Finite Group Databasebeta

← #26124113

Subgroups — #26124113

Order 12032.

866 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
1C2×#15689125C211yesmaximal, characteristic
2C2×#15689125C211yesmaximal, characteristic
3C2×#15689089C211yesmaximal, characteristic
4C2×#15688891C211yesmaximal, characteristic, complemented
5C2×#15688891C211yesmaximal, characteristic, complemented
6C2×#15688886C211yesmaximal, characteristic, complemented
7C2×C47×#341C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12#15689125—22no—
13#15689125—22no—
14#15689125—22no—
15#15689125C414yescomplemented
16C2×#13093949—21no—
17C2×#13093949—21no—
18C2×#13093946—21no—
19C2×#13093946—21no—
20#15689089—22no—
21#15689089—22no—
22C2×(C2×D47)⋊C8—22no—
23#15688891—22no—
24#15688891—22no—
25#15688886—22no—
26C22×M16×C47C2211yescharacteristic
27C22×M16×C47C2211yescharacteristic
28C23×C8×C47C2211yescharacteristic
29C47×#341—22no—
30C2×#10625350—21no—
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×#10625350C2×C412yes—
41C2×#10625350D412yes—
42C22×Dic94D411yescharacteristic
43C22×D188D411yescharacteristic
44C22×C22⋊D47—21no—
45C23×Dic47—21no—
46C23×Dic47—21no—
47C22×C4×D47—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329D412yes—
54C22×C47⋊C8—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2×C412yes—
66C2×C4⋊Dic47D412yes—
67#13093949—24no—
68#13093949—24no—
69#13093946—24no—
70#13093946—24no—
71(C2×D47)⋊C8—28no—
72C23×C4×C47C2311yescharacteristic
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
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×C47C2×C412yes—
84C2×M16×C47D412yes—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C22×C8×C47—21no—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C22×C8×C47—21no—
93C22×C8×C47D412yes—
94C24×C47#4111yescharacteristic
95C23×D47—21no—
96C22×C4×C47C22×C411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47#4111yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C2×C22⋊D47—22no—
111C2×C22⋊D47—22no—
112C2×C22⋊D47—41no—
113C2×C22⋊D47—41no—
114C2×C22⋊D47—41no—
115C2×C22⋊D47—41no—
116C22×Dic47—21no—
117C22×Dic47—22no—
118C22×Dic47—22no—
119C22×Dic47—41no—
120C22×Dic47—41no—
121C22×Dic47—41no—
122C22×Dic47—41no—
123C22×Dic47—81no—
124C22×Dic47—81no—
125C22×Dic47—81no—
126C22×Dic47—81no—
127#10625350—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—22no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139#10625350—41no—
140#10625350—41no—
141#10625350—41no—
142#10625350—41no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188C22⋊C412yes—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—41no—
152C2×C4×D47—41no—
153C2×C4×D47—41no—
154C2×C4×D47—41no—
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94C22⋊C412yes—
161M16×C47—22no—
162M16×C47—22no—
163M16×C47—22no—
164M16×C47—22no—
165M16×C47—41no—
166M16×C47—41no—
167M16×C47—41no—
168M16×C47—41no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C2×C8×C47—22no—
174C2×C8×C47—41no—
175C2×C8×C47—41no—
176C2×C8×C47—41no—
177C2×C8×C47—41no—
178C2×C8×C47—41no—
179C2×C8×C47—41no—
180C2×C8×C47—41no—
181C2×C8×C47—41no—
182C4⋊Dic47—22no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47—22no—
186C4⋊Dic47—41no—
187C4⋊Dic47—41no—
188C4⋊Dic47—41no—
189C4⋊Dic47—41no—
190#10625329—22no—
191#10625329—22no—
192#10625329—41no—
