Finite Group Databasebeta

← #15646084

Subgroups — #15646084

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082392C211yesmaximal, characteristic, complemented
2#13082174C211yesmaximal, characteristic, complemented
3#13081640C212yesmaximal, complemented
4#13081327C212yesmaximal, complemented
5#13080861C212yesmaximal, complemented
6#13080633C214yesmaximal, complemented
7#13080211C212yesmaximal, complemented
8#13080096C214yesmaximal, complemented
9#13079974C212yesmaximal, complemented
10#13079933C211yesmaximal, characteristic, complemented
11#13079633C212yesmaximal, complemented
12#13079557C211yesmaximal, characteristic, complemented
13#13078764C212yesmaximal, complemented
14#13078616C211yesmaximal, characteristic, complemented
15#13078091C212yesmaximal, complemented
16#13077734C211yesmaximal, characteristic, complemented
17C2×C11×#459C211yesmaximal, characteristic, complemented
18C2×#67037—21no—
19C22×C11×D8C2212yescomplemented
20C2×C11×#127C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic, complemented
22#10623337C2212yescomplemented
23#10623336—21no—
24D4×C22⋊D11—22no—
25D4×C22⋊D11C2214yes—
26#10623322—21no—
27C2×#66979—21no—
28C2×#66964C2214yescomplemented
29#10623249—21no—
30#10623249C2212yescomplemented
31#10623248—21no—
32#10623248C2212yescomplemented
33#10623247C2212yescomplemented
34#10623246—22no—
35D11×#127C2212yescomplemented
36#10623096—21no—
37#10623094C2211yescharacteristic, complemented
38#10623088C2212yescomplemented
39#10623086C2211yescharacteristic, complemented
40#10623074C2211yescharacteristic, complemented
41#10623073C2211yescharacteristic, complemented
42#10623072—21no—
43#10623069—22no—
44C4×#4341C2212yescomplemented
45#10623044C2212yescomplemented
46#10623026—22no—
47#10623008C2211yescharacteristic
48C4×#4339C2211yescharacteristic
49#10623001C2211yescharacteristic, complemented
50C11×#459C2212yescomplemented
51C11×#459C2212yescomplemented
52C11×#459C2212yescomplemented
53C11×#459C2212yescomplemented
54C2×C11×C4⋊C8C2211yescharacteristic, complemented
55C2×C11×#102C2212yescomplemented
56#10622831C2214yescomplemented
57#10622830C2212yescomplemented
58#10622772C2214yescomplemented
59#10622771C2214yescomplemented
60#10622769C2214yescomplemented
61#10622767C2214yescomplemented
62#10622766C2214yescomplemented
63#10622765C2214yescomplemented
64#10622763C2214yescomplemented
65#10622727C2214yescomplemented
66#10622724C2214yescomplemented
67#10622689C2212yescomplemented
68#10622688C2212yescomplemented
69#10622688C2212yescomplemented
70#10622683C2212yescomplemented
71#10622628C2211yescharacteristic, complemented
72#10622628C2211yescharacteristic, complemented
73C4×#4323C2212yescomplemented
74C4×#4323C2212yescomplemented
75#10622620C2211yescharacteristic, complemented
76#10622620C2211yescharacteristic, complemented
77#10622580C2212yescomplemented
78#10622538C2211yescharacteristic, complemented
79#10622464C2212yescomplemented
80#10622461C2212yescomplemented
81#10622455C2212yescomplemented
82#10622454C2212yescomplemented
83#10622451C2212yescomplemented
84#10622450C2212yescomplemented
85#10622448C2212yescomplemented
