Finite Group Databasebeta

← #26137877

Subgroups — #26137877

Order 12032.

2390 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689024C211yesmaximal, characteristic
2C2×#15689001C212yesmaximal
3C2×C4×(C2×D47)⋊C4C212yesmaximal, complemented
4C2×#15688970C212yesmaximal, complemented
5#20241624C212yesmaximal, complemented
6#20241624C212yesmaximal, complemented
7#20241620C211yesmaximal, characteristic, complemented
8#95×Dic47C212yesmaximal, complemented
9C47×#1436C211yesmaximal, characteristic, complemented
10C23×D188C2211yescharacteristic
11C23×C4×D47C2212yes—
12C22×(C2×D47)⋊C4C2212yes—
13C22×(C2×D47)⋊C4C2212yes—
14C22×(C2×D47)⋊C4C2212yes—
15C22×(C2×D47)⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×C4×Dic47C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15689024C418yescomplemented
22#15689001C4116yescomplemented
23C4×(C2×D47)⋊C4—28no—
24#15688970—28no—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C22×C4⋊C4×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C2×#95×C47C2212yes—
33C2×#95×C47C2211yescharacteristic
34C2×#95×C47C2212yes—
35C24×D47C2312yes—
36C22×D188—41no—
37C22×D188—41no—
38C22×D188—42no—
39C22×D188C2×C418yes—
40C22×D188C2×C414yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C22×C4×D47—24no—
45C22×C4×D47—24no—
46C22×C4×D47—24no—
47C22×C4×D47—24no—
48C22×C4×D47—42no—
49C22×C4×D47—42no—
50C22×C4×D47C2×C418yescomplemented
51C2×(C2×D47)⋊C4—24no—
52C2×(C2×D47)⋊C4—24no—
53C2×(C2×D47)⋊C4—24no—
54C2×(C2×D47)⋊C4—24no—
55C2×(C2×D47)⋊C4—24no—
56C2×(C2×D47)⋊C4—24no—
57C2×(C2×D47)⋊C4—24no—
58C2×(C2×D47)⋊C4—24no—
59C2×(C2×D47)⋊C4—42no—
60C2×(C2×D47)⋊C4—42no—
61C2×(C2×D47)⋊C4C2×C418yes—
62C2×(C2×D47)⋊C4C2×C418yes—
63C2×(C2×D47)⋊C4C2×C418yescomplemented
64C2×(C2×D47)⋊C4C2×C418yescomplemented
65C2×(C2×D47)⋊C4C2×C418yescomplemented
66C2×C4×Dic47—24no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—42no—
72C2×C4×Dic47—42no—
73C2×C4×Dic47—41no—
74C2×C4×Dic47—42no—
75C2×C4×Dic47C2×C414yescomplemented
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—41no—
79C47⋊#95C2×C418yescomplemented
80C47⋊#95D418yescomplemented
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2312yes—
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2312yes—
86C2×C4⋊C4×C47—41no—
87C2×C4⋊C4×C47—41no—
88C2×C4⋊C4×C47C2×C414yescomplemented
89C2×C42×C47—24no—
90C2×C42×C47—41no—
91#95×C47—24no—
92#95×C47—41no—
93#95×C47C2×C418yescomplemented
94C24×C47C2411yescharacteristic
95C23×D47—22no—
96C23×D47—22no—
97C23×D47—22no—
98C23×D47—22no—
99C23×D47—22no—
100C23×D47—22no—
101C23×D47—22no—
102C23×D47—22no—
103C23×D47—22no—
104C23×D47—22no—
105C23×D47—22no—
106C23×D47—22no—
107C23×D47C22×C414yes—
108C23×D47C22×C414yes—
109C23×D47C22×C414yes—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C22×C414yes—
134C22×C4×C47C22×C412yes—
135C22×C4×C47C22×C414yes—
136C22×C4×C47C22×C414yes—
137C22×C4×C47C2×D414yes—
138C22×C4×C47#4114yes—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47C22×C414yes—
154C22×Dic47C22×C414yes—
155C22×Dic47C22×C414yes—
156C22×Dic47C2×D414yes—
157C22×Dic47C2×D414yes—
158C22×Dic47#4114yes—
159C22×Dic47#4114yes—
160C2×D188—44no—
161C2×D188—44no—
