Finite Group Databasebeta

← #26123269

Subgroups — #26123269

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689141C211yesmaximal, characteristic
2C2×#15689122C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4C2×#15688893C211yesmaximal, characteristic, complemented
5#20243107C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C47×#2316C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689141—22no—
13#15689141—22no—
14C2×#13093952—22no—
15#15689122—22no—
16#15689122—22no—
17C2×#13093947C412yescomplemented
18C2×#13093944C412yescomplemented
19#15689096—22no—
20#15689096—22no—
21C2×#13093938—22no—
22#15688893—22no—
23#15688885—22no—
24#15688879—22no—
25C2×#117×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#389—22no—
29C47×#389—22no—
30C47×#380—22no—
31C2×#10625350—21no—
32C2×#10625350—21no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350D412yes—
42C2×#10625350Q812yes—
43C22×Dic94C2×C411yescharacteristic
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47—21no—
46C22×C4×D47—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329D412yes—
59C22×C47⋊C8—21no—
60C22×C47⋊C8C2×C412yes—
61#13093983—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983D412yes—
65C2×C4⋊Dic47—21no—
66C2×C22⋊Dic47—21no—
67C2×C4×Dic47—21no—
68#13093952—28no—
69#13093947—24no—
70#13093944—24no—
71#13093938—28no—
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74#117×C47—21no—
75#117×C47—21no—
76#117×C47—21no—
77#117×C47—21no—
78#117×C47—21no—
79#117×C47—21no—
80#117×C47—21no—
81#117×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—24no—
88C2×C4⋊C4×C47C2×C412yes—
89C2×C4⋊C4×C47D412yes—
90C2×C4⋊C4×C47D412yes—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47D412yes—
93C2×C42×C47—21no—
94C2×C42×C47D412yes—
95#95×C47—24no—
96C24×C47C2×D411yescharacteristic
97C23×D47—21no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—82no—
104C22×C4×C47C22×C411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×Q811yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C2×C22⋊D47—22no—
119C2×C22⋊D47—22no—
120C2×C22⋊D47—41no—
121C2×C22⋊D47—41no—
122C2×C22⋊D47—41no—
123C2×C22⋊D47—41no—
124C22×Dic47—21no—
125C22×Dic47—41no—
126#10625350—22no—
127#10625350—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139#10625350—41no—
140#10625350—41no—
141#10625350—41no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188C4⋊C412yescomplemented
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×C4×D47—41no—
151C2×C4×D47—41no—
152C2×C4×D47—41no—
153C2×C4×D47—41no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94C4⋊C412yescomplemented
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47—41no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—84no—
168C4⋊C4×C47C22⋊C414yes—
169C22⋊C4×C47—22no—
170C22⋊C4×C47—22no—
171C22⋊C4×C47—41no—
172C22⋊C4×C47—41no—
173C42×C47—22no—
174C42×C47—22no—
175C42×C47—41no—
176C42×C47—41no—
177C22⋊Dic47—22no—
178C22⋊Dic47—41no—
179C4⋊Dic47—22no—
180C4⋊Dic47—41no—
181C4×Dic47—22no—
182C4×Dic47—41no—
183#10625329—22no—
184#10625329—22no—
185#10625329—41no—
186#10625329—41no—
187#10625329—41no—
188#10625329—41no—
189#10625329—41no—
190#10625329—41no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47C4×D411yescharacteristic
200C23×C47#12011yescharacteristic
201C23×C47#12011yescharacteristic
202C23×C47#12111yescharacteristic
203C23×C47#12111yescharacteristic
204C23×C47C22⋊Q811yescharacteristic
205C23×C47#12411yescharacteristic
206C22×D47—22no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—81no—
210C22×D47—81no—
211C2×C4×C47—24no—
212C2×C4×C47—44no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—82no—
220C2×C4×C47—82no—
221C2×C4×C47C2×C22⋊C411yescharacteristic
222C2×C4×C47C2×C4⋊C411yescharacteristic
223C2×C4×C47#11711yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47#12011yescharacteristic
228C2×C4×C47#12111yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47#12111yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47C22⋊Q811yescharacteristic
237C2×C4×C47C22⋊Q811yescharacteristic
238C2×C4×C47C22⋊Q811yescharacteristic
239C2×C4×C47#12311yescharacteristic
240C2×C4×C47#12311yescharacteristic
