Finite Group Databasebeta

← #26217512

Subgroups — #26217512

Order 12032.

1954 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689635C211yesmaximal, characteristic
2C22×#13093982C211yesmaximal, characteristic, complemented
3C2×#15689125C211yesmaximal, characteristic, complemented
4C2×#15689122C211yesmaximal, characteristic, complemented
5C2×#15689086C211yesmaximal, characteristic, complemented
6#20243709C214yesmaximal, complemented
7#20243699C214yesmaximal, complemented
8#20243109C211yesmaximal, characteristic, complemented
9C47×#1736C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C23×C4×D47C2211yescharacteristic
12C22×#10625329C2211yescharacteristic
13#15689635—24no—
14#15689635C418yescomplemented
15C2×#13094008—21no—
16C2×#13094004C2212yes—
17C2×#13093999C2212yes—
18C2×#13093994—21no—
19C2×C4×D188—22no—
20C2×#13093982—22no—
21C2×#13093982—24no—
22C2×#13093982—24no—
23C2×#13093982C2214yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4—21no—
26C22×C4×Dic47—21no—
27#15689125—24no—
28#15689122—24no—
29C2×#13093949C2212yescomplemented
30C2×#13093947C2212yescomplemented
31C2×#13093946C2212yescomplemented
32C2×#13093944C2212yescomplemented
33#15689086—24no—
34C2×(C2×D47)⋊C8C2214yes—
35#15688885C2214yescomplemented
36C22×M16×C47C2211yescharacteristic
37C2×#117×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C47×#340C2214yescomplemented
40C24×D47D411yescharacteristic
41C2×#10625350—22no—
42C2×#10625350—22no—
43C2×#10625350—22no—
44C2×#10625350—22no—
45C2×#10625350—22no—
46C2×#10625350C2×C414yes—
47C22×Dic94C2311yescharacteristic
48C22×D188—22no—
49C22×D188C2311yescharacteristic
50C22×C22⋊D47—21no—
51C23×Dic47—21no—
52C23×Dic47D411yescharacteristic
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—21no—
58C22×C4×D47C2×C414yes—
59C22×C4×D47D412yes—
60C22×C4×D47D414yes—
61C22×C4×D47C2312yes—
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C22×C47⋊C8C2312yes—
66#13094008—28no—
67#13094004—24no—
68#13094004C2×C418yescomplemented
69#13093999—24no—
70#13093999C2×C418yescomplemented
71#13093994—28no—
72C4×D188—216no—
73#13093982—216no—
74#13093982—28no—
75#13093982—28no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—22no—
79C2×C4⋊Dic47D414yescomplemented
80C2×C4⋊Dic47C2312yes—
81C2×(C2×D47)⋊C4—28no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×C4×Dic47—28no—
86C2×C4×Dic47—24no—
87#13093949—24no—
88#13093947—24no—
89#13093946—24no—
90#13093944—24no—
91(C2×D47)⋊C8—28no—
92C23×C4×C47—21no—
93C23×C4×C47C2311yescharacteristic
94C2×M16×C47—22no—
95C2×M16×C47—22no—
96C2×M16×C47—22no—
97C22×C8×C47C2312yes—
98#117×C47—22no—
99#117×C47C2×C414yes—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47D414yescomplemented
103C2×C4⋊C4×C47C2312yes—
104C2×C4⋊C4×C47C2312yes—
105C2×C22⋊C4×C47—21no—
106C2×C42×C47—21no—
107C24×C47C2×D411yescharacteristic
108C23×D47—22no—
109C23×D47—22no—
110C23×D47—21no—
111C23×D47—42no—
112C23×D47—42no—
113C23×D47C22⋊C414yes—
114C23×D47C2×D412yes—
115C22×C4×C47—24no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—44no—
119C22×C4×C47C22×C412yes—
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D412yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×D412yes—
124C22×C4×C47#4112yes—
125C22×C4×C47#4112yes—
126C22×C4×C47C2411yescharacteristic
127C2×C22⋊D47—24no—
128C2×C22⋊D47—42no—
129C2×C22⋊D47—42no—
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—24no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—44no—
