Finite Group Databasebeta

← #26123579

Subgroups — #26123579

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093957C211yesmaximal, characteristic, complemented
2C2×#15689125C211yesmaximal, characteristic
3C2×#15689122C211yesmaximal, characteristic
4C2×#15689091C211yesmaximal, characteristic
5C2×#15688891C211yesmaximal, characteristic, complemented
6C2×#15688887C211yesmaximal, characteristic, complemented
7C2×C47×#343C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C23×C47⋊C8C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C2×#13093957—22no—
13C2×#13093957—22no—
14C2×#13093957—22no—
15#15689125—22no—
16#15689125—22no—
17#15689122—22no—
18#15689122—22no—
19C2×#13093949—21no—
20C2×#13093947—21no—
21C2×#13093946—21no—
22C2×#13093944—21no—
23#15689091—22no—
24#15689091C414yescomplemented
25C2×(C2×D47)⋊C8—22no—
26#15688891—22no—
27#15688887—22no—
28C22×M16×C47C2211yescharacteristic
29C22×M16×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C47×#343—22no—
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×#10625350—21no—
42C2×#10625350C2×C412yes—
43C2×#10625350Q812yes—
44C22×Dic94D411yescharacteristic
45C22×D188D411yescharacteristic
46C22×C22⋊D47—21no—
47C23×Dic47—21no—
48C22×C4×D47—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329D412yes—
55C22×C47⋊C8—21no—
56C22×C47⋊C8—21no—
57C22×C47⋊C8—21no—
58C22×C47⋊C8—21no—
59C22×C47⋊C8—21no—
60C22×C47⋊C8C2×C412yes—
61C22×C47⋊C8D412yes—
62C22×C47⋊C8D412yes—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47D412yes—
69#13093957—28no—
70#13093949—24no—
71#13093947—24no—
72#13093946—24no—
73#13093944—24no—
74(C2×D47)⋊C8—28no—
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47—21no—
83C2×M16×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47C2×C412yes—
88C2×M16×C47D412yes—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47D412yes—
97C24×C47#4111yescharacteristic
98C23×D47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47—82no—
103C22×C4×C47C22×C411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
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
117C2×C22⋊D47—22no—
118C2×C22⋊D47—22no—
119C2×C22⋊D47—41no—
120C2×C22⋊D47—41no—
121C2×C22⋊D47—41no—
122C2×C22⋊D47—41no—
123C22×Dic47—21no—
124C22×Dic47—22no—
125C22×Dic47—41no—
126C22×Dic47—41no—
127C22×Dic47—82no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139#10625350—41no—
140#10625350—41no—
141#10625350—41no—
142#10625350—41no—
143#10625350—41no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188C4⋊C412yes—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—41no—
153C2×C4×D47—41no—
154C2×C4×D47—41no—
155C2×C4×D47—41no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94C4⋊C412yes—
162M16×C47—22no—
163M16×C47—22no—
164M16×C47—22no—
165M16×C47—22no—
166M16×C47—41no—
167M16×C47—41no—
168M16×C47—41no—
169M16×C47—41no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—41no—
173C2×C8×C47—41no—
174C2×C8×C47—41no—
175C2×C8×C47—41no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—22no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47—41no—
180C4⋊Dic47—22no—
181C4⋊Dic47—22no—
182C4⋊Dic47—41no—
183C4⋊Dic47—41no—
184#10625329—22no—
185#10625329—22no—
186#10625329—41no—
187#10625329—41no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C2×C47⋊C8C22⋊C414yes—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47#11711yescharacteristic
201C23×C47#12111yescharacteristic
202C23×C47#12111yescharacteristic
203C23×C47#12111yescharacteristic
204C23×C47C22⋊Q811yescharacteristic
205C23×C47#12611yescharacteristic
206C23×C47#12611yescharacteristic
207C22×D47—22no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—42no—
211C22×D47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—82no—
214C2×C4×C47—82no—
215C2×C4×C47—82no—
216C2×C4×C47C2×C22⋊C411yescharacteristic
217C2×C4×C47C2×C4⋊C411yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47C4×D411yescharacteristic
222C2×C4×C47#12011yescharacteristic
223C2×C4×C47#12011yescharacteristic
224C2×C4×C47#12011yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12111yescharacteristic
227C2×C4×C47#12111yescharacteristic
228C2×C4×C47#12111yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47C22⋊Q811yescharacteristic
231C2×C4×C47C22⋊Q811yescharacteristic
