Finite Group Databasebeta

← #26238735

Subgroups — #26238735

Order 12032.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689325C211yesmaximal, characteristic
2C2×#15689221C211yesmaximal, characteristic
3C2×C4×#10625336C211yesmaximal, characteristic
4#20246299C211yesmaximal, characteristic
5#20244209C211yesmaximal, characteristic, complemented
6#20244156C211yesmaximal, characteristic, complemented
7#20244081C211yesmaximal, characteristic, complemented
8#20244067C211yesmaximal, characteristic, complemented
9#20243725C211yesmaximal, characteristic
10#20243725C211yesmaximal, characteristic
11#20243656C211yesmaximal, characteristic, complemented
12#20243642C211yesmaximal, characteristic, complemented
13#20243263C211yesmaximal, characteristic, complemented
14#20243216C211yesmaximal, characteristic
15C47×#2365C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C22×#10625336C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21#15689325C418yescomplemented
22#15689221—24no—
23C4×#10625336—24no—
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37C2×C4×C47⋊C8C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15688994—21no—
41#15688994—21no—
42#15688989C2211yescharacteristic
43#15688982—21no—
44#95×D47—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C47×#391C2211yescharacteristic
55C47×#391C2211yescharacteristic
56C47×#389—21no—
57C47×#387—21no—
58C47×#387—21no—
59C4×C4⋊C4×C47—21no—
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C4⋊C4×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C4×D47—21no—
64C22×C4×D47—21no—
65C22×C4×D47—21no—
66C2×#10625336—22no—
67C2×#10625336—22no—
68C2×#10625336—22no—
69C2×#10625336—22no—
70C2×#10625336C2×C414yes—
71C2×#10625336C2×C414yes—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C4×D188—22no—
77C4×D188—22no—
78C4×D188—22no—
79C4×D188—41no—
80C4×D188—41no—
81C4×D188C2×C414yes—
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90#13093957—22no—
91#13093955—22no—
92C4⋊(C47⋊C8)C2×C414yescomplemented
93#13093948—22no—
94#13093948—22no—
95#13093948—41no—
96#13093948—41no—
97#13093948C2×C414yescomplemented
98#13093948C2×C414yescomplemented
99#13093944—22no—
100#13093944D414yes—
101#13093935—22no—
102#13093935—22no—
103C4×C47⋊C8—22no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C22×Q8×C47C2311yescharacteristic
109C22×Q8×C47C2311yescharacteristic
110C4⋊Q8×C47—22no—
111C4⋊Q8×C47C2×C414yescomplemented
112C4×Q8×C47—22no—
113C4×Q8×C47—22no—
114C4×Q8×C47—41no—
115C4×Q8×C47—41no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47D411yescharacteristic
121C2×C4⋊C4×C47D411yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47—21no—
126C2×C42×C47—21no—
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129C2×C42×C47C2311yescharacteristic
130#95×C47—21no—
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47D411yescharacteristic
136#95×C47D411yescharacteristic
137C23×D47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C22×C412yes—
149C2×Q8×C47C22×C412yes—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2411yescharacteristic
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C2×D188—21no—
