Finite Group Databasebeta

← D11×#1509 #14720896

Subgroups — D11×#1509 #14720896

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#529C211yesmaximal, characteristic
2D11×#432C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13067142C211yesmaximal, characteristic, complemented
5#13067141C211yesmaximal, characteristic, complemented
6#13067140C212yesmaximal, complemented
7#13067139C211yesmaximal, characteristic, complemented
8#13067138C212yesmaximal, complemented
9D11×#328C212yesmaximal, complemented
10D11×#327C212yesmaximal
11C11×#1509C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13#10623237—21no—
14D11×#126—21no—
15#10623222C411yescharacteristic, complemented
16D11×#125C411yescharacteristic, complemented
17#10623211C411yescharacteristic, complemented
18D11×#124C411yescharacteristic, complemented
19D11×#123—21no—
20#10623180—21no—
21D11×C22⋊Q8C2211yescharacteristic
22#10623155C2211yescharacteristic
23D11×#121C2211yescharacteristic
24#10623131C2211yescharacteristic
25#10623111C411yescharacteristic, complemented
26C4×Q8×D11C411yescharacteristic, complemented
27#10623088C411yescharacteristic, complemented
28C4×D4×D11—21no—
29C4×D4×D11C411yescharacteristic, complemented
30#10623069—21no—
31#10623059—21no—
32D11×#117—21no—
33C2×C4⋊C4×D11—21no—
34#10623010C2211yescharacteristic
35C2×C42×D11—21no—
36C2×C42×D11C2211yescharacteristic
37C11×#432C2211yescharacteristic, complemented
38C4×C11×C4⋊C4C2211yescharacteristic, complemented
39C4⋊C4×Dic11—21no—
40C4×C4⋊Dic11C2211yescharacteristic, complemented
41C4×Dic11⋊C4—21no—
42#10622539C2211yescharacteristic, complemented
43#10622448—21no—
44D11×C4⋊C8—21no—
45D11×C22⋊C8C2212yes—
46#10622332C2212yescomplemented
47#10622318—21no—
48D11×#97—21no—
49D11×#95C2212yes—
50#10622262C2212yescomplemented
51C11×#328C2212yescomplemented
52C11×#327C2212yes—
53#10622176C2212yescomplemented
54#10622175C2212yes—
55#10622108C2212yes—
56#10622105C2212yescomplemented
57#10622090C2212yescomplemented
58#10622089C2212yes—
59C2×Q8×D11C2×C411yescharacteristic
60C2×D4×D11—21no—
61C2×D4×D11C2×C411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—21no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C11×#126—21no—
68C11×#125C2×C411yescharacteristic, complemented
69C11×#124C2×C411yescharacteristic, complemented
70C11×#123—21no—
71C11×C22⋊Q8C2311yescharacteristic
72C11×#121C2311yescharacteristic
73C4×Q8×C11C2×C411yescharacteristic, complemented
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic, complemented
76C11×#117—21no—
77C2×C11×C4⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80#67000C2×C411yescharacteristic, complemented
81#66999C2×C411yescharacteristic
82Q8×Dic11C2×C411yescharacteristic, complemented
83#66992—21no—
84#66991C2×C411yescharacteristic
85#66989C2×C411yescharacteristic, complemented
86#66988—21no—
87D4×Dic11—21no—
88D4×Dic11C2×C411yescharacteristic, complemented
89#66983C2311yescharacteristic
90#66982—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93C4×C22⋊D11—21no—
94#66979—21no—
95C2×C4⋊Dic11—21no—
96#66977C2311yescharacteristic
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C2×C8×D11—22no—