241C2×C4×C47#12311yescharacteristic
242C2×C4×C47#12311yescharacteristic
243C2×C4×C47#12311yescharacteristic
244C2×C4×C47#12411yescharacteristic
245C2×C4×C47#12411yescharacteristic
246C2×C4×C47#12611yescharacteristic
247C2×C4×C47#12611yescharacteristic
248C2×C4×C47#12711yescharacteristic
249C22⋊D47—42no—
250C22⋊D47—42no—
251C22⋊D47—42no—
252C22⋊D47—42no—
253C2×Dic47—22no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—42no—
257C2×Dic47—81no—
258C2×Dic47—81no—
259D188—22no—
260D188—22no—
261D188—41no—
262D188—41no—
263C4×D47—42no—
264C4×D47—42no—
265C4×D47—42no—
266C4×D47—42no—
267Dic94—22no—
268Dic94—22no—
269Dic94—41no—
270Dic94—41no—
271C47⋊C8—42no—
272C47⋊C8—42no—
273#11057—471nomaximal, Sylow
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—21no—
277C22×C47—21no—
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47#38511yescharacteristic
285C22×C47#38611yescharacteristic
286C22×C47#38811yescharacteristic
287C22×C47#39211yescharacteristic
288C22×C47#39311yescharacteristic
289C22×C47#39411yescharacteristic
290C22×C47#39611yescharacteristic
291C2×D47—42no—
292C2×D47—82no—
293C2×D47—81no—
294C2×D47—81no—
295C2×D47—82no—
296C4×C47—44no—
297C4×C47—82no—
298C4×C47—82no—
299C4×C47#38011yescharacteristic
300C4×C47#38511yescharacteristic
301C4×C47#38811yescharacteristic
302C4×C47#39011yescharacteristic
303C4×C47#39411yescharacteristic
304C4×C47#39611yescharacteristic
305C4×C47#39711yescharacteristic
306C4×C47#39911yescharacteristic
307Dic47—42no—
308Dic47—82no—
309C2×#421—471no—
310C2×#417—471no—
311C2×#410—471no—
312#2316D4711yescharacteristic, complemented
313C2×#344—471no—
314#1736—471no—
315C2×H(3,ℤ/4)—471no—
316C2×C47—21no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47#143911yescharacteristic
323C2×C47#190411yescharacteristic
324C2×C47#190511yescharacteristic
325D47—82no—
326C22×#41—471no—
327C22×M16—471no—
328C22×M16—471no—
329C2×#117—471no—
330C2×#117C2×D4711yescharacteristic
331C2×#117C2×D4711yescharacteristic
332C22×C4⋊C4C2×D4711yescharacteristic
333#421—942no—
334#421—942no—
335C2×#104—942no—
336#417—942no—
337#417—942no—
338C2×#103—472no—
339C2×#102—472no—
340#410—942no—
341#410—942no—
342C2×#99—942no—
343#389—22no—
344#389—22no—
345#380—22no—
346#344—942no—
347#340—942no—
348H(3,ℤ/4)—942no—
349C47#1105711yescharacteristic, complemented, Sylow
350C2×#41—472no—
351C2×#41—472no—
352C2×#41—941no—
353C2×#41—941no—
354C2×#41—941no—
355C2×#41—941no—
356C2×#41—941no—
357C2×#41—941no—
358C2×#41—941no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C22×Q8—471no—
363C22×D4—471no—
364C22×D4—941no—
365C23×C4—21no—
366C23×C4—941no—
367C23×C4C22×D4711yescharacteristic
368C2×M16—472no—
369C2×M16—941no—
370C2×M16—941no—
371C2×M16—941no—
372C2×M16—941no—
373C2×M16—941no—
374C2×M16—941no—
375C2×M16—941no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C22×C8—472no—
381C22×C8—941no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—472no—
391#117—941no—
392#117—941no—
393#117—941no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4C4×D4712yes—
402C2×C4⋊C4D18812yes—
403C2×C4⋊C4C22⋊D4712yes—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—941no—
406C2×C22⋊C4C22⋊D4712yes—
407C2×C42—21no—
408C2×C42—941no—
409C2×C42C22⋊D4712yes—
410#104—948no—
411#103—944no—
412#102—944no—
413#99—948no—
414#95—24no—
415C24—941no—
416C24C2×C22⋊D4711yescharacteristic
417#41—942no—
418#41—942no—
419#41—942no—
420#41—942no—
421#41—942no—
422#41—942no—
423#41—942no—
424#41—942no—
425#41—1881no—
426#41—1881no—
427#41—1881no—
428#41—1881no—
429#41—1881no—
430#41—1881no—
431#41—1881no—
432#41—1881no—
433C2×Q8—472no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×D4—472no—
440C2×D4—942no—
441C2×D4—942no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—941no—
446C2×D4—941no—
447C2×D4—1881no—
448C2×D4—1881no—
449C2×D4—1881no—
450C2×D4—1881no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—82no—
457C22×C4—941no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4—1881no—
463C22×C4—1881no—
464C22×C4—1881no—
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4C2×D18811yescharacteristic
467C22×C4#1062535011yescharacteristic
