Finite Group Databasebeta

← #26137417

Subgroups — #26137417

Order 12032.

2294 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C211yesmaximal, characteristic
2C2×#15688970C212yesmaximal
3C2×#15688968C211yesmaximal, characteristic, complemented
4C2×C42×Dic47C211yesmaximal, characteristic, complemented
5#20241626C211yesmaximal, characteristic
6#20241624C212yesmaximal
7#20241624C211yesmaximal, characteristic
8#20241622C212yesmaximal, complemented
9#20241620C211yesmaximal, characteristic, complemented
10#95×Dic47C212yesmaximal, complemented
11C47×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C2×#13093982—24no—
14C2×#13093982—24no—
15C2×#13093982C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×(C2×D47)⋊C4C2211yescharacteristic
18C22×(C2×D47)⋊C4C2211yescharacteristic
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2212yes—
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2212yes—
25C22×C4×Dic47C2212yes—
26C22×C4×Dic47C2211yescharacteristic
27#15688970C4116yescomplemented
28#15688968—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C42×Dic47—24no—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C24×D47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C22×C4×D47—22no—
48C22×C4×D47—22no—
49C22×C4×D47—24no—
50C22×C4×D47C2×C418yes—
51C22×C4×D47C2×C414yes—
52#13093982—232no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47C2×C414yes—
56C2×(C2×D47)⋊C4—22no—
57C2×(C2×D47)⋊C4—22no—
58C2×(C2×D47)⋊C4—24no—
59C2×(C2×D47)⋊C4—24no—
60C2×(C2×D47)⋊C4—22no—
61C2×(C2×D47)⋊C4—22no—
62C2×(C2×D47)⋊C4—24no—
63C2×(C2×D47)⋊C4—24no—
64C2×(C2×D47)⋊C4C2×C418yes—
65C2×(C2×D47)⋊C4C2×C418yes—
66C2×(C2×D47)⋊C4C2×C414yes—
67C2×(C2×D47)⋊C4C2×C414yes—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—22no—
74C2×C4×Dic47—22no—
75C2×C4×Dic47—24no—
76C2×C4×Dic47—24no—
77C2×C4×Dic47—24no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47C2×C418yes—
80C2×C4×Dic47C2×C418yes—
81C2×C4×Dic47C2×C414yes—
82C2×C4×Dic47C2×C414yes—
83C2×C4×Dic47D414yes—
84C2×C4×Dic47D414yes—
85C47⋊#95—22no—
86C47⋊#95—24no—
87C47⋊#95—24no—
88C47⋊#95—24no—
89C47⋊#95—24no—
90C47⋊#95C2×C418yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2312yes—
93C23×C4×C47C2311yescharacteristic
94C23×C4×C47C2311yescharacteristic
95C23×C4×C47C2312yes—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47C2×C414yes—
99C2×C42×C47—22no—
100C2×C42×C47—24no—
101#95×C47—22no—
102#95×C47—24no—
103#95×C47C2×C418yes—
104C24×C47C2411yescharacteristic
105C23×D47—21no—
106C23×D47—21no—
107C23×D47—22no—
108C23×D47—22no—
109C23×D47—22no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47C22×C412yes—
113C23×D47C22×C414yes—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
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—21no—
124C22×C4×C47—21no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47C22×C412yes—
134C22×C4×C47C22×C414yes—
135C22×C4×C47C22×C412yes—
136C22×C4×C47C22×C414yes—
137C22×C4×C47C22×C412yes—
138C22×C4×C47C22×C414yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D412yes—
141C22×C4×C47#4114yes—
142C22×C4×C47#4114yes—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47C22×C414yes—
