Finite Group Databasebeta

← #26238117

Subgroups — #26238117

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689420C211yesmaximal, characteristic
2#20246299C211yesmaximal, characteristic
3#20244354C211yesmaximal, characteristic, complemented
4#20244156C211yesmaximal, characteristic, complemented
5#20244118C211yesmaximal, characteristic, complemented
6#20244113C211yesmaximal, characteristic, complemented
7#20243980C211yesmaximal, characteristic, complemented
8#20243973C211yesmaximal, characteristic, complemented
9#20243648C211yesmaximal, characteristic
10#20243634C211yesmaximal, characteristic
11C4⋊C4×C47⋊C8C211yesmaximal, characteristic, complemented
12C4×#13093944C211yesmaximal, characteristic
13C4×#13093944C211yesmaximal, characteristic
14C4×#13093944C211yesmaximal, characteristic
15C47×#2370C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19#15689420C418yescomplemented
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15688994—21no—
35#15688994—21no—
36#15688989C2211yescharacteristic
37#15688982—21no—
38#95×D47—21no—
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×#125×C47C2211yescharacteristic
50C47×#389—21no—
51C47×#389C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#387—21no—
54C47×#387—21no—
55C4×C4⋊C4×C47—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47—21no—
63C22×C4×D47—21no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C4×D188—22no—
69C4×D188—22no—
70C4×D188—22no—
71C4×D188—41no—
72C4×D188—41no—
73C4×D188C2×C414yes—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82#13093957—41no—
83#13093957C2×C414yescomplemented
84#13093955—41no—
85#13093955C2×C414yescomplemented
86C4⋊(C47⋊C8)C2×C414yescomplemented
87#13093944—22no—
88#13093944C2×C414yes—
89#13093944C2×C414yes—
90#13093944Q814yes—
91C4×C47⋊C8—22no—
92C4×C47⋊C8—41no—
93C4×C47⋊C8—41no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98#125×C47—22no—
99#125×C47C2×C414yescomplemented
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123C23×D47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2411yescharacteristic
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188C22×C412yes—
142C2×D188C2×Q812yes—
143C2×D188#4112yes—
144C2×C4×D47—24no—
145C2×C4×D47—42no—
146C2×C4×D47—42no—
147C2×C4×D47—42no—
148C2×C4×D47—42no—
149C2×C4×D47—81no—
150C2×C4×D47—81no—
151C2×C4×D47—81no—
152C2×C4×D47—81no—
153C4⋊C4×C47—24no—
154C4⋊C4×C47—24no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—22no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—42no—
163C4⋊C4×C47—81no—
164C4⋊C4×C47C22×C412yes—
165C4⋊C4×C47C22×C412yes—
166C4⋊C4×C47C2×Q812yes—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—42no—
172C42×C47—81no—
173C42×C47—81no—
174C42×C47C22×C412yes—
175C42×C47#4112yes—
176(C2×D47)⋊C4—24no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—42no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47C22×C412yes—
185Dic47⋊C4—81no—
186Dic47⋊C4—81no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C22×C412yes—
197C2×C47⋊C8C22×C412yes—
198C2×C47⋊C8C2×Q812yes—
199C23×C47C22×D411yescharacteristic
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—22no—
203C22×D47—41no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47C4×D412yes—
234C2×C4×C47C4×D412yes—
235C2×C4×C47#13512yes—
236C2×C4×C47#13512yes—
237C2×C4×C47C23×C411yescharacteristic
238C2×C4×C47C22×Q811yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47H(5,𝔽2)11yescharacteristic
242C2×C4×C472−1+411yescharacteristic
