Finite Group Databasebeta

← D11×#3399 #15634747

Subgroups — D11×#3399 #15634747

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#559C211yesmaximal, characteristic, complemented
2D11×#550C211yesmaximal, characteristic, complemented
3#13081663C211yesmaximal, characteristic, complemented
4#13081662C211yesmaximal, characteristic, complemented
5#13081661C212yesmaximal, complemented
6#13081660C211yesmaximal, characteristic, complemented
7#13081659C212yesmaximal, complemented
8#13081658C211yesmaximal, characteristic, complemented
9#13081657C211yesmaximal, characteristic, complemented
10#13081656C211yesmaximal, characteristic, complemented
11#13081655C212yesmaximal, complemented
12#13081654C211yesmaximal, characteristic, complemented
13#13081653C212yesmaximal, complemented
14D11×#496C212yesmaximal, complemented
15D11×#493C211yesmaximal, characteristic, complemented
16D11×#460C211yesmaximal, characteristic, complemented
17D11×#463C212yesmaximal, complemented
18D11×#459C212yesmaximal, complemented
19D11×#459C211yesmaximal, characteristic, complemented
20D11×#446C211yesmaximal, characteristic, complemented
21D11×#442C212yesmaximal, complemented
22C4×SD16×D11C211yesmaximal, characteristic, complemented
23C11×#3399C211yesmaximal, characteristic, complemented
24C2×#41×D11—21no—
25C11×#559C2211yescharacteristic, complemented
26C11×#550C2211yescharacteristic, complemented
27#10623365—21no—
28C2×SD16×D11C2211yescharacteristic
29C2×SD16×D11C2212yes—
30C2×D8×D11C2212yes—
31C2×D8×D11C2212yes—
32C2×D8×D11C2212yes—
33#10623249C2212yescomplemented
34#10623249C2211yescharacteristic, complemented
35D11×#127C2212yes—
36D11×#127C2211yescharacteristic
37D11×#127C2211yescharacteristic
38#10623244C2211yescharacteristic, complemented
39#10623212—21no—
40#10623212C2212yescomplemented
41D11×#124—21no—
42D11×#124C2212yes—
43#10623195—22no—
44D11×#123—22no—
45D11×#121—21no—
46D11×#121—22no—
47#10623130—21no—
48#10623130—22no—
49#10623116C2211yescharacteristic, complemented
50#10623116C2211yescharacteristic, complemented
51#10623108C2211yescharacteristic, complemented
52C4×Q8×D11C2211yescharacteristic
53C4×Q8×D11C2211yescharacteristic
54#10623090—21no—
55#10623090C2212yescomplemented
56#10623084C2212yescomplemented
57#10623084C2211yescharacteristic, complemented
58C4×D4×D11—21no—
59C4×D4×D11C2212yes—
60C4×D4×D11C2211yescharacteristic
61C4×D4×D11C2212yes—
62C11×#496C2212yescomplemented
63C11×#493C2211yescharacteristic, complemented
64C11×#463C2212yescomplemented
65C11×#460C2211yescharacteristic, complemented
66C11×#459C2212yescomplemented
67C11×#459C2211yescharacteristic, complemented
68C11×#446C2211yescharacteristic, complemented
69C11×#442C2212yescomplemented
70C4×C11×SD16C2211yescharacteristic, complemented
71#10622789C2212yescomplemented
72#10622789C2212yescomplemented
73#10622778C2212yescomplemented
74#10622776C2212yescomplemented
75SD16×Dic11C2211yescharacteristic, complemented
76#10622767C2212yescomplemented
77#10622767C2212yescomplemented
78#10622766C2212yescomplemented
79#10622765C2212yescomplemented
80#10622764C2212yescomplemented
81#10622764C2212yescomplemented
82#10622763C2212yescomplemented
83#10622763C2212yescomplemented
84#10622763C2212yescomplemented
85#10622688C2211yescharacteristic, complemented
86#10622687C2212yescomplemented
87#10622686C2211yescharacteristic, complemented
88#10622686C2211yescharacteristic, complemented
89#10622685C2211yescharacteristic, complemented
90#10622685C2212yescomplemented
91#10622671C2212yescomplemented
92#10622670C2212yescomplemented
93#10622640C2211yescharacteristic, complemented
94C4×#4325C2211yescharacteristic, complemented
95#10622637C2211yescharacteristic, complemented
96C4×#4324C2211yescharacteristic, complemented
97#10622629C2212yescomplemented
