Finite Group Databasebeta

← #14960507

Subgroups — #14960507

Order 2816.

4154 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623205C211yesmaximal, characteristic, complemented
2C2×D11×#120C211yesmaximal, characteristic, complemented
3#13076894C212yesmaximal, complemented
4#13074999C212yesmaximal, complemented
5#13074992C211yesmaximal, characteristic, complemented
6#13074834C211yesmaximal, characteristic, complemented
7#13074833C211yesmaximal, characteristic, complemented
8#13074831C212yesmaximal, complemented
9#13074826C212yesmaximal, complemented
10#13074824C212yesmaximal, complemented
11#13074823C212yesmaximal, complemented
12#13074821C212yesmaximal, complemented
13#13074390C212yesmaximal, complemented
14#13072888C212yesmaximal, complemented
15#13071989C212yesmaximal, complemented
16#13071985C212yesmaximal, complemented
17#13071936C212yesmaximal, complemented
18#13071190C211yesmaximal, characteristic, complemented
19C11×#2684C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic
21C22×#4343C2211yescharacteristic, complemented
22C22×D4×D11C2212yes—
23C22×D4×D11C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic, complemented
25C2×C11×#120C2211yescharacteristic
26C2×#67006C2211yescharacteristic
27C2×#67006C2212yescomplemented
28C2×#67000C2211yescharacteristic, complemented
29C2×#66993C2211yescharacteristic, complemented
30C2×#66992C2212yescomplemented
31C2×#66990C2211yescharacteristic
32C2×#66990C2212yes—
33C2×#66983C2212yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
35#10623205—28no—
36D11×#120—28no—
37C2×#66948C2212yescomplemented
38C2×#66937C2212yescomplemented
39C2×#66937C2212yescomplemented
40C2×#66937C2212yescomplemented
41C2×#66935C2212yes—
42C2×#66935C2212yes—
43C2×#66935C2211yescharacteristic
44C2×#66935C2212yes—
45C2×#66935C2212yes—
46C2×#66935C2212yescomplemented
47C2×#66935C2212yescomplemented
48C2×#66935C2212yescomplemented
49C2×#66935C2212yescomplemented
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic, complemented
53C2×#66927C2211yescharacteristic, complemented
54C2×#66925C2211yescharacteristic, complemented
55C11×#397C2212yescomplemented
56C11×#394C2212yescomplemented
57C11×#393C2212yescomplemented
58C11×#388C2212yescomplemented
59C11×#386C2211yescharacteristic, complemented
60C11×#386C2212yescomplemented
61C11×#379C2212yescomplemented
62#10622844C2212yescomplemented
63#10622836C2212yescomplemented
64#10622833C2211yescharacteristic, complemented
65#10622826C2211yescharacteristic, complemented
66#10622605C2212yescomplemented
67#10622604C2212yescomplemented
68#10622602C2212yescomplemented
69#10622574C2212yescomplemented
70#10622574C2212yescomplemented
71#10622573C2212yescomplemented
72#10622573C2212yescomplemented
73#10622573C2212yescomplemented
74#10622572C2212yescomplemented
75#10622572C2212yescomplemented
76#10622571C2212yescomplemented
77#10622571C2211yescharacteristic, complemented
78#10622569C2212yescomplemented
79#10622569C2212yescomplemented
80#10622569C2212yescomplemented
81#10622569C2212yescomplemented
82#10622568C2212yes—
83#10622568C2212yes—
84#10622568C2212yes—
85#10622568C2212yescomplemented
86#10622568C2212yescomplemented
87#10622568C2212yescomplemented
88#10622565C2212yescomplemented
89#10622565C2212yescomplemented
90#10622562C2212yescomplemented
91#10622557C2212yescomplemented
92#10622553C2212yescomplemented
93#10622288C2212yescomplemented
