Finite Group Databasebeta

← #26138762

Subgroups — #26138762

Order 12032.

1370 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×#15689022C211yesmaximal, characteristic
2C2×C4⋊C4×Dic47C211yesmaximal, characteristic
3#20241647C212yesmaximal
4#20241644C212yesmaximal
5#20241618C211yesmaximal, characteristic
6#20241617C212yesmaximal
7#20241617C211yesmaximal, characteristic
8#20241617C211yesmaximal, characteristic
9#20241614C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C2×C47×#389C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4×Dic47C2211yescharacteristic
16C22×C4×Dic47C2211yescharacteristic
17C22×C4×Dic47C2212yes—
18#15689022—24no—
19C4⋊C4×Dic47C418yescomplemented
20C2×C47⋊#95C2212yes—
21C2×C47⋊#95C2211yescharacteristic
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2211yescharacteristic
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2212yes—
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C47×#389—24no—
37C2×#95×C47C2212yes—
38C23×Dic47C2312yes—
39C23×Dic47C2311yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—24no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47—42no—
52C2×C4⋊Dic47C2×C414yes—
53C2×C4×Dic47—22no—
54C2×C4×Dic47—22no—
55C2×C4×Dic47—22no—
56C2×C4×Dic47—22no—
57C2×C4×Dic47—22no—
58C2×C4×Dic47—42no—
59C2×C4×Dic47—42no—
60C2×C4×Dic47C2×C414yes—
61C2×C4×Dic47C2×C418yes—
62C47⋊#95—24no—
63C47⋊#95—22no—
64C47⋊#95—22no—
65C47⋊#95—22no—
66C47⋊#95—24no—
67C47⋊#95—42no—
68C47⋊#95—42no—
69C47⋊#95—42no—
70C47⋊#95—42no—
71C47⋊#95—42no—
72C47⋊#95C2×C418yes—
73C47⋊#95Q814yes—
74C23×C4×C47C2312yes—
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2312yes—
78C23×C4×C47C2311yescharacteristic
79C2×C4⋊C4×C47—24no—
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47—24no—
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—22no—
84C2×C4⋊C4×C47—42no—
85C2×C4⋊C4×C47C2×C414yes—
86C2×C4⋊C4×C47D414yes—
87C2×C4⋊C4×C47Q814yes—
88C2×C42×C47—22no—
89C2×C42×C47—22no—
90C2×C42×C47—22no—
91#95×C47—24no—
92C24×C47C2411yescharacteristic
93C22×C4×C47—22no—
94C22×C4×C47—22no—
95C22×C4×C47—22no—
96C22×C4×C47—22no—
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
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—22no—
116C22×C4×C47C22×C414yes—
117C22×C4×C47C22×C412yes—
118C22×C4×C47C2×D414yes—
119C22×C4×C47C2×D412yes—
120C22×C4×C47C2×Q812yes—
121C22×C4×C47C2×Q814yes—
122C22×C4×C47C2×Q812yes—
123C22×C4×C47#4112yes—
124C22×C4×C47#4112yes—
125C22×C4×C47#4112yes—
126C22×C4×C47#4112yes—
127C22×C4×C47#4112yes—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—21no—
153C22×Dic47—22no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47C22×C412yes—
164C22×Dic47C22×C414yes—
165C22×Dic47C22×C412yes—
166C22×Dic47C2×Q812yes—
167C22×Dic47C2×Q812yes—
168C22×Dic47#4112yes—
169C22×Dic47#4112yes—
170C4⋊C4×C47—48no—
171C4⋊C4×C47—44no—
172C4⋊C4×C47C4⋊C4116yes—
173C42×C47—44no—
174C4⋊Dic47—28no—
175C4⋊Dic47—48no—
176C4⋊Dic47—44no—
177C4×Dic47—28no—
178C4×Dic47—48no—
179C4×Dic47—44no—
180C23×C47C23×C411yescharacteristic
181C23×C47C22×D411yescharacteristic
182C23×C47C22×Q811yescharacteristic
183C23×C47C22×Q811yescharacteristic
