Finite Group Databasebeta

← #27087053

Subgroups — #27087053

Order 12032.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic, complemented
2C2×#15689634C211yesmaximal, characteristic, complemented
3#20254230C214yesmaximal, complemented
4#20254220C212yesmaximal, complemented
5#20254204C212yesmaximal, complemented
6#20254181C214yesmaximal, complemented
7#20254171C212yesmaximal, complemented
8#20254155C212yesmaximal, complemented
9#20253337C211yesmaximal, characteristic, complemented
10#20253329C211yesmaximal, characteristic, complemented
11#20253321C212yesmaximal, complemented
12#20253018C212yesmaximal, complemented
13#20253007C212yesmaximal, complemented
14#20252650C211yesmaximal, characteristic, complemented
15#20252642C211yesmaximal, characteristic, complemented
16#20252633C212yesmaximal, complemented
17C2×C47×#407C211yesmaximal, characteristic, complemented
18C22×#10625350C2211yescharacteristic
19C22×#10625350C2211yescharacteristic, complemented
20C2×#13094057C2212yescomplemented
21C2×#13094052C2212yescomplemented
22#15689634—21no—
23#15689634—21no—
24#15689634—21no—
25#15689634—21no—
26#15689634—21no—
27#15689634—21no—
28#15689634—21no—
29#15689634—21no—
30#15689634C2212yes—
31#15689634C2212yes—
32#15689634C2212yes—
33#15689634C2212yes—
34#15689634C2212yescomplemented
35#15689634C2212yescomplemented
36#15689634C2212yescomplemented
37#15689634C2212yescomplemented
38C2×#13094007—21no—
39C2×#13094007—21no—
40C2×#13094003C2211yescharacteristic
41C2×#13094003C2211yescharacteristic, complemented
42C2×#13094003C2211yescharacteristic, complemented
43C2×#13094003C2211yescharacteristic, complemented
44C2×#13093998C2211yescharacteristic
45C2×#13093998C2211yescharacteristic, complemented
46C2×#13093998C2211yescharacteristic, complemented
47C2×#13093998C2211yescharacteristic, complemented
48C2×#13093993—21no—
49C2×#13093993—21no—
50C2×C4×C22⋊D47—21no—
51C2×C4×C22⋊D47—21no—
52C2×C4×C22⋊D47—21no—
53C2×C4×C22⋊D47—21no—
54C2×#13093983C2211yescharacteristic
55C2×#13093983C2211yescharacteristic, complemented
56#15689465C2214yescomplemented
57#15689465C2214yescomplemented
58#15689465C2214yescomplemented
59#15689459C2212yescomplemented
60#15689454C2212yescomplemented
61#15689448C2214yescomplemented
62#15689448C2214yescomplemented
63#15689448C2214yescomplemented
64#15689442C2212yescomplemented
65#15689437C2212yescomplemented
66#15689381C2214yescomplemented
67#15689376C2214yescomplemented
68#15689369C2214yescomplemented
69#15689369C2214yescomplemented
70#15689364C2214yescomplemented
71#15689359C2214yescomplemented
72#15689352C2214yescomplemented
73#15689352C2214yescomplemented
74#15689287C2214yescomplemented
75#15689287C2214yescomplemented
76#15689287C2214yescomplemented
77#15689281C2212yescomplemented
78#15689276C2212yescomplemented
79#15689270C2214yescomplemented
80#15689270C2214yescomplemented
81#15689270C2214yescomplemented
82#15689264C2212yescomplemented
83#15689259C2212yescomplemented
84#15689165C2212yescomplemented
85#15689165C2212yescomplemented
86#15689133C2212yescomplemented
87#15689129C2212yescomplemented
88#15689125C2212yescomplemented
89#15689125C2212yescomplemented
90C24×C4×C47C2211yescharacteristic
91C22×M16×C47C2212yescomplemented
92C47×#407C2211yescharacteristic
93C47×#407C2211yescharacteristic
94C47×#407C2212yescomplemented
95C47×#407C2212yescomplemented