94#10622288C2212yescomplemented
95#10622287C2212yescomplemented
96#10622285C2212yescomplemented
97#10622285C2212yescomplemented
98#10622284C2212yescomplemented
99#10622284C2212yescomplemented
100#10622283C2212yescomplemented
101#10622281C2212yescomplemented
102#10622278C2212yescomplemented
103#10622278C2212yescomplemented
104#10622278C2212yescomplemented
105#10622278C2212yescomplemented
106#10622278C2212yescomplemented
107#10622278C2212yescomplemented
108#10622277C2212yescomplemented
109C25×C11C2311yescharacteristic
110C24×D11—24no—
111C24×D11—44no—
112C24×D11—42no—
113C24×D11—42no—
114C24×D11—44no—
115C24×D11C2312yes—
116C24×D11C2311yescharacteristic
117C24×D11C2312yes—
118C24×D11C2311yescharacteristic
119C24×D11C2311yescharacteristic
120C22×Q8×C11C2311yescharacteristic, complemented
121C22×D4×C11C2312yes—
122C22×D4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic, complemented
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2312yescomplemented
132C23×Dic11C2311yescharacteristic, complemented
133C2×#4343—24no—
134C2×#4343—42no—
135C2×#4343—42no—
136C2×D4×D11—28no—
137C2×D4×D11—42no—
138C2×D4×D11—42no—
139C2×D4×D11—44no—
140C2×D4×D11—44no—
141C2×D4×D11D418yescomplemented
142C22×D44C2312yes—
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×D44C2312yes—
146C22×D44C2312yes—
147C22×D44C2311yescharacteristic
148C22×D44C2312yescomplemented
149C22×D44C2311yescharacteristic, complemented
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yescomplemented
153C22×C4×D11C2312yescomplemented
154C11×#124—24no—
155C11×#120—24no—
156C2×C11×C4⋊C4C2312yescomplemented
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yescomplemented
166C2×C11×C22⋊C4C2311yescharacteristic, complemented
167C2×C42×C11C2311yescharacteristic, complemented
168#67006—24no—
169#67006—44no—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic, complemented
176#67000—24no—
177#66993—24no—
178#66992—44no—
179#66990—24no—
180#66990—28no—
181#66983—44no—
182C2×(C2×D11)⋊C4—42no—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yescomplemented
199C2×(C2×D11)⋊C4C2312yescomplemented
200C2×(C2×D11)⋊C4C2312yescomplemented
201C2×(C2×D11)⋊C4C2312yescomplemented
202C2×(C2×D11)⋊C4C2312yescomplemented
203C2×(C2×D11)⋊C4C2312yescomplemented
204C2×C4⋊Dic11C2312yescomplemented
205C2×Dic11⋊C4C2312yescomplemented
206C2×Dic11⋊C4C2312yescomplemented
207C2×Dic11⋊C4C2312yescomplemented
208C2×C4×Dic11C2311yescharacteristic, complemented
209#66948—44no—
210#66937—28no—
211#66937—28no—
212#66937—44no—
213#66935—28no—
214#66935—28no—
215#66935—24no—
216#66935—28no—
217#66935—44no—
218#66935—44no—
219#66935—44no—
220#66935—44no—
221#66935—44no—
222C22⋊C4×D11—24no—
223C22⋊C4×D11—28no—
224C22⋊C4×D11—42no—
225#66927—24no—
226#66925—24no—
227C11×#95C2312yescomplemented
228C11×#95C2312yescomplemented
229C11×#95C2312yescomplemented
230C11×#95C2312yescomplemented
231C11⋊#95C2312yescomplemented
232C11⋊#95C2312yescomplemented
233C11⋊#95C2312yescomplemented
234C11⋊#95C2312yescomplemented
235C11⋊#95C2312yescomplemented
236C11⋊#95C2312yescomplemented
237C11⋊#95C2312yescomplemented
238C11⋊#95C2312yescomplemented
239#36702—111nomaximal, Sylow
240C24×C11—22no—
241C24×C11—24no—
242C24×C11—42no—
243C24×C11—41no—
244C24×C11—41no—
245C24×C11C2411yescharacteristic
246C24×C11C2411yescharacteristic
247C24×C11C2412yes—
248C23×D11—24no—
249C23×D11—24no—
