Finite Group Databasebeta

← #15638609

Subgroups — #15638609

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic, complemented
2C2×#10623161C211yesmaximal, characteristic
3#13080703C214yesmaximal, complemented
4#13080695C214yesmaximal, complemented
5#13080123C214yesmaximal, complemented
6#13080119C214yesmaximal, complemented
7#13079618C212yesmaximal, complemented
8#13079421C212yesmaximal, complemented
9#13079388C211yesmaximal, characteristic, complemented
10#13078712C212yesmaximal, complemented
11#13077875C212yesmaximal, complemented
12C2×#10622344C211yesmaximal, characteristic, complemented
13C2×#10622659C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C11×#3189C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20Q8×C22⋊D11C2212yescomplemented
21C2×#67000C2211yescharacteristic
22C22×#4325C2212yescomplemented
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66971C2214yescomplemented
26C22×#4314C2212yescomplemented
27#10623167—22no—
28#10623166C2212yescomplemented
29#10623165—21no—
30#10623163C2212yescomplemented
31#10623161—22no—
32#10623161—22no—
33#10623161C2214yes—
34#10623161C2214yes—
35D11×C22⋊Q8C2212yescomplemented
36#10623154—21no—
37#10623153C2212yescomplemented
38#10623042—22no—
39#10623042C2212yescomplemented
40C2×#66948—21no—
41C2×#66948C2211yescharacteristic
42C2×#66947—21no—
43C2×#66946C2211yescharacteristic
44C2×#66935—21no—
45#10623017—21no—
46C2×C22⋊C4×D11—21no—
47#10623014—21no—
48C11×#484C2212yescomplemented
49C11×#484C2212yescomplemented
50C11×#467C2214yescomplemented
51C11×#451C2212yescomplemented
52C11×#451C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622841C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622803C2214yescomplemented
57#10622800C2214yescomplemented
58#10622798C2214yescomplemented
59C2×#66885C2212yescomplemented
60#10622724C2214yescomplemented
61#10622664C2214yescomplemented
62#10622663C2212yescomplemented
63#10622659C2212yes—
64#10622659C2212yes—
65#10622659C2214yescomplemented
66#10622657C2212yescomplemented
67#10622583C2212yescomplemented
68C2×#66873C2212yescomplemented
69#10622503C2214yescomplemented
70#10622502C2214yescomplemented
71#10622499C2214yescomplemented
72#10622495C2214yescomplemented
73#10622431C2214yescomplemented
74#10622430C2214yescomplemented
75#10622425C2214yescomplemented
76#10622423C2214yescomplemented
77#10622419C2214yescomplemented
78#10622416C2214yescomplemented
79#10622411C2214yescomplemented
80#10622408C2214yescomplemented
81#10622344C2212yes—
82#10622344C2212yes—
83#10622344C2214yescomplemented
84#10622343C2214yescomplemented
85#10622339C2212yescomplemented
86#10622332C2212yescomplemented
87C24×D11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×Q8×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11D411yescharacteristic
92C2×#4343—22no—
93C2×#4343—44no—
94C2×#4343C2314yes—
95C2×Q8×D11C2312yescomplemented
96C22×D44—21no—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—44no—
102C22×D44C2311yescharacteristic
103C22×D44C2312yes—
104C22×D44C2312yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C2×C11×Q16C2314yescomplemented
111C22×C8×C11C2312yes—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8C2312yes—
117C11×C22⋊Q8C2312yes—
118C11×C22⋊Q8C2312yes—
119C11×C22⋊Q8C2312yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11D411yescharacteristic
128#67000—22no—
129#67000C2314yes—
130#66999—22no—
131#66999C2312yescomplemented
132Q8×Dic11C2312yescomplemented
133#66997—22no—
134#66997C2312yescomplemented
135C2×#4326C2314yescomplemented
136C2×#4325—44no—
137C2×#4325C2314yes—
138C2×#4325C2314yes—
139C4×C22⋊D11—22no—
140C4×C22⋊D11—22no—
141C4×C22⋊D11D412yes—
142C4×C22⋊D11D412yes—
143C4×C22⋊D11C2312yes—
144C4×C22⋊D11C2312yes—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151#66977—21no—
152#66977—21no—