104#66951—21no—
105#66951—21no—
106#66951—21no—
107#66950C2×C411yescharacteristic
108#66949—21no—
109#66948C2×C411yescharacteristic
110#66947—21no—
111#66947—21no—
112#66946—21no—
113#66946C2×C411yescharacteristic, complemented
114#66945—21no—
115#66945—21no—
116C4⋊C4×D11—28no—
117C4⋊C4×D11—21no—
118C4⋊C4×D11—21no—
119C4⋊C4×D11—21no—
120C4⋊C4×D11—21no—
121C4⋊C4×D11C2×C411yescharacteristic
122C4⋊C4×D11C2×C411yescharacteristic
123#66943C2×C411yescharacteristic, complemented
124#66943C2×C411yescharacteristic, complemented
125#66942—21no—
126#66942—21no—
127#66940—21no—
128#66940C2×C411yescharacteristic, complemented
129#66939—21no—
130#66938—21no—
131#66938—21no—
132#66937—21no—
133#66936—21no—
134#66936—21no—
135(C22⋊D11)⋊C4—21no—
136(C22⋊D11)⋊C4—21no—
137(C22⋊D11)⋊C4—21no—
138C22⋊C4×D11—21no—
139C22⋊C4×D11—21no—
140C22⋊C4×D11—21no—
141C22⋊C4×D11—21no—
142C22⋊C4×D11—21no—
143#66932—21no—
144#66932—21no—
145#66932—21no—
146#66931—21no—
147#66930—21no—
148#66930—21no—
149#66929—21no—
150#66928C2×C411yescharacteristic, complemented
151C4×D44—21no—
152C4×D44C2×C411yescharacteristic, complemented
153#66925—21no—
154#66925—21no—
155C42×D11—21no—
156C42×D11—44no—
157C42×D11C2×C411yescharacteristic
158C42×D11C2×C411yescharacteristic
159C42×D11C2×C411yescharacteristic
160C42×D11C2×C411yescharacteristic
161C42×D11D411yescharacteristic
162C42×D11D411yescharacteristic
163C42×D11D411yescharacteristic
164C42×D11D411yescharacteristic
165#66923C2×C411yescharacteristic, complemented
166C4×Dic22—21no—
167C4×Dic22C2×C411yescharacteristic, complemented
168C11×C4⋊C8—21no—
169C11×C22⋊C8C2312yes—
170C11×#97—21no—
171C11×#95C2312yes—
172C11⋊#95—22no—
173C11⋊#95C2312yes—
174C22⋊(C11⋊C8)C2312yes—
175(C2×D11)⋊C8—22no—
176#66879—22no—
177Dic11⋊C8—22no—
178C4⋊(C11⋊C8)—21no—
179#66867—21no—
180C2×#1509—111nomaximal, Sylow
181C23×D11—21no—
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11C22×C411yescharacteristic
184C2×D4×C11—21no—
185C2×D4×C11C22×C411yescharacteristic
186C22×C4×C11—22no—
187C22×C4×C11—21no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—21no—
192C2×C22⋊D11—21no—
193C2×C22⋊D11—21no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11C2×D411yescharacteristic
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199Q8×D11—42no—
200D4×D11—42no—
201D4×D11—42no—
202D4×D11—42no—
203C2×D44—21no—
204C2×D44C22×C411yescharacteristic
205C2×C4×D11—24no—
206C2×C4×D11—28no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—21no—
214C2×C4×D11—42no—
215C2×C4×D11—44no—
216C2×C4×D11—44no—
217C2×C4×D11—44no—
218C2×C4×D11C22⋊C411yescharacteristic
219C2×C4×D11C22⋊C411yescharacteristic
220C2×C4×D11C22⋊C411yescharacteristic
221C2×C4×D11C22⋊C411yescharacteristic
222C2×C4×D11C22⋊C411yescharacteristic
223C2×C4×D11C22⋊C411yescharacteristic
224C2×C4×D11C22⋊C411yescharacteristic
225C2×C4×D11C22⋊C411yescharacteristic
226C2×C4×D11C22×C411yescharacteristic
227C2×C4×D11C22×C411yescharacteristic
228C2×C4×D11C2×D411yescharacteristic
229C2×C4×D11C2×D411yescharacteristic
230C2×Dic22—21no—
231C2×Dic22C22×C411yescharacteristic
232C2×C8×C11—22no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4C22×C411yescharacteristic