136C22×Dic47C22⋊C414yes—
137C22×Dic47C2×D412yes—
138#10625350—28no—
139#10625350—28no—
140#10625350—44no—
141#10625350—44no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—28no—
147C2×D188—21no—
148C2×D188—44no—
149C2×D188—44no—
150C2×D188C22×C412yes—
151C2×C4×D47—28no—
152C2×C4×D47—28no—
153C2×C4×D47—24no—
154C2×C4×D47—28no—
155C2×C4×D47—28no—
156C2×C4×D47—24no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—24no—
162C2×C4×D47—42no—
163C2×C4×D47—42no—
164C2×C4×D47C22⋊C418yes—
165C2×C4×D47C22×C414yes—
166C2×C4×D47C2×D414yes—
167C2×Dic94—21no—
168C2×Dic94—21no—
169C2×Dic94—21no—
170C2×Dic94—21no—
171C2×Dic94—21no—
172C2×Dic94C22×C412yes—
173M16×C47—44no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C4⋊C4×C47—24no—
178C4⋊C4×C47—22no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47C22×C414yes—
181C4⋊C4×C47C2×D414yes—
182C22⋊C4×C47—24no—
183C42×C47—24no—
184(C2×D47)⋊C4—216no—
185(C2×D47)⋊C4—28no—
186(C2×D47)⋊C4—28no—
187C4⋊Dic47—24no—
188C4⋊Dic47—22no—
189C4⋊Dic47—28no—
190C4⋊Dic47C2×D414yes—
191C4×Dic47—216no—
192#10625329—44no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—22no—
196C23×C47—22no—
197C23×C47—22no—
198C23×C47C2×C22⋊C412yes—
199C23×C47#12012yes—
200C23×C47#12312yes—
201C23×C47C22×D411yescharacteristic
202C22×D47—22no—
203C22×D47—22no—
204C22×D47—22no—
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—22no—
208C22×D47—28no—
209C22×D47—22no—
210C22×D47—48no—
211C22×D47—48no—
212C22×D47—44no—
213C22×D47—44no—
214C22×D47—41no—
215C22×D47—41no—
216C22×D47—42no—
217C22×D47—42no—
218C22×D47C2×C22⋊C414yes—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—48no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—44no—
225C2×C4×C47C2×C22⋊C412yes—
226C2×C4×C47C4×D414yes—
227C2×C4×C47C4×D414yes—
228C2×C4×C47#12012yes—
229C2×C4×C47#12114yes—
230C2×C4×C47#12114yes—
231C2×C4×C47#12312yes—
232C2×C4×C47C23×C411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C22⋊D47—48no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—28no—
242C2×Dic47—22no—
243C2×Dic47—24no—
244C2×Dic47—48no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—44no—
248C2×Dic47C2×C22⋊C414yes—
249D188—22no—
250D188—22no—
251D188—416no—
252D188—41no—
253D188—41no—
254C4×D47—24no—
255C4×D47—24no—
256C4×D47—24no—
257C4×D47—24no—
258C4×D47—216no—
259C4×D47—48no—
260Dic94—22no—
261Dic94—22no—
262Dic94—41no—
263Dic94—41no—
264C8×C47—42no—
265C47⋊C8—42no—
266#20910—471nomaximal, Sylow
267C22×C47—24no—
268C22×C47—24no—
269C22×C47—22no—
270C22×C47—22no—
271C22×C47#38614yes—
272C22×C47C22×C22⋊C411yescharacteristic
273C22×C47C2×#12011yescharacteristic
274C22×C47C2×#12311yescharacteristic
275C22×C47#57512yes—
276C22×C47#57512yes—
277C2×D47—24no—
278C2×D47—24no—
279C2×D47—24no—
280C2×D47—416no—
281C2×D47—42no—
282C2×D47—42no—
283C2×D47—42no—
284C2×D47—42no—
285C2×D47—44no—
286C2×D47—42no—
287C2×D47—82no—
288C2×D47—81no—
289C2×D47—81no—
290C4×C47—44no—
291C4×C47—44no—
292C4×C47#38614yes—
293C4×C47C2×C4×D411yescharacteristic
294C4×C47C2×C4×D411yescharacteristic
295C4×C47C2×#12111yescharacteristic
296C4×C47C2×#12111yescharacteristic
297Dic47—24no—
298Dic47—44no—
299Dic47—42no—
300C2×#525—471no—
301C22×#117—471no—
302C2×#417—471no—
303C2×#417—471no—
304C2×#407—471no—
305#1875—474no—
306#1873—474no—
307#1736—471no—
308#1736D4711yescharacteristic, complemented
309C2×C47—24no—
