Finite Group Databasebeta

← #27084785

Subgroups — #27084785

Order 12032.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256589C211yesmaximal, characteristic, complemented
2#20253659C214yesmaximal, complemented
3#20253644C214yesmaximal, complemented
4#20253611C214yesmaximal, complemented
5#20253566C214yesmaximal, complemented
6#20253332C211yesmaximal, characteristic, complemented
7#20253324C211yesmaximal, characteristic, complemented
8#20253197C212yesmaximal, complemented
9#20252878C212yesmaximal, complemented
10#20252646C211yesmaximal, characteristic, complemented
11#20252638C211yesmaximal, characteristic
12C4×#13094055C212yesmaximal, complemented
13C4×#13094050C212yesmaximal, complemented
14#20252026C211yesmaximal, characteristic, complemented
15C2×C47×#542C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094055C2212yes—
18C2×#13094050C2212yes—
19#15689604—21no—
20#15689604—21no—
21#15689603C2212yescomplemented
22#15689603C2212yescomplemented
23#15689600C2212yescomplemented
24#15689597C2212yescomplemented
25#15689596—21no—
26#15689596—21no—
27C4×#10625350C2212yes—
28C4×#10625350C2212yes—
29#15689591—22no—
30C2×#13093983C2211yescharacteristic
31#117×D47—22no—
32#15689461C2214yescomplemented
33#15689456C2212yescomplemented
34#15689451C2212yescomplemented
35#15689444C2214yes—
36#15689439C2212yescomplemented
37#15689434C2212yescomplemented
38#15689415C2214yescomplemented
39#15689410C2214yescomplemented
40#15689405C2214yescomplemented
41#15689400C2214yescomplemented
42#15689342C2214yescomplemented
43#15689342C2214yescomplemented
44#15689335C2214yescomplemented
45#15689335C2214yescomplemented
46#15689283C2214yescomplemented
47#15689278C2212yescomplemented
48#15689273C2212yescomplemented
49#15689266C2214yes—
50#15689261C2212yes—
51#15689256C2212yes—
52#15689233C2214yescomplemented
53#15689228C2214yescomplemented
54#15689223C2214yescomplemented
55#15689221C2214yescomplemented
56C4×#10625337C2214yescomplemented
57C4×#10625336C2214yescomplemented
58C4×#10625335C2214yescomplemented
59C4×#10625334C2214yescomplemented
60#15689184C2214yescomplemented
61#15689184C2214yescomplemented
62#15689163C2212yescomplemented
63#15689163C2212yescomplemented
64#15689147C2212yescomplemented
65#15689132C2212yescomplemented
66#15689128C2212yescomplemented
67#15689122C2212yes—
68#15689122C2212yes—
69#15689087C2211yescharacteristic
70#15689087C2211yescharacteristic
71C4×#10625329C2212yescomplemented
72C47×#542—22no—
73C47×#542—22no—
74C47×#542C2214yes—
75C47×#542C2214yescomplemented
76C2×C4⋊Q8×C47C2211yescharacteristic, complemented
77C2×#126×C47—21no—
78C2×#124×C47—21no—
79C2×#124×C47C2211yescharacteristic, complemented
80C2×#123×C47—21no—
81C2×C22⋊Q8×C47—21no—
82C2×C22⋊Q8×C47C2211yescharacteristic
83C2×#121×C47C2211yescharacteristic
84C2×C4×Q8×C47C2211yescharacteristic, complemented
85C2×C4×D4×C47C2211yescharacteristic, complemented
86C2×#117×C47C2211yescharacteristic
87C2×#10625350—21no—
88C2×#10625350—21no—
89C2×#10625350—28no—
90C2×#10625350C2312yes—
91C2×#10625350C2312yes—
92C22×Dic94C2311yescharacteristic
93C22×D188C2311yescharacteristic
94C22×C22⋊D47—21no—
95C22×C4×D47—21no—
96#13094055—28no—
97#13094050—28no—
98C2×#10625337C2314yes—
99C2×#10625335C2314yes—
