Finite Group Databasebeta

← #26122784

Subgroups — #26122784

Order 12032.

1922 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093998C211yesmaximal, characteristic
2C22×#13093944C212yesmaximal, complemented
3C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
4C2×#15688885C212yesmaximal, complemented
5C2×C47×#380C211yesmaximal, characteristic, complemented
6C23×D188C2211yescharacteristic
7C23×C22⋊D47—21no—
8C23×C47⋊C8C2212yes—
9C2×#13093998—24no—
10C2×#13093998—24no—
11C2×#13093998—22no—
12C2×#13093998C414yescomplemented
13C22×C4⋊Dic47C2211yescharacteristic
14C22×(C2×D47)⋊C4—21no—
15C2×#13093944—24no—
16C2×#13093944—24no—
17C2×#13093944—24no—
18C2×C22⋊(C47⋊C8)—24no—
19C2×C22⋊(C47⋊C8)—22no—
20#15688885—24no—
21C24×C4×C47C2211yescharacteristic
22C22×C4⋊C4×C47C2212yes—
23C22×C22⋊C4×C47—21no—
24C47×#380—24no—
25C2×#95×C47—21no—
26C24×D47—21no—
27C22×D188—22no—
28C22×D188—22no—
29C22×D188—22no—
30C22×D188—22no—
31C22×D188—22no—
32C22×D188—21no—
33C22×D188C2×C412yes—
34C22×D188D414yes—
35C22×C22⋊D47—28no—
36C22×C22⋊D47—24no—
37C22×C22⋊D47—44no—
38C22×C22⋊D47—42no—
39C22×C22⋊D47—42no—
40C23×Dic47—21no—
41C22×C47⋊C8—22no—
42C22×C47⋊C8—22no—
43C22×C47⋊C8—22no—
44C22×C47⋊C8—22no—
45C22×C47⋊C8—22no—
46C22×C47⋊C8—22no—
47C22×C47⋊C8D414yescomplemented
48#13093998—216no—
49#13093998—28no—
50#13093998—28no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—21no—
53C2×C4⋊Dic47C2×C412yes—
54C2×C4⋊Dic47D414yes—
55C2×(C2×D47)⋊C4—28no—
56C2×(C2×D47)⋊C4—24no—
57#13093944—216no—
58C22⋊(C47⋊C8)—28no—
59C25×C47D411yescharacteristic
60C23×C4×C47—22no—
61C23×C4×C47—22no—
62C23×C4×C47—22no—
63C23×C4×C47—22no—
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47—22no—
67C23×C4×C47C2×C412yes—
68C23×C4×C47D411yescharacteristic
69C23×C4×C47D412yes—
70C23×C4×C47C2311yescharacteristic
71C2×C4⋊C4×C47—22no—
72C2×C4⋊C4×C47—22no—
73C2×C4⋊C4×C47—22no—
74C2×C4⋊C4×C47—22no—
75C2×C4⋊C4×C47—22no—
76C2×C4⋊C4×C47D414yescomplemented
77C2×C22⋊C4×C47—24no—
78C2×C22⋊C4×C47—42no—
79C2×C22⋊C4×C47—42no—
80#95×C47—24no—
81C24×C47—21no—
82C24×C47—22no—
83C24×C47—22no—
84C24×C47—21no—
85C24×C47—22no—
86C24×C47—21no—
87C24×C47—22no—
88C24×C47—21no—
89C24×C47C22⋊C412yes—
90C24×C47D812yes—
91C24×C47SD1612yes—
92C24×C47C2×D411yescharacteristic
93C23×D47—22no—
94C23×D47—24no—
95C23×D47—41no—
96C23×D47—42no—
97C23×D47—41no—
98C23×D47—41no—
99C23×D47—41no—
100C23×D47—42no—
101C23×D47—42no—
102C23×D47—41no—
103C23×D47—41no—
104C22×C4×C47—22no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—24no—
111C22×C4×C47—24no—
112C22×C4×C47—22no—
113C22×C4×C47—24no—
114C22×C4×C47—24no—
115C22×C4×C47—22no—
116C22×C4×C47—24no—
117C22×C4×C47—42no—
118C22×C4×C47—42no—
119C22×C4×C47—42no—
