Finite Group Databasebeta

← #14729057

Subgroups — #14729057

Order 2816.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079413C211yesmaximal, characteristic, complemented
2#13079377C211yesmaximal, characteristic, complemented
3#13076618C211yesmaximal, characteristic, complemented
4#13067664C211yesmaximal, characteristic, complemented
5#13067653C211yesmaximal, characteristic, complemented
6#13067647C211yesmaximal, characteristic, complemented
7#13067636C211yesmaximal, characteristic, complemented
8#13067562C211yesmaximal, characteristic, complemented
9#13067551C211yesmaximal, characteristic, complemented
10#13067545C211yesmaximal, characteristic, complemented
11#13067534C211yesmaximal, characteristic, complemented
12#13067184C211yesmaximal, characteristic, complemented
13#13067159C211yesmaximal, characteristic, complemented
14#13066964C211yesmaximal, characteristic, complemented
15C11×#3534C211yesmaximal, characteristic, complemented
16C11×#562—21no—
17C11×#560—21no—
18C11×#553—21no—
19C11×#551—21no—
20C11×#546—21no—
21C11×#546—21no—
22C11×#546—21no—
23D42×C11—21no—
24C11×#540—21no—
25C11×#539—21no—
26C11×#539C2211yescharacteristic
27C11×#538—21no—
28C11×#538C2211yescharacteristic
29C11×#537C2211yescharacteristic
30C11×#534—21no—
31C11×#534C2211yescharacteristic
32C11×#525C2211yescharacteristic
33C2×C11×#123C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C2×#66983C2211yescharacteristic, complemented
36#10622851—21no—
37#10622836—21no—
38#10622830—21no—
39#10622825C2211yescharacteristic, complemented
40#10622820C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
42#10622661—21no—
43#10622659C2211yescharacteristic, complemented
44#10622657C2211yescharacteristic, complemented
45#10622652—21no—
46#10622652—21no—
47#10622651—21no—
48#10622649C2211yescharacteristic
49#10622649C2211yescharacteristic, complemented
50#10622649C2211yescharacteristic, complemented
51#10622647C2211yescharacteristic
52#10622647C2211yescharacteristic, complemented
53#10622647C2211yescharacteristic, complemented
54#10622616—21no—
55#10622607—21no—
56#10622604C2211yescharacteristic, complemented
57#10622599C2211yescharacteristic, complemented
58#10622581—21no—
59#10622574—21no—
60#10622573C2211yescharacteristic, complemented
61#10622572—21no—
62#10622562C2211yescharacteristic, complemented
63#10622176C2211yescharacteristic, complemented
64#10622176C2211yescharacteristic, complemented
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622175C2211yescharacteristic, complemented
68#10622175C2211yescharacteristic, complemented
69#10622175C2211yescharacteristic, complemented
70#10622175C2211yescharacteristic, complemented
71#10622166C2211yescharacteristic, complemented
72#10622166C2211yescharacteristic, complemented
73#10622163C2211yescharacteristic, complemented
74#10622163C2211yescharacteristic, complemented
75C2×C11×#41—21no—
76C2×C11×#41D411yescharacteristic, complemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11D411yescharacteristic, complemented
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×D44C2311yescharacteristic
86C11×#127—21no—
87C11×#126—21no—
88C11×#126—21no—
89C11×#126—21no—
90C11×#126—21no—
91C11×#125—21no—
92C11×#125—21no—
93C11×#124—21no—
94C11×#124—21no—
95C11×#124—21no—
96C11×#123—21no—
97C11×#123—21no—
98C11×#123—21no—
99C11×#123—21no—
100C11×#123—21no—
101C11×#123—21no—
102C11×#123—21no—
103C11×#123—21no—
104C11×#123—21no—
105C11×#123—21no—
106C11×#123—21no—
107C11×#123—21no—
108C11×#123—21no—
109C11×#123—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8D411yescharacteristic, complemented
116C11×C22⋊Q8C2311yescharacteristic
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121D411yescharacteristic, complemented
133C11×#121D411yescharacteristic, complemented
134C11×#121D411yescharacteristic, complemented
135C11×#121C2311yescharacteristic
136C11×#121C2311yescharacteristic
137C11×#121C2311yescharacteristic