184C23×C47C2×#4111yescharacteristic
185C23×C47C2×#4111yescharacteristic
186C23×C47C2×#4111yescharacteristic
187C23×C47C2×#4111yescharacteristic
188C23×C47C2×#4111yescharacteristic
189C23×C47C2×#4111yescharacteristic
190C23×C47C2×#4111yescharacteristic
191C23×C47H(5,𝔽2)11yescharacteristic
192C23×C47H(5,𝔽2)11yescharacteristic
193C23×C47H(5,𝔽2)11yescharacteristic
194C23×C472−1+411yescharacteristic
195C2×C4×C47—24no—
196C2×C4×C47—24no—
197C2×C4×C47—24no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47C2×C4⋊C418yes—
223C2×C4×C47C2×C4⋊C414yes—
224C2×C4×C47#11714yes—
225C2×C4×C47#11714yes—
226C2×C4×C47#12414yes—
227C2×C4×C47#12414yes—
228C2×C4×C47#12514yes—
229C2×C4×C47#12514yes—
230C2×Dic47—22no—
231C2×Dic47—22no—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—42no—
251C2×Dic47—41no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47C4×Q814yes—
272#13933—471nomaximal, Sylow
273C22×C47C22×C4⋊C411yescharacteristic
274C22×C47C2×#11711yescharacteristic
275C22×C47C2×#11711yescharacteristic
276C22×C47C2×C4×Q811yescharacteristic
277C22×C47C4×#4111yescharacteristic
278C22×C47#51811yescharacteristic
279C22×C47#52011yescharacteristic
280C22×C47C2×#12411yescharacteristic
281C22×C47C2×#12411yescharacteristic
282C22×C47C2×#12511yescharacteristic
283C22×C47C2×#12511yescharacteristic
284C22×C47#52911yescharacteristic
285C22×C47#52911yescharacteristic
286C22×C47#53311yescharacteristic
287C22×C47#53311yescharacteristic
288C22×C47#54011yescharacteristic
289C22×C47#54011yescharacteristic
290C22×C47#54211yescharacteristic
291C22×C47#54211yescharacteristic
292C22×C47#54611yescharacteristic
293C22×C47#54611yescharacteristic
294C22×C47D4×Q811yescharacteristic
295C22×C47#55011yescharacteristic
296C22×C47#55311yescharacteristic
297C22×C47#55311yescharacteristic
298C22×C47#55311yescharacteristic
299C22×C47#55311yescharacteristic
300C22×C47#55411yescharacteristic
301C22×C47#55411yescharacteristic
302C22×C47#55411yescharacteristic
303C22×C47#55411yescharacteristic
304C22×C47#55611yescharacteristic
305C22×C47#55611yescharacteristic
306C22×C47#55711yescharacteristic
307C22×C47Q8211yescharacteristic
308C4×C47—28no—
309C4×C47—42no—
310C4×C47—42no—
311C4×C47—82no—
312C4×C47#38218yes—
313Dic47—24no—
314Dic47—44no—
315Dic47—42no—
316Dic47—42no—
317Dic47—42no—
318Dic47—82no—
319C2×#389—471no—
320C2×#389D4711yescharacteristic
321C2×C4×C4⋊C4—471no—
322#1442—472no—
323#1442—472no—
324C4⋊#95—471no—
325C4⋊#95—471no—
326C4⋊#95—471no—
327C4⋊#95—472no—
328#1434—472no—
329C4×#95—471no—
330C2×C47C2×#38211yescharacteristic
331C2×C47#229511yescharacteristic
332C2×C47#231911yescharacteristic
333C2×C47#234511yescharacteristic
334C2×C47#234711yescharacteristic
335C2×C47#234911yescharacteristic
336C2×C47Q8×C4⋊C411yescharacteristic
337C2×C47#249011yescharacteristic
338C2×C47#249011yescharacteristic
339C2×C47#249211yescharacteristic
340C2×C47#249211yescharacteristic
341C2×C47#250711yescharacteristic
342C2×C47#250711yescharacteristic
343C2×C47#250911yescharacteristic
344C2×C47#250911yescharacteristic
345C22×C4⋊C4—471no—
346C22×C4⋊C4—471no—
347C22×C4⋊C4—472no—
348C22×C4⋊C4C2×D4711yescharacteristic