162C2×D188—48no—
163C2×D188—48no—
164C2×D188C42116yescomplemented
165C2×C4×D47—216no—
166C2×C4×D47—216no—
167C2×C4×D47—48no—
168C2×C4×D47—48no—
169C2×C4×D47—48no—
170C2×C4×D47—48no—
171C2×C4×D47—48no—
172C4⋊C4×C47—44no—
173C42×C47—44no—
174(C2×D47)⋊C4—216no—
175(C2×D47)⋊C4—216no—
176(C2×D47)⋊C4—216no—
177(C2×D47)⋊C4—216no—
178(C2×D47)⋊C4—48no—
179C4×Dic47—44no—
180C4×Dic47—44no—
181C4×Dic47—48no—
182C4×Dic47—48no—
183C23×C47C23×C411yescharacteristic
184C23×C47C23×C412yes—
185C23×C47C22×D412yes—
186C23×C47C2×#4112yes—
187C23×C47C2×#4112yes—
188C23×C47C2×#4112yes—
189C23×C47H(5,𝔽2)11yescharacteristic
190C23×C47H(5,𝔽2)11yescharacteristic
191C23×C47H(5,𝔽2)12yes—
192C22×D47—24no—
193C22×D47—24no—
194C22×D47—24no—
195C22×D47—24no—
196C22×D47—24no—
197C22×D47—24no—
198C22×D47—24no—
199C22×D47—24no—
200C22×D47—24no—
201C22×D47—24no—
202C22×D47—24no—
203C22×D47—24no—
204C22×D47—24no—
205C22×D47—24no—
206C22×D47—24no—
207C22×D47—24no—
208C22×D47—24no—
209C22×D47—24no—
210C22×D47—42no—
211C22×D47—42no—
212C22×D47—42no—
213C22×D47—42no—
214C22×D47—42no—
215C22×D47—42no—
216C22×D47—42no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—42no—
220C22×D47—42no—
221C22×D47—42no—
222C22×D47—42no—
223C22×D47—42no—
224C22×D47—42no—
225C22×D47—42no—
226C22×D47C2×C4218yes—
227C2×C4×C47—24no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—24no—
234C2×C4×C47—24no—
235C2×C4×C47—24no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—24no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47C2×C4214yes—
255C2×C4×C47C4×D418yes—
256C2×Dic47—24no—
257C2×Dic47—24no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—24no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—24no—
264C2×Dic47—24no—
265C2×Dic47—24no—
266C2×Dic47—24no—
267C2×Dic47—24no—
268C2×Dic47—24no—
269C2×Dic47—24no—
270C2×Dic47—24no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47C4×D418yes—
276C2×Dic47C4×D418yes—
277D188—416no—
278C4×D47—432no—
279#13824—471nomaximal, Sylow
280C22×C47C22×C4211yescharacteristic
281C22×C47C2×C4×D412yes—
282C22×C47C2×C4×D412yes—
283C22×C47C2×C4×D412yes—
284C22×C47C4×#4112yes—
285C22×C47C4×#4112yes—
286C22×C47C4×#4112yes—
287C22×C47#51812yes—
288C22×C47#51812yes—
289C22×C47#51811yescharacteristic
290C22×C47#51811yescharacteristic
291C22×C47D4211yescharacteristic
292C22×C47#54612yes—
293C22×C47#54612yes—
294C22×C47#55012yes—
295C22×C47#55112yes—
296C22×C47#55312yes—
297C22×C47#55312yes—
298C22×C47#55511yescharacteristic
299C22×C47#55511yescharacteristic
300C22×C47#55911yescharacteristic
301C2×D47—28no—
302C2×D47—28no—
303C2×D47—28no—
304C2×D47—44no—
305C2×D47—44no—
306C2×D47—44no—
307C2×D47—44no—
308C2×D47—44no—
309C2×D47—44no—
310C2×D47—44no—
311C2×D47—44no—
312C2×D47—44no—
313C2×D47—44no—
314C2×D47—44no—
315C2×D47—44no—
316C4×C47—28no—
317C4×C47—24no—
318C4×C47—44no—
319C4×C47—42no—
320C4×C47—42no—
321Dic47—28no—
322Dic47—28no—
323Dic47—44no—
324C2×#390—471no—
325C2×#386—472no—
326C2×C4×C22⋊C4—472no—
327C2×C4×C22⋊C4—472no—
328#1437—472no—
329#1437—472no—
330#1436—471no—
331#1436D4711yescharacteristic, complemented
332C4×#95—472no—
333C2×C47C42×D412yes—
