Finite Group Databasebeta

← #27084767

Subgroups — #27084767

Order 12032.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256778C211yesmaximal, characteristic, complemented
2#20253665C214yesmaximal, complemented
3#20253650C214yesmaximal, complemented
4#20253602C214yesmaximal, complemented
5#20253587C214yesmaximal, complemented
6#20253311C212yesmaximal, complemented
7#20253193C211yesmaximal, characteristic, complemented
8#20253185C211yesmaximal, characteristic, complemented
9#20252860C211yesmaximal, characteristic, complemented
10#20252852C211yesmaximal, characteristic, complemented
11#20252630C212yesmaximal, complemented
12C4×#13094055C212yesmaximal, complemented
13C4×#13094050C212yesmaximal, complemented
14#20252026C211yesmaximal, characteristic, complemented
15C2×C47×#520C211yesmaximal, characteristic, complemented
16C2×#13094055C2212yes—
17C2×#13094050C2212yes—
18#15689744C2212yescomplemented
19#15689744C2212yescomplemented
20#15689735C2212yescomplemented
21#15689728C2212yescomplemented
22#15689720—21no—
23#15689720—21no—
24#15689711—21no—
25#15689711—21no—
26#15689680C2211yescharacteristic
27#15689673C2211yescharacteristic
28#15689651—22no—
29#15689651—22no—
30#15689634C2212yes—
31C4×#10625350C2212yes—
32#15689458C2214yescomplemented
33#15689453C2214yescomplemented
34#15689441C2214yescomplemented
35#15689436C2214yescomplemented
36#15689430C2214yescomplemented
37#15689423C2214yescomplemented
38#15689418C2212yescomplemented
39#15689413C2212yescomplemented
40#15689408C2212yescomplemented
41#15689403C2212yescomplemented
42#15689345C2214yescomplemented
43#15689338C2214yescomplemented
44#15689333C2212yescomplemented
45#15689328C2212yescomplemented
46#15689323C2212yescomplemented
47#15689318C2212yescomplemented
48#15689285C2214yes—
49#15689285C2214yes—
50#15689268C2214yes—
51#15689268C2214yes—
52#15689233C2214yescomplemented
53#15689228C2214yescomplemented
54#15689223C2214yescomplemented
55#15689221C2214yescomplemented
56C4×#10625337C2214yescomplemented
57C4×#10625336C2214yescomplemented
58C4×#10625335C2214yescomplemented
59C4×#10625334C2214yescomplemented
60#15689184C2214yescomplemented
61#15689184C2214yescomplemented
62#15689163C2212yes—
63#15689163C2212yes—
64#15689147C2211yescharacteristic
65#15689147C2211yescharacteristic
66#15689132C2212yes—
67#15689128C2212yes—
68#15689122C2212yes—
69#15689122C2212yes—
70#15689087C2212yes—
71C4×#10625329C2212yes—
72C22×#41×C47C2211yescharacteristic
73C47×#520—22no—
74C47×#520—22no—
75C47×#520C2214yes—
76C47×#520C2214yes—
77C2×C4×Q8×C47C2211yescharacteristic
78C2×C4×Q8×C47C2211yescharacteristic
79C2×C4×D4×C47—21no—
80C2×C4×D4×C47—21no—
81C2×C4×D4×C47C2211yescharacteristic
82C2×C4×D4×C47C2211yescharacteristic
83C2×#117×C47—21no—
84C2×#117×C47C2211yescharacteristic
85C22×C4⋊C4×C47—21no—
86C22×C4⋊C4×C47C2211yescharacteristic
87C2×#10625350C2312yes—
88#13094055—28no—
89#13094050—28no—
90C2×#10625337C2314yes—
91C2×#10625335C2314yes—
92C2×#10625336C2314yes—
93C2×#10625334C2314yes—
94C2×#10625329C2312yes—
95C2×#10625329C2312yes—
96#13094024C2311yescharacteristic
97#13094024C2311yescharacteristic
