Finite Group Databasebeta

← #26186210

Subgroups — #26186210

Order 12032.

766 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253386C211yesmaximal, characteristic
2#20252095C211yesmaximal, characteristic, complemented
3C8×D4×D47C211yesmaximal, characteristic, complemented
4#20242255C211yesmaximal, characteristic, complemented
5#20242253C211yesmaximal, characteristic, complemented
6#20242251C211yesmaximal, characteristic, complemented
7#20242249C211yesmaximal, characteristic, complemented
8#20242213C211yesmaximal, characteristic, complemented
9#20242210C211yesmaximal, characteristic, complemented
10#20242210C211yesmaximal, characteristic, complemented
11#20242157C211yesmaximal, characteristic, complemented
12#20241811C211yesmaximal, characteristic, complemented
13#20241785C211yesmaximal, characteristic, complemented
14#20241679C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C2×#13094030—21no—
17C22×C8×D47—21no—
18#15689670C2211yescharacteristic
19C4×D4×D47C2211yescharacteristic
20#15689438C411yescharacteristic
21#15689435C411yescharacteristic
22#15689402C411yescharacteristic
23#15689401C411yescharacteristic
24#15689317C411yescharacteristic
25#15689316C411yescharacteristic
26#15689258C411yescharacteristic
27#15689255C411yescharacteristic
28C4×D376C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689201C2211yescharacteristic, complemented
32#15689200C2211yescharacteristic, complemented
33#15689198—21no—
34C8×D188C2211yescharacteristic
35C8×D188C2211yescharacteristic, complemented
36D4×C47⋊C8C2211yescharacteristic
37#15689188C2211yescharacteristic
38C8×C22⋊D47—21no—
39C8×C22⋊D47—21no—
40(C22⋊D47)⋊C8—21no—
41#15689174C2211yescharacteristic
42#15689174C2211yescharacteristic
43#15689145C2211yescharacteristic
44C4⋊C8×D47C2211yescharacteristic
45#15689088—21no—
46C22⋊C8×D47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688874C2211yescharacteristic, complemented
49#15688873C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688852C2211yescharacteristic
52#15688852C2211yescharacteristic, complemented
53D4⋊(C47⋊C8)C2211yescharacteristic
54D4⋊(C47⋊C8)C2211yescharacteristic, complemented
55#15688850C2211yescharacteristic
56#15688850C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59#15688844C2211yescharacteristic, complemented
60C4×D8×C47C2211yescharacteristic
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic, complemented
63C47×#334C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic, complemented
66C47×#322C2211yescharacteristic, complemented
67C2×#10625350—21no—
68C2×D4×D47C2×C411yescharacteristic
69C22×C4×D47—21no—
70C2×D376C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625334C2×C411yescharacteristic
73#13094030—44no—
74C2×#10625329—21no—
75C2×#10625324—21no—
76C2×#10625324—21no—
77C22×C47⋊C8—21no—
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80C2×C8×D47—21no—
81C2×C8×D47—21no—
82C2×C8×D47—44no—
83C2×C8×D47D411yescharacteristic
84C2×C8×D47D411yescharacteristic
85#13094023C2×C411yescharacteristic
86#13094020C2×C411yescharacteristic
87#13094010—21no—
88#13093999C2×C411yescharacteristic
89#13093997—21no—
90#13093995C2×C411yescharacteristic
91C4×D188C2311yescharacteristic
92C4×D188C2311yescharacteristic
93D4×Dic47C2×C411yescharacteristic
94#13093986C2×C411yescharacteristic
95C4×C22⋊D47—21no—
96C4×C22⋊D47—21no—
97(C22⋊D47)⋊C4—21no—
98C4⋊C4×D47C2×C411yescharacteristic
99C22⋊C4×D47—21no—
100C42×D47C2311yescharacteristic
101#13093958C2×C411yescharacteristic
102#13093957C2×C411yescharacteristic
103#13093957C2×C411yescharacteristic
104C4⋊(C47⋊C8)C2311yescharacteristic
105C4⋊(C47⋊C8)C2311yescharacteristic
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109Dic47⋊C8C2×C411yescharacteristic
110Dic47⋊C8C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093945C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116#13093944C2×C411yescharacteristic