250C23×D11—24no—
251C23×D11—22no—
252C23×D11—22no—
253C23×D11—22no—
254C23×D11—22no—
255C23×D11—22no—
256C23×D11—24no—
257C23×D11—24no—
258C23×D11—24no—
259C23×D11—24no—
260C23×D11—24no—
261C23×D11—24no—
262C23×D11—42no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—41no—
267C23×D11—42no—
268C23×D11—41no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11—42no—
275C23×D11—432no—
276C23×D11—416no—
277C23×D11—416no—
278C23×D11—432no—
279C23×D11—416no—
280C23×D11C2×D414yes—
281C23×D11C2×D414yes—
282C23×D11C2412yes—
283C23×D11C2411yescharacteristic
284C23×D11C2411yescharacteristic
285C23×D11C2412yes—
286C23×D11C2411yescharacteristic
287C2×Q8×C11—22no—
288C2×Q8×C11—41no—
289C2×Q8×C11—41no—
290C2×D4×C11—24no—
291C2×D4×C11—24no—
292C2×D4×C11—41no—
293C2×D4×C11—41no—
294C2×D4×C11—42no—
295C2×D4×C11C2×D414yes—
296C22×C4×C11—41no—
297C22×C4×C11—42no—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—41no—
313C2×C22⋊D11—41no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—41no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—41no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11—42no—
325C2×C22⋊D11—42no—
326C2×C22⋊D11C2×D414yes—
327C2×C22⋊D11C2×D414yes—
328C22×Dic11—41no—
329C22×Dic11—42no—
330C22×Dic11C2412yes—
331C22×Dic11C2412yes—
332C22×Dic11C2412yes—
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335#4343—416no—
336D4×D11—416no—
337D4×D11—432no—
338C2×D44—24no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—24no—
342C2×D44—24no—
343C2×D44—24no—
344C2×D44—24no—
345C2×D44—24no—
346C2×D44—24no—
347C2×D44—22no—
348C2×D44—41no—
349C2×D44—41no—
350C2×D44—42no—
351C2×D44—41no—
352C2×D44—41no—
353C2×D44—42no—
354C2×D44—42no—
355C2×D44—42no—
356C2×D44—42no—
357C2×D44—42no—
358C2×D44—42no—
359C2×D44—42no—
360C2×D44—42no—
361C2×D44C2×D414yes—
362C2×C4×D11—24no—
363C2×C4×D11—24no—
364C2×C4×D11—22no—
365C2×C4×D11—22no—
366C2×C4×D11—42no—
367C2×C4×D11—42no—
368C2×C4×D11—42no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—42no—
372C2×C4×D11—42no—
373C2×C4×D11C2×D414yes—
374C11×C4⋊C4—42no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—24no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—24no—
380C11×C22⋊C4—41no—
381C11×C22⋊C4—42no—
382C11×C22⋊C4—42no—
383C11×C22⋊C4—42no—
384C11×C22⋊C4—42no—
385C42×C11—22no—
386C22⋊Dic11—24no—
387C22⋊Dic11—22no—
388C22⋊Dic11—24no—
389C22⋊Dic11—41no—
390C22⋊Dic11—42no—
391C22⋊Dic11—42no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—42no—
403(C2×D11)⋊C4—42no—
404(C2×D11)⋊C4—42no—
405(C2×D11)⋊C4—42no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408(C2×D11)⋊C4—42no—
409(C2×D11)⋊C4—42no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4—42no—
412(C2×D11)⋊C4—42no—
413C4⋊Dic11—42no—
414Dic11⋊C4—24no—
415Dic11⋊C4—42no—
416Dic11⋊C4—42no—
417C4×Dic11—22no—
418C2×#535—111no—
419C22×#120—111no—
420#2846—112no—
421#2684—112no—
422#2684—111no—
423#2684D1111yescharacteristic, complemented
424#2669—112no—
425#2669—111no—
426#2669—111no—
427#2668—112no—
428#2668—112no—
429#2668—112no—
430#2668—112no—
431#2622—112no—
432#2482—112no—
433#2410—112no—
434#2410—112no—
435#2404—112no—
436#2308—111no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—48no—
452C23×C11—44no—
453C23×C11—44no—
454C23×C11—48no—
455C23×C11—44no—
456C23×C11C22×D412yes—
457C23×C11C22×D412yes—
458C23×C11H(5,𝔽2)14yes—
459C23×C11C2511yescharacteristic
