Finite Group Databasebeta

← #26142881

Subgroups — #26142881

Order 12032.

1502 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic
2C2×#15688992C211yesmaximal, characteristic
3C2×#15688968C211yesmaximal, characteristic
4#20241642C211yesmaximal, characteristic
5#20241641C211yesmaximal, characteristic
6#20241640C212yesmaximal
7#20241639C212yesmaximal
8#20241638C211yesmaximal, characteristic
9Dic47⋊#95C212yesmaximal
10Dic47⋊#95C212yesmaximal
11C47×#1441C211yesmaximal, characteristic
12C2×#13094014—24no—
13C2×#13094014—24no—
14C2×#13094014C418yescomplemented
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2212yes—
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25#15688992—24no—
26#15688968—24no—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2312yes—
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46#13094014—232no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—42no—
51C2×C4⋊Dic47C2×C414yes—
52C2×Dic47⋊C4—22no—
53C2×Dic47⋊C4—22no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—22no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—42no—
65C2×Dic47⋊C4—42no—
66C2×Dic47⋊C4C2×C414yes—
67C2×Dic47⋊C4C2×C414yes—
68C2×Dic47⋊C4C2×C414yes—
69C2×Dic47⋊C4C2×C414yes—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47C2×C414yes—
73C2×C4×Dic47D414yes—
74C2×C4×Dic47D414yes—
75C2×C4×Dic47Q818yes—
76C47⋊#95—22no—
77C47⋊#95—24no—
78C47⋊#95—42no—
79C47⋊#95—42no—
80C47⋊#95—42no—
81C47⋊#95—42no—
82C47⋊#95—42no—
83C47⋊#95—42no—
84C23×C4×C47C2312yes—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2312yes—
88C23×C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47—42no—
93C2×C4⋊C4×C47C2×C414yes—
94#95×C47—22no—
95#95×C47—42no—
96#95×C47—42no—
97C24×C47C2411yescharacteristic
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
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×C47C22×C412yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×Q814yes—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C412yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C22×C412yes—
160C22×Dic47C2×D412yes—
161C22×Dic47C2×D412yes—
162C22×Dic47C2×D412yes—
163C22×Dic47C2×D412yes—
164C22×Dic47C2×Q814yes—
165C22×Dic47C2×Q814yes—
166C22×Dic47#4114yes—
167C4⋊C4×C47—28no—
168C4⋊C4×C47—44no—
169C4⋊Dic47—28no—
170C4⋊Dic47—44no—
171Dic47⋊C4—28no—
172Dic47⋊C4—28no—
173Dic47⋊C4—28no—
174Dic47⋊C4—28no—
175Dic47⋊C4—48no—
176Dic47⋊C4—48no—
177C4×Dic47—216no—
178C4×Dic47C22⋊C4116yes—
179C23×C47C23×C411yescharacteristic
180C23×C47C22×D411yescharacteristic
181C23×C47C22×D411yescharacteristic
182C23×C47C22×Q812yes—
183C23×C47C2×#4112yes—
184C23×C47H(5,𝔽2)12yes—
185C23×C47H(5,𝔽2)11yescharacteristic
186C23×C47H(5,𝔽2)11yescharacteristic
187C23×C472−1+411yescharacteristic
188C23×C472−1+412yes—
189C23×C472−1+411yescharacteristic
190C2×C4×C47—24no—
191C2×C4×C47—22no—
192C2×C4×C47—22no—
193C2×C4×C47—24no—
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—24no—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—41no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47—41no—
209C2×C4×C47—42no—
210C2×C4×C47—41no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47C2×C22⋊C414yes—
221C2×Dic47—22no—
222C2×Dic47—22no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—22no—
226C2×Dic47—22no—
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—24no—
