Finite Group Databasebeta

← #14721565

Subgroups — #14721565

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082444C211yesmaximal, characteristic
2#13077655C211yesmaximal, characteristic, complemented
3#13071558C211yesmaximal, characteristic, complemented
4#13067192C211yesmaximal, characteristic, complemented
5#13067190C211yesmaximal, characteristic, complemented
6#13067157C211yesmaximal, characteristic, complemented
7#13067147C211yesmaximal, characteristic, complemented
8#13067143C211yesmaximal, characteristic, complemented
9#13067134C211yesmaximal, characteristic, complemented
10#13067130C211yesmaximal, characteristic, complemented
11#13067121C211yesmaximal, characteristic, complemented
12#13067120C211yesmaximal, characteristic, complemented
13#13067101C211yesmaximal, characteristic, complemented
14#13067099C211yesmaximal, characteristic, complemented
15C11×#1513C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17#10623362C411yescharacteristic, complemented
18#10623360C411yescharacteristic, complemented
19#10623322C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21#10623192—21no—
22#10623190—21no—
23#10623170C411yescharacteristic, complemented
24#10623164C411yescharacteristic, complemented
25D11×C22⋊Q8C2211yescharacteristic
26#10623155C2211yescharacteristic
27#10623145C411yescharacteristic, complemented
28#10623143C411yescharacteristic, complemented
29D11×#121C2211yescharacteristic
30#10623131C2211yescharacteristic
31#10623124—21no—
32#10623120—21no—
33#10623095—21no—
34#10623089—21no—
35#10623087—21no—
36#10623076—21no—
37#10623061C411yescharacteristic, complemented
38#10623060C411yescharacteristic, complemented
39C11×#407C2211yescharacteristic, complemented
40C11×#380C2211yescharacteristic, complemented
41C2×C11⋊#95C2211yescharacteristic, complemented
42#10622820C2211yescharacteristic, complemented
43#10622741—21no—
44#10622741—21no—
45#10622603—21no—
46#10622591—21no—
47#10622571—21no—
48C22⋊C4×Dic11—21no—
49#10622342—21no—
50#10622342—21no—
51#10622339C2211yescharacteristic
52#10622339C2211yescharacteristic
53#10622331C2211yescharacteristic, complemented
54#10622331C2211yescharacteristic, complemented
55#10622279C2211yescharacteristic
56#10622277C2211yescharacteristic
57#10622264C2211yescharacteristic, complemented
58#10622261C2211yescharacteristic, complemented
59C11×#328C2211yescharacteristic, complemented
60C11×#328C2211yescharacteristic, complemented
61C11×#327C2211yescharacteristic
62C11×#327C2211yescharacteristic
63#10622176C2211yescharacteristic, complemented
64#10622176C2211yescharacteristic, complemented
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622108C2211yescharacteristic
68#10622108C2211yescharacteristic
69#10622105C2211yescharacteristic, complemented
70#10622105C2211yescharacteristic, complemented
71#10622090C2211yescharacteristic, complemented
72#10622090C2211yescharacteristic, complemented
73#10622089C2211yescharacteristic
74#10622089C2211yescharacteristic
75C2×C11×#41C2×C411yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C2×Q8×D11C2×C411yescharacteristic, complemented
80C2×D4×D11—21no—
81C2×D4×D11C2×C411yescharacteristic, complemented
82C2×#4339C2×C411yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C2×C11×M16—21no—
85C11×#123—21no—
86C11×C22⋊Q8C2×C411yescharacteristic
87C11×C22⋊Q8C2311yescharacteristic
88C11×#121C2×C411yescharacteristic
89C11×#121C2311yescharacteristic
90C11×#120—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C11×#117C2×C411yescharacteristic
94C2×C11×C4⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96#67006—21no—
