Finite Group Databasebeta

← #15618571

Subgroups — #15618571

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2#13077678C211yesmaximal, characteristic, complemented
3#13077676C212yesmaximal, complemented
4#13077671C212yesmaximal, complemented
5#13077668C212yesmaximal, complemented
6#13077663C214yesmaximal, complemented
7#13077660C214yesmaximal, complemented
8#13077352C214yesmaximal, complemented
9#13077349C214yesmaximal, complemented
10#13077250C212yesmaximal, complemented
11#13077058C212yesmaximal, complemented
12D11×#407C212yesmaximal, complemented
13C11×#2978C211yesmaximal, characteristic, complemented
14C2×#41×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C11×#525C2211yescharacteristic
17#10623359C2211yescharacteristic
18#10623322C2211yescharacteristic
19C2×M16×D11C2214yes—
20C2×M16×D11C2212yescomplemented
21C22×#4313C2212yescomplemented
22#10623187C412yes—
23D11×#123C412yes—
24#10623158C412yes—
25D11×C22⋊Q8C412yes—
26#10623137C412yes—
27D11×#121C412yes—
28D11×#120C412yes—
29#10623117C412yes—
30#10623078C2214yes—
31C4×D4×D11C2214yes—
32#10623055C2211yescharacteristic
33D11×#117C2211yescharacteristic
34C11×#436C2214yescomplemented
35C11×#435C2214yescomplemented
36C11×#433C2212yescomplemented
37C11×#408C2212yescomplemented
38C11×#407C2212yescomplemented
39#10622847C2212yescomplemented
40#10622820C2212yescomplemented
41#10622742C2212yescomplemented
42#10622741C2214yescomplemented
43#10622740C2214yescomplemented
44#10622740C2214yescomplemented
45#10622739C2214yescomplemented
46#10622723C2212yescomplemented
47C8×C22⋊D11C2214yescomplemented
48#10622625C2214yescomplemented
49#10622624C2214yescomplemented
50#10622613C2212yescomplemented
51#10622453C2214yescomplemented
52#10622450C2214yescomplemented
53#10622449C2214yescomplemented
54#10622447C2214yescomplemented
55#10622342C2214yescomplemented
56#10622341C2214yescomplemented
57#10622341C2214yescomplemented
58#10622340C2214yescomplemented
59#10622340C2214yescomplemented
60#10622339C2214yes—
61#10622339C2212yes—
62#10622339C2212yes—
63#10622339C2214yescomplemented
64(C22⋊D11)⋊C8C2214yescomplemented
65D11×C22⋊C8C2212yescomplemented
66D11×C22⋊C8C2212yescomplemented
67D11×C22⋊C8C2214yescomplemented
68#10622333C2214yescomplemented
69#10622322C2212yescomplemented
70#10622320C2212yescomplemented
71#10622319C2214yescomplemented
72#10622303C2212yescomplemented
73C4×#4313C2212yescomplemented
74C8×D44C2214yescomplemented
75C24×D11C2×C411yescharacteristic
76C2×C11×#41C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11C2×C411yescharacteristic
79#41×D11—44no—
80C2×#4343C2×C411yescharacteristic
81C2×Q8×D11C2×C411yescharacteristic
82C2×#4341C2×C412yes—
83C2×#4341C2×C411yescharacteristic
84C2×D4×D11C2×C414yes—
85C2×D4×D11C2×C412yes—
86C2×D4×D11C2×C411yescharacteristic
87C2×#4339C2312yes—