98#10622628C2212yescomplemented
99#10622628C2211yescharacteristic, complemented
100#10622627C2212yescomplemented
101#10622627C2212yescomplemented
102#10622482C2212yescomplemented
103D11×#106C2211yescharacteristic
104#10622465C2211yescharacteristic, complemented
105#10622461C2211yescharacteristic, complemented
106#10622457C2212yescomplemented
107#10622456C2212yescomplemented
108#10622456C2211yescharacteristic, complemented
109D11×C4⋊C8C2212yes—
110D11×C4⋊C8C2211yescharacteristic
111#10622444C2211yescharacteristic, complemented
112#10622441C2212yescomplemented
113#10622432C2212yescomplemented
114D11×#103C2211yescharacteristic
115#10622401C2211yescharacteristic, complemented
116#10622400C2212yescomplemented
117#10622399C2212yescomplemented
118#10622399C2212yescomplemented
119#10622399C2212yescomplemented
120#10622398C2212yescomplemented
121#10622398C2212yescomplemented
122D11×#102C2211yescharacteristic
123D11×#102C2212yes—
124D11×#102C2212yes—
125#10622375C2212yescomplemented
126#10622371C2211yescharacteristic, complemented
127#10622325C2212yescomplemented
128#10622324C2212yescomplemented
129D11×#97C2212yes—
130#10622314C2212yescomplemented
131#10622308C2211yescharacteristic, complemented
132C4×#4314C2211yescharacteristic, complemented
133C4×C8×D11C2211yescharacteristic
134#10622292C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136#41×D11—48no—
137C2×#4343—21no—
138C2×Q8×D11D411yescharacteristic
139C2×Q8×D11C2311yescharacteristic
140C2×#4341—21no—
141C2×#4341—22no—
142C2×D4×D11—21no—
143C2×D4×D11—22no—
144C2×D4×D11—21no—
145C2×D4×D11—22no—
146C2×D4×D11—21no—
147C2×D4×D11—21no—
148C2×D4×D11C2312yes—
149C2×D4×D11C2311yescharacteristic
150C2×D4×D11C2312yes—
151C2×#4339—21no—
152C2×#4339—22no—
153C22×C4×D11—22no—
154C22×C4×D11—21no—
155C22×C4×D11—22no—
156C2×C11×SD16C2311yescharacteristic
157C2×C11×SD16C2312yes—
158C2×C11×D8C2312yes—
159C2×C11×D8C2312yes—
160C2×C11×D8C2312yes—
161C11×#127C2311yescharacteristic
162C11×#127C2311yescharacteristic
163C11×#127C2312yes—
164C11×#124—21no—
165C11×#124C2312yes—
166C11×#123—22no—
167C11×#121—21no—
168C11×#121—22no—
169C4×Q8×C11C2311yescharacteristic
170C4×Q8×C11C2311yescharacteristic
171C4×D4×C11—21no—
172C4×D4×C11C2312yes—
173C4×D4×C11C2311yescharacteristic
174C4×D4×C11C2312yes—
175#67000—21no—
176#67000C2312yes—
177Q8×Dic11D411yescharacteristic
178Q8×Dic11C2311yescharacteristic
179C2×#4325C2311yescharacteristic
180C2×#4325C2312yes—
181#66993—21no—
182#66993—21no—
183#66993—22no—
184#66993—22no—
185#66993—21no—
186#66993—21no—
187#66993C2312yes—
188#66993C2312yes—
189#66993C2312yes—
190#66993C2312yes—
191#66992—22no—
192#66992—22no—
193#66992—22no—
194#66991—21no—
195#66991—22no—
196#66989—21no—
197#66989C2312yes—
198#66988—22no—
199D4×Dic11—21no—
200D4×Dic11C2312yes—
201D4×Dic11C2311yescharacteristic
202D4×Dic11C2312yes—
203C2×#4324C2311yescharacteristic
204C2×#4324C2312yes—
205C2×#4323C2312yes—
206C2×#4323C2312yes—
207C2×#4323C2312yes—
208C2×#4323C2312yes—
209C2×#4323C2312yes—
210C2×#4323C2312yes—
211#66983—21no—
212#66983—22no—
213#66982—22no—
214C4×C22⋊D11—22no—
215C4×C22⋊D11—22no—
216C4×C22⋊D11—21no—
217C4×C22⋊D11—22no—
218SD16×D11—24no—
219SD16×D11—44no—
220D8×D11—28no—
221D8×D11—44no—
222D8×D11—44no—
223C2×D88C2312yes—
224C2×D88C2312yes—
225C2×D88C2312yes—
226C2×#4314C2311yescharacteristic
227C2×#4314C2312yes—
228C2×C8×D11C2311yescharacteristic
229C2×C8×D11C2312yes—
230C2×C8×D11C2311yescharacteristic
231#66948—21no—
232#66948—22no—
233#66947—22no—
234#66947—22no—
235#66946—21no—
236#66946C2311yescharacteristic
237#66946C2312yes—
238#66946C2312yes—
239C4⋊C4×D11—21no—
240C4⋊C4×D11D411yescharacteristic
241C4⋊C4×D11D412yes—
242C4⋊C4×D11C2311yescharacteristic
243C4⋊C4×D11C2311yescharacteristic
244#66940—21no—
245#66940D411yescharacteristic