232C2×C4×C47C22⋊Q811yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47#12311yescharacteristic
236C2×C4×C47#12311yescharacteristic
237C2×C4×C47#12311yescharacteristic
238C2×C4×C47#12311yescharacteristic
239C2×C4×C47#12311yescharacteristic
240C2×C4×C47#12411yescharacteristic
241C2×C4×C47#12411yescharacteristic
242C2×C4×C47#12411yescharacteristic
243C2×C4×C47#12711yescharacteristic
244C22⋊D47—42no—
245C22⋊D47—42no—
246C22⋊D47—42no—
247C22⋊D47—42no—
248C2×Dic47—22no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—42no—
252C2×Dic47—82no—
253C2×Dic47—82no—
254C2×Dic47—82no—
255D188—22no—
256D188—22no—
257D188—41no—
258D188—41no—
259C4×D47—42no—
260C4×D47—42no—
261C4×D47—42no—
262C4×D47—42no—
263Dic94—22no—
264Dic94—22no—
265Dic94—41no—
266Dic94—41no—
267C8×C47—42no—
268C8×C47—42no—
269C47⋊C8—24no—
270C47⋊C8—42no—
271#11107—471nomaximal, Sylow
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—22no—
275C22×C47—22no—
276C22×C47—21no—
277C22×C47—21no—
278C22×C47—21no—
279C22×C47—21no—
280C22×C47#38011yescharacteristic
281C22×C47#38811yescharacteristic
282C22×C47#38811yescharacteristic
283C22×C47#39211yescharacteristic
284C22×C47#39611yescharacteristic
285C22×C47#39611yescharacteristic
286C22×C47#39711yescharacteristic
287C22×C47#47212yes—
288C22×C47#47312yes—
289C2×D47—44no—
290C2×D47—42no—
291C2×D47—82no—
292C2×D47—81no—
293C2×D47—81no—
294C4×C47—82no—
295C4×C47#38511yescharacteristic
296C4×C47#38511yescharacteristic
297C4×C47#38611yescharacteristic
298C4×C47#39011yescharacteristic
299C4×C47#39311yescharacteristic
300C4×C47#39411yescharacteristic
301C4×C47#39411yescharacteristic
302C4×C47#39911yescharacteristic
303Dic47—42no—
304Dic47—82no—
305C22×#107—471no—
306C2×#417—471no—
307C2×#417—471no—
308C2×#408—471no—
309C2×#343—471no—
310C2×#343D4711yescharacteristic, complemented
311C2×#341—471no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47—21no—
315C2×C47—21no—
316C2×C47#143911yescharacteristic
317C2×C47#181612yes—
318C2×C47#201811yescharacteristic
319C2×C47#202011yescharacteristic
320C2×C47#207812yes—
321D47—82no—
322C22×#41—471no—
323C22×M16—471no—
324C22×M16C2×D4711yescharacteristic
325C22×M16C2×D4711yescharacteristic
326C23×C8—471no—
327C22×C4⋊C4—471no—
328C22×C4⋊C4C2×D4711yescharacteristic
329C2×#107—942no—
330C2×#107—942no—
331C2×#107—942no—
332#417—942no—
333#417—942no—
334#417—942no—
335#417—942no—
336C2×#103—941no—
337C2×#103—941no—
338C2×#102—941no—
339C2×#102—941no—
340#408—474no—
341#408—942no—
342C2×C22⋊C8—942no—
343#343—22no—
344#343—942no—
345#341—942no—
346C47#1110711yescharacteristic, complemented, Sylow
347C2×#41—472no—
348C2×#41—472no—
349C2×#41—941no—
350C2×#41—941no—
351C2×#41—941no—
352C2×#41—941no—
353C2×#41—941no—
354C2×#41—941no—
355C2×#41—941no—
356C2×#41—941no—
357C2×#41—941no—
358C2×#41—941no—
359C22×Q8—471no—
360C22×D4—471no—
361C22×D4—941no—
362C23×C4—21no—
363C23×C4—941no—
364C23×C4—941no—
365C23×C4C22×D4711yescharacteristic
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—472no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16C4×D4712yes—
383C2×M16C22⋊D4712yes—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—472no—
387C22×C8—472no—
388C22×C8—472no—
389C22×C8—941no—
390C22×C8—941no—
391C22×C8—941no—
392C22×C8—941no—
393C22×C8—941no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—472no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4D18812yes—
406#107—948no—
407#103—944no—
408#103—944no—
409#102—944no—
410#102—944no—
411C22⋊C8—948no—
412C24—941no—
413C24#1062535011yescharacteristic
414#41—942no—
415#41—942no—
416#41—942no—
417#41—942no—
418#41—942no—
419#41—942no—
420#41—942no—
421#41—942no—
422#41—1881no—
423#41—1881no—
424#41—1881no—
425#41—1881no—
426#41—1881no—
427#41—1881no—
428#41—1881no—
429#41—1881no—
430C2×Q8—472no—
431C2×Q8—941no—
432C2×Q8—941no—
433C2×Q8—941no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×D4—472no—
437C2×D4—942no—
438C2×D4—942no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—1881no—
445C2×D4—1881no—
446C2×D4—1881no—
447C2×D4—1881no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—82no—
452C22×C4—941no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—3762no—
457C22×C4—1881no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4—1881no—