468C22×C4#1062535011yescharacteristic
469C22×C4D4×D4711yescharacteristic
470C22×C4D4×D4711yescharacteristic
471C22×C4D4×D4711yescharacteristic
472C22×C4#1062535211yescharacteristic
473C22×C4Q8×D4711yescharacteristic
474C22×C4#1062535411yescharacteristic
475C22×C4#1062535411yescharacteristic
476C22×C4#1062535411yescharacteristic
477C22×C4C2×C22⋊D4711yescharacteristic
478C22×C4C2×C22⋊D4711yescharacteristic
479M16—942no—
480M16—942no—
481M16—1881no—
482M16—1881no—
483M16—1881no—
484M16—1881no—
485M16—1881no—
486M16—1881no—
487C2×C8—942no—
488C2×C8—942no—
489C2×C8—942no—
490C2×C8—942no—
491C2×C8—1881no—
492C2×C8—1881no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—84no—
501C4⋊C4—942no—
502C4⋊C4—1881no—
503C4⋊C4(C2×D47)⋊C414yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—942no—
509C22⋊C4—1881no—
510C42—22no—
511C42—22no—
512C42—41no—
513C42—41no—
514C42—942no—
515C42—1881no—
516C23—41no—
517C23—41no—
518C23—942no—
519C23—3761no—
520C23—3761no—
521C23—1881no—
522C23—1881no—
523C23C4×C22⋊D4711yescharacteristic
524C23#1309399211yescharacteristic
525C23#1309399311yescharacteristic
526C23#1309399611yescharacteristic
527C23#1309399811yescharacteristic
528C23#1309400011yescharacteristic
529C23#1309401311yescharacteristic
530Q8—942no—
531Q8—942no—
532Q8—1881no—
533Q8—1881no—
534D4—942no—
535D4—942no—
536D4—1882no—
537D4—1882no—
538D4—1882no—
539D4—1882no—
540D4—1881no—
541D4—1881no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—942no—
553C2×C4—3761no—
554C2×C4—3761no—
555C2×C4—1882no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4C2×(C2×D47)⋊C411yescharacteristic
563C2×C4C4⋊C4×D4711yescharacteristic
564C2×C4#1309398211yescharacteristic
565C2×C4C4×C22⋊D4711yescharacteristic
566C2×C4#1309398611yescharacteristic
567C2×C4#1309398611yescharacteristic
568C2×C4#1309399211yescharacteristic
569C2×C4#1309399511yescharacteristic
570C2×C4#1309399611yescharacteristic
571C2×C4#1309399811yescharacteristic
572C2×C4#1309399911yescharacteristic
573C2×C4#1309399911yescharacteristic
574C2×C4#1309399911yescharacteristic
575C2×C4#1309400011yescharacteristic
576C2×C4#1309400011yescharacteristic
577C2×C4#1309400211yescharacteristic
578C2×C4#1309400211yescharacteristic
579C2×C4#1309400411yescharacteristic
580C2×C4#1309400711yescharacteristic
581C2×C4#1309400911yescharacteristic
582C2×C4#1309400911yescharacteristic
583C2×C4#1309400911yescharacteristic
584C2×C4#1309400911yescharacteristic
585C2×C4#1309401311yescharacteristic
586C2×C4#1309401311yescharacteristic
587C2×C4#1309401911yescharacteristic
588C2×C4#1309401911yescharacteristic
589C2×C4#1309402011yescharacteristic
590C8—1882no—
591C8—1882no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—3762no—
603C22—3762no—
604C22—3761no—
605C22—3761no—
606C22—1882no—
607C22#1568899411yescharacteristic
608C22#1568900211yescharacteristic
609C22#1568901311yescharacteristic
610C22#1568903111yescharacteristic
611C22#1568903411yescharacteristic
612C22#1568904011yescharacteristic
613C22#1568904511yescharacteristic
614C4—44no—
615C4—82no—
616C4—82no—
617C4—3762no—
618C4—1882no—
619C4#1568898011yescharacteristic
620C4#1568899411yescharacteristic
621C4#1568901311yescharacteristic
622C4#1568902411yescharacteristic
623C4#1568904011yescharacteristic
624C4#1568904511yescharacteristic
625C4#1568904911yescharacteristic
626C4#1568905811yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—3762no—
634C2#2024163011yescharacteristic
635C2#2024387511yescharacteristic
636C2#2024388211yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2316C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#2316D47
hypocenterC47#11057
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
4. C2×#15688893C2semidirect
5. #20243107C2semidirect
6. C2×#15688879C2semidirect
7. C47×#2316C2semidirect
17. C2×#13093947C4semidirect
18. C2×#13093944C4semidirect
147. C2×D188C4⋊C4semidirect
159. C2×Dic94C4⋊C4semidirect
312. #2316D47semidirect
349. C47#11057semidirect

Maximal subgroups

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

subgroupindex
C2×#156891412
C2×#156891222
C2×#156890962
C2×#156888932
#202431072
C2×#156888792
C47×#23162
#1105747