246#66940D412yes—
247#66940C2311yescharacteristic
248#66939—22no—
249#66938—22no—
250#66938—22no—
251#66938—22no—
252#66938—22no—
253#66937—22no—
254#66937—22no—
255#66937—22no—
256#66936—22no—
257#66936—22no—
258(C22⋊D11)⋊C4—22no—
259(C22⋊D11)⋊C4—22no—
260(C22⋊D11)⋊C4—21no—
261(C22⋊D11)⋊C4—22no—
262C22⋊C4×D11—22no—
263C22⋊C4×D11—22no—
264C22⋊C4×D11—21no—
265C22⋊C4×D11—22no—
266C22⋊C4×D11—22no—
267#66928—21no—
268#66928C2312yes—
269#66927C2311yescharacteristic
270#66927C2311yescharacteristic
271#66927C2312yes—
272C4×D44—21no—
273C4×D44C2311yescharacteristic
274C4×D44C2312yes—
275C4×D44C2312yes—
276C42×D11—21no—
277C42×D11C2311yescharacteristic
278C42×D11C2312yes—
279C4×Dic22—21no—
280C4×Dic22C2311yescharacteristic
281C4×Dic22C2311yescharacteristic
282C4×Dic22C2312yes—
283C11×#106C2311yescharacteristic
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2312yes—
286C11×#103C2311yescharacteristic
287C11×#102C2311yescharacteristic
288C11×#102C2312yes—
289C11×#102C2312yes—
290C11×#97C2312yes—
291C4×C8×C11C2311yescharacteristic
292#66899C2311yescharacteristic
293#66896C2311yescharacteristic
294#66896C2312yes—
295#66896C2312yes—
296#66885C2311yescharacteristic
297#66885C2312yes—
298#66885C2312yes—
299#66881C2311yescharacteristic
300#66880C2311yescharacteristic
301#66879C2312yes—
302#66879C2312yes—
303Dic11⋊C8C2312yes—
304Dic11⋊C8C2312yes—
305Dic11⋊C8C2312yes—
306C8×Dic11C2311yescharacteristic
307C8×Dic11C2311yescharacteristic
308#66874C2311yescharacteristic
309#66873C2311yescharacteristic
310#66873C2312yes—
311#66873C2312yes—
312#66872C2311yescharacteristic
313#66872C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4⋊(C11⋊C8)C2312yes—
316#66867C2312yes—
317C4×C11⋊C8C2311yescharacteristic
318C2×#3399—111nomaximal, Sylow
319C23×D11—22no—
320C23×D11—22no—
321C23×D11—21no—
322C11×#41—44no—
323C2×Q8×C11C2×D411yescharacteristic
324C2×Q8×C11C2411yescharacteristic
325C2×D4×C11—21no—
326C2×D4×C11—22no—
327C2×D4×C11—21no—
328C2×D4×C11—21no—
329C2×D4×C11—21no—
330C2×D4×C11—22no—
331C2×D4×C11C2412yes—
332C2×D4×C11C2412yes—
333C2×D4×C11C2411yescharacteristic
334C22×C4×C11—22no—
335C22×C4×C11—21no—
336C22×C4×C11—22no—
337C2×C22⋊D11—22no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—21no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—22no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C22×Dic11—22no—
349C22×Dic11—21no—
350C22×Dic11—22no—
351#4343—44no—
352Q8×D11—24no—
353Q8×D11—22no—
354Q8×D11—22no—
355#4341—48no—
356#4341—44no—
357D4×D11—24no—
358D4×D11—24no—
359D4×D11—22no—
360D4×D11—22no—
361D4×D11—24no—
362D4×D11—24no—
363D4×D11—48no—
364D4×D11—44no—
365D4×D11—44no—
366D4×D11—82no—
367D4×D11—84no—
368D4×D11—82no—
369#4339—48no—
370#4339—44no—
371C2×D44—21no—
372C2×D44—22no—
373C2×D44—21no—
374C2×D44—21no—
375C2×D44—22no—
376C2×D44—21no—
377C2×D44C2411yescharacteristic
378C2×D44C2412yes—
379C2×D44C2412yes—
380C2×C4×D11—22no—
381C2×C4×D11—21no—
382C2×C4×D11—22no—
383C2×C4×D11—21no—
384C2×C4×D11—21no—
385C2×C4×D11—21no—
386C2×C4×D11—22no—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—48no—
390C2×C4×D11—44no—
391C2×C4×D11—84no—
392C2×C4×D11C2×D412yes—
393C2×C4×D11C2×D412yes—
394C2×C4×D11C2×D411yescharacteristic
395C2×C4×D11C2×D411yescharacteristic
396C2×C4×D11C2411yescharacteristic
397C2×Dic22—21no—
398C2×Dic22C2×D411yescharacteristic
399C2×Dic22C2×D412yes—
400C2×Dic22C2411yescharacteristic
401C11×SD16—22no—
402C11×SD16—42no—
403C11×D8—24no—
404C11×D8—42no—
405C11×D8—42no—
406C2×C8×C11C2411yescharacteristic
407C2×C8×C11C2412yes—
408C2×C8×C11C2411yescharacteristic
409C11×C4⋊C4—21no—
410C11×C4⋊C4C2×D411yescharacteristic
411C11×C4⋊C4C2×D412yes—
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—21no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C42×C11—21no—