98#13094024C2311yescharacteristic
99#13094021C2311yescharacteristic
100#13094019—22no—
101#13094019—22no—
102#13094017—22no—
103#13094017—22no—
104#13094016C2312yes—
105#13094014—22no—
106#13094014—22no—
107#13094012C2312yes—
108#13094010—22no—
109#13094010—22no—
110#13094009—22no—
111#13094009—22no—
112#13094007—22no—
113#13094006—22no—
114#13094006—22no—
115#13094003—21no—
116#13094003—21no—
117#13094003C2312yes—
118#13094003C2312yes—
119#13094002—22no—
120#13094002—22no—
121#13093998—21no—
122#13093998—21no—
123#13093998C2312yes—
124#13093998C2312yes—
125#13093997—22no—
126#13093997—22no—
127#13093993—22no—
128C4×Dic94—21no—
129C4×Dic94—21no—
130C4×Dic94C2312yes—
131C4×Dic94C2312yes—
132C4×D188—21no—
133C4×D188—21no—
134C4×D188C2312yes—
135C4×D188C2312yes—
136C4×C22⋊D47—22no—
137C4×C22⋊D47—22no—
138C4×C22⋊D47—22no—
139C4×C22⋊D47—22no—
140#13093983C2312yes—
141#13093981—22no—
142C42×D47—22no—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093955C2314yes—
146#13093955C2314yes—
147C4⋊(C47⋊C8)C2312yes—
148C4⋊(C47⋊C8)C2312yes—
149C4⋊(C47⋊C8)C2312yes—
150C4⋊(C47⋊C8)C2312yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093945C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161#13093935C2314yes—
162C4×C47⋊C8C2314yes—
163C2×#41×C47—24no—
164C2×#41×C47—24no—
165C2×#41×C47—22no—
166C2×#41×C47C2314yes—
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47—21no—
169C22×D4×C47C2311yescharacteristic
170C23×C4×C47—21no—
171C23×C4×C47—21no—
172C23×C4×C47—21no—
173C23×C4×C47—21no—
174C23×C4×C47C2311yescharacteristic
175C4×Q8×C47—22no—
176C4×Q8×C47—21no—
177C4×Q8×C47—21no—
178C4×Q8×C47C2314yes—
179C4×Q8×C47C2312yes—
180C4×Q8×C47C2312yes—
181C4×D4×C47—24no—
182C4×D4×C47—24no—
183C4×D4×C47—24no—
184C4×D4×C47—24no—
185C4×D4×C47—22no—
186C4×D4×C47—21no—
187C4×D4×C47—21no—
188C4×D4×C47C2314yes—
189C4×D4×C47C2312yes—
190C4×D4×C47C2312yes—
191#117×C47—24no—
192#117×C47—24no—
193#117×C47D412yes—
194#117×C47D412yes—
195#117×C47C2312yes—
196#117×C47C2312yes—
197C2×C4⋊C4×C47—21no—
198C2×C4⋊C4×C47—21no—
199C2×C4⋊C4×C47—21no—
200C2×C4⋊C4×C47—22no—
201C2×C4⋊C4×C47—24no—
202C2×C4⋊C4×C47—24no—
203C2×C4⋊C4×C47D411yescharacteristic
204C2×C4⋊C4×C47D411yescharacteristic
205C2×C4⋊C4×C47C2311yescharacteristic
206C2×C4⋊C4×C47C2311yescharacteristic
207C2×C4⋊C4×C47C2314yes—
208C2×C22⋊C4×C47—21no—
209C2×C22⋊C4×C47—21no—
210C2×C22⋊C4×C47D411yescharacteristic
211C2×C22⋊C4×C47D411yescharacteristic
212C2×C42×C47—21no—
213C2×C42×C47—21no—
214C2×C42×C47C2311yescharacteristic
215C2×C42×C47C2311yescharacteristic
216C24×C47—21no—
217C24×C47C2×D411yescharacteristic
218#41×C47—216no—
219#41×C47—28no—
220#41×C47—28no—
221C2×Q8×C47—21no—
222C2×Q8×C47—22no—
223C2×Q8×C47#4114yes—
224C2×Q8×C47C2412yes—
225C2×D4×C47—28no—
226C2×D4×C47—24no—
227C2×D4×C47—21no—
228C2×D4×C47—22no—
229C2×D4×C47#4114yes—
230C2×D4×C47C2412yes—
231C22×C4×C47—28no—
232C22×C4×C47—21no—
233C22×C4×C47—24no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—24no—
239C22×C4×C47—24no—
240C22×C4×C47—22no—
241C22×C4×C47—22no—
242C22×C4×C47—82no—
243C22×C4×C47—82no—
244C22×C4×C47—82no—
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2412yes—
