Finite Group Databasebeta

← #26138255

Subgroups — #26138255

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093983C211yesmaximal, characteristic
2C2×#15688992C211yesmaximal, characteristic, complemented
3C2×#15688988C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic47C211yesmaximal, characteristic
5#20241631C214yesmaximal
6#20241619C214yesmaximal, complemented
7#20241617C211yesmaximal, characteristic, complemented
8#20241617C211yesmaximal, characteristic, complemented
9C2×C47×#380C211yesmaximal, characteristic
10C2×#13093983—24no—
11C2×#13093983—24no—
12C2×#13093983—24no—
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×Dic47⋊C4C2214yes—
16C22×C22⋊Dic47C2212yes—
17C22×C22⋊Dic47C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15688992—24no—
22#15688988—24no—
23C4×C22⋊Dic47C418yescomplemented
24C2×C47⋊#95C2214yes—
25C2×C47⋊#95C2214yes—
26C2×C47⋊#95C2214yes—
27C2×C47⋊#95C2212yes—
28C24×C4×C47C2211yescharacteristic
29C22×C4⋊C4×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2212yes—
32C47×#380—24no—
33C2×#95×C47C2212yes—
34C23×Dic47C2312yes—
35C23×Dic47C2312yes—
36C23×Dic47C2312yes—
37C23×Dic47C2312yes—
38#13093983—232no—
39C2×C4⋊Dic47—22no—
40C2×C4⋊Dic47—22no—
41C2×C4⋊Dic47—22no—
42C2×C4⋊Dic47—22no—
43C2×C4⋊Dic47D414yes—
44C2×C4⋊Dic47D414yes—
45C2×Dic47⋊C4—28no—
46C2×Dic47⋊C4—28no—
47C2×Dic47⋊C4—44no—
48C2×C22⋊Dic47—24no—
49C2×C22⋊Dic47—24no—
50C2×C22⋊Dic47—24no—
51C2×C22⋊Dic47—24no—
52C2×C22⋊Dic47—24no—
53C2×C22⋊Dic47C2×C418yes—
54C2×C4×Dic47—22no—
55C2×C4×Dic47—22no—
56C2×C4×Dic47—24no—
57C2×C4×Dic47—22no—
58C2×C4×Dic47—22no—
59C2×C4×Dic47—24no—
60C2×C4×Dic47—24no—
61C2×C4×Dic47C2×C414yes—
62C2×C4×Dic47C2×C414yes—
63C47⋊#95—28no—
64C47⋊#95—28no—
65C47⋊#95—44no—
66C47⋊#95C2×C418yes—
67C25×C47C2311yescharacteristic
68C23×C4×C47—22no—
69C23×C4×C47—22no—
70C23×C4×C47—22no—
71C23×C4×C47—22no—
72C23×C4×C47C2×C414yes—
73C23×C4×C47D414yes—
74C23×C4×C47Q814yes—
75C23×C4×C47C2312yes—
76C23×C4×C47C2312yes—
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—22no—
84C2×C4⋊C4×C47—22no—
85C2×C22⋊C4×C47—24no—
86C2×C22⋊C4×C47—44no—
87#95×C47—24no—
88C24×C47—21no—
89C24×C47—21no—
90C24×C47—21no—
91C24×C47—21no—
92C24×C47—22no—
93C24×C47—22no—
94C24×C47—22no—
95C24×C47—22no—
96C24×C47C22×C412yes—
97C24×C47C2×D412yes—
98C24×C47C2×Q812yes—
99C24×C47C2411yescharacteristic
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—28no—
105C22×C4×C47—28no—
106C22×C4×C47—28no—
107C22×C4×C47—28no—
108C22×C4×C47—28no—
109C22×C4×C47—28no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—24no—
117C22×C4×C47—24no—
118C22×C4×C47—24no—
119C22×C4×C47—24no—
120C22×C4×C47C4⋊C4116yescomplemented
121C22×C4×C47C22×C412yes—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C2×D412yes—
124C22×C4×C47C2×D412yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×Q812yes—
128C22×C4×C47C2×Q812yes—
129C22×C4×C47#4112yes—
130C22×C4×C47#4112yes—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—24no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—24no—