420C42×C11C2411yescharacteristic
421C42×C11C2412yes—
422C22⋊Dic11—22no—
423C22⋊Dic11—22no—
424C22⋊Dic11—22no—
425C22⋊Dic11—21no—
426C22⋊Dic11—22no—
427#4325—22no—
428#4325—42no—
429#4324—22no—
430#4324—42no—
431#4323—24no—
432#4323—24no—
433#4323—42no—
434#4323—42no—
435#4323—42no—
436#4323—42no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—21no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447C4⋊Dic11—21no—
448C4⋊Dic11C2×D411yescharacteristic
449C4⋊Dic11C2×D412yes—
450C4⋊Dic11C2411yescharacteristic
451C4⋊Dic11C2411yescharacteristic
452Dic11⋊C4—21no—
453Dic11⋊C4—21no—
454Dic11⋊C4—21no—
455Dic11⋊C4—21no—
456Dic11⋊C4C2×D412yes—
457Dic11⋊C4C2×D412yes—
458Dic11⋊C4C2×D412yes—
459C4×Dic11—21no—
460C4×Dic11—21no—
461C4×Dic11—21no—
462C4×Dic11C2×D411yescharacteristic
463C4×Dic11C2×D412yes—
464C4×Dic11C2×D412yes—
465C4×Dic11C2×D411yescharacteristic
466C4×Dic11C2411yescharacteristic
467C4×Dic11C2412yes—
468C2×C11⋊C8C2411yescharacteristic
469C2×C11⋊C8C2412yes—
470C2×C11⋊C8C2411yescharacteristic
471D88—24no—
472D88—42no—
473D88—42no—
474#4314—22no—
475#4314—42no—
476C8×D11—22no—
477C8×D11—24no—
478C8×D11#4114yescomplemented
479C2×#559—111no—
480C2×#550—111no—
481#3399—112no—
482#3399—111no—
483#3399—112no—
484#3399—111no—
485#3399—112no—
486#3399—111no—
487#3399—111no—
488#3399—112no—
489#3399—111no—
490#3399—111no—
491#3399—111no—
492#3399D1111yescharacteristic, direct product factor
493C2×#496—112no—
494C2×#493—111no—
495C2×#460—111no—
496C2×#463—112no—
497C2×#459—111no—
498C2×#459—112no—
499C2×#446—111no—
500C2×#442—112no—
501C2×C4×SD16—111no—
502C23×C11—22no—
503C23×C11—22no—
504C23×C11—21no—
505C22×D11—22no—
506C22×D11—21no—
507C22×D11—22no—
508C22×D11—44no—
509C22×D11—44no—
510C22×D11—42no—
511C22×D11—44no—
512C22×D11—42no—
513C22×D11—44no—
514C22×D11—44no—
515C22×D11—42no—
516C22×D11—44no—
517C22×D11C22×D411yescharacteristic
518Q8×C11—22no—
519Q8×C11—21no—
520Q8×C11—21no—
521D4×C11—22no—
522D4×C11—22no—
523D4×C11—21no—
524D4×C11—22no—
525D4×C11—21no—
526D4×C11—22no—
527D4×C11—44no—
528D4×C11—42no—
529D4×C11—42no—
530D4×C11—82no—
531D4×C11—81no—
532D4×C11—81no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—44no—
537C2×C4×C11—42no—
538C2×C4×C11—82no—
539C2×C4×C11C22×D411yescharacteristic
540C2×C4×C11C22×D412yes—
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C2511yescharacteristic
544C22⋊D11—44no—
545C22⋊D11—44no—
546C22⋊D11—44no—
547C22⋊D11—44no—
548C22⋊D11—42no—
549C22⋊D11—44no—
550C22⋊D11—44no—
551C22⋊D11—82no—
552C22⋊D11—82no—
553C22⋊D11—82no—
554C22⋊D11—82no—
555C2×Dic11—21no—
556C2×Dic11—21no—
557C2×Dic11—21no—
558C2×Dic11—44no—
559C2×Dic11—42no—
560C2×Dic11—82no—
561C2×Dic11C22×D411yescharacteristic
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D412yes—
564C2×Dic11C22×D411yescharacteristic
565C2×Dic11C22×D411yescharacteristic
566D44—21no—
567D44—22no—
568D44—22no—
569D44—22no—
570D44—21no—
571D44—22no—
572D44—44no—
573D44—42no—
574D44—42no—
575D44—82no—
576D44—81no—
577D44—81no—
578C4×D11—24no—
579C4×D11—24no—
580C4×D11—22no—
581C4×D11—44no—
582C4×D11—44no—
583C4×D11—42no—
584C4×D11—42no—
585C4×D11—42no—
586C4×D11—42no—
587C4×D11—42no—
588C4×D11—82no—
589C4×D11—82no—
590C4×D11AGL(1,ℤ/8)14yes—
591C4×D11C2×#4112yes—
592C4×D11H(5,𝔽2)12yes—
593Dic22—22no—
594Dic22—24no—
595Dic22—21no—
596Dic22—21no—
597Dic22—42no—
598C8×C11—22no—
599C8×C11—21no—
600C8×C11C2×#4112yescomplemented
601C11⋊C8—21no—
602C11⋊C8—22no—
603C11⋊C8C2×#4112yescomplemented
604C22×#41—221no—
605C22×SD16—111no—
606C22×SD16—112no—
607C22×D8—112no—
608C22×D8—112no—
609C22×D8—112no—
610#559—111no—
611#559—112no—
612#559—111no—
613#559—111no—
614#559—112no—
615#559—221no—
616#559—222no—
617#559—221no—
618#559C2×D1111yescharacteristic, complemented
619#550—112no—
620#550—111no—
