Finite Group Databasebeta

← #26275146

Subgroups — #26275146

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689164C211yesmaximal, characteristic
2#20247108C211yesmaximal, characteristic
3#20247075C211yesmaximal, characteristic
4#20244873C211yesmaximal, characteristic, complemented
5#20244872C211yesmaximal, characteristic, complemented
6#20244723C211yesmaximal, characteristic, complemented
7#20244713C211yesmaximal, characteristic, complemented
8#20244126C211yesmaximal, characteristic, complemented
9#20244122C211yesmaximal, characteristic, complemented
10#20243586C211yesmaximal, characteristic
11#20243574C211yesmaximal, characteristic
12#20243549C211yesmaximal, characteristic, complemented
13#20243418C211yesmaximal, characteristic
14#20243173C211yesmaximal, characteristic
15C2×C47×#501C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C2×#13093982C2211yescharacteristic
18C2×C4⋊C4×D47C2211yescharacteristic
19#15689164—24no—
20C2×#13093958C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093956C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×C8×Dic47C2211yescharacteristic
28#15689061—21no—
29#15689056—21no—
30#15689045—21no—
31#15689034—21no—
32#15689030—21no—
33#15689022C2211yescharacteristic
34#15689022C2211yescharacteristic
35#15689021C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689004—21no—
38#15688994—21no—
39#15688988C2211yescharacteristic
40#15688988C2211yescharacteristic
41#15688980—21no—
42#15688980C2211yescharacteristic
43#15688980C2211yescharacteristic
44C4×(C2×D47)⋊C4C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×C4⋊Q8×C47C2211yescharacteristic
54C2×#125×C47C2211yescharacteristic
55C47×#501—24no—
56C2×#107×C47C2211yescharacteristic
57C2×#107×C47C2211yescharacteristic
58C2×#106×C47C2211yescharacteristic
59C2×#106×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47C2311yescharacteristic
63C2×#10625324—22no—
64C2×#10625324—22no—
65C2×#10625324Q814yescomplemented
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13093982—22no—
69#13093982—41no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C4⋊C4×D47—22no—
80C4⋊C4×D47—41no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4D411yescharacteristic
85C2×(C2×D47)⋊C4D411yescharacteristic
86C2×C4×Dic47—21no—
87C2×C4×Dic47C2311yescharacteristic
88#13093958—22no—
89#13093957—22no—
90#13093957—41no—
91#13093957—41no—
92#13093956—22no—
93#13093955—22no—
94(C2×D47)⋊C8Q814yescomplemented
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⋊#95—21no—
106C47⋊#95D411yescharacteristic
107C47⋊#95D411yescharacteristic
108C22×Q8×C47—21no—
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C4⋊Q8×C47—22no—
112C4⋊Q8×C47—41no—
113#125×C47—22no—
114#125×C47—41no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#107×C47—22no—
124#107×C47D414yes—
125#106×C47—22no—
126#106×C47—22no—
127#97×C47—22no—
128C23×D47C2×D411yescharacteristic
129C2×Q8×C47—42no—
130C2×Q8×C47—42no—
131C2×Q8×C47—81no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47C2×D411yescharacteristic
144C22×Dic47C2×D411yescharacteristic
145C22×Dic47C2×D411yescharacteristic
146C2×C4×D47—21no—
147C2×C4×D47—21no—
148C2×C4×D47—21no—
149C2×C4×D47—21no—
150C2×C4×D47—42no—
151C2×C4×D47—42no—
152C2×C4×D47—81no—
153C2×C4×D47C2×Q812yes—
154C2×C4×D47C2×Q812yes—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47C2×D412yes—
158C2×C8×C47C2×Q812yes—
159C2×C8×C47C2×Q812yes—
160C2×C8×C47#4112yes—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—42no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47—42no—
170C4⋊C4×C47C2×D412yes—
171C4⋊C4×C47C2×D412yes—
172C42×C47—21no—
173C42×C47—21no—
174(C2×D47)⋊C4—41no—
175(C2×D47)⋊C4—41no—
176(C2×D47)⋊C4—42no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—81no—
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—81no—
