Finite Group Databasebeta

← #26236113

Subgroups — #26236113

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689233C211yesmaximal, characteristic
2#20246335C211yesmaximal, characteristic, complemented
3#20244263C211yesmaximal, characteristic
4#20244253C211yesmaximal, characteristic
5#20244015C211yesmaximal, characteristic, complemented
6#20244012C211yesmaximal, characteristic, complemented
7#20244008C211yesmaximal, characteristic, complemented
8#20244005C211yesmaximal, characteristic, complemented
9#20243557C211yesmaximal, characteristic, complemented
10#20243395C211yesmaximal, characteristic, complemented
11#20243388C211yesmaximal, characteristic, complemented
12#20243286C211yesmaximal, characteristic, complemented
13C4×#13093955C211yesmaximal, characteristic, complemented
14#20243263C211yesmaximal, characteristic, complemented
15C47×#2357C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093982—21no—
19#15689233C418yescomplemented
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×#13093935C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689025C2211yescharacteristic
37#15689015—21no—
38#15689015—21no—
39#15688993C2211yescharacteristic
40#15688980—21no—
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#388—21no—
53C47×#388—21no—
54C47×#382C2211yescharacteristic
55C47×#381—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47—21no—
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C2×#10625334—22no—
63C2×#10625334—22no—
64C2×#10625334C2×C414yes—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C4×D188—22no—
70C4×D188C2×C414yes—
71#13093982—44no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84#13093957—22no—
85#13093957—41no—
86#13093955—22no—
87#13093955—41no—
88#13093955C2×C414yes—
89C4⋊(C47⋊C8)—22no—
90#13093945—41no—
91#13093945—41no—
92#13093945C2×C414yes—
93#13093944—41no—
94#13093944—41no—
95#13093944C2×C414yes—
96#13093935—22no—
97#13093935C2×C414yes—
98C4×C47⋊C8—22no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47—21no—
103C4×D4×C47—22no—
104C4×D4×C47C2×C414yes—
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C42×C47—21no—
116C2×C42×C47—21no—
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47D411yescharacteristic
125#95×C47D411yescharacteristic
126C24×C47—21no—
127C23×D47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47C22×C412yes—
134C22×C4×C47—21no—
135C22×C4×C47—24no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—81no—
139C22×C4×C47—81no—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2411yescharacteristic
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188C22×C412yes—
156C2×C4×D47—24no—
157C2×C4×D47—42no—
158C2×C4×D47—42no—
159C4⋊C4×C47—22no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—41no—
166C4⋊C4×C47C22×C412yes—
167C22⋊C4×C47—24no—
168C22⋊C4×C47—42no—
169C22⋊C4×C47—42no—
170C22⋊C4×C47—81no—
171C22⋊C4×C47—81no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—81no—
177C42×C47—81no—
178C42×C47C22×C412yes—
179C42×C47#4112yes—
180#10625334—28no—
181(C2×D47)⋊C4—24no—
182(C2×D47)⋊C4—42no—
183(C2×D47)⋊C4—42no—
184(C2×D47)⋊C4—81no—
185(C2×D47)⋊C4—81no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—42no—
192C4⋊Dic47—81no—
193C4⋊Dic47C22×C412yes—
194C4×Dic47—42no—
195C4×Dic47—42no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8C22×C412yes—
205C2×C47⋊C8C22×C412yes—
206C2×C47⋊C8#4112yes—
207C2×C47⋊C8#4112yes—
208C23×C47—22no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47—41no—
214C23×C47—41no—
215C23×C47C22×D411yescharacteristic
216C22×D47—22no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47—41no—
220C22×D47—41no—
221C22×D47—41no—
222C22×D47—41no—
223D4×C47—22no—
224D4×C47—22no—
225D4×C47—41no—
226D4×C47—41no—
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—22no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—84no—
252C2×C4×C47C4×D412yes—
253C2×C4×C47C4×D412yes—