138C11×#120—21no—
139C11×#120—21no—
140C11×#120—21no—
141C11×#120—21no—
142C11×#120—21no—
143C11×#120—21no—
144C11×#120—21no—
145C11×#120—21no—
146C4×D4×C11—21no—
147C4×D4×C11—21no—
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C4×D4×C11—21no—
151C4×D4×C11—21no—
152C4×D4×C11—21no—
153C4×D4×C11—21no—
154C11×#117—21no—
155C11×#117D411yescharacteristic, complemented
156C2×C11×C4⋊C4D411yescharacteristic
157C2×C11×C4⋊C4D411yescharacteristic, complemented
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4—21no—
162C2×C11×C22⋊C4D411yescharacteristic
163C2×C11×C22⋊C4D411yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C22⋊Dic11—21no—
166C2×C22⋊Dic11—21no—
167C2×#4325—21no—
168C2×#4323—21no—
169C2×#4323—21no—
170C2×#4323—21no—
171#66983—21no—
172#66983—21no—
173#66983—21no—
174#66983—21no—
175C2×(C2×D11)⋊C4—21no—
176C2×(C2×D11)⋊C4—21no—
177C2×(C2×D11)⋊C4—21no—
178C2×(C2×D11)⋊C4—21no—
179C2×C4⋊Dic11—21no—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×Dic11⋊C4—21no—
182C2×#4318—21no—
183C22×C11⋊C8—21no—
184#66899—21no—
185#66896—21no—
186#66896—21no—
187#66896—21no—
188C11⋊#95—21no—
189C11⋊#95—21no—
190C11⋊#95C2311yescharacteristic
191C11⋊#95C2311yescharacteristic
192C22⋊(C11⋊C8)—21no—
193C22⋊(C11⋊C8)—21no—
194C22⋊(C11⋊C8)C2311yescharacteristic
195C22⋊(C11⋊C8)C2311yescharacteristic
196C22⋊(C11⋊C8)C2311yescharacteristic
197C22⋊(C11⋊C8)C2311yescharacteristic
198#66873—21no—
199#66873—21no—
200#66873—21no—
201#66873—21no—
202#66872—21no—
203#66872—21no—
204#66872—21no—
205#66871—21no—
206#18446—111nomaximal, Sylow
207C24×C11—21no—
208C24×C11—21no—
209C24×C11C2×D411yescharacteristic
210C24×C11C2×D411yescharacteristic
211C23×D11—21no—
212C11×#41—81no—
213C11×#41—81no—
214C11×#41—81no—
215C2×Q8×C11—21no—
216C2×Q8×C11C2×D411yescharacteristic
217C2×D4×C11—21no—
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—81no—
235C2×D4×C11—81no—
236C2×D4×C11—81no—
237C2×D4×C11—81no—
238C2×D4×C11—81no—
239C2×D4×C11—81no—
240C2×D4×C11—82no—
241C2×D4×C11C2×D411yescharacteristic
242C2×D4×C11C2×D411yescharacteristic
243C2×D4×C11C2×D411yescharacteristic
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—81no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—41no—
262C2×C22⋊D11—41no—
263C2×C22⋊D11—81no—
264C2×C22⋊D11—81no—
265C2×C22⋊D11—81no—
266C2×C22⋊D11—81no—
267C2×C22⋊D11—81no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C2×D44—21no—
272C2×D44—21no—
273C2×D44—81no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C22⋊C4—21no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—21no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—21no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—21no—
316C42×C11—21no—
317C42×C11—21no—
318C42×C11—21no—
319C22⋊Dic11—81no—
320C22⋊Dic11—81no—
321#4325—81no—
322#4323—81no—
323#4323—81no—
324#4323—81no—
325(C2×D11)⋊C4—41no—
326(C2×D11)⋊C4—41no—
327(C2×D11)⋊C4—81no—
328(C2×D11)⋊C4—81no—
329(C2×D11)⋊C4—81no—
330C4⋊Dic11—21no—
331C4⋊Dic11—21no—
332C4⋊Dic11—81no—
333Dic11⋊C4—81no—
334#4318—81no—
335C2×C11⋊C8—21no—
336C2×C11⋊C8—21no—
337C2×C11⋊C8—21no—
338C2×C11⋊C8—21no—
339C2×C11⋊C8—81no—
340#3534D1111yescharacteristic, complemented
341#3192—111no—
342#3188—111no—
343#2813—111no—
344#1618—111no—
345#1616—111no—
346#1615—111no—
347#1613—111no—
348#1600—111no—
349#1598—111no—
350#1597—111no—
351#1595—111no—
352#1519—111no—
353#1513—111no—
354#1468—111no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—21no—
358C23×C11—21no—
359C23×C11—21no—
360C23×C11—21no—
361C23×C11—21no—
362C23×C11—21no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—42no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—81no—
369C23×C11—81no—
370C23×C11—81no—
371C23×C11—81no—
372C23×C11—81no—
373C23×C11#12011yescharacteristic
374C23×C11#12011yescharacteristic
375C23×C11C22×D411yescharacteristic
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383Q8×C11—41no—
384Q8×C11—81no—
385D4×C11—41no—
