Finite Group Databasebeta

← #26137741

Subgroups — #26137741

Order 12032.

1790 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688985C211yesmaximal, characteristic
2C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
3C2×#15688970C211yesmaximal, characteristic
4#20241626C212yesmaximal
5#20241624C212yesmaximal
6#20241615C211yesmaximal, characteristic, complemented
7#20241614C212yesmaximal, complemented
8#20241613C211yesmaximal, characteristic, complemented
9C4×C47⋊#95C212yesmaximal, complemented
10#95×Dic47C211yesmaximal, characteristic, complemented
11C4×#95×C47C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×(C2×D47)⋊C4C2212yes—
14C22×(C2×D47)⋊C4C2211yescharacteristic
15C22×(C2×D47)⋊C4C2211yescharacteristic
16C22×(C2×D47)⋊C4C2212yes—
17C22×C4×Dic47C2212yes—
18C22×C4×Dic47C2211yescharacteristic
19C22×C4×Dic47C2212yes—
20#15688985C418yescomplemented
21C4×(C2×D47)⋊C4C418yescomplemented
22#15688970C418yescomplemented
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C22×C42×C47C2212yes—
34C22×C42×C47C2211yescharacteristic
35C2×#95×C47C2212yes—
36C2×#95×C47C2211yescharacteristic
37C2×#95×C47C2211yescharacteristic
38C24×D47C2311yescharacteristic
39C23×Dic47C2312yes—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C22×C4×D47—42no—
45C22×C4×D47—42no—
46C22×C4×D47C2×C414yes—
47C22×C4×D47C2×C414yes—
48C22×C4×D47C2×C414yes—
49C2×(C2×D47)⋊C4—24no—
50C2×(C2×D47)⋊C4—24no—
51C2×(C2×D47)⋊C4—22no—
52C2×(C2×D47)⋊C4—22no—
53C2×(C2×D47)⋊C4—22no—
54C2×(C2×D47)⋊C4—22no—
55C2×(C2×D47)⋊C4—42no—
56C2×(C2×D47)⋊C4—42no—
57C2×(C2×D47)⋊C4C2×C418yes—
58C2×(C2×D47)⋊C4C2×C414yes—
59C2×(C2×D47)⋊C4C2×C414yes—
60C2×(C2×D47)⋊C4C2×C418yes—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—42no—
64C2×C4×Dic47—42no—
65C2×C4×Dic47—42no—
66C2×C4×Dic47—42no—
67C2×C4×Dic47C2×C418yes—
68C2×C4×Dic47C2×C414yes—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—42no—
73C47⋊#95—42no—
74C47⋊#95C2×C414yes—
75C47⋊#95C2×C414yes—
76C47⋊#95C2×C414yes—
77C47⋊#95C2×C414yes—
78C47⋊#95C2×C418yes—
79C23×C4×C47C2312yes—
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2312yes—
84C2×C42×C47—24no—
85C2×C42×C47—24no—
86C2×C42×C47—42no—
87C2×C42×C47—42no—
88C2×C42×C47C2×C414yes—
89#95×C47—24no—
90#95×C47C2×C414yes—
91#95×C47C2×C414yes—
92C24×C47C2411yescharacteristic
93C23×D47—21no—
94C23×D47—21no—
95C23×D47—22no—
96C23×D47—21no—
97C23×D47—22no—
98C23×D47—21no—
99C23×D47—22no—
100C23×D47—22no—
101C23×D47C22×C412yes—
102C23×D47C22×C412yes—
103C23×D47C22×C412yes—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C22×C414yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C414yes—
129C22×C4×C47#4114yes—
130C22×C4×C47#4114yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47C22×C414yes—
154C22×Dic47C22×C414yes—
155C22×Dic47C22×C412yes—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C412yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C22×C412yes—
160C22×Dic47#4112yes—
161C22×Dic47#4112yes—
162C2×C4×D47—48no—
163C2×C4×D47—44no—
164C2×C4×D47—44no—