239C11×C4⋊C4C22×C411yescharacteristic
240C11×C22⋊C4—21no—
241C11×C22⋊C4—21no—
242C11×C22⋊C4—21no—
243C11×C22⋊C4—21no—
244C11×C22⋊C4—21no—
245C42×C11—21no—
246C42×C11—42no—
247C42×C11C22×C411yescharacteristic
248C42×C11C22×C411yescharacteristic
249C42×C11C2×D411yescharacteristic
250C42×C11C2×D411yescharacteristic
251C22⋊Dic11—21no—
252C22⋊Dic11—21no—
253C22⋊Dic11—21no—
254C22⋊Dic11—21no—
255C22⋊Dic11—21no—
256(C2×D11)⋊C4—21no—
257(C2×D11)⋊C4—21no—
258(C2×D11)⋊C4—21no—
259(C2×D11)⋊C4—21no—
260(C2×D11)⋊C4—21no—
261(C2×D11)⋊C4—21no—
262(C2×D11)⋊C4—21no—
263(C2×D11)⋊C4—21no—
264(C2×D11)⋊C4—21no—
265(C2×D11)⋊C4—21no—
266C4⋊Dic11—24no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11C22×C411yescharacteristic
272C4⋊Dic11C22×C411yescharacteristic
273Dic11⋊C4—28no—
274Dic11⋊C4—21no—
275Dic11⋊C4—21no—
276Dic11⋊C4—21no—
277Dic11⋊C4—21no—
278Dic11⋊C4—21no—
279Dic11⋊C4—21no—
280Dic11⋊C4—21no—
281Dic11⋊C4—21no—
282Dic11⋊C4—21no—
283Dic11⋊C4—21no—
284C4×Dic11—21no—
285C4×Dic11—21no—
286C4×Dic11—21no—
287C4×Dic11—42no—
288C4×Dic11—44no—
289C4×Dic11C22⋊C411yescharacteristic
290C4×Dic11C22⋊C411yescharacteristic
291C4×Dic11C22⋊C411yescharacteristic
292C4×Dic11C22⋊C411yescharacteristic
293C4×Dic11C22⋊C411yescharacteristic
294C4×Dic11C22⋊C411yescharacteristic
295C4×Dic11C22⋊C411yescharacteristic
296C4×Dic11C22⋊C411yescharacteristic
297C4×Dic11C22×C411yescharacteristic
298C4×Dic11C22×C411yescharacteristic
299C4×Dic11C2×D411yescharacteristic
300C4×Dic11C2×D411yescharacteristic
301C2×C11⋊C8—22no—
302C8×D11—44no—
303C2×#529—111no—
304C2×#432—111no—
305C2×C4×C4⋊C4—111no—
306#1509—111no—
307#1509—111no—
308#1509—112no—
309#1509—112no—
310#1509—111no—
311#1509D1111yescharacteristic, direct product factor
312C2×#328—112no—
313C2×#327—112no—
314C23×C11—21no—
315C23×C11C22×D411yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—21no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11C2×C22⋊C411yescharacteristic
323C22×D11C2×C22⋊C411yescharacteristic
324C22×D11AGL(1,ℤ/8)12yes—
325C22×D11#13712yes—
326Q8×C11—41no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—41no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—24no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—41no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11C2×C22⋊C411yescharacteristic
342C2×C4×C11C2×C22⋊C411yescharacteristic
343C2×C4×C11C2×C22⋊C411yescharacteristic
344C2×C4×C11C2×C22⋊C411yescharacteristic
345C2×C4×C11C23×C411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C22⋊D11—42no—
348C22⋊D11—41no—
349C22⋊D11—41no—
350C22⋊D11—42no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—22no—
354C2×Dic11—24no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—41no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11C2×C22⋊C411yescharacteristic
363C2×Dic11C2×C22⋊C411yescharacteristic
364C2×Dic11C2×C22⋊C411yescharacteristic
365C2×Dic11C2×C22⋊C411yescharacteristic
366C2×Dic11C2×C22⋊C411yescharacteristic
367C2×Dic11C2×C22⋊C411yescharacteristic
368D44—41no—
369D44—42no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—41no—
380C4×D11—41no—
