Finite Group Databasebeta

← #26226087

Subgroups — #26226087

Order 12032.

1158 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689657C211yesmaximal, characteristic
2#20245795C211yesmaximal, characteristic, complemented
3#20244373C212yesmaximal, complemented
4#20244224C212yesmaximal
5#20243844C214yesmaximal, complemented
6#20243373C214yesmaximal, complemented
7C47×#2283C211yesmaximal, characteristic, complemented
8#15689657—21no—
9#15689657—21no—
10#15689657—21no—
11#15689657—21no—
12#15689657—21no—
13#15689657—21no—
14#15689657—21no—
15#15689657—21no—
16C2×#13094018C412yescomplemented
17C2×#13094016C411yescharacteristic, complemented
18C2×#13094012C411yescharacteristic, complemented
19C2×#13094007C2212yes—
20C2×#13094003C2211yescharacteristic
21C2×#13093998C2211yescharacteristic
22C2×C4×Dic94C411yescharacteristic, complemented
23C2×C4×D188C411yescharacteristic, complemented
24C2×C4×C22⋊D47C2212yes—
25C2×#13093983C2212yes—
26C2×#13093981C412yescomplemented
27C2×#13093938C2218yes—
28#15688993—21no—
29#15688989—21no—
30#15688983C2212yes—
31#15688983C2212yes—
32C4×C4⋊Dic47—21no—
33C4×C4⋊Dic47—21no—
34#15688889C2218yes—
35C22×C42×C47C2211yescharacteristic
36C47×#383—21no—
37C47×#382—21no—
38C47×#381C2212yes—
39C47×#380C2212yes—
40C4×C4⋊C4×C47—21no—
41C4×C22⋊C4×C47C2212yes—
42C47×#376—21no—
43C22×Dic94C2×C411yescharacteristic
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47C2312yes—
46C22×C4×D47C2×C412yes—
47#13094018—22no—
48#13094018—22no—
49#13094018—22no—
50#13094018—22no—
51#13094016—21no—
52#13094016—21no—
53#13094016—21no—
54#13094016—21no—
55#13094012—21no—
56#13094012—21no—
57#13094012—21no—
58#13094012—21no—
59#13094007—22no—
60#13094007—22no—
61#13094007—22no—
62#13094007—22no—
63#13094003—21no—
64#13094003—21no—
65#13094003—21no—
66#13094003—21no—
67#13093998—21no—
68#13093998—21no—
69#13093998—21no—
70#13093998—21no—
71C4×Dic94—21no—
72C4×Dic94—21no—
73C4×Dic94—21no—
74C4×Dic94—21no—
75C4×D188—21no—
76C4×D188—21no—
77C4×D188—21no—
78C4×D188—21no—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83#13093983—44no—
84#13093981—22no—
85#13093981—22no—
86#13093981—22no—
87#13093981—22no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—22no—
91C2×C4⋊Dic47C2×C411yescharacteristic
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×Dic47⋊C4C2×C412yes—
94C2×Dic47⋊C4C2×C412yes—
95C2×Dic47⋊C4C2×C412yes—
96C2×Dic47⋊C4C2×C412yes—
97C2×C22⋊Dic47C2314yes—
98C2×C22⋊Dic47C2312yes—
99C2×(C2×D47)⋊C4C2×C412yes—
100C2×(C2×D47)⋊C4C2×C412yes—
101C2×(C2×D47)⋊C4C2×C412yes—
102C2×(C2×D47)⋊C4C2×C412yes—
103C2×C4×Dic47—22no—
104C2×C4×Dic47C2×C412yes—
105#13093938—48no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C23×C4×C47C2311yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47—22no—
112C2×C22⋊C4×C47C2314yes—
113C2×C42×C47—22no—