188C4⋊Dic47—81no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191Dic47⋊C4—81no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—42no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8C2×Q812yes—
200C2×C47⋊C8C2×Q812yes—
201#10625324—28no—
202C23×C47C22×D411yescharacteristic
203C22×D47—21no—
204C22×D47—21no—
205C22×D47—21no—
206C22×D47—21no—
207C22×D47—21no—
208C22×D47—21no—
209C22×D47C4⋊Q812yes—
210Q8×C47—84no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
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—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
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×C47C22×D411yescharacteristic
230C2×C4×C47C22×Q811yescharacteristic
231C2×C4×C47C22×Q811yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47H(5,𝔽2)11yescharacteristic
234C2×C4×C472−1+411yescharacteristic
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
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—
255C2×Dic47C4⋊Q812yes—
256C4×D47—22no—
257C4×D47—22no—
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—84no—
261C8×C47—22no—
262C8×C47C22⋊Q814yes—
263C47⋊C8—22no—
264C47⋊C8—22no—
265#26079—471nomaximal, Sylow
266C22×C47C2×C4⋊Q811yescharacteristic
267C22×C47D4211yescharacteristic
268C22×C47#54711yescharacteristic
269C22×C47#57511yescharacteristic
270C22×C47#57511yescharacteristic
271C22×C47#57611yescharacteristic
272C22×C47#57811yescharacteristic
273C2×D47—22no—
274C2×D47—22no—
275C2×D47—22no—
276C2×D47—41no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—41no—
280C4×C47—42no—
281C4×C47—41no—
282C4×C47—42no—
283C4×C47—41no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47C2×C22⋊Q811yescharacteristic
287C4×C47#54411yescharacteristic
288C4×C47D4×Q811yescharacteristic
289C4×C47#55411yescharacteristic
290Dic47—22no—
291Dic47—41no—
292Dic47—41no—
293Dic47—81no—
294Dic47—81no—
295Dic47—81no—
296Dic47—81no—
297C2×#501D4711yescharacteristic, complemented
298C2×#428—471no—
299#2442—471no—
300#2439—471no—
301#2085—471no—
302#2085—471no—
303#2059—471no—
304#2057—471no—
305#1943—471no—
306#1942—471no—
307#1854—471no—
308#1852—471no—
309#1846—471no—
310#1809—471no—
311#1753—471no—
312C2×C47#244011yescharacteristic
313C2×C47#316411yescharacteristic
314C2×C47#316611yescharacteristic
315C2×C47#327311yescharacteristic
316C2×C47#327711yescharacteristic
317C2×C47#334711yescharacteristic
318C2×C47#334911yescharacteristic
319D47—42no—
320C22×M16—471no—
321C2×C4⋊Q8C2×D4711yescharacteristic
322C2×#125C2×D4711yescharacteristic
323C2×#117—471no—
324C22×C4⋊C4—471no—
325#501—24no—
326#428—944no—
327C2×#107—471no—
328C2×#107—471no—
329C2×#107—471no—
330C2×#107—471no—
331C2×#107C2×D4711yescharacteristic
332C2×#107C2×D4711yescharacteristic
333C2×#106—471no—
334C2×#106—471no—
335C2×#106C2×D4711yescharacteristic
336C2×#106C2×D4711yescharacteristic
337C2×C22⋊C8—471no—
338C2×#97C2×D4711yescharacteristic
339C2×C4×C8—471no—
340#400—941no—
341#398—941no—
342#396—941no—
343#393—941no—
344#391—941no—
345#389—471no—
346#389—471no—
347#389—471no—
348#389—471no—
349#387—941no—
350#385—941no—
351#382—471no—
352#382—471no—
353#380—471no—
354#380—471no—
355#380—941no—
356C4×C22⋊C4—471no—
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#336—471no—
364#336—471no—
365C47#2607911yescharacteristic, complemented, Sylow
366C22×Q8—21no—
367C23×C4—471no—
368C23×C4—941no—
369C2×M16—474no—
370C2×M16—942no—
371C2×M16—942no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8C22×D4711yescharacteristic
375C22×C8C22×D4711yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—41no—
378#125—22no—
379#125—41no—
380#117—942no—
381#117—1881no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—942no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—1881no—