153#66977—22no—
154#66977—22no—
155#66977C2312yes—
156#66977C2312yes—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4D411yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2312yes—
161#66971—48no—
162C2×#4314—44no—
163C2×#4314C2314yes—
164C2×#4314C2314yes—
165C2×#4313C2314yescomplemented
166#66950—22no—
167#66950C2312yescomplemented
168#66949—22no—
169#66949—22no—
170#66949—22no—
171#66948—22no—
172#66948—24no—
173#66948—24no—
174#66948C2314yes—
175#66947—24no—
176#66947—24no—
177#66946—22no—
178#66946C2314yes—
179C4⋊C4×D11—22no—
180C4⋊C4×D11C2312yescomplemented
181#66942—22no—
182#66942—22no—
183#66942—22no—
184#66941—22no—
185#66941C2312yescomplemented
186#66940—22no—
187#66940C2312yescomplemented
188#66935—24no—
189#66935—24no—
190(C22⋊D11)⋊C4—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—22no—
193C22⋊C4×D11—24no—
194C22⋊C4×D11—24no—
195#66931—22no—
196#66931—22no—
197#66931—22no—
198#66931—22no—
199#66930—22no—
200C11×#107C2314yescomplemented
201C11×#103C2314yescomplemented
202C11×#103C2314yescomplemented
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66899C2314yescomplemented
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208#66885C2314yes—
209#66885C2314yes—
210(C2×D11)⋊C8C2314yescomplemented
211#66879C2314yescomplemented
212Dic11⋊C8C2314yescomplemented
213#66874C2314yescomplemented
214#66873C2314yes—
215#66873C2314yes—
216#66871C2314yescomplemented
217#61570—111nomaximal, Sylow
218C24×C11C2×D411yescharacteristic
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—44no—
224C23×D11—44no—
225C23×D11—82no—
226C23×D11C2×D411yescharacteristic
227C2×Q8×C11—21no—
228C2×Q8×C11—21no—
229C2×Q8×C11—42no—
230C2×Q8×C11—42no—
231C2×Q8×C11C2412yes—
232C2×Q8×C11C2412yes—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—42no—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C2×C22⋊D11—24no—
245C2×C22⋊D11C2×D412yes—
246C2×C22⋊D11C2×D412yes—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11C2×D411yescharacteristic
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252#4343—28no—
253#4343—44no—
254#4343—48no—
255Q8×D11—44no—
256C2×D44—24no—
257C2×D44—24no—
258C2×D44—24no—
259C2×D44—24no—
260C2×D44—24no—
261C2×D44—21no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—21no—
265C2×D44—42no—
266C2×D44—42no—
267C2×D44—42no—
268C2×D44—44no—
269C2×D44—44no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—82no—
273C2×D44C2412yes—
274C2×D44C2412yes—
275C2×C4×D11—24no—
276C2×C4×D11—24no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—42no—
280C2×C4×D11—44no—
281C2×C4×D11—82no—
282C2×C4×D11C2×D412yes—
283C2×C4×D11C2412yes—
284C2×Dic22—22no—
285C2×Dic22—22no—
286C2×Dic22—21no—
287C2×Dic22—42no—
288C2×Dic22C2412yes—
289C11×Q16—44no—
290C2×C8×C11—42no—
291C2×C8×C11C2414yes—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4C2412yes—
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—22no—
306C22⋊Dic11C2×D412yes—
307C22⋊Dic11C2×D412yes—
308#4326—44no—
309#4325—28no—
310#4325—44no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4C2×D412yes—
318(C2×D11)⋊C4C2×D412yes—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—21no—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4C2×D412yes—
332Dic11⋊C4C2×D412yes—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11C2×D412yes—
336C4×Dic11C2412yes—
337C2×C11⋊C8—42no—
338C2×C11⋊C8C2414yes—
339#4314—28no—
340#4314—44no—
341#4313—44no—
342#3501—111no—
343C2×#546—111no—
344#3314—114no—
345#3314—114no—
346#3266—114no—
347#3266—114no—
348#3215—112no—
349#3193—112no—
350#3189—111no—
351#3189D1111yescharacteristic, complemented
352#3110—112no—
353#3007—112no—
354C2×#450—111no—
355C2×#450—111no—
356#2973—111no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11#13714yescomplemented
360C23×C11C22×D411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C23×C11C22×D411yescharacteristic