252C22×C4×C47C2411yescharacteristic
253C2×C22⋊D47—22no—
254C2×C22⋊D47—22no—
255C2×C22⋊D47—22no—
256#10625350—24no—
257#10625350—24no—
258C2×D188—21no—
259C2×D188—21no—
260C2×D188C2412yes—
261C2×C4×D47—22no—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×Dic94—21no—
265C2×Dic94—21no—
266C2×Dic94C2412yes—
267C4⋊C4×C47—24no—
268C4⋊C4×C47—24no—
269C4⋊C4×C47—22no—
270C4⋊C4×C47—22no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47C2×D412yes—
274C4⋊C4×C47C2×D412yes—
275C4⋊C4×C47C2×D412yes—
276C4⋊C4×C47C2×D412yes—
277C4⋊C4×C47C2412yes—
278C4⋊C4×C47C2412yes—
279C22⋊C4×C47—24no—
280C22⋊C4×C47—22no—
281C22⋊C4×C47—22no—
282C22⋊C4×C47C2×D412yes—
283C22⋊C4×C47C2×D412yes—
284C22⋊C4×C47C2×D412yes—
285C22⋊C4×C47C2×D412yes—
286C42×C47—24no—
287C42×C47—22no—
288C42×C47—22no—
289C42×C47C2×D412yes—
290C42×C47C2×D411yescharacteristic
291C42×C47C2×D411yescharacteristic
292C42×C47C2412yes—
293C42×C47C2411yescharacteristic
294C42×C47C2411yescharacteristic
295C22⋊Dic47—22no—
296C22⋊Dic47—22no—
297C22⋊Dic47—22no—
298#10625337—28no—
299#10625336—28no—
300#10625335—28no—
301#10625334—28no—
302(C2×D47)⋊C4—22no—
303(C2×D47)⋊C4—22no—
304(C2×D47)⋊C4—22no—
305(C2×D47)⋊C4—22no—
306(C2×D47)⋊C4—22no—
307(C2×D47)⋊C4—22no—
308C4⋊Dic47—21no—
309C4⋊Dic47—21no—
310C4⋊Dic47—21no—
311C4⋊Dic47—21no—
312C4⋊Dic47C2412yes—
313C4⋊Dic47C2412yes—
314Dic47⋊C4—22no—
315Dic47⋊C4—22no—
316Dic47⋊C4—22no—
317Dic47⋊C4—22no—
318Dic47⋊C4—22no—
319Dic47⋊C4—22no—
320C4×Dic47—22no—
321C4×Dic47—22no—
322C4×Dic47—22no—
323#10625329—24no—
324#10625329—24no—
325C2×C47⋊C8C2414yes—
326C2×C47⋊C8C2414yes—
327C23×C47—22no—
328C23×C47—24no—
329C23×C47—22no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—42no—
333C23×C47—42no—
334C23×C47C22×D412yes—
335C23×C47C22×D411yescharacteristic
336C22×D47—22no—
337Q8×C47—24no—
338Q8×C47—22no—
339Q8×C47C2×#4114yes—
340D4×C47—216no—
341D4×C47—24no—
342D4×C47—22no—
343D4×C47C2×#4114yes—
344C2×C4×C47—216no—
345C2×C4×C47—22no—
346C2×C4×C47—24no—
347C2×C4×C47—22no—
348C2×C4×C47—24no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—42no—
358C2×C4×C47—42no—
359C2×C4×C47—82no—
360C2×C4×C47—84no—
361C2×C4×C47—82no—
362C2×C4×C47—84no—
363C2×C4×C47C22×D412yes—
364C2×C4×C47C22×D412yes—
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C2×C4×C47C22×D412yes—
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C22×D411yescharacteristic
371C2×C4×C47C2×#4112yes—
372C2×C4×C47C2×#4112yes—
373C2×C4×C47C2511yescharacteristic
374C22⋊D47—44no—
375C22⋊D47—82no—
376C22⋊D47—82no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380D188—22no—
381D188—22no—
382D188—81no—
383D188—81no—
384C4×D47—44no—
385C4×D47—82no—
386C4×D47—82no—
387Dic94—22no—
388Dic94—22no—
389Dic94—81no—
390Dic94—81no—
391C47⋊C8—24no—
392C47⋊C8—24no—
393#60565—471nomaximal, Sylow
394C22×C47—21no—
395C22×C47—21no—
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—24no—
400C22×C47—44no—
401C22×C47—48no—
402C22×C47—42no—
403C22×C47—42no—
404C22×C47#52512yes—
405C22×C47C23×D411yescharacteristic
406C2×D47—42no—
407C2×D47—42no—
408C2×D47—42no—
409C4×C47—21no—
410C4×C47—22no—