97C2×C22⋊Dic11D411yescharacteristic
98#67000C2×C411yescharacteristic, complemented
99#66999C2×C411yescharacteristic, complemented
100Q8×Dic11C2×C411yescharacteristic, complemented
101#66992—21no—
102#66992—21no—
103#66991—21no—
104#66991—21no—
105#66991—21no—
106#66991C2×C411yescharacteristic, complemented
107#66990—21no—
108#66990—21no—
109#66989—21no—
110#66989C2×C411yescharacteristic, complemented
111#66988—21no—
112#66988—21no—
113D4×Dic11—21no—
114D4×Dic11C2×C411yescharacteristic, complemented
115#66983C2×C411yescharacteristic
116#66983C2311yescharacteristic
117#66982—21no—
118#66982—21no—
119C4×C22⋊D11—21no—
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11C2×C411yescharacteristic
123C4×C22⋊D11C2×C411yescharacteristic
124C4×C22⋊D11C2×C411yescharacteristic
125C4×C22⋊D11C2×C411yescharacteristic
126C4×C22⋊D11D411yescharacteristic
127C4×C22⋊D11D411yescharacteristic
128C4×C22⋊D11D411yescharacteristic
129C4×C22⋊D11D411yescharacteristic
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4D411yescharacteristic
134#66979C2×C411yescharacteristic
135#66977—21no—
136#66977C2×C411yescharacteristic
137#66977C2311yescharacteristic
138C2×Dic11⋊C4D411yescharacteristic
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11C2311yescharacteristic
142C2×#4318—21no—
143C2×#4313—21no—
144C2×#4313—21no—
145#66951—21no—
146#66950C2×C411yescharacteristic, complemented
147#66949—21no—
148#66949—21no—
149#66948C2×C411yescharacteristic, complemented
150#66946—21no—
151#66946C2×C411yescharacteristic, complemented
152#66945—21no—
153#66945—21no—
154C4⋊C4×D11—21no—
155C4⋊C4×D11C2×C411yescharacteristic, complemented
156C4⋊C4×D11C2×C411yescharacteristic, complemented
157#66943C2×C411yescharacteristic, complemented
158#66943C2×C411yescharacteristic, complemented
159#66942—21no—
160#66940C2×C411yescharacteristic, complemented
161#66939—21no—
162#66938—21no—
163#66937—21no—
164#66937—21no—
165#66937—21no—
166#66936—21no—
167#66936—21no—
168#66936—21no—
169#66936—21no—
170(C22⋊D11)⋊C4—21no—
171(C22⋊D11)⋊C4—21no—
172C22⋊C4×D11—21no—
173C22⋊C4×D11—21no—
174C22⋊C4×D11—21no—
175#66932—21no—
176#66932—21no—
177#66932—21no—
178#66932—21no—
179#66931—21no—
180#66930—21no—
181#66929—21no—
182C4×D44—21no—
183#66925—21no—
184#66923—21no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8C2311yescharacteristic
187C11×C22⋊C8C2311yescharacteristic
188C11×#95C2311yescharacteristic
189C11×#95C2311yescharacteristic
190C11⋊#95—21no—
191C11⋊#95—21no—
192C11⋊#95—21no—
193C11⋊#95—21no—
194C11⋊#95—21no—
195C11⋊#95C2311yescharacteristic
196C11⋊#95C2311yescharacteristic
197C22⋊(C11⋊C8)—21no—
198C22⋊(C11⋊C8)C2311yescharacteristic
199C22⋊(C11⋊C8)C2311yescharacteristic
200(C2×D11)⋊C8—21no—
201(C2×D11)⋊C8—21no—
202Dic11⋊C8—21no—
203Dic11⋊C8—21no—
204C8×Dic11—21no—
205C8×Dic11—21no—
206#17623—111nomaximal, Sylow
207C24×C11C2×D411yescharacteristic
208C23×D11—21no—
209C23×D11C2×D411yescharacteristic
210C11×#41—81no—
211C2×Q8×C11C22×C411yescharacteristic
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11C22×C411yescharacteristic
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—81no—
220C22×C4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—21no—
227C2×C22⋊D11—21no—
228C2×C22⋊D11—21no—
229C2×C22⋊D11—21no—
230C2×C22⋊D11—21no—
231C2×C22⋊D11—41no—
232C2×C22⋊D11—41no—
233C2×C22⋊D11C22⋊C411yescharacteristic
234C2×C22⋊D11C22⋊C411yescharacteristic
235C2×C22⋊D11C22⋊C411yescharacteristic
236C2×C22⋊D11C22⋊C411yescharacteristic
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—81no—
