Finite Group Databasebeta

← #15638607

Subgroups — #15638607

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×#10623337C211yesmaximal, characteristic
3#13080701C214yesmaximal, complemented
4#13080693C214yesmaximal, complemented
5#13080130C214yesmaximal, complemented
6#13080126C214yesmaximal, complemented
7#13079616C212yesmaximal, complemented
8#13079419C212yesmaximal, complemented
9#13079391C211yesmaximal, characteristic, complemented
10#13079388C211yesmaximal, characteristic, complemented
11#13078710C212yesmaximal, complemented
12#13077871C212yesmaximal, complemented
13C2×#10622831C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C2×C11×#450C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4341C2211yescharacteristic
18C22×C11×SD16C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#67006—21no—
21C22×C22⋊Dic11—21no—
22Q8×C22⋊D11C2212yescomplemented
23#10623337—22no—
24#10623337—22no—
25#10623337C2214yes—
26#10623337C2214yes—
27C2×#66992—21no—
28C2×#66991C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C2×#66988—21no—
31C2×D4×Dic11C2211yescharacteristic
32C22×#4324C2212yescomplemented
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C2×#66968C2214yescomplemented
37#10623167—22no—
38#10623166C2212yescomplemented
39#10623165—21no—
40#10623163C2212yescomplemented
41D11×C22⋊Q8C2212yescomplemented
42#10623154—21no—
43#10623153C2212yescomplemented
44#10623042—22no—
45#10623042C2212yescomplemented
46#10623017—21no—
47#10623014—21no—
48C11×#450C2212yes—
49C11×#450C2212yes—
50C11×#450C2214yescomplemented
51C2×C11×#102C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic
53#10622841C2212yescomplemented
54#10622831C2212yes—
55#10622831C2212yes—
56#10622831C2214yescomplemented
57C2×#66896C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic
59#10622787C2214yescomplemented
60#10622786C2214yescomplemented
61#10622783C2214yescomplemented
62#10622780C2214yescomplemented
63#10622779C2214yescomplemented
64#10622777C2214yescomplemented
65#10622775C2214yescomplemented
66#10622729C2214yescomplemented
67#10622724C2214yescomplemented
68#10622664C2214yescomplemented
69#10622663C2212yescomplemented
70#10622657C2212yescomplemented
71#10622583C2212yescomplemented
72#10622396C2214yescomplemented
73#10622393C2214yescomplemented
74#10622387C2214yescomplemented
75#10622384C2214yescomplemented
76#10622380C2214yescomplemented
77#10622378C2214yescomplemented
78#10622372C2214yescomplemented
79#10622370C2214yescomplemented
80#10622352C2212yescomplemented
81#10622352C2212yescomplemented
82#10622343C2214yescomplemented
83#10622339C2212yescomplemented
84#10622335C2212yescomplemented
85#10622335C2212yescomplemented
86#10622332C2212yescomplemented
87C25×C11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—44no—
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2312yes—
95C22×D4×C11C2312yes—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11D411yescharacteristic
101C23×Dic11—21no—
102C23×Dic11—21no—
103C2×Q8×D11C2312yescomplemented
104C2×#4341—22no—
105C2×#4341—44no—
106C2×#4341C2314yes—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C2×C11×SD16—44no—
111C2×C11×SD16C2314yes—
112C2×C11×SD16C2314yes—
113C22×C8×C11C2312yes—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8C2312yes—
117C11×C22⋊Q8C2312yes—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121#67006—24no—
122#67006—24no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11D411yescharacteristic