100C2×#10625336C2314yes—
101C2×#10625334C2314yes—
102C2×#10625329C2312yes—
103C2×#10625329C2312yes—
104C4×Dic94C2312yes—
105C4×Dic94C2312yes—
106C4×Dic94C2312yes—
107C4×Dic94C2312yes—
108#13093989—22no—
109#13093989—22no—
110C4×D188C2312yes—
111C4×D188C2312yes—
112C4×D188C2312yes—
113C4×D188C2312yes—
114#13093986—22no—
115#13093986—22no—
116C4×C22⋊D47—22no—
117C4×C22⋊D47—22no—
118C4×C22⋊D47—22no—
119C4×C22⋊D47—22no—
120(C22⋊D47)⋊C4—22no—
121(C22⋊D47)⋊C4—22no—
122(C22⋊D47)⋊C4—22no—
123(C22⋊D47)⋊C4—22no—
124#13093983—21no—
125#13093983—21no—
126#13093983C2312yes—
127#13093983C2312yes—
128#13093982—22no—
129#13093982—22no—
130#13093981—22no—
131#13093981—22no—
132#13093980—22no—
133#13093980—22no—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C4⋊C4×D47—22no—
137C4⋊C4×D47—22no—
138C2×C22⋊Dic47—21no—
139C22⋊C4×D47—22no—
140C22⋊C4×D47—22no—
141C2×C4×Dic47—21no—
142C42×D47—22no—
143C42×D47—22no—
144#13093957C2314yes—
145#13093957C2314yes—
146#13093955C2314yes—
147#13093955C2314yes—
148C4⋊(C47⋊C8)C2314yes—
149C4⋊(C47⋊C8)C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093947C2314yes—
153#13093947C2314yes—
154#13093945C2314yes—
155#13093945C2314yes—
156#13093944C2314yes—
157#13093944C2314yes—
158C22⋊(C47⋊C8)C2312yes—
159C22⋊(C47⋊C8)C2312yes—
160C22⋊(C47⋊C8)C2312yes—
161C22⋊(C47⋊C8)C2312yes—
162#13093935C2314yes—
163C4×C47⋊C8C2314yes—
164C22×Q8×C47—21no—
165C22×Q8×C47C2311yescharacteristic
166C22×D4×C47—21no—
167C22×D4×C47C2311yescharacteristic
168C23×C4×C47—21no—
169C23×C4×C47C2311yescharacteristic
170C4⋊Q8×C47—22no—
171C4⋊Q8×C47C2314yes—
172#126×C47—24no—
173#126×C47—24no—
174#124×C47—24no—
175#124×C47—24no—
176#124×C47—22no—
177#124×C47C2314yes—
178#123×C47—24no—
179#123×C47—24no—
180C22⋊Q8×C47—21no—
181C22⋊Q8×C47—21no—
182C22⋊Q8×C47—24no—
183C22⋊Q8×C47—24no—
184C22⋊Q8×C47C2312yes—
185C22⋊Q8×C47C2312yes—
186#121×C47—21no—
187#121×C47—21no—
188#121×C47C2312yes—
189#121×C47C2312yes—
190C4×Q8×C47—22no—
191C4×Q8×C47C2314yes—
192C4×D4×C47—22no—
193C4×D4×C47C2314yes—
194#117×C47D412yes—
195#117×C47D412yes—
196#117×C47C2312yes—
197#117×C47C2312yes—
198C2×C4⋊C4×C47—21no—
199C2×C4⋊C4×C47—21no—
200C2×C4⋊C4×C47—21no—
201C2×C4⋊C4×C47D411yescharacteristic
202C2×C4⋊C4×C47D411yescharacteristic
203C2×C4⋊C4×C47C2311yescharacteristic
204C2×C4⋊C4×C47C2311yescharacteristic
205C2×C22⋊C4×C47—21no—
206C2×C22⋊C4×C47—21no—
207C2×C22⋊C4×C47—21no—
208C2×C22⋊C4×C47—21no—
209C2×C22⋊C4×C47—21no—
210C2×C22⋊C4×C47D411yescharacteristic
211C2×C22⋊C4×C47D411yescharacteristic
212C2×C42×C47—21no—
213C2×C42×C47C2311yescharacteristic
214C2×C42×C47C2311yescharacteristic
215C24×C47—21no—
216C24×C47C2×D411yescharacteristic
217C23×D47—21no—
218C2×Q8×C47—21no—
219C2×Q8×C47—24no—
220C2×Q8×C47—24no—
221C2×Q8×C47—82no—
222C2×Q8×C47C2412yes—
223C2×D4×C47—22no—
224C2×D4×C47—22no—
225C2×D4×C47—21no—
226C2×D4×C47—24no—
227C2×D4×C47—82no—
228C2×D4×C47C2412yes—
229C22×C4×C47—24no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—24no—
234C22×C4×C47—82no—
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2411yescharacteristic
243C22×C4×C47C2411yescharacteristic
244C22×C4×C47C2411yescharacteristic
245C2×C22⋊D47—28no—
246C2×C22⋊D47—22no—
247C2×C22⋊D47—22no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251#10625350—28no—
