Finite Group Databasebeta

← #26138832

Subgroups — #26138832

Order 12032.

1766 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093989C211yesmaximal, characteristic
2C2×#15689027C212yesmaximal
3C2×#15688987C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic
5#20241642C211yesmaximal, characteristic
6#20241641C211yesmaximal, characteristic
7#20241638C211yesmaximal, characteristic
8Dic47⋊#95C212yesmaximal
9#20241614C212yesmaximal
10#20241613C212yesmaximal
11C47×#1441C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13093989—24no—
14C2×#13093989—24no—
15C2×#13093989C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×C4×Dic47C2212yes—
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689027—28no—
25#15688987—24no—
26C4⋊C4×Dic47—24no—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2212yes—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94C2×C414yes—
46C22×Dic94D414yes—
47C22×Dic94Q814yes—
48C23×Dic47C2312yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54#13093989—232no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4C2×C414yes—
65C2×Dic47⋊C4C2×C414yes—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47C2×C414yes—
74C2×C4×Dic47C2×C414yes—
75C2×C4×Dic47C2×C414yes—
76C2×C4×Dic47D414yes—
77C2×C4×Dic47D414yes—
78C47⋊#95—22no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C23×C4×C47C2312yes—
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2312yes—
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—24no—
96C2×C4⋊C4×C47C2×C414yes—
97#95×C47—22no—
98#95×C47—24no—
99#95×C47—24no—
100C24×C47C2411yescharacteristic
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×Q812yes—
131C22×C4×C47#4114yes—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47C22×C412yes—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C412yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C2×D412yes—
160C22×Dic47C2×D412yes—
161C22×Dic47C2×D412yes—
162C22×Dic47C2×D412yes—
163C22×Dic47C2×D412yes—
164C22×Dic47C2×D412yes—
165C22×Dic47C2×Q812yes—
166C22×Dic47C2×Q812yes—
167C22×Dic47#4114yes—
168C22×Dic47#4112yes—
169C22×Dic47#4112yes—
170C2×Dic94—28no—
171C2×Dic94—28no—
172C2×Dic94—28no—
173C2×Dic94—28no—
174C2×Dic94—28no—
175C2×Dic94—28no—
176C2×Dic94C4⋊C4116yescomplemented
177C4⋊C4×C47—28no—
178C4⋊C4×C47—28no—
179C4⋊Dic47—28no—
180Dic47⋊C4—28no—
181Dic47⋊C4—28no—
182Dic47⋊C4—48no—
183C4×Dic47—28no—
184C4×Dic47—28no—
185C4×Dic47—48no—
186C4×Dic47C22⋊C4116yes—
187C23×C47C23×C411yescharacteristic
188C23×C47C22×D411yescharacteristic
189C23×C47C22×D411yescharacteristic
190C23×C47C22×D411yescharacteristic
191C23×C47C22×Q811yescharacteristic
192C23×C47C2×#4111yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C23×C47C2×#4112yes—
195C23×C47C2×#4112yes—
196C23×C472−1+412yes—
197C23×C472−1+412yes—
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—24no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—24no—
208C2×C4×C47—22no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—24no—
212C2×C4×C47—24no—
213C2×C4×C47—42no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47C2×C22⋊C414yes—
228C2×C4×C47C2×C4⋊C414yes—
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—24no—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—24no—
243C2×Dic47—24no—
244C2×Dic47—42no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47C2×C22⋊C414yes—
259C2×Dic47C2×C22⋊C414yes—