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—22no—
414C4×C47—21no—
415C4×C47—22no—
416C4×C47—24no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47#52512yes—
420C4×C47C22×#4111yescharacteristic
421C4×C47C22×#4111yescharacteristic
422Dic47—42no—
423Dic47—42no—
424Dic47—42no—
425#3455—471no—
426C2×#520D4711yescharacteristic, complemented
427#3125—474no—
428#3124—474no—
429#3120—474no—
430#3119—474no—
431#3092—472no—
432#3078—471no—
433#3077—471no—
434#3037—471no—
435#3036—471no—
436#3005—472no—
437C4×#137—472no—
438C4×AGL(1,ℤ/8)—472no—
439#2921—471no—
440C2×C47—22no—
441C2×C47—42no—
442C2×C47—44no—
443C2×C47C2×#52511yescharacteristic
444C2×C47#358511yescharacteristic
445C2×C47#358611yescharacteristic
446D47—82no—
447C22×#41C2×D4711yescharacteristic
448C2×#137—472no—
449C2×AGL(1,ℤ/8)—472no—
450#542—472no—
451#542—472no—
452#541—472no—
453#540—472no—
454#539—941no—
455#539—941no—
456#538—941no—
457#538—941no—
458#533—471no—
459#532—471no—
460#529—942no—
461#529—942no—
462#525—472no—
463#520—22no—
464#520—22no—
465#520C2×D4714yes—
466#520C2×D4714yes—
467C4×#41—472no—
468C2×C4×Q8C2×D4711yescharacteristic
469C2×C4×Q8C2×D4711yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4—21no—
472C2×C4×D4C2×D4711yescharacteristic
473C2×C4×D4C2×D4711yescharacteristic
474C2×#117—21no—
475C2×#117C2×D4711yescharacteristic
476C22×C4⋊C4—21no—
477C22×C4⋊C4C2×D4711yescharacteristic
478#484—474no—
479#483—474no—
480#481—474no—
481#480—474no—
482#479—474no—
483#478—474no—
484#477—472no—
485#476—472no—
486#475—472no—
487#474—472no—
488#464—474no—
489#463—474no—
490#462—472no—
491#461—472no—
492#460—472no—
493#459—472no—
494#452—474no—
495#452—474no—
496#449—474no—
497#449—474no—
498#442—474no—
499#441—474no—
500#440—474no—
501#440—474no—
502C4×Q16—474no—
503C4×SD16—474no—
504C4×SD16—474no—
505C4×D8—474no—
506#433—474no—
507#433—474no—
508#428—472no—
509#428—472no—
510#423—471no—
511#423—471no—
512#419—472no—
513#418—472no—
514#417—472no—
515#417—472no—
516#407—472no—
517C4×M16—472no—
518C47#6056511yescharacteristic, complemented, Sylow
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—22no—
522C2×#41—472no—
523C2×#41C22×D4714yes—
524C22×Q8C22×D4711yescharacteristic
525C22×D4—21no—
526C22×D4C22×D4711yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D4711yescharacteristic
532#137—948no—
533AGL(1,ℤ/8)—948no—
534C2×Q16—474no—
535C2×SD16—474no—
536C2×SD16—474no—
537C2×D8—474no—
538C2×M16—472no—
539C2×M16—472no—
540C4⋊Q8—471no—
541C4⋊Q8—471no—
542C4⋊Q8—471no—
543#127—471no—
544#126—942no—
545#126—942no—
546#126—942no—
547#126—942no—
548#125—472no—
549#125—942no—
550#125—942no—
551#124—472no—
552#124—942no—
553#124—942no—
554#123—942no—
555#123—942no—
556#123—942no—
557#123—942no—
558#123—942no—
559C22⋊Q8—472no—
560C22⋊Q8—472no—
561C22⋊Q8—941no—
562C22⋊Q8—941no—
563C22⋊Q8—942no—
564C22⋊Q8—942no—
565#121—472no—
566#121—472no—
567#121—941no—
568#121—941no—
569#121—942no—
570#121—942no—
571#120—942no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—472no—
576C4×Q8—472no—
577C4×Q8—941no—
578C4×Q8—941no—
579C4×Q8C22×D4714yes—
580C4×Q8C22×D4712yes—