88C2×#4339C2311yescharacteristic
89C22×C4×D11—44no—
90C22×C4×D11C2×C412yes—
91C22×C4×D11C2×C412yes—
92C22×C4×D11C2×C411yescharacteristic
93C22×C4×D11C2×C411yescharacteristic
94C22×C4×D11C2312yes—
95C22×C4×D11C2312yes—
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2312yes—
98C22×C4×D11C2311yescharacteristic
99C2×C11×M16C2314yes—
100C2×C11×M16C2312yescomplemented
101C22×C8×C11C2312yescomplemented
102C11×#123C2×C412yes—
103C11×C22⋊Q8C2×C412yes—
104C11×#121C2×C412yes—
105C11×#120C2×C412yes—
106C4×D4×C11C2314yes—
107C11×#117C2311yescharacteristic
108#67006C2×C412yes—
109#66999C2×C412yes—
110#66992C2×C414yes—
111#66991C2×C412yes—
112#66990C2×C414yes—
113#66990C2×C412yes—
114#66988C2×C412yes—
115D4×Dic11C2×C414yes—
116#66983C2×C412yes—
117#66982C2×C412yes—
118C4×C22⋊D11C2314yes—
119C4×C22⋊D11C2314yes—
120#66979C2311yescharacteristic
121#66977C2×C412yes—
122C2×#4318C2314yes—
123C2×#4318C2312yescomplemented
124C22×C11⋊C8C2312yescomplemented
125M16×D11—48no—
126M16×D11—44no—
127C2×#4313—44no—
128C2×#4313C2314yes—
129C2×#4313C2314yes—
130C2×#4313C2314yescomplemented
131C2×C8×D11C2314yes—
132C2×C8×D11C2314yes—
133C2×C8×D11C2314yescomplemented
134#66950C2×C412yes—
135#66949C2×C414yes—
136#66948C2×C412yes—
137#66947C2×C414yes—
138#66946C2×C414yes—
139#66945C2×C412yes—
140C4⋊C4×D11C2×C412yes—
141C4⋊C4×D11C2×C414yes—
142#66939C2×C412yes—
143#66937C2×C414yes—
144#66936C2×C414yes—
145#66935C2×C412yes—
146#66935C2×C414yes—
147(C22⋊D11)⋊C4C2×C414yes—
148(C22⋊D11)⋊C4C2×C414yes—
149C22⋊C4×D11C2×C412yes—
150C22⋊C4×D11C2×C414yes—
151C22⋊C4×D11C2×C414yes—
152#66931C2×C414yes—
153#66930C2×C412yes—
154C4×D44C2314yes—
155#66925C2312yes—
156C42×D11C2312yes—
157C11×C4⋊C8C2314yescomplemented
158C11×C22⋊C8C2314yes—
159C11×C22⋊C8C2312yes—
160C11×C22⋊C8C2312yes—
161C11×C22⋊C8C2314yescomplemented
162C11×#97C2312yescomplemented
163C4×C8×C11C2312yescomplemented
164C22⋊(C11⋊C8)C2312yes—
165C22⋊(C11⋊C8)C2312yes—
166C22⋊(C11⋊C8)C2314yes—
167C22⋊(C11⋊C8)C2314yescomplemented
168(C2×D11)⋊C8C2314yes—
169(C2×D11)⋊C8C2314yes—
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yescomplemented
173(C2×D11)⋊C8C2314yescomplemented
174#66879C2314yescomplemented
175Dic11⋊C8C2314yescomplemented
176Dic11⋊C8C2314yescomplemented
177C8×Dic11C2314yescomplemented
178C4⋊(C11⋊C8)C2314yescomplemented
179#66867C2312yescomplemented
180C4×C11⋊C8C2312yescomplemented
181#60231—111nomaximal, Sylow
182C24×C11C22×C411yescharacteristic
183C23×D11—42no—
184C23×D11—44no—
185C23×D11C22×C412yes—
186C23×D11C22×C411yescharacteristic
187C23×D11C22×C411yescharacteristic
188C23×D11C22×C412yes—
189C23×D11C22×C412yes—
190C11×#41—42no—
191C2×Q8×C11C22×C411yescharacteristic
192C2×D4×C11C22×C414yes—
193C2×D4×C11C22×C412yes—
194C2×D4×C11C22×C411yescharacteristic