193#10625329—41no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47C4×D411yescharacteristic
202C23×C47#12111yescharacteristic
203C23×C47#12311yescharacteristic
204C23×C47#12311yescharacteristic
205C23×C47#12411yescharacteristic
206C23×C47#12611yescharacteristic
207C23×C47#12611yescharacteristic
208C22×D47—22no—
209C22×D47—41no—
210C22×D47—41no—
211C22×D47—41no—
212C22×D47—41no—
213C22×D47—41no—
214C22×D47—41no—
215C2×C4×C47C2×C22⋊C411yescharacteristic
216C2×C4×C47#11711yescharacteristic
217C2×C4×C47#11711yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47#12011yescharacteristic
222C2×C4×C47#12011yescharacteristic
223C2×C4×C47#12111yescharacteristic
224C2×C4×C47#12111yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12111yescharacteristic
227C2×C4×C47#12111yescharacteristic
228C2×C4×C47#12111yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47#12311yescharacteristic
231C2×C4×C47#12311yescharacteristic
232C2×C4×C47#12311yescharacteristic
233C2×C4×C47#12311yescharacteristic
234C2×C4×C47#12311yescharacteristic
235C2×C4×C47#12311yescharacteristic
236C2×C4×C47#12311yescharacteristic
237C2×C4×C47#12311yescharacteristic
238C2×C4×C47#12411yescharacteristic
239C2×C4×C47#12411yescharacteristic
240C2×C4×C47#12411yescharacteristic
241C2×C4×C47#12611yescharacteristic
242C2×C4×C47#12611yescharacteristic
243C22⋊D47—42no—
244C22⋊D47—42no—
245C22⋊D47—42no—
246C22⋊D47—42no—
247C2×Dic47—22no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—82no—
253C2×Dic47—82no—
254C2×Dic47—81no—
255C2×Dic47—81no—
256C2×Dic47—81no—
257C2×Dic47—81no—
258C2×Dic47—82no—
259C2×Dic47—82no—
260D188—22no—
261D188—22no—
262D188—41no—
263D188—41no—
264C4×D47—42no—
265C4×D47—42no—
266C4×D47—42no—
267C4×D47—42no—
268Dic94—22no—
269Dic94—22no—
270Dic94—41no—
271Dic94—41no—
272C8×C47—42no—
273C8×C47—42no—
274C8×C47—42no—
275C47⋊C8—42no—
276#11192—471nomaximal, Sylow
277C22×C47—21no—
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47—21no—
283C22×C47—21no—
284C22×C47—21no—
285C22×C47—21no—
286C22×C47—21no—
287C22×C47—21no—
288C22×C47—21no—
289C22×C47#38611yescharacteristic
290C22×C47#38811yescharacteristic
291C22×C47#38811yescharacteristic
292C22×C47#39411yescharacteristic
293C22×C47#39711yescharacteristic
294C22×C47#39711yescharacteristic
295C22×C47#39711yescharacteristic
296C22×C47#47111yescharacteristic
297C22×C47#47111yescharacteristic
298C22×C47#47211yescharacteristic
299C22×C47#47311yescharacteristic
300C2×D47—42no—
301C2×D47—42no—
302C2×D47—42no—
303C2×D47—81no—
304C2×D47—81no—
305C2×D47—81no—
306C2×D47—81no—
307C4×C47#38111yescharacteristic
308C4×C47#38611yescharacteristic
309C4×C47#38811yescharacteristic
310C4×C47#38811yescharacteristic
311C4×C47#39411yescharacteristic
312C4×C47#39411yescharacteristic
313C4×C47#39411yescharacteristic
314C4×C47#39711yescharacteristic
315Dic47—42no—
316Dic47—82no—
317Dic47—82no—
318C2×#417—471no—
319C2×#417—471no—
320C2×#408—471no—
321C2×#343—471no—
322C2×#343—471no—
323C2×#341D4711yescharacteristic, complemented
324C2×#340—471no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47#144011yescharacteristic
330C2×C47#190711yescharacteristic
331C2×C47#190811yescharacteristic
332C2×C47#205111yescharacteristic
333C2×C47#205211yescharacteristic
334C2×C47#207811yescharacteristic
335C2×C47#207911yescharacteristic
336D47—82no—
337C22×#41—471no—
338C22×M16—471no—
339C22×M16C2×D4711yescharacteristic