86#10622444C2212yescomplemented
87#10622393C2214yescomplemented
88#10622392C2214yescomplemented
89#10622389C2214yescomplemented
90#10622383C2214yescomplemented
91#10622377C2214yescomplemented
92#10622376C2214yescomplemented
93#10622375C2214yescomplemented
94#10622370C2214yescomplemented
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11C2311yescharacteristic
98C22×D4×C11C2312yes—
99C23×C4×C11—21no—
100C22×C22⋊D11—24no—
101#67037—48no—
102C2×#4341—22no—
103C2×#4341—22no—
104C2×#4341C2312yes—
105C2×D4×D11—22no—
106C2×D4×D11—22no—
107C2×D4×D11—22no—
108C2×D4×D11C2314yes—
109C2×#4339—21no—
110C2×#4339D411yescharacteristic
111C2×C11×D8—44no—
112C2×C11×D8C2314yes—
113C2×C11×D8C2314yes—
114C22×C8×C11C2312yes—
115C11×#127—21no—
116C11×#127—21no—
117C11×#127C2312yes—
118C11×#127C2312yes—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11C2311yescharacteristic
122C4×D4×C11C2311yescharacteristic
123C4×D4×C11C2311yescharacteristic
124C4×D4×C11C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127C2×C42×C11C2311yescharacteristic
128#67006—22no—
129#67006—24no—
130C2×C22⋊Dic11—22no—
131#66993—22no—
132#66993—22no—
133#66993C2314yes—
134#66992—22no—
135#66992—24no—
136#66992—24no—
137#66991—22no—
138#66991—22no—
139#66991—22no—
140#66991C2314yes—
141#66991C2312yes—
142#66990—24no—
143#66990—24no—
144#66989—22no—
145#66989C2312yes—
146#66988—22no—
147D4×Dic11—22no—
148D4×Dic11C2314yes—
149D4×Dic11C2312yes—
150C2×#4324C2314yes—
151C2×#4324C2314yes—
152C2×#4323C2312yes—
153C2×#4323C2312yes—
154#66983—21no—
155#66983—21no—
156#66983—21no—
157#66983C2312yes—
158#66982—22no—
159C4×C22⋊D11—22no—
160C4×C22⋊D11—22no—
161C4×C22⋊D11D412yes—
162C4×C22⋊D11C2312yes—
163#66979—21no—
164#66979—22no—
165#66979—21no—
166#66979—21no—
167#66979—22no—
168#66979D411yescharacteristic
169C2×C4⋊Dic11—21no—
170C2×C4⋊Dic11—21no—
171#66977—21no—
172#66977—21no—
173#66977—21no—
174#66977C2312yes—
175C2×C4×Dic11—22no—
176#66964—48no—
177C2×#4314C2314yes—
178C2×#4313C2314yes—
179#66951—22no—
180#66950C2312yes—
181#66945C2312yes—
182#66943C2312yes—
183#66942—22no—
184#66940C2312yes—
185#66939—22no—
186#66938—22no—
187#66936—22no—
188(C22⋊D11)⋊C4—22no—
189#66932—22no—
190#66932—22no—
191#66931—22no—
192#66930—22no—
193#66928—21no—
194#66927C2311yescharacteristic
195C4×D44—21no—
196C4×D44D411yescharacteristic
197C4×D44C2311yescharacteristic
198C4×D44C2312yes—
199#66925D412yes—
200C42×D11C2312yes—
201#66923—21no—
202#66922C2311yescharacteristic
203#66922C2311yescharacteristic
204#66922C2311yescharacteristic
205C4×Dic22—21no—
206C4×Dic22D411yescharacteristic
207C4×Dic22C2312yes—
208C4×Dic22C2311yescharacteristic
209C11×C4⋊C8C2312yes—
210C11×C4⋊C8C2312yes—
211C11×#102C2314yes—
212C11×#102C2314yes—
213#66896C2314yes—
214#66896C2312yes—
215#66896C2314yes—
216#66896C2312yes—
217C22⋊(C11⋊C8)C2312yes—
218#66885C2314yes—
219(C2×D11)⋊C8C2314yes—
220#66881C2314yes—
221#66880C2314yes—
222#66879C2314yes—
223Dic11⋊C8C2314yes—
224#66873C2312yes—
225#66873C2312yes—
226#66871C2312yes—
227#66871C2312yes—
228C4⋊(C11⋊C8)C2311yescharacteristic
229C4⋊(C11⋊C8)C2311yescharacteristic