621#550—111no—
622#550—112no—
623#550—111no—
624#550—221no—
625#550—222no—
626#550—221no—
627#550C2×D1111yescharacteristic, complemented
628C2×#127—111no—
629C2×#127—111no—
630C2×#127—112no—
631C2×#124—112no—
632C2×#124—221no—
633C2×#123—222no—
634C2×#121—221no—
635C2×#121—222no—
636C2×C4×Q8—111no—
637C2×C4×Q8—111no—
638C2×C4×D4—111no—
639C2×C4×D4—112no—
640C2×C4×D4—112no—
641C2×C4×D4—221no—
642#496—112no—
643#496—112no—
644#496—112no—
645#496—112no—
646#496—112no—
647#496—112no—
648#496—112no—
649#496C2×D1112yescomplemented
650#493—112no—
651#493—112no—
652#493—111no—
653#493—111no—
654#493—111no—
655#493C2×D1111yescharacteristic, complemented
656#463—112no—
657#463—112no—
658#463—112no—
659#463—112no—
660#463—112no—
661#463—112no—
662#463—112no—
663#463C2×D1112yescomplemented
664#460—112no—
665#460—111no—
666#460—111no—
667#460—111no—
668#460—112no—
669#460C2×D1111yescharacteristic, complemented
670#459—112no—
671#459—112no—
672#459—112no—
673#459—112no—
674#459—111no—
675#459—112no—
676#459—111no—
677#459—112no—
678#459—111no—
679#459—112no—
680#459—112no—
681#459—112no—
682#459C2×D1112yescomplemented
683#459C2×D1111yescharacteristic, complemented
684#446—111no—
685#446—112no—
686#446—111no—
687#446—112no—
688#446—111no—
689#446C2×D1111yescharacteristic, complemented
690#442—112no—
691#442—112no—
692#442—112no—
693#442—112no—
694#442—112no—
695#442—112no—
696#442—112no—
697#442C2×D1112yescomplemented
698C4×SD16—111no—
699C4×SD16—111no—
700C4×SD16—111no—
701C4×SD16—111no—
702C4×SD16—111no—
703C4×SD16—111no—
704C4×SD16—111no—
705C4×SD16C2×D1111yescharacteristic, complemented
706C2×#106—111no—
707C2×C4⋊C8—112no—
708C2×C4⋊C8—111no—
709C2×#103—111no—
710C2×#102—111no—
711C2×#102—112no—
712C2×#102—112no—
713C2×#97—112no—
714C2×C4×C8—111no—
715C22×C11—42no—
716C22×C11—42no—
717C22×C11—41no—
718C22×C11—42no—
719C22×C11—41no—
720C22×C11—42no—
721C22×C11—42no—
722C22×C11—41no—
723C22×C11—42no—
724C22×C11C23×D411yescharacteristic
725C2×D11—42no—
726C2×D11—41no—
727C2×D11—42no—
728C2×D11—42no—
729C2×D11—41no—
730C2×D11—42no—
731C2×D11—42no—
732C2×D11—41no—
733C2×D11—42no—
734C2×D11—88no—
735C2×D11—84no—
736C2×D11—88no—
737C2×D11#55012yes—
738C2×D11C2×AGL(1,ℤ/8)12yes—
739C2×D11#57612yes—
740C4×C11—22no—
741C4×C11—22no—
742C4×C11—21no—
743C4×C11—41no—
744C4×C11—41no—
745C4×C11—41no—
746C4×C11C2×AGL(1,ℤ/8)12yes—
747C4×C11C22×#4111yescharacteristic
748C4×C11C2×H(5,𝔽2)11yescharacteristic
749Dic11—22no—
750Dic11—22no—
751Dic11—21no—
752Dic11—41no—
753Dic11—41no—
754Dic11—41no—
755Dic11#55012yes—
756Dic11C2×AGL(1,ℤ/8)12yes—
757C2×#41—21no—
758C2×#41—222no—
759C2×#41—221no—
760C2×#41—222no—
761C2×#41—221no—
762C2×#41—221no—
763C2×#41—448no—
764C22×Q8—111no—
765C22×Q8—111no—
766C22×D4—112no—
767C22×D4—112no—
768C22×D4—111no—
769C22×D4—221no—
770C22×D4—221no—
771C22×D4—222no—
772C22×D4—222no—
773C22×D4—221no—
774C22×D4—221no—
775C23×C4—221no—
776C23×C4—222no—
777C23×C4—222no—
778C2×SD16—111no—
779C2×SD16—111no—
780C2×SD16—112no—
781C2×SD16—112no—
782C2×SD16—111no—
783C2×SD16—112no—
784C2×SD16—224no—
785C2×SD16—444no—
786C2×SD16C22×D1111yescharacteristic
787C2×SD16C22×D1112yes—
788C2×D8—112no—
789C2×D8—112no—
790C2×D8—112no—
791C2×D8—112no—
792C2×D8—112no—
793C2×D8—112no—
794C2×D8—112no—
795C2×D8—112no—
796C2×D8—112no—
797C2×D8—228no—
798C2×D8—444no—
799C2×D8—444no—
800C2×D8C22×D1112yes—
801C2×D8C22×D1112yes—
802C2×D8C22×D1112yes—
803C22×C8—111no—
804C22×C8—111no—
805C22×C8—112no—
806#127—112no—
807#127—112no—
808#127—112no—
809#127—112no—
810#127—112no—
811#127—111no—
812#127—111no—
813#127—222no—
814#127—222no—
815#127—221no—
816#127—221no—
817#127—221no—
818#127—221no—
819#127C22×D1112yes—
820#127C22×D1111yescharacteristic
821#127C22×D1111yescharacteristic
822#124—21no—
823#124—112no—
824#124—112no—