117C22⋊(C47⋊C8)—21no—
118C22⋊(C47⋊C8)—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121(C2×D47)⋊C8—21no—
122(C2×D47)⋊C8—21no—
123(C2×D47)⋊C8—21no—
124(C2×D47)⋊C8C2×C411yescharacteristic
125(C2×D47)⋊C8C2×C411yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C4×C47⋊C8C2311yescharacteristic
129C8×Dic47D411yescharacteristic
130C8×Dic47D411yescharacteristic
131C2×D8×C47C2×C411yescharacteristic
132C22×C8×C47—21no—
133C22×C8×C47—21no—
134C4×D4×C47C2311yescharacteristic
135C4×D4×C47C2311yescharacteristic
136#107×C47C2×C411yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139#102×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141C22⋊C8×C47—21no—
142C22⋊C8×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C4×C8×C47C2311yescharacteristic
146C23×D47—21no—
147C2×D4×C47C22×C411yescharacteristic
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C2×C22⋊D47—21no—
152C2×C22⋊D47—21no—
153C2×C22⋊D47—21no—
154C2×C22⋊D47—21no—
155C22×Dic47—21no—
156D4×D47—22no—
157D4×D47—22no—
158#10625350—42no—
159#10625350—42no—
160C2×D188—21no—
161C2×D188C22×C411yescharacteristic
162C2×D188C22×C411yescharacteristic
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—42no—
168C2×C4×D47—42no—
169C2×C4×D47C22×C411yescharacteristic
170C2×C4×D47C2×D411yescharacteristic
171C2×C4×D47#4111yescharacteristic
172C2×Dic94—21no—
173D8×C47—22no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—42no—
178C2×C8×C47—42no—
179C2×C8×C47C22×C411yescharacteristic
180C2×C8×C47C22×C411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C4⋊C4×C47C22×C411yescharacteristic
184C4⋊C4×C47C22×C411yescharacteristic
185C22⋊C4×C47—21no—
186C22⋊C4×C47—21no—
187C42×C47C2411yescharacteristic
188C22⋊Dic47—21no—
189C22⋊Dic47—21no—
190#10625334—22no—
191#10625334—22no—
192(C2×D47)⋊C4—21no—
193(C2×D47)⋊C4—21no—
194(C2×D47)⋊C4—21no—
195(C2×D47)⋊C4—21no—
196C4⋊Dic47C22×C411yescharacteristic
197C4⋊Dic47C22×C411yescharacteristic
198Dic47⋊C4—21no—
199Dic47⋊C4—21no—
200C4×Dic47C22×C411yescharacteristic
201C4×Dic47C2×D411yescharacteristic
202C4×Dic47#4111yescharacteristic
203#10625329—42no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—42no—
208C2×C47⋊C8C22×C411yescharacteristic
209C2×C47⋊C8C22×C411yescharacteristic
210C2×C47⋊C8C2×D411yescharacteristic
211C2×C47⋊C8C2×D411yescharacteristic
212D376—22no—
213#10625324—42no—
214#10625324—42no—
215C8×D47—22no—
216C8×D47—22no—
217C8×D47—42no—
218C8×D47—42no—
219C8×D47—42no—
220C8×D47—42no—
221C23×C47—21no—
222C23×C47—21no—
223C22×D47—24no—
224C22×D47—21no—
225C22×D47—21no—
226C22×D47—42no—
227C22×D47—42no—
228C22×D47C4×D411yescharacteristic
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—21no—
232D4×C47#13112yescomplemented
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47C23×C411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C22⋊D47—24no—
243C22⋊D47—42no—
244C22⋊D47—42no—
245C22⋊D47—42no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—42no—
249C2×Dic47C4×D411yescharacteristic
250C2×Dic47C4×D411yescharacteristic
251C2×Dic47C4×D411yescharacteristic
252D188—21no—
253D188—21no—
254D188—21no—
255D188—42no—
256D188#13112yescomplemented
257C4×D47—21no—
258C4×D47—21no—
259C4×D47—41no—
260C4×D47—42no—
261C4×D47—41no—
262C4×D47—41no—
263C4×D47—41no—
264C4×D47—41no—
265C4×D47—42no—
266C4×D47AGL(1,ℤ/8)12yes—
267C4×D47AGL(1,ℤ/8)12yes—
268Dic94—42no—
269C8×C47—21no—
270C8×C47—21no—
271C8×C47—21no—
272C8×C47—21no—
273C8×C47—41no—
274C8×C47—41no—
275C8×C47—41no—
276C47⋊C8—21no—
277C47⋊C8—21no—
278C47⋊C8—21no—
279C47⋊C8—21no—
280C47⋊C8—41no—
281C47⋊C8—41no—
282C47⋊C8—41no—
283#17907—471nomaximal, Sylow
284C22×C47—22no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47C2×C4×D411yescharacteristic
291C2×D47—21no—
292C2×D47—21no—
293C2×D47—22no—
294C2×D47—48no—