252#10625350—28no—
253#10625350—24no—
254#10625350—24no—
255#10625350—24no—
256#10625350#4118yes—
257C2×D188—21no—
258C2×D188—24no—
259C2×D188C2412yes—
260C2×C4×D47—28no—
261C2×C4×D47—22no—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—22no—
265C2×C4×D47—22no—
266C2×C4×D47—22no—
267C2×Dic94—21no—
268C2×Dic94—24no—
269C2×Dic94C2412yes—
270C4⋊C4×C47—24no—
271C4⋊C4×C47—22no—
272C4⋊C4×C47—22no—
273C4⋊C4×C47—24no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47C2×D412yes—
277C4⋊C4×C47C2×D412yes—
278C4⋊C4×C47C2×D412yes—
279C4⋊C4×C47C2×D412yes—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—22no—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—22no—
286C22⋊C4×C47—22no—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—24no—
289C22⋊C4×C47C2×D412yes—
290C22⋊C4×C47C2×D412yes—
291C22⋊C4×C47C2×D412yes—
292C22⋊C4×C47C2×D412yes—
293C42×C47—24no—
294C42×C47C2×D412yes—
295C42×C47C2×D412yes—
296C42×C47C2412yes—
297C42×C47C2412yes—
298C22⋊Dic47—22no—
299C22⋊Dic47—22no—
300#10625337—28no—
301#10625336—28no—
302#10625335—28no—
303#10625334—28no—
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⋊Dic47C2412yes—
311C4⋊Dic47C2412yes—
312Dic47⋊C4—22no—
313Dic47⋊C4—22no—
314Dic47⋊C4—22no—
315Dic47⋊C4—22no—
316C4×Dic47—22no—
317C4×Dic47—22no—
318C4×Dic47—22no—
319C4×Dic47—22no—
320C4×Dic47—22no—
321C4×Dic47—22no—
322#10625329—24no—
323#10625329—24no—
324C2×C47⋊C8C2414yes—
325C2×C47⋊C8C2414yes—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47—42no—
333C23×C47C22×D411yescharacteristic
334C23×C47C22×D411yescharacteristic
335C23×C47C22×D411yescharacteristic
336C22×D47—22no—
337C22×D47—24no—
338C22×D47—81no—
339C22×D47—81no—
340Q8×C47—24no—
341Q8×C47—42no—
342Q8×C47—84no—
343D4×C47—24no—
344D4×C47—42no—
345D4×C47—82no—
346D4×C47—82no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—42no—
360C2×C4×C47—42no—
361C2×C4×C47—42no—
362C2×C4×C47—84no—
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D412yes—
365C2×C4×C47C22×D412yes—
366C2×C4×C47C22×D412yes—
367C2×C4×C47C22×D412yes—
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C2×#4114yes—
371C2×C4×C47C2511yescharacteristic
372C22⋊D47—28no—
373C22⋊D47—28no—
374C2×Dic47—24no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—81no—
379C2×Dic47—81no—
380D188—24no—
381D188—22no—
382D188C2×#4114yes—
383C4×D47—28no—
384C4×D47—28no—
385C4×D47—82no—
386C4×D47—82no—
387C4×D47—82no—
388C4×D47—82no—
389Dic94—24no—
390Dic94—22no—
391Dic94C2×#4114yes—
392C47⋊C8—24no—
393C47⋊C8—24no—
394#60567—471nomaximal, Sylow
395C22×C47—21no—
396C22×C47—21no—
397C22×C47—21no—
398C22×C47—21no—
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—42no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—82no—
407C22×C47—84no—
408C22×C47#52512yes—
409C22×C47C23×D411yescharacteristic
410C2×D47—24no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—84no—
414C4×C47—22no—
415C4×C47—22no—
416C4×C47—22no—
417C4×C47—22no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—42no—
421C4×C47—42no—
422C4×C47—42no—
423C4×C47#52512yes—
424C4×C47C22×#4112yes—
425Dic47—24no—
426Dic47—42no—
427Dic47—42no—
428C2×#542D4711yescharacteristic, complemented
429#3428—471no—
430#3125—474no—
431#3124—474no—
432#3121—474no—