96C47×#407C2212yescomplemented
97C2×C22⋊C8×C47C2212yescomplemented
98C2×C22⋊C8×C47C2212yescomplemented
99C2×#10625350—21no—
100C2×#10625350—21no—
101C2×#10625350—21no—
102C2×#10625350—21no—
103C2×#10625350—44no—
104C2×#10625350—44no—
105C2×#10625350C2312yes—
106C2×#10625350C2312yes—
107C2×#10625350C2312yes—
108C2×#10625350C2312yes—
109C22×Dic94C2311yescharacteristic
110C22×Dic94C2311yescharacteristic
111C22×D188C2311yescharacteristic
112C22×D188C2311yescharacteristic
113C22×C22⋊D47—21no—
114C22×C22⋊D47—21no—
115C22×C22⋊D47—21no—
116C22×C22⋊D47—21no—
117C22×C22⋊D47—21no—
118C22×C22⋊D47—21no—
119C22×C4×D47—21no—
120C22×C4×D47—21no—
121#13094057—44no—
122#13094052—44no—
123C2×Dic188C2314yescomplemented
124C2×#10625325C2314yescomplemented
125C2×#10625325C2314yescomplemented
126C2×D376C2314yescomplemented
127#13094007—22no—
128#13094007—22no—
129#13094007—22no—
130#13094007—22no—
131#13094007—22no—
132#13094007—22no—
133#13094007—22no—
134#13094007—22no—
135#13094003—21no—
136#13094003—21no—
137#13094003—21no—
138#13094003—21no—
139#13094003—21no—
140#13094003—21no—
141#13094003—21no—
142#13094003—21no—
143#13094003C2312yes—
144#13094003C2312yes—
145#13094003C2312yes—
146#13094003C2312yes—
147#13094003C2312yes—
148#13094003C2312yes—
149#13094003C2312yes—
150#13094003C2312yes—
151#13093998—21no—
152#13093998—21no—
153#13093998—21no—
154#13093998—21no—
155#13093998—21no—
156#13093998—21no—
157#13093998—21no—
158#13093998—21no—
159#13093998C2312yes—
160#13093998C2312yes—
161#13093998C2312yes—
162#13093998C2312yes—
163#13093998C2312yes—
164#13093998C2312yes—
165#13093998C2312yes—
166#13093998C2312yes—
167#13093993—22no—
168#13093993—22no—
169#13093993—22no—
170#13093993—22no—
171#13093993—22no—
172#13093993—22no—
173#13093993—22no—
174#13093993—22no—
175C4×C22⋊D47—22no—
176C4×C22⋊D47—22no—
177C4×C22⋊D47—22no—
178C4×C22⋊D47—22no—
179C4×C22⋊D47—22no—
180C4×C22⋊D47—22no—
181C4×C22⋊D47—22no—
182C4×C22⋊D47—22no—
183C4×C22⋊D47—22no—
184C4×C22⋊D47—22no—
185C4×C22⋊D47—22no—
186C4×C22⋊D47—22no—
187C4×C22⋊D47—22no—
188C4×C22⋊D47—22no—
189C4×C22⋊D47—22no—
190C4×C22⋊D47—22no—
191#13093983—21no—
192#13093983—21no—
193#13093983—21no—
194#13093983—21no—
195#13093983C2312yes—
196#13093983C2312yes—
197#13093983C2312yes—
198#13093983C2312yes—
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×Dic47⋊C4—21no—
204C2×Dic47⋊C4—21no—
205C2×Dic47⋊C4—21no—
206C2×Dic47⋊C4—21no—
207C2×C22⋊Dic47—21no—
208C2×C22⋊Dic47—21no—
209C2×C22⋊Dic47—21no—
210C2×C22⋊Dic47—21no—
211C2×C22⋊Dic47—21no—
212C2×C22⋊Dic47—21no—
213C2×(C2×D47)⋊C4—21no—
214C2×(C2×D47)⋊C4—21no—
215C2×(C2×D47)⋊C4—21no—
216C2×(C2×D47)⋊C4—21no—
217C2×C4×Dic47—21no—
218C2×C4×Dic47—21no—
219#13093958C2314yescomplemented
220#13093958C2314yescomplemented
221#13093956C2314yescomplemented
222#13093956C2314yescomplemented
223#13093949C2314yescomplemented
224#13093949C2314yescomplemented
225#13093949C2314yescomplemented
226#13093949C2314yescomplemented
227#13093946C2314yescomplemented
228#13093946C2314yescomplemented
229#13093946C2314yescomplemented
230#13093946C2314yescomplemented
231C25×C47D411yescharacteristic
232C23×C4×C47—44no—
233C23×C4×C47D411yescharacteristic
234C23×C4×C47D411yescharacteristic
235C23×C4×C47D411yescharacteristic
236C23×C4×C47D411yescharacteristic
237C23×C4×C47D411yescharacteristic
238C23×C4×C47D411yescharacteristic
