Finite Group Databasebeta

← #26183607

Subgroups — #26183607

Order 12032.

1046 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689657C211yesmaximal, characteristic
2#20245786C211yesmaximal, characteristic, complemented
3#20241966C214yesmaximal, complemented
4#20241961C212yesmaximal, complemented
5#20241957C212yesmaximal
6#20241875C214yesmaximal, complemented
7C2×C47×#431C211yesmaximal, characteristic, complemented
8#15689657—21no—
9#15689657—21no—
10#15689657—21no—
11#15689657—21no—
12#15689657C412yescomplemented
13#15689657C412yescomplemented
14#15689657C2212yes—
15#15689657C2212yes—
16C2×#13094018—21no—
17C2×#13094016C411yescharacteristic, complemented
18C2×#13094012C411yescharacteristic, complemented
19C2×#13094007—21no—
20C2×#13094003C2211yescharacteristic
21C2×#13093998C2211yescharacteristic
22C2×C4×Dic94C411yescharacteristic, complemented
23C2×C4×D188C411yescharacteristic, complemented
24C2×C4×C22⋊D47—21no—
25C2×#13093981—21no—
26#15688991C2212yescomplemented
27#15688989—21no—
28#15688986—21no—
29#15688983C2212yes—
30C4×C4⋊Dic47—21no—
31C4×C22⋊Dic47—21no—
32#15688969C2212yescomplemented
33#15688861C2218yescomplemented
34#15688858C2218yes—
35C22×C42×C47C2211yescharacteristic
36C47×#431—21no—
37C47×#431—21no—
38C47×#431C2212yescomplemented
39C47×#431C2212yescomplemented
40C2×C4⋊C8×C47—21no—
41C2×C22⋊C8×C47C2212yes—
42C2×C4×C8×C47—21no—
43C22×Dic94C2×C411yescharacteristic
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47—21no—
46C22×C4×D47—21no—
47#13094018—22no—
48#13094018—22no—
49#13094018—22no—
50#13094018—22no—
51#13094016—21no—
52#13094016—21no—
53#13094016C2×C412yes—
54#13094016C2×C412yes—
55#13094012—21no—
56#13094012—21no—
57#13094012C2×C412yes—
58#13094012C2×C412yes—
59#13094007—22no—
60#13094007—22no—
61#13094007—22no—
62#13094007—22no—
63#13094003—21no—
64#13094003—21no—
65#13094003C2×C412yes—
66#13094003C2312yes—
67#13093998—21no—
68#13093998—21no—
69#13093998C2×C412yes—
70#13093998C2312yes—
71C4×Dic94—21no—
72C4×Dic94—21no—
73C4×Dic94C2×C412yes—
74C4×Dic94C2×C412yes—
75C4×D188—21no—
76C4×D188—21no—
77C4×D188C2×C412yes—
78C4×D188C2×C412yes—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83#13093981—22no—
84#13093981—22no—
85#13093981—22no—
86#13093981—22no—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47C2×C411yescharacteristic
89C2×C4⋊Dic47C2×C411yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—21no—
92C2×Dic47⋊C4—21no—
93C2×Dic47⋊C4—21no—
94C2×C22⋊Dic47—21no—
95C2×C22⋊Dic47—22no—
96C2×(C2×D47)⋊C4—21no—
97C2×(C2×D47)⋊C4—21no—
98C2×(C2×D47)⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95C2314yes—
106C23×C4×C47D411yescharacteristic
107C23×C4×C47D411yescharacteristic
108C23×C4×C47C2311yescharacteristic
109C22×C8×C47—22no—
110C2×C42×C47C2×C411yescharacteristic
111C2×C42×C47C2×C411yescharacteristic
112C2×C42×C47C2×C411yescharacteristic
113C2×C42×C47C2×C411yescharacteristic
114C2×C42×C47D411yescharacteristic
115C2×C42×C47D411yescharacteristic
116C2×C42×C47D411yescharacteristic
117C2×C42×C47D411yescharacteristic
118C2×C42×C47D411yescharacteristic
119C2×C42×C47D411yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C4⋊C8×C47—22no—
123C4⋊C8×C47—22no—
124C22⋊C8×C47—22no—
125C22⋊C8×C47C2314yes—
126C4×C8×C47—22no—
127C4×C8×C47—22no—
128C24×C47C2×D411yescharacteristic
129C23×D47—21no—
130C22×C4×C47—24no—
131C22×C4×C47—42no—
132C22×C4×C47—42no—
133C22×C4×C47C22⋊C411yescharacteristic
