Finite Group Databasebeta

← #15638603

Subgroups — #15638603

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic
3#13080698C214yesmaximal, complemented
4#13080690C214yesmaximal, complemented
5#13080124C214yesmaximal, complemented
6#13080120C214yesmaximal, complemented
7#13079618C212yesmaximal, complemented
8#13079423C211yesmaximal, characteristic, complemented
9#13079418C211yesmaximal, characteristic, complemented
10#13079389C212yesmaximal, complemented
11#13078710C212yesmaximal, complemented
12#13077876C211yesmaximal, characteristic, complemented
13D11×#450C212yesmaximal, complemented
14#13077643C211yesmaximal, characteristic, complemented
15C11×#3007C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C2×C11×#137C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20#10623360—22no—
21#10623360—22no—
22#10623360C2214yes—
23#10623360C2214yes—
24C2×#67004C2212yescomplemented
25Q8×C22⋊D11C2212yescomplemented
26C2×#67000C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×#66992—21no—
29C2×#66990—21no—
30C2×D4×Dic11C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66982—21no—
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4—21no—
35C2×#66977C2211yescharacteristic, complemented
36C2×SD16×D11C2214yescomplemented
37#10623167—22no—
38#10623166C2212yescomplemented
39#10623165—21no—
40#10623163C2212yescomplemented
41D11×C22⋊Q8C2212yes—
42#10623154—21no—
43#10623153C2212yescomplemented
44#10623042—22no—
45#10623042C2212yescomplemented
46#10623017—21no—
47#10623014—21no—
48C11×#452C2214yescomplemented
49C11×#451C2212yescomplemented
50C11×#450C2212yes—
51C11×#417C2212yescomplemented
52C11×#407C2211yescharacteristic, complemented
53#10622852C2214yescomplemented
54#10622845C2212yescomplemented
55#10622841C2212yescomplemented
56#10622840C2212yescomplemented
57#10622831C2212yes—
58#10622820C2211yescharacteristic, complemented
59#10622803C2214yescomplemented
60#10622801C2214yescomplemented
61#10622799C2214yescomplemented
62#10622798C2214yescomplemented
63#10622782C2214yescomplemented
64#10622777C2214yescomplemented
65#10622775C2214yescomplemented
66#10622747C2214yescomplemented
67#10622740C2214yescomplemented
68#10622662C2214yescomplemented
69#10622659C2212yes—
70#10622657C2212yescomplemented
71#10622580C2212yescomplemented
72#10622426C2214yescomplemented
73#10622422C2214yescomplemented
74#10622411C2214yescomplemented
75#10622408C2214yescomplemented
76#10622389C2214yescomplemented
77D11×#102C2214yescomplemented
78#10622372C2214yescomplemented
79#10622370C2214yescomplemented
80#10622351C2212yescomplemented
81#10622349C2212yescomplemented
82#10622344C2212yes—
83#10622341C2214yescomplemented
84D11×C22⋊C8C2212yes—
85#10622335C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41—44no—
91C2×C11×#41C2312yes—
92C2×C11×#41C2312yes—
93C22×Q8×C11C2311yescharacteristic
94C22×Q8×C11C2311yescharacteristic, complemented
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11D411yescharacteristic
102C23×Dic11—21no—
103C2×Q8×D11C2312yes—
104C2×D4×D11—22no—
105C2×D4×D11—44no—
106C2×D4×D11C2314yes—
107C22×D44C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2311yescharacteristic, complemented
110C11×#137—44no—
111C2×C11×Q16C2314yescomplemented
112C2×C11×SD16C2314yes—
113C2×C11×M16C2312yescomplemented
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8C2312yes—
117C11×C22⋊Q8C2312yescomplemented
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic, complemented