363C22×D11—24no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—42no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—42no—
378C22×D11—82no—
379C22×D11—82no—
380C22×D11—816no—
381C22×D11C22×D412yes—
382Q8×C11—24no—
383Q8×C11—24no—
384Q8×C11—42no—
385Q8×C11—81no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—81no—
399C2×C4×C11—81no—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—24no—
405C22⋊D11—24no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—81no—
412C2×Dic11—81no—
413C2×Dic11C22×D412yes—
414C2×Dic11C22×D412yes—
415C2×Dic11C22×D412yes—
416D44—24no—
417D44—22no—
418D44—22no—
419D44—22no—
420D44—44no—
421D44—44no—
422D44—42no—
423D44—48no—
424D44—84no—
425D44H(5,𝔽2)14yes—
426C4×D11—24no—
427C4×D11—42no—
428C4×D11—48no—
429C4×D11—84no—
430C4×D11—82no—
431C4×D11—82no—
432Dic22—24no—
433Dic22—82no—
434Dic22—82no—
435Dic22—81no—
436C8×C11—24no—
437C11⋊C8—24no—
438C22×#41—111no—
439C23×D4—111no—
440C2×#137—114no—
441C22×SD16—112no—
442C22×SD16—112no—
443#554—112no—
444#554—112no—
445#554—222no—
446#554—222no—
447D4×Q8—112no—
448D4×Q8—112no—
449#546—114no—
450#546—114no—
451#546—222no—
452#546—222no—
453#544—221no—
454#543—221no—
455#543—221no—
456#533—112no—
457C2×#124—111no—
458C2×#123—221no—
459C2×C22⋊Q8—111no—
460C2×C22⋊Q8—112no—
461C2×C22⋊Q8C2×D1111yescharacteristic
462C2×C22⋊Q8C2×D1111yescharacteristic
463C2×#121—111no—
464C2×#121—221no—
465C2×#120—221no—
466#518—221no—
467C2×C4×D4—111no—
468C2×C4×D4—111no—
469C22×C22⋊C4—221no—
470#497—114no—
471#489—114no—
472#484—112no—
473#484—112no—
474#484C2×D1112yescomplemented
475#484C2×D1112yescomplemented
476#480—114no—
477#474—114no—
478#468—114no—
479#468—114no—
480#467—114no—
481#467C2×D1114yescomplemented
482#464—114no—
483#464—114no—
484#461—114no—
485#452—114no—
486#452—114no—
487#451—112no—
488#451—112no—
489#451C2×D1112yescomplemented
490#451C2×D1112yescomplemented
491#450—112no—
492#450—112no—
493#450—114no—
494#450—112no—
495#450—112no—
496#450—114no—
497#448—114no—
498#440—114no—
499#440—114no—
500#435—114no—
501#435—114no—
502#432—112no—
503#417—114no—
504C2×#102—112no—
505C2×#102—112no—
506#407—112no—
507C2×C22⋊C8—111no—
508C2×C22⋊C8C2×D1111yescharacteristic
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—44no—
516C22×C11C2×#13712yes—
517C22×C11C2×#13712yes—
518C22×C11C2×#13712yes—
519C22×C11C23×D411yescharacteristic
520C2×D11—22no—
521C2×D11—24no—
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—48no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—82no—
531C2×D11—88no—
532C2×D11—88no—
533C2×D11—84no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—21no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11C2×H(5,𝔽2)12yes—
542Dic11—22no—
543Dic11—22no—
544Dic11—22no—
545Dic11—42no—
546Dic11—42no—
547C25—221no—
548C2×#41—114no—
549C2×#41—222no—
550C2×#41—444no—
551C22×Q8—112no—
552C22×Q8—111no—
553C22×Q8C22×D1111yescharacteristic
554C22×Q8C22×D1111yescharacteristic
555C22×D4—111no—
556C22×D4—111no—
557C22×D4—112no—
558C22×D4—112no—
559C22×D4—111no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—221no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—444no—
566C23×C4—111no—
567C23×C4—221no—
568C23×C4—221no—
569C23×C4C22×D1111yescharacteristic
570#137—448no—
571C2×Q16—114no—
572C2×Q16C22×D1114yescomplemented
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—114no—
576C2×SD16—114no—
577C2×SD16—444no—
578C2×SD16—444no—
579C2×M16—114no—
580C22×C8—112no—
581C22×C8C22×D1112yes—
582C4⋊Q8—112no—
583C4⋊Q8—112no—
584C4⋊Q8—222no—
585C4⋊Q8—222no—
586#125—222no—
587#125—222no—
588#125—222no—
589#124—114no—
590#124—222no—
591#123—224no—
592#123—224no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—112no—
598C22⋊Q8—112no—
599C22⋊Q8—112no—
600C22⋊Q8—112no—