165C2×D188—21no—
166C2×D188—21no—
167C2×D188C22×C412yes—
168C2×D188C2×D412yes—
169C2×D188#4112yes—
170C2×C4×D47—24no—
171C2×C4×D47—42no—
172C2×C4×D47—42no—
173C2×C4×D47—42no—
174C2×C4×D47—42no—
175C2×C4×D47—81no—
176C2×C4×D47—81no—
177C2×C4×D47—81no—
178C2×C4×D47—81no—
179C4⋊C4×C47—24no—
180C4⋊C4×C47—24no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—41no—
186C4⋊C4×C47—42no—
187C4⋊C4×C47—42no—
188C4⋊C4×C47C2×D412yes—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—42no—
194C42×C47—42no—
195C42×C47—42no—
196C42×C47C22×C412yes—
197C42×C47#4112yes—
198#10625336—28no—
199#10625336—28no—
200(C2×D47)⋊C4—24no—
201(C2×D47)⋊C4—42no—
202(C2×D47)⋊C4—42no—
203C4⋊Dic47—21no—
204C4⋊Dic47—21no—
205C4⋊Dic47—21no—
206C4⋊Dic47—21no—
207C4⋊Dic47—21no—
208C4⋊Dic47C22×C412yes—
209Dic47⋊C4—81no—
210Dic47⋊C4—81no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—21no—
216C2×C47⋊C8—21no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8C22×C412yes—
221C2×C47⋊C8C22×C412yes—
222C2×C47⋊C8C2×D412yes—
223C23×C47C22×D411yescharacteristic
224C22×D47—22no—
225C22×D47—22no—
226C22×D47—22no—
227C22×D47—41no—
228C22×D47—41no—
229C22×D47—41no—
230C22×D47—41no—
231Q8×C47—22no—
232Q8×C47—22no—
233Q8×C47—22no—
234Q8×C47—22no—
235Q8×C47—41no—
236Q8×C47—41no—
237Q8×C47—41no—
238Q8×C47—41no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—22no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47C4×D412yes—
267C2×C4×C47C4×D412yes—
268C2×C4×C47#13712yes—
269C2×C4×C47C23×C411yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47H(5,𝔽2)11yescharacteristic
274C2×C4×C472−1+411yescharacteristic
275C2×Dic47—22no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284D188—22no—
285D188—22no—
286D188—22no—
287D188C4×D414yes—
288C4×D47—84no—
289C4×D47—84no—
290C4×D47—84no—
291C47⋊C8—22no—
292C47⋊C8—22no—
293C47⋊C8—22no—
294C47⋊C8—41no—
295#23012—471nomaximal, Sylow
296C22×C47C2×C4×D411yescharacteristic
297C22×C47D4211yescharacteristic
298C22×C47#54811yescharacteristic
299C22×C47C2×#13711yescharacteristic
300C22×C47#57511yescharacteristic
301C22×C47#57711yescharacteristic
302C22×C47#57711yescharacteristic
303C2×D47—24no—
304C2×D47—42no—
305C2×D47—42no—
306C2×D47—42no—
307C2×D47—42no—
308C2×D47—42no—
309C2×D47—42no—
310C4×C47—22no—
311C4×C47—22no—
312C4×C47—22no—
313C4×C47—42no—
314C4×C47—42no—
315C4×C47—41no—
316C4×C47—41no—
317C4×C47—41no—
318C4×C47—42no—
319C4×C47—81no—
320C4×C47C2×C4×D411yescharacteristic
321C4×C47#52011yescharacteristic
322C4×C47#54711yescharacteristic
323C4×C47#55311yescharacteristic
324Dic47—42no—
325Dic47—81no—
326Dic47—81no—
327C2×#461—471no—
328C2×#440—471no—
329C2×C4×SD16—471no—
330#2365D4711yescharacteristic, complemented
331#2349—471no—
332#1960—471no—
333#1949—471no—
334#1935—471no—
335#1933—471no—
336#1877—471no—
337#1877—471no—
338#1865—471no—
339#1863—471no—
340#1771—471no—
341#1762—471no—
342C2×C47#236111yescharacteristic
343C2×C47C4×#13711yescharacteristic
344C2×C47#294911yescharacteristic
345C2×C47#326611yescharacteristic
346C2×C47#326711yescharacteristic
347C2×C47#337211yescharacteristic
348C2×C47#337611yescharacteristic