243C2×Dic47—22no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252D188—22no—
253D188—22no—
254D188—22no—
255D188C4×Q814yes—
256C4×D47—84no—
257C4×D47—84no—
258C4×D47—84no—
259C47⋊C8—22no—
260C47⋊C8—22no—
261C47⋊C8—22no—
262C47⋊C8—41no—
263#22966—471nomaximal, Sylow
264C22×C47C2×C4×D411yescharacteristic
265C22×C47#54611yescharacteristic
266C22×C47D4×Q811yescharacteristic
267C22×C47C2×#13511yescharacteristic
268C22×C47C2×#13511yescharacteristic
269C22×C47#57611yescharacteristic
270C22×C47#57711yescharacteristic
271C2×D47—24no—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—42no—
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—42no—
283C4×C47—42no—
284C4×C47—42no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—81no—
288C4×C47C2×C4×Q811yescharacteristic
289C4×C47#52011yescharacteristic
290C4×C47#55211yescharacteristic
291C4×C47#55411yescharacteristic
292Dic47—42no—
293Dic47—81no—
294Dic47—81no—
295C2×#478—471no—
296#2370D4711yescharacteristic, complemented
297#2349—471no—
298#1991—471no—
299#1949—471no—
300#1942—471no—
301#1941—471no—
302#1921—471no—
303#1920—471no—
304#1864—471no—
305#1862—471no—
306C8×C4⋊C4—471no—
307C4×#102—471no—
308C4×#102—471no—
309C4×#102—471no—
310C2×C47#236011yescharacteristic
311C2×C47C4×#13511yescharacteristic
312C2×C47#294611yescharacteristic
313C2×C47#329611yescharacteristic
314C2×C47#329711yescharacteristic
315C2×C47#338011yescharacteristic
316C2×C47#338111yescharacteristic
317D47—44no—
318C2×#125C2×D4711yescharacteristic
319C2×C4×D4—471no—
320C2×C4×D4—471no—
321C2×C4×D4—471no—
322#478—478no—
323C2×#107—471no—
324C2×#107—471no—
325C2×#106—471no—
326C2×#106—471no—
327C2×C4⋊C8—471no—
328C2×#102—471no—
329C2×#102—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×C4×C8—471no—
333C2×C4×C8—471no—
334C2×C4×C8—471no—
335#389—21no—
336#389—471no—
337#389—471no—
338#389C2×D4711yescharacteristic
339#389C2×D4711yescharacteristic
340#387—21no—
341#387—21no—
342#385—941no—
343#385—941no—
344#382—471no—
345#380—941no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4C2×D4711yescharacteristic
348C4×C4⋊C4C2×D4711yescharacteristic
349C4×C4⋊C4C2×D4711yescharacteristic
350C4×C4⋊C4C2×D4711yescharacteristic
351C2×#95—941no—
352#340—471no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340—471no—
358#340—471no—
359#340—471no—
360#336—471no—
361#336—471no—
362C47#2296611yescharacteristic, complemented, Sylow
363C22×D4—471no—
364C23×C4—941no—
365C23×C4—941no—
366C23×C4—941no—
367C22×C8—471no—
368C22×C8—471no—
369C22×C8—471no—
370C22×C8—471no—
371#125—22no—
372#125C4×D4714yescomplemented
373C4×D4—474no—
374C4×D4—942no—
375C4×D4—942no—
376C4×D4—942no—
377C4×D4—1881no—
378C4×D4—1881no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4C22⋊D4711yescharacteristic
389C2×C4⋊C4C22⋊D4711yescharacteristic
390C2×C4⋊C4C22×D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C4⋊C4C22×D4711yescharacteristic
393C2×C4⋊C4C22×D4711yescharacteristic
394C2×C22⋊C4—941no—
395C2×C22⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C22×D4711yescharacteristic
401C2×C42C22×D4711yescharacteristic
402C2×C42C22×D4711yescharacteristic
403#107—474no—
404#107—1881no—
405#106—474no—
406#106—1881no—
407C4⋊C8—474no—
408#102—474no—
409#102—474no—
410#102—474no—
411#102—942no—
412C4×C8—942no—
413C4×C8—1881no—
414C4×C8—1881no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95—941no—
424#95C22⋊D4711yescharacteristic
425#95C22⋊D4711yescharacteristic