260C2×Dic47C2×C4⋊C414yes—
261C2×Dic47C2×C4⋊C414yes—
262C2×Dic47#11714yes—
263C2×Dic47#12114yes—
264C2×Dic47#12114yes—
265C2×Dic47C22⋊Q814yes—
266C2×Dic47C22⋊Q814yes—
267Dic94—232no—
268#13942—471nomaximal, Sylow
269C22×C47C22×C22⋊C411yescharacteristic
270C22×C47C22×C4⋊C411yescharacteristic
271C22×C47C2×#11711yescharacteristic
272C22×C47C4×#4112yes—
273C22×C47#51912yes—
274C22×C47C2×#12111yescharacteristic
275C22×C47C2×#12111yescharacteristic
276C22×C47C2×C22⋊Q811yescharacteristic
277C22×C47C2×C22⋊Q811yescharacteristic
278C22×C47#52511yescharacteristic
279C22×C47#52511yescharacteristic
280C22×C47#53212yes—
281C22×C47#53611yescharacteristic
282C22×C47#53612yes—
283C22×C47#53611yescharacteristic
284C22×C47#54812yes—
285C22×C47#54812yes—
286C22×C47#55212yes—
287C22×C47#55212yes—
288C22×C47#55612yes—
289C22×C47#55612yes—
290C22×C47#55712yes—
291C22×C47#55712yes—
292C4×C47—24no—
293C4×C47—24no—
294C4×C47—44no—
295C4×C47—42no—
296C4×C47—82no—
297Dic47—24no—
298Dic47—24no—
299Dic47—44no—
300Dic47—42no—
301Dic47—82no—
302Dic47#38018yes—
303C22×C4×Q8—471no—
304C2×#391—472no—
305C2×#382—471no—
306C2×C4×C4⋊C4—471no—
307#1441—471no—
308#1441—471no—
309#1441—471no—
310#1441D4711yescharacteristic
311C4⋊#95—472no—
312#1434—472no—
313#1434—472no—
314C2×C47C2×#38011yescharacteristic
315C2×C47#229711yescharacteristic
316C2×C47#231011yescharacteristic
317C2×C47#235112yes—
318C2×C47#235612yes—
319C2×C47#253611yescharacteristic
320C2×C47#253611yescharacteristic
321C2×C47#254512yes—
322C2×C47#256512yes—
323C2×C47#258111yescharacteristic
324C2×C47#258111yescharacteristic
325C23×Q8—471no—
326C2×C4×Q8—478no—
327C2×C4×Q8—944no—
328C2×C4×Q8—944no—
329C22×C4⋊C4—471no—
330C22×C4⋊C4—471no—
331C22×C4⋊C4—472no—
332C22×C4⋊C4—471no—
333C22×C4⋊C4C2×D4711yescharacteristic
334C22×C4⋊C4C2×D4711yescharacteristic
335C22×C42—471no—
336C22×C42—471no—
337C22×C42—471no—
338C22×C42—472no—
339#391—948no—
340#382—944no—
341C4×C4⋊C4—944no—
342C2×#95—472no—
343C2×#95—472no—
344C2×#95—472no—
345C2×#95—472no—
346C2×#95—472no—
347C2×#95—472no—
348C2×#95—472no—
349C2×#95—472no—
350C2×#95—471no—
351C2×#95C2×D4712yes—
352C2×#95C2×D4712yes—
353C2×#95C2×D4711yescharacteristic
354C47#1394211yescharacteristic, complemented, Sylow
355C22×Q8—474no—
356C22×Q8—474no—
357C22×Q8—474no—
358C22×Q8—942no—
359C22×Q8—942no—
360C22×Q8—942no—
361C22×Q8—942no—
362C23×C4—471no—
363C23×C4—471no—
364C23×C4—471no—
365C23×C4—471no—
366C23×C4—472no—
367C23×C4—472no—
368C23×C4C22×D4712yes—
369C23×C4C22×D4711yescharacteristic
370C23×C4C22×D4712yes—
371C23×C4C22×D4711yescharacteristic
372C23×C4C22×D4711yescharacteristic
373C4×Q8—9432no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—474no—
379C2×C4⋊C4—474no—
380C2×C4⋊C4—942no—
381C2×C4⋊C4—942no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—942no—
384C2×C4⋊C4—942no—
385C2×C4⋊C4—942no—
386C2×C4⋊C4—944no—
387C2×C4⋊C4—944no—
388C2×C4⋊C4—944no—
389C2×C4⋊C4C4×D4714yes—
390C2×C42—474no—
391C2×C42—474no—
392C2×C42—474no—
393C2×C42—474no—
394C2×C42—474no—
395C2×C42—942no—
396C2×C42—942no—
397C2×C42—942no—
398C2×C42—942no—
399C2×C42—944no—
400C2×C42—944no—
401C2×C42—944no—
402#95—22no—
403#95—24no—
404#95—24no—
405#95—944no—
406#95—944no—
407#95—944no—
408#95—944no—
409#95—944no—
410#95—944no—
411#95—942no—
412#95—944no—
413#95—944no—
414C24C23×D4711yescharacteristic
415C2×Q8—4716no—
416C2×Q8—948no—
417C2×Q8—948no—