239C23×C4×C47D411yescharacteristic
240C23×C4×C47C2311yescharacteristic
241C23×C4×C47C2311yescharacteristic
242C23×C4×C47C2311yescharacteristic
243C23×C4×C47C2311yescharacteristic
244C23×C4×C47C2311yescharacteristic
245C23×C4×C47C2311yescharacteristic
246C23×C4×C47C2311yescharacteristic
247C2×M16×C47—44no—
248C2×M16×C47C2312yes—
249C2×M16×C47C2312yes—
250C2×M16×C47C2314yes—
251C22×C8×C47C2314yes—
252C22⋊C8×C47C2312yes—
253C22⋊C8×C47C2312yes—
254C22⋊C8×C47C2314yes—
255C22⋊C8×C47C2314yes—
256C22⋊C8×C47C2312yes—
257C22⋊C8×C47C2312yes—
258C24×C47—42no—
259C24×C47—42no—
260C24×C47—42no—
261C24×C47C2×D411yescharacteristic
262C24×C47C2×D411yescharacteristic
263C24×C47C2×D411yescharacteristic
264C24×C47C2×D411yescharacteristic
265C24×C47C2×D411yescharacteristic
266C24×C47C2×D411yescharacteristic
267C24×C47C2×D411yescharacteristic
268C23×D47—21no—
269C23×D47—21no—
270C22×C4×C47—24no—
271C22×C4×C47—24no—
272C22×C4×C47—24no—
273C22×C4×C47—42no—
274C22×C4×C47—42no—
275C22×C4×C47—42no—
276C22×C4×C47—42no—
277C22×C4×C47—42no—
278C22×C4×C47—42no—
279C22×C4×C47—42no—
280C22×C4×C47—42no—
281C22×C4×C47—42no—
282C22×C4×C47—42no—
283C22×C4×C47—42no—
284C22×C4×C47C2×D411yescharacteristic
285C22×C4×C47C2×D411yescharacteristic
286C22×C4×C47C2×D411yescharacteristic
287C22×C4×C47C2×D411yescharacteristic
288C22×C4×C47C2×D411yescharacteristic
289C22×C4×C47C2×D411yescharacteristic
290C22×C4×C47C2×D411yescharacteristic
291C22×C4×C47C2×D411yescharacteristic
292C22×C4×C47C2×D411yescharacteristic
293C22×C4×C47C2×D411yescharacteristic
294C22×C4×C47C2×D411yescharacteristic
295C22×C4×C47C2×D411yescharacteristic
296C22×C4×C47C2×D411yescharacteristic
297C22×C4×C47C2×D411yescharacteristic
298C22×C4×C47C2×D411yescharacteristic
299C22×C4×C47C2×D411yescharacteristic
300C22×C4×C47C2×D411yescharacteristic
301C22×C4×C47C2×D411yescharacteristic
302C22×C4×C47C2×D411yescharacteristic
303C22×C4×C47C2×D411yescharacteristic
304C22×C4×C47C2×D411yescharacteristic
305C22×C4×C47C2411yescharacteristic
306C22×C4×C47C2411yescharacteristic
307C22×C4×C47C2411yescharacteristic
308C22×C4×C47C2411yescharacteristic
309C22×C4×C47C2411yescharacteristic
310C22×C4×C47C2411yescharacteristic
311C22×C4×C47C2411yescharacteristic
312C2×C22⋊D47—22no—
313C2×C22⋊D47—22no—
314C2×C22⋊D47—22no—
315C2×C22⋊D47—22no—
316C2×C22⋊D47—22no—
317C2×C22⋊D47—22no—
318C2×C22⋊D47—22no—
319C2×C22⋊D47—22no—
320C2×C22⋊D47—22no—
321C2×C22⋊D47—22no—
322C2×C22⋊D47—22no—
323C2×C22⋊D47—22no—
324C2×C22⋊D47—44no—
325C2×C22⋊D47—44no—
326C2×C22⋊D47—44no—
327C2×C22⋊D47—44no—
328C2×C22⋊D47—44no—
329C2×C22⋊D47—44no—
330C22×Dic47—21no—
331C22×Dic47—21no—
332C22×Dic47—21no—
333C22×Dic47—21no—
334C22×Dic47—21no—
335C22×Dic47—21no—
336#10625350—24no—
337#10625350—24no—
338#10625350—42no—
339#10625350—44no—
340#10625350—44no—
341#10625350—42no—
342#10625350—44no—
343#10625350—44no—
344#10625350—44no—
345#10625350—44no—
346C2×D188—24no—
347C2×D188—21no—
348C2×D188—21no—
349C2×D188—42no—
350C2×D188C2412yes—
351C2×D188C2412yes—
352C2×C4×D47—22no—
353C2×C4×D47—22no—
354C2×C4×D47—22no—
355C2×C4×D47—22no—
356C2×C4×D47—44no—
357C2×C4×D47—44no—
358C2×Dic94—24no—
359C2×Dic94—21no—
360C2×Dic94—21no—
361C2×Dic94—42no—
362C2×Dic94C2412yes—
363C2×Dic94C2412yes—
364M16×C47—24no—
365M16×C47—24no—
366M16×C47—44no—
367C2×C8×C47—44no—
368C2×C8×C47C2414yes—
369C2×C8×C47C2414yes—
370C22⋊Dic47—22no—