132#66999—22no—
133#66999C2312yescomplemented
134Q8×Dic11C2312yescomplemented
135#66997—22no—
136#66997C2312yescomplemented
137C2×#4326C2314yescomplemented
138#66992—24no—
139#66992—24no—
140#66991—22no—
141#66991C2314yes—
142#66989—22no—
143#66989C2314yes—
144#66988—24no—
145#66988—24no—
146D4×Dic11—22no—
147D4×Dic11C2314yes—
148C2×#4324—44no—
149C2×#4324C2314yes—
150C2×#4324C2314yes—
151C4×C22⋊D11—22no—
152C4×C22⋊D11—22no—
153C4×C22⋊D11D412yes—
154C4×C22⋊D11D412yes—
155C4×C22⋊D11C2312yes—
156C4×C22⋊D11C2312yes—
157C2×(C2×D11)⋊C4D411yescharacteristic
158C2×C4⋊Dic11C2311yescharacteristic
159C2×C4⋊Dic11C2311yescharacteristic
160#66977—21no—
161#66977—21no—
162#66977—21no—
163#66977—21no—
164#66977—22no—
165#66977—22no—
166#66977C2312yes—
167#66977C2312yes—
168#66977C2312yes—
169#66977C2312yes—
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4D411yescharacteristic
173C2×C4×Dic11C2311yescharacteristic
174C22×C11⋊C8C2312yes—
175#66968—48no—
176C2×Dic44C2314yescomplemented
177C2×#4313C2314yescomplemented
178#66950—22no—
179#66950C2312yescomplemented
180#66949—22no—
181#66949—22no—
182#66949—22no—
183C4⋊C4×D11—22no—
184C4⋊C4×D11C2312yescomplemented
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×#102C2314yes—
201C11×#102C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yes—
204#66899C2314yescomplemented
205#66896C2314yes—
206#66896C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209(C2×D11)⋊C8C2314yescomplemented
210#66882C2314yescomplemented
211#66880C2314yescomplemented
212#66880C2314yescomplemented
213#66879C2314yescomplemented
214Dic11⋊C8C2314yescomplemented
215#66874C2314yescomplemented
216#66871C2314yescomplemented
217#61570—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11—21no—
220C24×C11—22no—
221C24×C11—22no—
222C24×C11—44no—
223C24×C11—44no—
224C24×C11—82no—
225C24×C11C2×D411yescharacteristic
226C23×D11C2×D411yescharacteristic
227C2×Q8×C11—21no—
228C2×Q8×C11—42no—
229C2×Q8×C11C2412yes—
230C2×D4×C11—24no—
231C2×D4×C11—24no—
232C2×D4×C11—24no—
233C2×D4×C11—21no—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—21no—
237C2×D4×C11—42no—
238C2×D4×C11—42no—
239C2×D4×C11—42no—
240C2×D4×C11—44no—
241C2×D4×C11—44no—
242C2×D4×C11—44no—
243C2×D4×C11C2412yes—
244C2×D4×C11C2412yes—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—42no—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—82no—
259C2×C22⋊D11C2×D412yes—
260C2×C22⋊D11C2×D412yes—
261C22×Dic11—24no—
262C22×Dic11—24no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—44no—
268C22×Dic11—82no—
269C22×Dic11C2×D411yescharacteristic
270C22×Dic11C2×D411yescharacteristic
271C22×Dic11C2×D411yescharacteristic
272Q8×D11—44no—
273#4341—28no—
274#4341—44no—
275#4341—48no—
276C2×C4×D11—22no—
277C2×C4×D11—22no—
278C2×C4×D11—42no—
279C2×C4×D11C2×D412yes—
280C2×C4×D11C2412yes—
281C2×Dic22—22no—
282C2×Dic22—22no—
283C2×Dic22—21no—
284C2×Dic22—21no—
285C2×Dic22—42no—
286C2×Dic22—42no—
287C2×Dic22C2412yes—
288C2×Dic22C2412yes—
289C11×SD16—28no—
290C11×SD16—44no—
291C2×C8×C11—42no—
292C2×C8×C11C2414yes—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C2412yes—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C22⋊Dic11—24no—
300C22⋊Dic11—24no—
301C22⋊Dic11—24no—
302C22⋊Dic11—24no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—22no—
306C22⋊Dic11—22no—
307C22⋊Dic11C2×D412yes—
308C22⋊Dic11C2×D412yes—
309#4326—44no—
310#4324—28no—
311#4324—44no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4C2×D412yes—