230C4×C11⋊C8C2312yes—
231#61959—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11—22no—
234C23×D11—24no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—21no—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—41no—
243C2×D4×C11—42no—
244C2×D4×C11—42no—
245C2×D4×C11—44no—
246C2×D4×C11—82no—
247C2×D4×C11C2414yes—
248C2×D4×C11C2411yescharacteristic
249C2×D4×C11C2411yescharacteristic
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—44no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C2×C22⋊D11—24no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—24no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—416no—
267C2×C22⋊D11C2×D412yes—
268C22×Dic11—22no—
269C22×Dic11—24no—
270C22×Dic11—22no—
271#4341—24no—
272#4341—42no—
273#4341—48no—
274#4341—48no—
275D4×D11—44no—
276D4×D11—44no—
277D4×D11—48no—
278D4×D11—48no—
279D4×D11—84no—
280#4339—24no—
281#4339—44no—
282C2×D44—21no—
283C2×D44—21no—
284C2×D44C2×D411yescharacteristic
285C2×D44C2412yes—
286C2×C4×D11—22no—
287C2×C4×D11C2×D412yes—
288C2×C4×D11C2×D412yes—
289C2×C4×D11C2412yes—
290C2×Dic22—21no—
291C2×Dic22—21no—
292C2×Dic22C2×D411yescharacteristic
293C2×Dic22C2412yes—
294C11×D8—28no—
295C11×D8—44no—
296C2×C8×C11—42no—
297C2×C8×C11C2414yes—
298C11×C4⋊C4—21no—
299C11×C4⋊C4C2411yescharacteristic
300C11×C4⋊C4C2411yescharacteristic
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2411yescharacteristic
308C42×C11C2411yescharacteristic
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311C22⋊Dic11—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—24no—
314C22⋊Dic11—24no—
315C22⋊Dic11—22no—
316C22⋊Dic11C2×D412yes—
317#4324—44no—
318#4324—44no—
319#4323—24no—
320#4323—42no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4C2×D412yes—
326(C2×D11)⋊C4C2×D412yes—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—21no—
330C4⋊Dic11—21no—
331C4⋊Dic11—21no—
332C4⋊Dic11—21no—
333C4⋊Dic11C2×D411yescharacteristic
334C4⋊Dic11C2×D411yescharacteristic
335C4⋊Dic11C2412yes—
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4C2×D412yes—
342Dic11⋊C4C2×D412yes—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11C2×D412yes—
347C4×Dic11C2×D412yes—
348C4×Dic11C2412yes—
349C2×C11⋊C8C2412yes—
350C2×C11⋊C8C2412yes—
351#4314—44no—
352#4313—44no—
353#3498—111no—
354#3475—111no—
355#3397—112no—
356#3366—112no—
357#3325—112no—
358#3310—114no—
359#3272—112no—
360#3264—114no—
361#3251—112no—
362#3246—111no—
363#3217—112no—
364#3208—111no—
365#3115—112no—
366#3100—111no—
367#3038—112no—
368C2×#459D1111yescharacteristic, complemented
369#2989—111no—
370C23×C11—21no—
371C23×C11—21no—
372C23×C11—24no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—44no—
376C23×C11—81no—
377C23×C11—82no—
378C23×C11—82no—
379C23×C11C22×D411yescharacteristic
380C22×D11—22no—
381C22×D11—48no—
382C22×D11—84no—
383C22×D11—84no—
384C22×D11C22×D412yes—
385D4×C11—24no—
386D4×C11—21no—
387D4×C11—21no—
388D4×C11—21no—
389D4×C11—24no—
390D4×C11—42no—
391D4×C11—44no—
392D4×C11—44no—
393D4×C11—44no—
394D4×C11—82no—
395D4×C11—82no—
396D4×C11H(5,𝔽2)12yescomplemented
