Finite Group Databasebeta

← #26123529

Subgroups — #26123529

Order 12032.

1006 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
1C22×#13093959C211yesmaximal, characteristic, complemented
2C2×#15689086C211yesmaximal, characteristic
3C2×#15689086C211yesmaximal, characteristic
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic
5C2×#15688888C211yesmaximal, characteristic, complemented
6C2×#15688887C211yesmaximal, characteristic, complemented
7C2×C47×#341C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C23×C47⋊C8C2211yescharacteristic
12C2×#13093959—22no—
13C2×#13093959—22no—
14C2×#13093959—22no—
15#15689086—22no—
16#15689086—22no—
17#15689086—22no—
18#15689086—22no—
19C2×(C2×D47)⋊C8—22no—
20C2×(C2×D47)⋊C8—22no—
21C2×(C2×D47)⋊C8—22no—
22C2×(C2×D47)⋊C8—22no—
23C2×(C2×D47)⋊C8C414yes—
24#15688888—22no—
25#15688887—22no—
26C22×M16×C47C2211yescharacteristic
27C22×M16×C47C2211yescharacteristic
28C23×C8×C47C2211yescharacteristic
29C47×#341—22no—
30C24×D47Q811yescharacteristic
31C23×Dic47Q811yescharacteristic
32C22×C4×D47—21no—
33C22×C4×D47—21no—
34C22×C4×D47—21no—
35C22×C4×D47—21no—
36C22×C4×D47—21no—
37C22×C4×D47—21no—
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47C2×C412yes—
45C22×C4×D47D412yes—
46C2×#10625329—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×#10625329D412yes—
57C2×#10625329D412yes—
58C22×C47⋊C8—21no—
59C22×C47⋊C8—21no—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63C22×C47⋊C8—21no—
64C22×C47⋊C8C2×C412yes—
65C22×C47⋊C8D412yes—
66C22×C47⋊C8D412yes—
67#13093959—28no—
68(C2×D47)⋊C8—28no—
69(C2×D47)⋊C8—28no—
70(C2×D47)⋊C8—28no—
71C23×C4×C47C2311yescharacteristic
72C2×M16×C47—21no—
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×C47D412yes—
83C2×M16×C47D412yes—
84C22×C8×C47—21no—
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×C47C2×C412yes—
93C24×C47C2×Q811yescharacteristic
94C23×D47—21no—
95C23×D47—21no—
96C23×D47—24no—
97C23×D47—21no—
98C23×D47—21no—
99C23×D47—21no—
100C23×D47—21no—
101C23×D47—42no—
102C23×D47C4⋊C412yes—
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×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×Dic47—21no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—21no—
123C22×Dic47C4⋊C412yes—
124C2×C4×D47—22no—
125C2×C4×D47—22no—
126C2×C4×D47—22no—
127C2×C4×D47—22no—
128C2×C4×D47—22no—
129C2×C4×D47—22no—
130C2×C4×D47—22no—
131C2×C4×D47—22no—
132C2×C4×D47—22no—
133C2×C4×D47—22no—
134C2×C4×D47—22no—
135C2×C4×D47—22no—
136C2×C4×D47—41no—
137C2×C4×D47—41no—
138C2×C4×D47—41no—
139C2×C4×D47—41no—
140C2×C4×D47—41no—
141C2×C4×D47—41no—
142C2×C4×D47—41no—
143C2×C4×D47—41no—
144C2×C4×D47—41no—
145C2×C4×D47—41no—
146C2×C4×D47—41no—
147C2×C4×D47—41no—
148C2×C4×D47—41no—
149C2×C4×D47—41no—
150C2×C4×D47—41no—
151C2×C4×D47—41no—
152M16×C47—22no—
153M16×C47—22no—
154M16×C47—22no—
155M16×C47—22no—
156M16×C47—41no—
157M16×C47—41no—
158M16×C47—41no—
159M16×C47—41no—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C2×C8×C47—22no—
164C2×C8×C47—22no—
165C2×C8×C47—41no—
166C2×C8×C47—41no—
167C2×C8×C47—41no—
168C2×C8×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C2×C8×C47—41no—
172C2×C8×C47—41no—
173#10625329—22no—
174#10625329—22no—
175#10625329—22no—
176#10625329—22no—
177#10625329—41no—
178#10625329—41no—
179#10625329—41no—
180#10625329—41no—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8—22no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—41no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8—41no—
192C2×C47⋊C8—41no—
193C2×C47⋊C8C22⋊C414yes—
194C23×C47—22no—
195C23×C47—22no—
196C23×C47C2×C4⋊C411yescharacteristic
197C23×C47C22⋊Q811yescharacteristic
198C23×C47C22⋊Q811yescharacteristic
199C23×C47C22⋊Q811yescharacteristic
200C23×C47C22⋊Q811yescharacteristic
201C23×C47C22⋊Q811yescharacteristic
202C23×C47C22⋊Q811yescharacteristic
203C22×D47—24no—
204C22×D47—24no—
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—22no—