165C2×C4×D47—48no—
166C2×C4×D47C42116yescomplemented
167C42×C47—44no—
168C42×C47—48no—
169(C2×D47)⋊C4—216no—
170(C2×D47)⋊C4—28no—
171(C2×D47)⋊C4—28no—
172(C2×D47)⋊C4—48no—
173C4×Dic47—48no—
174C4×Dic47—44no—
175C4×Dic47—48no—
176C23×C47C23×C411yescharacteristic
177C23×C47C23×C411yescharacteristic
178C23×C47C23×C411yescharacteristic
179C23×C47C2×#4111yescharacteristic
180C23×C47C2×#4111yescharacteristic
181C23×C47C2×#4111yescharacteristic
182C23×C47C2×#4112yes—
183C23×C47C2×#4112yes—
184C23×C47C2×#4111yescharacteristic
185C23×C47H(5,𝔽2)12yes—
186C23×C47H(5,𝔽2)12yes—
187C22×D47—22no—
188C22×D47—24no—
189C22×D47—22no—
190C22×D47—22no—
191C22×D47—22no—
192C22×D47—22no—
193C22×D47—22no—
194C22×D47—24no—
195C22×D47—22no—
196C22×D47—22no—
197C22×D47—24no—
198C22×D47—24no—
199C22×D47—22no—
200C22×D47—22no—
201C22×D47—42no—
202C22×D47—42no—
203C22×D47—42no—
204C22×D47—42no—
205C22×D47—42no—
206C22×D47—42no—
207C22×D47—42no—
208C22×D47—42no—
209C22×D47C2×C4214yes—
210C2×C4×C47—24no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—22no—
225C2×C4×C47—24no—
226C2×C4×C47—22no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47C2×C4214yes—
237C2×C4×C47#11718yes—
238C2×C4×C47#11714yes—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—24no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—22no—
255C2×Dic47—24no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47C2×C4214yes—
267C2×Dic47#11714yes—
268C4×D47—416no—
269#13807—471nomaximal, Sylow
270C22×C47C22×C4211yescharacteristic
271C22×C47C2×#11711yescharacteristic
272C22×C47C2×#11712yes—
273C22×C47C2×#11711yescharacteristic
274C22×C47C4×#4111yescharacteristic
275C22×C47C4×#4111yescharacteristic
276C22×C47C4×#4111yescharacteristic
277C22×C47C4×#4111yescharacteristic
278C22×C47C4×#4112yes—
279C22×C47C4×#4111yescharacteristic
280C22×C47C4×#4111yescharacteristic
281C22×C47#51812yes—
282C22×C47#51812yes—
283C22×C47#51811yescharacteristic
284C22×C47#51811yescharacteristic
285C22×C47#55112yes—
286C22×C47#55112yes—
287C22×C47#55312yes—
288C22×C47#55312yes—
289C22×C47#55312yes—
290C22×C47#55312yes—
291C22×C47#55912yes—
292C22×C47#55912yes—
293C2×D47—24no—
294C2×D47—24no—
295C2×D47—24no—
296C2×D47—44no—
297C2×D47—42no—
298C2×D47—42no—
299C2×D47—44no—
300C2×D47—42no—
301C2×D47—42no—
302C2×D47—44no—
303C2×D47—44no—
304C4×C47—28no—
305C4×C47—24no—
306C4×C47—24no—
307C4×C47—42no—
308C4×C47—44no—
309Dic47—24no—
310Dic47—24no—
311Dic47—44no—
312Dic47—42no—
313Dic47—44no—
314C2×#381—471no—
315C2×C4×C22⋊C4—471no—
316C2×C4×C22⋊C4—471no—
317#1437—472no—
318#1437—472no—
319#1434—471no—
320#1434—471no—
321#1434—472no—
322C4×#95—472no—
323C4×#95—471no—
324C4×#95D4711yescharacteristic, complemented
325C2×C47C4×#11711yescharacteristic
326C2×C47C4×#11711yescharacteristic
327C2×C47#227311yescharacteristic
328C2×C47#235312yes—
329C2×C47#235311yescharacteristic
330C2×C47#235311yescharacteristic
331C2×C47#235712yes—
332C2×C47#235711yescharacteristic
333C2×C47#235711yescharacteristic
334C2×C47#237412yes—