340C22×M16C2×D4711yescharacteristic
341C23×C8C2×D4711yescharacteristic
342C22×C4⋊C4—471no—
343C22×C4⋊C4—471no—
344#417—474no—
345#417—942no—
346#417—942no—
347#417—942no—
348C2×#103—941no—
349C2×#103—941no—
350C2×#102—941no—
351C2×#102—941no—
352#408—942no—
353#408—942no—
354C2×C22⋊C8—942no—
355#343—942no—
356#343—942no—
357#341—22no—
358#340—942no—
359C47#1119211yescharacteristic, complemented, Sylow
360C2×#41—472no—
361C2×#41—472no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C2×#41—941no—
369C2×#41—941no—
370C2×#41—941no—
371C2×#41—941no—
372C22×Q8—471no—
373C22×D4—471no—
374C22×D4—941no—
375C23×C4—941no—
376C23×C4—941no—
377C23×C4—941no—
378C23×C4C22×D4711yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—472no—
390C2×M16—941no—
391C2×M16—941no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16C4×D4712yes—
396C2×M16C22⋊D4712yes—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—21no—
404C22×C8—21no—
405C22×C8—941no—
406C22×C8D18812yes—
407C2×C4⋊C4—472no—
408C2×C4⋊C4—472no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—941no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4—941no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4—941no—
419#103—944no—
420#103—944no—
421#102—944no—
422#102—944no—
423C22⋊C8—948no—
424C24—941no—
425C24#1062535411yescharacteristic
426#41—942no—
427#41—942no—
428#41—942no—
429#41—942no—
430#41—942no—
431#41—942no—
432#41—942no—
433#41—942no—
434#41—1881no—
435#41—1881no—
436#41—1881no—
437#41—1881no—
438#41—1881no—
439#41—1881no—
440#41—1881no—
441#41—1881no—
442C2×Q8—472no—
443C2×Q8—941no—
444C2×Q8—941no—
445C2×Q8—941no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×D4—472no—
449C2×D4—942no—
450C2×D4—942no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4—941no—
455C2×D4—941no—
456C2×D4—1881no—
457C2×D4—1881no—
458C2×D4—1881no—
459C2×D4—1881no—
460C22×C4—941no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—3761no—
466C22×C4—3761no—
467C22×C4—3761no—
468C22×C4—3761no—
469C22×C4—1881no—
470C22×C4—1881no—
471C22×C4—1881no—
472C22×C4—1881no—
473C22×C4—1881no—
474C22×C4—1881no—
475C22×C4—1881no—
476C22×C4—1881no—
477C22×C4C2×C4×D4711yescharacteristic
478C22×C4C2×D18811yescharacteristic
479C22×C4#1062535011yescharacteristic
480C22×C4#1062535011yescharacteristic
481C22×C4#1062535011yescharacteristic
482C22×C4#1062535011yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4D4×D4711yescharacteristic
487C22×C4#1062535211yescharacteristic
488C22×C4#1062535211yescharacteristic
489C22×C4#1062535411yescharacteristic
490C22×C4C2×C22⋊D4711yescharacteristic
491M16—22no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—41no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—942no—
500M16—942no—
501M16—1881no—
502M16—1881no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—942no—
517C2×C8—1881no—
518C2×C8—1881no—
519C4⋊C4—942no—
520C4⋊C4—942no—
521C4⋊C4—942no—
522C4⋊C4—942no—
523C4⋊C4—1881no—
524C4⋊C4—1881no—
525C4⋊C4—1881no—
526C4⋊C4—1881no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—942no—
532C23—1881no—
533C23—1881no—
534C23—1881no—
535C23—1881no—
536C23—1881no—
537C23—1881no—
538C23#1309398611yescharacteristic
539C23#1309399911yescharacteristic
540C23#1309400911yescharacteristic
541C23#1309400911yescharacteristic
542C23#1309401311yescharacteristic