145C22×Dic47—22no—
146C22×Dic47—24no—
147C22×Dic47—22no—
148C22×Dic47—24no—
149C22×Dic47C22×C414yes—
150C22×Dic47C22×C414yes—
151C22×Dic47C2×D414yes—
152C22×Dic47C2×D414yes—
153C22×Dic47#4114yes—
154C22×Dic47#4114yes—
155C4⋊C4×C47—44no—
156C4⋊C4×C47—44no—
157C22⋊C4×C47—48no—
158C22⋊Dic47—216no—
159C22⋊Dic47—216no—
160C4⋊Dic47—28no—
161C4⋊Dic47—28no—
162Dic47⋊C4—416no—
163C4×Dic47—216no—
164C4×Dic47—28no—
165C4×Dic47—28no—
166C23×C47—24no—
167C23×C47—22no—
168C23×C47—22no—
169C23×C47—24no—
170C23×C47—22no—
171C23×C47—22no—
172C23×C47—22no—
173C23×C47—22no—
174C23×C47—22no—
175C23×C47—22no—
176C23×C47—24no—
177C23×C47—22no—
178C23×C47—22no—
179C23×C47—24no—
180C23×C47—42no—
181C23×C47—42no—
182C23×C47—42no—
183C23×C47—42no—
184C23×C47—42no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47C2×C4⋊C414yes—
189C23×C47C23×C411yescharacteristic
190C23×C47C22×D411yescharacteristic
191C23×C47C22×D411yescharacteristic
192C23×C47C22×D411yescharacteristic
193C23×C47C22×Q811yescharacteristic
194C23×C47C2×#4112yes—
195C23×C47C2×#4112yes—
196C23×C47C2×#4111yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47H(5,𝔽2)12yes—
199C23×C472−1+412yes—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—232no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—44no—
214C2×C4×C47—44no—
215C2×C4×C47—44no—
216C2×C4×C47—44no—
217C2×C4×C47C2×C4⋊C414yes—
218C2×C4×C47C2×C4⋊C414yes—
219C2×C4×C47C4×D414yes—
220C2×C4×C47C4×D414yes—
221C2×C4×C47#12014yes—
222C2×C4×C47C22⋊Q814yes—
223C2×C4×C47C22⋊Q814yes—
224C2×C4×C47#12314yes—
225C2×Dic47—24no—
226C2×Dic47—24no—
227C2×Dic47—24no—
228C2×Dic47—24no—
229C2×Dic47—24no—
230C2×Dic47—24no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—28no—
237C2×Dic47—28no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—44no—
244C2×Dic47—42no—
245C2×Dic47—44no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47#11718yescomplemented
249#13879—471nomaximal, Sylow
250C22×C47—24no—
251C22×C47—24no—
252C22×C47—24no—
253C22×C47—44no—
254C22×C47—44no—
255C22×C47—42no—
256C22×C47—42no—
257C22×C47—44no—
258C22×C47—44no—
259C22×C47—42no—
260C22×C47—42no—
261C22×C47C22×C4⋊C411yescharacteristic
262C22×C47C2×#11712yes—
263C22×C47C2×C4×D411yescharacteristic
264C22×C47C2×C4×D411yescharacteristic
265C22×C47#52012yes—
266C22×C47C2×#12011yescharacteristic
267C22×C47C2×C22⋊Q811yescharacteristic
268C22×C47C2×C22⋊Q811yescharacteristic
269C22×C47C2×#12311yescharacteristic
270C22×C47#53211yescharacteristic
271C22×C47#53211yescharacteristic
272C22×C47#53312yes—
273C22×C47#53511yescharacteristic
274C22×C47#53611yescharacteristic
275C22×C47#54412yes—
276C22×C47#54612yes—
277C22×C47#54712yes—
278C22×C47#54812yes—
279C22×C47#55012yes—
280C22×C47#55212yes—
281C22×C47#55312yes—
282C22×C47#55512yes—
283C22×C47#55612yes—
284C4×C47—24no—
285C4×C47—82no—
286C4×C47—82no—
287C4×C47#38518yes—
288Dic47—28no—
289Dic47—44no—
290Dic47—44no—
291Dic47—44no—
292C22×#117—471no—
293C2×#384—471no—
294C2×#382—471no—