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—222no—
611C22⋊Q8—222no—
612C22⋊Q8—221no—
613C22⋊Q8—221no—
614C22⋊Q8C22×D1112yes—
615C22⋊Q8C22×D1112yes—
616C22⋊Q8C22×D1112yes—
617C22⋊Q8C22×D1112yes—
618#121—114no—
619#121—224no—
620#121—224no—
621#121—222no—
622#120—224no—
623#120—224no—
624C4×Q8—112no—
625C4×Q8—112no—
626C4×Q8—222no—
627C4×D4—112no—
628C4×D4—112no—
629C4×D4—112no—
630C4×D4—112no—
631C4×D4—114no—
632C4×D4—222no—
633C4×D4—222no—
634C4×D4—222no—
635C4×D4—222no—
636C4×D4—222no—
637#117—222no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—222no—
644C2×C4⋊C4—221no—
645C2×C4⋊C4C22×D1111yescharacteristic
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4—224no—
652C2×C22⋊C4—224no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C22⋊C4—221no—
657C2×C22⋊C4—221no—
658C2×C22⋊C4—221no—
659C2×C42—111no—
660#107—114no—
661#107C22×D1114yescomplemented
662C4⋊C8—114no—
663#103—114no—
664#103—114no—
665#103C22×D1114yescomplemented
666#103C22×D1114yescomplemented
667#102—114no—
668#102—114no—
669#102—114no—
670#102—114no—
671C22⋊C8—112no—
672C22⋊C8—112no—
673C22⋊C8—114no—
674C22⋊C8C22×D1112yes—
675C22⋊C8C22×D1112yes—
676#97—114no—
677C2×C11—22no—
678C2×C11—22no—
679C2×C11—22no—
680C2×C11#348411yescharacteristic
681C2×C11C22×#13711yescharacteristic
682C2×C11#358511yescharacteristic
683D11—42no—
684D11—44no—
685D11—82no—
686C24—111no—
687C24—221no—
688C24—221no—
689C24—222no—
690C24—222no—
691C24—444no—
692C24—444no—
693C24—882no—
694C24D4×D1111yescharacteristic
695#41—228no—
696#41—444no—
697#41—448no—
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—112no—
711C2×D4—112no—
712C2×D4—112no—
713C2×D4—112no—
714C2×D4—224no—
715C2×D4—224no—
716C2×D4—224no—
717C2×D4—224no—
718C2×D4—224no—
719C2×D4—224no—
720C2×D4—221no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—221no—
724C2×D4—442no—
725C2×D4—442no—
726C2×D4—442no—
727C2×D4—444no—
728C2×D4—444no—
729C2×D4—444no—
730C2×D4—444no—
731C2×D4—882no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—42no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—442no—
749C22×C4—444no—
750C22×C4—882no—
751C22×C4D4×D1111yescharacteristic
752C22×C4D4×D1111yescharacteristic
753C22×C4D4×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757Q16—44no—
758Q16—444no—
759SD16—228no—
760SD16—228no—
761SD16—444no—
762SD16—444no—
763M16—444no—
764C2×C8—42no—
765C2×C8—114no—
766C2×C8—442no—
767C2×C8C23×D1114yes—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—112no—
775C4⋊C4—112no—
776C4⋊C4—112no—
777C4⋊C4—222no—
778C4⋊C4—222no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—222no—
782C4⋊C4—222no—
783C4⋊C4—222no—
784C4⋊C4—222no—
785C4⋊C4—221no—
786C4⋊C4—222no—
787C4⋊C4—222no—
788C4⋊C4C23×D1112yes—
789C4⋊C4C23×D1112yes—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—112no—
795C22⋊C4—112no—
796C22⋊C4—112no—
797C22⋊C4—112no—
798C22⋊C4—224no—
799C22⋊C4—224no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C42—112no—
807C42—112no—
808C42—222no—
809C42—222no—
810C11#6157011yescharacteristic, complemented, Sylow
811C23—41no—
812C23—41no—
813C23—112no—
814C23—224no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—441no—
819C23—441no—
820C23—444no—
821C23—444no—
822C23—442no—
823C23—442no—
824C23—442no—
825C23—442no—
826C23—444no—
827C23—444no—
828C23—442no—
829C23—882no—
830C23—882no—
831C23—8816no—
832C23#6697114yescomplemented
833C23C2×D4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×D4×D1111yescharacteristic
836Q8—24no—
837Q8—24no—
838Q8—42no—
839Q8—81no—
840Q8—224no—
841Q8—881no—
842Q8—882no—
843Q8—882no—
844D4—114no—
845D4—224no—
846D4—224no—
847D4—224no—
848D4—222no—
849D4—222no—
850D4—222no—
851D4—444no—
852D4—444no—
853D4—442no—
854D4—448no—
855D4—884no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—222no—