114C2×C42×C47C2×C411yescharacteristic
115C2×C42×C47C2×C411yescharacteristic
116C2×C42×C47C2×C411yescharacteristic
117C2×C42×C47C2×C411yescharacteristic
118C2×C42×C47D411yescharacteristic
119C2×C42×C47D411yescharacteristic
120C2×C42×C47D411yescharacteristic
121C2×C42×C47D411yescharacteristic
122C2×C42×C47D411yescharacteristic
123C2×C42×C47D411yescharacteristic
124C2×C42×C47D411yescharacteristic
125C2×C42×C47D411yescharacteristic
126#95×C47—22no—
127#95×C47—22no—
128#95×C47—22no—
129#95×C47—22no—
130C24×C47C2411yescharacteristic
131C23×D47C22×C412yes—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—24no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C2×C22⋊D47—22no—
156C2×C22⋊D47—22no—
157C2×C22⋊D47—24no—
158C2×C22⋊D47—24no—
159C22×Dic47—24no—
160C22×Dic47C22×C412yes—
161C22×Dic47C22×C412yes—
162C22×Dic47C22×C412yes—
163C2×D188—21no—
164C2×D188—21no—
165C2×D188—42no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—44no—
169C2×Dic94—21no—
170C2×Dic94—21no—
171C2×Dic94—42no—
172C4⋊C4×C47—44no—
173C22⋊C4×C47—24no—
174C22⋊C4×C47—24no—
175C42×C47—44no—
176C42×C47C22⋊C411yescharacteristic
177C42×C47C22⋊C411yescharacteristic
178C42×C47C22⋊C411yescharacteristic
179C42×C47C22⋊C411yescharacteristic
180C42×C47C22⋊C411yescharacteristic
181C42×C47C22⋊C411yescharacteristic
182C42×C47C22⋊C411yescharacteristic
183C42×C47C22⋊C411yescharacteristic
184C42×C47C22⋊C411yescharacteristic
185C42×C47C22⋊C411yescharacteristic
186C42×C47C22⋊C411yescharacteristic
187C42×C47C22⋊C411yescharacteristic
188C42×C47C22⋊C411yescharacteristic
189C42×C47C22⋊C411yescharacteristic
190C42×C47C22⋊C411yescharacteristic
191C42×C47C22⋊C411yescharacteristic
192C22⋊Dic47—22no—
193C22⋊Dic47—22no—
194C22⋊Dic47—28no—
195(C2×D47)⋊C4—22no—
196(C2×D47)⋊C4—22no—
197(C2×D47)⋊C4—22no—
198(C2×D47)⋊C4—22no—
199(C2×D47)⋊C4—22no—
200(C2×D47)⋊C4—22no—
201(C2×D47)⋊C4—22no—
202(C2×D47)⋊C4—22no—
203C4⋊Dic47—21no—
204C4⋊Dic47—21no—
205C4⋊Dic47—21no—
206C4⋊Dic47—21no—
207C4⋊Dic47—44no—
208C4⋊Dic47—44no—
209C4⋊Dic47—44no—
210Dic47⋊C4—22no—
211Dic47⋊C4—22no—
212Dic47⋊C4—22no—
213Dic47⋊C4—22no—
214Dic47⋊C4—22no—
215Dic47⋊C4—22no—
216Dic47⋊C4—22no—
217Dic47⋊C4—22no—
218C4×Dic47—22no—
219C4×Dic47—22no—
220C4×Dic47—44no—
221C23×C47—41no—
222C23×C47—41no—
223C23×C47C23×C411yescharacteristic
224C23×C47C22×D411yescharacteristic
225C23×C47C22×D411yescharacteristic
226C23×C47H(5,𝔽2)12yes—
227C23×C472−1+412yes—
228C22×D47—22no—
229C22×D47—24no—
230C22×D47—42no—
231C22×D47—42no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—44no—
253C2×C4×C47—44no—
254C2×C4×C47—44no—
255C2×C4×C47C2×C22⋊C411yescharacteristic
256C2×C4×C47C2×C22⋊C411yescharacteristic
257C2×C4×C47C2×C22⋊C411yescharacteristic
258C2×C4×C47C2×C22⋊C411yescharacteristic
259C2×C4×C47C2×C22⋊C411yescharacteristic