581C4×Q8C22×D4712yes—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—472no—
590C4×D4—472no—
591C4×D4—942no—
592C4×D4—942no—
593C4×D4—942no—
594C4×D4—942no—
595C4×D4—941no—
596C4×D4—941no—
597C4×D4C22×D4714yes—
598C4×D4C22×D4712yes—
599C4×D4C22×D4712yes—
600#117—24no—
601#117—24no—
602#117—472no—
603#117—942no—
604#117C22⋊D4712yes—
605#117C22⋊D4712yes—
606#117C22×D4712yes—
607#117C22×D4712yes—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4C22⋊D4711yescharacteristic
615C2×C4⋊C4C22⋊D4711yescharacteristic
616C2×C4⋊C4C22×D4711yescharacteristic
617C2×C4⋊C4C22×D4711yescharacteristic
618C2×C4⋊C4C22×D4714yes—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C22⋊D4711yescharacteristic
622C2×C22⋊C4C22⋊D4711yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—942no—
626C2×C42C22×D4711yescharacteristic
627C2×C42C22×D4711yescharacteristic
628#107—474no—
629#107—474no—
630#106—474no—
631#106—474no—
632C4⋊C8—472no—
633C4⋊C8—472no—
634C4⋊C8—472no—
635C4⋊C8—472no—
636#103—474no—
637#103—474no—
638#103—474no—
639#103—474no—
640#102—474no—
641#102—474no—
642#102—474no—
643#102—474no—
644C22⋊C8—474no—
645C22⋊C8—474no—
646#97—474no—
647C4×C8—474no—
648C24—21no—
649C24C2×C22⋊D4711yescharacteristic
650#41—216no—
651#41—28no—
652#41—28no—
653#41—944no—
654#41—944no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—472no—
658C2×Q8—941no—
659C2×Q8—941no—
660C2×Q8#1062535014yes—
661C2×Q8C23×D4712yes—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—472no—
667C2×D4—942no—
668C2×D4—942no—
669C2×D4—942no—
670C2×D4—941no—
671C2×D4—941no—
672C2×D4#1062535014yes—
673C2×D4C23×D4712yes—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—82no—
686C22×C4—82no—
687C22×C4—82no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4C2×C22⋊D4711yescharacteristic
692C22×C4C2×C22⋊D4712yes—
693C22×C4C2×C22⋊D4711yescharacteristic
694C22×C4C2×C22⋊D4711yescharacteristic
695C22×C4C2×C22⋊D4711yescharacteristic
696C22×C4C2×C22⋊D4711yescharacteristic
697C22×C4C23×D4712yes—
698C22×C4C23×D4711yescharacteristic
699Q16—948no—
700SD16—948no—
701SD16—948no—
702D8—948no—
703M16—944no—
704M16—944no—
705C2×C8—474no—
706C2×C8—474no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—472no—
714C4⋊C4—472no—
715C4⋊C4—942no—
716C4⋊C4—942no—
717C4⋊C4—942no—
718C4⋊C4—942no—
719C4⋊C4—942no—
720C4⋊C4—942no—
721C4⋊C4—941no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4—941no—
725C4⋊C4C2×C22⋊D4712yes—
726C4⋊C4C2×C22⋊D4712yes—
727C4⋊C4C2×C22⋊D4712yes—
728C4⋊C4C2×C22⋊D4712yes—
729C4⋊C4C23×D4712yes—
730C4⋊C4C23×D4712yes—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—942no—
735C22⋊C4—942no—
736C22⋊C4—942no—
737C22⋊C4—942no—
738C22⋊C4—942no—
739C22⋊C4—942no—
740C22⋊C4—942no—
741C22⋊C4—942no—
742C22⋊C4—942no—
743C22⋊C4C2×C22⋊D4712yes—
744C22⋊C4C2×C22⋊D4712yes—
745C22⋊C4C2×C22⋊D4712yes—
746C22⋊C4C2×C22⋊D4712yes—
747C42—24no—
748C42—22no—
749C42—22no—
750C42—942no—
751C42—942no—
752C42—942no—
753C42C2×C22⋊D4712yes—
754C42C2×C22⋊D4711yescharacteristic
755C42C2×C22⋊D4711yescharacteristic
756C42C23×D4712yes—
757C42C23×D4711yescharacteristic
758C42C23×D4711yescharacteristic
759C23—22no—