463C22×C4C2×C4×D4711yescharacteristic
464C22×C4C2×D18811yescharacteristic
465C22×C4#1062535011yescharacteristic
466C22×C4#1062535011yescharacteristic
467C22×C4#1062535011yescharacteristic
468C22×C4D4×D4711yescharacteristic
469C22×C4D4×D4711yescharacteristic
470C22×C4D4×D4711yescharacteristic
471C22×C4D4×D4711yescharacteristic
472C22×C4D4×D4711yescharacteristic
473C22×C4#1062535211yescharacteristic
474C22×C4Q8×D4711yescharacteristic
475C22×C4#1062535411yescharacteristic
476C22×C4C2×C22⋊D4711yescharacteristic
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—942no—
486M16—942no—
487M16—1881no—
488M16—1881no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—474no—
496C2×C8—942no—
497C2×C8—942no—
498C2×C8—942no—
499C2×C8—942no—
500C2×C8—942no—
501C2×C8—942no—
502C2×C8—942no—
503C2×C8—1881no—
504C2×C8—1881no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—1881no—
512C4⋊C4—1881no—
513C23—22no—
514C23—22no—
515C23—942no—
516C23—1881no—
517C23—1881no—
518C23—1882no—
519C23—1882no—
520C23#1309398111yescharacteristic
521C23#1309399711yescharacteristic
522C23#1309399711yescharacteristic
523C23#1309399811yescharacteristic
524C23#1309400211yescharacteristic
525C23#1309401811yescharacteristic
526C23#1309401911yescharacteristic
527Q8—942no—
528Q8—942no—
529Q8—1881no—
530Q8—1881no—
531D4—942no—
532D4—942no—
533D4—1882no—
534D4—1882no—
535D4—1882no—
536D4—1882no—
537D4—1881no—
538D4—1881no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—942no—
544C2×C4—3762no—
545C2×C4—3762no—
546C2×C4—3762no—
547C2×C4—1882no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4C22⋊C4×D4711yescharacteristic
555C2×C4C4⋊C4×D4711yescharacteristic
556C2×C4(C22⋊D47)⋊C411yescharacteristic
557C2×C4C4×C22⋊D4711yescharacteristic
558C2×C4#1309398611yescharacteristic
559C2×C4C4×D18811yescharacteristic
560C2×C4#1309399211yescharacteristic
561C2×C4#1309399411yescharacteristic
562C2×C4#1309399411yescharacteristic
563C2×C4#1309399611yescharacteristic
564C2×C4#1309399711yescharacteristic
565C2×C4#1309399711yescharacteristic
566C2×C4#1309399711yescharacteristic
567C2×C4#1309399911yescharacteristic
568C2×C4#1309400011yescharacteristic
569C2×C4#1309400211yescharacteristic
570C2×C4#1309400211yescharacteristic
571C2×C4#1309400211yescharacteristic
572C2×C4#1309400411yescharacteristic
573C2×C4#1309400611yescharacteristic
574C2×C4#1309400711yescharacteristic
575C2×C4#1309400911yescharacteristic
576C2×C4#1309400911yescharacteristic
577C2×C4#1309400911yescharacteristic
578C2×C4#1309401011yescharacteristic
579C2×C4#1309401011yescharacteristic
580C2×C4#1309401211yescharacteristic
581C2×C4#1309402011yescharacteristic
582C8—42no—
583C8—42no—
584C8—944no—
585C8—1882no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—3761no—
595C22—3761no—
596C22—3762no—
597C22—1882no—
598C22—1884no—
599C22#1568898211yescharacteristic
600C22#1568901211yescharacteristic
601C22#1568901411yescharacteristic
602C22#1568903211yescharacteristic
603C22#1568904511yescharacteristic
604C22#1568904711yescharacteristic
605C22#1568905211yescharacteristic
606C22#1568939212yes—
607C22#1568939712yes—
608C4—82no—
609C4—3762no—
610C4—1882no—
611C4#1568899411yescharacteristic
612C4#1568899711yescharacteristic
613C4#1568900111yescharacteristic
614C4#1568902311yescharacteristic
615C4#1568903611yescharacteristic
616C4#1568903811yescharacteristic
617C4#1568904111yescharacteristic
618C4#1568905811yescharacteristic
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—3762no—
624C2#2024163211yescharacteristic
625C2#2024345112yes—
626C2#2024449611yescharacteristic
627C2#2024450811yescharacteristic
628C2#2024483212yes—
subgroupG/H
centerC23#13093997
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#343C2
socleC23×C47#121
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#343D47
hypocenterC47#11107
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
1. C22×#13093957C2semidirect
5. C2×#15688891C2semidirect
6. C2×#15688887C2semidirect
7. C2×C47×#343C2semidirect
24. #15689091C4semidirect
310. C2×#343D47semidirect
346. C47#11107semidirect

Maximal subgroups

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

subgroupindex
C22×#130939572
C2×#156891252
C2×#156891222
C2×#156890912
C2×#156888912
C2×#156888872
C2×C47×#3432
#1110747