386D4×C11—41no—
387D4×C11—41no—
388D4×C11—42no—
389D4×C11—42no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—41no—
394D4×C11—41no—
395D4×C11—41no—
396D4×C11—81no—
397D4×C11—81no—
398D4×C11—81no—
399D4×C11—81no—
400D4×C11—81no—
401D4×C11—81no—
402D4×C11—81no—
403D4×C11—81no—
404D4×C11—81no—
405D4×C11—81no—
406D4×C11—81no—
407D4×C11—81no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—81no—
427C2×C4×C11—81no—
428C2×C4×C11—81no—
429C2×C4×C11—81no—
430C2×C4×C11—81no—
431C2×C4×C11—81no—
432C2×C4×C11—81no—
433C2×C4×C11#12011yescharacteristic
434C2×C4×C11#12011yescharacteristic
435C2×C4×C11C22×D411yescharacteristic
436C2×C4×C11C22×D411yescharacteristic
437C22⋊D11—82no—
438C22⋊D11—82no—
439C22⋊D11—84no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449D44—41no—
450D44—41no—
451D44—41no—
452D44—41no—
453C11⋊C8—41no—
454C11⋊C8—41no—
455C11⋊C8—41no—
456C11⋊C8—41no—
457#562—21no—
458#560—21no—
459#553—21no—
460#551—21no—
461#546—21no—
462#546—21no—
463#546—21no—
464D42—21no—
465#540—21no—
466#539—21no—
467#539C2×D1111yescharacteristic
468#538—21no—
469#538C2×D1111yescharacteristic
470#537C2×D1111yescharacteristic
471#534—21no—
472#534C2×D1111yescharacteristic
473#525C2×D1111yescharacteristic
474C2×#123C2×D1111yescharacteristic
475C2×#121—111no—
476C2×#121C2×D1111yescharacteristic
477#484—111no—
478#482—221no—
479#481—111no—
480#481—111no—
481#481—111no—
482#481—221no—
483#469—221no—
484#469—221no—
485#466—221no—
486#465—221no—
487#450—111no—
488#449—221no—
489#447—111no—
490#447—111no—
491#447—111no—
492#447—221no—
493#407—111no—
494C2×C22⋊C8—111no—
495#400—111no—
496#399—111no—
497#396—221no—
498#394—111no—
499#394—221no—
500#394—221no—
501#392—111no—
502#392—221no—
503#380—111no—
504#328—111no—
505#328—111no—
506#327—111no—
507#327—111no—
508#327—111no—
509#327—111no—
510#327—111no—
511#327—111no—
512#324—111no—
513#324—111no—
514#323—111no—
515#323—111no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—41no—
525C22×C11—41no—
526C22×C11—41no—
527C22×C11—41no—
528C22×C11—41no—
529C22×C11—41no—
530C22×C11—41no—
531C22×C11—41no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11—41no—
535C22×C11—41no—
536C22×C11—81no—
537C22×C11—81no—
538C22×C11—81no—
539C22×C11—81no—
540C22×C11—162no—
541C22×C11—162no—
542C22×C11C2×#12011yescharacteristic
543C22×C11#57611yescharacteristic
544C22×C11#57711yescharacteristic
545C2×D11—81no—
546C2×D11—81no—
547C2×D11—81no—
548C2×D11—81no—
549C2×D11—81no—
550C2×D11—81no—
551C2×D11—81no—
552C4×C11—21no—
553C4×C11—21no—
554C4×C11—21no—
555C4×C11—21no—
556C4×C11—41no—
557C4×C11—41no—
558C4×C11—41no—
559C4×C11—41no—
560C4×C11—41no—
561C4×C11—41no—
562C4×C11—41no—
563C4×C11—41no—
564Dic11—81no—
565Dic11—81no—
566Dic11—81no—
567C2×#41—21no—
568C2×#41C22⋊D1111yescharacteristic, complemented
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—111no—
573C22×D4—221no—
574C22×D4—221no—
575C22×D4C22⋊D1111yescharacteristic
576C22×D4C22⋊D1111yescharacteristic, complemented
577C23×C4C22×D1111yescharacteristic
578C2×SD16—221no—
579C2×D8—221no—
580C2×D8—221no—
581C2×D8—221no—
582C2×M16—221no—
583C22×C8—221no—
584#127—21no—
585#126—21no—
586#126—21no—
587#126—21no—
588#126—21no—
589#125—21no—
590#125—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607#123—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8C22⋊D1111yescharacteristic, complemented
614C22⋊Q8C22×D1111yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—221no—
631#121—221no—
632#121—221no—
633#121—221no—
634#121C22⋊D1111yescharacteristic, complemented
635#121C22⋊D1111yescharacteristic, complemented
636#121C22⋊D1111yescharacteristic, complemented
637#121C22×D1111yescharacteristic
638#121C22×D1111yescharacteristic
639#121C22×D1111yescharacteristic
640#120—21no—
641#120—21no—
642#120—21no—
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656#117—21no—
657#117C22⋊D1111yescharacteristic, complemented
658C2×C4⋊C4—111no—