310C2×C47C2×#38611yescharacteristic
311C2×C47#289612yes—
312C2×C47#300511yescharacteristic
313C2×C47#300511yescharacteristic
314C2×C47#309312yes—
315D47—44no—
316D47—82no—
317C22×#41—471no—
318C24×C4—471no—
319C22×M16—471no—
320C22×M16C2×D4711yescharacteristic
321#525—478no—
322#525—944no—
323C2×#123—941no—
324C2×C22⋊Q8—472no—
325C2×#121—472no—
326C2×#120—941no—
327C2×C4×D4—942no—
328C2×#117—474no—
329C2×#117—944no—
330C2×#117—942no—
331C2×#117—944no—
332C2×#117C2×D4711yescharacteristic
333C22×C4⋊C4—471no—
334C22×C4⋊C4C2×D4711yescharacteristic
335C22×C22⋊C4—941no—
336C22×C42—941no—
337#417—944no—
338#417—944no—
339C2×#103—472no—
340C2×#103—472no—
341C2×#102—472no—
342C2×#102—472no—
343#407—944no—
344C2×C22⋊C8—474no—
345#340—474no—
346#340C2×D4714yescomplemented
347C47#2091011yescharacteristic, complemented, Sylow
348C25—471no—
349C2×#41—474no—
350C2×#41—942no—
351C2×#41—942no—
352C2×#41—942no—
353C2×#41—942no—
354C2×#41—942no—
355C22×Q8—471no—
356C22×D4—471no—
357C22×D4—942no—
358C22×D4—941no—
359C23×C4—21no—
360C23×C4—471no—
361C23×C4—474no—
362C23×C4—472no—
363C23×C4—474no—
364C23×C4—472no—
365C23×C4—942no—
366C23×C4—942no—
367C23×C4—942no—
368C23×C4—942no—
369C23×C4—941no—
370C23×C4—941no—
371C23×C4C22×D4711yescharacteristic
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—942no—
376C2×M16—942no—
377C2×M16—942no—
378C22×C8—472no—
379C22×C8C22×D4712yes—
380#123—948no—
381C22⋊Q8—478no—
382C22⋊Q8—944no—
383#121—478no—
384#121—944no—
385#120—948no—
386C4×D4—9416no—
387#117—22no—
388#117—948no—
389#117—9416no—
390#117—948no—
391#117C4×D4714yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—474no—
395C2×C4⋊C4—472no—
396C2×C4⋊C4—942no—
397C2×C4⋊C4—942no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4D18814yescomplemented
400C2×C4⋊C4C22×D4712yes—
401C2×C4⋊C4C22×D4712yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—942no—
404C2×C22⋊C4—944no—
405C2×C22⋊C4—942no—
406C2×C22⋊C4—948no—
407C2×C42—21no—
408C2×C42—944no—
409C2×C42—948no—
410#103—944no—
411#103—944no—
412#102—944no—
413#102—944no—
414C22⋊C8—948no—
415C24—472no—
416C24—474no—
417C24—942no—
418C24—942no—
419C24—941no—
420C24—1882no—
421C24—1882no—
422C24D4×D4711yescharacteristic
423#41—948no—
424#41—948no—
425#41—1884no—
426#41—1884no—
427C2×Q8—472no—
428C2×Q8—941no—
429C2×Q8—941no—
430C2×Q8—941no—
431C2×Q8—941no—
432C2×Q8—941no—
433C2×D4—472no—
434C2×D4—948no—
435C2×D4—944no—
436C2×D4—941no—
437C2×D4—941no—
438C2×D4—941no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—1884no—
442C2×D4—1884no—
443C2×D4—1882no—
444C2×D4—1882no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—44no—
449C22×C4—474no—
450C22×C4—472no—
451C22×C4—478no—
452C22×C4—474no—
453C22×C4—474no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—948no—
457C22×C4—948no—
458C22×C4—944no—
459C22×C4—948no—
460C22×C4—948no—
461C22×C4—944no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—944no—
467C22×C4—942no—
468C22×C4—941no—
469C22×C4—944no—
470C22×C4—1884no—
471C22×C4—1882no—
472C22×C4—1882no—
473C22×C4C2×C4×D4712yes—
474C22×C4C2×D18812yes—
475C22×C4#1062535012yes—
476C22×C4D4×D4711yescharacteristic
477C22×C4D4×D4712yes—
478C22×C4D4×D4712yes—
479C22×C4#1062535412yes—
480C22×C4C23×D4711yescharacteristic
481M16—44no—
482M16—1884no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—942no—
487C2×C8—942no—
488C2×C8—942no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—474no—