371C22⋊Dic47—22no—
372C22⋊Dic47—22no—
373C22⋊Dic47—22no—
374C22⋊Dic47—22no—
375C22⋊Dic47—22no—
376C22⋊Dic47—22no—
377C22⋊Dic47—22no—
378C22⋊Dic47—22no—
379C22⋊Dic47—22no—
380C22⋊Dic47—22no—
381C22⋊Dic47—22no—
382(C2×D47)⋊C4—22no—
383(C2×D47)⋊C4—22no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—22no—
386(C2×D47)⋊C4—22no—
387(C2×D47)⋊C4—22no—
388(C2×D47)⋊C4—22no—
389(C2×D47)⋊C4—22no—
390C4⋊Dic47—21no—
391C4⋊Dic47—21no—
392C4⋊Dic47—21no—
393C4⋊Dic47—21no—
394C4⋊Dic47C2412yes—
395C4⋊Dic47C2412yes—
396C4⋊Dic47C2412yes—
397C4⋊Dic47C2412yes—
398Dic47⋊C4—22no—
399Dic47⋊C4—22no—
400Dic47⋊C4—22no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—22no—
405Dic47⋊C4—22no—
406C4×Dic47—22no—
407C4×Dic47—22no—
408C4×Dic47—22no—
409C4×Dic47—22no—
410Dic188—44no—
411D376—44no—
412#10625325—44no—
413#10625325—44no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—22no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—22no—
423C23×C47—41no—
424C23×C47—41no—
425C23×C47—41no—
426C23×C47—41no—
427C23×C47—41no—
428C23×C47—41no—
429C23×C47—41no—
430C23×C47—41no—
431C23×C47—41no—
432C23×C47—41no—
433C23×C47—41no—
434C23×C47—41no—
435C23×C47—416no—
436C23×C47C22×D411yescharacteristic
437C23×C47C22×D411yescharacteristic
438C23×C47C22×D411yescharacteristic
439C23×C47C22×D411yescharacteristic
440C23×C47C22×D411yescharacteristic
441C23×C47C22×D411yescharacteristic
442C23×C47C22×D411yescharacteristic
443C22×D47—22no—
444C22×D47—22no—
445C22×D47—42no—
446C22×D47—42no—
447C22×D47—42no—
448C22×D47—42no—
449C22×D47—42no—
450C22×D47—42no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—41no—
467C2×C4×C47—41no—
468C2×C4×C47—41no—
469C2×C4×C47—41no—
470C2×C4×C47—41no—
471C2×C4×C47—41no—
472C2×C4×C47—41no—
473C2×C4×C47—41no—
474C2×C4×C47—41no—
475C2×C4×C47—41no—
476C2×C4×C47—41no—
477C2×C4×C47—41no—
478C2×C4×C47C22×D411yescharacteristic
479C2×C4×C47C22×D411yescharacteristic
480C2×C4×C47C22×D411yescharacteristic
481C2×C4×C47C22×D411yescharacteristic
482C2×C4×C47C22×D411yescharacteristic
483C2×C4×C47C22×D411yescharacteristic
484C2×C4×C47C22×D411yescharacteristic
485C2×C4×C47H(5,𝔽2)14yes—
486C2×C4×C47C2511yescharacteristic
487C22⋊D47—44no—
488C22⋊D47—44no—
489C22⋊D47—44no—
490C22⋊D47—44no—
491C22⋊D47—44no—
492C22⋊D47—44no—
493C22⋊D47—44no—
494C22⋊D47—44no—
495C22⋊D47—44no—
496C22⋊D47—44no—
497C22⋊D47—44no—
498C22⋊D47—44no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—42no—
506C2×Dic47—42no—
507C2×Dic47—42no—
508C2×Dic47—42no—
509C2×Dic47—42no—
510C2×Dic47—42no—
511D188—22no—
512D188—24no—
513D188—22no—
514D188—42no—
515D188—42no—
516C4×D47—44no—
517C4×D47—44no—
518C4×D47—44no—
519C4×D47—44no—
520Dic94—22no—
521Dic94—24no—
522Dic94—22no—
523Dic94—42no—
524Dic94—42no—
525C8×C47—24no—
526C8×C47—24no—
527#60752—471nomaximal, Sylow
528C22×C47—21no—
529C22×C47—21no—
530C22×C47—21no—
531C22×C47—21no—
532C22×C47—21no—
533C22×C47—21no—
534C22×C47—21no—
535C22×C47—21no—
536C22×C47—21no—
537C22×C47—21no—
538C22×C47—21no—
539C22×C47—21no—
540C22×C47—21no—
541C22×C47—21no—
542C22×C47—21no—
543C22×C47—21no—
544C22×C47—21no—
545C22×C47—21no—
546C22×C47—44no—
547C22×C47—44no—
548C22×C47—44no—
549C22×C47—44no—
550C22×C47—44no—
551C22×C47—44no—
552C22×C47—44no—
553C22×C47#53412yes—
554C22×C47#57512yes—
555C22×C47#57512yes—
556C22×C47C23×D411yescharacteristic
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—42no—