134C22×C4×C47C22⋊C411yescharacteristic
135C22×C4×C47C22⋊C411yescharacteristic
136C22×C4×C47C22⋊C411yescharacteristic
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×C47C2411yescharacteristic
151C2×C22⋊D47—22no—
152C2×C22⋊D47—22no—
153C2×C22⋊D47—44no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—24no—
158C2×D188—21no—
159C2×D188—42no—
160C2×D188C22×C412yes—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—44no—
164C2×Dic94—21no—
165C2×Dic94—42no—
166C2×Dic94C22×C412yes—
167C2×C8×C47—24no—
168C2×C8×C47—44no—
169C42×C47C22⋊C411yescharacteristic
170C42×C47C22⋊C411yescharacteristic
171C42×C47C22⋊C411yescharacteristic
172C42×C47C22⋊C411yescharacteristic
173C42×C47C22⋊C411yescharacteristic
174C42×C47C22⋊C411yescharacteristic
175C42×C47C22⋊C411yescharacteristic
176C42×C47C22⋊C411yescharacteristic
177C42×C47C22×C411yescharacteristic
178C42×C47C22×C411yescharacteristic
179C42×C47C22×C411yescharacteristic
180C42×C47C22×C411yescharacteristic
181C42×C47C2×D411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47C2×D411yescharacteristic
184C42×C47C2×D411yescharacteristic
185C22⋊Dic47—22no—
186C22⋊Dic47—22no—
187C22⋊Dic47—44no—
188(C2×D47)⋊C4—22no—
189(C2×D47)⋊C4—22no—
190(C2×D47)⋊C4—22no—
191(C2×D47)⋊C4—22no—
192(C2×D47)⋊C4—22no—
193(C2×D47)⋊C4—22no—
194(C2×D47)⋊C4—22no—
195(C2×D47)⋊C4—22no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—44no—
199C4⋊Dic47C22×C412yes—
200C4⋊Dic47C22×C412yes—
201Dic47⋊C4—22no—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209C4×Dic47—22no—
210C4×Dic47—22no—
211C4×Dic47—44no—
212C23×C47—41no—
213C23×C47—41no—
214C23×C47C2×C22⋊C411yescharacteristic
215C23×C47C2×C22⋊C411yescharacteristic
216C23×C47#13514yes—
217C23×C47C22×D411yescharacteristic
218C22×D47—22no—
219C22×D47—42no—
220C22×D47—42no—
221C22×D47—42no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47C2×C22⋊C411yescharacteristic
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47C2×C22⋊C411yescharacteristic
243C2×C4×C47C2×C22⋊C411yescharacteristic
244C2×C4×C47C2×C22⋊C411yescharacteristic
245C2×C4×C47C2×C22⋊C411yescharacteristic
246C2×C4×C47C2×C22⋊C411yescharacteristic
247C2×C4×C47C2×C22⋊C411yescharacteristic
248C2×C4×C47C2×C22⋊C411yescharacteristic
249C2×C4×C47C2×C22⋊C411yescharacteristic
250C2×C4×C47C23×C411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C22⋊D47—44no—
253C22⋊D47—44no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—44no—
261C2×Dic47—44no—
262C2×Dic47—44no—
263D188—42no—
264D188—42no—
265C4×D47—44no—
266C4×D47—44no—
267Dic94—42no—
268Dic94—42no—
269C8×C47—44no—
270#17567—471nomaximal, Sylow
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—21no—
277C22×C47—44no—
278C22×C47#41612yes—
279C22×C47#41612yes—
280C22×C47C22×C22⋊C411yescharacteristic
281C22×C47C2×#13512yes—
282C2×D47—42no—
283C2×D47—42no—
284C2×D47—42no—
285C2×D47—84no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—21no—
289C4×C47—21no—
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—21no—
293C4×C47—21no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47#41012yes—
297C4×C47#42112yes—
298Dic47—42no—
299Dic47—42no—
300Dic47—42no—
301Dic47—84no—
302C2×#529—471no—
303C2×#431D4711yescharacteristic, complemented
304#2283—471no—
305#1521—474no—
306#1520—472no—
307#1519—472no—
308#1500—474no—
309C2×C47—22no—
310C2×C47—22no—
311C2×C47—22no—
312C2×C47C2×#41011yescharacteristic
313C2×C47C2×#41611yescharacteristic
314C2×C47C2×#42111yescharacteristic