295C2×D47—41no—
296C2×D47—41no—
297C2×D47—41no—
298C2×D47—41no—
299C2×D47—41no—
300C2×D47#44212yes—
301C4×C47—21no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47C2×#13111yescharacteristic
305C4×C47C2×#13111yescharacteristic
306C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
308Dic47—21no—
309Dic47—21no—
310Dic47—41no—
311Dic47—41no—
312Dic47#44212yes—
313#3100—471no—
314#2931—471no—
315C2×C8×D4—471no—
316#1586—471no—
317#1586—471no—
318#1586—471no—
319#1586—471no—
320#1580—471no—
321#1580—471no—
322#1580—471no—
323#1580D4711yescharacteristic, complemented
324#1570—471no—
325#1486—471no—
326#1480—471no—
327#1452—471no—
328C2×C47—42no—
329C2×C47—81no—
330C2×C47#292911yescharacteristic
331C2×C47C2×#44211yescharacteristic
332C2×C47#295511yescharacteristic
333D47—22no—
334D47—42no—
335D47—81no—
336C2×#131—941no—
337C23×C8—941no—
338#532—471no—
339C2×C4×D4—471no—
340#480—471no—
341#480—471no—
342#474—471no—
343#474—471no—
344#459—471no—
345#459—471no—
346#447—471no—
347#447—471no—
348C4×D8—471no—
349C4×D8—471no—
350C4×D8—471no—
351C4×D8C2×D4711yescharacteristic
352#436—471no—
353#436—471no—
354#436—941no—
355C8×D4—471no—
356C8×D4—471no—
357C8×D4—471no—
358C8×D4—471no—
359C8×D4—941no—
360C8×D4—941no—
361C8×D4—941no—
362C8×D4C2×D4711yescharacteristic
363C8×D4C2×D4711yescharacteristic, complemented
364#431—471no—
365#431—471no—
366#423—471no—
367C2×C4⋊C8—471no—
368#408—941no—
369C2×C22⋊C8—941no—
370C2×C4×C8—471no—
371#334—471no—
372#334—471no—
373#334—471no—
374#334C2×D4711yescharacteristic, complemented
375D4⋊C8—471no—
376D4⋊C8—471no—
377D4⋊C8—471no—
378D4⋊C8—471no—
379D4⋊C8—471no—
380D4⋊C8—471no—
381D4⋊C8C2×D4711yescharacteristic
382D4⋊C8C2×D4711yescharacteristic, complemented
383#322—471no—
384#322—471no—
385#322—471no—
386#322C2×D4711yescharacteristic, complemented
387C47#1790711yescharacteristic, complemented, Sylow
388C2×#41—941no—
389C22×D4—471no—
390C23×C4—941no—
391C2×D8—471no—
392C2×D8—471no—
393C2×D8—471no—
394C2×D8C4×D4711yescharacteristic
395#131—1884no—
396C2×M16—941no—
397C2×M16—941no—
398C2×M16—941no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—471no—
402C22×C8—471no—
403C22×C8—941no—
404C22×C8—941no—
405C22×C8—941no—
406C22×C8—941no—
407C22×C8—941no—
408C22×C8—1884no—
409C4⋊Q8—471no—
410#127—471no—
411#124—941no—
412#121—471no—
413#121—471no—
414#121—941no—
415C4×D4—471no—
416C4×D4—471no—
417C4×D4—471no—
418C4×D4—471no—
419C4×D4—941no—
420C4×D4—941no—
421C4×D4—941no—
422C4×D4C22×D4711yescharacteristic
423C4×D4C22×D4711yescharacteristic
424C2×C4⋊C4—471no—
425C2×C22⋊C4—941no—
426C2×C42—471no—
427#107—471no—
428#107—471no—
429#107—471no—
430#107C4×D4711yescharacteristic
431C4⋊C8—471no—
432C4⋊C8—471no—
433C4⋊C8—471no—
434C4⋊C8—471no—
435C4⋊C8—941no—
436C4⋊C8—941no—
437C4⋊C8—941no—
438C4⋊C8C22×D4711yescharacteristic
439C4⋊C8C22×D4711yescharacteristic
440#102—471no—
441#102—471no—
442#102—471no—
443#102—471no—
444#102—471no—
445#102—471no—
446#102C4×D4711yescharacteristic
447#102C4×D4711yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—471no—
451C22⋊C8—471no—
452C22⋊C8—941no—
453C22⋊C8—941no—
454C22⋊C8—941no—
455C22⋊C8—941no—
456C22⋊C8—941no—
457C22⋊C8—941no—
458C22⋊C8—941no—
459C4×C8—471no—
460C4×C8—471no—
461C4×C8—471no—
462C4×C8—471no—
463C4×C8—471no—
464C4×C8C22×D4711yescharacteristic
465C4×C8C22×D4711yescharacteristic
466C4×C8C22×D4711yescharacteristic
467C24—941no—
468#41—1882no—
469#41—1882no—
470C2×Q8—941no—
471C2×D4—471no—
472C2×D4—471no—
473C2×D4—941no—
474C2×D4—941no—
475C2×D4—941no—
476C2×D4—941no—
477C2×D4—942no—
478C2×D4—942no—
479C2×D4—941no—
480C2×D4C2×C4×D4711yescharacteristic
481C2×D4C2×C4×D4711yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—471no—
485C22×C4—471no—
486C22×C4—471no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—1882no—
493C22×C4—1882no—
494D8—22no—
495D8—942no—