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—41no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11—42no—
406C2×C4×C11—42no—
407C2×C4×C11AGL(1,ℤ/8)14yescomplemented
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C2511yescharacteristic
414C22⋊D11—24no—
415C22⋊D11—48no—
416C22⋊D11—44no—
417C22⋊D11—48no—
418C22⋊D11—44no—
419C22⋊D11—84no—
420C22⋊D11—84no—
421C22⋊D11—82no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—44no—
426C2×Dic11—48no—
427C2×Dic11—82no—
428C2×Dic11C22×D412yes—
429C2×Dic11C22×D412yes—
430C2×Dic11C22×D412yes—
431D44—22no—
432D44—22no—
433D44—22no—
434D44—42no—
435D44—42no—
436C4×D11—24no—
437C4×D11—22no—
438C4×D11—22no—
439C4×D11—42no—
440C4×D11—44no—
441Dic22—22no—
442Dic22—22no—
443Dic22—22no—
444Dic22—42no—
445Dic22—81no—
446C8×C11—24no—
447C11⋊C8—22no—
448C11⋊C8—22no—
449C2×H(5,𝔽2)—221no—
450C2×AGL(1,ℤ/8)—114no—
451C22×D8C2×D1112yescomplemented
452#556—111no—
453#555—111no—
454#554—111no—
455#553—221no—
456#552—112no—
457#552—221no—
458#551—222no—
459#550—112no—
460#550—221no—
461#547—111no—
462#546—112no—
463D42—114no—
464D42—112no—
465D42—221no—
466D42—222no—
467#535—222no—
468#535—221no—
469#533—111no—
470#532—112no—
471#532—111no—
472C2×#127—112no—
473C2×#127C2×D1111yescharacteristic
474#529—112no—
475#529—222no—
476#525—221no—
477C4×#41—111no—
478C4×#41—112no—
479C2×C4×D4C2×D1111yescharacteristic, complemented
480C2×#117—221no—
481#496—114no—
482#492—112no—
483#490—114no—
484#486—112no—
485#482—114no—
486#480—112no—
487#478—114no—
488#476—112no—
489#475—112no—
490#474—111no—
491#474—111no—
492#469—114no—
493#468—114no—
494#465—114no—
495#463—114no—
496#461—112no—
497#460—112no—
498#460—112no—
499#460—112no—
500#460—114no—
501#459—114no—
502#459—111no—
503#459—111no—
504#459C2×D1112yescomplemented
505#459C2×D1112yescomplemented
506#459C2×D1112yescomplemented
507#459C2×D1112yescomplemented
508#450—114no—
509#450—114no—
510#449—114no—
511#447—112no—
512#447—114no—
513#446—112no—
514#442—114no—
515#440—114no—
516C4×D8—112no—
517C4×D8—112no—
518#436—112no—
519#435—114no—
520#432—112no—
521#431—111no—
522#423—112no—
523C2×C4⋊C8C2×D1111yescharacteristic, complemented
524#418—114no—
525C2×#102C2×D1112yescomplemented
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—22no—
529C22×C11—41no—
530C22×C11—41no—
531C22×C11—44no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11—44no—
535C22×C11—41no—
536C22×C11—44no—
537C22×C11—84no—
538C22×C11—164no—
539C22×C11C2×AGL(1,ℤ/8)12yes—
540C22×C11C23×D411yescharacteristic
541C2×D11—22no—
542C2×D11—22no—
543C2×D11—22no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—168no—
548C4×C11—21no—
549C4×C11—21no—
550C4×C11—21no—
551C4×C11—41no—
552C4×C11—41no—
553C4×C11C2×AGL(1,ℤ/8)12yes—
554C4×C11C2×AGL(1,ℤ/8)12yes—
555C4×C11C2×H(5,𝔽2)11yescharacteristic
556C4×C11#58511yescharacteristic
557Dic11—22no—
558Dic11—22no—
559Dic11—22no—
560Dic11—42no—
561Dic11—42no—
562Dic11—42no—
563H(5,𝔽2)—448no—
564C2×#41—111no—
565C2×#41—112no—
566C2×#41—222no—
567C2×#41—222no—
568C2×#41—221no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—114no—
572C22×D4—222no—
573C22×D4—222no—
574C22×D4—222no—
575C22×D4—224no—
