Finite Group Databasebeta

← #26183413

Subgroups — #26183413

Order 12032.

1116 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689657C211yesmaximal, characteristic
2C4×#13093983C211yesmaximal, characteristic, complemented
3#20241914C214yesmaximal, complemented
4#20241909C212yesmaximal, complemented
5#20241905C212yesmaximal
6#20241875C214yesmaximal, complemented
7C47×#2920C211yesmaximal, 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×#13093983—21no—
26C2×#13093981—21no—
27C4×C4⋊Dic47—21no—
28C4×C4⋊Dic47C2212yescomplemented
29C4×C22⋊Dic47—21no—
30C4×C22⋊Dic47C2212yes—
31#15688969C2212yescomplemented
32C42×Dic47—21no—
33#15688861C2218yescomplemented
34#15688858C2218yes—
35C22×C42×C47C2211yescharacteristic
36C47×#432—21no—
37C47×#432C2212yescomplemented
38C47×#431—21no—
39C47×#431C2212yescomplemented
40C47×#423—21no—
41C47×#407C2212yes—
42C4×M16×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#13093983—28no—
84#13093981—22no—
85#13093981—22no—
86#13093981—22no—
87#13093981—22no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47C2×C411yescharacteristic
90C2×C4⋊Dic47C2×C411yescharacteristic
91C2×Dic47⋊C4—21no—
92C2×Dic47⋊C4—21no—
93C2×Dic47⋊C4—21no—
94C2×Dic47⋊C4—21no—
95C2×C22⋊Dic47—22no—
96C2×C22⋊Dic47—21no—
97C2×(C2×D47)⋊C4—21no—
98C2×(C2×D47)⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C47⋊#95—22no—
106C47⋊#95C2314yes—
107C23×C4×C47D411yescharacteristic
108C23×C4×C47D411yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C2×M16×C47—22no—
111C2×C42×C47C2×C411yescharacteristic
112C2×C42×C47C2×C411yescharacteristic
113C2×C42×C47C2×C411yescharacteristic
114C2×C42×C47C2×C411yescharacteristic
115C2×C42×C47D411yescharacteristic
116C2×C42×C47D411yescharacteristic
117C2×C42×C47D411yescharacteristic
118C2×C42×C47D411yescharacteristic
119C2×C42×C47D411yescharacteristic
120C2×C42×C47D411yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C4⋊C8×C47—22no—
124C4⋊C8×C47—22no—
125C22⋊C8×C47—22no—
126C22⋊C8×C47C2314yes—
127#97×C47—22no—
128C4×C8×C47—22no—
129C24×C47C2×D411yescharacteristic
130C23×D47—21no—
131C22×C4×C47—24no—
132C22×C4×C47—42no—
133C22×C4×C47—42no—
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×C47C22×C411yescharacteristic
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×C47C2411yescharacteristic
152C2×C22⋊D47—22no—
153C2×C22⋊D47—22no—
154C2×C22⋊D47—44no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—24no—
159C2×D188—21no—
160C2×D188—42no—
161C2×D188C22×C412yes—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—44no—
165C2×Dic94—21no—
166C2×Dic94—42no—
167C2×Dic94C22×C412yes—
168M16×C47—44no—
169C2×C8×C47—24no—
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×C47C22×C411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47C2×D411yescharacteristic
184C42×C47C2×D411yescharacteristic
185C42×C47C2×D411yescharacteristic
186C22⋊Dic47—28no—
187C22⋊Dic47—22no—
188C22⋊Dic47—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—
196(C2×D47)⋊C4—22no—
197C4⋊Dic47—28no—