260C2×C4×C47C2×C22⋊C411yescharacteristic
261C2×C4×C47C2×C22⋊C411yescharacteristic
262C2×C4×C47C2×C22⋊C411yescharacteristic
263C2×C4×C47C2×C22⋊C411yescharacteristic
264C2×C4×C47C2×C22⋊C411yescharacteristic
265C2×C4×C47C2×C22⋊C411yescharacteristic
266C2×C4×C47C2×C22⋊C411yescharacteristic
267C22⋊D47—42no—
268C22⋊D47—42no—
269C22⋊D47—44no—
270C2×Dic47—22no—
271C2×Dic47—22no—
272C2×Dic47—22no—
273C2×Dic47—24no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—44no—
277C2×Dic47—44no—
278C2×Dic47—44no—
279D188—42no—
280D188—42no—
281C4×D47—44no—
282C4×D47—44no—
283Dic94—42no—
284Dic94—42no—
285#21875—471nomaximal, Sylow
286C22×C47—21no—
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—21no—
291C22×C47—21no—
292C22×C47—42no—
293C22×C47—42no—
294C22×C47C22×C22⋊C411yescharacteristic
295C22×C47#52012yes—
296C22×C47#53511yescharacteristic
297C22×C47#53611yescharacteristic
298C22×C47#53712yes—
299C2×D47—42no—
300C2×D47—42no—
301C2×D47—42no—
302C2×D47—84no—
303C4×C47—21no—
304C4×C47—21no—
305C4×C47—21no—
306C4×C47—21no—
307C4×C47—21no—
308C4×C47—21no—
309C4×C47—21no—
310C4×C47—21no—
311C4×C47—21no—
312C4×C47—21no—
313C4×C47—84no—
314C4×C47#41012yes—
315C4×C47#41012yes—
316Dic47—42no—
317Dic47—42no—
318Dic47—42no—
319Dic47—84no—
320C2×#529—471no—
321#2285—471no—
322#2283D4711yescharacteristic, complemented
323#1996—472no—
324#1964—472no—
325#1899—474no—
326#1799—474no—
327C2×C47—21no—
328C2×C47—22no—
329C2×C47—22no—
330C2×C47—21no—
331C2×C47#231111yescharacteristic
332C2×C47C2×#41011yescharacteristic
333C2×C47C2×#41011yescharacteristic
334D47—82no—
335#529—941no—
336#529—941no—
337#529—941no—
338#529—941no—
339#529—941no—
340#529—941no—
341#529—941no—
342#529—941no—
343C2×#126—472no—
344C2×#125—471no—
345C2×#124—471no—
346C2×#123—472no—
347C2×C22⋊Q8—471no—
348C2×#121—471no—
349C2×C4×Q8—471no—
350C2×C4×D4—472no—
351C2×C4×D4—471no—
352C2×#117—472no—
353C2×#117—472no—
354C22×C42C2×D4711yescharacteristic
355C2×#99—478no—
356#384—941no—
357#383—21no—
358#382—21no—
359#382—941no—
360#381C2×D4712yes—
361#380—472no—
362#380—472no—
363#380C2×D4712yes—
364C4×C4⋊C4—21no—
365C4×C4⋊C4—941no—
366C4×C4⋊C4—941no—
367C4×C22⋊C4C2×D4712yes—
368#376—21no—
369#342—478no—
370C47#2187511yescharacteristic, complemented, Sylow
371C22×Q8—471no—
372C22×D4—472no—
373C22×D4—471no—
374C23×C4—472no—
375C23×C4C22×D4711yescharacteristic
376C23×C4C22×D4711yescharacteristic
377C23×C4C22×D4711yescharacteristic
378#126—942no—
379#126—942no—
380#126—942no—
381#126—942no—
382#125—941no—
383#125—941no—
384#125—941no—
385#125—941no—
386#124—941no—
387#124—941no—
388#124—941no—
389#124—941no—
390#123—942no—
391#123—942no—
392#123—942no—
393#123—942no—
394C22⋊Q8—941no—
395C22⋊Q8—941no—
396C22⋊Q8—941no—
397C22⋊Q8—941no—
398#121—941no—
399#121—941no—
400#121—941no—
401#121—941no—
402C4×Q8—941no—
403C4×Q8—941no—
