Finite Group Databasebeta

← #26187689

Subgroups — #26187689

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252548C211yesmaximal, characteristic, complemented
2#20252520C211yesmaximal, characteristic, complemented
3#20242291C211yesmaximal, characteristic, complemented
4#20242273C211yesmaximal, characteristic, complemented
5#20242267C211yesmaximal, characteristic, complemented
6#20242267C211yesmaximal, characteristic, complemented
7#20242239C211yesmaximal, characteristic, complemented
8#20242218C211yesmaximal, characteristic, complemented
9SD16⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
10Q16×C47⋊C8C211yesmaximal, characteristic, complemented
11#20242163C211yesmaximal, characteristic, complemented
12#20241853C211yesmaximal, characteristic, complemented
13#20241775C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#3102C211yesmaximal, characteristic
16#15689254C2211yescharacteristic
17Q8×C47⋊C8C2211yescharacteristic
18Q8×C47⋊C8C2211yescharacteristic
19Q8×C47⋊C8C2211yescharacteristic
20#15689201—21no—
21#15689201—21no—
22#15689201C2211yescharacteristic
23#15689201C2211yescharacteristic
24#15689201C2211yescharacteristic
25#15689195—21no—
26D4×C47⋊C8—21no—
27D4×C47⋊C8C2211yescharacteristic
28#15689184—21no—
29#15689176—21no—
30#15689176C2211yescharacteristic
31#15689176C2211yescharacteristic
32#15689150—21no—
33#15689147—21no—
34#15689147C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36#15688876C2211yescharacteristic
37#15688876C2211yescharacteristic
38#15688876C2211yescharacteristic
39#15688876C2211yescharacteristic
40Q8⋊(C47⋊C8)C2211yescharacteristic
41Q8⋊(C47⋊C8)C2211yescharacteristic
42Q8⋊(C47⋊C8)C2211yescharacteristic
43Q8⋊(C47⋊C8)C2211yescharacteristic
44D4⋊(C47⋊C8)C2211yescharacteristic
45D4⋊(C47⋊C8)C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48#15688845C2211yescharacteristic
49#15688845C2211yescharacteristic
50#15688844C2211yescharacteristic
51C8×C47⋊C8C2211yescharacteristic
52C47×#529C2211yescharacteristic
53C4×#41×C47C2211yescharacteristic
54C47×#485C411yescharacteristic
55C47×#482C411yescharacteristic
56C47×#479C411yescharacteristic
57C47×#478C411yescharacteristic
58C47×#464C411yescharacteristic
59C47×#463C411yescharacteristic
60C47×#452C411yescharacteristic
61C47×#449C411yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C4×SD16×C47C2211yescharacteristic
64C4×SD16×C47C2211yescharacteristic
65C4×D8×C47C2211yescharacteristic
66C47×#431C2211yescharacteristic
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C22×C47⋊C8—21no—
72C22×C47⋊C8—21no—
73C4⋊(C47⋊C8)—21no—
74C4⋊(C47⋊C8)—21no—
75C4⋊(C47⋊C8)—21no—
76C4⋊(C47⋊C8)—21no—
77C4⋊(C47⋊C8)—21no—
78C4⋊(C47⋊C8)—21no—
79C4⋊(C47⋊C8)—21no—
80C4⋊(C47⋊C8)D411yescharacteristic
81C4⋊(C47⋊C8)D411yescharacteristic
82C4⋊(C47⋊C8)C2311yescharacteristic
83C4⋊(C47⋊C8)C2311yescharacteristic
84C4⋊(C47⋊C8)C2311yescharacteristic
85C4⋊(C47⋊C8)C2311yescharacteristic
86C22⋊(C47⋊C8)—21no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)D411yescharacteristic
92C22⋊(C47⋊C8)D411yescharacteristic
93#13093935—21no—
94C4×C47⋊C8—21no—
95C4×C47⋊C8—21no—
96C4×C47⋊C8—21no—
97C4×C47⋊C8C2311yescharacteristic
98C4×C47⋊C8C2311yescharacteristic
99C4×C47⋊C8C2311yescharacteristic
100C4×C47⋊C8C2311yescharacteristic
101C2×#41×C47C2×C411yescharacteristic
102C2×Q16×C47C2×C411yescharacteristic
103C2×SD16×C47C2×C411yescharacteristic
104C2×SD16×C47C2×C411yescharacteristic
105C2×D8×C47C2×C411yescharacteristic
106#126×C47—21no—
107#125×C47C2×C411yescharacteristic
108#124×C47C2×C411yescharacteristic
109#123×C47—21no—
110C22⋊Q8×C47C2×C411yescharacteristic
111#121×C47C2×C411yescharacteristic
112C4×Q8×C47C2×C411yescharacteristic
113C4×Q8×C47C2311yescharacteristic
114C4×Q8×C47C2311yescharacteristic
115C4×D4×C47—21no—
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47C2×C411yescharacteristic
119C4×D4×C47C2311yescharacteristic
120C4×D4×C47C2311yescharacteristic
121#117×C47—21no—
122#117×C47—21no—
123#117×C47C2×C411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126#107×C47C2×C411yescharacteristic