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11D411yescharacteristic
124#67004—44no—
125#67000—22no—
126#67000C2314yes—
127#66999—22no—
128#66999—22no—
129#66999C2312yes—
130#66999C2314yes—
131Q8×Dic11C2312yescomplemented
132#66997—22no—
133#66997C2312yescomplemented
134C2×#4326C2314yescomplemented
135C2×#4325C2314yes—
136#66992—24no—
137#66992—24no—
138#66990—24no—
139#66990—24no—
140D4×Dic11—22no—
141D4×Dic11C2314yes—
142C2×#4324C2314yes—
143#66983—21no—
144#66983—21no—
145#66983C2312yes—
146#66983C2312yes—
147#66982—24no—
148#66982—24no—
149C4×C22⋊D11—22no—
150C4×C22⋊D11—22no—
151C4×C22⋊D11D412yes—
152C4×C22⋊D11D412yes—
153C4×C22⋊D11C2312yes—
154C4×C22⋊D11C2312yes—
155C2×(C2×D11)⋊C4—21no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—24no—
160C2×(C2×D11)⋊C4—24no—
161C2×(C2×D11)⋊C4D411yescharacteristic
162C2×C4⋊Dic11C2311yescharacteristic
163C2×C4⋊Dic11C2311yescharacteristic, complemented
164#66977—21no—
165#66977—21no—
166#66977—22no—
167#66977—22no—
168#66977C2312yes—
169#66977C2312yescomplemented
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4D411yescharacteristic
173C2×C4×Dic11C2311yescharacteristic
174C2×#4318C2312yescomplemented
175SD16×D11—48no—
176C2×#4314C2314yes—
177C2×C8×D11C2314yes—
178#66950—22no—
179#66950C2312yes—
180#66949—22no—
181#66949—22no—
182#66949—22no—
183C4⋊C4×D11—22no—
184C4⋊C4×D11C2312yes—
185#66942—22no—
186#66942—22no—
187#66942—22no—
188#66941—22no—
189#66941C2312yescomplemented
190#66940—22no—
191#66940C2312yescomplemented
192(C22⋊D11)⋊C4—22no—
193(C22⋊D11)⋊C4—22no—
194C22⋊C4×D11—22no—
195#66931—22no—
196#66931—22no—
197#66931—22no—
198#66931—22no—
199#66930—22no—
200C11×#103C2314yescomplemented
201C11×#102C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yescomplemented
204#66899C2314yescomplemented
205#66899C2314yescomplemented
206#66896C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210(C2×D11)⋊C8C2314yes—
211#66882C2314yescomplemented
212#66880C2314yescomplemented
213#66879C2314yescomplemented
214Dic11⋊C8C2314yescomplemented
215#66873C2314yes—
216#66871C2314yescomplemented
217#61570—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C23×D11—21no—
221C23×D11—24no—
222C23×D11—44no—
223C23×D11—44no—
224C23×D11—82no—
225C23×D11C2×D411yescharacteristic
226C11×#41—24no—
227C11×#41—24no—
228C11×#41—42no—
229C11×#41—42no—
230C11×#41—44no—
231C11×#41—44no—
232C2×Q8×C11—21no—
233C2×Q8×C11—21no—
234C2×Q8×C11—42no—
235C2×Q8×C11—42no—
236C2×Q8×C11C2412yes—
237C2×Q8×C11C2412yes—
238C2×D4×C11—24no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—21no—
242C2×D4×C11—44no—
243C2×D4×C11C2412yes—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—42no—
250C22×C4×C11—44no—
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C2×C22⋊D11—24no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—82no—
263C2×C22⋊D11C2×D412yes—
264C2×C22⋊D11C2×D412yes—
265C22×Dic11—24no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—82no—
270C22×Dic11C2×D411yescharacteristic
271C22×Dic11C2×D411yescharacteristic
272C22×Dic11C2×D411yescharacteristic
273Q8×D11—44no—
274D4×D11—28no—
275D4×D11—44no—
276D4×D11—48no—
277C2×D44—21no—
278C2×D44—42no—
279C2×D44C2412yes—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—42no—
283C2×C4×D11C2×D412yes—
284C2×C4×D11C2412yes—
285C2×Dic22—22no—
286C2×Dic22—22no—
287C2×Dic22—21no—
288C2×Dic22—42no—
289C2×Dic22C2412yes—
290C11×Q16—44no—
291C11×SD16—28no—