426C24—941no—
427C2×D4—472no—
428C2×D4—472no—
429C2×D4—472no—
430C2×D4—941no—
431C2×D4—941no—
432C2×D4—941no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—941no—
438C22×C4—944no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—3761no—
442C22×C4—3761no—
443C22×C4—3761no—
444C22×C4—3761no—
445C22×C4—1882no—
446C22×C4—1882no—
447C22×C4—1882no—
448C22×C4—1882no—
449C22×C4C2×C22⋊D4711yescharacteristic
450C22×C4C2×C22⋊D4711yescharacteristic
451C22×C4C2×C22⋊D4711yescharacteristic
452C22×C4C2×C22⋊D4711yescharacteristic
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C23×D4711yescharacteristic
456C2×C8—472no—
457C2×C8—472no—
458C2×C8—472no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—472no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—3761no—
486C4⋊C4—3761no—
487C4⋊C4C2×C4×D4712yes—
488C4⋊C4C2×C4×D4712yes—
489C4⋊C4Q8×D4712yes—
490C22⋊C4—944no—
491C22⋊C4—1882no—
492C22⋊C4—1882no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—81no—
499C42—81no—
500C42C2×C4×D4712yes—
501C42#1062535012yes—
502C23—942no—
503C23—942no—
504C23—942no—
505C23—1881no—
506C23—1881no—
507C23—1881no—
508C23—1881no—
509C23C22×C22⋊D4711yescharacteristic
510D4—474no—
511D4—942no—
512D4—942no—
513D4—942no—
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—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—942no—
541C2×C4—3764no—
542C2×C4—3764no—
543C2×C4—3764no—
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×C4C4×C22⋊D4712yes—
553C2×C4C4×C22⋊D4712yes—
554C2×C4#1309404412yes—
555C2×C4#1309404412yes—
556C2×C4C22×C4×D4711yescharacteristic
557C2×C4C2×Q8×D4711yescharacteristic
558C2×C4#41×D4711yescharacteristic
559C2×C4C2×#1062535011yescharacteristic
560C2×C4#1309407011yescharacteristic
561C2×C4#1309407211yescharacteristic
562C8—942no—
563C8—942no—
564C8—942no—
565C8—1881no—
566C22—944no—
567C22—1882no—
568C22—1882no—
569C22—1882no—
570C22—1882no—
571C22—1882no—
572C22—1882no—
573C22C2×C4×C22⋊D4711yescharacteristic
574C22#1568976111yescharacteristic
575C22Q8×C22⋊D4711yescharacteristic
576C22C2×#1309404411yescharacteristic
577C22C2×#1309404411yescharacteristic
578C22#1568992611yescharacteristic
579C22#1568993111yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—42no—
589C4—81no—
590C4—3761no—
591C4—3761no—
592C4—1882no—
593C4C4×Q8×D4711yescharacteristic
594C4#1568960511yescharacteristic
595C4#1568981411yescharacteristic
596C4#1568983311yescharacteristic
597C2—1884no—
598C2#2024638911yescharacteristic
599C2C4×#1309404411yescharacteristic
600C2#2025221611yescharacteristic
601C2#2025521711yescharacteristic
602C2#2025523211yescharacteristic
603C2#2025625111yescharacteristic
604C2#2025625911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2370C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#2370D47
hypocenterC47#22966
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #20244354C2semidirect
4. #20244156C2semidirect
5. #20244118C2semidirect
6. #20244113C2semidirect
7. #20243980C2semidirect
8. #20243973C2semidirect
11. C4⋊C4×C47⋊C8C2semidirect
15. C47×#2370C2semidirect
19. #15689420C4semidirect
83. #13093957C2×C4semidirect
85. #13093955C2×C4semidirect
86. C4⋊(C47⋊C8)C2×C4semidirect
99. #125×C47C2×C4semidirect
296. #2370D47semidirect
362. C47#22966semidirect
372. #125C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894202
#202462992
#202443542
#202441562
#202441182
#202441132
#202439802
#202439732
#202436482
#202436342
C4⋊C4×C47⋊C82
C4×#130939442
C47×#23702
#2296647