381C4×D11—416no—
382C4×D11—42no—
383C4×D11—42no—
384C4×D11—42no—
385C4×D11—42no—
386C4×D11—42no—
387C4×D11#10414yes—
388Dic22—42no—
389Dic22—41no—
390C8×C11—42no—
391C11⋊C8—42no—
392#529—111no—
393#529—111no—
394#529—111no—
395#529—111no—
396#529—111no—
397#529—111no—
398#529—111no—
399#529—221no—
400#529—221no—
401#529—221no—
402#529—221no—
403#529C2×D1111yescharacteristic
404C2×#126—221no—
405C2×#125—111no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×C4×Q8—111no—
411C2×C4×D4—111no—
412C2×C4×D4—221no—
413C2×#117—221no—
414C22×C4⋊C4—221no—
415C22×C42—111no—
416C22×C42—221no—
417#432—111no—
418#432—112no—
419#432—221no—
420#432—221no—
421#432C2×D1111yescharacteristic, complemented
422C2×C4⋊C8—221no—
423C2×C22⋊C8—112no—
424C2×#97—221no—
425C4×C4⋊C4—111no—
426C4×C4⋊C4—112no—
427C4×C4⋊C4—221no—
428C4×C4⋊C4—221no—
429C4×C4⋊C4C2×D1111yescharacteristic, complemented
430C2×#95—112no—
431#328—112no—
432#328—112no—
433#328—112no—
434#328C2×D1112yescomplemented
435#327—112no—
436#327—112no—
437#327—112no—
438#327C2×D1112yes—
439C22×C11—21no—
440C22×C11—21no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11C22×C22⋊C411yescharacteristic
445C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C11C2×#13711yescharacteristic
447C2×D11—21no—
448C2×D11—21no—
449C2×D11—24no—
450C2×D11—24no—
451C2×D11—41no—
452C2×D11—41no—
453C2×D11—41no—
454C2×D11—84no—
455C2×D11#41012yes—
456C2×D11#41712yes—
457C2×D11#41712yes—
458C2×D11C2×#10412yes—
459C4×C11—21no—
460C4×C11—21no—
461C4×C11—21no—
462C4×C11—21no—
463C4×C11—21no—
464C4×C11—44no—
465C4×C11—41no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11C2×#10412yes—
469Dic11—21no—
470Dic11—21no—
471Dic11—21no—
472Dic11—21no—
473Dic11—21no—
474Dic11—44no—
475Dic11—41no—
476Dic11—41no—
477Dic11—41no—
478Dic11C2×#10412yes—
479C22×Q8—111no—
480C22×D4—111no—
481C22×D4—221no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—221no—
486C23×C4—222no—
487C22×C8—222no—
488#126—21no—
489#126—221no—
490#126—221no—
491#126—221no—
492#126—221no—
493#126—221no—
494#126—221no—
495#126—221no—
496#125—111no—
497#125—111no—
498#125—111no—
499#125—221no—
500#125—221no—
501#125C4×D1111yescharacteristic, complemented
502#124—111no—
503#124—111no—
504#124—111no—
505#124—221no—
506#124—221no—
507#124C4×D1111yescharacteristic, complemented
508#123—21no—
509#123—221no—
510#123—221no—
511#123—221no—
512#123—221no—
513#123—221no—
514#123—221no—
515#123—221no—
516C22⋊Q8—111no—
517C22⋊Q8—111no—
518C22⋊Q8—111no—
519C22⋊Q8—221no—
520C22⋊Q8—221no—
521C22⋊Q8C22×D1111yescharacteristic
522#121—111no—
523#121—111no—
524#121—111no—
525#121—221no—
526#121—221no—
527#121C22×D1111yescharacteristic
528C4×Q8—111no—
529C4×Q8—111no—
530C4×Q8—111no—
531C4×Q8—221no—
532C4×Q8—221no—
533C4×Q8C4×D1111yescharacteristic, complemented
534C4×D4—21no—
535C4×D4—111no—
536C4×D4—111no—
537C4×D4—111no—
538C4×D4—221no—
539C4×D4—221no—
540C4×D4—221no—
541C4×D4—221no—
542C4×D4—221no—
543C4×D4—221no—
544C4×D4—221no—
545C4×D4—221no—
546C4×D4—221no—
547C4×D4C4×D1111yescharacteristic, complemented
548#117—21no—
549#117—221no—
550#117—221no—
551#117—221no—
552#117—221no—