659C2×C4⋊C4—221no—
660C2×C4⋊C4—221no—
661C2×C4⋊C4C22⋊D1111yescharacteristic
662C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—221no—
668C2×C22⋊C4—221no—
669C2×C22⋊C4—221no—
670C2×C22⋊C4—221no—
671C2×C22⋊C4—221no—
672C2×C22⋊C4—221no—
673C2×C22⋊C4C22⋊D1111yescharacteristic
674C2×C22⋊C4C22⋊D1111yescharacteristic
675C2×C22⋊C4C22×D1111yescharacteristic
676#107—221no—
677#106—221no—
678#106—221no—
679#106—221no—
680#103—221no—
681#102—221no—
682#102—221no—
683#102—221no—
684#102—221no—
685#102—221no—
686#102—221no—
687#102—221no—
688C22⋊C8—111no—
689C22⋊C8—111no—
690C22⋊C8—111no—
691C22⋊C8—111no—
692C22⋊C8—221no—
693C22⋊C8—221no—
694#95—111no—
695#95—111no—
696#95—221no—
697#95—221no—
698C2×C11—21no—
699C2×C11—21no—
700C2×C11—41no—
701C2×C11—41no—
702C2×C11—81no—
703C2×C11—81no—
704C2×C11—81no—
705C2×C11—81no—
706C2×C11#301211yescharacteristic
707C2×C11#302111yescharacteristic
708C2×C11#302611yescharacteristic
709D11—161no—
710C24—21no—
711C24—21no—
712C24—221no—
713C24C2×C22⋊D1111yescharacteristic
714C24C2×C22⋊D1111yescharacteristic
715#41—81no—
716#41—81no—
717#41—81no—
718C2×Q8—21no—
719C2×Q8C2×C22⋊D1111yescharacteristic
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—82no—
744C2×D4—221no—
745C2×D4—221no—
746C2×D4—441no—
747C2×D4—441no—
748C2×D4—881no—
749C2×D4—881no—
750C2×D4—881no—
751C2×D4—881no—
752C2×D4—881no—
753C2×D4—881no—
754C2×D4C2×C22⋊D1111yescharacteristic
755C2×D4C2×C22⋊D1111yescharacteristic
756C2×D4C2×C22⋊D1111yescharacteristic
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—81no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4C2×C22⋊D1111yescharacteristic
769C22×C4C2×C22⋊D1111yescharacteristic
770C22×C4C2×C22⋊D1111yescharacteristic
771C22×C4C2×C22⋊D1111yescharacteristic
772C22×C4C2×C22⋊D1111yescharacteristic
773C22×C4C2×C22⋊D1111yescharacteristic
774C22×C4C2×C22⋊D1111yescharacteristic
775C22×C4C2×C22⋊D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777SD16—881no—
778D8—881no—
779D8—881no—
780D8—881no—
781M16—881no—
782C2×C8—221no—
783C2×C8—221no—
784C2×C8—221no—
785C2×C8—221no—
786C2×C8—881no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—221no—
801C4⋊C4—221no—
802C4⋊C4—881no—
803C4⋊C4—881no—
804C4⋊C4C2×C22⋊D1111yescharacteristic
805C4⋊C4C2×C22⋊D1111yescharacteristic
806C4⋊C4C2×C22⋊D1111yescharacteristic
807C4⋊C4C2×C22⋊D1111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—441no—
834C22⋊C4—441no—
835C22⋊C4—881no—
836C22⋊C4—881no—
837C22⋊C4—881no—
838C22⋊C4—881no—
839C22⋊C4—881no—
840C42—21no—
841C42—21no—
842C42—21no—
843C11#1844611yescharacteristic, complemented, Sylow
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—81no—
858C23—81no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—441no—
863C23—441no—
864C23—441no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23#6700611yescharacteristic
870C23#6700611yescharacteristic
871C23C22×C22⋊D1111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—441no—
898D4—441no—
899D4—441no—
900D4—441no—
901D4—882no—
902D4—882no—
903D4—884no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4#6700611yescharacteristic
939C2×C4#6700611yescharacteristic
940C2×C4C22×C22⋊D1111yescharacteristic
941C2×C4C22×C22⋊D1111yescharacteristic
942C8—441no—
943C8—441no—
944C8—441no—
945C8—441no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—162no—
971C22—162no—
972C22—881no—
973C22—881no—
974C22—881no—
975C22—881no—
976C22—881no—
977C22—881no—
978C22—881no—
979C22#1062336611yescharacteristic
980C22#1062336711yescharacteristic
981C22C2×#6700611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—881no—
995C4—881no—
996C4—881no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—1761no—
1006C2#1307792011yescharacteristic
1007C2#1307798811yescharacteristic
1008C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3534C2
socleC22×C11C2×#120
hypercenter#3534D11
hypocenterC11#18446
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3534