127#107×C47C2×C411yescharacteristic
128#106×C47C2×C411yescharacteristic
129#106×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47C2×C411yescharacteristic
132#103×C47C2×C411yescharacteristic
133#103×C47C2×C411yescharacteristic
134#103×C47C2×C411yescharacteristic
135#103×C47C2×C411yescharacteristic
136#102×C47C2×C411yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141C22⋊C8×C47C2×C411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—41no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×Q8×C47C22×C411yescharacteristic
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47C22×C411yescharacteristic
151C2×D4×C47C22×C411yescharacteristic
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47#4111yescharacteristic
159Q16×C47—22no—
160SD16×C47—22no—
161SD16×C47—41no—
162D8×C47—41no—
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C22×C411yescharacteristic
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C4⋊C4×C47C22×C411yescharacteristic
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C22⋊C4×C47—21no—
181C22⋊C4×C47—21no—
182C22⋊C4×C47—21no—
183C22⋊C4×C47—21no—
184C22⋊C4×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47C22×C411yescharacteristic
190C42×C47C2×D411yescharacteristic
191C42×C47#4111yescharacteristic
192C42×C47C2411yescharacteristic
193#10625329—81no—
194#10625329—81no—
195#10625329—81no—
196#10625329—81no—
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—81no—
204C2×C47⋊C8—81no—
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C23×C47—21no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47#13112yes—
216D4×C47—21no—
217D4×C47—21no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47—42no—
221D4×C47—42no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259#18033—471nomaximal, Sylow
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47C2×C4×D411yescharacteristic
270C4×C47—21no—
271C4×C47—22no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47C2×#13111yescharacteristic
281C4×C47#56811yescharacteristic
282C4×C47#57611yescharacteristic
283C4×C47#57811yescharacteristic
284#3102D4711yescharacteristic
285#2994—471no—
286#2991—471no—
287#1592—471no—
288#1589—471no—
289#1588—471no—
290#1588—471no—
291#1584—471no—
292#1581—471no—
293SD16⋊C8—471no—
294C8×Q16—471no—
295#1571—471no—
296#1495—471no—
297#1477—471no—
298#1454—471no—
299C2×C47—41no—
300C2×C47—81no—
301C2×C47—81no—
302C2×C47#293311yescharacteristic
303C2×C47#295111yescharacteristic
304C2×C47#295511yescharacteristic
305#529C2×D4711yescharacteristic
306C4×#41C2×D4711yescharacteristic
307#485Dic4711yescharacteristic
308#482Dic4711yescharacteristic
309#479Dic4711yescharacteristic
310#478Dic4711yescharacteristic
311#464Dic4711yescharacteristic
312#463Dic4711yescharacteristic
313#452Dic4711yescharacteristic
314#449Dic4711yescharacteristic
315#446—471no—
316C8×Q8—471no—
317C8×Q8—471no—
318C8×Q8—471no—
319C4×Q16C2×D4711yescharacteristic
320C4×SD16C2×D4711yescharacteristic
321C4×SD16C2×D4711yescharacteristic
322C4×D8C2×D4711yescharacteristic
323#436—471no—
324#436—471no—
325#436—471no—
326#436—941no—
327#436—941no—
328#435—941no—
329C8×D4—471no—
330C8×D4—941no—
331#433—941no—
332#431—471no—
333#431—471no—
334#431—941no—
335#431C2×D4711yescharacteristic
336#424—941no—
337#423—471no—
338#423—941no—
339C2×C4⋊C8—471no—
340#335—471no—
341#335—471no—
342#335—471no—
343#335—471no—
344Q8⋊C8—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348D4⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8—471no—
352#322—471no—
353#322—471no—
354#322—471no—
355C82—471no—
356C47#1803311yescharacteristic, complemented, Sylow
357C2×#41C2×Dic4711yescharacteristic
358C2×Q16C2×Dic4711yescharacteristic
359C2×SD16C2×Dic4711yescharacteristic
360C2×SD16C2×Dic4711yescharacteristic
361C2×D8C2×Dic4711yescharacteristic
362C2×M16—941no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C22×C8—941no—
367C22×C8—941no—
368#126—21no—
369#125C2×Dic4711yescharacteristic
370#124C2×Dic4711yescharacteristic
371#123—21no—
372C22⋊Q8C2×Dic4711yescharacteristic
373#121C2×Dic4711yescharacteristic