230C2×Dic47—22no—
231C2×Dic47—22no—
232C2×Dic47—24no—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—41no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47C2×C22⋊C414yes—
254C2×Dic47C2×C22⋊C414yes—
255C2×Dic47C4×Q818yes—
256C2×Dic47C22⋊Q818yes—
257C2×Dic47#12414yes—
258C2×Dic47C4⋊Q814yes—
259#14283—471nomaximal, Sylow
260C22×C47C22×C22⋊C411yescharacteristic
261C22×C47C2×C4×Q812yes—
262C22×C47#52012yes—
263C22×C47#52011yescharacteristic
264C22×C47#52011yescharacteristic
265C22×C47C2×C22⋊Q812yes—
266C22×C47C2×#12411yescharacteristic
267C22×C47C2×C4⋊Q811yescharacteristic
268C22×C47#53511yescharacteristic
269C22×C47#53511yescharacteristic
270C22×C47#53611yescharacteristic
271C22×C47#53611yescharacteristic
272C22×C47#53712yes—
273C22×C47#53711yescharacteristic
274C22×C47#53711yescharacteristic
275C22×C47#54012yes—
276C22×C47#54012yes—
277C22×C47#54112yes—
278C22×C47#54112yes—
279C22×C47#54412yes—
280C22×C47#54412yes—
281C22×C47#54412yes—
282C22×C47#54412yes—
283C4×C47—24no—
284C4×C47—42no—
285C4×C47—42no—
286C4×C47—44no—
287C4×C47—82no—
288Dic47—24no—
289Dic47—42no—
290Dic47—42no—
291Dic47—44no—
292Dic47—82no—
293Dic47#39118yes—
294C22×#125—471no—
295C2×#384—471no—
296C2×#376—471no—
297#1441—472no—
298#1441—472no—
299#1441—471no—
300#1441—471no—
301#1441—471no—
302#1441D4711yescharacteristic
303C4⋊#95—472no—
304C4⋊#95—472no—
305C2×C47C2×#39111yescharacteristic
306C2×C47#231111yescharacteristic
307C2×C47#231111yescharacteristic
308C2×C47#233012yes—
309C2×C47#233012yes—
310C2×C47#262912yes—
311C2×C47#262912yes—
312C2×C47#264111yescharacteristic
313C2×C47#264211yescharacteristic
314C2×C47#266011yescharacteristic
315C2×C47#266011yescharacteristic
316C2×#125—478no—
317C2×#125—944no—
318C2×#125—944no—
319C22×C4⋊C4—471no—
320C22×C4⋊C4—471no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—471no—
324C22×C4⋊C4—472no—
325C22×C4⋊C4—472no—
326C22×C4⋊C4—471no—
327C22×C4⋊C4C2×D4711yescharacteristic
328C22×C4⋊C4C2×D4711yescharacteristic
329C22×C42—471no—
330C22×C42—472no—
331#384—944no—
332#376—944no—
333C2×#95—472no—
334C2×#95—471no—
335C2×#95—472no—
336C2×#95—472no—
337C2×#95—472no—
338C2×#95—472no—
339C2×#95—472no—
340C2×#95—472no—
341C2×#95C2×D4711yescharacteristic
342C2×#95C2×D4712yes—
343C2×#95C2×D4712yes—
344C47#1428311yescharacteristic, complemented, Sylow
345C23×C4—471no—
346C23×C4—471no—
347C23×C4—471no—
348C23×C4—471no—
349C23×C4—472no—
350C23×C4—472no—
351C23×C4C22×D4712yes—
352C23×C4C22×D4711yescharacteristic
353C23×C4C22×D4711yescharacteristic
354C23×C4C22×D4712yes—
355C23×C4C22×D4711yescharacteristic
356#125—9432no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—474no—
362C2×C4⋊C4—474no—
363C2×C4⋊C4—474no—
364C2×C4⋊C4—474no—
365C2×C4⋊C4—474no—
366C2×C4⋊C4—942no—
367C2×C4⋊C4—942no—
368C2×C4⋊C4—942no—
369C2×C4⋊C4—942no—
370C2×C4⋊C4—942no—
371C2×C4⋊C4—942no—
372C2×C4⋊C4—942no—
373C2×C4⋊C4—942no—
374C2×C4⋊C4—942no—
375C2×C4⋊C4—942no—
376C2×C4⋊C4—944no—
377C2×C4⋊C4—944no—
378C2×C4⋊C4—944no—
379C2×C4⋊C4—944no—
380C2×C4⋊C4—942no—
381C2×C4⋊C4—1882no—
382C2×C4⋊C4—1882no—
383C2×C4⋊C4—1882no—
384C2×C4⋊C4C4×D4714yes—
385C2×C42—474no—
386C2×C42—474no—
387C2×C42—474no—
388C2×C42—478no—
389C2×C42—944no—
390C2×C42—944no—
391#95—22no—
392#95—42no—
393#95—42no—
394#95—944no—
395#95—942no—
396#95—1882no—
397#95—1882no—
398#95—1882no—