825#124—112no—
826#124—221no—
827#124—222no—
828#124—222no—
829#124—222no—
830#124—222no—
831#124—221no—
832#124—221no—
833#124C22×D1112yes—
834#123—22no—
835#123—222no—
836#123—222no—
837#123—222no—
838#123—222no—
839#123—222no—
840#123—222no—
841#123—222no—
842#121—21no—
843#121—22no—
844#121—222no—
845#121—222no—
846#121—222no—
847#121—221no—
848#121—222no—
849#121—221no—
850#121—222no—
851#121—222no—
852#121—222no—
853#121—222no—
854#121—221no—
855#121—222no—
856C4×Q8—111no—
857C4×Q8—112no—
858C4×Q8—111no—
859C4×Q8—112no—
860C4×Q8—111no—
861C4×Q8—111no—
862C4×Q8—111no—
863C4×Q8—111no—
864C4×Q8—221no—
865C4×Q8—221no—
866C4×Q8C22×D1111yescharacteristic
867C4×Q8C22×D1111yescharacteristic
868C4×D4—21no—
869C4×D4—111no—
870C4×D4—112no—
871C4×D4—112no—
872C4×D4—111no—
873C4×D4—112no—
874C4×D4—112no—
875C4×D4—111no—
876C4×D4—112no—
877C4×D4—112no—
878C4×D4—221no—
879C4×D4—222no—
880C4×D4—221no—
881C4×D4—222no—
882C4×D4—222no—
883C4×D4—221no—
884C4×D4—222no—
885C4×D4—222no—
886C4×D4—222no—
887C4×D4—221no—
888C4×D4—221no—
889C4×D4C22×D1111yescharacteristic
890C4×D4C22×D1112yes—
891C4×D4C22×D1112yes—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—111no—
895C2×C4⋊C4—111no—
896C2×C4⋊C4—221no—
897C2×C22⋊C4—222no—
898C2×C22⋊C4—221no—
899C2×C22⋊C4—222no—
900C2×C22⋊C4—222no—
901C2×C22⋊C4—222no—
902C2×C42—112no—
903C2×C42—111no—
904C2×C42—221no—
905#106—111no—
906#106—111no—
907#106—111no—
908#106C22×D1111yescharacteristic
909C4⋊C8—112no—
910C4⋊C8—112no—
911C4⋊C8—112no—
912C4⋊C8—111no—
913C4⋊C8—112no—
914C4⋊C8C22×D1111yescharacteristic
915C4⋊C8C22×D1112yes—
916#103—111no—
917#103—111no—
918#103—111no—
919#103C22×D1111yescharacteristic
920#102—111no—
921#102—112no—
922#102—112no—
923#102—111no—
924#102—112no—
925#102—112no—
926#102—111no—
927#102—112no—
928#102—112no—
929#102C22×D1111yescharacteristic
930#102C22×D1112yes—
931#102C22×D1112yes—
932#97—112no—
933#97—112no—
934#97—112no—
935#97C22×D1112yes—
936C4×C8—111no—
937C4×C8—111no—
938C4×C8—111no—
939C4×C8C22×D1111yescharacteristic
940C2×C11—82no—
941C2×C11—81no—
942C2×C11—82no—
943C2×C11C2×#55011yescharacteristic
944C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
945C2×C11C2×#57611yescharacteristic
946D11—81no—
947D11—82no—
948D11—82no—
949D11#339914yesdirect product factor
950C24—222no—
951C24—221no—
952C24—222no—
953#41—44no—
954#41—448no—
955#41—444no—
956#41—448no—
957#41—444no—
958#41—444no—
959C2×Q8—112no—
960C2×Q8—111no—
961C2×Q8—111no—
962C2×Q8—221no—
963C2×Q8—224no—
964C2×Q8—222no—
965C2×Q8—222no—
966C2×Q8D4×D1111yescharacteristic
967C2×Q8C23×D1111yescharacteristic
968C2×D4—21no—
969C2×D4—22no—
970C2×D4—21no—
971C2×D4—22no—
972C2×D4—21no—
973C2×D4—21no—
974C2×D4—112no—
975C2×D4—112no—
976C2×D4—111no—
977C2×D4—224no—
978C2×D4—224no—
979C2×D4—224no—
980C2×D4—222no—
981C2×D4—224no—
982C2×D4—222no—
983C2×D4—222no—
984C2×D4—222no—
985C2×D4—222no—
986C2×D4—221no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—222no—
990C2×D4—222no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—222no—
994C2×D4—221no—
995C2×D4—222no—
996C2×D4—221no—
997C2×D4—222no—
998C2×D4—221no—
999C2×D4—221no—
1000C2×D4—444no—
1001C2×D4—444no—
1002C2×D4—448no—
1003C2×D4—884no—
1004C2×D4—882no—
1005C2×D4—882no—
1006C2×D4C23×D1112yes—
1007C2×D4C23×D1112yes—
1008C2×D4C23×D1111yescharacteristic
1009C22×C4—22no—
1010C22×C4—21no—
1011C22×C4—22no—
1012C22×C4—111no—
1013C22×C4—111no—
1014C22×C4—112no—
1015C22×C4—112no—
1016C22×C4—111no—
1017C22×C4—221no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—222no—
1027C22×C4—221no—
1028C22×C4—222no—
1029C22×C4—444no—
1030C22×C4—448no—
1031C22×C4—884no—
1032SD16—22no—
1033SD16—42no—
1034SD16—222no—
1035SD16—222no—
1036SD16—222no—
1037SD16—442no—
1038SD16—442no—
1039SD16—442no—
1040D8—24no—
1041D8—42no—