198C4⋊Dic47—21no—
199C4⋊Dic47—21no—
200C4⋊Dic47C22×C412yes—
201C4⋊Dic47C22×C412yes—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210C4×Dic47—28no—
211C4×Dic47—22no—
212C4×Dic47—22no—
213C4×Dic47—44no—
214C4×Dic47—44no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—41no—
218C23×C47C2×C22⋊C411yescharacteristic
219C23×C47C2×C22⋊C411yescharacteristic
220C23×C47C22×D411yescharacteristic
221C22×D47—22no—
222C22×D47—42no—
223C22×D47—42no—
224C22×D47—42no—
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—22no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47#10414yes—
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×C47C2×C22⋊C411yescharacteristic
251C2×C4×C47C2×C22⋊C411yescharacteristic
252C2×C4×C47C2×C22⋊C411yescharacteristic
253C2×C4×C47C23×C411yescharacteristic
254C2×C4×C47C22×D411yescharacteristic
255C22⋊D47—44no—
256C22⋊D47—44no—
257C2×Dic47—28no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—44no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—44no—
265C2×Dic47—42no—
266D188—42no—
267D188—42no—
268C4×D47—44no—
269C4×D47—44no—
270Dic94—42no—
271Dic94—42no—
272C8×C47—44no—
273#17537—471nomaximal, Sylow
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—21no—
277C22×C47—21no—
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—44no—
282C22×C47C2×#10412yes—
283C22×C47C22×C22⋊C411yescharacteristic
284C22×C47#57512yes—
285C2×D47—42no—
286C2×D47—42no—
287C2×D47—42no—
288C2×D47—84no—
289C4×C47—21no—
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—21no—
293C4×C47—21no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47#41012yes—
299C4×C47C2×#10412yes—
300C4×C47C2×#10412yes—
301Dic47—48no—
302Dic47—42no—
303Dic47—42no—
304Dic47—42no—
305C2×#529—471no—
306#2920D4711yescharacteristic, complemented
307C4×#117—471no—
308#1509—474no—
309#1508—472no—
310#1507—472no—
311#1500—474no—
312C2×C47—22no—
313C2×C47—22no—
314C2×C47—41no—
315C2×C47C2×#41011yescharacteristic
316C2×C47#289611yescharacteristic
317C2×C47C22×#10411yescharacteristic
318D47—82no—
319#529—472no—
320#529—472no—
321#529—472no—
322#529—472no—
323#529—941no—
324#529—941no—
325#529—941no—
326#529—941no—
327C2×#126—941no—
328C2×#125—471no—
329C2×#124—471no—
330C2×#123—941no—
331C2×C22⋊Q8—471no—
332C2×#121—471no—
333C2×C4×Q8—471no—
334C2×C4×D4—471no—
335C2×C4×D4—941no—
336C2×#117—941no—
337C2×#117—941no—
338C22×C42C2×D4711yescharacteristic
339#432—21no—
340#432C2×D4712yescomplemented
341#431—21no—
342#431C2×D4712yescomplemented
343#423—21no—
344#407C2×D4712yes—
345C4×M16—21no—
346C4×C4⋊C4—472no—
347C4×C4⋊C4—941no—
348C4×C22⋊C4—472no—
349C4×C22⋊C4—941no—
350#376—472no—
351C43—941no—
352#328—478no—
353#327—478no—
354C47#1753711yescharacteristic, complemented, Sylow
355C22×Q8—471no—
356C22×D4—471no—
357C22×D4—941no—
358C23×C4—941no—
359C23×C4D18811yescharacteristic
360C23×C4D18811yescharacteristic
361C23×C4C22×D4711yescharacteristic
362C2×M16—22no—
363#126—942no—
364#126—942no—
365#126—942no—
366#126—942no—
367#125—472no—
368#125—472no—