243C22×Dic11C2×D411yescharacteristic
244C22×Dic11C2×D411yescharacteristic
245C22×Dic11C2×D411yescharacteristic
246Q8×D11—81no—
247D4×D11—42no—
248D4×D11—42no—
249D4×D11—81no—
250#4339—81no—
251C2×D44—21no—
252C2×D44C22×C411yescharacteristic
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—81no—
259C2×C4×D11C22×C411yescharacteristic
260C2×C4×D11C22×C411yescharacteristic
261C2×C4×D11C2×D411yescharacteristic
262C2×C4×D11C2×D411yescharacteristic
263C2×Dic22—21no—
264C2×Dic22C22×C411yescharacteristic
265C11×M16—81no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—81no—
271C11×C4⋊C4C22×C411yescharacteristic
272C11×C4⋊C4C22×C411yescharacteristic
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—21no—
277C11×C22⋊C4—21no—
278C11×C22⋊C4—42no—
279C42×C11—21no—
280C22⋊Dic11—21no—
281C22⋊Dic11—21no—
282C22⋊Dic11—21no—
283C22⋊Dic11—21no—
284C22⋊Dic11—21no—
285C22⋊Dic11—21no—
286C22⋊Dic11—21no—
287C22⋊Dic11C22⋊C411yescharacteristic
288C22⋊Dic11C22⋊C411yescharacteristic
289C22⋊Dic11C22⋊C411yescharacteristic
290C22⋊Dic11C22⋊C411yescharacteristic
291(C2×D11)⋊C4—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—42no—
300(C2×D11)⋊C4—81no—
301(C2×D11)⋊C4C22⋊C411yescharacteristic
302(C2×D11)⋊C4C22⋊C411yescharacteristic
303(C2×D11)⋊C4C22⋊C411yescharacteristic
304(C2×D11)⋊C4C22⋊C411yescharacteristic
305C4⋊Dic11—21no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11—21no—
309C4⋊Dic11C22×C411yescharacteristic
310C4⋊Dic11C22×C411yescharacteristic
311Dic11⋊C4—21no—
312Dic11⋊C4—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4C22⋊C411yescharacteristic
320Dic11⋊C4C22⋊C411yescharacteristic
321Dic11⋊C4C22⋊C411yescharacteristic
322Dic11⋊C4C22⋊C411yescharacteristic
323C4×Dic11—21no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—42no—
327C4×Dic11—81no—
328C4×Dic11C22×C411yescharacteristic
329C4×Dic11C22×C411yescharacteristic
330C4×Dic11C2×D411yescharacteristic
331C4×Dic11C2×D411yescharacteristic
332#4318—81no—
333C2×C11⋊C8—21no—
334C2×C11⋊C8—21no—
335#4313—81no—
336#4313—81no—
337#3505—111no—
338#2975—111no—
339#2353—111no—
340#1521—111no—
341#1521—111no—
342#1513—111no—
343#1513D1111yescharacteristic, complemented
344#1511—111no—
345#1510—111no—
346#1508—111no—
347#1507—111no—
348#1504—111no—
349#1504—111no—
350#1500—111no—
351#1500—111no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11C2×C22⋊C411yescharacteristic
358C23×C11C2×C22⋊C411yescharacteristic
359C23×C11C22×D411yescharacteristic
360C22×D11—21no—
361C22×D11—21no—
362C22×D11—21no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—42no—
366C22×D11—81no—
367C22×D11—81no—
368C22×D11C2×C22⋊C411yescharacteristic
369C22×D11C2×C22⋊C411yescharacteristic
370Q8×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—81no—
375D4×C11—81no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—81no—
392C2×C4×C11C2×C22⋊C411yescharacteristic
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C23×C411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C22⋊D11—41no—
397C22⋊D11—41no—
398C22⋊D11—41no—
399C22⋊D11—41no—
400C22⋊D11—42no—
401C22⋊D11—41no—
402C22⋊D11—41no—
403C22⋊D11—81no—
404C22⋊D11—81no—
405C22⋊D11—81no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—22no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—81no—
420C2×Dic11—84no—
421C2×Dic11C2×C22⋊C411yescharacteristic
422C2×Dic11C2×C22⋊C411yescharacteristic
423C2×Dic11C2×C22⋊C411yescharacteristic
424C2×Dic11C2×C22⋊C411yescharacteristic
425C2×Dic11C2×C22⋊C411yescharacteristic
426C2×Dic11C2×C22⋊C411yescharacteristic
427D44—41no—
428D44—42no—
429C4×D11—41no—