195C22×C4×C11—42no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C2×C22⋊D11C22×C414yes—
202C2×C22⋊D11C22×C414yes—
203C2×C22⋊D11C22×C412yes—
204C2×C22⋊D11C22×C412yes—
205C2×C22⋊D11C22×C412yes—
206C22×Dic11—42no—
207C22×Dic11C22×C411yescharacteristic
208C22×Dic11C22×C412yes—
209C22×Dic11C22×C412yes—
210C22×Dic11C22×C412yes—
211C22×Dic11C22×C411yescharacteristic
212#4343—42no—
213Q8×D11—42no—
214#4341—42no—
215#4341—44no—
216D4×D11—44no—
217D4×D11—42no—
218D4×D11—48no—
219#4339—42no—
220#4339—42no—
221#4339—42no—
222C2×D44C22×C414yes—
223C2×D44C22×C412yes—
224C2×D44C22×C411yescharacteristic
225C2×C4×D11—24no—
226C2×C4×D11—28no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—44no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—44no—
233C2×C4×D11—42no—
234C2×C4×D11—44no—
235C2×C4×D11C22×C412yes—
236C2×C4×D11C22×C412yes—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C22×C412yes—
239C2×C4×D11C22×C411yescharacteristic
240C2×C4×D11C22×C411yescharacteristic
241C2×C4×D11C22×C414yes—
242C2×C4×D11C22×C412yes—
243C2×C4×D11C22×C412yes—
244C2×C4×D11C22×C412yes—
245C2×C4×D11C2411yescharacteristic
246C2×C4×D11C2412yes—
247C2×C4×D11C2412yes—
248C2×C4×D11C2411yescharacteristic
249C2×Dic22C22×C412yes—
250C2×Dic22C22×C411yescharacteristic
251C11×M16—44no—
252C11×M16—42no—
253C2×C8×C11—42no—
254C2×C8×C11C2414yes—
255C2×C8×C11C2414yes—
256C11×C4⋊C4C22×C412yes—
257C11×C4⋊C4C22×C414yes—
258C11×C22⋊C4C22×C412yes—
259C11×C22⋊C4C22×C414yes—
260C11×C22⋊C4C22×C414yes—
261C42×C11C2412yes—
262C22⋊Dic11C22×C412yes—
263C22⋊Dic11C22×C414yes—
264C22⋊Dic11C22×C414yes—
265(C2×D11)⋊C4C22×C414yes—
266(C2×D11)⋊C4C22×C414yes—
267(C2×D11)⋊C4C22×C414yes—
268(C2×D11)⋊C4C22×C414yes—
269(C2×D11)⋊C4C22×C414yes—
270C4⋊Dic11C22×C414yes—
271C4⋊Dic11C22×C412yes—
272Dic11⋊C4C22×C414yes—
273Dic11⋊C4C22×C414yes—
274Dic11⋊C4C22×C414yes—
275C4×Dic11C22×C414yes—
276C4×Dic11C2412yes—
277#4318—44no—
278#4318—42no—
279C2×C11⋊C8—42no—
280C2×C11⋊C8C2414yes—
281C2×C11⋊C8C2414yes—
282#4313—28no—
283#4313—28no—
284#4313—44no—
285C8×D11—44no—
286C8×D11—44no—
287C8×D11—44no—
288C2×#525—111no—
289#2978—112no—
290#2978—111no—
291#2978D1111yescharacteristic, complemented
292#2977—112no—
293#2977—112no—
294#2976—114no—
295#2976—114no—
296D4×M16—114no—
297D4×M16—114no—
298#2921—112no—
299#2879—112no—
300C2×#407—112no—
301C23×C11—41no—
302C23×C11—42no—
303C23×C11C23×C411yescharacteristic
304C23×C11C23×C412yes—
305C23×C11C23×C412yes—
306C22×D11—22no—
307C22×D11—24no—
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—24no—
311C22×D11—24no—
312C22×D11—41no—
313C22×D11—42no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—44no—
318C22×D11—416no—
319C22×D11C23×C411yescharacteristic
320C22×D11C23×C412yes—
321C22×D11C23×C411yescharacteristic
322C22×D11C23×C412yes—
323Q8×C11—41no—
324D4×C11—41no—
325D4×C11—42no—
326D4×C11—44no—