433#3118—474no—
434#3095—471no—
435#3094—471no—
436#3079—472no—
437#3040—472no—
438#3007—471no—
439#3006—471no—
440C4×#137—472no—
441C4×AGL(1,ℤ/8)—472no—
442#2921—471no—
443C2×C47—22no—
444C2×C47—41no—
445C2×C47—41no—
446C2×C47—82no—
447C2×C47C2×#52511yescharacteristic
448C2×C47#358511yescharacteristic
449C2×C47#358611yescharacteristic
450D47—44no—
451C22×#41—471no—
452C2×#137—472no—
453C2×AGL(1,ℤ/8)—472no—
454#542—22no—
455#542—22no—
456#542C2×D4714yes—
457#542C2×D4714yescomplemented
458C2×C4⋊Q8C2×D4711yescharacteristic, complemented
459C2×#126—21no—
460C2×#124—21no—
461C2×#124C2×D4711yescharacteristic, complemented
462C2×#123—21no—
463C2×C22⋊Q8—21no—
464C2×C22⋊Q8C2×D4711yescharacteristic
465C2×#121C2×D4711yescharacteristic
466#520—472no—
467#520—472no—
468#520—941no—
469#520—941no—
470#519—472no—
471#518—472no—
472#518—941no—
473#518—941no—
474C4×#41—472no—
475C4×#41—472no—
476C4×#41—942no—
477C2×C4×Q8C2×D4711yescharacteristic, complemented
478C2×C4×D4C2×D4711yescharacteristic, complemented
479C2×#117—471no—
480C2×#117—942no—
481C2×#117C2×D4711yescharacteristic
482#485—474no—
483#484—472no—
484#483—472no—
485#482—474no—
486#481—472no—
487#480—472no—
488#477—474no—
489#476—474no—
490#475—474no—
491#474—474no—
492#464—474no—
493#464—474no—
494#463—474no—
495#463—474no—
496#452—474no—
497#451—472no—
498#450—472no—
499#449—474no—
500#448—472no—
501#447—472no—
502#442—474no—
503#441—474no—
504#440—474no—
505#440—474no—
506C4×Q16—474no—
507C4×SD16—474no—
508C4×SD16—474no—
509C4×D8—474no—
510#433—474no—
511#433—474no—
512#428—472no—
513#428—472no—
514#423—472no—
515#419—472no—
516#418—472no—
517#417—472no—
518#417—472no—
519#407—471no—
520#407—471no—
521C4×M16—472no—
522C47#6056711yescharacteristic, complemented, Sylow
523C2×#41—472no—
524C2×#41—472no—
525C2×#41—948no—
526C2×#41—941no—
527C2×#41—941no—
528C22×Q8—21no—
529C22×Q8—471no—
530C22×Q8C22×D4711yescharacteristic
531C22×D4—21no—
532C22×D4—471no—
533C22×D4—941no—
534C22×D4C22×D4711yescharacteristic
535C23×C4—21no—
536C23×C4—941no—
537C23×C4C22×D4711yescharacteristic
538#137—948no—
539AGL(1,ℤ/8)—948no—
540C2×Q16—474no—
541C2×SD16—474no—
542C2×SD16—474no—
543C2×D8—474no—
544C2×M16—472no—
545C2×M16—472no—
546C4⋊Q8—22no—
547C4⋊Q8C22×D4714yes—
548#126—24no—
549#126—24no—
550#124—24no—
551#124—24no—
552#124—22no—
553#124C22×D4714yes—
554#123—24no—
555#123—24no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—24no—
559C22⋊Q8—24no—
560C22⋊Q8C22×D4712yes—
561C22⋊Q8C22×D4712yes—
562#121—21no—
563#121—21no—
564#121C22×D4712yes—
565#121C22×D4712yes—
566C4×Q8—22no—
567C4×Q8—472no—
568C4×Q8—472no—
569C4×Q8—472no—
570C4×Q8—472no—
571C4×Q8—942no—
572C4×Q8—942no—
573C4×Q8C22×D4714yes—
574C4×D4—22no—
575C4×D4—472no—
576C4×D4—472no—
577C4×D4—472no—
578C4×D4—472no—
579C4×D4—942no—
580C4×D4—942no—
581C4×D4—942no—
582C4×D4—942no—
583C4×D4—942no—
584C4×D4—942no—
585C4×D4—942no—
586C4×D4—942no—
587C4×D4—942no—
588C4×D4—942no—
589C4×D4C22×D4714yes—
590#117—472no—
591#117—472no—
592#117—941no—
593#117—941no—
594#117—942no—
595#117—942no—
596#117—942no—
597#117—942no—
598#117—942no—
599#117—942no—
600#117C22⋊D4712yes—
601#117C22⋊D4712yes—
602#117C22×D4712yes—
603#117C22×D4712yes—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—471no—