369#125—941no—
370#125—941no—
371#124—472no—
372#124—472no—
373#124—941no—
374#124—941no—
375#123—942no—
376#123—942no—
377#123—942no—
378#123—942no—
379C22⋊Q8—472no—
380C22⋊Q8—472no—
381C22⋊Q8—941no—
382C22⋊Q8—941no—
383#121—472no—
384#121—472no—
385#121—941no—
386#121—941no—
387C4×Q8—472no—
388C4×Q8—472no—
389C4×Q8—941no—
390C4×Q8—941no—
391C4×D4—472no—
392C4×D4—472no—
393C4×D4—942no—
394C4×D4—942no—
395C4×D4—942no—
396C4×D4—942no—
397C4×D4—941no—
398C4×D4—941no—
399#117—948no—
400#117—942no—
401#117—942no—
402#117—942no—
403#117—942no—
404C2×C4⋊C4—471no—
405C2×C4⋊C4—471no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4—941no—
409C2×C4⋊C4—942no—
410C2×C4⋊C4—941no—
411C2×C22⋊C4—942no—
412C2×C22⋊C4—941no—
413C2×C22⋊C4—941no—
414C2×C22⋊C4—941no—
415C2×C22⋊C4—941no—
416C2×C22⋊C4—941no—
417C2×C42—941no—
418C2×C42—942no—
419C2×C42—942no—
420C2×C42—942no—
421C2×C42C4×D4711yescharacteristic
422C2×C42C4×D4711yescharacteristic
423C2×C42C4×D4711yescharacteristic
424C2×C42C4×D4711yescharacteristic
425C2×C42D18811yescharacteristic
426C2×C42D18811yescharacteristic
427C2×C42C22⋊D4711yescharacteristic
428C2×C42C22⋊D4711yescharacteristic
429C2×C42C22⋊D4711yescharacteristic
430C2×C42C22⋊D4711yescharacteristic
431C2×C42C22×D4711yescharacteristic
432C2×C42C22×D4711yescharacteristic
433C4⋊C8—22no—
434C4⋊C8—22no—
435C22⋊C8—22no—
436C22⋊C8C22×D4714yes—
437#97—22no—
438C4×C8—22no—
439#95—474no—
440#95—942no—
441C24—941no—
442C24C2×D18811yescharacteristic
443C2×Q8—472no—
444C2×Q8—941no—
445C2×Q8—1882no—
446C2×D4—472no—
447C2×D4—942no—
448C2×D4—942no—
449C2×D4—941no—
450C2×D4—1882no—
451C2×D4—1884no—
452C22×C4—24no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—944no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—1884no—
462C22×C4(C2×D47)⋊C411yescharacteristic
463C22×C4(C2×D47)⋊C411yescharacteristic
464C22×C4(C2×D47)⋊C411yescharacteristic
465C22×C4(C2×D47)⋊C411yescharacteristic
466C22×C4(C2×D47)⋊C411yescharacteristic
467C22×C4(C2×D47)⋊C411yescharacteristic
468C22×C4(C2×D47)⋊C411yescharacteristic
469C22×C4(C2×D47)⋊C411yescharacteristic
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4C2×C4×D4711yescharacteristic
472C22×C4C2×D18811yescharacteristic
473C22×C4C2×D18811yescharacteristic
474C22×C4C2×D18811yescharacteristic
475C22×C4C2×D18811yescharacteristic
476C22×C4C2×D18811yescharacteristic
477C22×C4C2×C22⋊D4711yescharacteristic
478C22×C4C2×C22⋊D4711yescharacteristic
479C22×C4C23×D4711yescharacteristic
480M16—44no—
481C2×C8—24no—
482C4⋊C4—472no—
483C4⋊C4—472no—
484C4⋊C4—948no—
485C4⋊C4—942no—
486C4⋊C4—942no—
487C4⋊C4—942no—
488C4⋊C4—942no—
489C4⋊C4—942no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—942no—
495C22⋊C4—948no—
496C22⋊C4—942no—
497C22⋊C4—942no—
498C22⋊C4—942no—
499C22⋊C4—942no—
500C22⋊C4—942no—
501C22⋊C4—942no—
502C22⋊C4—942no—
503C22⋊C4—942no—
504C22⋊C4—942no—
505C22⋊C4—942no—
506C42—948no—
507C42—942no—
508C42—942no—
509C42—1884no—
510C42—1884no—
511C42(C2×D47)⋊C411yescharacteristic
512C42(C2×D47)⋊C411yescharacteristic