553#117—221no—
554#117—221no—
555#117—221no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—228no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C42—21no—
572C2×C42—111no—
573C2×C42—111no—
574C2×C42—111no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—111no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—111no—
581C2×C42—111no—
582C2×C42—111no—
583C2×C42—221no—
584C2×C42—222no—
585C2×C42—221no—
586C2×C42—444no—
587C2×C42C22×D1111yescharacteristic
588C4⋊C8—21no—
589C4⋊C8—222no—
590C4⋊C8—221no—
591C22⋊C8—112no—
592C22⋊C8—222no—
593C22⋊C8C22×D1112yes—
594#97—21no—
595#97—222no—
596#97—221no—
597#95—112no—
598#95—222no—
599#95C22×D1112yes—
600C2×C11—21no—
601C2×C11—21no—
602C2×C11—81no—
603C2×C11C2×#41011yescharacteristic
604C2×C11C2×#41711yescharacteristic
605C2×C11C22×#10411yescharacteristic
606D11—22no—
607D11—81no—
608D11#150914yesdirect product factor
609C24—111no—
610C24—221no—
611C2×Q8—111no—
612C2×Q8—221no—
613C2×Q8—442no—
614C2×Q8C2×C4×D1111yescharacteristic
615C2×D4—21no—
616C2×D4—111no—
617C2×D4—221no—
618C2×D4—221no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—442no—
622C2×D4—442no—
623C2×D4—442no—
624C2×D4C2×C4×D1111yescharacteristic
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—224no—
643C22×C4—221no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—228no—
650C22×C4—221no—
651C22×C4—222no—
652C22×C4—221no—
653C22×C4—444no—
654C22×C4—442no—
655C22×C4—444no—
656C22×C4—444no—
657C22×C4D4×D1111yescharacteristic
658C22×C4D4×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C2×C8—22no—
661C2×C8—222no—
662C2×C8—444no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—111no—
669C4⋊C4—111no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—228no—
681C4⋊C4—224no—
682C4⋊C4—221no—
683C4⋊C4—221no—
684C4⋊C4—221no—
685C4⋊C4—221no—
686C4⋊C4C2×C4×D1111yescharacteristic
687C4⋊C4C2×C4×D1111yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—221no—
694C22⋊C4—221no—
695C22⋊C4—221no—
696C22⋊C4—221no—
697C22⋊C4—221no—
698C22⋊C4—221no—
699C22⋊C4—221no—
700C22⋊C4—221no—
701C22⋊C4—221no—
702C22⋊C4—221no—
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—221no—
708C42—21no—
709C42—42no—
710C42—111no—
711C42—111no—
712C42—111no—
713C42—111no—
714C42—111no—
715C42—111no—
716C42—111no—
717C42—111no—
718C42—111no—
719C42—111no—
720C42—111no—
721C42—111no—
722C42—221no—
723C42—221no—
724C42—221no—
725C42—442no—
726C42—444no—
727C42C2×C4×D1111yescharacteristic
728C42C2×C4×D1111yescharacteristic
729C42D4×D1111yescharacteristic
730C42D4×D1111yescharacteristic
731C11C2×#150911yescharacteristic, complemented, Sylow
732C23—21no—
733C23—111no—
734C23—111no—
735C23—112no—
736C23—112no—
737C23—222no—
738C23—222no—
739C23—221no—
740C23—442no—
741C23—442no—
742C23—442no—
743C23C2×D4×D1111yescharacteristic
744Q8—41no—
745Q8—441no—
746Q8—442no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—441no—
751D4—442no—
752D4—442no—
753D4—442no—
754D4—441no—
755D4—441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—111no—
768C2×C4—114no—
769C2×C4—111no—
770C2×C4—111no—
771C2×C4—111no—
772C2×C4—111no—