560C2×D47—42no—
561C2×D47—42no—
562C2×D47—42no—
563C2×D47—84no—
564C2×D47—84no—
565C4×C47—21no—
566C4×C47—21no—
567C4×C47—21no—
568C4×C47—21no—
569C4×C47—21no—
570C4×C47—21no—
571C4×C47#53412yes—
572C4×C47C2×H(5,𝔽2)12yes—
573Dic47—42no—
574Dic47—42no—
575Dic47—42no—
576Dic47—42no—
577Dic47—42no—
578Dic47—42no—
579C2×#525—471no—
580C2×#525—471no—
581#3197—474no—
582#3196—472no—
583#3194—472no—
584#3191—474no—
585#3190—472no—
586#3188—472no—
587#3095—471no—
588#3094—471no—
589#3093—472no—
590#3056—472no—
591#3055—472no—
592#3007—471no—
593#3006—471no—
594#3005—472no—
595C2×#407D4711yescharacteristic, complemented
596C2×C47—22no—
597C2×C47—22no—
598C2×C47—22no—
599C2×C47—41no—
600C2×C47—41no—
601C2×C47—41no—
602C2×C47—41no—
603C2×C47C2×#53411yescharacteristic
604C2×C47C2×#57511yescharacteristic
605C2×C47C2×#57511yescharacteristic
606D47—82no—
607D47—82no—
608C22×#41—471no—
609C22×#41—471no—
610C24×C4C2×D4711yescharacteristic
611C2×#137—472no—
612C2×AGL(1,ℤ/8)—472no—
613C22×M16C2×D4712yescomplemented
614#525—472no—
615#525—472no—
616#525—472no—
617#525—472no—
618#525—472no—
619#525—472no—
620#525—472no—
621#525—472no—
622#525—941no—
623#525—941no—
624#525—941no—
625#525—941no—
626#525—941no—
627#525—941no—
628#525—941no—
629#525—941no—
630C2×#123—941no—
631C2×#123—941no—
632C2×C22⋊Q8—471no—
633C2×C22⋊Q8—471no—
634C2×C22⋊Q8—471no—
635C2×C22⋊Q8—471no—
636C2×#121—471no—
637C2×#121—471no—
638C2×#121—471no—
639C2×#121—471no—
640C2×#120—941no—
641C2×#120—941no—
642C2×C4×D4—941no—
643C2×C4×D4—941no—
644C2×C4×D4—941no—
645C2×C4×D4—941no—
646C2×#117—471no—
647C2×#117—471no—
648#485—474no—
649#485—474no—
650#485—474no—
651#484—472no—
652#483—472no—
653#482—474no—
654#482—474no—
655#482—474no—
656#481—472no—
657#480—472no—
658#470—474no—
659#469—474no—
660#468—474no—
661#468—474no—
662#467—474no—
663#466—474no—
664#465—474no—
665#465—474no—
666#452—474no—
667#452—474no—
668#452—474no—
669#451—472no—
670#450—472no—
671#449—474no—
672#449—474no—
673#449—474no—
674#448—472no—
675#447—472no—
676#428—472no—
677#428—472no—
678#419—472no—
679#418—472no—
680#417—472no—
681#417—472no—
682#407C2×D4711yescharacteristic
683#407C2×D4711yescharacteristic
684#407C2×D4712yescomplemented
685#407C2×D4712yescomplemented
686#407C2×D4712yescomplemented
687C2×C22⋊C8C2×D4712yescomplemented
688C2×C22⋊C8C2×D4712yescomplemented
689C47#6075211yescharacteristic, complemented, Sylow
690C25D18811yescharacteristic
691C2×#41—472no—
692C2×#41—472no—
693C2×#41—472no—
694C2×#41—472no—
695C2×#41—941no—
696C2×#41—941no—
697C2×#41—941no—
698C2×#41—941no—
699C2×#41—1884no—
700C2×#41—1884no—
701C22×Q8—471no—
702C22×Q8—471no—
703C22×D4—471no—
704C22×D4—471no—
705C22×D4—941no—
706C22×D4—941no—
707C22×D4—941no—
708C22×D4—941no—
709C22×D4—941no—
710C22×D4—941no—
711C23×C4—44no—
712C23×C4—941no—
713C23×C4—941no—
714C23×C4D18811yescharacteristic
715C23×C4D18811yescharacteristic
716C23×C4D18811yescharacteristic
717C23×C4D18811yescharacteristic
718C23×C4D18811yescharacteristic
719C23×C4D18811yescharacteristic
720C23×C4D18811yescharacteristic
721C23×C4C22×D4711yescharacteristic
722C23×C4C22×D4711yescharacteristic
723C23×C4C22×D4711yescharacteristic
724C23×C4C22×D4711yescharacteristic
725C23×C4C22×D4711yescharacteristic
726C23×C4C22×D4711yescharacteristic
727C23×C4C22×D4711yescharacteristic
728#137—1884no—