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—216no—
463C22×D11—22no—
464C22×D11—21no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—21no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—28no—
478C22×D11—28no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—48no—
487C22×D11—48no—
488C22×D11—48no—
489C22×D11—48no—
490C22×D11—44no—
491C22×D11—48no—
492C22×D11—48no—
493C22×D11—48no—
494C22×D11—48no—
495C22×D11—48no—
496C22×D11—48no—
497C22×D11—48no—
498C22×D11—48no—
499C22×D11—44no—
500C22×D11—44no—
501C22×D11—48no—
502C22×D11—48no—
503C22×D11—48no—
504C22×D11—44no—
505C22×D11—48no—
506C22×D11—4128no—
507C22×D11—48no—
508C22×D11—44no—
509C22×D11—48no—
510C22×D11—82no—
511C22×D11—82no—
512C22×D11—84no—
513C22×D11C22×D412yes—
514C22×D11C22×D412yes—
515C22×D11C22×D412yes—
516C22×D11H(5,𝔽2)14yes—
517C22×D11H(5,𝔽2)12yes—
518C22×D11H(5,𝔽2)12yes—
519Q8×C11—44no—
520D4×C11—44no—
521D4×C11—48no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—82no—
540C2×C4×C11C22×D412yes—
541C22⋊D11—44no—
542C22⋊D11—44no—
543C22⋊D11—48no—
544C22⋊D11—48no—
545C22⋊D11—84no—
546C22⋊D11—84no—
547C22⋊D11—84no—
548C22⋊D11—84no—
549C2×Dic11—21no—
550C2×Dic11—21no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—82no—
564C2×Dic11C22×D412yes—
565D44—44no—
566D44—44no—
567D44—48no—
568D44—48no—
569D44—84no—
570D44—84no—
571D44—84no—
572D44—84no—
573C4×D11—28no—
574C4×D11—48no—
575C4×D11—48no—
576C4×D11—84no—
577C26—111no—
578C22×#41—111no—
579C23×D4—111no—
580C23×D4—112no—
581#535—228no—
582C2×#127—111no—
583C2×#127—111no—
584C2×#124—111no—
585C2×#124C2×D1111yescharacteristic, complemented
586C2×#121—112no—
587C2×#121—112no—
588C2×#121—112no—
589C2×#121—112no—
590C2×#121—112no—
591C2×#121—112no—
592C2×#120—111no—
593C2×#120—112no—
594C2×#120—111no—
595C2×#120—112no—
596C2×#120—112no—
597C2×#120—111no—
598C2×#120—112no—
599C2×#120—112no—
600C2×#120—112no—
601C2×#120—112no—
602C2×#120—112no—
603C2×#120—112no—
604C2×#120—112no—
605C2×#120—228no—
606C2×#120C2×D1111yescharacteristic
607C2×#117—111no—
608C22×C22⋊C4—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—112no—
611C22×C22⋊C4—111no—
612#399—112no—
613#399—112no—
614#397—112no—
615#397—112no—
616#397—112no—
617#397—112no—
618#397—112no—
619#397C2×D1112yescomplemented
620#394—112no—
621#394—112no—
622#394—112no—
623#394—112no—
624#394—112no—
625#394—112no—
626#394—112no—
627#394C2×D1112yescomplemented
628#393—112no—
629#393C2×D1112yescomplemented
630#392—112no—
631#392—112no—
632#392—112no—
633#392—112no—
634#392—112no—
635#392—112no—
636#388—112no—
637#388—112no—
638#388—112no—
639#388C2×D1112yescomplemented
640#386—111no—
641#386—111no—
642#386—112no—
643#386—112no—
644#386—112no—
645#386—112no—
646#386—111no—
647#386—112no—
648#386—112no—
649#386—112no—
650#386—112no—
651#386—112no—
652#386—112no—
653#386—112no—
654#386C2×D1111yescharacteristic, complemented
655#386C2×D1112yescomplemented
656#385—112no—
657#385—112no—
658#381—112no—
659#379—112no—
660#379—112no—
661#379—112no—
662#379—112no—
663#379—112no—
664#379—112no—
665#379C2×D1112yescomplemented
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—24no—
669C22×C11—24no—
670C22×C11—24no—
671C22×C11—24no—
672C22×C11—24no—
673C22×C11—416no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—41no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—41no—
680C22×C11—41no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—41no—