254C2×C4×C47AGL(1,ℤ/8)12yes—
255C2×C4×C47C23×C411yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C2×C4×C47H(5,𝔽2)11yescharacteristic
260C2×C4×C472−1+411yescharacteristic
261C2×Dic47—22no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270D188—22no—
271D188—22no—
272D188—41no—
273D188—41no—
274C4×D47—48no—
275C47⋊C8—22no—
276C47⋊C8—41no—
277C47⋊C8—41no—
278C47⋊C8#11714yescomplemented
279#22817—471nomaximal, Sylow
280C22×C47—42no—
281C22×C47—42no—
282C22×C47—42no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47—81no—
287C22×C47C2×C4×D411yescharacteristic
288C22×C47#54711yescharacteristic
289C22×C47#55011yescharacteristic
290C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C47#57511yescharacteristic
292C22×C47#57611yescharacteristic
293C22×C47#57711yescharacteristic
294C2×D47—42no—
295C2×D47—42no—
296C2×D47—42no—
297C2×D47—81no—
298C2×D47—81no—
299C2×D47—81no—
300C2×D47—81no—
301C4×C47—22no—
302C4×C47—22no—
303C4×C47—22no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—42no—
308C4×C47—81no—
309C4×C47—81no—
310C4×C47C2×#11711yescharacteristic
311C4×C47#52011yescharacteristic
312C4×C47#55511yescharacteristic
313C4×C47#55611yescharacteristic
314Dic47—42no—
315Dic47—81no—
316Dic47—81no—
317C2×#442—471no—
318#2357D4711yescharacteristic, complemented
319#2354—471no—
320#1972—471no—
321#1970—471no—
322#1926—471no—
323#1926—471no—
324#1925—471no—
325#1925—471no—
326#1847—471no—
327#1804—471no—
328#1802—471no—
329#1776—471no—
330C4×#106—471no—
331#1771—471no—
332C2×C47—82no—
333C2×C47#235411yescharacteristic
334C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
335C2×C47#294611yescharacteristic
336C2×C47#334511yescharacteristic
337C2×C47#334711yescharacteristic
338C2×C47#339911yescharacteristic
339C2×C47#340111yescharacteristic
340D47—82no—
341C22×D8—471no—
342C2×C4×D4—471no—
343C2×C4×D4C2×D4711yescharacteristic
344C2×#117—941no—
345#442—478no—
346C2×#107—471no—
347C2×#107—471no—
348C2×#106—471no—
349C2×#106—471no—
350C2×#106—471no—
351C2×C4⋊C8—471no—
352C2×#102—471no—
353C2×#102—471no—
354C2×#102—471no—
355C2×#102—471no—
356C2×#102—471no—
357C2×#102—471no—
358C2×#97—471no—
359C2×#97—471no—
360C2×C4×C8—471no—
361#390—471no—
362#390—471no—
363#390C2×D4711yescharacteristic
364#390C2×D4711yescharacteristic
365#388—21no—
366#388—21no—
367#388—941no—
368#388—941no—
369#384—471no—
370#382C2×D4711yescharacteristic
371#381—21no—
372#380—941no—
373C4×C4⋊C4—471no—
374C4×C4⋊C4—471no—
375C4×C4⋊C4C2×D4711yescharacteristic
376C4×C4⋊C4C2×D4711yescharacteristic
377C4×C4⋊C4C2×D4711yescharacteristic
378C4×C22⋊C4—21no—
379#340—471no—
380#340—471no—
381#340—471no—
382#340—471no—
383#336—471no—
384#336—471no—
385C47#2281711yescharacteristic, complemented, Sylow
386C22×D4—471no—
387C22×D4C22×D4711yescharacteristic
388C23×C4—21no—
389C23×C4—941no—
390C2×D8—474no—
391C2×D8—942no—
392C2×D8—942no—
393C22×C8—471no—
394C22×C8—471no—
395C22×C8—471no—
396C22×C8—471no—
397C4×D4—22no—
398C4×D4—474no—
399C4×D4—942no—
400C4×D4C4×D4714yes—
401#117—1884no—
402C2×C4⋊C4—471no—
403C2×C4⋊C4—471no—
404C2×C4⋊C4—471no—
405C2×C4⋊C4—941no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4C22⋊D4711yescharacteristic
408C2×C4⋊C4C22⋊D4711yescharacteristic
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C4⋊C4C22×D4711yescharacteristic
411C2×C4⋊C4C22×D4711yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—941no—
419C2×C22⋊C4—941no—
420C2×C22⋊C4—941no—
421C2×C22⋊C4—941no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—941no—
425C2×C42—941no—
426C2×C42C22×D4711yescharacteristic
427C2×C42C22×D4711yescharacteristic
428C2×C42C22×D4711yescharacteristic
429#107—942no—
430#107—1881no—
431#106—474no—
432#106—942no—
433#106—1881no—
434C4⋊C8—942no—
435#102—474no—
436#102—474no—
437#102—1881no—
438#102—1881no—
439#102—1881no—
440#102—1881no—
441#97—474no—
442#97—942no—
443C4×C8—942no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—941no—