404C4×Q8—941no—
405C4×Q8—941no—
406C4×D4—942no—
407C4×D4—942no—
408C4×D4—942no—
409C4×D4—942no—
410C4×D4—941no—
411C4×D4—941no—
412C4×D4—941no—
413C4×D4—941no—
414#117—942no—
415#117—942no—
416#117—942no—
417#117—942no—
418#117—1884no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—472no—
421C2×C4⋊C4—472no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—472no—
424C2×C4⋊C4—471no—
425C2×C4⋊C4—472no—
426C2×C4⋊C4—942no—
427C2×C4⋊C4—942no—
428C2×C4⋊C4—942no—
429C2×C22⋊C4—472no—
430C2×C22⋊C4—472no—
431C2×C22⋊C4—472no—
432C2×C22⋊C4—472no—
433C2×C22⋊C4—472no—
434C2×C22⋊C4—474no—
435C2×C22⋊C4C22×D4714yes—
436C2×C42—22no—
437C2×C42—472no—
438C2×C42—942no—
439C2×C42C4×D4711yescharacteristic
440C2×C42C4×D4711yescharacteristic
441C2×C42C4×D4711yescharacteristic
442C2×C42C4×D4711yescharacteristic
443C2×C42D18811yescharacteristic
444C2×C42D18811yescharacteristic
445C2×C42D18811yescharacteristic
446C2×C42D18811yescharacteristic
447C2×C42C22⋊D4711yescharacteristic
448C2×C42C22⋊D4711yescharacteristic
449C2×C42C22⋊D4711yescharacteristic
450C2×C42C22⋊D4711yescharacteristic
451#99—1888no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—942no—
457#95—942no—
458C24—472no—
459C24C23×D4711yescharacteristic
460C2×Q8—941no—
461C2×Q8—941no—
462C2×Q8—1882no—
463C2×D4—942no—
464C2×D4—942no—
465C2×D4—944no—
466C2×D4—944no—
467C2×D4—941no—
468C2×D4—941no—
469C2×D4—1882no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—472no—
476C22×C4—472no—
477C22×C4—472no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—944no—
481C22×C4—1884no—
482C22×C4C2×C4×D4711yescharacteristic
483C22×C4C2×C4×D4711yescharacteristic
484C22×C4C2×C4×D4711yescharacteristic
485C22×C4C2×C4×D4711yescharacteristic
486C22×C4C2×C4×D4711yescharacteristic
487C22×C4C2×C4×D4711yescharacteristic
488C22×C4C2×D18811yescharacteristic
489C22×C4C2×D18811yescharacteristic
490C22×C4C2×D18811yescharacteristic
491C22×C4C2×D18811yescharacteristic
492C22×C4C2×D18811yescharacteristic
493C22×C4C2×D18811yescharacteristic
494C22×C4C2×C22⋊D4711yescharacteristic
495C22×C4C2×C22⋊D4711yescharacteristic
496C22×C4C2×C22⋊D4711yescharacteristic
497C22×C4C2×C22⋊D4711yescharacteristic
498C22×C4C2×C22⋊D4711yescharacteristic
499C22×C4C2×C22⋊D4711yescharacteristic
500C4⋊C4—44no—
501C4⋊C4—942no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—1884no—
514C4⋊C4—1884no—
515C4⋊C4—1884no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C22⋊C4—942no—
522C22⋊C4—942no—
523C22⋊C4—942no—
524C22⋊C4—942no—
525C22⋊C4—942no—
526C22⋊C4—942no—
527C22⋊C4—942no—
528C22⋊C4—948no—
529C42—44no—
530C42—942no—
531C42—942no—
532C42—1884no—
533C42(C2×D47)⋊C411yescharacteristic
534C42(C2×D47)⋊C411yescharacteristic
535C42(C2×D47)⋊C411yescharacteristic
536C42(C2×D47)⋊C411yescharacteristic
537C42(C2×D47)⋊C411yescharacteristic