349D47—44no—
350C22×SD16—471no—
351C22×SD16—471no—
352C2×C4⋊Q8C2×D4711yescharacteristic
353C2×C4×Q8C2×D4711yescharacteristic
354C2×C4×Q8C2×D4711yescharacteristic
355C2×C4×D4—471no—
356C2×C4×D4—471no—
357C2×C4×D4—471no—
358#461—478no—
359#440—944no—
360C4×SD16—944no—
361C2×#107—471no—
362C2×#106—471no—
363C2×C4⋊C8—471no—
364C2×#103—471no—
365C2×#103—471no—
366C2×#103—471no—
367C2×#103—471no—
368C2×#103—471no—
369C2×#103—471no—
370C2×#102—471no—
371C2×#102—471no—
372C2×#97—471no—
373C2×#97—471no—
374C2×C4×C8—471no—
375#391C2×D4711yescharacteristic
376#391C2×D4711yescharacteristic
377#389—21no—
378#389—471no—
379#389—471no—
380#387—21no—
381#387—21no—
382#385—941no—
383#385—941no—
384#382—471no—
385#380—941no—
386C4×C4⋊C4—21no—
387C4×C4⋊C4C2×D4711yescharacteristic
388C4×C4⋊C4C2×D4711yescharacteristic
389C2×#95—941no—
390#340—471no—
391#340—471no—
392#340—471no—
393#340—471no—
394#336—471no—
395#336—471no—
396C47#2301211yescharacteristic, complemented, Sylow
397C22×Q8C22×D4711yescharacteristic
398C22×Q8C22×D4711yescharacteristic
399C22×D4—471no—
400C23×C4—941no—
401C23×C4—941no—
402C23×C4—941no—
403C2×SD16—474no—
404C2×SD16—474no—
405C2×SD16—942no—
406C2×SD16—942no—
407C2×SD16—942no—
408C2×SD16—942no—
409C22×C8—471no—
410C22×C8—471no—
411C22×C8—471no—
412C22×C8—471no—
413C4⋊Q8—22no—
414C4⋊Q8C4×D4714yescomplemented
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×Q8—41no—
419C4×D4—474no—
420C4×D4—942no—
421C4×D4—942no—
422C4×D4—942no—
423C4×D4—1881no—
424C4×D4—1881no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—471no—
430C2×C4⋊C4—471no—
431C2×C4⋊C4—471no—
432C2×C4⋊C4—941no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4C22⋊D4711yescharacteristic
435C2×C4⋊C4C22⋊D4711yescharacteristic
436C2×C4⋊C4C22×D4711yescharacteristic
437C2×C4⋊C4C22×D4711yescharacteristic
438C2×C22⋊C4—941no—
439C2×C22⋊C4—941no—
440C2×C22⋊C4—941no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C22×D4711yescharacteristic
445C2×C42C22×D4711yescharacteristic
446C2×C42C22×D4711yescharacteristic
447#107—942no—
448#106—942no—
449C4⋊C8—474no—
450#103—474no—
451#103—474no—
452#103—942no—
453#103—942no—
454#103—1881no—
455#103—1881no—
456#102—474no—
457#102—942no—
458#97—942no—
459#97—942no—
460C4×C8—942no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—941no—
467#95—941no—
468#95—941no—
469#95—941no—
470#95C22⋊D4711yescharacteristic
471#95C22⋊D4711yescharacteristic
472C24—941no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C2×C4×D4712yes—
484C2×Q8C2×C4×D4712yes—
485C2×D4—472no—
486C2×D4—472no—
487C2×D4—472no—
488C2×D4—941no—
489C2×D4—941no—
490C2×D4—941no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—941no—
496C22×C4—944no—
497C22×C4—941no—
498C22×C4—941no—
499C22×C4—3761no—
500C22×C4—3761no—
501C22×C4—3761no—
502C22×C4—3761no—
503C22×C4—1882no—
504C22×C4—1882no—
505C22×C4—1882no—
506C22×C4—1882no—
507C22×C4C2×C22⋊D4711yescharacteristic
508C22×C4C2×C22⋊D4711yescharacteristic
509C22×C4C2×C22⋊D4711yescharacteristic
510C22×C4C2×C22⋊D4711yescharacteristic
511C22×C4C2×C22⋊D4711yescharacteristic
512C22×C4C2×C22⋊D4711yescharacteristic
513C22×C4C23×D4711yescharacteristic