334C2×C47#227311yescharacteristic
335C2×C47#235812yes—
336C2×C47#236312yes—
337C2×C47#236312yes—
338C2×C47#236412yes—
339C2×C47#236611yescharacteristic
340C2×C47#237211yescharacteristic
341C2×C47#237412yes—
342D47—48no—
343C23×D4—471no—
344C24×C4—472no—
345C22×C4⋊C4C2×D4711yescharacteristic
346C22×C22⋊C4—472no—
347C22×C22⋊C4—472no—
348C22×C22⋊C4—472no—
349C22×C22⋊C4—472no—
350C22×C22⋊C4—472no—
351C22×C42—471no—
352C22×C42—472no—
353C22×C42—472no—
354C22×C42—471no—
355C22×C42C2×D4711yescharacteristic
356#390—478no—
357#386—4716no—
358C4×C22⋊C4—948no—
359C4×C22⋊C4—948no—
360C2×#95—472no—
361C2×#95—472no—
362C2×#95—472no—
363C2×#95—472no—
364C2×#95—471no—
365C2×#95C2×D4712yes—
366C2×#95C2×D4711yescharacteristic
367C2×#95C2×D4712yes—
368C47#1382411yescharacteristic, complemented, Sylow
369C25—472no—
370C22×D4—478no—
371C22×D4—474no—
372C22×D4—1881no—
373C22×D4—1881no—
374C22×D4—1882no—
375C23×C4—472no—
376C23×C4—472no—
377C23×C4—472no—
378C23×C4—478no—
379C23×C4—944no—
380C23×C4—944no—
381C23×C4—944no—
382C23×C4—944no—
383C23×C4—1882no—
384C23×C4—1882no—
385C23×C4C22×D4711yescharacteristic
386C23×C4C22×D4711yescharacteristic
387C23×C4C22×D4712yes—
388C23×C4C22×D4711yescharacteristic
389C23×C4C22×D4712yes—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4C4×D4714yescomplemented
393C2×C22⋊C4—478no—
394C2×C22⋊C4—478no—
395C2×C22⋊C4—478no—
396C2×C22⋊C4—478no—
397C2×C22⋊C4—478no—
398C2×C22⋊C4—944no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4—944no—
401C2×C22⋊C4—944no—
402C2×C22⋊C4—944no—
403C2×C22⋊C4—944no—
404C2×C22⋊C4—944no—
405C2×C22⋊C4—944no—
406C2×C22⋊C4—1882no—
407C2×C22⋊C4—1882no—
408C2×C42—24no—
409C2×C42—41no—
410C2×C42—474no—
411C2×C42—944no—
412C2×C42—944no—
413C2×C42—944no—
414C2×C42—944no—
415C2×C42—944no—
416C2×C42—1882no—
417C2×C42—1882no—
418C2×C42—1881no—
419C2×C42—1882no—
420#95—24no—
421#95—41no—
422#95—478no—
423#95—478no—
424#95—944no—
425#95—944no—
426#95—1881no—
427#95C4×D4718yescomplemented
428C24—474no—
429C24—474no—
430C24—474no—
431C24—942no—
432C24—942no—
433C24—942no—
434C24—942no—
435C24—942no—
436C24—942no—
437C24—942no—
438C24—942no—
439C24—942no—
440C24—942no—
441C24—942no—
442C24—942no—
443C24C23×D4711yescharacteristic
444C2×D4—4716no—
445C2×D4—1888no—
446C2×D4—1888no—
447C2×D4—1884no—
448C2×D4—1884no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—474no—
471C22×C4—474no—
472C22×C4—474no—
473C22×C4—474no—
474C22×C4—474no—
475C22×C4—474no—
476C22×C4—474no—
477C22×C4—9416no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—9416no—
493C22×C4—1888no—
494C22×C4—1888no—
495C22×C4—1888no—
496C22×C4—1888no—
497C22×C4—1888no—
498C22×C4C2×C4×D4714yes—
499C22×C4C2×C4×D4712yes—
500C22×C4C2×C4×D4712yes—
501C22×C4C2×C4×D4714yes—
502C22×C4C2×C4×D4712yes—
503C22×C4C2×C4×D4714yes—
504C22×C4D4×D4714yes—
505C22×C4#1062535414yes—
506C4⋊C4—44no—
507C22⋊C4—9416no—
508C22⋊C4—9416no—
509C22⋊C4—9416no—
510C22⋊C4—9416no—
511C22⋊C4—1888no—
512C42—44no—
513C42—1884no—
514C42—1888no—
515C42—1884no—
516C42—1888no—
517C23—478no—
518C23—944no—
519C23—944no—
520C23—944no—
521C23—944no—
522C23—944no—
523C23—944no—
524C23—944no—
525C23—944no—
526C23—944no—