335C2×C47#237412yes—
336D47—44no—
337C24×C4—471no—
338C22×C22⋊C4—471no—
339C22×C22⋊C4—472no—
340C22×C22⋊C4—471no—
341C22×C22⋊C4—472no—
342C22×C42—471no—
343C22×C42—472no—
344C22×C42—472no—
345C22×C42C2×D4712yes—
346C22×C42C2×D4711yescharacteristic
347#381—478no—
348C4×C22⋊C4—478no—
349C4×C22⋊C4—478no—
350C2×#95—471no—
351C2×#95—472no—
352C2×#95—471no—
353C2×#95—471no—
354C2×#95—471no—
355C2×#95—472no—
356C2×#95—472no—
357C2×#95—472no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95C2×D4712yes—
361C2×#95C2×D4711yescharacteristic
362C2×#95C2×D4711yescharacteristic
363C47#1380711yescharacteristic, complemented, Sylow
364C25—471no—
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—474no—
368C23×C4—474no—
369C23×C4—474no—
370C23×C4—472no—
371C23×C4—472no—
372C23×C4—471no—
373C23×C4—1882no—
374C23×C4—1882no—
375C23×C4C22×D4712yes—
376C23×C4C22×D4711yescharacteristic
377C23×C4C22×D4711yescharacteristic
378C23×C4C22×D4712yes—
379C23×C4C22×D4711yescharacteristic
380C2×C22⋊C4—474no—
381C2×C22⋊C4—478no—
382C2×C22⋊C4—474no—
383C2×C22⋊C4—478no—
384C2×C22⋊C4—942no—
385C2×C22⋊C4—942no—
386C2×C22⋊C4—944no—
387C2×C22⋊C4—944no—
388C2×C22⋊C4—942no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4—1882no—
391C2×C22⋊C4—1882no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—474no—
397C2×C42—478no—
398C2×C42—944no—
399C2×C42—944no—
400C2×C42—1882no—
401C2×C42—1882no—
402C2×C42—1882no—
403C2×C42—1882no—
404C2×C42C4×D4714yes—
405#95—24no—
406#95—474no—
407#95—474no—
408#95—474no—
409#95—478no—
410#95—474no—
411#95—944no—
412#95—944no—
413#95—944no—
414#95—1882no—
415#95—1882no—
416#95C4×D4714yes—
417#95C4×D4714yes—
418C24—472no—
419C24—472no—
420C24—472no—
421C24—941no—
422C24—941no—
423C24—941no—
424C24—942no—
425C24—942no—
426C24—941no—
427C24—942no—
428C24—942no—
429C24C23×D4711yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—472no—
449C22×C4—472no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—472no—
453C22×C4—472no—
454C22×C4—4716no—
455C22×C4—474no—
456C22×C4—474no—
457C22×C4—472no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—941no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—941no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—1888no—
479C22×C4—1888no—
480C22×C4—1884no—
481C22×C4—1884no—
482C22×C4C2×C4×D4714yes—
483C22×C4C2×C4×D4712yes—
484C22×C4C2×C4×D4712yes—
485C22×C4C2×C4×D4712yes—
486C22×C4C2×C4×D4712yes—
487C22×C4C2×C4×D4714yes—
488C22×C4C2×C4×D4712yes—
489C22×C4#1062535014yes—
490C22×C4#1062535014yes—
491C22×C4#1062535212yes—
492C22×C4#1062535412yes—
493C22⋊C4—948no—
494C22⋊C4—9416no—
495C22⋊C4—948no—
496C22⋊C4—1888no—
497C42—44no—
498C42—48no—
499C42—1888no—
500C42—1884no—
501C42—1888no—
502C23—474no—
503C23—942no—
504C23—944no—
505C23—942no—
506C23—942no—
507C23—942no—
508C23—942no—
509C23—942no—
510C23—944no—
511C23—942no—
512C23—942no—
513C23—944no—
514C23—944no—
515C23—942no—
516C23—942no—
517C23—1882no—
518C23—1882no—
519C23—1882no—
520C23—1882no—
521C23—1882no—
522C23—1882no—
523C23—1882no—