295C2×#380D4711yescharacteristic
296C2×C4×C22⋊C4—471no—
297#1439—474no—
298#1436—474no—
299C4⋊#95—471no—
300C4⋊#95—471no—
301C2×C47—44no—
302C2×C47#228511yescharacteristic
303C2×C47C2×#38511yescharacteristic
304C2×C47#231711yescharacteristic
305C2×C47#235212yes—
306C2×C47#235412yes—
307C2×C47#243111yescharacteristic
308C2×C47#243211yescharacteristic
309C2×C47#243912yes—
310C2×C47#244112yes—
311C2×C47#249911yescharacteristic
312C2×C47#250011yescharacteristic
313C24×C4C2×D4711yescharacteristic
314C2×#117—944no—
315C2×#117—944no—
316C2×#117—944no—
317C22×C4⋊C4—471no—
318C22×C4⋊C4—471no—
319C22×C4⋊C4—474no—
320C22×C4⋊C4C2×D4711yescharacteristic
321C22×C4⋊C4C2×D4711yescharacteristic
322C22×C22⋊C4—472no—
323C22×C22⋊C4—472no—
324C22×C22⋊C4C2×D4712yes—
325C22×C42—471no—
326C22×C42—471no—
327C22×C42—472no—
328#384—944no—
329#382—944no—
330#380—24no—
331C4×C22⋊C4—478no—
332C2×#95—472no—
333C2×#95—474no—
334C2×#95—474no—
335C2×#95—474no—
336C2×#95C2×D4712yes—
337C47#1387911yescharacteristic, complemented, Sylow
338C25C22×D4711yescharacteristic
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—472no—
344C23×C4—472no—
345C23×C4—472no—
346C23×C4—472no—
347C23×C4Dic9414yes—
348C23×C4C4×D4714yes—
349C23×C4C22⋊D4714yes—
350C23×C4C22×D4712yes—
351C23×C4C22×D4712yes—
352C23×C4C22×D4711yescharacteristic
353C23×C4C22×D4711yescharacteristic
354#117—9432no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—474no—
362C2×C4⋊C4—474no—
363C2×C4⋊C4—942no—
364C2×C4⋊C4—942no—
365C2×C4⋊C4—942no—
366C2×C4⋊C4—942no—
367C2×C4⋊C4—948no—
368C2×C4⋊C4—948no—
369C2×C4⋊C4—1884no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—478no—
373C2×C22⋊C4—944no—
374C2×C22⋊C4—944no—
375C2×C22⋊C4—944no—
376C2×C22⋊C4—944no—
377C2×C22⋊C4—944no—
378C2×C42—474no—
379C2×C42—474no—
380C2×C42—944no—
381C2×C42—944no—
382C2×C42—942no—
383C2×C42—942no—
384C2×C42—942no—
385C2×C42—942no—
386C2×C42—944no—
387#95—24no—
388#95—478no—
389#95—948no—
390#95—948no—
391#95—1884no—
392C24—21no—
393C24—21no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24C2×Dic9412yes—
401C24C2×C4×D4712yes—
402C24C2×C22⋊D4712yes—
403C24C23×D4711yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—474no—
425C22×C4—474no—
426C22×C4—474no—
427C22×C4—474no—
428C22×C4—474no—
429C22×C4—474no—
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—944no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—944no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—944no—
446C22×C4—944no—
447C22×C4—942no—
448C22×C4Dic47⋊C4116yescomplemented
449C22×C4C2×Dic9412yes—
450C22×C4C2×Dic9412yes—
451C22×C4C2×C4×D4712yes—
452C22×C4C2×C4×D4712yes—
453C22×C4D4×D4712yes—
454C22×C4D4×D4712yes—
455C22×C4#1062535212yes—
456C22×C4#1062535212yes—
457C22×C4C2×C22⋊D4712yes—
458C22×C4C2×C22⋊D4712yes—
459C4⋊C4—44no—
460C4⋊C4—44no—
461C4⋊C4—948no—
462C4⋊C4—948no—
463C4⋊C4—18816no—
464C22⋊C4—48no—
465C22⋊C4—9416no—
466C22⋊C4—9416no—
467C42—9416no—
468C42—948no—
469C42—948no—
470C23—24no—
471C23—24no—
472C23—22no—
473C23—22no—