543C23#1309401911yescharacteristic
544C23#1309401911yescharacteristic
545Q8—942no—
546Q8—942no—
547Q8—1881no—
548Q8—1881no—
549D4—942no—
550D4—942no—
551D4—1882no—
552D4—1882no—
553D4—1882no—
554D4—1882no—
555D4—1881no—
556D4—1881no—
557C2×C4—942no—
558C2×C4—3762no—
559C2×C4—3762no—
560C2×C4—3761no—
561C2×C4—3761no—
562C2×C4—3761no—
563C2×C4—3761no—
564C2×C4—3762no—
565C2×C4—3762no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1882no—
571C2×C4—1882no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4C22⋊C4×D4711yescharacteristic
575C2×C4#1309398111yescharacteristic
576C2×C4#1309398211yescharacteristic
577C2×C4(C22⋊D47)⋊C411yescharacteristic
578C2×C4C4×C22⋊D4711yescharacteristic
579C2×C4C4×D18811yescharacteristic
580C2×C4#1309399211yescharacteristic
581C2×C4#1309399411yescharacteristic
582C2×C4#1309399511yescharacteristic
583C2×C4#1309399611yescharacteristic
584C2×C4#1309399711yescharacteristic
585C2×C4#1309399711yescharacteristic
586C2×C4#1309399711yescharacteristic
587C2×C4#1309399811yescharacteristic
588C2×C4#1309399911yescharacteristic
589C2×C4#1309400611yescharacteristic
590C2×C4#1309400611yescharacteristic
591C2×C4#1309400611yescharacteristic
592C2×C4#1309400711yescharacteristic
593C2×C4#1309400811yescharacteristic
594C2×C4#1309400911yescharacteristic
595C2×C4#1309400911yescharacteristic
596C2×C4#1309400911yescharacteristic
597C2×C4#1309401011yescharacteristic
598C2×C4#1309401011yescharacteristic
599C2×C4#1309401211yescharacteristic
600C2×C4#1309401811yescharacteristic
601C2×C4#1309401911yescharacteristic
602C8—42no—
603C8—42no—
604C8—42no—
605C8—1882no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—3761no—
619C22—3761no—
620C22—3761no—
621C22—3761no—
622C22—1882no—
623C22—1882no—
624C22—1882no—
625C22#1568900111yescharacteristic
626C22#1568901211yescharacteristic
627C22#1568901311yescharacteristic
628C22#1568904011yescharacteristic
629C22#1568904911yescharacteristic
630C22#1568905011yescharacteristic
631C22#1568905211yescharacteristic
632C22#1568938711yescharacteristic
633C22#1568938711yescharacteristic
634C22#1568939411yescharacteristic
635C22#1568939911yescharacteristic
636C4—3762no—
637C4—3762no—
638C4—1882no—
639C4#1568898511yescharacteristic
640C4#1568899911yescharacteristic
641C4#1568901411yescharacteristic
642C4#1568901511yescharacteristic
643C4#1568903811yescharacteristic
644C4#1568903911yescharacteristic
645C4#1568904111yescharacteristic
646C4#1568905211yescharacteristic
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—3762no—
652C2#2024163611yescharacteristic
653C2#2024389511yescharacteristic
654C2#2024390211yescharacteristic
655C2#2024468211yescharacteristic
656C2#2024468911yescharacteristic
657C2#2024483011yescharacteristic
658C2#2024483511yescharacteristic
subgroupG/H
centerC23#13093999
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#341C2
socleC23×C47#121
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#341D47
hypocenterC47#11192
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#15688891C2semidirect
5. C2×#15688891C2semidirect
6. C2×#15688886C2semidirect
7. C2×C47×#341C2semidirect
15. #15689125C4semidirect
323. C2×#341D47semidirect
359. C47#11192semidirect

Maximal subgroups

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

subgroupindex
C2×#156891252
C2×#156890892
C2×#156888912
C2×#156888862
C2×C47×#3412
#1119247