349C22×C4⋊C4C2×D4712yes—
350C22×C4⋊C4C2×D4711yescharacteristic
351C22×C42—471no—
352C22×C42—472no—
353C22×C42—471no—
354C22×C42C2×D4711yescharacteristic
355#389—24no—
356#389—944no—
357C4×C4⋊C4—478no—
358C2×#95—471no—
359C2×#95—472no—
360C2×#95—471no—
361C2×#95—471no—
362C2×#95—471no—
363C2×#95—472no—
364C2×#95—472no—
365C2×#95—472no—
366C2×#95—472no—
367C2×#95—472no—
368C2×#95—472no—
369C2×#95—472no—
370C2×#95C2×D4712yes—
371C47#1393311yescharacteristic, complemented, Sylow
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—472no—
375C23×C4—471no—
376C23×C4—471no—
377C23×C4—472no—
378C23×C4C22×D4712yes—
379C23×C4C22×D4711yescharacteristic
380C23×C4C22×D4711yescharacteristic
381C23×C4C22×D4712yes—
382C23×C4C22×D4711yescharacteristic
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—474no—
390C2×C4⋊C4—942no—
391C2×C4⋊C4—942no—
392C2×C4⋊C4—944no—
393C2×C4⋊C4—942no—
394C2×C4⋊C4—942no—
395C2×C4⋊C4—944no—
396C2×C4⋊C4—942no—
397C2×C4⋊C4—1882no—
398C2×C4⋊C4Dic9414yes—
399C2×C4⋊C4C4×D4714yes—
400C2×C4⋊C4C22⋊D4714yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—474no—
405C2×C42—478no—
406C2×C42—942no—
407C2×C42—942no—
408C2×C42—942no—
409C2×C42—942no—
410C2×C42—942no—
411C2×C42—1882no—
412C2×C42—1882no—
413#95—24no—
414#95—478no—
415#95—474no—
416#95—942no—
417#95—942no—
418#95—944no—
419#95—942no—
420#95—944no—
421#95—1882no—
422#95—1882no—
423#95—1882no—
424#95—1882no—
425#95—1882no—
426C24C23×D4711yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—472no—
453C22×C4—472no—
454C22×C4—474no—
455C22×C4—472no—
456C22×C4—472no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—941no—
466C22×C4—941no—
467C22×C4—941no—
468C22×C4—942no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—941no—
474C22×C4—942no—
475C22×C4—941no—
476C22×C4—942no—
477C22×C4—941no—
478C22×C4—942no—
479C22×C4—941no—
480C22×C4—942no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—942no—
484C22×C4—941no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4C2×Dic9414yes—
493C22×C4C2×Dic9412yes—
494C22×C4C2×C4×D4714yes—
495C22×C4C2×C4×D4712yes—
496C22×C4#1062535212yes—
497C22×C4#1062535212yes—
498C22×C4#1062535212yes—
499C22×C4Q8×D4712yes—
500C22×C4#1062535412yes—
501C22×C4#1062535412yes—
502C22×C4C2×C22⋊D4714yes—
503C22×C4C2×C22⋊D4712yes—
504C4⋊C4—48no—
505C4⋊C4—44no—
506C4⋊C4—948no—
507C4⋊C4—1888no—
508C4⋊C4—1884no—
509C4⋊C4Dic47⋊C4116yes—
510C42—44no—
511C42—948no—
512C42—1888no—
513C42—1884no—
514C23C22×C4×D4711yescharacteristic
515C23C22×C22⋊D4711yescharacteristic
516C23C2×Q8×D4711yescharacteristic
517C23C22×Dic9411yescharacteristic
518C23#41×D4711yescharacteristic
519C23#41×D4711yescharacteristic
520C23C2×#1062535211yescharacteristic
521C23C2×#1062535211yescharacteristic
522C23C2×#1062535211yescharacteristic
523C23C2×#1062535411yescharacteristic
524C23C2×#1062535411yescharacteristic
525C23#1309406911yescharacteristic
526C23#1309407011yescharacteristic
527C23#1309407011yescharacteristic
528C23#1309407211yescharacteristic
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—474no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—942no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—944no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—944no—