315D47—82no—
316#529—472no—
317#529—472no—
318#529—472no—
319#529—472no—
320#529—941no—
321#529—941no—
322#529—941no—
323#529—941no—
324C2×#126—941no—
325C2×#125—471no—
326C2×#124—471no—
327C2×#123—941no—
328C2×C22⋊Q8—471no—
329C2×#121—471no—
330C2×C4×Q8—471no—
331C2×C4×D4—471no—
332C2×C4×D4—941no—
333C2×#117—941no—
334C22×C42C2×D4711yescharacteristic
335#431—21no—
336#431—21no—
337#431C2×D4712yescomplemented
338#431C2×D4712yescomplemented
339C2×C4⋊C8—21no—
340C2×C22⋊C8C2×D4712yes—
341C2×C4×C8—21no—
342#383—472no—
343#382—941no—
344#381—941no—
345#380—472no—
346C4×C4⋊C4—941no—
347C4×C22⋊C4—941no—
348#376—472no—
349#328—478no—
350#327—478no—
351C47#1756711yescharacteristic, complemented, Sylow
352C22×Q8—471no—
353C22×D4—471no—
354C22×D4—941no—
355C23×C4—941no—
356C23×C4D18811yescharacteristic
357C23×C4D18811yescharacteristic
358C23×C4C22×D4711yescharacteristic
359C22×C8—22no—
360#126—942no—
361#126—942no—
362#126—942no—
363#126—942no—
364#125—472no—
365#125—472no—
366#125—941no—
367#125—941no—
368#124—472no—
369#124—472no—
370#124—941no—
371#124—941no—
372#123—942no—
373#123—942no—
374#123—942no—
375#123—942no—
376C22⋊Q8—472no—
377C22⋊Q8—472no—
378C22⋊Q8—941no—
379C22⋊Q8—941no—
380#121—472no—
381#121—472no—
382#121—941no—
383#121—941no—
384C4×Q8—472no—
385C4×Q8—472no—
386C4×Q8—941no—
387C4×Q8—941no—
388C4×D4—472no—
389C4×D4—472no—
390C4×D4—942no—
391C4×D4—942no—
392C4×D4—942no—
393C4×D4—942no—
394C4×D4—941no—
395C4×D4—941no—
396#117—942no—
397#117—942no—
398#117—942no—
399#117—942no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—941no—
406C2×C4⋊C4—942no—
407C2×C22⋊C4—941no—
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C22⋊C4—941no—
411C2×C22⋊C4—941no—
412C2×C22⋊C4—942no—
413C2×C42—941no—
414C2×C42—942no—
415C2×C42C4×D4711yescharacteristic
416C2×C42C4×D4711yescharacteristic
417C2×C42C4×D4711yescharacteristic
418C2×C42C4×D4711yescharacteristic
419C2×C42D18811yescharacteristic
420C2×C42D18811yescharacteristic
421C2×C42C22⋊D4711yescharacteristic
422C2×C42C22⋊D4711yescharacteristic
423C2×C42C22⋊D4711yescharacteristic
424C2×C42C22⋊D4711yescharacteristic
425C2×C42C22×D4711yescharacteristic
426C2×C42C22×D4711yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429C22⋊C8—22no—
430C22⋊C8C22×D4714yes—
431C4×C8—22no—
432C4×C8—22no—
433#95—474no—
434#95—942no—
435#95—942no—
436#95—942no—
437C24—941no—
438C24C2×D18811yescharacteristic
439C2×Q8—472no—
440C2×Q8—941no—
441C2×Q8—1882no—
442C2×D4—472no—
443C2×D4—942no—
444C2×D4—942no—
445C2×D4—941no—
446C2×D4—1882no—
447C2×D4—1884no—
448C22×C4—24no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—944no—
457C22×C4—1884no—
458C22×C4(C2×D47)⋊C411yescharacteristic
459C22×C4(C2×D47)⋊C411yescharacteristic
460C22×C4(C2×D47)⋊C411yescharacteristic
461C22×C4(C2×D47)⋊C411yescharacteristic
462C22×C4(C2×D47)⋊C411yescharacteristic
463C22×C4(C2×D47)⋊C411yescharacteristic
464C22×C4(C2×D47)⋊C411yescharacteristic
465C22×C4(C2×D47)⋊C411yescharacteristic
466C22×C4C2×C4×D4711yescharacteristic
467C22×C4C2×C4×D4711yescharacteristic
468C22×C4C2×D18811yescharacteristic
469C22×C4C2×D18811yescharacteristic
470C22×C4C2×D18811yescharacteristic
471C22×C4C2×D18811yescharacteristic
472C22×C4C2×D18811yescharacteristic
473C22×C4C2×C22⋊D4711yescharacteristic
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C23×D4711yescharacteristic
476C2×C8—24no—
477C2×C8—44no—
478C4⋊C4—472no—
479C4⋊C4—472no—