449#95—941no—
450#95C22⋊D4711yescharacteristic
451#95C22⋊D4711yescharacteristic
452C24—21no—
453C24—941no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—472no—
460C2×D4—941no—
461C2×D4—941no—
462C2×D4—941no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4C2×C4×D4712yes—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—941no—
473C22×C4—944no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—1882no—
477C22×C4—1882no—
478C22×C4C2×C22⋊D4711yescharacteristic
479C22×C4C2×C22⋊D4711yescharacteristic
480C22×C4C2×C22⋊D4711yescharacteristic
481C22×C4C2×C22⋊D4711yescharacteristic
482C22×C4C2×C22⋊D4711yescharacteristic
483C22×C4C2×C22⋊D4711yescharacteristic
484C22×C4C23×D4711yescharacteristic
485D8—948no—
486C2×C8—472no—
487C2×C8—472no—
488C2×C8—472no—
489C2×C8—472no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—941no—
497C2×C8—941no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—472no—
506C4⋊C4—941no—
507C4⋊C4—941no—
508C4⋊C4—941no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—3761no—
512C4⋊C4—1882no—
513C4⋊C4C2×C4×D4712yes—
514C22⋊C4—24no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C22⋊C4—944no—
520C22⋊C4—3761no—
521C22⋊C4—3761no—
522C22⋊C4—1882no—
523C22⋊C4—1882no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—81no—
529C42—81no—
530C42—1882no—
531C42—1882no—
532C42C2×C4×D4712yes—
533C42#1062535012yes—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—942no—
542C23—1881no—
543C23—1881no—
544C23—1881no—
545C23—1881no—
546C23—1881no—
547C23—1881no—
548C23C22×C22⋊D4711yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—942no—
554D4—942no—
555D4—1881no—
556D4—1881no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—942no—
583C2×C4—1888no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4C4×C22⋊D4712yes—
593C2×C4C4×C22⋊D4712yes—
594C2×C4#1309404912yes—
595C2×C4C22×C4×D4711yescharacteristic
596C2×C4#41×D4711yescharacteristic
597C2×C4#41×D4711yescharacteristic
598C2×C4C2×#1062535011yescharacteristic
599C2×C4#1309407011yescharacteristic
600C2×C4#1309407111yescharacteristic
601C8—474no—
602C8—942no—
603C8—1881no—
604C8—1881no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—3761no—
613C22—3761no—
614C22—3761no—
615C22—3761no—
616C22—1882no—
617C22—1882no—
618C22—1882no—
619C22C2×C4×C22⋊D4711yescharacteristic
620C22#1568977211yescharacteristic
621C22#1568979211yescharacteristic
622C22C2×#1309404911yescharacteristic
623C22#1568992111yescharacteristic
624C22#1568992611yescharacteristic
625C22#1568993411yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—3761no—
636C4—3761no—
637C4—1882no—
638C4#117×D4711yescharacteristic
639C4#1568960311yescharacteristic
640C4#1568983611yescharacteristic
641C4#1568984111yescharacteristic
642C2—82no—
643C2—3762no—
644C2#2024633811yescharacteristic
645C2C4×#1309404911yescharacteristic
646C2#2025222011yescharacteristic
647C2#2025585211yescharacteristic
648C2#2025588211yescharacteristic
649C2#2025642611yescharacteristic
650C2#2025644811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2357C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
cosocleC22×C4×C47C24
hypercenter#2357D47
hypocenterC47#22817
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #20246335C2semidirect
5. #20244015C2semidirect
6. #20244012C2semidirect
7. #20244008C2semidirect
8. #20244005C2semidirect
9. #20243557C2semidirect
10. #20243395C2semidirect
11. #20243388C2semidirect
12. #20243286C2semidirect
13. C4×#13093955C2semidirect
14. #20243263C2semidirect
15. C47×#2357C2semidirect
19. #15689233C4semidirect
278. C47⋊C8#117semidirect
318. #2357D47semidirect
385. C47#22817semidirect

Maximal subgroups

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

subgroupindex
C2×#156892332
#202463352
#202442632
#202442532
#202440152
#202440122
#202440082
#202440052
#202435572
#202433952
#202433882
#202432862
C4×#130939552
#202432632
C47×#23572
#2281747