684C22×C11C23×D411yescharacteristic
685C22×C11C2×H(5,𝔽2)12yes—
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11C2×H(5,𝔽2)12yes—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—24no—
696C2×D11—24no—
697C2×D11—24no—
698C2×D11—24no—
699C2×D11—24no—
700C2×D11—432no—
701C2×D11—416no—
702C2×D11—432no—
703C2×D11—416no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—42no—
708C2×D11—42no—
709C2×D11—41no—
710C2×D11—41no—
711C2×D11—41no—
712C2×D11—41no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—88no—
722C2×D11#53414yes—
723C4×C11—22no—
724C4×C11—42no—
725C4×C11—42no—
726C4×C11—42no—
727C4×C11—42no—
728C4×C11—42no—
729Dic11—22no—
730Dic11—42no—
731Dic11—42no—
732Dic11—42no—
733Dic11—42no—
734C25—111no—
735C25—111no—
736C25—112no—
737C25—112no—
738C25—111no—
739C25—224no—
740C25—444no—
741C25—442no—
742C25—444no—
743C25—442no—
744C25C22×D1111yescharacteristic
745C2×#41—224no—
746C2×#41—442no—
747C2×#41—442no—
748C22×Q8C22×D1111yescharacteristic, complemented
749C22×D4—111no—
750C22×D4—111no—
751C22×D4—118no—
752C22×D4—112no—
753C22×D4—112no—
754C22×D4—112no—
755C22×D4—112no—
756C22×D4—112no—
757C22×D4—112no—
758C22×D4—111no—
759C22×D4—112no—
760C22×D4—112no—
761C22×D4—112no—
762C22×D4—112no—
763C22×D4—112no—
764C22×D4—112no—
765C22×D4—111no—
766C22×D4—228no—
767C22×D4—442no—
768C22×D4—442no—
769C22×D4—444no—
770C22×D4—444no—
771C22×D4C22×D1112yes—
772C22×D4C22×D1111yescharacteristic
773C23×C4—111no—
774C23×C4—111no—
775C23×C4—112no—
776C23×C4—112no—
777C23×C4—112no—
778C23×C4C22×D1111yescharacteristic, complemented
779#127—224no—
780#127—224no—
781#124—24no—
782#124—224no—
783#121—228no—
784#121—228no—
785#121—444no—
786#121—444no—
787#121—444no—
788#121—444no—
789#120—24no—
790#120—224no—
791#120—228no—
792#120—228no—
793#120—228no—
794#120—228no—
795#120—224no—
796#120—224no—
797#120—444no—
798#120—444no—
799#120—444no—
800#120—444no—
801#120—444no—
802#120—444no—
803#117—224no—
804C2×C4⋊C4—112no—
805C2×C4⋊C4—112no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—112no—
808C2×C4⋊C4C22×D1112yescomplemented
809C2×C22⋊C4—112no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—111no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—112no—
829C2×C22⋊C4—112no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—228no—
837C2×C22⋊C4—224no—
838C2×C22⋊C4—442no—
839C2×C22⋊C4—442no—
840C2×C22⋊C4C22×D1112yes—
841C2×C22⋊C4C22×D1111yescharacteristic
842C2×C22⋊C4C22×D1112yes—
843C2×C22⋊C4C22×D1112yes—
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1112yes—
846C2×C22⋊C4C22×D1112yes—
847C2×C22⋊C4C22×D1112yes—
848C2×C22⋊C4C22×D1112yescomplemented
849C2×C22⋊C4C22×D1111yescharacteristic, complemented
850C2×C42—111no—
851C2×C42C22×D1111yescharacteristic, complemented
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856#95—112no—
857#95—112no—
858#95—112no—
859#95—112no—
860#95C22×D1112yescomplemented
861#95C22×D1112yescomplemented
862#95C22×D1112yescomplemented
863#95C22×D1112yescomplemented
864C2×C11—42no—
865C2×C11—44no—
866C2×C11—42no—
867C2×C11C2×#53411yescharacteristic
868C2×C11#348412yes—
869C2×C11#353212yes—
870C2×C11#353211yescharacteristic
871C2×C11#353211yescharacteristic
872D11—24no—
873D11—42no—
874D11—44no—
875D11—42no—
876D11—82no—
877C24—22no—
878C24—24no—
879C24—42no—
880C24—41no—
881C24—41no—
882C24—111no—
883C24—111no—
884C24—112no—
885C24—111no—