524C23—1882no—
525C23C22×C4×D4711yescharacteristic
526C23C22×C4×D4711yescharacteristic
527C23C22×C4×D4711yescharacteristic
528C23#41×D4711yescharacteristic
529C23#41×D4711yescharacteristic
530C23C2×#1062535211yescharacteristic
531C23C2×#1062535012yes—
532C23C2×#1062535012yes—
533C23C2×#1062535411yescharacteristic
534C23#1309406912yes—
535C23#1309407012yes—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—474no—
563C2×C4—474no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—942no—
567C2×C4—944no—
568C2×C4—944no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—944no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—944no—
576C2×C4—944no—
577C2×C4—944no—
578C2×C4—944no—
579C2×C4—944no—
580C2×C4—942no—
581C2×C4—18816no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4—1882no—
585C2×C4—1882no—
586C2×C4—1882no—
587C2×C4—1882no—
588C2×C4—1882no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4C42×D4714yes—
593C2×C4#1309398118yes—
594C2×C4#1309398214yes—
595C22—944no—
596C22—944no—
597C22—944no—
598C22—1884no—
599C22—1882no—
600C22—1882no—
601C22—1884no—
602C22—1882no—
603C22—1882no—
604C22—1884no—
605C22—1884no—
606C22C2×C42×D4711yescharacteristic
607C22#117×D4711yescharacteristic
608C22C2×#1309398112yes—
609C22C2×#1309398211yescharacteristic
610C22C4×#1062535211yescharacteristic
611C22C4×#1062535211yescharacteristic
612C22C4×#1062535011yescharacteristic
613C22C4×#1062535011yescharacteristic
614C22C4×#1062535012yes—
615C22C4×#1062535411yescharacteristic
616C22C4×#1062535411yescharacteristic
617C22#1568959512yes—
618C22#1568959512yes—
619C22#1568959611yescharacteristic
620C22#1568959711yescharacteristic
621C22#1568979712yes—
622C22#1568979912yes—
623C22#1568981712yes—
624C22#1568981912yes—
625C22#1568982112yes—
626C22#1568982212yes—
627C22#1568985612yes—
628C22#1568985812yes—
629C4—28no—
630C4—24no—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—944no—
635C4—944no—
636C4—1884no—
637C4—1882no—
638C4—1884no—
639C2—1884no—
640C2C4×#1309398211yescharacteristic
641C2C4×#1309398111yescharacteristic
642C2#2024574011yescharacteristic
643C2#2024632212yes—
644C2#2024632411yescharacteristic
645C2#2024632911yescharacteristic
646C2#2024635712yes—
647C2#2024635911yescharacteristic
648C2#2024636211yescharacteristic
649C2#2024651712yes—
650C2#2024652212yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4×#95D47
hypocenterC47#13807
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
6. #20241615C2semidirect
7. #20241614C2semidirect
8. #20241613C2semidirect
9. C4×C47⋊#95C2semidirect
10. #95×Dic47C2semidirect
11. C4×#95×C47C2semidirect
20. #15688985C4semidirect
21. C4×(C2×D47)⋊C4C4semidirect
22. #15688970C4semidirect
166. C2×C4×D47C42semidirect
324. C4×#95D47semidirect
363. C47#13807semidirect

Maximal subgroups

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

subgroupindex
C2×#156889852
C2×C4×(C2×D47)⋊C42
C2×#156889702
#202416262
#202416242
#202416152
#202416142
#202416132
C4×C47⋊#952
#95×Dic472
C4×#95×C472
#1380747