327C2×C4×C11—22no—
328C2×C4×C11—24no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—42no—
332C2×C4×C11—41no—
333C2×C4×C11C23×C414yes—
334C2×C4×C11C23×C412yes—
335C2×C4×C11C23×C412yes—
336C2×C4×C11C23×C411yescharacteristic
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—28no—
339C22⋊D11—42no—
340C22⋊D11—42no—
341C22⋊D11—42no—
342C22⋊D11—44no—
343C2×Dic11—22no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—42no—
347C2×Dic11—41no—
348C2×Dic11C23×C414yes—
349C2×Dic11C23×C411yescharacteristic
350C2×Dic11C23×C412yes—
351C2×Dic11C23×C412yes—
352C2×Dic11C23×C411yescharacteristic
353D44—28no—
354D44—41no—
355D44—42no—
356C4×D11—24no—
357C4×D11—22no—
358C4×D11—24no—
359C4×D11—24no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—24no—
364C4×D11—22no—
365C4×D11—24no—
366C4×D11—42no—
367C4×D11—42no—
368C4×D11—42no—
369C4×D11—44no—
370C4×D11H(5,𝔽2)14yes—
371Dic22—42no—
372Dic22—41no—
373C8×C11—24no—
374C8×C11—24no—
375C11⋊C8—24no—
376C11⋊C8—24no—
377C22×#41—111no—
378C24×C4—111no—
379C22×M16—114no—
380C22×M16—112no—
381C22×M16—112no—
382#525—111no—
383#525—111no—
384#525—112no—
385#525—112no—
386#525—112no—
387#525—112no—
388#525—114no—
389#525—111no—
390#525C2×D1111yescharacteristic
391C2×#123—112no—
392C2×C22⋊Q8—112no—
393C2×#121—112no—
394C2×#120—112no—
395C2×C4×D4—114no—
396C2×#117—111no—
397#436—114no—
398#436—114no—
399#436—114no—
400#436C2×D1114yescomplemented
401#435—114no—
402#435—114no—
403#435—114no—
404#435—114no—
405#435—114no—
406#435—114no—
407#435—114no—
408#435C2×D1114yescomplemented
409C8×D4—114no—
410C8×D4—114no—
411C8×D4—114no—
412C8×D4—114no—
413#433—112no—
414#433—114no—
415#433—114no—
416#433—112no—
417#433—112no—
418#433C2×D1112yescomplemented
419#423—114no—
420#408—112no—
421#408—112no—
422#408—112no—
423#408—114no—
424#408—114no—
425#408C2×D1112yescomplemented
426#407—112no—
427#407—114no—
428#407—114no—
429#407—112no—
430#407—112no—
431#407—114no—
432#407C2×D1112yescomplemented
433C2×C22⋊C8—112no—
434C2×C22⋊C8—112no—
435C2×C22⋊C8—114no—
436C4×M16—112no—
437C4×M16—112no—
438C22×C11—21no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—24no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—44no—
446C22×C11C24×C411yescharacteristic
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—21no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—24no—
454C2×D11—48no—
455C2×D11—44no—
456C2×D11—44no—
457C2×D11—48no—
458C2×D11—84no—
459C2×D11#51812yes—
460C2×D11#56814yes—
461C4×C11—21no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—24no—
465C4×C11C2×H(5,𝔽2)12yes—
466Dic11—21no—
467Dic11—22no—
468Dic11—22no—
469Dic11—24no—
470Dic11#51812yes—
471C25—111no—
472C2×#41—111no—
473C2×#41—112no—
474C2×#41—111no—
475C2×#41—112no—
476C2×#41—111no—
477C2×#41—444no—
478C2×#41C22×D1111yescharacteristic