120C22×C4×C47—42no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47—42no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47C22⋊C412yes—
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47#4112yes—
139C22×C4×C47#4112yes—
140C2×C22⋊D47—216no—
141C2×C22⋊D47—48no—
142C2×C22⋊D47—416no—
143C2×C22⋊D47—416no—
144C2×C22⋊D47—48no—
145C22×Dic47—22no—
146C22×Dic47—24no—
147C22×Dic47—41no—
148C22×Dic47—41no—
149C22×Dic47—42no—
150C2×D188—24no—
151C2×D188—24no—
152C2×D188—24no—
153C2×D188—24no—
154C2×D188—24no—
155C2×D188—24no—
156C2×D188—22no—
157C2×D188—24no—
158C2×D188—41no—
159C2×D188—42no—
160C2×D188—42no—
161C2×D188—42no—
162C2×D188—41no—
163C2×D188—42no—
164C2×D188—42no—
165C2×D188C22⋊C414yescomplemented
166C4⋊C4×C47—24no—
167C4⋊C4×C47—24no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47—42no—
170C22⋊C4×C47—48no—
171(C2×D47)⋊C4—216no—
172C4⋊Dic47—22no—
173C4⋊Dic47—24no—
174C4⋊Dic47C22⋊C414yescomplemented
175C2×C47⋊C8—24no—
176C2×C47⋊C8—24no—
177C2×C47⋊C8—24no—
178C2×C47⋊C8—42no—
179C2×C47⋊C8—42no—
180C2×C47⋊C8—42no—
181C2×C47⋊C8—42no—
182C23×C47—22no—
183C23×C47—22no—
184C23×C47—22no—
185C23×C47—22no—
186C23×C47—22no—
187C23×C47—22no—
188C23×C47—22no—
189C23×C47—24no—
190C23×C47—22no—
191C23×C47—24no—
192C23×C47—24no—
193C23×C47—24no—
194C23×C47—22no—
195C23×C47—22no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47—42no—
200C23×C47—42no—
201C23×C47—42no—
202C23×C47—42no—
203C23×C47—42no—
204C23×C47#10214yescomplemented
205C23×C47C2×C22⋊C411yescharacteristic
206C23×C47#12012yes—
207C23×C47#12011yescharacteristic
208C23×C47#12112yes—
209C23×C47#12311yescharacteristic
210C23×C47C2×D811yescharacteristic
211C23×C47C2×SD1611yescharacteristic
212C23×C47#13512yes—
213C23×C47AGL(1,ℤ/8)12yes—
214C23×C47AGL(1,ℤ/8)11yescharacteristic
215C23×C47#13711yescharacteristic
216C22×D47—24no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—44no—
220C22×D47—44no—
221C22×D47—42no—
222C22×D47—42no—
223C22×D47—42no—
224C22×D47—42no—
225C22×D47—44no—
226C22×D47—44no—
227C22×D47—44no—
228C22×D47—44no—
229C22×D47—81no—
230C22×D47—81no—
231C22×D47—82no—
232C22×D47—82no—
233C22×D47—82no—
234C22×D47—82no—
235C22×D47—82no—
236C22×D47—81no—
237C22×D47—81no—
238C22×D47—82no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—44no—
245C2×C4×C47—44no—
246C2×C4×C47—44no—
247C2×C4×C47—44no—
248C2×C4×C47—44no—
249C2×C4×C47—44no—
250C2×C4×C47—44no—
251C2×C4×C47—82no—
252C2×C4×C47—82no—
253C2×C4×C47—82no—
254C2×C4×C47—82no—
255C2×C4×C47C2×C22⋊C411yescharacteristic
256C2×C4×C47C2×C22⋊C411yescharacteristic
257C2×C4×C47C4×D412yes—
258C2×C4×C47C4×D412yes—
259C2×C4×C47#12012yes—
260C2×C4×C47#12011yescharacteristic
261C2×C4×C47#12012yes—
262C2×C4×C47#12112yes—
263C2×C4×C47#12112yes—
264C2×C4×C47#12112yes—
265C2×C4×C47#12112yes—
266C2×C4×C47#12112yes—
267C2×C4×C47#12312yes—