513C42(C2×D47)⋊C411yescharacteristic
514C42(C2×D47)⋊C411yescharacteristic
515C42(C2×D47)⋊C411yescharacteristic
516C42(C2×D47)⋊C411yescharacteristic
517C42(C2×D47)⋊C411yescharacteristic
518C42(C2×D47)⋊C411yescharacteristic
519C42C2×C4×D4711yescharacteristic
520C42C2×C4×D4711yescharacteristic
521C42C2×C4×D4711yescharacteristic
522C42C2×C4×D4711yescharacteristic
523C42C2×C22⋊D4711yescharacteristic
524C42C2×C22⋊D4711yescharacteristic
525C42C2×C22⋊D4711yescharacteristic
526C42C2×C22⋊D4711yescharacteristic
527C23—22no—
528C23—22no—
529C23—41no—
530C23—942no—
531C23—1882no—
532C23—1882no—
533C23—1882no—
534C23C2×(C2×D47)⋊C411yescharacteristic
535C23C2×(C2×D47)⋊C411yescharacteristic
536C23C22×D18811yescharacteristic
537Q8—1882no—
538Q8—1882no—
539D4—1882no—
540D4—1884no—
541D4—1884no—
542D4—1882no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—948no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—1884no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1884no—
569C2×C4—1884no—
570C2×C4—1884no—
571C2×C4#1309395014yes—
572C2×C4C2×(C2×D47)⋊C411yescharacteristic
573C2×C4C2×(C2×D47)⋊C411yescharacteristic
574C2×C4C2×(C2×D47)⋊C411yescharacteristic
575C2×C4C2×(C2×D47)⋊C411yescharacteristic
576C2×C4C2×(C2×D47)⋊C411yescharacteristic
577C2×C4C2×(C2×D47)⋊C411yescharacteristic
578C2×C4C2×(C2×D47)⋊C411yescharacteristic
579C2×C4C2×(C2×D47)⋊C411yescharacteristic
580C2×C4C2×(C2×D47)⋊C411yescharacteristic
581C2×C4C2×(C2×D47)⋊C411yescharacteristic
582C2×C4C22×C4×D4711yescharacteristic
583C2×C4C22×C22⋊D4711yescharacteristic
584C8—44no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—44no—
593C22—3764no—
594C22—1882no—
595C22—1882no—
596C22—1882no—
597C22C2×#1309395012yes—
598C22C22×(C2×D47)⋊C411yescharacteristic
599C22#1568992312yes—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—1888no—
610C4—1882no—
611C4—1882no—
612C4—1882no—
613C4#1568909612yes—
614C4C2×#1309395012yes—
615C4C2×#1309395012yes—
616C2—22no—
617C2—22no—
618C2—41no—
619C2—3762no—
620C2C2×#1568909611yescharacteristic
621C2#2025190811yescharacteristic
622C2C22×#1309395011yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2920C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenter#2920D47
hypocenterC47#17537
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C4×#13093983C2semidirect
3. #20241914C2semidirect
4. #20241909C2semidirect
6. #20241875C2semidirect
7. C47×#2920C2semidirect
12. #15689657C4semidirect
13. #15689657C4semidirect
17. C2×#13094016C4semidirect
18. C2×#13094012C4semidirect
22. C2×C4×Dic94C4semidirect
23. C2×C4×D188C4semidirect
28. C4×C4⋊Dic47C22semidirect
31. #15688969C22semidirect
33. #15688861C22semidirect
37. C47×#432C22semidirect
39. C47×#431C22semidirect
306. #2920D47semidirect
340. #432C2×D47semidirect
342. #431C2×D47semidirect
354. C47#17537semidirect

Maximal subgroups

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

subgroupindex
C2×#156896572
C4×#130939832
#202419142
#202419092
#202419052
#202418752
C47×#29202
#1753747