292C11×M16—42no—
293C2×C8×C11C2414yes—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2412yes—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C22⋊Dic11—24no—
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303C22⋊Dic11C2×D412yes—
304C22⋊Dic11C2×D412yes—
305#4326—44no—
306#4325—44no—
307#4324—28no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4C2×D412yes—
316(C2×D11)⋊C4C2×D412yes—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11C2412yes—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—24no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4C2×D412yes—
333Dic11⋊C4C2×D412yes—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11C2×D412yes—
337C4×Dic11C2412yes—
338#4318—42no—
339C2×C11⋊C8C2414yes—
340#4314—44no—
341C8×D11—44no—
342#3501—111no—
343C2×#546—111no—
344#3314—114no—
345#3314—114no—
346#3266—114no—
347#3266—114no—
348#3215—112no—
349#3193—111no—
350#3193—111no—
351#3189—112no—
352#3110—112no—
353#3007—111no—
354#3007D1111yescharacteristic, complemented
355C2×#450—112no—
356#2973—111no—
357C23×C11—24no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—42no—
363C23×C11—42no—
364C23×C11C22×D411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C22×D11—22no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—48no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—48no—
375C22×D11—84no—
376C22×D11—816no—
377C22×D11#13714yescomplemented
378C22×D11C22×D412yes—
379Q8×C11—24no—
380Q8×C11—22no—
381Q8×C11—22no—
382Q8×C11—42no—
383Q8×C11—81no—
384D4×C11—24no—
385D4×C11—22no—
386D4×C11—44no—
387D4×C11—44no—
388D4×C11H(5,𝔽2)14yes—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—44no—
399C2×C4×C11—44no—
400C2×C4×C11—42no—
401C2×C4×C11—81no—
402C2×C4×C11—81no—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C2511yescharacteristic
407C22⋊D11—24no—
408C22⋊D11—24no—
409C22⋊D11—48no—
410C22⋊D11—82no—
411C22⋊D11—82no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—42no—
419C2×Dic11—84no—
420C2×Dic11—81no—
421C2×Dic11—81no—
422C2×Dic11C22×D412yes—
423C2×Dic11C22×D412yes—
424C2×Dic11C22×D412yes—
425D44—24no—
426D44—42no—
427C4×D11—24no—
428C4×D11—42no—
429C4×D11—82no—
430C4×D11—82no—
431Dic22—24no—
432Dic22—82no—
433Dic22—82no—
434Dic22—81no—
435C8×C11—24no—
436C11⋊C8—24no—
437C22×#41C2×D1111yescharacteristic
438C23×D4—111no—
439C2×#137—112no—
440C2×#137C2×D1112yescomplemented
441C22×SD16—114no—
442#554—112no—
443#554—112no—
444#554—222no—
445#554—222no—
446D4×Q8—112no—
447D4×Q8—112no—
448#546—114no—
449#546—114no—
450#546—222no—
451#546—222no—
452#544—221no—
453#543—221no—
454#543—221no—
455#533—112no—
456C2×#124—111no—
457C2×#123—221no—
458C2×C22⋊Q8—111no—
459C2×C22⋊Q8—111no—
460C2×C22⋊Q8—112no—
461C2×C22⋊Q8C2×D1111yescharacteristic, complemented
462C2×#121—111no—
463C2×#121—221no—
464C2×#120—221no—
465#518—221no—
466C2×C4×D4—111no—
467C2×C4×D4—111no—
468C22×C22⋊C4—221no—
469#497—114no—
470#489—114no—
471#484—112no—
472#484—114no—
473#484—112no—
474#480—112no—
475#480—112no—
476#474—114no—
477#468—114no—
478#468—114no—
479#467—114no—
480#467—114no—
481#464—114no—
482#464—114no—
483#461—114no—
484#452—114no—
485#452C2×D1114yescomplemented
486#451—112no—
487#451—114no—
488#451C2×D1112yescomplemented
489#450—112no—
490#450—114no—
491#450—112no—
492#450—114no—
493#450—112no—
494#450C2×D1112yes—
495#448—112no—
496#448—112no—
497#440—114no—
498#440—114no—
499#435—114no—
500#435—114no—
501#432—112no—
502#417—112no—