208C22×D47—22no—
209C22×D47—22no—
210C22×D47—22no—
211C22×D47—44no—
212C22×D47—44no—
213C22×D47—44no—
214C22×D47—44no—
215C22×D47—42no—
216C22×D47—42no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47—41no—
220C22×D47—41no—
221C22×D47#10814yescomplemented
222C2×C4×C47C2×C22⋊C411yescharacteristic
223C2×C4×C47#11711yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47#12011yescharacteristic
229C2×C4×C47#12011yescharacteristic
230C2×C4×C47#12011yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12111yescharacteristic
236C2×C4×C47#12111yescharacteristic
237C2×C4×C47#12111yescharacteristic
238C2×C4×C47#12111yescharacteristic
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#12411yescharacteristic
247C2×C4×C47#12611yescharacteristic
248C2×C4×C47#12611yescharacteristic
249C2×C4×C47#12711yescharacteristic
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C4×D47—42no—
258C4×D47—42no—
259C4×D47—42no—
260C4×D47—42no—
261C4×D47—42no—
262C4×D47—42no—
263C4×D47—42no—
264C4×D47—42no—
265C8×C47—42no—
266C8×C47—42no—
267C8×C47—42no—
268C47⋊C8—24no—
269C47⋊C8—42no—
270C47⋊C8—42no—
271#11097—471nomaximal, Sylow
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—22no—
277C22×C47—22no—
278C22×C47—22no—
279C22×C47—22no—
280C22×C47#38011yescharacteristic
281C22×C47#38511yescharacteristic
282C22×C47#38511yescharacteristic
283C22×C47#39311yescharacteristic
284C22×C47#39611yescharacteristic
285C22×C47#39611yescharacteristic
286C22×C47#39911yescharacteristic
287C22×C47C2×#10812yes—
288C22×C47#43012yes—
289C2×D47—24no—
290C2×D47—24no—
291C2×D47—24no—
292C2×D47—44no—
293C2×D47—44no—
294C2×D47—44no—
295C2×D47—44no—
296C2×D47—42no—
297C2×D47—42no—
298C2×D47—42no—
299C2×D47—42no—
300C4×C47#38611yescharacteristic
301C4×C47#38811yescharacteristic
302C4×C47#38811yescharacteristic
303C4×C47#39011yescharacteristic
304C4×C47#39211yescharacteristic
305C4×C47#39411yescharacteristic
306C4×C47#39411yescharacteristic
307C4×C47#39711yescharacteristic
308Dic47—42no—
309C22×#108—471no—
310C2×#407—471no—
311C2×#407—471no—
312C22×C22⋊C8—471no—
313C2×#341—471no—
314C2×#341—471no—
315C2×#341D4711yescharacteristic, complemented
316C2×C47—21no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47#143911yescharacteristic
321C2×C47#181011yescharacteristic
322C2×C47#181111yescharacteristic
323C2×C47#185512yes—
324C2×C47#185512yes—
325D47—44no—
326C24×C4—471no—
327C22×M16—471no—
328C22×M16—471no—
329C22×M16C2×D4711yescharacteristic
330C22×M16C2×D4711yescharacteristic
331C23×C8—471no—
332C23×C8C2×D4711yescharacteristic
333C2×#108—942no—
334C2×#108—942no—
335C2×#108—942no—
336#407—942no—
337#407—942no—
338#407—942no—
339#407—942no—
340C2×C22⋊C8—474no—
341C2×C22⋊C8—942no—
342C2×C22⋊C8—942no—
343C2×C22⋊C8—942no—
344C2×C22⋊C8—942no—
345#341—22no—
346#341—942no—
347#341—942no—
348C47#1109711yescharacteristic, complemented, Sylow
349C25—471no—
350C23×C4—471no—
351C23×C4—472no—
352C23×C4—472no—
353C23×C4—941no—
354C23×C4—941no—
355C23×C4—941no—
356C23×C4—941no—
357C23×C4—941no—
358C23×C4—941no—
359C23×C4—941no—
360C23×C4—941no—
361C23×C4—941no—
362C23×C4—941no—
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—472no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C2×M16—941no—
388C2×M16D18812yes—
389C2×M16C22⋊D4712yes—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—472no—
399C22×C8—472no—
400C22×C8—472no—
401C22×C8—941no—
402C22×C8—941no—
403C22×C8—941no—
404C22×C8—941no—
405C22×C8—941no—
406C22×C8—941no—
407C22×C8C4×D4712yes—
408#108—948no—
409C22⋊C8—948no—
410C22⋊C8—948no—
411C22⋊C8—948no—
412C24—472no—
413C24—944no—
414C24—941no—
415C24—941no—
416C24—941no—
417C24—941no—
418C24—941no—
419C24—941no—
420C24—1882no—
421C24Q8×D4711yescharacteristic
422C22×C4—472no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4—1881no—
447C22×C4—1881no—
448C22×C4—1881no—
449C22×C4—1881no—
450C22×C4—1881no—
451C22×C4—1881no—
452C22×C4—1881no—