1042D8—42no—
1043D8—224no—
1044D8—224no—
1045D8—224no—
1046D8—442no—
1047D8—442no—
1048D8—442no—
1049D8—442no—
1050D8—442no—
1051D8—442no—
1052C2×C8—111no—
1053C2×C8—114no—
1054C2×C8—111no—
1055C2×C8—112no—
1056C2×C8—222no—
1057C2×C8—224no—
1058C2×C8C23×D1111yescharacteristic
1059C2×C8C23×D1112yes—
1060C2×C8C23×D1111yescharacteristic
1061C4⋊C4—21no—
1062C4⋊C4—112no—
1063C4⋊C4—111no—
1064C4⋊C4—112no—
1065C4⋊C4—112no—
1066C4⋊C4—112no—
1067C4⋊C4—111no—
1068C4⋊C4—111no—
1069C4⋊C4—221no—
1070C4⋊C4—221no—
1071C4⋊C4—221no—
1072C4⋊C4—221no—
1073C4⋊C4—221no—
1074C4⋊C4D4×D1111yescharacteristic
1075C4⋊C4D4×D1112yes—
1076C4⋊C4C23×D1111yescharacteristic
1077C4⋊C4C23×D1111yescharacteristic
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—21no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—222no—
1084C22⋊C4—221no—
1085C22⋊C4—222no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4—222no—
1089C22⋊C4—221no—
1090C22⋊C4—222no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—221no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C42—21no—
1099C42—112no—
1100C42—112no—
1101C42—111no—
1102C42—111no—
1103C42—111no—
1104C42—112no—
1105C42—221no—
1106C42—221no—
1107C42—221no—
1108C42C23×D1111yescharacteristic
1109C42C23×D1112yes—
1110C11C2×#339911yescharacteristic, complemented, Sylow
1111C23—22no—
1112C23—22no—
1113C23—21no—
1114C23—111no—
1115C23—222no—
1116C23—222no—
1117C23—221no—
1118C23—442no—
1119C23—444no—
1120C23—444no—
1121C23—444no—
1122C23—444no—
1123C23—442no—
1124C23—444no—
1125C23—442no—
1126C23—444no—
1127Q8—22no—
1128Q8—21no—
1129Q8—21no—
1130Q8—224no—
1131Q8—222no—
1132Q8—221no—
1133Q8—221no—
1134Q8—442no—
1135D4—22no—
1136D4—22no—
1137D4—21no—
1138D4—22no—
1139D4—21no—
1140D4—22no—
1141D4—44no—
1142D4—42no—
1143D4—42no—
1144D4—82no—
1145D4—81no—
1146D4—81no—
1147D4—222no—
1148D4—222no—
1149D4—221no—
1150D4—222no—
1151D4—221no—
1152D4—222no—
1153D4—444no—
1154D4—444no—
1155D4—444no—
1156D4—442no—
1157D4—444no—
1158D4—444no—
1159D4—444no—
1160D4—444no—
1161D4—442no—
1162D4—442no—
1163D4—882no—
1164D4—881no—
1165D4—881no—
1166D4—882no—
1167D4—882no—
1168D4—882no—
1169D4—882no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—44no—
1174C2×C4—42no—
1175C2×C4—82no—
1176C2×C4—111no—
1177C2×C4—111no—
1178C2×C4—114no—
1179C2×C4—112no—
1180C2×C4—112no—
1181C2×C4—112no—
1182C2×C4—112no—
1183C2×C4—111no—
1184C2×C4—224no—
1185C2×C4—224no—
1186C2×C4—222no—
1187C2×C4—221no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—444no—
1191C2×C4—442no—
1192C2×C4—444no—
1193C2×C4—442no—
1194C2×C4—442no—
1195C2×C4—442no—
1196C2×C4—442no—
1197C2×C4—444no—
1198C2×C4—442no—
1199C2×C4—882no—
1200C2×C4—882no—
1201C2×C4—882no—
1202C2×C4C2×D4×D1112yes—
1203C2×C4C2×D4×D1112yes—
1204C2×C4C2×D4×D1111yescharacteristic
1205C2×C4C2×D4×D1111yescharacteristic
1206C2×C4C24×D1111yescharacteristic
1207C8—21no—
1208C8—22no—
1209C8—112no—
1210C8—221no—
1211C8—222no—
1212C8#41×D1112yescomplemented
1213C22—42no—
1214C22—41no—
1215C22—42no—
1216C22—42no—
1217C22—41no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—41no—
1222C22—112no—
1223C22—112no—
1224C22—112no—
1225C22—442no—
1226C22—441no—
1227C22—442no—
1228C22—442no—
1229C22—441no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—441no—
1234C22—884no—
1235C22—888no—
1236C22—888no—
1237C22C22×D4×D1111yescharacteristic
1238C4—22no—
1239C4—22no—
1240C4—21no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—112no—
1245C4—112no—
1246C4—222no—
1247C4—222no—
1248C4—221no—
1249C4—441no—
1250C4—441no—
1251C4—441no—
1252C4D11×AGL(1,ℤ/8)12yes—
1253C4C2×#41×D1111yescharacteristic
1254C4D11×H(5,𝔽2)11yescharacteristic
1255C2—82no—
1256C2—81no—
1257C2—82no—
1258C2—114no—
1259C2—882no—
1260C2—881no—
1261C2—882no—
1262C2D11×#55011yescharacteristic