576C22×D4C22×D1111yescharacteristic
577C22×D4C22×D1112yes—
578C23×C4—21no—
579AGL(1,ℤ/8)—448no—
580C2×SD16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×D8—44no—
584C2×D8—112no—
585C2×D8—112no—
586C2×D8C22×D1114yes—
587C2×D8C22×D1114yes—
588C2×M16—114no—
589C22×C8C22×D1112yes—
590C4⋊Q8—111no—
591C4⋊Q8—111no—
592C4⋊Q8—111no—
593#127—21no—
594#127—21no—
595#127—114no—
596#127—111no—
597#127—222no—
598#127—222no—
599#127C22×D1112yes—
600#127C22×D1112yes—
601#126—222no—
602#126—222no—
603#126—222no—
604#125—112no—
605#125—222no—
606#125—221no—
607#124—112no—
608#124—222no—
609#124—222no—
610#124—221no—
611#123—222no—
612#123—222no—
613#123—222no—
614#123—222no—
615C22⋊Q8—112no—
616C22⋊Q8—112no—
617C22⋊Q8—222no—
618C22⋊Q8—221no—
619C22⋊Q8—221no—
620C22⋊Q8—221no—
621#121—112no—
622#121—114no—
623#121—112no—
624#121—222no—
625#121—222no—
626#121—224no—
627#121—222no—
628#121—224no—
629#121—221no—
630#121—221no—
631#121—222no—
632#121—221no—
633#120—224no—
634#120—224no—
635#120—224no—
636#120—222no—
637C4×Q8—111no—
638C4×Q8—111no—
639C4×Q8—112no—
640C4×Q8—112no—
641C4×Q8—221no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—112no—
645C4×D4—112no—
646C4×D4—112no—
647C4×D4—114no—
648C4×D4—111no—
649C4×D4—111no—
650C4×D4—112no—
651C4×D4—222no—
652C4×D4—222no—
653C4×D4—222no—
654C4×D4—222no—
655C4×D4—221no—
656C4×D4C22×D1111yescharacteristic
657C4×D4C22×D1111yescharacteristic
658C4×D4C22×D1111yescharacteristic
659C4×D4C22×D1111yescharacteristic
660#117—111no—
661#117—112no—
662#117—112no—
663#117—222no—
664#117—222no—
665#117—222no—
666#117—221no—
667#117—221no—
668#117—221no—
669C2×C4⋊C4—221no—
670C2×C4⋊C4—221no—
671C2×C4⋊C4C22×D1111yescharacteristic
672C2×C22⋊C4—21no—
673C2×C22⋊C4—222no—
674C2×C42—112no—
675C2×C42—222no—
676C2×C42C22×D1111yescharacteristic
677#107—112no—
678#107—112no—
679#106—114no—
680C4⋊C8—114no—
681C4⋊C8—111no—
682C4⋊C8—111no—
683C4⋊C8C22×D1112yes—
684C4⋊C8C22×D1112yes—
685#103—114no—
686#102—114no—
687#102—112no—
688#102—112no—
689#102—114no—
690#102—114no—
691#102—112no—
692#102—112no—
693#102C22×D1114yes—
694#102C22×D1114yes—
695C22⋊C8—112no—
696C22⋊C8—114no—
697#97—114no—
698C4×C8—112no—
699C2×C11—22no—
700C2×C11—42no—
701C2×C11—84no—
702C2×C11—81no—
703C2×C11#348811yescharacteristic
704C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
705C2×C11#358511yescharacteristic
706D11—42no—
707D11—82no—
708C24—21no—
709C24—22no—
710C24—224no—
711#41—224no—
712#41—224no—
713#41—442no—
714#41—448no—
715#41—448no—
716#41—444no—
717C2×Q8—111no—
718C2×Q8—112no—
719C2×Q8—221no—
720C2×Q8—221no—
721C2×D4—22no—
722C2×D4—21no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—41no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—44no—
732C2×D4—82no—
733C2×D4—112no—
734C2×D4—111no—
735C2×D4—112no—
736C2×D4—224no—
737C2×D4—224no—
738C2×D4—224no—
739C2×D4—222no—
740C2×D4—224no—
741C2×D4—222no—
742C2×D4—222no—
743C2×D4—221no—
744C2×D4—221no—
745C2×D4—444no—
746C2×D4—444no—
747C2×D4—448no—
748C2×D4—448no—
749C2×D4—4416no—
750C2×D4—884no—
751C2×D4C23×D1114yes—
752C2×D4C23×D1111yescharacteristic
753C2×D4C23×D1111yescharacteristic