608C2×C4⋊C4—471no—
609C2×C4⋊C4—942no—
610C2×C4⋊C4—942no—
611C2×C4⋊C4C22⋊D4711yescharacteristic
612C2×C4⋊C4C22⋊D4711yescharacteristic
613C2×C4⋊C4C22×D4711yescharacteristic
614C2×C4⋊C4C22×D4711yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—942no—
622C2×C22⋊C4—942no—
623C2×C22⋊C4C22⋊D4711yescharacteristic
624C2×C22⋊C4C22⋊D4711yescharacteristic
625C2×C42—21no—
626C2×C42—941no—
627C2×C42—942no—
628C2×C42—942no—
629C2×C42C22×D4711yescharacteristic
630C2×C42C22×D4711yescharacteristic
631#107—474no—
632#107—474no—
633#106—474no—
634#106—474no—
635C4⋊C8—474no—
636C4⋊C8—474no—
637#103—474no—
638#103—474no—
639#103—474no—
640#103—474no—
641#102—474no—
642#102—474no—
643#102—474no—
644#102—474no—
645C22⋊C8—472no—
646C22⋊C8—472no—
647C22⋊C8—472no—
648C22⋊C8—472no—
649#97—474no—
650C4×C8—474no—
651C24—21no—
652C24—941no—
653C24C2×C22⋊D4711yescharacteristic
654#41—478no—
655#41—944no—
656#41—944no—
657#41—948no—
658#41—948no—
659#41—944no—
660C2×Q8—21no—
661C2×Q8—24no—
662C2×Q8—24no—
663C2×Q8—82no—
664C2×Q8—472no—
665C2×Q8—944no—
666C2×Q8—941no—
667C2×Q8C23×D4712yes—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—82no—
673C2×D4—472no—
674C2×D4—944no—
675C2×D4—948no—
676C2×D4—942no—
677C2×D4—942no—
678C2×D4—941no—
679C2×D4C23×D4712yes—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—82no—
686C22×C4—948no—
687C22×C4—941no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—941no—
691C22×C4—941no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4C2×C22⋊D4711yescharacteristic
697C22×C4C2×C22⋊D4711yescharacteristic
698C22×C4C2×C22⋊D4711yescharacteristic
699C22×C4C2×C22⋊D4711yescharacteristic
700C22×C4C2×C22⋊D4711yescharacteristic
701C22×C4C2×C22⋊D4711yescharacteristic
702C22×C4C2×C22⋊D4711yescharacteristic
703C22×C4C23×D4711yescharacteristic
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706Q16—948no—
707SD16—948no—
708SD16—948no—
709D8—948no—
710M16—944no—
711M16—944no—
712C2×C8—474no—
713C2×C8—474no—
714C4⋊C4—24no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—24no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—472no—
721C4⋊C4—472no—
722C4⋊C4—942no—
723C4⋊C4—942no—
724C4⋊C4—942no—
725C4⋊C4—942no—
726C4⋊C4—941no—
727C4⋊C4—941no—
728C4⋊C4C2×C22⋊D4712yes—
729C4⋊C4C2×C22⋊D4712yes—
730C4⋊C4C2×C22⋊D4712yes—
731C4⋊C4C2×C22⋊D4712yes—
732C4⋊C4C23×D4712yes—
733C4⋊C4C23×D4712yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—942no—
742C22⋊C4—942no—
743C22⋊C4—942no—
744C22⋊C4—942no—
745C22⋊C4—942no—
746C22⋊C4—942no—
747C22⋊C4C2×C22⋊D4712yes—
748C22⋊C4C2×C22⋊D4712yes—
749C22⋊C4C2×C22⋊D4712yes—
750C22⋊C4C2×C22⋊D4712yes—
751C42—24no—
752C42—942no—
753C42—942no—
754C42—942no—
755C42—942no—
756C42—942no—
757C42—942no—
758C42C2×C22⋊D4712yes—
759C42C2×C22⋊D4712yes—
760C42C23×D4712yes—
761C42C23×D4712yes—
762C23—22no—
763C23—22no—
764C23—41no—
765C23—41no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—944no—
770C23—942no—
771C23—3761no—
772C23—3761no—
773C23C22×C22⋊D4711yescharacteristic
774C23C22×C22⋊D4711yescharacteristic
775C23C22×C22⋊D4711yescharacteristic
776Q8—24no—
777Q8—42no—
778Q8—84no—
779Q8—474no—
780Q8—944no—
781Q8—942no—
782D4—24no—
783D4—42no—
784D4—82no—
785D4—82no—
786D4—474no—
787D4—944no—
788D4—948no—