430C4×D11—41no—
431C4×D11—41no—
432C4×D11—41no—
433C4×D11—42no—
434C4×D11—81no—
435C4×D11—81no—
436C4×D11—81no—
437C4×D11—81no—
438Dic22—41no—
439Dic22—81no—
440C8×C11—41no—
441C8×C11—41no—
442C11⋊C8—41no—
443C11⋊C8—41no—
444#553—111no—
445#553—111no—
446#553—221no—
447#553—221no—
448#552—111no—
449#552—111no—
450#551—221no—
451#551—221no—
452#548—111no—
453#548—111no—
454#546—111no—
455#546—111no—
456#539—221no—
457#538—221no—
458#534—221no—
459#529—111no—
460#529—111no—
461#525—111no—
462#525C2×D1111yescharacteristic
463C2×C22⋊Q8—111no—
464C2×#121—111no—
465#518—221no—
466C2×C4×D4—111no—
467#436—221no—
468#436—221no—
469#436—221no—
470#436—221no—
471#431—111no—
472#431—111no—
473#407—111no—
474#407—111no—
475#407—111no—
476#407C2×D1111yescharacteristic, complemented
477#388—221no—
478#387—221no—
479#386—221no—
480#383—111no—
481#381—111no—
482#380C2×D1111yescharacteristic, complemented
483C4×C22⋊C4—111no—
484C4×C22⋊C4—221no—
485#376—111no—
486C2×#95—111no—
487#328—111no—
488#328—111no—
489#328—111no—
490#328—111no—
491#328—111no—
492#328—111no—
493#328C2×D1111yescharacteristic, complemented
494#328C2×D1111yescharacteristic, complemented
495#327—111no—
496#327—111no—
497#327—111no—
498#327—111no—
499#327—111no—
500#327—111no—
501#327C2×D1111yescharacteristic
502#327C2×D1111yescharacteristic
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—41no—
514C22×C11—41no—
515C22×C11—41no—
516C22×C11C22×C22⋊C411yescharacteristic
517C22×C11#57511yescharacteristic
518C22×C11#57511yescharacteristic
519C2×D11—21no—
520C2×D11—21no—
521C2×D11—21no—
522C2×D11—21no—
523C2×D11—21no—
524C2×D11—21no—
525C2×D11—41no—
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—81no—
529C2×D11—81no—
530C2×D11—162no—
531C4×C11—21no—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—41no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11—81no—
539C4×C11—81no—
540Dic11—21no—
541Dic11—21no—
542Dic11—21no—
543Dic11—21no—
544Dic11—21no—
545Dic11—21no—
546Dic11—42no—
547Dic11—41no—
548Dic11—41no—
549Dic11—41no—
550Dic11—81no—
551C2×#41—111no—
552C2×#41C4×D1111yescharacteristic
553C22×Q8—111no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—221no—
557C23×C4—111no—
558C23×C4—221no—
559C23×C4C22×D1111yescharacteristic
560C2×M16—21no—
561C2×M16—221no—
562C2×M16—221no—
563C2×M16—221no—
564#126—221no—
565#126—221no—
566#126—221no—
567#126—221no—
568#126—221no—
569#126—221no—
570#125—111no—
571#125—111no—
572#125—221no—
573#125—221no—
574#124—111no—
575#124—111no—
576#124—221no—
577#124—221no—
578#123—21no—
579#123—221no—
580#123—221no—
581#123—221no—
582#123—221no—
583#123—221no—
584#123—221no—
585#123—221no—
586#123—221no—
587#123—221no—
588C22⋊Q8—111no—
589C22⋊Q8—111no—
590C22⋊Q8—111no—
591C22⋊Q8—111no—
592C22⋊Q8—221no—
593C22⋊Q8—221no—
594C22⋊Q8—221no—
595C22⋊Q8—221no—
596C22⋊Q8C4×D1111yescharacteristic
597C22⋊Q8C22×D1111yescharacteristic
598#121—111no—
599#121—111no—
600#121—111no—
601#121—111no—
602#121—221no—
603#121—221no—
604#121—221no—
605#121—221no—
606#121—221no—
607#121—221no—
608#121—221no—
609#121—221no—
610#121C4×D1111yescharacteristic
611#121C22×D1111yescharacteristic
612#120—21no—
613#120—221no—
614#120—221no—
615#120—221no—
616C4×Q8—111no—
617C4×Q8—111no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—111no—
621C4×D4—111no—
622C4×D4—111no—
623C4×D4—111no—
624C4×D4—111no—
625C4×D4—111no—
626C4×D4—111no—
627C4×D4—111no—
628C4×D4—111no—
629C4×D4—111no—
630C4×D4—221no—
631C4×D4—221no—
632C4×D4—221no—
633C4×D4—221no—
634C4×D4—221no—
635C4×D4—221no—
636C4×D4—221no—
637C4×D4—221no—