886C24—114no—
887C24—114no—
888C24—112no—
889C24—224no—
890C24—222no—
891C24—222no—
892C24—224no—
893C24—222no—
894C24—222no—
895C24—224no—
896C24—224no—
897C24—224no—
898C24—224no—
899C24—224no—
900C24—224no—
901C24—222no—
902C24—224no—
903C24—442no—
904C24—442no—
905C24—442no—
906C24—442no—
907C24—442no—
908C24—442no—
909C24—442no—
910C24—442no—
911C24—442no—
912C24—441no—
913C24—441no—
914C24—442no—
915C24—442no—
916C24—4432no—
917C24—4416no—
918C24—4416no—
919C24—4432no—
920C24—4416no—
921C24C23×D1111yescharacteristic
922C24C23×D1111yescharacteristic
923C24C23×D1112yes—
924#41—4416no—
925C2×Q8—22no—
926C2×Q8—41no—
927C2×Q8—41no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—42no—
933C2×D4—114no—
934C2×D4—114no—
935C2×D4—114no—
936C2×D4—224no—
937C2×D4—224no—
938C2×D4—224no—
939C2×D4—224no—
940C2×D4—224no—
941C2×D4—224no—
942C2×D4—224no—
943C2×D4—224no—
944C2×D4—224no—
945C2×D4—224no—
946C2×D4—224no—
947C2×D4—224no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—224no—
951C2×D4—224no—
952C2×D4—224no—
953C2×D4—222no—
954C2×D4—441no—
955C2×D4—441no—
956C2×D4—442no—
957C2×D4—441no—
958C2×D4—441no—
959C2×D4—442no—
960C2×D4—442no—
961C2×D4—442no—
962C2×D4—442no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—442no—
966C2×D4—442no—
967C2×D4—4416no—
968C2×D4—441no—
969C2×D4—441no—
970C2×D4—441no—
971C2×D4—441no—
972C2×D4—442no—
973C2×D4—442no—
974C2×D4—442no—
975C2×D4—442no—
976C2×D4—442no—
977C2×D4—442no—
978C2×D4—442no—
979C2×D4—442no—
980C2×D4—442no—
981C2×D4—442no—
982C2×D4—4432no—
983C2×D4D4×D1114yes—
984C22×C4—41no—
985C22×C4—42no—
986C22×C4—111no—
987C22×C4—114no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—224no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—224no—
996C22×C4—442no—
997C22×C4—442no—
998C22×C4—442no—
999C22×C4—442no—
1000C22×C4—442no—
1001C22×C4—442no—
1002C22×C4—442no—
1003C22×C4—441no—
1004C22×C4—442no—
1005C22×C4C23×D1112yes—
1006C22×C4C23×D1112yes—
1007C22×C4C23×D1112yes—
1008C22×C4C23×D1112yes—
1009C22×C4C23×D1112yes—
1010C22×C4C23×D1111yescharacteristic
1011C4⋊C4—42no—
1012C4⋊C4—224no—
1013C4⋊C4—442no—
1014C4⋊C4—442no—
1015C4⋊C4—442no—
1016C22⋊C4—22no—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—41no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—224no—
1027C22⋊C4—224no—
1028C22⋊C4—224no—
1029C22⋊C4—224no—
1030C22⋊C4—224no—
1031C22⋊C4—224no—
1032C22⋊C4—224no—
1033C22⋊C4—224no—
1034C22⋊C4—224no—
1035C22⋊C4—224no—
1036C22⋊C4—222no—
1037C22⋊C4—224no—
1038C22⋊C4—224no—
1039C22⋊C4—442no—
1040C22⋊C4—442no—
1041C22⋊C4—442no—
1042C22⋊C4—442no—
1043C22⋊C4—442no—
1044C22⋊C4—442no—
1045C22⋊C4—442no—
1046C22⋊C4—442no—
1047C22⋊C4—442no—
1048C22⋊C4—442no—
1049C22⋊C4—442no—
1050C22⋊C4—441no—
1051C22⋊C4—442no—
1052C22⋊C4—442no—
1053C42—22no—
1054C42—222no—
1055C11#3670211yescharacteristic, complemented, Sylow
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—21no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—21no—
1069C23—22no—
1070C23—48no—
1071C23—44no—
1072C23—44no—
1073C23—48no—
1074C23—44no—
1075C23—112no—
1076C23—112no—
1077C23—112no—
1078C23—112no—
1079C23—112no—
1080C23—114no—
1081C23—228no—
1082C23—228no—
1083C23—2216no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—221no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—221no—
1097C23—222no—
1098C23—221no—
1099C23—221no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—448no—