874C2×C4—224no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—442no—
878C2×C4—448no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—884no—
882C2×C4—882no—
883C2×C4—882no—
884C2×C4—881no—
885C2×C4—881no—
886C2×C4C2×D4×D1111yescharacteristic
887C2×C4C2×D4×D1111yescharacteristic
888C2×C4C2×D4×D1111yescharacteristic
889C2×C4C24×D1111yescharacteristic
890C8—24no—
891C8—224no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—44no—
899C22—222no—
900C22—222no—
901C22—224no—
902C22—222no—
903C22—448no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—882no—
910C22—888no—
911C22—888no—
912C22—884no—
913C22C2×#6697112yes—
914C22C2×#6697112yes—
915C22C2×#6697112yes—
916C22C22×D4×D1111yescharacteristic
917C4—21no—
918C4—21no—
919C4—21no—
920C4—42no—
921C4—42no—
922C4—42no—
923C4—42no—
924C4—222no—
925C4—222no—
926C4—222no—
927C4—442no—
928C4—442no—
929C4D11×H(5,𝔽2)12yes—
930C2—22no—
931C2—22no—
932C2—22no—
933C2—442no—
934C2—444no—
935C2—882no—
936C2#1308224811yescharacteristic
937C2C22×#6697111yescharacteristic
938C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3189C2
socleC22×C11C23×D4
prime radicalC2×#10623161C2
hypercenter#3189D11
hypocenterC11#61570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
1. #13082412C2semidirect
3. #13080703C2semidirect
4. #13080695C2semidirect
5. #13080123C2semidirect
6. #13080119C2semidirect
7. #13079618C2semidirect
8. #13079421C2semidirect
9. #13079388C2semidirect
10. #13078712C2semidirect
11. #13077875C2semidirect
12. C2×#10622344C2semidirect
13. C2×#10622659C2semidirect
14. #13077642C2semidirect
15. C11×#3189C2semidirect
20. Q8×C22⋊D11C22semidirect
22. C22×#4325C22semidirect
25. C2×#66971C22semidirect
26. C22×#4314C22semidirect
28. #10623166C22semidirect
30. #10623163C22semidirect
35. D11×C22⋊Q8C22semidirect
37. #10623153C22semidirect
39. #10623042C22semidirect
48. C11×#484C22semidirect
49. C11×#484C22semidirect
50. C11×#467C22semidirect
51. C11×#451C22semidirect
52. C11×#451C22semidirect
54. #10622841C22semidirect
56. #10622803C22semidirect
57. #10622800C22semidirect
58. #10622798C22semidirect
59. C2×#66885C22semidirect
60. #10622724C22semidirect
61. #10622664C22semidirect
62. #10622663C22semidirect
65. #10622659C22semidirect
66. #10622657C22semidirect
67. #10622583C22semidirect
68. C2×#66873C22semidirect
69. #10622503C22semidirect
70. #10622502C22semidirect
71. #10622499C22semidirect
72. #10622495C22semidirect
73. #10622431C22semidirect
74. #10622430C22semidirect
75. #10622425C22semidirect
76. #10622423C22semidirect
77. #10622419C22semidirect
78. #10622416C22semidirect
79. #10622411C22semidirect
80. #10622408C22semidirect
83. #10622344C22semidirect
84. #10622343C22semidirect
85. #10622339C22semidirect
86. #10622332C22semidirect
95. C2×Q8×D11C23semidirect
110. C2×C11×Q16C23semidirect
131. #66999C23semidirect
132. Q8×Dic11C23semidirect
134. #66997C23semidirect
135. C2×#4326C23semidirect
165. C2×#4313C23semidirect
167. #66950C23semidirect
180. C4⋊C4×D11C23semidirect
185. #66941C23semidirect
187. #66940C23semidirect
200. C11×#107C23semidirect
201. C11×#103C23semidirect
202. C11×#103C23semidirect
205. #66899C23semidirect
210. (C2×D11)⋊C8C23semidirect
211. #66879C23semidirect
212. Dic11⋊C8C23semidirect
213. #66874C23semidirect
216. #66871C23semidirect
351. #3189D11semidirect
359. C23×C11#137semidirect
474. #484C2×D11semidirect
475. #484C2×D11semidirect
481. #467C2×D11semidirect
489. #451C2×D11semidirect
490. #451C2×D11semidirect
572. C2×Q16C22×D11semidirect
661. #107C22×D11semidirect
665. #103C22×D11semidirect
666. #103C22×D11semidirect
810. C11#61570semidirect
832. C23#66971semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×#106231612
#130807032
#130806952
#130801232
#130801192
#130796182
#130794212
#130793882
#130787122
#130778752
C2×#106223442
C2×#106226592
#130776422
C11×#31892
#6157011