729AGL(1,ℤ/8)—1884no—
730C2×Q16—474no—
731C2×SD16—474no—
732C2×SD16—474no—
733C2×D8—474no—
734C2×M16—44no—
735C2×M16C22×D4712yes—
736C2×M16C22×D4712yes—
737C2×M16C22×D4714yes—
738C22×C8C22×D4714yes—
739#123—942no—
740#123—942no—
741#123—942no—
742#123—942no—
743#123—942no—
744#123—942no—
745#123—942no—
746#123—942no—
747C22⋊Q8—472no—
748C22⋊Q8—472no—
749C22⋊Q8—472no—
750C22⋊Q8—472no—
751C22⋊Q8—472no—
752C22⋊Q8—472no—
753C22⋊Q8—472no—
754C22⋊Q8—472no—
755C22⋊Q8—941no—
756C22⋊Q8—941no—
757C22⋊Q8—941no—
758C22⋊Q8—941no—
759C22⋊Q8—941no—
760C22⋊Q8—941no—
761C22⋊Q8—941no—
762C22⋊Q8—941no—
763#121—472no—
764#121—472no—
765#121—472no—
766#121—472no—
767#121—472no—
768#121—472no—
769#121—472no—
770#121—472no—
771#121—941no—
772#121—941no—
773#121—941no—
774#121—941no—
775#121—941no—
776#121—941no—
777#121—941no—
778#121—941no—
779#120—942no—
780#120—942no—
781#120—942no—
782#120—942no—
783#120—942no—
784#120—942no—
785#120—942no—
786#120—942no—
787C4×D4—942no—
788C4×D4—942no—
789C4×D4—942no—
790C4×D4—942no—
791C4×D4—942no—
792C4×D4—942no—
793C4×D4—942no—
794C4×D4—942no—
795C4×D4—942no—
796C4×D4—942no—
797C4×D4—942no—
798C4×D4—942no—
799C4×D4—942no—
800C4×D4—942no—
801C4×D4—942no—
802C4×D4—942no—
803#117—472no—
804#117—472no—
805#117—472no—
806#117—472no—
807#117—941no—
808#117—941no—
809#117—941no—
810#117—941no—
811C2×C4⋊C4—471no—
812C2×C4⋊C4—471no—
813C2×C4⋊C4—471no—
814C2×C4⋊C4—471no—
815C2×C4⋊C4—941no—
816C2×C4⋊C4—941no—
817C2×C4⋊C4—941no—
818C2×C4⋊C4—941no—
819C2×C22⋊C4—941no—
820C2×C22⋊C4—941no—
821C2×C22⋊C4—941no—
822C2×C22⋊C4—941no—
823C2×C22⋊C4—941no—
824C2×C22⋊C4—941no—
825C2×C22⋊C4—941no—
826C2×C22⋊C4—941no—
827C2×C22⋊C4—941no—
828C2×C22⋊C4—941no—
829C2×C42—941no—
830C2×C42—941no—
831#107—474no—
832#107—474no—
833#106—474no—
834#106—474no—
835#103—474no—
836#103—474no—
837#103—474no—
838#103—474no—
839#102—474no—
840#102—474no—
841#102—474no—
842#102—474no—
843C22⋊C8C22×D4712yes—
844C22⋊C8C22×D4712yes—
845C22⋊C8C22×D4712yes—
846C22⋊C8C22×D4712yes—
847C22⋊C8C22×D4714yes—
848C22⋊C8C22×D4714yes—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—941no—
853C24—941no—
854C24C2×D18811yescharacteristic
855C24C2×D18811yescharacteristic
856C24C2×D18811yescharacteristic
857C24C2×D18811yescharacteristic
858C24C2×D18811yescharacteristic
859C24C2×D18811yescharacteristic
860C24C2×D18811yescharacteristic
861#41—944no—
862#41—944no—
863#41—1882no—
864#41—1884no—
865#41—1884no—
866#41—1882no—
867#41—1884no—
868#41—1884no—
869#41—1884no—
870#41—1884no—
871C2×Q8—472no—
872C2×Q8—472no—
873C2×Q8—941no—
874C2×Q8—941no—
875C2×Q8—944no—
876C2×Q8—1882no—
877C2×D4—472no—
878C2×D4—472no—
879C2×D4—942no—
880C2×D4—942no—
881C2×D4—942no—
882C2×D4—942no—
883C2×D4—942no—
884C2×D4—942no—
885C2×D4—942no—
886C2×D4—942no—
887C2×D4—942no—
888C2×D4—942no—
889C2×D4—942no—
890C2×D4—942no—
891C2×D4—941no—
892C2×D4—941no—
893C2×D4—944no—
894C2×D4—1882no—
895C2×D4—1884no—
896C2×D4—1884no—
897C2×D4—1884no—
898C2×D4—1884no—
899C2×D4—1884no—
900C2×D4—1884no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—941no—
916C22×C4—941no—
917C22×C4—941no—
918C22×C4—941no—
919C22×C4—941no—
920C22×C4—941no—
921C22×C4—942no—
922C22×C4—942no—
923C22×C4—942no—
924C22×C4—942no—
925C22×C4—1884no—
926C22×C4—1884no—
927C22×C4C2×D18811yescharacteristic
928C22×C4C2×D18811yescharacteristic
929C22×C4C2×D18811yescharacteristic