503#417C2×D1112yescomplemented
504C2×#102—114no—
505#407—111no—
506#407C2×D1111yescharacteristic, complemented
507C2×C22⋊C8—112no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—24no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—48no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—82no—
521C22×C11C2×#13712yes—
522C22×C11C23×D411yescharacteristic
523C2×D11—22no—
524C2×D11—22no—
525C2×D11—44no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—816no—
530C2×D11—84no—
531C2×D11C2×#13714yes—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11C2×H(5,𝔽2)12yes—
539Dic11—22no—
540Dic11—22no—
541Dic11—22no—
542Dic11—42no—
543Dic11—42no—
544Dic11—42no—
545C25—221no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—44no—
549C2×#41C22×D1112yes—
550C2×#41C22×D1112yes—
551C22×Q8—112no—
552C22×Q8—111no—
553C22×Q8C22×D1111yescharacteristic
554C22×Q8C22×D1111yescharacteristic, complemented
555C22×D4—21no—
556C22×D4—111no—
557C22×D4—114no—
558C22×D4—111no—
559C22×D4—222no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—444no—
563C22×D4C22×D1111yescharacteristic
564C23×C4—21no—
565C23×C4—111no—
566C23×C4—221no—
567C23×C4C22×D1111yescharacteristic
568#137—44no—
569#137—444no—
570C2×Q16—114no—
571C2×Q16C22×D1114yescomplemented
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—448no—
576C2×SD16C22×D1114yes—
577C2×M16—112no—
578C2×M16C22×D1112yescomplemented
579C22×C8—114no—
580C4⋊Q8—112no—
581C4⋊Q8—112no—
582C4⋊Q8—222no—
583C4⋊Q8—222no—
584#125—222no—
585#125—222no—
586#125—222no—
587#124—114no—
588#124—222no—
589#123—224no—
590#123—224no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—114no—
594C22⋊Q8—112no—
595C22⋊Q8—112no—
596C22⋊Q8—112no—
597C22⋊Q8—112no—
598C22⋊Q8—222no—
599C22⋊Q8—222no—
600C22⋊Q8—222no—
601C22⋊Q8—222no—
602C22⋊Q8—222no—
603C22⋊Q8—222no—
604C22⋊Q8—222no—
605C22⋊Q8—222no—
606C22⋊Q8—222no—
607C22⋊Q8—222no—
608C22⋊Q8—222no—
609C22⋊Q8—222no—
610C22⋊Q8—221no—
611C22⋊Q8—221no—
612C22⋊Q8C22×D1112yes—
613C22⋊Q8C22×D1112yescomplemented
614#121—112no—
615#121—112no—
616#121—224no—
617#121—224no—
618#121—221no—
619#121—221no—
620#120—224no—
621#120—224no—
622C4×Q8—112no—
623C4×Q8—112no—
624C4×Q8—222no—
625C4×D4—112no—
626C4×D4—112no—
627C4×D4—112no—
628C4×D4—112no—
629C4×D4—114no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4—222no—
633C4×D4—222no—
634C4×D4—222no—
635#117—222no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—222no—
642C2×C4⋊C4—221no—
643C2×C4⋊C4—221no—
644C2×C4⋊C4C22×D1111yescharacteristic, complemented
645C2×C22⋊C4—21no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—111no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4—224no—
650C2×C22⋊C4—224no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C22⋊C4—221no—
657C2×C42—111no—
658#107—114no—
659#107—114no—
660C4⋊C8—114no—
661#103—114no—
662#103—114no—
663#103—114no—
664#103C22×D1114yescomplemented
665#102—114no—
666#102—114no—
667#102—114no—
668#102C22×D1114yes—
669C22⋊C8—112no—
670C22⋊C8—112no—
671C22⋊C8—114no—
672C22⋊C8C22×D1112yes—
673C22⋊C8C22×D1112yescomplemented
674#97—114no—
675C2×C11—22no—
676C2×C11—44no—
677C2×C11—41no—
678C2×C11—41no—
679C2×C11#348411yescharacteristic
680C2×C11C22×#13711yescharacteristic
681C2×C11#358511yescharacteristic
682D11—24no—
683D11—82no—
684C24—21no—
685C24—111no—
686C24—224no—
687C24—221no—
688C24—444no—
689C24—444no—
690C24—882no—
691C24D4×D1111yescharacteristic
692#41—24no—
693#41—24no—