571C2×C4—942no—
572C2×C4—944no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—1882no—
576C2×C4—1882no—
577C2×C4—1882no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4—1882no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4—1881no—
584C2×C4—1882no—
585C2×C4—1882no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4—1881no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4—1881no—
596C2×C4—1881no—
597C2×C4—1882no—
598C2×C4C2×Dic47⋊C418yes—
599C2×C4C2×Dic47⋊C414yes—
600C2×C4#1309398214yes—
601C2×C4#1309398214yes—
602C2×C4#1309401114yes—
603C2×C4#1309401314yes—
604C2×C4#1309401514yes—
605C2×C4#1309401514yes—
606C22C22×Dic47⋊C411yescharacteristic
607C22C2×#1309398211yescharacteristic
608C22C2×#1309398211yescharacteristic
609C22C4×Q8×D4711yescharacteristic
610C22C4×#1062535211yescharacteristic
611C22#1568959511yescharacteristic
612C22#1568960511yescharacteristic
613C22C2×#1309401111yescharacteristic
614C22C2×#1309401311yescharacteristic
615C22C2×#1309401511yescharacteristic
616C22C2×#1309401511yescharacteristic
617C22#1568965411yescharacteristic
618C22#1568965811yescharacteristic
619C22#1568967511yescharacteristic
620C22#1568967811yescharacteristic
621C22#1568972611yescharacteristic
622C22#1568972911yescharacteristic
623C22#1568974611yescharacteristic
624C22#1568974711yescharacteristic
625C22#1568976111yescharacteristic
626C22#1568976711yescharacteristic
627C22Q8×C22⋊D4711yescharacteristic
628C22#1568979211yescharacteristic
629C22#1568982011yescharacteristic
630C22#1568982511yescharacteristic
631C22#1568982611yescharacteristic
632C22#1568982611yescharacteristic
633C22#1568983011yescharacteristic
634C22#1568983111yescharacteristic
635C22#1568983211yescharacteristic
636C22#1568983411yescharacteristic
637C22#1568984411yescharacteristic
638C22#1568984711yescharacteristic
639C22#1568984911yescharacteristic
640C22Q8×Dic9411yescharacteristic
641C4—28no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4—944no—
646C4—3762no—
647C4—1882no—
648C4—1884no—
649C4—1882no—
650C4—1882no—
651C4#1568898818yes—
652C2C2×#1568898811yescharacteristic
653C2#2024585911yescharacteristic
654C2#2024602711yescharacteristic
655C2#2024626411yescharacteristic
656C2#2024628011yescharacteristic
657C2#2024629311yescharacteristic
658C2Q8×Dic47⋊C411yescharacteristic
659C2#2024774211yescharacteristic
660C2#2024774311yescharacteristic
661C2#2024776411yescharacteristic
662C2#2024776511yescharacteristic
663C2#2024791711yescharacteristic
664C2#2024791811yescharacteristic
665C2#2024793911yescharacteristic
666C2#2024794011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#389C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#389D47
hypocenterC47#13933
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
19. C4⋊C4×Dic47C4semidirect
371. C47#13933semidirect

Maximal subgroups

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

subgroupindex
C2×#156890222
C2×C4⋊C4×Dic472
#202416472
#202416442
#202416182
#202416172
#202416142
C4×C47⋊#952
C2×C47×#3892
#1393347