315(C2×D11)⋊C4C2×D412yes—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11C2412yes—
321C4⋊Dic11C2412yes—
322Dic11⋊C4—22no—
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⋊C4—22no—
332Dic11⋊C4C2×D412yes—
333Dic11⋊C4C2×D412yes—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11C2×D412yes—
337C4×Dic11C2412yes—
338C2×C11⋊C8—42no—
339C2×C11⋊C8C2414yes—
340Dic44—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#3189—111no—
352#3110—112no—
353#3007—112no—
354C2×#450—111no—
355C2×#450D1111yescharacteristic, complemented
356#2973—111no—
357C23×C11—24no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—44no—
363C23×C11—44no—
364C23×C11—42no—
365C23×C11—42no—
366C23×C11—42no—
367C23×C11—42no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—42no—
371C23×C11—82no—
372C23×C11—82no—
373C23×C11—816no—
374C23×C11#13714yescomplemented
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C22×D11—22no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11C22×D412yes—
382Q8×C11—24no—
383Q8×C11—81no—
384D4×C11—24no—
385D4×C11—22no—
386D4×C11—22no—
387D4×C11—22no—
388D4×C11—44no—
389D4×C11—44no—
390D4×C11—42no—
391D4×C11H(5,𝔽2)14yes—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—81no—
401C2×C4×C11—81no—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C2511yescharacteristic
406C22⋊D11—24no—
407C22⋊D11—24no—
408C22⋊D11—48no—
409C22⋊D11—84no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—48no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420C2×Dic11—84no—
421C2×Dic11—81no—
422C2×Dic11—81no—
423C2×Dic11C22×D412yes—
424C2×Dic11C22×D412yes—
425C2×Dic11C22×D412yes—
426C4×D11—24no—
427C4×D11—42no—
428C4×D11—82no—
429C4×D11—82no—
430Dic22—24no—
431Dic22—24no—
432Dic22—42no—
433Dic22—82no—
434Dic22—82no—
435Dic22—81no—
436C8×C11—24no—
437C11⋊C8—24no—
438C22×#41—111no—
439C23×D4C2×D1111yescharacteristic
440C2×#137—114no—
441C22×SD16—112no—
442C22×SD16C2×D1112yescomplemented
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—111no—
461C2×C22⋊Q8—112no—
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#484—112no—
475#484—112no—
476#480—114no—
477#474—114no—
478#468—114no—
479#468—114no—
480#467—114no—
481#467—114no—
482#464—114no—
483#464—114no—
484#461—114no—
485#452—114no—
486#452—114no—
487#451—112no—
488#451—112no—
489#451—112no—
490#451—112no—
491#450—112no—
492#450—112no—
493#450—114no—
494#450C2×D1112yes—
495#450C2×D1112yes—
496#450C2×D1114yescomplemented
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×#102C2×D1112yescomplemented
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—24no—
516C22×C11—44no—
517C22×C11—48no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—88no—
524C22×C11—88no—
525C22×C11—84no—
526C22×C11C2×#13712yes—
527C22×C11C2×#13712yes—
528C22×C11C2×#13712yes—
529C22×C11C23×D411yescharacteristic
530C2×D11—22no—
531C2×D11—22no—
532C2×D11—22no—
533C2×D11—82no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—21no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11C2×H(5,𝔽2)12yes—
540Dic11—22no—
541Dic11—22no—
542Dic11—22no—
543Dic11—42no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547C25—21no—
548C2×#41—114no—
549C2×#41—222no—
550C2×#41—444no—
551C22×Q8—112no—
552C22×Q8—111no—
553C22×Q8—111no—
554C22×Q8C22×D1111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—44no—
559C22×D4—111no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4C22×D1111yescharacteristic