930C22×C4C2×D18811yescharacteristic
931C22×C4C2×D18811yescharacteristic
932C22×C4C2×D18811yescharacteristic
933C22×C4C2×D18811yescharacteristic
934C22×C4C2×D18811yescharacteristic
935C22×C4C2×D18811yescharacteristic
936C22×C4C2×D18811yescharacteristic
937C22×C4C2×D18811yescharacteristic
938C22×C4C2×D18811yescharacteristic
939C22×C4C2×D18811yescharacteristic
940C22×C4C2×D18811yescharacteristic
941C22×C4C2×D18811yescharacteristic
942C22×C4C2×D18811yescharacteristic
943C22×C4C2×D18811yescharacteristic
944C22×C4C2×D18811yescharacteristic
945C22×C4C2×D18811yescharacteristic
946C22×C4C2×D18811yescharacteristic
947C22×C4C2×D18811yescharacteristic
948C22×C4C23×D4711yescharacteristic
949C22×C4C23×D4711yescharacteristic
950C22×C4C23×D4711yescharacteristic
951C22×C4C23×D4711yescharacteristic
952C22×C4C23×D4711yescharacteristic
953C22×C4C23×D4711yescharacteristic
954C22×C4C23×D4711yescharacteristic
955Q16—1884no—
956SD16—1884no—
957SD16—1884no—
958D8—1884no—
959M16—24no—
960M16—24no—
961M16—44no—
962C2×C8—44no—
963C2×C8C23×D4714yes—
964C2×C8C23×D4714yes—
965C4⋊C4—472no—
966C4⋊C4—472no—
967C4⋊C4—472no—
968C4⋊C4—472no—
969C4⋊C4—942no—
970C4⋊C4—942no—
971C4⋊C4—942no—
972C4⋊C4—942no—
973C4⋊C4—942no—
974C4⋊C4—942no—
975C4⋊C4—942no—
976C4⋊C4—942no—
977C4⋊C4—941no—
978C4⋊C4—941no—
979C4⋊C4—941no—
980C4⋊C4—941no—
981C22⋊C4—942no—
982C22⋊C4—942no—
983C22⋊C4—942no—
984C22⋊C4—942no—
985C22⋊C4—942no—
986C22⋊C4—942no—
987C22⋊C4—942no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—942no—
991C22⋊C4—942no—
992C22⋊C4—942no—
993C22⋊C4—942no—
994C22⋊C4—942no—
995C22⋊C4—942no—
996C22⋊C4—942no—
997C22⋊C4—942no—
998C22⋊C4—942no—
999C22⋊C4—942no—
1000C22⋊C4—942no—
1001C42—942no—
1002C42—942no—
1003C42—942no—
1004C42—942no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—416no—
1027C23—942no—
1028C23—942no—
1029C23—1882no—
1030C23—1882no—
1031C23—1882no—
1032C23—1882no—
1033C23—1882no—
1034C23—1882no—
1035C23C22×D18811yescharacteristic
1036C23C22×D18811yescharacteristic
1037C23C22×D18811yescharacteristic
1038C23C22×D18811yescharacteristic
1039C23C22×D18811yescharacteristic
1040C23C22×D18811yescharacteristic
1041C23C22×D18811yescharacteristic
1042Q8—942no—
1043Q8—944no—
1044Q8—942no—
1045Q8—1882no—
1046Q8—1882no—
1047D4—942no—
1048D4—944no—
1049D4—942no—
1050D4—1882no—
1051D4—1884no—
1052D4—1884no—
1053D4—1884no—
1054D4—1884no—
1055D4—1884no—
1056D4—1884no—
1057D4—1884no—
1058D4—1884no—
1059D4—1884no—
1060D4—1884no—
1061D4—1884no—
1062D4—1884no—
1063D4—1882no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—1884no—
1098C2×C4—1884no—
1099C2×C4—1884no—
1100C2×C4—1882no—
1101C2×C4—1882no—
1102C2×C4—1882no—
1103C2×C4—1882no—
1104C2×C4—1882no—
1105C2×C4—1882no—
1106C2×C4—1884no—
1107C2×C4C22×D18811yescharacteristic
1108C2×C4C22×D18811yescharacteristic
1109C2×C4C22×D18811yescharacteristic
1110C2×C4C22×D18811yescharacteristic
1111C2×C4C22×D18811yescharacteristic
1112C2×C4C22×D18811yescharacteristic
1113C2×C4C22×D18811yescharacteristic
1114C2×C4#1309406914yes—
1115C2×C4C24×D4711yescharacteristic
1116C8—24no—
1117C8—24no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—3764no—
1144C22—3764no—
1145C22—1882no—
1146C22—1882no—
1147C22—1882no—
1148C22—1882no—
1149C22—1882no—
1150C22—1882no—
1151C22#1568968512yes—
1152C22#1568992312yes—
1153C22#1568992312yes—