479C22×Q8—111no—
480C22×D4—114no—
481C22×D4—112no—
482C22×D4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—112no—
486C23×C4—112no—
487C23×C4—112no—
488C23×C4—111no—
489C23×C4—111no—
490C23×C4—112no—
491C23×C4—111no—
492C23×C4—112no—
493C23×C4—444no—
494C23×C4C22×D1111yescharacteristic
495C2×M16—114no—
496C2×M16—112no—
497C2×M16—114no—
498C2×M16—114no—
499C2×M16—114no—
500C2×M16—444no—
501C2×M16—448no—
502C2×M16—444no—
503C2×M16C22×D1114yes—
504C2×M16C22×D1112yescomplemented
505C22×C8—112no—
506C22×C8—114no—
507C22×C8—114no—
508C22×C8—114no—
509C22×C8C22×D1112yescomplemented
510#123—112no—
511#123—112no—
512#123—114no—
513#123—114no—
514#123—112no—
515#123C4×D1112yes—
516C22⋊Q8—112no—
517C22⋊Q8—112no—
518C22⋊Q8—114no—
519C22⋊Q8—112no—
520C22⋊Q8—114no—
521C22⋊Q8C4×D1112yes—
522#121—112no—
523#121—114no—
524#121—112no—
525#121—112no—
526#121—114no—
527#121C4×D1112yes—
528#120—112no—
529#120—112no—
530#120—114no—
531#120—114no—
532#120—112no—
533#120C4×D1112yes—
534C4×D4—114no—
535C4×D4—114no—
536C4×D4—114no—
537C4×D4—114no—
538C4×D4—114no—
539C4×D4—114no—
540C4×D4—114no—
541C4×D4C22×D1114yes—
542#117—111no—
543#117—112no—
544#117—112no—
545#117—112no—
546#117C22×D1111yescharacteristic
547C2×C4⋊C4—112no—
548C2×C4⋊C4—114no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C42—112no—
553C4⋊C8—114no—
554C4⋊C8—114no—
555C4⋊C8—114no—
556C4⋊C8C22×D1114yescomplemented
557C22⋊C8—114no—
558C22⋊C8—112no—
559C22⋊C8—112no—
560C22⋊C8—114no—
561C22⋊C8—114no—
562C22⋊C8—114no—
563C22⋊C8—114no—
564C22⋊C8—114no—
565C22⋊C8—114no—
566C22⋊C8—114no—
567C22⋊C8C22×D1114yes—
568C22⋊C8C22×D1112yes—
569C22⋊C8C22×D1112yes—
570C22⋊C8C22×D1114yescomplemented
571#97—114no—
572#97—112no—
573#97C22×D1112yescomplemented
574C4×C8—114no—
575C4×C8—112no—
576C4×C8C22×D1112yescomplemented
577C2×C11—41no—
578C2×C11—42no—
579C2×C11—42no—
580C2×C11C2×#51811yescharacteristic
581C2×C11C2×#56812yes—
582D11—22no—
583D11—24no—
584D11—41no—
585D11—42no—
586C24—112no—
587C24—111no—
588C24—111no—
589C24—112no—
590C24—112no—
591C24—442no—
592C24—444no—
593C24C2×C4×D1111yescharacteristic
594#41—42no—
595#41—442no—
596#41—442no—
597#41—442no—
598#41—442no—
599#41—444no—
600#41—442no—
601C2×Q8—111no—
602C2×Q8—112no—
603C2×Q8—442no—
604C2×Q8C2×C4×D1111yescharacteristic
605C2×D4—114no—
606C2×D4—114no—
607C2×D4—112no—
608C2×D4—112no—
609C2×D4—112no—
610C2×D4—114no—
611C2×D4—112no—
612C2×D4—111no—
613C2×D4—442no—
614C2×D4—444no—
615C2×D4—448no—
616C2×D4C2×C4×D1114yes—
617C2×D4C2×C4×D1112yes—
618C2×D4C2×C4×D1111yescharacteristic
619C22×C4—42no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—111no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—111no—