418C2×Q8—948no—
419C2×Q8—948no—
420C2×Q8—948no—
421C2×Q8—948no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—472no—
446C22×C4—472no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—472no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—472no—
453C22×C4—472no—
454C22×C4—472no—
455C22×C4—472no—
456C22×C4—472no—
457C22×C4—472no—
458C22×C4—472no—
459C22×C4—474no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4C2×C4×D4712yes—
484C22×C4C2×C4×D4712yes—
485C22×C4C2×C4×D4712yes—
486C22×C4D4×D4712yes—
487C22×C4D4×D4712yes—
488C22×C4D4×D4712yes—
489C22×C4#1062535214yes—
490C22×C4Q8×D4712yes—
491C4⋊C4—28no—
492C4⋊C4—28no—
493C4⋊C4—948no—
494C4⋊C4—948no—
495C4⋊C4—948no—
496C4⋊C4—1888no—
497C42—4716no—
498C42—948no—
499C42—948no—
500C42—1888no—
501C23C22×C4×D4711yescharacteristic
502C23C2×D4×D4711yescharacteristic
503C23C2×D4×D4711yescharacteristic
504C23C2×D4×D4711yescharacteristic
505C23C2×Q8×D4711yescharacteristic
506C23#41×D4712yes—
507C23#41×D4711yescharacteristic
508C23#41×D4711yescharacteristic
509C23C2×#1062535212yes—
510C23#1309407112yes—
511C23#1309407212yes—
512Q8—9432no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—474no—
543C2×C4—474no—
544C2×C4—474no—
545C2×C4—474no—
546C2×C4—474no—
547C2×C4—474no—
548C2×C4—474no—
549C2×C4—474no—
550C2×C4—474no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—944no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—944no—
560C2×C4—942no—
561C2×C4—944no—
562C2×C4—944no—
563C2×C4—942no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4—1882no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4—1882no—
575C2×C4—1882no—
576C2×C4—1881no—
577C2×C4—1881no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4C22⋊C4×D4714yes—
581C2×C4C4⋊C4×D4714yes—
582C22C2×C22⋊C4×D4711yescharacteristic
583C22C2×C4⋊C4×D4711yescharacteristic
584C22#117×D4711yescharacteristic
585C22C4×#1062535212yes—
586C22#1568959912yes—
587C22#121×D4711yescharacteristic
588C22#121×D4711yescharacteristic
589C22C22⋊Q8×D4711yescharacteristic
590C22C22⋊Q8×D4711yescharacteristic
591C22#1568962911yescharacteristic
592C22#1568963111yescharacteristic
593C22#1568966812yes—
594C22#1568969311yescharacteristic
595C22#1568969612yes—
596C22#1568969811yescharacteristic
597C22#1568977912yes—
598C22#1568978312yes—
599C22#1568980512yes—
600C22#1568981012yes—
601C22#1568984012yes—
602C22#1568984412yes—
603C22#1568984812yes—
604C22#1568985012yes—
605C4—24no—
606C4—24no—
607C4—42no—
608C4—44no—
609C4—82no—
610C4—478no—
611C4—944no—
612C4—944no—
613C4—3762no—
614C4—1882no—
615C4—1884no—
616C2#380×D4711yescharacteristic
617C2#2024587311yescharacteristic
618C2#2024597111yescharacteristic
619C2#2024630712yes—
620C2#2024635012yes—
621C2#2024829211yescharacteristic
622C2#2024829411yescharacteristic
623C2#2024836312yes—
624C2#2024857412yes—
625C2#2024874911yescharacteristic
626C2#2024875111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1441C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1441D47
hypocenterC47#13942
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
15. C2×#13093989C4semidirect
176. C2×Dic94C4⋊C4semidirect
354. C47#13942semidirect

Maximal subgroups

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

subgroupindex
C22×#130939892
C2×#156890272
C2×#156889872
C2×C4⋊C4×Dic472
#202416422
#202416412
#202416382
Dic47⋊#952
#202416142
#202416132
C47×#14412
#1394247