268C2×C4×C47#12311yescharacteristic
269C2×C4×C47#12412yes—
270C2×C4×C47#12712yes—
271C22⋊D47—432no—
272C2×Dic47—24no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—44no—
276C2×Dic47—44no—
277D188—28no—
278D188—44no—
279D188—44no—
280D188—44no—
281C47⋊C8—44no—
282#10969—471nomaximal, Sylow
283C22×C47—24no—
284C22×C47—24no—
285C22×C47—24no—
286C22×C47—42no—
287C22×C47—42no—
288C22×C47—42no—
289C22×C47—44no—
290C22×C47—44no—
291C22×C47—44no—
292C22×C47—44no—
293C22×C47—42no—
294C22×C47#37911yescharacteristic
295C22×C47#38611yescharacteristic
296C22×C47#38611yescharacteristic
297C22×C47#39212yes—
298C22×C47#39412yes—
299C22×C47C2×#10211yescharacteristic
300C22×C47#41611yescharacteristic
301C22×C47#41711yescharacteristic
302C22×C47#41811yescharacteristic
303C22×C47#44712yes—
304C22×C47#44711yescharacteristic
305C22×C47#44811yescharacteristic
306C22×C47#44912yes—
307C22×C47#44912yes—
308C22×C47#45012yes—
309C22×C47#45212yes—
310C22×C47#46512yes—
311C22×C47#46612yes—
312C22×C47#46812yes—
313C22×C47#46912yes—
314C22×C47#48011yescharacteristic
315C22×C47#48111yescharacteristic
316C22×C47#48212yes—
317C2×D47—44no—
318C2×D47—44no—
319C2×D47—44no—
320C2×D47—82no—
321C2×D47—82no—
322C2×D47—82no—
323C2×D47—82no—
324C2×D47—84no—
325C2×D47—84no—
326C2×D47—84no—
327C2×D47—84no—
328C4×C47—42no—
329C4×C47—84no—
330C4×C47#38612yes—
331C4×C47#39012yes—
332C4×C47#39212yes—
333C4×C47#39412yes—
334Dic47—44no—
335C22×#121—471no—
336C22×#102—472no—
337C22×C22⋊C8—471no—
338C2×#380D4711yescharacteristic, complemented
339C2×#340—472no—
340C2×C47—44no—
341C2×C47#143811yescharacteristic
342C2×C47#178611yescharacteristic
343C2×C47#178811yescharacteristic
344C2×C47#187411yescharacteristic
345C2×C47#187511yescharacteristic
346C2×C47#189311yescharacteristic
347C2×C47#189511yescharacteristic
348C2×C47#199912yes—
349C2×C47#200012yes—
350C2×C47#203312yes—
351C2×C47#203412yes—
352D47—84no—
353C23×D4—471no—
354C23×D4—941no—
355C24×C4C2×D4711yescharacteristic
356C23×C8—472no—
357C2×#121—474no—
358C2×#121—944no—
359C2×#121—944no—
360C2×#121—942no—
361C22×C4⋊C4—471no—
362C22×C4⋊C4C2×D4712yes—
363C22×C22⋊C4—21no—
364C22×C22⋊C4—941no—
365C2×#102—944no—
366C2×#102—944no—
367C2×#102—944no—
368C2×C22⋊C8—944no—
369C2×C22⋊C8—942no—
370#380—24no—
371C2×#95—21no—
372#340—944no—
373C47#1096911yescharacteristic, complemented, Sylow
374C25—941no—
375C25C22⋊D4711yescharacteristic
376C22×D4—472no—
377C22×D4—474no—
378C22×D4—948no—
379C22×D4—944no—
380C22×D4—941no—
381C22×D4—942no—
382C22×D4—942no—
383C22×D4—942no—
384C22×D4—942no—
385C22×D4—942no—
386C22×D4—1884no—
387C22×D4—1882no—
388C22×D4—1882no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—941no—
397C23×C4C4×D4712yes—
398C23×C4D18812yes—
399C23×C4C22⋊D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C22×C8—474no—