694#41—42no—
695#41—42no—
696#41—44no—
697#41—44no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—42no—
701C2×Q8—42no—
702C2×Q8—112no—
703C2×Q8—222no—
704C2×Q8—222no—
705C2×Q8—221no—
706C2×Q8—442no—
707C2×Q8—444no—
708C2×Q8C23×D1112yes—
709C2×Q8C23×D1112yes—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—21no—
714C2×D4—44no—
715C2×D4—112no—
716C2×D4—112no—
717C2×D4—112no—
718C2×D4—224no—
719C2×D4—224no—
720C2×D4—228no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—221no—
724C2×D4—442no—
725C2×D4—444no—
726C2×D4—448no—
727C2×D4—444no—
728C2×D4—882no—
729C2×D4C23×D1112yes—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—42no—
736C22×C4—44no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—224no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—442no—
749C22×C4—882no—
750C22×C4D4×D1111yescharacteristic
751C22×C4D4×D1111yescharacteristic
752C22×C4D4×D1111yescharacteristic
753C22×C4C23×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756Q16—44no—
757Q16—444no—
758SD16—28no—
759SD16—228no—
760SD16—444no—
761SD16—444no—
762M16—42no—
763M16—442no—
764C2×C8—114no—
765C2×C8—444no—
766C2×C8C23×D1114yes—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—21no—
770C4⋊C4—112no—
771C4⋊C4—112no—
772C4⋊C4—112no—
773C4⋊C4—112no—
774C4⋊C4—222no—
775C4⋊C4—224no—
776C4⋊C4—222no—
777C4⋊C4—222no—
778C4⋊C4—222no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—222no—
782C4⋊C4—222no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4—222no—
786C4⋊C4—222no—
787C4⋊C4C23×D1112yes—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—112no—
791C22⋊C4—112no—
792C22⋊C4—112no—
793C22⋊C4—112no—
794C22⋊C4—224no—
795C22⋊C4—224no—
796C22⋊C4—224no—
797C22⋊C4—222no—
798C22⋊C4—222no—
799C22⋊C4—224no—
800C22⋊C4—222no—
801C22⋊C4—222no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C42—112no—
805C42—112no—
806C42—222no—
807C42—222no—
808C11#6157011yescharacteristic, complemented, Sylow
809C23—24no—
810C23—22no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—112no—
817C23—114no—
818C23—222no—
819C23—441no—
820C23—441no—
821C23—448no—
822C23—442no—
823C23—442no—
824C23—448no—
825C23—442no—
826C23—884no—
827C23—8816no—
828C23C2×D4×D1111yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23C2×D4×D1111yescharacteristic
831Q8—24no—
832Q8—22no—
833Q8—22no—
834Q8—42no—
835Q8—81no—
836Q8—224no—
837Q8—881no—
838Q8—882no—
839Q8—882no—
840D4—24no—
841D4—22no—
842D4—44no—
843D4—44no—
844D4—224no—
845D4—224no—
846D4—224no—
847D4—442no—
848D4—448no—
849D4—882no—
850D4—882no—
851D4#6703714yes—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—42no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—112no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—222no—
870C2×C4—224no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—442no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—442no—
878C2×C4—882no—
879C2×C4—882no—
880C2×C4—884no—
881C2×C4—881no—
882C2×C4—881no—
883C2×C4C2×D4×D1111yescharacteristic
884C2×C4C2×D4×D1111yescharacteristic
885C2×C4C2×D4×D1111yescharacteristic
886C2×C4C24×D1111yescharacteristic
887C8—24no—
888C8—224no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—24no—
896C22—21no—
897C22—21no—
898C22—48no—
899C22—42no—
900C22—42no—
901C22—82no—
902C22—114no—
903C22—222no—
904C22—222no—
905C22—444no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—884no—
910C22—8816no—
911C22D11×#13712yes—
912C22C22×D4×D1111yescharacteristic