399#95—1882no—
400#95—1882no—
401#95—1882no—
402C24C23×D4711yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—472no—
429C22×C4—472no—
430C22×C4—472no—
431C22×C4—474no—
432C22×C4—474no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—474no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—942no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—941no—
452C22×C4—942no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—941no—
457C22×C4—942no—
458C22×C4—941no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4C2×C4×D4712yes—
467C22×C4C2×C4×D4712yes—
468C22×C4C2×C4×D4712yes—
469C22×C4D4×D4712yes—
470C22×C4D4×D4712yes—
471C22×C4Q8×D4714yes—
472C4⋊C4—28no—
473C4⋊C4—44no—
474C4⋊C4—948no—
475C4⋊C4—948no—
476C4⋊C4—948no—
477C4⋊C4—948no—
478C4⋊C4—948no—
479C4⋊C4—1884no—
480C4⋊C4—1888no—
481C4⋊C4—1888no—
482C42—4716no—
483C42—9416no—
484C23C22×C4×D4711yescharacteristic
485C23C2×D4×D4711yescharacteristic
486C23C2×D4×D4711yescharacteristic
487C23C2×Q8×D4712yes—
488C23#41×D4712yes—
489C23#1309406912yes—
490C23#1309406911yescharacteristic
491C23#1309407011yescharacteristic
492C23#1309407111yescharacteristic
493C23#1309407112yes—
494C23#1309407211yescharacteristic
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—474no—
526C2×C4—478no—
527C2×C4—478no—
528C2×C4—474no—
529C2×C4—474no—
530C2×C4—474no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—942no—
534C2×C4—942no—
535C2×C4—942no—
536C2×C4—942no—
537C2×C4—944no—
538C2×C4—944no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—944no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—944no—
545C2×C4—1882no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1881no—
560C2×C4—1882no—
561C2×C4—1881no—
562C2×C4—1882no—
563C2×C4C22⋊C4×D4714yes—
564C22C2×C22⋊C4×D4711yescharacteristic
565C22C4×Q8×D4712yes—
566C22#1568960212yes—
567C22#1568960311yescharacteristic
568C22#1568960411yescharacteristic
569C22C22⋊Q8×D4712yes—
570C22#124×D4711yescharacteristic
571C22C4⋊Q8×D4711yescharacteristic
572C22#1568968811yescharacteristic
573C22#1568968911yescharacteristic
574C22#1568969511yescharacteristic
575C22#1568969611yescharacteristic
576C22#1568970012yes—
577C22#1568970211yescharacteristic
578C22#1568970311yescharacteristic
579C22#1568972312yes—
580C22#1568972512yes—
581C22#1568973012yes—
582C22#1568973212yes—
583C22#1568975012yes—
584C22#1568975212yes—
585C22#1568975212yes—
586C22#1568975312yes—
587C4—24no—
588C4—44no—
589C4—42no—
590C4—42no—
591C4—82no—
592C4—478no—
593C4—944no—
594C4—3762no—
595C4—1884no—
596C4—1882no—
597C4—1882no—
598C2#391×D4711yescharacteristic
599C2#2024597511yescharacteristic
600C2#2024597711yescharacteristic
601C2#2024612412yes—
602C2#2024612612yes—
603C2#2024921712yes—
604C2#2024922012yes—
605C2#2024933011yescharacteristic
606C2#2024933511yescharacteristic
607C2#2024950611yescharacteristic
608C2#2024951111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1441C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1441D47
hypocenterC47#14283
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
14. C2×#13094014C4semidirect
344. C47#14283semidirect

Maximal subgroups

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

subgroupindex
C22×#130940142
C2×#156889922
C2×#156889682
#202416422
#202416412
#202416402
#202416392
#202416382
Dic47⋊#952
C47×#14412
#1428347