160C22×Dic47C22×C412yes—
161C22×Dic47C22×C412yes—
162C22×Dic47C22×C414yes—
163C22×Dic47C22×C412yes—
164C22×Dic47C22×C414yes—
165C22×Dic47C2×D412yes—
166C22×Dic47C2×D412yes—
167C22×Dic47C2×D412yes—
168C22×Dic47C2×D412yes—
169C22×Dic47#4114yes—
170C22×Dic47#4114yes—
171C22×Dic47#4114yes—
172C2×C4×D47—28no—
173C2×C4×D47—28no—
174C2×C4×D47—216no—
175C2×C4×D47—216no—
176C2×C4×D47C42116yescomplemented
177C4⋊C4×C47—28no—
178C42×C47—28no—
179(C2×D47)⋊C4—28no—
180(C2×D47)⋊C4—216no—
181(C2×D47)⋊C4—28no—
182(C2×D47)⋊C4—216no—
183C4⋊Dic47—28no—
184C4×Dic47—216no—
185C4×Dic47—28no—
186C4×Dic47—28no—
187C4×Dic47—216no—
188C4×Dic47—216no—
189C4×Dic47C22⋊C4116yescomplemented
190C23×C47C23×C411yescharacteristic
191C23×C47C23×C412yes—
192C23×C47C22×D411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C2×#4112yes—
195C23×C47C2×#4112yes—
196C23×C47C2×#4112yes—
197C23×C47C2×#4112yes—
198C23×C47C2×#4112yes—
199C22×D47—22no—
200C22×D47—24no—
201C22×D47—24no—
202C22×D47—22no—
203C22×D47—24no—
204C22×D47—24no—
205C22×D47—24no—
206C22×D47—24no—
207C22×D47—24no—
208C22×D47—24no—
209C22×D47—41no—
210C22×D47—41no—
211C22×D47—42no—
212C22×D47—42no—
213C22×D47—42no—
214C22×D47—42no—
215C22×D47—42no—
216C22×D47—42no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47C2×C4214yes—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47—22no—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—24no—
234C2×C4×C47—22no—
235C2×C4×C47—24no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—24no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—42no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—42no—
246C2×C4×C47C2×C4214yes—
247C2×C4×C47C2×C22⋊C414yes—
248C2×C4×C47#11718yescomplemented
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—24no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—24no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—24no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—41no—
269C2×Dic47—42no—
270C2×Dic47—41no—
271C2×Dic47C2×C4214yes—
272C2×Dic47C2×C22⋊C414yes—
273C2×Dic47C2×C22⋊C414yes—
274C2×Dic47#11714yes—
275C2×Dic47#11718yescomplemented
276C2×Dic47C4×D418yes—
277C2×Dic47C4×D418yes—
278C4×D47—232no—
279#13761—471nomaximal, Sylow
280C22×C47C22×C4211yescharacteristic
281C22×C47C22×C22⋊C411yescharacteristic
282C22×C47C2×#11711yescharacteristic
283C22×C47C2×#11712yes—
284C22×C47C2×#11712yes—
285C22×C47C2×C4×D412yes—
286C22×C47C2×C4×D412yes—
287C22×C47C4×#4112yes—
288C22×C47C4×#4112yes—
289C22×C47C4×#4112yes—
290C22×C47C4×#4112yes—
291C22×C47#52511yescharacteristic
292C22×C47#52511yescharacteristic
293C22×C47#52512yes—
294C22×C47#52912yes—
295C22×C47#52912yes—
296C22×C47#52912yes—
297C22×C47#52912yes—
298C22×C47#53212yes—
299C22×C47#53211yescharacteristic
300C22×C47#53211yescharacteristic
301C2×D47—24no—
302C2×D47—28no—
303C2×D47—44no—
304C2×D47—44no—
305C2×D47—44no—
306C2×D47—44no—
307C2×D47—42no—
308C2×D47—42no—
309C2×D47—44no—
310C4×C47—24no—
311C4×C47—28no—
312C4×C47—24no—
313C4×C47—44no—
314C4×C47—42no—
315Dic47—28no—
316Dic47—24no—
317Dic47—44no—
318Dic47—42no—
319Dic47C4×C22⋊C418yes—
320C22×#117—471no—