789D4—948no—
790D4—942no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—84no—
807C2×C4—948no—
808C2×C4—944no—
809C2×C4—942no—
810C2×C4—948no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—3762no—
814C2×C4—3762no—
815C2×C4—3762no—
816C2×C4—3762no—
817C2×C4—3761no—
818C2×C4—3761no—
819C2×C4C22×C22⋊D4712yes—
820C2×C4C22×C22⋊D4711yescharacteristic
821C2×C4C22×C22⋊D4712yes—
822C2×C4C22×C22⋊D4712yes—
823C2×C4C22×C22⋊D4712yes—
824C2×C4C22×C22⋊D4711yescharacteristic
825C2×C4C22×C22⋊D4711yescharacteristic
826C2×C4#41×D4714yes—
827C2×C4C24×D4711yescharacteristic
828C8—944no—
829C8—944no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—944no—
844C22—3764no—
845C22—1882no—
846C22—1882no—
847C22#1568963012yes—
848C22C23×C22⋊D4711yescharacteristic
849C4—21no—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—944no—
859C4—1882no—
860C4—1882no—
861C4#1568963012yes—
862C4C2×#41×D4712yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—82no—
867C2—1884no—
868C2C2×#1568963011yescharacteristic
869C2#2025816811yescharacteristic
870C2#2025817511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#542C2
socleC22×C47C23×D4
prime radical#20252638C2
hypercenterC2×#542D47
hypocenterC47#60567
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #20256589C2semidirect
2. #20253659C2semidirect
3. #20253644C2semidirect
4. #20253611C2semidirect
5. #20253566C2semidirect
6. #20253332C2semidirect
7. #20253324C2semidirect
8. #20253197C2semidirect
9. #20252878C2semidirect
10. #20252646C2semidirect
12. C4×#13094055C2semidirect
13. C4×#13094050C2semidirect
14. #20252026C2semidirect
15. C2×C47×#542C2semidirect
21. #15689603C22semidirect
22. #15689603C22semidirect
23. #15689600C22semidirect
24. #15689597C22semidirect
32. #15689461C22semidirect
33. #15689456C22semidirect
34. #15689451C22semidirect
36. #15689439C22semidirect
37. #15689434C22semidirect
38. #15689415C22semidirect
39. #15689410C22semidirect
40. #15689405C22semidirect
41. #15689400C22semidirect
42. #15689342C22semidirect
43. #15689342C22semidirect
44. #15689335C22semidirect
45. #15689335C22semidirect
46. #15689283C22semidirect
47. #15689278C22semidirect
48. #15689273C22semidirect
52. #15689233C22semidirect
53. #15689228C22semidirect
54. #15689223C22semidirect
55. #15689221C22semidirect
56. C4×#10625337C22semidirect
57. C4×#10625336C22semidirect
58. C4×#10625335C22semidirect
59. C4×#10625334C22semidirect
60. #15689184C22semidirect
61. #15689184C22semidirect
62. #15689163C22semidirect
63. #15689163C22semidirect
64. #15689147C22semidirect
65. #15689132C22semidirect
66. #15689128C22semidirect
71. C4×#10625329C22semidirect
75. C47×#542C22semidirect
76. C2×C4⋊Q8×C47C22semidirect
79. C2×#124×C47C22semidirect
84. C2×C4×Q8×C47C22semidirect
85. C2×C4×D4×C47C22semidirect
428. C2×#542D47semidirect
457. #542C2×D47semidirect
458. C2×C4⋊Q8C2×D47semidirect
461. C2×#124C2×D47semidirect
477. C2×C4×Q8C2×D47semidirect
478. C2×C4×D4C2×D47semidirect
522. C47#60567semidirect

Maximal subgroups

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

subgroupindex
#202565892
#202536592
#202536442
#202536112
#202535662
#202533322
#202533242
#202531972
#202528782
#202526462
#202526382
C4×#130940552
C4×#130940502
#202520262
C2×C47×#5422
#6056747