402C22×C8—942no—
403C22×C8—942no—
404C22×C8—942no—
405C22×C8—942no—
406C22×C8—942no—
407C22×C8—942no—
408#121—948no—
409#121—948no—
410#121—9416no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—472no—
417C2×C4⋊C4—474no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4—942no—
420C2×C4⋊C4C22⋊D4714yescomplemented
421C2×C22⋊C4—24no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—948no—
425C2×C22⋊C4—944no—
426#102—9416no—
427C22⋊C8—948no—
428#95—24no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—942no—
438C24—944no—
439C24—1881no—
440C24—1882no—
441C24—1881no—
442C24—1881no—
443C24—1881no—
444C24—1882no—
445C24—1882no—
446C24—1881no—
447C24—1881no—
448C24(C2×D47)⋊C412yes—
449C24#1062533412yes—
450C24#1062533612yes—
451C24C2×C22⋊D4711yescharacteristic
452C2×D4—474no—
453C2×D4—9416no—
454C2×D4—942no—
455C2×D4—944no—
456C2×D4—944no—
457C2×D4—944no—
458C2×D4—944no—
459C2×D4—944no—
460C2×D4—944no—
461C2×D4—944no—
462C2×D4—18816no—
463C2×D4—18816no—
464C2×D4—1888no—
465C2×D4—1888no—
466C2×D4—1881no—
467C2×D4—1882no—
468C2×D4—1882no—
469C2×D4—1882no—
470C2×D4—1881no—
471C2×D4—1882no—
472C2×D4—1882no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—942no—
501C22×C4—944no—
502C22×C4—1881no—
503C22×C4—1881no—
504C22×C4—1882no—
505C22×C4(C2×D47)⋊C412yes—
506C22×C4C2×C4×D4711yescharacteristic
507C22×C4C2×D18811yescharacteristic
508C22×C4#1062535012yes—
509C22×C4D4×D4712yes—
510C22×C4D4×D4712yes—
511C22×C4D4×D4712yes—
512C22×C4#1062535212yes—
513C22×C4C2×C22⋊D4712yes—
514C2×C8—944no—
515C2×C8—944no—
516C2×C8—944no—
517C2×C8—1882no—
518C2×C8—1882no—
519C2×C8—1882no—
520C2×C8—1882no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—474no—
526C4⋊C4—942no—
527C4⋊C4—944no—
528C22⋊C4—48no—
529C22⋊C4—9416no—
530C23—22no—
531C23—22no—
532C23—24no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—944no—
553C23—3761no—
554C23—3761no—
555C23—3762no—
556C23—3762no—
557C23—3762no—
558C23—3762no—
559C23—3762no—
560C23—3761no—
561C23—3761no—
562C23—3762no—
563C23—1882no—
564C23—1884no—
565C23—1882no—
566C23—1884no—
567C23—1884no—
568C23—1884no—
569C23—1884no—
570C23—1884no—
571C23—1882no—
572C23—1882no—
573C23—1882no—
574C23—1882no—
575C23#1309394414yescomplemented
576C23C2×(C2×D47)⋊C411yescharacteristic
577C23#1309399212yes—
578C23#1309399311yescharacteristic
579C23#1309399612yes—
580C23#1309400711yescharacteristic
581C23C2×#1062533411yescharacteristic
582C23C2×#1062533611yescharacteristic
583C23#1309404412yes—
584C23#1309404912yes—
585C23#1309405011yescharacteristic
586C23#1309405511yescharacteristic
587D4—948no—
588D4—18832no—
589D4—1884no—
590D4—1884no—
591D4—1884no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—944no—
609C2×C4—1884no—
610C2×C4—1884no—