321C2×C4×C22⋊C4—472no—
322C2×#376—471no—
323C2×C43—471no—
324#1437—471no—
325#1437—471no—
326#1437—472no—
327#1436—472no—
328#1436—471no—
329#1436D4711yescharacteristic, complemented
330C4×#95—472no—
331C2×C47C2×C4×C22⋊C411yescharacteristic
332C2×C47C4×#11712yes—
333C2×C47#229012yes—
334C2×C47#229012yes—
335C2×C47#229312yes—
336C2×C47#229312yes—
337C2×C47#229711yescharacteristic
338C2×C47#229711yescharacteristic
339C2×C47#229812yes—
340D47—44no—
341C24×C4—471no—
342C2×#117—478no—
343C2×#117—944no—
344C2×#117—944no—
345C22×C4⋊C4—471no—
346C22×C4⋊C4C2×D4711yescharacteristic
347C22×C22⋊C4—471no—
348C22×C22⋊C4—471no—
349C22×C22⋊C4—472no—
350C22×C22⋊C4—472no—
351C22×C42—471no—
352C22×C42—471no—
353C22×C42—472no—
354C22×C42—472no—
355C22×C42—472no—
356C22×C42—471no—
357C22×C42C2×D4711yescharacteristic
358C4×C22⋊C4—4716no—
359#376—944no—
360C2×#95—472no—
361C2×#95—472no—
362C2×#95—472no—
363C2×#95—472no—
364C2×#95—472no—
365C2×#95—471no—
366C2×#95C2×D4712yes—
367C2×#95C2×D4711yescharacteristic
368C2×#95C2×D4712yes—
369C43—944no—
370C47#1376111yescharacteristic, complemented, Sylow
371C25—471no—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—472no—
375C23×C4—474no—
376C23×C4—478no—
377C23×C4—471no—
378C23×C4—472no—
379C23×C4—942no—
380C23×C4—942no—
381C23×C4—944no—
382C23×C4C22×D4711yescharacteristic
383C23×C4C22×D4712yes—
384C23×C4C22×D4711yescharacteristic
385C23×C4C22×D4711yescharacteristic
386C23×C4C22×D4712yes—
387#117—9432no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—474no—
391C2×C4⋊C4—942no—
392C2×C4⋊C4—942no—
393C2×C4⋊C4C4×D4714yes—
394C2×C22⋊C4—474no—
395C2×C22⋊C4—474no—
396C2×C22⋊C4—478no—
397C2×C22⋊C4—478no—
398C2×C22⋊C4—942no—
399C2×C22⋊C4—942no—
400C2×C22⋊C4—944no—
401C2×C22⋊C4—944no—
402C2×C22⋊C4—942no—
403C2×C22⋊C4—942no—
404C2×C22⋊C4—944no—
405C2×C22⋊C4—944no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—474no—
409C2×C42—474no—
410C2×C42—474no—
411C2×C42—474no—
412C2×C42—478no—
413C2×C42—478no—
414C2×C42—942no—
415C2×C42—942no—
416C2×C42—944no—
417C2×C42—944no—
418C2×C42—944no—
419C2×C42—944no—
420C2×C42—944no—
421C2×C42—944no—
422C2×C42—944no—
423C2×C42—942no—
424C2×C42—944no—
425#95—22no—
426#95—24no—
427#95—478no—
428#95—944no—
429#95—944no—
430#95—944no—
431#95—942no—
432#95—944no—
433#95C4×D4718yes—
434C24—472no—
435C24—474no—
436C24—941no—
437C24—941no—
438C24—942no—
439C24—942no—
440C24—942no—
441C24—942no—
442C24—942no—
443C24C23×D4711yescharacteristic
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—472no—
464C22×C4—474no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—474no—
468C22×C4—474no—
469C22×C4—472no—
470C22×C4—472no—
471C22×C4—472no—
472C22×C4—474no—
473C22×C4—474no—
474C22×C4—4716no—
475C22×C4—474no—
476C22×C4—472no—
477C22×C4—948no—
478C22×C4—948no—
479C22×C4—9416no—
480C22×C4—9416no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4C2×C4×D4714yes—
498C22×C4C2×C4×D4712yes—
499C22×C4C2×C4×D4714yes—
500C22×C4C2×C4×D4712yes—
501C22×C4C2×C4×D4712yes—
502C22×C4C2×C4×D4714yes—
503C22×C4D4×D4712yes—
504C22×C4D4×D4712yes—
505C22×C4#1062535214yes—
506C22×C4#1062535414yes—
507C4⋊C4—28no—