629C22×C4—111no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—111no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—114no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—228no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—444no—
644C22×C4—442no—
645C22×C4—444no—
646C22×C4—442no—
647C22×C4—444no—
648C22×C4—442no—
649C22×C4—442no—
650C22×C4C2×C4×D1112yes—
651C22×C4C2×C4×D1111yescharacteristic
652C22×C4C23×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655M16—44no—
656M16—42no—
657M16—228no—
658M16—228no—
659M16—444no—
660M16—444no—
661M16—442no—
662C2×C8—42no—
663C2×C8—114no—
664C2×C8—114no—
665C2×C8—444no—
666C2×C8—444no—
667C2×C8—444no—
668C2×C8—442no—
669C2×C8C23×D1114yes—
670C2×C8C23×D1114yes—
671C4⋊C4—114no—
672C4⋊C4—112no—
673C4⋊C4—114no—
674C4⋊C4—114no—
675C4⋊C4—114no—
676C4⋊C4C2×C4×D1112yes—
677C4⋊C4C2×C4×D1114yes—
678C22⋊C4—112no—
679C22⋊C4—114no—
680C22⋊C4—114no—
681C22⋊C4—114no—
682C22⋊C4—114no—
683C22⋊C4—114no—
684C22⋊C4—114no—
685C22⋊C4—114no—
686C22⋊C4C2×C4×D1112yes—
687C22⋊C4C2×C4×D1114yes—
688C22⋊C4C2×C4×D1114yes—
689C42—114no—
690C42—112no—
691C42C23×D1112yes—
692C11#6023111yescharacteristic, complemented, Sylow
693C23—41no—
694C23—42no—
695C23—112no—
696C23—111no—
697C23—111no—
698C23—112no—
699C23—222no—
700C23—224no—
701C23—224no—
702C23—224no—
703C23—224no—
704C23—224no—
705C23—441no—
706C23—442no—
707C23—442no—
708C23—442no—
709C23—442no—
710C23—444no—
711C23—4416no—
712C23C22×C4×D1112yes—
713C23C22×C4×D1111yescharacteristic
714C23C22×C4×D1112yes—
715Q8—41no—
716Q8—441no—
717Q8—442no—
718D4—44no—
719D4—41no—
720D4—42no—
721D4—228no—
722D4—228no—
723D4—441no—
724D4—442no—
725D4—442no—
726D4—442no—
727D4—442no—
728D4—444no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—111no—
736C2×C4—114no—
737C2×C4—114no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—111no—
741C2×C4—222no—
742C2×C4—224no—
743C2×C4—224no—
744C2×C4—222no—
745C2×C4—224no—
746C2×C4—224no—
747C2×C4—222no—
748C2×C4—224no—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—444no—
758C2×C4—442no—
759C2×C4—441no—
760C2×C4C22×C4×D1114yes—
761C2×C4C22×C4×D1112yes—
762C2×C4C22×C4×D1112yes—
763C2×C4C22×C4×D1111yescharacteristic
764C2×C4C24×D1111yescharacteristic
765C8—24no—
766C8—24no—
767C8—224no—
768C8—224no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—22no—
773C22—21no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—114no—
778C22—112no—
779C22—222no—
780C22—222no—
781C22—222no—
782C22—224no—
783C22—222no—
784C22—221no—
785C22—222no—
786C22—448no—
787C22—444no—
788C22—444no—
789C22—448no—
790C22—884no—
791C22C23×C4×D1111yescharacteristic
792C4—24no—
793C4—21no—
794C4—22no—
795C4—22no—
796C4—112no—
797C4—224no—
798C4—221no—
799C4—222no—
800C4—222no—
801C4D11×H(5,𝔽2)12yes—
802C2—42no—
803C2—41no—
804C2—42no—
805C2—222no—
806C2—224no—
807C2—441no—
808C2—442no—
809C2D11×#51811yescharacteristic
810C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2978C2