514SD16—948no—
515SD16—948no—
516C2×C8—472no—
517C2×C8—472no—
518C2×C8—472no—
519C2×C8—941no—
520C2×C8—941no—
521C2×C8—941no—
522C2×C8—941no—
523C2×C8—941no—
524C2×C8—941no—
525C2×C8—941no—
526C2×C8—941no—
527C2×C8—941no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—472no—
538C4⋊C4—941no—
539C4⋊C4—941no—
540C4⋊C4—941no—
541C4⋊C4—941no—
542C4⋊C4—941no—
543C4⋊C4—3761no—
544C4⋊C4—3761no—
545C4⋊C4D4×D4712yes—
546C22⋊C4—944no—
547C22⋊C4—1882no—
548C22⋊C4—1882no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—42no—
555C42—42no—
556C42C2×C4×D4712yes—
557C42#1062535012yes—
558C23—942no—
559C23—942no—
560C23—942no—
561C23—1881no—
562C23—1881no—
563C23—1881no—
564C23—1881no—
565C23C22×C22⋊D4711yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574D4—474no—
575D4—942no—
576D4—942no—
577D4—942no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—942no—
606C2×C4—3764no—
607C2×C4—3764no—
608C2×C4—3764no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4—1881no—
612C2×C4—1881no—
613C2×C4—1881no—
614C2×C4—1881no—
615C2×C4—1881no—
616C2×C4—1881no—
617C2×C4C4×C22⋊D4712yes—
618C2×C4C4×C22⋊D4712yes—
619C2×C4#1309405512yes—
620C2×C4C22×C4×D4711yescharacteristic
621C2×C4C2×D4×D4711yescharacteristic
622C2×C4#41×D4711yescharacteristic
623C2×C4C2×#1062535011yescharacteristic
624C2×C4#1309406911yescharacteristic
625C2×C4#1309407111yescharacteristic
626C8—942no—
627C8—942no—
628C8—942no—
629C8—1881no—
630C22—944no—
631C22—1882no—
632C22—1882no—
633C22—1882no—
634C22—1882no—
635C22—1882no—
636C22—1882no—
637C22C2×C4×C22⋊D4711yescharacteristic
638C22D4×C22⋊D4711yescharacteristic
639C22#1568978011yescharacteristic
640C22C2×#1309405511yescharacteristic
641C22#1568992111yescharacteristic
642C22#1568993111yescharacteristic
643C22#1568993111yescharacteristic
644C4—22no—
645C4—22no—
646C4—22no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—3761no—
655C4—3761no—
656C4—1882no—
657C4C4×D4×D4711yescharacteristic
658C4#1568960211yescharacteristic
659C4#1568977811yescharacteristic
660C4#1568982311yescharacteristic
661C2—1884no—
662C2#2024640011yescharacteristic
663C2C4×#1309405511yescharacteristic
664C2#2025224711yescharacteristic
665C2#2025489911yescharacteristic
666C2#2025491411yescharacteristic
667C2#2025616511yescharacteristic
668C2#2025620911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2365C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#2365D47
hypocenterC47#23012
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
5. #20244209C2semidirect
6. #20244156C2semidirect
7. #20244081C2semidirect
8. #20244067C2semidirect
11. #20243656C2semidirect
12. #20243642C2semidirect
13. #20243263C2semidirect
15. C47×#2365C2semidirect
21. #15689325C4semidirect
92. C4⋊(C47⋊C8)C2×C4semidirect
97. #13093948C2×C4semidirect
98. #13093948C2×C4semidirect
111. C4⋊Q8×C47C2×C4semidirect
330. #2365D47semidirect
396. C47#23012semidirect
414. C4⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156893252
C2×#156892212
C2×C4×#106253362
#202462992
#202442092
#202441562
#202440812
#202440672
#202437252
#202436562
#202436422
#202432632
#202432162
C47×#23652
#2301247