773C2×C4—111no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—221no—
784C2×C4—221no—
785C2×C4—222no—
786C2×C4—224no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—442no—
796C2×C4—4416no—
797C2×C4—442no—
798C2×C4—441no—
799C2×C4—442no—
800C2×C4—442no—
801C2×C4—442no—
802C2×C4C22⋊C4×D1111yescharacteristic
803C2×C4C22⋊C4×D1111yescharacteristic
804C2×C4C22⋊C4×D1111yescharacteristic
805C2×C4C22⋊C4×D1111yescharacteristic
806C2×C4C22×C4×D1111yescharacteristic
807C2×C4C2×D4×D1111yescharacteristic
808C8—42no—
809C8—442no—
810C22—21no—
811C22—21no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—112no—
816C22—112no—
817C22—112no—
818C22—112no—
819C22—224no—
820C22—224no—
821C22—221no—
822C22—221no—
823C22—441no—
824C22—441no—
825C22—441no—
826C22—884no—
827C22C2×C22⋊C4×D1111yescharacteristic
828C22D11×AGL(1,ℤ/8)11yescharacteristic
829C22D11×#13711yescharacteristic
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—44no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—112no—
840C4—221no—
841C4—221no—
842C4—221no—
843C4—221no—
844C4—221no—
845C4—444no—
846C4—441no—
847C4—441no—
848C4—441no—
849C4D11×#10412yes—
850C2—21no—
851C2—21no—
852C2—81no—
853C2—114no—
854C2—222no—
855C2—881no—
856C2D11×#41011yescharacteristic
857C2D11×#41711yescharacteristic
858C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1509C2
socleC22×C11C22×C22⋊C4
prime radicalD11×#121C22
cosocleC22×C4×C11C24
hypercenter#1509D11
hypocenterC11C2×#1509
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. D11×#432C2semidirect
3. C4×C4⋊C4×D11C2semidirect
4. #13067142C2semidirect
5. #13067141C2semidirect
6. #13067140C2semidirect
7. #13067139C2semidirect
8. #13067138C2semidirect
9. D11×#328C2semidirect
11. C11×#1509C2semidirect
15. #10623222C4semidirect
16. D11×#125C4semidirect
17. #10623211C4semidirect
18. D11×#124C4semidirect
25. #10623111C4semidirect
26. C4×Q8×D11C4semidirect
27. #10623088C4semidirect
29. C4×D4×D11C4semidirect
37. C11×#432C22semidirect
38. C4×C11×C4⋊C4C22semidirect
40. C4×C4⋊Dic11C22semidirect
42. #10622539C22semidirect
46. #10622332C22semidirect
50. #10622262C22semidirect
51. C11×#328C22semidirect
53. #10622176C22semidirect
56. #10622105C22semidirect
57. #10622090C22semidirect
68. C11×#125C2×C4semidirect
69. C11×#124C2×C4semidirect
73. C4×Q8×C11C2×C4semidirect
75. C4×D4×C11C2×C4semidirect
80. #67000C2×C4semidirect
82. Q8×Dic11C2×C4semidirect
85. #66989C2×C4semidirect
88. D4×Dic11C2×C4semidirect
113. #66946C2×C4semidirect
123. #66943C2×C4semidirect
124. #66943C2×C4semidirect
128. #66940C2×C4semidirect
150. #66928C2×C4semidirect
152. C4×D44C2×C4semidirect
165. #66923C2×C4semidirect
167. C4×Dic22C2×C4semidirect
311. #1509D11direct (N × H)
421. #432C2×D11semidirect
429. C4×C4⋊C4C2×D11semidirect
434. #328C2×D11semidirect
501. #125C4×D11semidirect
507. #124C4×D11semidirect
533. C4×Q8C4×D11semidirect
547. C4×D4C4×D11semidirect
608. D11#1509direct (N × H)
731. C11C2×#1509semidirect

Maximal subgroups

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

subgroupindex
D11×#5292
D11×#4322
C4×C4⋊C4×D112
#130671422
#130671412
#130671402
#130671392
#130671382
D11×#3282
D11×#3272
C11×#15092
C2×#150911