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—44no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—222no—
764C22×C4—224no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4D4×D1111yescharacteristic
768C22×C4D4×D1111yescharacteristic
769C22×C4C23×D1111yescharacteristic
770SD16—444no—
771SD16—444no—
772SD16—444no—
773D8—28no—
774D8—44no—
775D8—224no—
776D8—442no—
777M16—444no—
778C2×C8—42no—
779C2×C8—112no—
780C2×C8—112no—
781C2×C8C23×D1114yes—
782C4⋊C4—21no—
783C4⋊C4—111no—
784C4⋊C4—111no—
785C4⋊C4—112no—
786C4⋊C4—112no—
787C4⋊C4—112no—
788C4⋊C4—112no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—222no—
792C4⋊C4—222no—
793C4⋊C4—221no—
794C4⋊C4—221no—
795C4⋊C4—222no—
796C4⋊C4—221no—
797C4⋊C4—222no—
798C4⋊C4—221no—
799C4⋊C4C23×D1111yescharacteristic
800C4⋊C4C23×D1111yescharacteristic
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—112no—
806C22⋊C4—112no—
807C22⋊C4—112no—
808C22⋊C4—222no—
809C22⋊C4—222no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4—222no—
813C22⋊C4—224no—
814C22⋊C4—224no—
815C22⋊C4—222no—
816C22⋊C4—222no—
817C22⋊C4—222no—
818C22⋊C4—222no—
819C42—112no—
820C42—112no—
821C42—112no—
822C42—222no—
823C42—222no—
824C42—222no—
825C42D4×D1111yescharacteristic
826C42D4×D1111yescharacteristic
827C42C23×D1111yescharacteristic
828C42C23×D1111yescharacteristic
829C11#6195911yescharacteristic, complemented, Sylow
830C23—21no—
831C23—21no—
832C23—24no—
833C23—42no—
834C23—42no—
835C23—44no—
836C23—81no—
837C23—82no—
838C23—82no—
839C23—112no—
840C23—222no—
841C23—448no—
842C23—884no—
843C23—884no—
844C23C2×D4×D1111yescharacteristic
845Q8—222no—
846Q8—222no—
847Q8—222no—
848Q8—442no—
849Q8—881no—
850D4—24no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—24no—
855D4—42no—
856D4—44no—
857D4—44no—
858D4—44no—
859D4—82no—
860D4—82no—
861D4—224no—
862D4—222no—
863D4—222no—
864D4—222no—
865D4—442no—
866D4—448no—
867D4—444no—
868D4—448no—
869D4—444no—
870D4—442no—
871D4—884no—
872D4—884no—
873D4—882no—
874D4#6703712yescomplemented
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—112no—
886C2×C4—112no—
887C2×C4—112no—
888C2×C4—224no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—442no—
895C2×C4—444no—
896C2×C4—448no—
897C2×C4—444no—
898C2×C4—882no—
899C2×C4#6696414yescomplemented
900C2×C4C2×D4×D1111yescharacteristic
901C2×C4C2×D4×D1111yescharacteristic
902C2×C4C2×D4×D1111yescharacteristic
903C2×C4C2×D4×D1111yescharacteristic
904C2×C4C2×D4×D1111yescharacteristic
905C2×C4C24×D1111yescharacteristic
906C8—24no—
907C8—222no—
908C8—222no—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—41no—
913C22—41no—
914C22—44no—
915C22—41no—
916C22—41no—
917C22—44no—
918C22—41no—
919C22—44no—
920C22—84no—
921C22—164no—
922C22—222no—
923C22—222no—
924C22—222no—
925C22—442no—
926C22—442no—
927C22—442no—
928C22—1768no—
929C22C2×#6696412yes—
930C22C22×D4×D1111yescharacteristic
931C4—21no—
932C4—21no—
933C4—21no—
934C4—41no—
935C4—41no—
936C4—222no—
937C4—222no—
938C4—222no—
939C4—442no—
940C4—442no—
941C4—442no—
942C4C2×#6696412yes—
943C4C2×#6696412yes—
944C4C2×#6703711yescharacteristic