508C4⋊C4—948no—
509C22⋊C4—9416no—
510C22⋊C4—948no—
511C22⋊C4—948no—
512C22⋊C4—9416no—
513C42—28no—
514C42—4716no—
515C42—9416no—
516C42—9416no—
517C42—948no—
518C42—948no—
519C42—9416no—
520C23—474no—
521C23—942no—
522C23—944no—
523C23—942no—
524C23—944no—
525C23—944no—
526C23—944no—
527C23—944no—
528C23—944no—
529C23—944no—
530C23—944no—
531C23—1881no—
532C23—1881no—
533C23—1882no—
534C23—1882no—
535C23—1882no—
536C23—1882no—
537C23—1882no—
538C23—1882no—
539C23—1881no—
540C23—1881no—
541C23C22×C4×D4711yescharacteristic
542C23C22×C4×D4712yes—
543C23C2×D4×D4711yescharacteristic
544C23C2×D4×D4711yescharacteristic
545C23#41×D4712yes—
546C23#41×D4712yes—
547C23#41×D4712yes—
548C23C2×#1062535212yes—
549C23C2×#1062535412yes—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—474no—
577C2×C4—474no—
578C2×C4—474no—
579C2×C4—478no—
580C2×C4—478no—
581C2×C4—474no—
582C2×C4—478no—
583C2×C4—9432no—
584C2×C4—944no—
585C2×C4—944no—
586C2×C4—944no—
587C2×C4—944no—
588C2×C4—944no—
589C2×C4—944no—
590C2×C4—944no—
591C2×C4—944no—
592C2×C4—942no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—944no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1881no—
604C2×C4—1882no—
605C2×C4—1881no—
606C2×C4C42×D4714yes—
607C2×C4C22⋊C4×D4714yes—
608C2×C4#1309398218yescomplemented
609C22—944no—
610C22—948no—
611C22—1884no—
612C22—1884no—
613C22—1884no—
614C22—1884no—
615C22—1882no—
616C22—1882no—
617C22—1884no—
618C22C2×C42×D4711yescharacteristic
619C22C2×C22⋊C4×D4711yescharacteristic
620C22#117×D4712yes—
621C22#117×D4711yescharacteristic
622C22C2×#1309398212yes—
623C22C4×D4×D4712yes—
624C22C4×D4×D4712yes—
625C22C4×#1062535212yes—
626C22C4×#1062535212yes—
627C22C4×#1062535412yes—
628C22C4×#1062535412yes—
629C22#1568962911yescharacteristic
630C22#1568963111yescharacteristic
631C22#1568963612yes—
632C22#1568965012yes—
633C22#1568965612yes—
634C22#1568965812yes—
635C22#1568965912yes—
636C22#1568966812yes—
637C22#1568967211yescharacteristic
638C22#1568967411yescharacteristic
639C4—28no—
640C4—24no—
641C4—24no—
642C4—44no—
643C4—42no—
644C4—478no—
645C4—948no—
646C4—944no—
647C4—1884no—
648C4—1882no—
649C2—1884no—
650C2C4×C22⋊C4×D4711yescharacteristic
651C2C4×#1309398212yes—
652C2#2024582412yes—
653C2#2024582612yes—
654C2#2024584612yes—
655C2#2024584812yes—
656C2#2024587311yescharacteristic
657C2#2024587711yescharacteristic
658C2#2024588012yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1436D47
hypocenterC47#13761
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#15688968C2semidirect
4. C2×C42×Dic47C2semidirect
8. #20241622C2semidirect
9. #20241620C2semidirect
10. #95×Dic47C2semidirect
11. C47×#1436C2semidirect
15. C2×#13093982C4semidirect
27. #15688970C4semidirect
176. C2×C4×D47C42semidirect
189. C4×Dic47C22⋊C4semidirect
248. C2×C4×C47#117semidirect
275. C2×Dic47#117semidirect
329. #1436D47semidirect
370. C47#13761semidirect
608. C2×C4#13093982semidirect

Maximal subgroups

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

subgroupindex
C22×#130939822
C2×#156889702
C2×#156889682
C2×C42×Dic472
#202416262
#202416242
#202416222
#202416202
#95×Dic472
C47×#14362
#1376147