396C2×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C4⋊C4C22×D4711yescharacteristic
400C2×C22⋊C4—471no—
401C2×C22⋊C4—471no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C42—471no—
406C2×C42—941no—
407C2×C42C22×D4711yescharacteristic
408#107—22no—
409#107—942no—
410#107—942no—
411#107—1881no—
412#107—1881no—
413#107C22⋊D4714yes—
414#106—22no—
415#106—22no—
416#106—942no—
417#106—942no—
418C22⋊C8—474no—
419#97—22no—
420C4×C8—942no—
421#95—471no—
422#95—471no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95—941no—
430#95—941no—
431#95—941no—
432#95—941no—
433C24—471no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—81no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—471no—
442C22×C4—472no—
443C22×C4—472no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—3761no—
455C22×C4—1882no—
456C22×C4—1882no—
457C22×C4D4×D4711yescharacteristic
458C22×C4D4×D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460M16—948no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—472no—
464C2×C8—472no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8Q8×D4712yes—
470C2×C8Q8×D4712yes—
471C2×C8#1062535412yes—
472C2×C8C2×C22⋊D4712yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—3761no—
491C4⋊C4—3761no—
492C4⋊C4—3761no—
493C4⋊C4—1882no—
494C4⋊C4—1882no—
495C4⋊C4C2×C22⋊D4712yes—
496C4⋊C4C2×C22⋊D4712yes—
497C22⋊C4—3761no—
498C22⋊C4—1881no—
499C22⋊C4—1881no—
500C22⋊C4—1882no—
501C22⋊C4—1882no—
502C42—21no—
503C42—21no—
504C42—941no—
505C42—941no—
506C42—1882no—
507C23—472no—
508C23—941no—
509C23—941no—
510C23—941no—
511C23—941no—
512C23—941no—
513C23—941no—
514C23C2×D4×D4711yescharacteristic
515Q8—84no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—472no—
535C2×C4—941no—
536C2×C4—941no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—941no—
547C2×C4—3764no—
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×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4C22×C22⋊D4711yescharacteristic
561C2×C4C2×Q8×D4711yescharacteristic
562C2×C4C2×Q8×D4711yescharacteristic
563C2×C4C2×#1062535411yescharacteristic
564C2×C4#1309406911yescharacteristic
565C2×C4#1309407211yescharacteristic
566C8—22no—
567C8—942no—
568C8—942no—
569C8#1309400014yes—
570C22—942no—
571C22—942no—
572C22—942no—
573C22—1881no—
574C22—1881no—
575C22—1881no—
576C22—1881no—
577C22C4⋊Q8×D4711yescharacteristic
578C22D4×C22⋊D4711yescharacteristic
579C22#1568977611yescharacteristic
580C22#1568991911yescharacteristic
581C22#1568992211yescharacteristic
582C22#1568992711yescharacteristic
583C22#1568993911yescharacteristic
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—942no—
591C4—3761no—
592C4—3761no—
593C4—3761no—
594C4—3761no—
595C4—1881no—
596C4—1881no—
597C4C2×#1309400011yescharacteristic
598C4#1568975011yescharacteristic
599C4Q8×C22⋊D4711yescharacteristic
600C4#1568983411yescharacteristic
601C2—1882no—
602C2#2024708611yescharacteristic
603C2#2025392311yescharacteristic
604C2#2025393911yescharacteristic
605C2#2025499311yescharacteristic
606C2#2025503911yescharacteristic
607C2#2025588711yescharacteristic
608C2#2025591711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#501D47
hypocenterC47#26079
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
4. #20244873C2semidirect
5. #20244872C2semidirect
6. #20244723C2semidirect
7. #20244713C2semidirect
8. #20244126C2semidirect
9. #20244122C2semidirect
12. #20243549C2semidirect
15. C2×C47×#501C2semidirect
65. C2×#10625324Q8semidirect
94. (C2×D47)⋊C8Q8semidirect
297. C2×#501D47semidirect
365. C47#26079semidirect

Maximal subgroups

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

subgroupindex
C2×#156891642
#202471082
#202470752
#202448732
#202448722
#202447232
#202447132
#202441262
#202441222
#202435862
#202435742
#202435492
#202434182
#202431732
C2×C47×#5012
#2607947