527C23—944no—
528C23—944no—
529C23—944no—
530C23—944no—
531C23—944no—
532C23—944no—
533C23—944no—
534C23—944no—
535C23—944no—
536C23—1882no—
537C23—1882no—
538C23—1882no—
539C23—1882no—
540C23—1882no—
541C23—1882no—
542C23—1882no—
543C23—1882no—
544C23—1882no—
545C23—1882no—
546C23—1882no—
547C23—1882no—
548C23—1882no—
549C23—1882no—
550C23—1882no—
551C23—1882no—
552C23C22×C4×D4711yescharacteristic
553C23C22×C4×D4712yes—
554C23C2×D4×D4712yes—
555C23#41×D4712yes—
556C23#41×D4712yes—
557C23C2×#1062535412yes—
558C23#1309406911yescharacteristic
559C23#1309406911yescharacteristic
560C23#1309407012yes—
561D4—18816no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—478no—
590C2×C4—478no—
591C2×C4—944no—
592C2×C4—944no—
593C2×C4—944no—
594C2×C4—944no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—944no—
599C2×C4—944no—
600C2×C4—944no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—944no—
604C2×C4—944no—
605C2×C4—944no—
606C2×C4—18832no—
607C2×C4—1882no—
608C2×C4—1882no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4C42×D4714yes—
612C2×C4#1309398618yes—
613C22—948no—
614C22—948no—
615C22—948no—
616C22—1884no—
617C22—1884no—
618C22—1884no—
619C22—1884no—
620C22—1884no—
621C22—1884no—
622C22—1884no—
623C22—1884no—
624C22—1884no—
625C22—1884no—
626C22—1884no—
627C22—1884no—
628C22C2×C42×D4711yescharacteristic
629C22C4×D4×D4712yes—
630C22C4×D4×D4712yes—
631C22C2×#1309398612yes—
632C22#1568959112yes—
633C22C4×#1062535412yes—
634C22C4×#1062535412yes—
635C22#1568959512yes—
636C22#1568959512yes—
637C22#1568959611yescharacteristic
638C22#1568959711yescharacteristic
639C22#1568975511yescharacteristic
640C22#1568976412yes—
641C22#1568976512yes—
642C22#1568979112yes—
643C22#1568980012yes—
644C22#1568982412yes—
645C22#1568982612yes—
646C22#1568983511yescharacteristic
647C22#1568983911yescharacteristic
648C22#1568985711yescharacteristic
649C4—28no—
650C4—24no—
651C4—44no—
652C4—42no—
653C4—42no—
654C4—948no—
655C4—948no—
656C4—1884no—
657C2—1888no—
658C2C4×#1309398612yes—
659C2#2024574011yescharacteristic
660C2#2024636412yes—
661C2#2024642112yes—
662C2#2024642512yes—
663C2#2024643412yes—
664C2#2024645111yescharacteristic
665C2#2024649911yescharacteristic
666C2#2024652012yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenter#1436D47
hypocenterC47#13824
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D47)⋊C4C2semidirect
4. C2×#15688970C2semidirect
5. #20241624C2semidirect
6. #20241624C2semidirect
7. #20241620C2semidirect
8. #95×Dic47C2semidirect
9. C47×#1436C2semidirect
21. #15689024C4semidirect
22. #15689001C4semidirect
50. C22×C4×D47C2×C4semidirect
63. C2×(C2×D47)⋊C4C2×C4semidirect
64. C2×(C2×D47)⋊C4C2×C4semidirect
65. C2×(C2×D47)⋊C4C2×C4semidirect
75. C2×C4×Dic47C2×C4semidirect
79. C47⋊#95C2×C4semidirect
80. C47⋊#95D4semidirect
88. C2×C4⋊C4×C47C2×C4semidirect
93. #95×C47C2×C4semidirect
164. C2×D188C42semidirect
331. #1436D47semidirect
368. C47#13824semidirect
392. C2×C4⋊C4C4×D47semidirect
427. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890242
C2×#156890012
C2×C4×(C2×D47)⋊C42
C2×#156889702
#202416242
#202416202
#95×Dic472
C47×#14362
#1382447