563C22×D4C22×D1112yes—
564C22×D4C22×D1112yes—
565C22×D4C22×D1111yescharacteristic
566C23×C4—111no—
567C23×C4—221no—
568C23×C4—221no—
569C23×C4C22×D1111yescharacteristic
570#137—448no—
571C2×Q16—114no—
572C2×Q16—114no—
573C2×SD16—44no—
574C2×SD16—114no—
575C2×SD16—114no—
576C2×SD16—444no—
577C2×SD16C22×D1114yes—
578C2×SD16C22×D1114yes—
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—112no—
596C22⋊Q8—112no—
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⋊Q8—221no—
615C22⋊Q8—221no—
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—111no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—222no—
644C2×C4⋊C4—221no—
645C2×C4⋊C4—221no—
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—111no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—224no—
652C2×C22⋊C4—224no—
653C2×C22⋊C4—221no—
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#107—114no—
662C4⋊C8—114no—
663#103—114no—
664#103—114no—
665#103—114no—
666#103—114no—
667#102—114no—
668#102—114no—
669#102C22×D1114yes—
670#102C22×D1114yes—
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—44no—
681C2×C11—82no—
682C2×C11#348411yescharacteristic
683C2×C11C22×#13711yescharacteristic
684C2×C11#358511yescharacteristic
685D11—42no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—22no—
690C24—44no—
691C24—44no—
692C24—82no—
693C24—111no—
694C24D4×D1111yescharacteristic
695#41—228no—
696#41—444no—
697#41—448no—
698C2×Q8—21no—
699C2×Q8—42no—
700C2×Q8—112no—
701C2×Q8—112no—
702C2×Q8—222no—
703C2×Q8—222no—
704C2×Q8—221no—
705C2×Q8—221no—
706C2×Q8—442no—
707C2×Q8—442no—
708C2×Q8—444no—
709C2×Q8C23×D1112yes—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—21no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—112no—
724C2×D4—112no—
725C2×D4—224no—
726C2×D4—224no—
727C2×D4—224no—
728C2×D4—444no—
729C2×D4—882no—
730C2×D4C23×D1112yes—
731C2×D4C23×D1112yes—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—42no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—221no—
745C22×C4—221no—
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—444no—
758Q16—444no—
759SD16—28no—
760SD16—44no—
761SD16—228no—
762SD16—444no—
763M16—444no—
764C2×C8—42no—
765C2×C8—114no—
766C2×C8—442no—
767C2×C8C23×D1114yes—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—21no—
771C4⋊C4—112no—
772C4⋊C4—112no—
773C4⋊C4—112no—
774C4⋊C4—112no—
775C4⋊C4—222no—
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⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4C23×D1112yes—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—112no—
793C22⋊C4—112no—
794C22⋊C4—112no—
795C22⋊C4—112no—
796C22⋊C4—222no—
797C22⋊C4—222no—
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—24no—
812C23—22no—
813C23—22no—
814C23—41no—
815C23—41no—
816C23—44no—
817C23—44no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—44no—
823C23—44no—
824C23—42no—
825C23—82no—
826C23—82no—
827C23—816no—
828C23—112no—
829C23—222no—
830C23—441no—
831C23—441no—
832C23#6696814yescomplemented
833C23C2×D4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×D4×D1111yescharacteristic
836Q8—24no—
837Q8—81no—
838Q8—224no—
839Q8—224no—
840Q8—442no—
841Q8—881no—
842Q8—882no—
843Q8—882no—
844D4—24no—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—44no—
849D4—44no—
850D4—42no—
851D4—224no—
852D4—224no—
853D4—448no—
854D4—884no—
855D4#6703714yes—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
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—222no—