760C23—24no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—942no—
767C23C22×C22⋊D4712yes—
768C23C22×C22⋊D4711yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—942no—
772Q8—942no—
773Q8—3761no—
774Q8—3761no—
775Q8C2×#1062535014yes—
776D4—216no—
777D4—24no—
778D4—22no—
779D4—942no—
780D4—942no—
781D4—3761no—
782D4—3761no—
783D4—3762no—
784D4—3762no—
785D4—1884no—
786D4C2×#1062535014yes—
787C2×C4—216no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—942no—
807C2×C4—942no—
808C2×C4—942no—
809C2×C4—3762no—
810C2×C4—3762no—
811C2×C4—1884no—
812C2×C4C22×C22⋊D4712yes—
813C2×C4C22×C22⋊D4711yescharacteristic
814C2×C4C22×C22⋊D4711yescharacteristic
815C2×C4C22×C22⋊D4712yes—
816C2×C4C22×C22⋊D4711yescharacteristic
817C2×C4C22×C22⋊D4711yescharacteristic
818C2×C4C22×C22⋊D4712yes—
819C2×C4C22×C22⋊D4711yescharacteristic
820C2×C4C2×#1062535012yes—
821C2×C4C2×#1062535012yes—
822C2×C4C24×D4711yescharacteristic
823C8—944no—
824C8—944no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—1882no—
836C22—1882no—
837C22—1882no—
838C22#1568963412yes—
839C22C23×C22⋊D4711yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—1882no—
851C4—1882no—
852C4—1882no—
853C4#1568963412yes—
854C4C22×#1062535011yescharacteristic
855C4C22×#1062535011yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—3762no—
860C2C2×#1568963411yescharacteristic
861C2#2025816811yescharacteristic
862C2#2025817511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#520C2
socleC22×C47C23×D4
hypercenterC2×#520D47
hypocenterC47#60565
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20256778C2semidirect
2. #20253665C2semidirect
3. #20253650C2semidirect
4. #20253602C2semidirect
5. #20253587C2semidirect
6. #20253311C2semidirect
7. #20253193C2semidirect
8. #20253185C2semidirect
9. #20252860C2semidirect
10. #20252852C2semidirect
11. #20252630C2semidirect
12. C4×#13094055C2semidirect
13. C4×#13094050C2semidirect
14. #20252026C2semidirect
15. C2×C47×#520C2semidirect
18. #15689744C22semidirect
19. #15689744C22semidirect
20. #15689735C22semidirect
21. #15689728C22semidirect
32. #15689458C22semidirect
33. #15689453C22semidirect
34. #15689441C22semidirect
35. #15689436C22semidirect
36. #15689430C22semidirect
37. #15689423C22semidirect
38. #15689418C22semidirect
39. #15689413C22semidirect
40. #15689408C22semidirect
41. #15689403C22semidirect
42. #15689345C22semidirect
43. #15689338C22semidirect
44. #15689333C22semidirect
45. #15689328C22semidirect
46. #15689323C22semidirect
47. #15689318C22semidirect
52. #15689233C22semidirect
53. #15689228C22semidirect
54. #15689223C22semidirect
55. #15689221C22semidirect
56. C4×#10625337C22semidirect
57. C4×#10625336C22semidirect
58. C4×#10625335C22semidirect
59. C4×#10625334C22semidirect
60. #15689184C22semidirect
61. #15689184C22semidirect
426. C2×#520D47semidirect
518. C47#60565semidirect

Maximal subgroups

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

subgroupindex
#202567782
#202536652
#202536502
#202536022
#202535872
#202533112
#202531932
#202531852
#202528602
#202528522
#202526302
C4×#130940552
C4×#130940502
#202520262
C2×C47×#5202
#6056547