1154C22C23×D18811yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—1882no—
1162C4—1882no—
1163C4—1882no—
1164C4—1882no—
1165C4—1882no—
1166C4—1882no—
1167C4#1568968512yes—
1168C4C2×#1309406912yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—3762no—
1177C2—3762no—
1178C2C2×#1568968511yescharacteristic
1179C2C2×#1568992311yescharacteristic
1180C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#407C2
socleC22×C47C23×D4
hypercenterC2×#407D47
hypocenterC47#60752
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#15689634C2semidirect
2. C2×#15689634C2semidirect
3. #20254230C2semidirect
4. #20254220C2semidirect
5. #20254204C2semidirect
6. #20254181C2semidirect
7. #20254171C2semidirect
8. #20254155C2semidirect
9. #20253337C2semidirect
10. #20253329C2semidirect
11. #20253321C2semidirect
12. #20253018C2semidirect
13. #20253007C2semidirect
14. #20252650C2semidirect
15. #20252642C2semidirect
16. #20252633C2semidirect
17. C2×C47×#407C2semidirect
19. C22×#10625350C22semidirect
20. C2×#13094057C22semidirect
21. C2×#13094052C22semidirect
34. #15689634C22semidirect
35. #15689634C22semidirect
36. #15689634C22semidirect
37. #15689634C22semidirect
41. C2×#13094003C22semidirect
42. C2×#13094003C22semidirect
43. C2×#13094003C22semidirect
45. C2×#13093998C22semidirect
46. C2×#13093998C22semidirect
47. C2×#13093998C22semidirect
55. C2×#13093983C22semidirect
56. #15689465C22semidirect
57. #15689465C22semidirect
58. #15689465C22semidirect
59. #15689459C22semidirect
60. #15689454C22semidirect
61. #15689448C22semidirect
62. #15689448C22semidirect
63. #15689448C22semidirect
64. #15689442C22semidirect
65. #15689437C22semidirect
66. #15689381C22semidirect
67. #15689376C22semidirect
68. #15689369C22semidirect
69. #15689369C22semidirect
70. #15689364C22semidirect
71. #15689359C22semidirect
72. #15689352C22semidirect
73. #15689352C22semidirect
74. #15689287C22semidirect
75. #15689287C22semidirect
76. #15689287C22semidirect
77. #15689281C22semidirect
78. #15689276C22semidirect
79. #15689270C22semidirect
80. #15689270C22semidirect
81. #15689270C22semidirect
82. #15689264C22semidirect
83. #15689259C22semidirect
84. #15689165C22semidirect
85. #15689165C22semidirect
86. #15689133C22semidirect
87. #15689129C22semidirect
88. #15689125C22semidirect
89. #15689125C22semidirect
91. C22×M16×C47C22semidirect
94. C47×#407C22semidirect
95. C47×#407C22semidirect
96. C47×#407C22semidirect
97. C2×C22⋊C8×C47C22semidirect
98. C2×C22⋊C8×C47C22semidirect
123. C2×Dic188C23semidirect
124. C2×#10625325C23semidirect
125. C2×#10625325C23semidirect
126. C2×D376C23semidirect
219. #13093958C23semidirect
220. #13093958C23semidirect
221. #13093956C23semidirect
222. #13093956C23semidirect
223. #13093949C23semidirect
224. #13093949C23semidirect
225. #13093949C23semidirect
226. #13093949C23semidirect
227. #13093946C23semidirect
228. #13093946C23semidirect
229. #13093946C23semidirect
230. #13093946C23semidirect
595. C2×#407D47semidirect
613. C22×M16C2×D47semidirect
684. #407C2×D47semidirect
685. #407C2×D47semidirect
686. #407C2×D47semidirect
687. C2×C22⋊C8C2×D47semidirect
688. C2×C22⋊C8C2×D47semidirect
689. C47#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202542302
#202542202
#202542042
#202541812
#202541712
#202541552
#202533372
#202533292
#202533212
#202530182
#202530072
#202526502
#202526422
#202526332
C2×C47×#4072
#6075247