prime radicalD11×#525C2
cosocleC2×C4×C11C25
hypercenter#2978D11
hypocenterC11#60231
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2978

Complements

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

NH ≅ G/Ntype
2. #13077678C2semidirect
3. #13077676C2semidirect
4. #13077671C2semidirect
5. #13077668C2semidirect
6. #13077663C2semidirect
7. #13077660C2semidirect
8. #13077352C2semidirect
9. #13077349C2semidirect
10. #13077250C2semidirect
11. #13077058C2semidirect
12. D11×#407C2semidirect
13. C11×#2978C2semidirect
20. C2×M16×D11C22semidirect
21. C22×#4313C22semidirect
34. C11×#436C22semidirect
35. C11×#435C22semidirect
36. C11×#433C22semidirect
37. C11×#408C22semidirect
38. C11×#407C22semidirect
39. #10622847C22semidirect
40. #10622820C22semidirect
41. #10622742C22semidirect
42. #10622741C22semidirect
43. #10622740C22semidirect
44. #10622740C22semidirect
45. #10622739C22semidirect
46. #10622723C22semidirect
47. C8×C22⋊D11C22semidirect
48. #10622625C22semidirect
49. #10622624C22semidirect
50. #10622613C22semidirect
51. #10622453C22semidirect
52. #10622450C22semidirect
53. #10622449C22semidirect
54. #10622447C22semidirect
55. #10622342C22semidirect
56. #10622341C22semidirect
57. #10622341C22semidirect
58. #10622340C22semidirect
59. #10622340C22semidirect
63. #10622339C22semidirect
64. (C22⋊D11)⋊C8C22semidirect
65. D11×C22⋊C8C22semidirect
66. D11×C22⋊C8C22semidirect
67. D11×C22⋊C8C22semidirect
68. #10622333C22semidirect
69. #10622322C22semidirect
70. #10622320C22semidirect
71. #10622319C22semidirect
72. #10622303C22semidirect
73. C4×#4313C22semidirect
74. C8×D44C22semidirect
100. C2×C11×M16C23semidirect
101. C22×C8×C11C23semidirect
123. C2×#4318C23semidirect
124. C22×C11⋊C8C23semidirect
130. C2×#4313C23semidirect
133. C2×C8×D11C23semidirect
157. C11×C4⋊C8C23semidirect
161. C11×C22⋊C8C23semidirect
162. C11×#97C23semidirect
163. C4×C8×C11C23semidirect
167. C22⋊(C11⋊C8)C23semidirect
172. (C2×D11)⋊C8C23semidirect
173. (C2×D11)⋊C8C23semidirect
174. #66879C23semidirect
175. Dic11⋊C8C23semidirect
176. Dic11⋊C8C23semidirect
177. C8×Dic11C23semidirect
178. C4⋊(C11⋊C8)C23semidirect
179. #66867C23semidirect
180. C4×C11⋊C8C23semidirect
291. #2978D11semidirect
400. #436C2×D11semidirect
408. #435C2×D11semidirect
418. #433C2×D11semidirect
425. #408C2×D11semidirect
432. #407C2×D11semidirect
504. C2×M16C22×D11semidirect
509. C22×C8C22×D11semidirect
556. C4⋊C8C22×D11semidirect
570. C22⋊C8C22×D11semidirect
573. #97C22×D11semidirect
576. C4×C8C22×D11semidirect
692. C11#60231semidirect

Maximal subgroups

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

subgroupindex
D11×#5252
#130776782
#130776762
#130776712
#130776682
#130776632
#130776602
#130773522
#130773492
#130772502
#130770582
D11×#4072
C11×#29782
#6023111