C22⋊C4—941no—
352C4×C22⋊C4—941no—
353C4×C22⋊C4—941no—
354C43C2×D4711yescharacteristic
355#340—471no—
356#340—471no—
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#336C2×D4711yescharacteristic
364#336C2×D4711yescharacteristic
365C47#2161711yescharacteristic, complemented, Sylow
366C22×D4—471no—
367C23×C4—941no—
368C23×C4—941no—
369C23×C4—941no—
370C22×C8C22×D4711yescharacteristic
371C22×C8C22×D4711yescharacteristic
372C22×C8C22×D4711yescharacteristic
373C22×C8C22×D4711yescharacteristic
374#125—474no—
375#125—942no—
376C4×D4—474no—
377C4×D4—474no—
378C4×D4—942no—
379C4×D4—942no—
380C4×D4—942no—
381C4×D4—942no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C22⋊C4—941no—
394C2×C22⋊C4—941no—
395C2×C22⋊C4—941no—
396C2×C42—941no—
397C2×C42—941no—
398C2×C42—941no—
399C2×C42—941no—
400C2×C42—941no—
401C2×C42—1884no—
402C2×C42D18811yescharacteristic
403C2×C42D18811yescharacteristic
404C2×C42D18811yescharacteristic
405C2×C42D18811yescharacteristic
406C2×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#107—474no—
410#107—942no—
411#106—474no—
412#106—942no—
413C4⋊C8—22no—
414C4⋊C8C4×D4714yescomplemented
415#102—474no—
416#102—474no—
417#102—942no—
418#102—942no—
419#97—22no—
420#97—22no—
421#95—941no—
422#95—941no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95—941no—
430C24—941no—
431C2×D4—472no—
432C2×D4—472no—
433C2×D4—472no—
434C2×D4—941no—
435C2×D4—941no—
436C2×D4—941no—
437C22×C4—944no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—944no—
444C22×C4—944no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—1882no—
448C22×C4—1882no—
449C22×C4—1882no—
450C22×C4—1882no—
451C22×C4—1882no—
452C22×C4—1882no—
453C22×C4C2×D18811yescharacteristic
454C22×C4C2×D18811yescharacteristic
455C22×C4C2×D18811yescharacteristic
456C22×C4C2×D18811yescharacteristic
457C22×C4C2×D18811yescharacteristic
458C22×C4C2×D18811yescharacteristic
459C22×C4C23×D4711yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C4×D4712yes—
471C2×C8C2×C4×D4712yes—
472C4⋊C4—472no—
473C4⋊C4—472no—
474C4⋊C4—472no—
475C4⋊C4—472no—
476C4⋊C4—472no—
477C4⋊C4—944no—
478C4⋊C4—944no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—1882no—
489C4⋊C4—1882no—
490C22⋊C4—944no—
491C22⋊C4—944no—
492C22⋊C4—944no—
493C42—22no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42—1882no—
500C42—1882no—
501C42—1882no—
502C42—1882no—
503C42—1882no—
504C42C2×C4×D4712yes—
505C42#1062535012yes—
506C42#1062535212yes—
507C42Q8×D4712yes—
508C23—942no—
509C23—942no—
510C23—942no—
511C23—1881no—
512C23—1881no—
513C23—1881no—
514C23—1881no—
515C23C22×D18811yescharacteristic
516D4—474no—
517D4—942no—
518D4—942no—
519D4—942no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—942no—
534C2×C4—942no—
535C2×C4—942no—
536C2×C4—942no—
537C2×C4—942no—
538C2×C4—1888no—
539C2×C4—1888no—
540C2×C4—1888no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4C4×D18812yes—
558C2×C4C4×D18812yes—
559C2×C4#1309400412yes—
560C2×C4#1309400412yes—
561C2×C4#1309405212yes—
562C2×C4C22×C4×D4711yescharacteristic
563C2×C4C2×Q8×D4711yescharacteristic
564C2×C4#41×D4711yescharacteristic
565C2×C4#41×D4711yescharacteristic
566C2×C4C2×#1062535211yescharacteristic
567C2×C4C2×#1062535011yescharacteristic
568C8—22no—
569C8—22no—
570C8—41no—
571C8—41no—
572C22—944no—
573C22—1882no—
574C22—1882no—
575C22—1882no—
576C22—1882no—
577C22—1882no—
578C22—1882no—
579C22C2×C4×D18811yescharacteristic
580C22C2×#1309400411yescharacteristic
581C22#1568963511yescharacteristic
582C22C2×#1309405211yescharacteristic
583C22#1568992311yescharacteristic
584C22#1568992311yescharacteristic
585C22#1568992311yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—3761no—
593C4—3761no—
594C4—1882no—
595C4—1882no—
596C4—1882no—
597C4—1882no—
598C4—1882no—
599C4C4×Q8×D4711yescharacteristic
600C4C4×#1062535211yescharacteristic
601C4#1568965511yescharacteristic
602C4#1568967711yescharacteristic
603C2—1884no—
604C2C4×#1309400411yescharacteristic
605C2#2025219011yescharacteristic
606C2C4×#1309405211yescharacteristic
607C2#2025318711yescharacteristic
608C2#2025321111yescharacteristic
609C2#2025349911yescharacteristic
610C2#2025352811yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1767C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#1767D47
hypocenterC47#21617
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×#13094016C2semidirect
4. #20244343C2semidirect
5. #20244158C2semidirect
6. #20243974C2semidirect
7. #20243960C2semidirect
11. #20243285C2semidirect
12. #20243285C2semidirect
15. C47×#1767C2semidirect
21. #15689424C4semidirect
65. #13094016C2×C4semidirect
93. #13093958C2×C4semidirect
95. #13093956C2×C4semidirect
121. C4⋊C8×C47C2×C4semidirect
310. #1767D47semidirect
365. C47#21617semidirect
414. C4⋊C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894242
C4×#130940162
C42×D1882
#202443432
#202441582
#202439742
#202439602
#202436522
#202436382
#202433992
#202432852
#202432142
C47×#17672
#2161747