1108C23—448no—
1109C23—448no—
1110C23—448no—
1111C23—448no—
1112C23—448no—
1113C23—448no—
1114C23—444no—
1115C23—448no—
1116C23—448no—
1117C23—448no—
1118C23—448no—
1119C23—448no—
1120C23—444no—
1121C23—448no—
1122C23—448no—
1123C23—448no—
1124C23—448no—
1125C23—444no—
1126C23—444no—
1127C23—448no—
1128C23—44128no—
1129C23—448no—
1130C23—444no—
1131C23—884no—
1132C23—882no—
1133C23—882no—
1134C23C2×D4×D1112yes—
1135C23C2×D4×D1112yes—
1136C23#6704214yes—
1137C23C24×D1111yescharacteristic
1138Q8—44no—
1139D4—44no—
1140D4—48no—
1141D4—444no—
1142D4—444no—
1143D4—448no—
1144D4—448no—
1145D4—444no—
1146D4—444no—
1147D4—448no—
1148D4—448no—
1149D4—884no—
1150D4—884no—
1151D4—884no—
1152D4—884no—
1153D4—884no—
1154D4—884no—
1155D4—884no—
1156D4—884no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—82no—
1175C2×C4—112no—
1176C2×C4—228no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—448no—
1192C2×C4—448no—
1193C2×C4—884no—
1194C2×C4—882no—
1195C2×C4C2×D4×D1112yes—
1196C22—22no—
1197C22—22no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—416no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—42no—
1214C22—114no—
1215C22—224no—
1216C22—224no—
1217C22—222no—
1218C22—222no—
1219C22—222no—
1220C22—222no—
1221C22—224no—
1222C22—224no—
1223C22—224no—
1224C22—224no—
1225C22—224no—
1226C22—4416no—
1227C22—4432no—
1228C22—4416no—
1229C22—4432no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—442no—
1235C22—441no—
1236C22—442no—
1237C22—441no—
1238C22—441no—
1239C22—441no—
1240C22—442no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—888no—
1248C22C22×D4×D1111yescharacteristic
1249C22C2×#6704212yes—
1250C22D11×H(5,𝔽2)11yescharacteristic
1251C22D11×H(5,𝔽2)11yescharacteristic
1252C22D11×H(5,𝔽2)12yes—
1253C4—22no—
1254C4—42no—
1255C4—42no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—222no—
1260C4—442no—
1261C4—442no—
1262C4—442no—
1263C4—442no—
1264C2—42no—
1265C2—44no—
1266C2—42no—
1267C2—224no—
1268C2—442no—
1269C2—444no—
1270C2—442no—
1271C2—882no—
1272C2D11×#53411yescharacteristic
1273C2#1308224612yes—
1274C2#1308276712yes—
1275C2#1308277211yescharacteristic
1276C2#1308277311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2684C2
hypercenter#2684D11
hypocenterC11#36702
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2684

Complements

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

NH ≅ G/Ntype
1. C2×#10623205C2semidirect
2. C2×D11×#120C2semidirect
3. #13076894C2semidirect
4. #13074999C2semidirect
5. #13074992C2semidirect
6. #13074834C2semidirect
7. #13074833C2semidirect
8. #13074831C2semidirect
9. #13074826C2semidirect
10. #13074824C2semidirect
11. #13074823C2semidirect
12. #13074821C2semidirect
13. #13074390C2semidirect
14. #13072888C2semidirect
15. #13071989C2semidirect
16. #13071985C2semidirect
17. #13071936C2semidirect
18. #13071190C2semidirect
19. C11×#2684C2semidirect
21. C22×#4343C22semidirect
24. C2×C11×#124C22semidirect
27. C2×#67006C22semidirect
28. C2×#67000C22semidirect
29. C2×#66993C22semidirect
30. C2×#66992C22semidirect
33. C2×#66983C22semidirect
34. C22×(C2×D11)⋊C4C22semidirect
37. C2×#66948C22semidirect
38. C2×#66937C22semidirect
39. C2×#66937C22semidirect
40. C2×#66937C22semidirect
46. C2×#66935C22semidirect
47. C2×#66935C22semidirect
48. C2×#66935C22semidirect
49. C2×#66935C22semidirect
52. C2×C22⋊C4×D11C22semidirect