480C4⋊C4—942no—
481C4⋊C4—942no—
482C4⋊C4—942no—
483C4⋊C4—942no—
484C4⋊C4—942no—
485C4⋊C4—942no—
486C4⋊C4—942no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—942no—
490C4⋊C4—1884no—
491C22⋊C4—942no—
492C22⋊C4—942no—
493C22⋊C4—942no—
494C22⋊C4—942no—
495C22⋊C4—942no—
496C22⋊C4—942no—
497C22⋊C4—942no—
498C22⋊C4—942no—
499C22⋊C4—942no—
500C22⋊C4—942no—
501C22⋊C4—1884no—
502C42—942no—
503C42—942no—
504C42—1884no—
505C42(C2×D47)⋊C411yescharacteristic
506C42(C2×D47)⋊C411yescharacteristic
507C42(C2×D47)⋊C411yescharacteristic
508C42(C2×D47)⋊C411yescharacteristic
509C42(C2×D47)⋊C411yescharacteristic
510C42(C2×D47)⋊C411yescharacteristic
511C42(C2×D47)⋊C411yescharacteristic
512C42(C2×D47)⋊C411yescharacteristic
513C42C2×C4×D4711yescharacteristic
514C42C2×C4×D4711yescharacteristic
515C42C2×C4×D4711yescharacteristic
516C42C2×C4×D4711yescharacteristic
517C42C2×C22⋊D4711yescharacteristic
518C42C2×C22⋊D4711yescharacteristic
519C42C2×C22⋊D4711yescharacteristic
520C42C2×C22⋊D4711yescharacteristic
521C23—41no—
522C23—41no—
523C23—942no—
524C23—1882no—
525C23—1882no—
526C23—1882no—
527C23C2×(C2×D47)⋊C411yescharacteristic
528C23C2×(C2×D47)⋊C411yescharacteristic
529C23#1309404614yes—
530C23C22×D18811yescharacteristic
531Q8—1882no—
532Q8—1882no—
533D4—1882no—
534D4—1884no—
535D4—1884no—
536D4—1882no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—1884no—
559C2×C4—1884no—
560C2×C4—1884no—
561C2×C4—1884no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1884no—
566C2×C4C2×(C2×D47)⋊C411yescharacteristic
567C2×C4C2×(C2×D47)⋊C411yescharacteristic
568C2×C4C2×(C2×D47)⋊C411yescharacteristic
569C2×C4C2×(C2×D47)⋊C411yescharacteristic
570C2×C4C2×(C2×D47)⋊C411yescharacteristic
571C2×C4C2×(C2×D47)⋊C411yescharacteristic
572C2×C4C2×(C2×D47)⋊C411yescharacteristic
573C2×C4C2×(C2×D47)⋊C411yescharacteristic
574C2×C4C2×(C2×D47)⋊C411yescharacteristic
575C2×C4C2×(C2×D47)⋊C411yescharacteristic
576C2×C4C22×C4×D4711yescharacteristic
577C2×C4C22×C22⋊D4711yescharacteristic
578C8—44no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—44no—
586C22—3764no—
587C22—1882no—
588C22—1882no—
589C22—1882no—
590C22#1568912012yes—
591C22#1568912012yes—
592C22C22×(C2×D47)⋊C411yescharacteristic
593C22C2×#1309404612yes—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—3764no—
605C4—1882no—
606C4—1882no—
607C4—1882no—
608C4#1568909612yes—
609C4#1568913912yes—
610C2—22no—
611C2—22no—
612C2—22no—
613C2—3762no—
614C2C2×#1568909611yescharacteristic
615C2C2×#1568912011yescharacteristic
616C2C2×#1568913911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#431C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC2×#431D47
hypocenterC47#17567
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. #20245786C2semidirect
3. #20241966C2semidirect
4. #20241961C2semidirect
6. #20241875C2semidirect
7. C2×C47×#431C2semidirect
12. #15689657C4semidirect
13. #15689657C4semidirect
17. C2×#13094016C4semidirect
18. C2×#13094012C4semidirect
22. C2×C4×Dic94C4semidirect
23. C2×C4×D188C4semidirect
26. #15688991C22semidirect
32. #15688969C22semidirect
33. #15688861C22semidirect
38. C47×#431C22semidirect
39. C47×#431C22semidirect
303. C2×#431D47semidirect
337. #431C2×D47semidirect
338. #431C2×D47semidirect
351. C47#17567semidirect

Maximal subgroups

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

subgroupindex
C2×#156896572
#202457862
#202419662
#202419612
#202419572
#202418752
C2×C47×#4312
#1756747