875C2×C4—442no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—448no—
879C2×C4—442no—
880C2×C4—442no—
881C2×C4—882no—
882C2×C4—882no—
883C2×C4—884no—
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—24no—
899C22—44no—
900C22—48no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—88no—
907C22—88no—
908C22—84no—
909C22—222no—
910C22—222no—
911C22—222no—
912C22—882no—
913C22C2×#6696812yes—
914C22C2×#6696812yes—
915C22C2×#6696812yes—
916C22C22×D4×D1111yescharacteristic
917C4—21no—
918C4—21no—
919C4—21no—
920C4—42no—
921C4—42no—
922C4—222no—
923C4—222no—
924C4—222no—
925C4—442no—
926C4—442no—
927C4—442no—
928C4—442no—
929C4C2×#6703712yes—
930C2—22no—
931C2—22no—
932C2—22no—
933C2—44no—
934C2—82no—
935C2—442no—
936C2#1308224511yescharacteristic
937C2C22×#6696811yescharacteristic
938C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC22×C11C23×D4
prime radicalC2×#10623337C2
hypercenterC2×#450D11
hypocenterC11#61570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. #13082412C2semidirect
3. #13080701C2semidirect
4. #13080693C2semidirect
5. #13080130C2semidirect
6. #13080126C2semidirect
7. #13079616C2semidirect
8. #13079419C2semidirect
9. #13079391C2semidirect
10. #13079388C2semidirect
11. #13078710C2semidirect
12. #13077871C2semidirect
13. C2×#10622831C2semidirect
14. #13077642C2semidirect
15. C2×C11×#450C2semidirect
18. C22×C11×SD16C22semidirect
22. Q8×C22⋊D11C22semidirect
32. C22×#4324C22semidirect
36. C2×#66968C22semidirect
38. #10623166C22semidirect
40. #10623163C22semidirect
41. D11×C22⋊Q8C22semidirect
43. #10623153C22semidirect
45. #10623042C22semidirect
50. C11×#450C22semidirect
51. C2×C11×#102C22semidirect
53. #10622841C22semidirect
56. #10622831C22semidirect
57. C2×#66896C22semidirect
59. #10622787C22semidirect
60. #10622786C22semidirect
61. #10622783C22semidirect
62. #10622780C22semidirect
63. #10622779C22semidirect
64. #10622777C22semidirect
65. #10622775C22semidirect
66. #10622729C22semidirect
67. #10622724C22semidirect
68. #10622664C22semidirect
69. #10622663C22semidirect
70. #10622657C22semidirect
71. #10622583C22semidirect
72. #10622396C22semidirect
73. #10622393C22semidirect
74. #10622387C22semidirect
75. #10622384C22semidirect
76. #10622380C22semidirect
77. #10622378C22semidirect
78. #10622372C22semidirect
79. #10622370C22semidirect
80. #10622352C22semidirect
81. #10622352C22semidirect
82. #10622343C22semidirect
83. #10622339C22semidirect
84. #10622335C22semidirect
85. #10622335C22semidirect
86. #10622332C22semidirect
103. C2×Q8×D11C23semidirect
133. #66999C23semidirect
134. Q8×Dic11C23semidirect
136. #66997C23semidirect
137. C2×#4326C23semidirect
176. C2×Dic44C23semidirect
177. C2×#4313C23semidirect
179. #66950C23semidirect
184. C4⋊C4×D11C23semidirect
189. #66941C23semidirect
191. #66940C23semidirect
204. #66899C23semidirect
209. (C2×D11)⋊C8C23semidirect
210. #66882C23semidirect
211. #66880C23semidirect
212. #66880C23semidirect
213. #66879C23semidirect
214. Dic11⋊C8C23semidirect
215. #66874C23semidirect
216. #66871C23semidirect
355. C2×#450D11semidirect
374. C23×C11#137semidirect
442. C22×SD16C2×D11semidirect
496. #450C2×D11semidirect
505. C2×#102C2×D11semidirect
810. C11#61570semidirect
832. C23#66968semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×#106233372
#130807012
#130806932
#130801302
#130801262
#130796162
#130794192
#130793912
#130793882
#130787102
#130778712
C2×#106228312
#130776422
C2×C11×#4502
#6157011