53. C2×#66927C22semidirect
54. C2×#66925C22semidirect
55. C11×#397C22semidirect
56. C11×#394C22semidirect
57. C11×#393C22semidirect
58. C11×#388C22semidirect
59. C11×#386C22semidirect
60. C11×#386C22semidirect
61. C11×#379C22semidirect
62. #10622844C22semidirect
63. #10622836C22semidirect
64. #10622833C22semidirect
65. #10622826C22semidirect
66. #10622605C22semidirect
67. #10622604C22semidirect
68. #10622602C22semidirect
69. #10622574C22semidirect
70. #10622574C22semidirect
71. #10622573C22semidirect
72. #10622573C22semidirect
73. #10622573C22semidirect
74. #10622572C22semidirect
75. #10622572C22semidirect
76. #10622571C22semidirect
77. #10622571C22semidirect
78. #10622569C22semidirect
79. #10622569C22semidirect
80. #10622569C22semidirect
81. #10622569C22semidirect
85. #10622568C22semidirect
86. #10622568C22semidirect
87. #10622568C22semidirect
88. #10622565C22semidirect
89. #10622565C22semidirect
90. #10622562C22semidirect
91. #10622557C22semidirect
92. #10622553C22semidirect
93. #10622288C22semidirect
94. #10622288C22semidirect
95. #10622287C22semidirect
96. #10622285C22semidirect
97. #10622285C22semidirect
98. #10622284C22semidirect
99. #10622284C22semidirect
100. #10622283C22semidirect
101. #10622281C22semidirect
102. #10622278C22semidirect
103. #10622278C22semidirect
104. #10622278C22semidirect
105. #10622278C22semidirect
106. #10622278C22semidirect
107. #10622278C22semidirect
108. #10622277C22semidirect
120. C22×Q8×C11C23semidirect
123. C23×C4×C11C23semidirect
131. C22×C22⋊D11C23semidirect
132. C23×Dic11C23semidirect
141. C2×D4×D11D4semidirect
148. C22×D44C23semidirect
149. C22×D44C23semidirect
152. C22×C4×D11C23semidirect
153. C22×C4×D11C23semidirect
156. C2×C11×C4⋊C4C23semidirect
165. C2×C11×C22⋊C4C23semidirect
166. C2×C11×C22⋊C4C23semidirect
167. C2×C42×C11C23semidirect
175. C2×C22⋊Dic11C23semidirect
198. C2×(C2×D11)⋊C4C23semidirect
199. C2×(C2×D11)⋊C4C23semidirect
200. C2×(C2×D11)⋊C4C23semidirect
201. C2×(C2×D11)⋊C4C23semidirect
202. C2×(C2×D11)⋊C4C23semidirect
203. C2×(C2×D11)⋊C4C23semidirect
204. C2×C4⋊Dic11C23semidirect
205. C2×Dic11⋊C4C23semidirect
206. C2×Dic11⋊C4C23semidirect
207. C2×Dic11⋊C4C23semidirect
208. C2×C4×Dic11C23semidirect
227. C11×#95C23semidirect
228. C11×#95C23semidirect
229. C11×#95C23semidirect
230. C11×#95C23semidirect
231. C11⋊#95C23semidirect
232. C11⋊#95C23semidirect
233. C11⋊#95C23semidirect
234. C11⋊#95C23semidirect
235. C11⋊#95C23semidirect
236. C11⋊#95C23semidirect
237. C11⋊#95C23semidirect
238. C11⋊#95C23semidirect
423. #2684D11semidirect
585. C2×#124C2×D11semidirect
619. #397C2×D11semidirect
627. #394C2×D11semidirect
629. #393C2×D11semidirect
639. #388C2×D11semidirect
654. #386C2×D11semidirect
655. #386C2×D11semidirect
665. #379C2×D11semidirect
748. C22×Q8C22×D11semidirect
778. C23×C4C22×D11semidirect
808. C2×C4⋊C4C22×D11semidirect
848. C2×C22⋊C4C22×D11semidirect
849. C2×C22⋊C4C22×D11semidirect
851. C2×C42C22×D11semidirect
860. #95C22×D11semidirect
861. #95C22×D11semidirect
862. #95C22×D11semidirect
863. #95C22×D11semidirect
1055. C11#36702semidirect

Maximal subgroups

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

subgroupindex
C2×#106232052
C2×D11×#1202
#130768942
#130749992
#130749922
#130748342
#130748332
#130748312
#130748262
#130748242
#130748232
#130748212
#130743902
#130728882
#130719892
#130719852
#130719362
#130711902
C11×#26842
#3670211