638#117—111no—
639#117—221no—
640#117—221no—
641#117—221no—
642#117—221no—
643#117C4×D1111yescharacteristic
644C2×C4⋊C4—21no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—221no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4—111no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C22⋊C4—221no—
657C2×C22⋊C4—221no—
658C2×C42—111no—
659C2×C42—221no—
660C2×C42—221no—
661C4⋊C8—221no—
662C4⋊C8—221no—
663C22⋊C8—21no—
664C22⋊C8—111no—
665C22⋊C8—111no—
666C22⋊C8—221no—
667C22⋊C8—221no—
668C22⋊C8—221no—
669C22⋊C8C22×D1111yescharacteristic
670C22⋊C8C22×D1111yescharacteristic
671C4×C8—221no—
672C4×C8—221no—
673#95—111no—
674#95—111no—
675#95—221no—
676#95—221no—
677#95—221no—
678#95—221no—
679#95—221no—
680#95C22×D1111yescharacteristic
681#95C22×D1111yescharacteristic
682C2×C11—21no—
683C2×C11—21no—
684C2×C11—41no—
685C2×C11—41no—
686C2×C11—81no—
687C2×C11#288311yescharacteristic
688C2×C11#289611yescharacteristic
689C2×C11#290111yescharacteristic
690D11—41no—
691D11—41no—
692D11—81no—
693C24—111no—
694C24—221no—
695C24D4×D1111yescharacteristic
696#41—81no—
697#41—881no—
698C2×Q8—111no—
699C2×Q8—221no—
700C2×Q8—881no—
701C2×Q8C2×C4×D1111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—111no—
706C2×D4—111no—
707C2×D4—111no—
708C2×D4—111no—
709C2×D4—111no—
710C2×D4—221no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—221no—
714C2×D4—221no—
715C2×D4—221no—
716C2×D4—441no—
717C2×D4—441no—
718C2×D4—442no—
719C2×D4—442no—
720C2×D4—881no—
721C2×D4C2×C4×D1111yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—81no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—111no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—442no—
742C22×C4—442no—
743C22×C4—881no—
744C22×C4—881no—
745C22×C4C2×C4×D1111yescharacteristic
746C22×C4C2×C4×D1111yescharacteristic
747C22×C4D4×D1111yescharacteristic
748C22×C4D4×D1111yescharacteristic
749C22×C4D4×D1111yescharacteristic
750C22×C4C23×D1111yescharacteristic
751M16—81no—
752M16—881no—
753M16—881no—
754M16—881no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—221no—
758C2×C8—221no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—81no—
762C4⋊C4—111no—
763C4⋊C4—111no—
764C4⋊C4—111no—
765C4⋊C4—111no—
766C4⋊C4—111no—
767C4⋊C4—111no—
768C4⋊C4—221no—
769C4⋊C4—221no—
770C4⋊C4—221no—
771C4⋊C4—221no—
772C4⋊C4—221no—
773C4⋊C4—221no—
774C4⋊C4—221no—
775C4⋊C4—221no—
776C4⋊C4—221no—
777C4⋊C4—221no—
778C4⋊C4—221no—
779C4⋊C4—221no—
780C4⋊C4C2×C4×D1111yescharacteristic
781C4⋊C4C2×C4×D1111yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—42no—
788C22⋊C4—111no—
789C22⋊C4—111no—
790C22⋊C4—111no—
791C22⋊C4—111no—
792C22⋊C4—111no—
793C22⋊C4—111no—
794C22⋊C4—111no—
795C22⋊C4—111no—
796C22⋊C4—221no—
797C22⋊C4—221no—
798C22⋊C4—221no—
799C22⋊C4—221no—
800C22⋊C4—221no—
801C22⋊C4—221no—
802C22⋊C4—221no—
803C22⋊C4—221no—
804C22⋊C4—221no—
805C22⋊C4—221no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—442no—
812C22⋊C4—881no—
813C42—21no—
814C42—111no—
815C42—111no—
816C42—111no—
817C42—111no—
818C42—221no—
819C42—221no—
820C42—221no—
821C42—442no—
822C42—881no—
823C11#1762311yescharacteristic, complemented, Sylow
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—111no—
830C23—111no—
831C23—221no—
832C23—221no—
833C23—221no—
834C23—441no—
835C23—441no—
836C23—442no—
837C23—881no—
838C23—881no—
839C23C22⋊C4×D1111yescharacteristic
840C23C22⋊C4×D1111yescharacteristic
841C23C2×D4×D1111yescharacteristic
842Q8—41no—
843Q8—441no—
844Q8—881no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—81no—
849D4—81no—
850D4—441no—
851D4—442no—