1263C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1264C2D11×#57611yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3399C2
socleC22×C11C23×D4
hypercenter#3399D11
hypocenterC11C2×#3399
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3399

Complements

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

NH ≅ G/Ntype
1. D11×#559C2semidirect
2. D11×#550C2semidirect
3. #13081663C2semidirect
4. #13081662C2semidirect
5. #13081661C2semidirect
6. #13081660C2semidirect
7. #13081659C2semidirect
8. #13081658C2semidirect
9. #13081657C2semidirect
10. #13081656C2semidirect
11. #13081655C2semidirect
12. #13081654C2semidirect
13. #13081653C2semidirect
14. D11×#496C2semidirect
15. D11×#493C2semidirect
16. D11×#460C2semidirect
17. D11×#463C2semidirect
18. D11×#459C2semidirect
19. D11×#459C2semidirect
20. D11×#446C2semidirect
21. D11×#442C2semidirect
22. C4×SD16×D11C2semidirect
23. C11×#3399C2semidirect
25. C11×#559C22semidirect
26. C11×#550C22semidirect
33. #10623249C22semidirect
34. #10623249C22semidirect
38. #10623244C22semidirect
40. #10623212C22semidirect
49. #10623116C22semidirect
50. #10623116C22semidirect
51. #10623108C22semidirect
55. #10623090C22semidirect
56. #10623084C22semidirect
57. #10623084C22semidirect
62. C11×#496C22semidirect
63. C11×#493C22semidirect
64. C11×#463C22semidirect
65. C11×#460C22semidirect
66. C11×#459C22semidirect
67. C11×#459C22semidirect
68. C11×#446C22semidirect
69. C11×#442C22semidirect
70. C4×C11×SD16C22semidirect
71. #10622789C22semidirect
72. #10622789C22semidirect
73. #10622778C22semidirect
74. #10622776C22semidirect
75. SD16×Dic11C22semidirect
76. #10622767C22semidirect
77. #10622767C22semidirect
78. #10622766C22semidirect
79. #10622765C22semidirect
80. #10622764C22semidirect
81. #10622764C22semidirect
82. #10622763C22semidirect
83. #10622763C22semidirect
84. #10622763C22semidirect
85. #10622688C22semidirect
86. #10622687C22semidirect
87. #10622686C22semidirect
88. #10622686C22semidirect
89. #10622685C22semidirect
90. #10622685C22semidirect
91. #10622671C22semidirect
92. #10622670C22semidirect
93. #10622640C22semidirect
94. C4×#4325C22semidirect
95. #10622637C22semidirect
96. C4×#4324C22semidirect
97. #10622629C22semidirect
98. #10622628C22semidirect
99. #10622628C22semidirect
100. #10622627C22semidirect
101. #10622627C22semidirect
102. #10622482C22semidirect
104. #10622465C22semidirect
105. #10622461C22semidirect
106. #10622457C22semidirect
107. #10622456C22semidirect
108. #10622456C22semidirect
111. #10622444C22semidirect
112. #10622441C22semidirect
113. #10622432C22semidirect
115. #10622401C22semidirect
116. #10622400C22semidirect
117. #10622399C22semidirect
118. #10622399C22semidirect
119. #10622399C22semidirect
120. #10622398C22semidirect
121. #10622398C22semidirect
125. #10622375C22semidirect
126. #10622371C22semidirect
127. #10622325C22semidirect
128. #10622324C22semidirect
130. #10622314C22semidirect
131. #10622308C22semidirect
132. C4×#4314C22semidirect
134. #10622292C22semidirect
478. C8×D11#41semidirect
492. #3399D11direct (N × H)
600. C8×C11C2×#41semidirect
603. C11⋊C8C2×#41semidirect
618. #559C2×D11semidirect
627. #550C2×D11semidirect
649. #496C2×D11semidirect
655. #493C2×D11semidirect
663. #463C2×D11semidirect
669. #460C2×D11semidirect
682. #459C2×D11semidirect
683. #459C2×D11semidirect
689. #446C2×D11semidirect
697. #442C2×D11semidirect
705. C4×SD16C2×D11semidirect
949. D11#3399direct (N × H)
1110. C11C2×#3399semidirect
1212. C8#41×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#5592
D11×#5502
#130816632
#130816622
#130816612
#130816602
#130816592
#130816582
#130816572
#130816562
#130816552
#130816542
#130816532
D11×#4962
D11×#4932
D11×#4602
D11×#4632
D11×#4592
D11×#4462
D11×#4422
C4×SD16×D112
C11×#33992
C2×#339911