496D8—942no—
497D8—942no—
498M16—1882no—
499M16—1882no—
500M16—1882no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8—42no—
506C2×C8—471no—
507C2×C8—471no—
508C2×C8—471no—
509C2×C8—471no—
510C2×C8—942no—
511C2×C8—942no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—1882no—
516C2×C8—1882no—
517C2×C8—1882no—
518C2×C8—1882no—
519C2×C8—1882no—
520C2×C8C2×C4×D4711yescharacteristic
521C2×C8C2×C4×D4711yescharacteristic
522C2×C8D4×D4711yescharacteristic
523C2×C8D4×D4711yescharacteristic
524C4⋊C4—471no—
525C4⋊C4—471no—
526C4⋊C4—941no—
527C4⋊C4—941no—
528C4⋊C4C2×C4×D4711yescharacteristic
529C4⋊C4C2×C4×D4711yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—941no—
533C22⋊C4—941no—
534C22⋊C4—941no—
535C22⋊C4—941no—
536C22⋊C4—941no—
537C22⋊C4—941no—
538C42—471no—
539C42—471no—
540C42—471no—
541C42C23×D4711yescharacteristic
542C23—21no—
543C23—21no—
544C23—471no—
545C23—944no—
546C23—941no—
547C23—941no—
548C23—1882no—
549C23—1882no—
550Q8—1882no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—472no—
555D4—944no—
556D4—941no—
557D4—941no—
558D4—941no—
559D4—1882no—
560D4—1882no—
561D4—1882no—
562D4—1882no—
563D4#1309403012yescomplemented
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—471no—
571C2×C4—472no—
572C2×C4—472no—
573C2×C4—471no—
574C2×C4—471no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—1881no—
580C2×C4—1882no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4C22×C4×D4711yescharacteristic
588C2×C4C2×D4×D4711yescharacteristic
589C2×C4#41×D4711yescharacteristic
590C8—21no—
591C8—21no—
592C8—21no—
593C8—21no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—941no—
598C8—941no—
599C8—941no—
600C8—941no—
601C8—1881no—
602C8—1881no—
603C8—1881no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—472no—
611C22—941no—
612C22—941no—
613C22—942no—
614C22—1888no—
615C22—1881no—
616C22—1881no—
617C22—1881no—
618C22—1881no—
619C22—1881no—
620C22C4×D4×D4711yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—472no—
625C4—941no—
626C4—941no—
627C4—1881no—
628C4—1881no—
629C4#131×D4711yescharacteristic
630C4C2×#1309403011yescharacteristic
631C4AGL(1,ℤ/8)×D4711yescharacteristic
632C4AGL(1,ℤ/8)×D4711yescharacteristic
633C2—42no—
634C2—81no—
635C2—942no—
636C2—3761no—
637C2—1882no—
638C2#2025207711yescharacteristic
639C2#442×D4711yescharacteristic
640C2#2025228811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1580C2
socleC22×C47C2×C4×D4
prime radical#20253386C2
cosocleC42×C47C24
hypercenter#1580D47
hypocenterC47#17907
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #20252095C2semidirect
3. C8×D4×D47C2semidirect
4. #20242255C2semidirect
5. #20242253C2semidirect
6. #20242251C2semidirect
7. #20242249C2semidirect
8. #20242213C2semidirect
9. #20242210C2semidirect
10. #20242210C2semidirect
11. #20242157C2semidirect
12. #20241811C2semidirect
13. #20241785C2semidirect
14. #20241679C2semidirect
15. C47×#1580C2semidirect
31. #15689201C22semidirect
32. #15689200C22semidirect
35. C8×D188C22semidirect
48. #15688874C22semidirect
49. #15688873C22semidirect
50. #15688873C22semidirect
52. #15688852C22semidirect
54. D4⋊(C47⋊C8)C22semidirect
56. #15688850C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688844C22semidirect
62. C8×D4×C47C22semidirect
63. C47×#334C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×#322C22semidirect
232. D4×C47#131semidirect
256. D188#131semidirect
323. #1580D47semidirect
363. C8×D4C2×D47semidirect
374. #334C2×D47semidirect
382. D4⋊C8C2×D47semidirect
386. #322C2×D47semidirect
387. C47#17907semidirect
563. D4#13094030semidirect

Maximal subgroups

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

subgroupindex
#202533862
#202520952
C8×D4×D472
#202422552
#202422532
#202422512
#202422492
#202422132
#202422102
#202421572
#202418112
#202417852
#202416792
C47×#15802
#1790747