474C23—24no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C2×Dic47⋊C414yes—
493C23C22×C4×D4711yescharacteristic
494C23C2×D4×D4711yescharacteristic
495C23C2×D4×D4711yescharacteristic
496C23C22×C22⋊D4711yescharacteristic
497C23C22×Dic9411yescharacteristic
498C23#41×D4712yes—
499C23#41×D4712yes—
500C23C2×#1062535211yescharacteristic
501C23C2×#1062535211yescharacteristic
502C23#1309406912yes—
503C23#1309407212yes—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—232no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—478no—
522C2×C4—944no—
523C2×C4—944no—
524C2×C4—944no—
525C2×C4—944no—
526C2×C4—944no—
527C2×C4—944no—
528C2×C4—948no—
529C2×C4—948no—
530C2×C4—944no—
531C2×C4—944no—
532C2×C4—944no—
533C2×C4—944no—
534C2×C4—944no—
535C2×C4—1882no—
536C2×C4—1884no—
537C2×C4—1882no—
538C2×C4—1884no—
539C2×C4—1882no—
540C2×C4—1882no—
541C2×C4—1882no—
542C2×C4—1882no—
543C2×C4—1882no—
544C2×C4—1882no—
545C2×C4C2×Dic47⋊C414yes—
546C2×C4C2×Dic47⋊C414yes—
547C2×C4(C22⋊D47)⋊C414yes—
548C2×C4(C22⋊D47)⋊C414yes—
549C2×C4#1309399214yes—
550C2×C4#1309400114yes—
551C2×C4#1309400114yes—
552C2×C4#1309400514yes—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—44no—
558C22—44no—
559C22—42no—
560C22—44no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22C22×Dic47⋊C411yescharacteristic
565C22#117×D4712yes—
566C22C2×(C22⋊D47)⋊C411yescharacteristic
567C22C2×(C22⋊D47)⋊C411yescharacteristic
568C22#1568960412yes—
569C22C2×#1309399211yescharacteristic
570C22C2×#1309400111yescharacteristic
571C22C2×#1309400111yescharacteristic
572C22C2×#1309400511yescharacteristic
573C22#1568966911yescharacteristic
574C22#1568966911yescharacteristic
575C22#1568967612yes—
576C22#1568969011yescharacteristic
577C22#1568969711yescharacteristic
578C22#1568975412yes—
579C22#1568977012yes—
580C22#1568977512yes—
581C22#1568978312yes—
582C22#1568979112yes—
583C22#1568980712yes—
584C22#1568982012yes—
585C22#1568983712yes—
586C22#1568984412yes—
587C4—24no—
588C4—82no—
589C4—82no—
590C4—948no—
591C4—1884no—
592C4—1884no—
593C4—1884no—
594C4#1568899518yes—
595C2—44no—
596C2#2024579111yescharacteristic
597C2C2×#1568899511yescharacteristic
598C2#2024601211yescharacteristic
599C2#2024631012yes—
600C2#2024633212yes—
601C2#2024700811yescharacteristic
602C2#2024701711yescharacteristic
603C2#2024708012yes—
604C2#2024710212yes—
605C2#2024784211yescharacteristic
606C2#2024785111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#380C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#380D47
hypocenterC47#13879
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#15688992C2semidirect
3. C2×#15688988C2semidirect
6. #20241619C2semidirect
7. #20241617C2semidirect
8. #20241617C2semidirect
23. C4×C22⋊Dic47C4semidirect
120. C22×C4×C47C4⋊C4semidirect
248. C2×Dic47#117semidirect
337. C47#13879semidirect
448. C22×C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130939832
C2×#156889922
C2×#156889882
C2×C4×C22⋊Dic472
#202416312
#202416192
#202416172
C2×C47×#3802
#1387947