945C4#1062345311yescharacteristic
946C2—22no—
947C2—42no—
948C2—81no—
949C2—84no—
950C2—442no—
951C2—882no—
952C2#1308228111yescharacteristic
953C2C22×#6696411yescharacteristic
954C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC22×C11C23×D4
hypercenterC2×#459D11
hypocenterC11#61959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13082392C2semidirect
2. #13082174C2semidirect
3. #13081640C2semidirect
4. #13081327C2semidirect
5. #13080861C2semidirect
6. #13080633C2semidirect
7. #13080211C2semidirect
8. #13080096C2semidirect
9. #13079974C2semidirect
10. #13079933C2semidirect
11. #13079633C2semidirect
12. #13079557C2semidirect
13. #13078764C2semidirect
14. #13078616C2semidirect
15. #13078091C2semidirect
16. #13077734C2semidirect
17. C2×C11×#459C2semidirect
19. C22×C11×D8C22semidirect
21. C2×C4×D4×C11C22semidirect
22. #10623337C22semidirect
28. C2×#66964C22semidirect
30. #10623249C22semidirect
32. #10623248C22semidirect
33. #10623247C22semidirect
35. D11×#127C22semidirect
37. #10623094C22semidirect
38. #10623088C22semidirect
39. #10623086C22semidirect
40. #10623074C22semidirect
41. #10623073C22semidirect
44. C4×#4341C22semidirect
45. #10623044C22semidirect
49. #10623001C22semidirect
50. C11×#459C22semidirect
51. C11×#459C22semidirect
52. C11×#459C22semidirect
53. C11×#459C22semidirect
54. C2×C11×C4⋊C8C22semidirect
55. C2×C11×#102C22semidirect
56. #10622831C22semidirect
57. #10622830C22semidirect
58. #10622772C22semidirect
59. #10622771C22semidirect
60. #10622769C22semidirect
61. #10622767C22semidirect
62. #10622766C22semidirect
63. #10622765C22semidirect
64. #10622763C22semidirect
65. #10622727C22semidirect
66. #10622724C22semidirect
67. #10622689C22semidirect
68. #10622688C22semidirect
69. #10622688C22semidirect
70. #10622683C22semidirect
71. #10622628C22semidirect
72. #10622628C22semidirect
73. C4×#4323C22semidirect
74. C4×#4323C22semidirect
75. #10622620C22semidirect
76. #10622620C22semidirect
77. #10622580C22semidirect
78. #10622538C22semidirect
79. #10622464C22semidirect
80. #10622461C22semidirect
81. #10622455C22semidirect
82. #10622454C22semidirect
83. #10622451C22semidirect
84. #10622450C22semidirect
85. #10622448C22semidirect
86. #10622444C22semidirect
87. #10622393C22semidirect
88. #10622392C22semidirect
89. #10622389C22semidirect
90. #10622383C22semidirect
91. #10622377C22semidirect
92. #10622376C22semidirect
93. #10622375C22semidirect
94. #10622370C22semidirect
368. C2×#459D11semidirect
396. D4×C11H(5,𝔽2)semidirect
407. C2×C4×C11AGL(1,ℤ/8)semidirect
451. C22×D8C2×D11semidirect
479. C2×C4×D4C2×D11semidirect
504. #459C2×D11semidirect
505. #459C2×D11semidirect
506. #459C2×D11semidirect
507. #459C2×D11semidirect
523. C2×C4⋊C8C2×D11semidirect
525. C2×#102C2×D11semidirect
829. C11#61959semidirect
874. D4#67037semidirect
899. C2×C4#66964semidirect

Maximal subgroups

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

subgroupindex
#130823922
#130821742
#130816402
#130813272
#130808612
#130806332
#130802112
#130800962
#130799742
#130799332
#130796332
#130795572
#130787642
#130786162
#130780912
#130777342
C2×C11×#4592
#6195911