852D4—441no—
853D4—441no—
854D4—441no—
855D4—441no—
856D4—442no—
857D4—441no—
858D4—441no—
859D4—881no—
860D4—881no—
861D4—881no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—111no—
879C2×C4—111no—
880C2×C4—111no—
881C2×C4—111no—
882C2×C4—111no—
883C2×C4—111no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—222no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—442no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—881no—
903C2×C4—881no—
904C2×C4—881no—
905C2×C4—881no—
906C2×C4—881no—
907C2×C4—884no—
908C2×C4C22⋊C4×D1111yescharacteristic
909C2×C4C22⋊C4×D1111yescharacteristic
910C2×C4C22×C4×D1111yescharacteristic
911C2×C4C2×D4×D1111yescharacteristic
912C8—41no—
913C8—41no—
914C8—441no—
915C8—441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—42no—
925C22—42no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—221no—
930C22—221no—
931C22—221no—
932C22—221no—
933C22—221no—
934C22—221no—
935C22—441no—
936C22—441no—
937C22—441no—
938C22—881no—
939C22—881no—
940C22—1762no—
941C22C2×C22⋊C4×D1111yescharacteristic
942C22#1062330411yescharacteristic
943C22#1062330811yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C4—221no—
954C4—221no—
955C4—221no—
956C4—221no—
957C4—221no—
958C4—221no—
959C4—442no—
960C4—441no—
961C4—441no—
962C4—441no—
963C4—881no—
964C2—21no—
965C2—21no—
966C2—41no—
967C2—41no—
968C2—81no—
969C2—441no—
970C2—441no—
971C2—881no—
972C2#1307707411yescharacteristic
973C2#1307713211yescharacteristic
974C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1513C2
socleC22×C11C22×C22⋊C4
prime radical#13082444C2
cosocleC22×C4×C11C24
hypercenter#1513D11
hypocenterC11#17623
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #13077655C2semidirect
3. #13071558C2semidirect
4. #13067192C2semidirect
5. #13067190C2semidirect
6. #13067157C2semidirect
7. #13067147C2semidirect
8. #13067143C2semidirect
9. #13067134C2semidirect
10. #13067130C2semidirect
11. #13067121C2semidirect
12. #13067120C2semidirect
13. #13067101C2semidirect
14. #13067099C2semidirect
15. C11×#1513C2semidirect
17. #10623362C4semidirect
18. #10623360C4semidirect
23. #10623170C4semidirect
24. #10623164C4semidirect
27. #10623145C4semidirect
28. #10623143C4semidirect
37. #10623061C4semidirect
38. #10623060C4semidirect
39. C11×#407C22semidirect
40. C11×#380C22semidirect
41. C2×C11⋊#95C22semidirect
42. #10622820C22semidirect
53. #10622331C22semidirect
54. #10622331C22semidirect
57. #10622264C22semidirect
58. #10622261C22semidirect
59. C11×#328C22semidirect
60. C11×#328C22semidirect
63. #10622176C22semidirect
64. #10622176C22semidirect
69. #10622105C22semidirect
70. #10622105C22semidirect
71. #10622090C22semidirect
72. #10622090C22semidirect
79. C2×Q8×D11C2×C4semidirect
81. C2×D4×D11C2×C4semidirect
98. #67000C2×C4semidirect
99. #66999C2×C4semidirect
100. Q8×Dic11C2×C4semidirect
106. #66991C2×C4semidirect
110. #66989C2×C4semidirect
114. D4×Dic11C2×C4semidirect
146. #66950C2×C4semidirect
149. #66948C2×C4semidirect
151. #66946C2×C4semidirect
155. C4⋊C4×D11C2×C4semidirect
156. C4⋊C4×D11C2×C4semidirect
157. #66943C2×C4semidirect
158. #66943C2×C4semidirect
160. #66940C2×C4semidirect
343. #1513D11semidirect
476. #407C2×D11semidirect
482. #380C2×D11semidirect
493. #328C2×D11semidirect
494. #328C2×D11semidirect
823. C11#17623semidirect

Maximal subgroups

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

subgroupindex
#130824442
#130776552
#130715582
#130671922
#130671902
#130671572
#130671472
#130671432
#130671342
#130671302
#130671212
#130671202
#130671012
#130670992
C11×#15132
#1762311