538C42(C2×D47)⋊C411yescharacteristic
539C42(C2×D47)⋊C411yescharacteristic
540C42(C2×D47)⋊C411yescharacteristic
541C42(C2×D47)⋊C411yescharacteristic
542C42(C2×D47)⋊C411yescharacteristic
543C42(C2×D47)⋊C411yescharacteristic
544C42(C2×D47)⋊C411yescharacteristic
545C42(C2×D47)⋊C411yescharacteristic
546C42(C2×D47)⋊C411yescharacteristic
547C42(C2×D47)⋊C411yescharacteristic
548C42(C2×D47)⋊C411yescharacteristic
549C23—41no—
550C23—41no—
551C23—944no—
552C23—942no—
553C23—1882no—
554C23—1882no—
555C23C22×C4×D4711yescharacteristic
556C23C22×C22⋊D4711yescharacteristic
557C23C22×D18811yescharacteristic
558C23#1309407012yes—
559C23#1309407112yes—
560Q8—1882no—
561Q8—1882no—
562D4—1882no—
563D4—1882no—
564D4—1882no—
565D4—1884no—
566D4—1882no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—942no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—944no—
594C2×C4—1884no—
595C2×C4—1884no—
596C2×C4—1884no—
597C2×C4—1884no—
598C2×C4—1884no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4C2×(C2×D47)⋊C411yescharacteristic
602C2×C4C2×(C2×D47)⋊C411yescharacteristic
603C2×C4C2×(C2×D47)⋊C411yescharacteristic
604C2×C4C2×(C2×D47)⋊C411yescharacteristic
605C2×C4C2×(C2×D47)⋊C411yescharacteristic
606C2×C4C2×(C2×D47)⋊C411yescharacteristic
607C2×C4C2×(C2×D47)⋊C411yescharacteristic
608C2×C4C2×(C2×D47)⋊C411yescharacteristic
609C2×C4C2×(C2×D47)⋊C411yescharacteristic
610C2×C4C2×(C2×D47)⋊C411yescharacteristic
611C2×C4C2×(C2×D47)⋊C411yescharacteristic
612C2×C4C2×(C2×D47)⋊C411yescharacteristic
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—42no—
620C22—42no—
621C22—3764no—
622C22—1882no—
623C22—1882no—
624C22—1882no—
625C22C22×(C2×D47)⋊C411yescharacteristic
626C22#1568960312yes—
627C22#1568969211yescharacteristic
628C22#1568969911yescharacteristic
629C22#1568970112yes—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—84no—
641C4—3764no—
642C4—1882no—
643C4—1882no—
644C4—1882no—
645C4#1568909612yes—
646C4#1568909612yes—
647C2—22no—
648C2—21no—
649C2—22no—
650C2—21no—
651C2—3762no—
652C2#2024597611yescharacteristic
653C2C2×#1568909611yescharacteristic
654C2C2×#1568909611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2283C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#13093998C22
cosocleC24×C47C24
hypercenter#2283D47
hypocenterC47#21875
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. #20245795C2semidirect
3. #20244373C2semidirect
5. #20243844C2semidirect
6. #20243373C2semidirect
7. C47×#2283C2semidirect
16. C2×#13094018C4semidirect
17. C2×#13094016C4semidirect
18. C2×#13094012C4semidirect
22. C2×C4×Dic94C4semidirect
23. C2×C4×D188C4semidirect
26. C2×#13093981C4semidirect
322. #2283D47semidirect
370. C47#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#156896572
#202457952
#202443732
#202442242
#202438442
#202433732
C47×#22832
#2187547