611C2×C4—1882no—
612C2×C4—1882no—
613C2×C4C22⋊C4×D4711yescharacteristic
614C2×C4C22⋊C4×D4711yescharacteristic
615C2×C4(C22⋊D47)⋊C412yes—
616C2×C4C4×C22⋊D4712yes—
617C2×C4#1309399212yes—
618C2×C4#1309399411yescharacteristic
619C2×C4#1309399412yes—
620C2×C4#1309399512yes—
621C2×C4#1309399612yes—
622C2×C4#1309399712yes—
623C2×C4#1309399712yes—
624C2×C4#1309399812yes—
625C2×C4#1309400612yes—
626C2×C4#1309400811yescharacteristic
627C2×C4#1309401012yes—
628C2×C4#1309402012yes—
629C8—1884no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22—44no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—44no—
638C22—44no—
639C22—42no—
640C22—42no—
641C22—3764no—
642C22—3764no—
643C22—3762no—
644C22—3762no—
645C22—3764no—
646C22—3764no—
647C22—3762no—
648C22—3762no—
649C22—1884no—
650C22—1884no—
651C22—1884no—
652C22#1568897811yescharacteristic
653C22#1568900011yescharacteristic
654C22#1568900211yescharacteristic
655C22#1568903112yes—
656C22#1568903812yes—
657C22C2×#1309394411yescharacteristic
658C22#1568911711yescharacteristic
659C22#1568912211yescharacteristic
660C22#1568912711yescharacteristic
661C22#1568925612yes—
662C22#1568925711yescharacteristic
663C22#1568926211yescharacteristic
664C22#1568926612yes—
665C22#1568926812yes—
666C22#1568927312yes—
667C22#1568928312yes—
668C22#1568935412yes—
669C22#1568935712yes—
670C22#1568937112yes—
671C22#1568937412yes—
672C22#1568943611yescharacteristic
673C22#1568944111yescharacteristic
674C22#1568944712yes—
675C4—42no—
676C4—84no—
677C4—1884no—
678C4#1568899912yes—
679C4#1568902312yes—
680C4#1568903212yes—
681C4#1568903912yes—
682C2—44no—
683C2—3764no—
684C2#2024162711yescharacteristic
685C2#2024331811yescharacteristic
686C2#2024332611yescharacteristic
687C2#2024370511yescharacteristic
688C2#2024371011yescharacteristic
689C2#2024381411yescharacteristic
690C2#2024382411yescharacteristic
691C2#2024438412yes—
692C2#2024438912yes—
693C2#2024457012yes—
694C2#2024457712yes—
subgroupG/H
centerC24C2×C22⋊D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#380C2
socleC24×C47C2×D4
prime radicalC22×#13093998C2
cosocleC23×C4×C47C23
hypercenterC2×#380D47
hypocenterC47#10969
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#13093944C2semidirect
3. C22×C22⋊(C47⋊C8)C2semidirect
4. C2×#15688885C2semidirect
5. C2×C47×#380C2semidirect
12. C2×#13093998C4semidirect
47. C22×C47⋊C8D4semidirect
76. C2×C4⋊C4×C47D4semidirect
165. C2×D188C22⋊C4semidirect
174. C4⋊Dic47C22⋊C4semidirect
204. C23×C47#102semidirect
338. C2×#380D47semidirect
373. C47#10969semidirect
420. C2×C4⋊C4C22⋊D47semidirect
575. C23#13093944semidirect

Maximal subgroups

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

subgroupindex
C22×#130939982
C22×#130939442
C22×C22⋊(C47⋊C8)2
C2×#156888852
C2×C47×#3802
#1096947