Complements

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

NH ≅ G/Ntype
1. #13079413C2semidirect
2. #13079377C2semidirect
3. #13076618C2semidirect
4. #13067664C2semidirect
5. #13067653C2semidirect
6. #13067647C2semidirect
7. #13067636C2semidirect
8. #13067562C2semidirect
9. #13067551C2semidirect
10. #13067545C2semidirect
11. #13067534C2semidirect
12. #13067184C2semidirect
13. #13067159C2semidirect
14. #13066964C2semidirect
15. C11×#3534C2semidirect
35. C2×#66983C22semidirect
39. #10622825C22semidirect
40. #10622820C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622659C22semidirect
44. #10622657C22semidirect
49. #10622649C22semidirect
50. #10622649C22semidirect
52. #10622647C22semidirect
53. #10622647C22semidirect
56. #10622604C22semidirect
57. #10622599C22semidirect
60. #10622573C22semidirect
62. #10622562C22semidirect
63. #10622176C22semidirect
64. #10622176C22semidirect
67. #10622175C22semidirect
68. #10622175C22semidirect
69. #10622175C22semidirect
70. #10622175C22semidirect
71. #10622166C22semidirect
72. #10622166C22semidirect
73. #10622163C22semidirect
74. #10622163C22semidirect
76. C2×C11×#41D4semidirect
81. C22×D4×C11D4semidirect
115. C11×C22⋊Q8D4semidirect
132. C11×#121D4semidirect
133. C11×#121D4semidirect
134. C11×#121D4semidirect
155. C11×#117D4semidirect
157. C2×C11×C4⋊C4D4semidirect
340. #3534D11semidirect
568. C2×#41C22⋊D11semidirect
576. C22×D4C22⋊D11semidirect
613. C22⋊Q8C22⋊D11semidirect
634. #121C22⋊D11semidirect
635. #121C22⋊D11semidirect
636. #121C22⋊D11semidirect
657. #117C22⋊D11semidirect
662. C2×C4⋊C4C22⋊D11semidirect
843. C11#18446semidirect

Maximal subgroups

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

subgroupindex
#130794132
#130793772
#130766182
#130676642
#130676532
#130676472
#130676362
#130675622
#130675512
#130675452
#130675342
#130671842
#130671592
#130669642
C11×#35342
#1844611