913C4—21no—
914C4—21no—
915C4—21no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—222no—
920C4—222no—
921C4—222no—
922C4—442no—
923C4—442no—
924C4—442no—
925C4C2×#6703712yes—
926C2—22no—
927C2—41no—
928C2—41no—
929C2—44no—
930C2—224no—
931C2—882no—
932C2#1308224511yescharacteristic
933C2C2×D11×#13711yescharacteristic
934C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3007C2
socleC22×C11C23×D4
prime radicalC2×#10623360C2
hypercenter#3007D11
hypocenterC11#61570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. #13082412C2semidirect
3. #13080698C2semidirect
4. #13080690C2semidirect
5. #13080124C2semidirect
6. #13080120C2semidirect
7. #13079618C2semidirect
8. #13079423C2semidirect
9. #13079418C2semidirect
10. #13079389C2semidirect
11. #13078710C2semidirect
12. #13077876C2semidirect
13. D11×#450C2semidirect
14. #13077643C2semidirect
15. C11×#3007C2semidirect
18. C2×C11×#137C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
24. C2×#67004C22semidirect
25. Q8×C22⋊D11C22semidirect
35. C2×#66977C22semidirect
36. C2×SD16×D11C22semidirect
38. #10623166C22semidirect
40. #10623163C22semidirect
43. #10623153C22semidirect
45. #10623042C22semidirect
48. C11×#452C22semidirect
49. C11×#451C22semidirect
51. C11×#417C22semidirect
52. C11×#407C22semidirect
53. #10622852C22semidirect
54. #10622845C22semidirect
55. #10622841C22semidirect
56. #10622840C22semidirect
58. #10622820C22semidirect
59. #10622803C22semidirect
60. #10622801C22semidirect
61. #10622799C22semidirect
62. #10622798C22semidirect
63. #10622782C22semidirect
64. #10622777C22semidirect
65. #10622775C22semidirect
66. #10622747C22semidirect
67. #10622740C22semidirect
68. #10622662C22semidirect
70. #10622657C22semidirect
71. #10622580C22semidirect
72. #10622426C22semidirect
73. #10622422C22semidirect
74. #10622411C22semidirect
75. #10622408C22semidirect
76. #10622389C22semidirect
77. D11×#102C22semidirect
78. #10622372C22semidirect
79. #10622370C22semidirect
80. #10622351C22semidirect
81. #10622349C22semidirect
83. #10622341C22semidirect
85. #10622335C22semidirect
86. #10622332C22semidirect
94. C22×Q8×C11C23semidirect
109. C22×Dic22C23semidirect
111. C2×C11×Q16C23semidirect
113. C2×C11×M16C23semidirect
117. C11×C22⋊Q8C23semidirect
119. C2×C11×C4⋊C4C23semidirect
131. Q8×Dic11C23semidirect
133. #66997C23semidirect
134. C2×#4326C23semidirect
163. C2×C4⋊Dic11C23semidirect
169. #66977C23semidirect
174. C2×#4318C23semidirect
189. #66941C23semidirect
191. #66940C23semidirect
200. C11×#103C23semidirect
203. C11×C22⋊C8C23semidirect
204. #66899C23semidirect
205. #66899C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
211. #66882C23semidirect
212. #66880C23semidirect
213. #66879C23semidirect
214. Dic11⋊C8C23semidirect
216. #66871C23semidirect
354. #3007D11semidirect
377. C22×D11#137semidirect
440. C2×#137C2×D11semidirect
461. C2×C22⋊Q8C2×D11semidirect
485. #452C2×D11semidirect
488. #451C2×D11semidirect
503. #417C2×D11semidirect
506. #407C2×D11semidirect
554. C22×Q8C22×D11semidirect
571. C2×Q16C22×D11semidirect
578. C2×M16C22×D11semidirect
613. C22⋊Q8C22×D11semidirect
644. C2×C4⋊C4C22×D11semidirect
664. #103C22×D11semidirect
673. C22⋊C8C22×D11semidirect
808. C11#61570semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×#106233602
#130806982
#130806902
#130801242
#130801202
#130796182
#130794232
#130794182
#130793892
#130787102
#130778762
D11×#4502
#130776432
C11×#30072
#6157011