493C4⋊C4—948no—
494C4⋊C4—944no—
495C4⋊C4—942no—
496C4⋊C4C2×C4×D4714yes—
497C4⋊C4C2×D18814yes—
498C22⋊C4—24no—
499C22⋊C4—948no—
500C22⋊C4—948no—
501C22⋊C4—9416no—
502C42—24no—
503C42—9416no—
504C23—22no—
505C23—22no—
506C23—474no—
507C23—948no—
508C23—942no—
509C23—942no—
510C23—942no—
511C23—942no—
512C23—942no—
513C23—942no—
514C23—942no—
515C23—1888no—
516C23—1888no—
517C23—1884no—
518C23—1884no—
519C23—1881no—
520C23—1881no—
521C23—1882no—
522C23—1882no—
523C23C22⋊C4×D4712yes—
524C23#1309399412yes—
525C23#1309400912yes—
526C23C2×D4×D4711yescharacteristic
527Q8—942no—
528Q8—942no—
529Q8—1881no—
530Q8—1881no—
531D4—942no—
532D4—942no—
533D4—18816no—
534D4—1888no—
535D4—1881no—
536D4—1881no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—48no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—474no—
544C2×C4—948no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—9416no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—944no—
551C2×C4—944no—
552C2×C4—942no—
553C2×C4—944no—
554C2×C4—1888no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1884no—
558C2×C4—1888no—
559C2×C4C22⋊C4×D4712yes—
560C2×C4#1309398614yes—
561C2×C4C4×D18814yes—
562C2×C4#1309399412yes—
563C2×C4#1309399714yes—
564C2×C4#1309399914yes—
565C2×C4#1309400912yes—
566C2×C4C22×C4×D4711yescharacteristic
567C2×C4C2×D4×D4711yescharacteristic
568C2×C4C2×D4×D4711yescharacteristic
569C2×C4C22×D18811yescharacteristic
570C2×C4C2×#1062535011yescharacteristic
571C2×C4C2×#1062535411yescharacteristic
572C8—42no—
573C8—1882no—
574C22—24no—
575C22—24no—
576C22—22no—
577C22—22no—
578C22—944no—
579C22—944no—
580C22—944no—
581C22—3762no—
582C22—3761no—
583C22—3761no—
584C22—18816no—
585C22—1884no—
586C22—1882no—
587C22—1882no—
588C22—1882no—
589C22—1882no—
590C22—1882no—
591C22#1568900114yes—
592C22C2×C22⋊C4×D4711yescharacteristic
593C22C2×#1309399411yescharacteristic
594C22C2×#1309400911yescharacteristic
595C22#1568991912yes—
596C22#1568992212yes—
597C4—44no—
598C4—44no—
599C4—944no—
600C4—1882no—
601C4—1884no—
602C4#1568900114yes—
603C4C2×#1309398611yescharacteristic
604C4C2×C4×D18811yescharacteristic
605C4C2×#1309399711yescharacteristic
606C4C2×#1309399911yescharacteristic
607C2—24no—
608C2—3762no—
609C2—1884no—
610C2C2×#1568900111yescharacteristic
611C2#2025190412yes—
612C2#2025263211yescharacteristic
613C2#2025263411yescharacteristic
614C2#2025332212yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1736C2
socleC23×C47C22×D4
prime radicalC2×#15689635C2
cosocleC22×C4×C47C24
hypercenter#1736D47
hypocenterC47#20910
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C22×#13093982C2semidirect
3. C2×#15689125C2semidirect
4. C2×#15689122C2semidirect
5. C2×#15689086C2semidirect
6. #20243709C2semidirect
7. #20243699C2semidirect
8. #20243109C2semidirect
9. C47×#1736C2semidirect
14. #15689635C4semidirect
29. C2×#13093949C22semidirect
30. C2×#13093947C22semidirect
31. C2×#13093946C22semidirect
32. C2×#13093944C22semidirect
35. #15688885C22semidirect
39. C47×#340C22semidirect
68. #13094004C2×C4semidirect
70. #13093999C2×C4semidirect
79. C2×C4⋊Dic47D4semidirect
102. C2×C4⋊C4×C47D4semidirect
308. #1736D47semidirect
346. #340C2×D47semidirect
347. C47#20910semidirect
399. C2×C4⋊C4D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156896352
C22×#130939822
C2×#156891252
C2×#156891222
C2×#156890862
#202437092
#202436992
#202431092
C47×#17362
#2091047