453C22×C4—1881no—
454C22×C4—1881no—
455C22×C4—1881no—
456C22×C4—1881no—
457C22×C4C2×C4×D4711yescharacteristic
458C22×C4C2×D18811yescharacteristic
459C22×C4#1062535011yescharacteristic
460C22×C4#1062535011yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4#1062535011yescharacteristic
463C22×C4D4×D4711yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4D4×D4711yescharacteristic
468C22×C4#1062535211yescharacteristic
469C22×C4#1062535411yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—942no—
480M16—942no—
481M16—942no—
482M16—942no—
483M16—1881no—
484M16—1881no—
485M16—1881no—
486M16—1881no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—474no—
501C2×C8—942no—
502C2×C8—942no—
503C2×C8—942no—
504C2×C8—942no—
505C2×C8—942no—
506C2×C8—942no—
507C2×C8—942no—
508C2×C8—942no—
509C2×C8—1881no—
510C2×C8—1881no—
511C2×C8—1881no—
512C2×C8—1881no—
513C23—22no—
514C23—22no—
515C23—474no—
516C23—944no—
517C23—944no—
518C23—942no—
519C23—942no—
520C23—942no—
521C23—942no—
522C23—942no—
523C23—942no—
524C23—1884no—
525C23—1884no—
526C23—1884no—
527C23—1884no—
528C23—1882no—
529C23—1882no—
530C23—1881no—
531C23—1881no—
532C23—1881no—
533C23—1881no—
534C23C4⋊C4×D4711yescharacteristic
535C23#1309400011yescharacteristic
536C23#1309400211yescharacteristic
537C23#1309400211yescharacteristic
538C23#1309400211yescharacteristic
539C23#1309400211yescharacteristic
540C23#1309400411yescharacteristic
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4C22⋊C4×D4711yescharacteristic
557C2×C4#1309398111yescharacteristic
558C2×C4(C22⋊D47)⋊C411yescharacteristic
559C2×C4C4×C22⋊D4711yescharacteristic
560C2×C4#1309398611yescharacteristic
561C2×C4C4×D18811yescharacteristic
562C2×C4#1309399211yescharacteristic
563C2×C4#1309399411yescharacteristic
564C2×C4#1309399411yescharacteristic
565C2×C4#1309399611yescharacteristic
566C2×C4#1309399711yescharacteristic
567C2×C4#1309399711yescharacteristic
568C2×C4#1309399711yescharacteristic
569C2×C4#1309399711yescharacteristic
570C2×C4#1309399711yescharacteristic
571C2×C4#1309399811yescharacteristic
572C2×C4#1309399911yescharacteristic
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#1309401811yescharacteristic
582C2×C4#1309401911yescharacteristic
583C2×C4#1309402011yescharacteristic
584C8—42no—
585C8—42no—
586C8—42no—
587C8—944no—
588C8—1882no—
589C8—1882no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—944no—
599C22—944no—
600C22—944no—
601C22—1884no—
602C22—1884no—
603C22—1884no—
604C22—1884no—
605C22—1882no—
606C22—1882no—
607C22—1882no—
608C22—1882no—
609C22#1568898211yescharacteristic
610C22#1568899411yescharacteristic
611C22#1568899711yescharacteristic
612C22#1568903611yescharacteristic
613C22#1568904511yescharacteristic
614C22#1568904711yescharacteristic
615C22#1568905811yescharacteristic
616C22#108×D4712yes—
617C22#1568917012yes—
618C4—1882no—
619C4#1568900111yescharacteristic
620C4#1568901211yescharacteristic
621C4#1568901411yescharacteristic
622C4#1568902311yescharacteristic
623C4#1568903211yescharacteristic
624C4#1568903811yescharacteristic
625C4#1568904111yescharacteristic
626C4#1568905211yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—1884no—
632C2#2024163211yescharacteristic
633C2#2024342511yescharacteristic
634C2#2024342911yescharacteristic
635C2#2024359112yes—
636C2#2024359412yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#341C2
socleC23×C47C2×C4⋊C4
prime radicalC24×D47Q8
cosocleC23×C4×C47C23
hypercenterC2×#341D47
hypocenterC47#11097
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C22×#13093959C2semidirect
5. C2×#15688888C2semidirect
6. C2×#15688887C2semidirect
7. C2×C47×#341C2semidirect
221. C22×D47#108semidirect
315. C2×#341D47semidirect
348. C47#11097semidirect

Maximal subgroups

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

subgroupindex
C22×#130939592
C2×#156890862
C22×(C2×D47)⋊C82
C2×#156888882
C2×#156888872
C2×C47×#3412
#1109747