374C4×Q8C2×Dic4711yescharacteristic
375C4×Q8C22×D4711yescharacteristic
376C4×Q8C22×D4711yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×Dic4711yescharacteristic
381C4×D4C22×D4711yescharacteristic
382C4×D4C22×D4711yescharacteristic
383#117—21no—
384#117—21no—
385#117C2×Dic4711yescharacteristic
386C2×C42—21no—
387C2×C42C22×D4711yescharacteristic
388#107C2×Dic4711yescharacteristic
389#107C2×Dic4711yescharacteristic
390#106C2×Dic4711yescharacteristic
391#106C2×Dic4711yescharacteristic
392C4⋊C8—471no—
393C4⋊C8—471no—
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8—941no—
404C4⋊C8—941no—
405C4⋊C8C2×Dic4711yescharacteristic
406C4⋊C8C2×Dic4711yescharacteristic
407#103C2×Dic4711yescharacteristic
408#103C2×Dic4711yescharacteristic
409#103C2×Dic4711yescharacteristic
410#103C2×Dic4711yescharacteristic
411#102C2×Dic4711yescharacteristic
412#102C2×Dic4711yescharacteristic
413#102C2×Dic4711yescharacteristic
414#102C2×Dic4711yescharacteristic
415C22⋊C8—471no—
416C22⋊C8—471no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420C22⋊C8—941no—
421C22⋊C8—941no—
422C22⋊C8C2×Dic4711yescharacteristic
423C22⋊C8C2×Dic4711yescharacteristic
424#97—941no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434#41—22no—
435#41—41no—
436C2×Q8C22×Dic4711yescharacteristic
437C2×Q8C22×Dic4711yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×Dic4711yescharacteristic
441C2×D4C22×Dic4711yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4D4×D4711yescharacteristic
447C22×C4#1062535211yescharacteristic
448C22×C4C22×Dic4711yescharacteristic
449Q16—22no—
450SD16—22no—
451SD16—41no—
452D8—41no—
453M16—3761no—
454M16—3761no—
455M16—3761no—
456M16—3761no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—3761no—
468C2×C8—3761no—
469C2×C8C22×Dic4711yescharacteristic
470C2×C8C22×Dic4711yescharacteristic
471C2×C8C22×Dic4711yescharacteristic
472C2×C8C22×Dic4711yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C22×Dic4711yescharacteristic
480C4⋊C4C22×Dic4711yescharacteristic
481C4⋊C4C22×Dic4711yescharacteristic
482C4⋊C4C22×Dic4711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42D4×D4711yescharacteristic
496C42#1062535211yescharacteristic
497C42C22×Dic4711yescharacteristic
498C42C23×D4711yescharacteristic
499C23—21no—
500C23—21no—
501C23D4×Dic4711yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8#1309403112yes—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—42no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4D4×Dic4711yescharacteristic
530C2×C4D4×Dic4711yescharacteristic
531C2×C4D4×Dic4711yescharacteristic
532C2×C4C23×Dic4711yescharacteristic
533C2×C4C2×D4×D4711yescharacteristic
534C2×C4C2×#1062535211yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—941no—
540C8—941no—
541C8—941no—
542C8—941no—
543C8—1881no—
544C8—1881no—
545C8—1881no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C2×D4×Dic4711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4C2×#1309403111yescharacteristic
570C4#1568989011yescharacteristic
571C4#1568992511yescharacteristic
572C4#1568993711yescharacteristic
573C2—41no—
574C2—81no—
575C2—81no—
576C2#2025211511yescharacteristic
577C2#2025226411yescharacteristic
578C2#2025229111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#3102C2
socleC22×C47C2×C4×D4
prime radicalC47×#449C4
cosocleC42×C47C24
hypercenter#3102D47
hypocenterC47#18033
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #20252548C2semidirect
2. #20252520C2semidirect
3. #20242291C2semidirect
4. #20242273C2semidirect
5. #20242267C2semidirect
6. #20242267C2semidirect
7. #20242239C2semidirect
8. #20242218C2semidirect
9. SD16⋊(C47⋊C8)C2semidirect
10. Q16×C47⋊C8C2semidirect
11. #20242163C2semidirect
12. #20241853C2semidirect
13. #20241775C2semidirect
14. #20241688C2semidirect
356. C47#18033semidirect

Maximal subgroups

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

subgroupindex
#202525482
#202525202
#202422912
#202422732
#202422672
#202422392
#202422182
SD16⋊(C47⋊C8)2
Q16×C47⋊C82
#202421632
#202418532
#202417752
#202416882
C47×#31022
#1803347