Finite Group Databasebeta

← #14960696

Subgroups — #14960696

Order 2816.

4170 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C211yesmaximal, characteristic, complemented
2C2×D11×#120C211yesmaximal, characteristic, complemented
3#13076892C212yesmaximal, complemented
4#13075182C212yesmaximal, complemented
5#13075178C211yesmaximal, characteristic, complemented
6#13075177C211yesmaximal, characteristic, complemented
7#13074950C211yesmaximal, characteristic, complemented
8#13074950C212yesmaximal, complemented
9#13074948C212yesmaximal, complemented
10#13074947C212yesmaximal, complemented
11#13074938C212yesmaximal, complemented
12#13074937C212yesmaximal, complemented
13#13074388C212yesmaximal, complemented
14#13071998C212yesmaximal, complemented
15#13071994C212yesmaximal, complemented
16#13071938C212yesmaximal, complemented
17#13071927C212yesmaximal, complemented
18#13071195C211yesmaximal, characteristic, complemented
19C11×#2679C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic, complemented
21C23×C22⋊D11C2211yescharacteristic, complemented
22C22×D4×D11C2212yes—
23C22×D4×D11C2211yescharacteristic
24C2×C11×#120C2211yescharacteristic
25C2×C11×#120C2212yescomplemented
26C2×C11×#120C2211yescharacteristic, complemented
27C2×C11×#120C2212yescomplemented
28C2×#67006C2211yescharacteristic, complemented
29C2×#67006C2211yescharacteristic, complemented
30C2×#67006C2212yescomplemented
31C2×#66991C2212yescomplemented
32C2×#66990C2211yescharacteristic
33C2×#66990C2212yes—
34C2×#66990C2212yes—
35C2×#66990C2212yes—
36C2×#66990C2212yes—
37C2×#66990C2212yescomplemented
38C2×#66990C2212yescomplemented
39C2×#66990C2212yescomplemented
40C2×#66988C2211yescharacteristic, complemented
41#10623120—28no—
42D11×#120—28no—
43C2×#66947C2212yescomplemented
44C2×#66945C2211yescharacteristic, complemented
45C2×#66939C2211yescharacteristic, complemented
46C2×#66937C2212yescomplemented
47C2×#66936C2212yescomplemented
48C2×#66936C2212yescomplemented
49C2×#66935C2212yescomplemented
50C2×#66935C2211yescharacteristic, complemented
51C2×C22⋊C4×D11C2212yescomplemented
52C2×C22⋊C4×D11C2211yescharacteristic, complemented
53C2×C22⋊C4×D11C2211yescharacteristic, complemented
54C2×#66925C2211yescharacteristic, complemented
55C11×#394C2212yescomplemented
56C11×#394C2212yescomplemented
57C11×#394C2212yescomplemented
58C11×#390C2211yescharacteristic, complemented
59C11×#390C2212yescomplemented
60#10622860C2212yescomplemented
61#10622836C2212yescomplemented
62#10622836C2212yescomplemented
63#10622835C2212yescomplemented
64#10622835C2212yescomplemented
65#10622835C2212yescomplemented
66#10622834C2211yescharacteristic, complemented
67#10622834C2212yescomplemented
68#10622833C2212yescomplemented
69#10622607C2212yescomplemented
70#10622607C2212yescomplemented
71#10622606C2212yescomplemented
72#10622602C2212yescomplemented
73#10622601C2211yescharacteristic, complemented
74#10622574C2212yescomplemented
75#10622574C2212yescomplemented
76#10622574C2212yescomplemented
77#10622573C2212yescomplemented
78#10622573C2212yescomplemented
79#10622572C2212yescomplemented
80#10622572C2212yescomplemented
81#10622572C2212yescomplemented
82#10622571C2212yescomplemented
83#10622570C2212yescomplemented
84#10622570C2212yescomplemented
85#10622570C2212yescomplemented
86#10622570C2212yescomplemented
87#10622569C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622568C2212yescomplemented
91#10622568C2212yescomplemented
92#10622568C2212yescomplemented
93#10622568C2212yescomplemented
94#10622568C2212yescomplemented
95#10622568C2212yescomplemented
96#10622568C2212yescomplemented
97#10622566C2212yescomplemented
98#10622565C2212yescomplemented
99#10622564C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622558C2212yescomplemented
103#10622553C2212yescomplemented
104#10622552C2211yescharacteristic, complemented
105#10622288C2212yescomplemented
106#10622283C2212yescomplemented
107#10622281C2212yescomplemented
108#10622278C2212yescomplemented
109C25×C11C2311yescharacteristic
110C25×C11C2311yescharacteristic, complemented
111C24×D11—24no—
112C24×D11—44no—
113C24×D11—42no—
114C24×D11—42no—
115C24×D11—44no—
116C24×D11C2312yes—
117C24×D11C2311yescharacteristic
118C24×D11C2312yes—
119C24×D11C2311yescharacteristic
120C24×D11C2311yescharacteristic
121C22×D4×C11C2312yes—
122C22×D4×C11C2312yes—
123C22×D4×C11C2312yes—
124C22×D4×C11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×C22⋊D11—24no—
127C22×C22⋊D11—42no—
128C22×C22⋊D11—42no—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2312yescomplemented
138C23×Dic11C2311yescharacteristic, complemented
139C2×D4×D11—28no—
140C2×D4×D11—42no—
141C2×D4×D11—42no—
142C2×D4×D11—44no—
143C2×D4×D11—44no—
144C2×D4×D11D418yescomplemented
145C22×D44C2312yes—
146C22×D44C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yescomplemented
150C11×#120—24no—
151C11×#120—24no—
152C11×#120—44no—
153C11×#120—44no—
154C2×C11×C4⋊C4C2311yescharacteristic, complemented
155C2×C11×C4⋊C4C2312yescomplemented
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic, complemented
162C2×C11×C22⋊C4C2312yescomplemented
163C2×C11×C22⋊C4C2312yescomplemented
164C2×C11×C22⋊C4C2312yescomplemented
165C2×C11×C22⋊C4C2312yescomplemented
166C2×C42×C11C2311yescharacteristic, complemented
167#67006—24no—
168#67006—24no—
169#67006—44no—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic, complemented
179C2×C22⋊Dic11C2312yescomplemented
180C2×C22⋊Dic11C2312yescomplemented
181C2×C22⋊Dic11C2312yescomplemented
182C2×C22⋊Dic11C2312yescomplemented
183#66991—28no—
184#66990—28no—
185#66990—24no—
186#66990—28no—
187#66990—44no—
188#66990—44no—
189#66990—44no—
190#66990—44no—
191#66990—44no—
192#66988—24no—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yescomplemented
209C2×(C2×D11)⋊C4C2312yescomplemented
210C2×C4⋊Dic11C2312yescomplemented
211C2×C4⋊Dic11C2312yescomplemented
212C2×C4⋊Dic11C2311yescharacteristic, complemented
213C2×Dic11⋊C4C2312yescomplemented
214C2×Dic11⋊C4C2312yescomplemented
215C2×Dic11⋊C4C2312yescomplemented
216C2×Dic11⋊C4C2312yescomplemented
217C2×C4×Dic11C2311yescharacteristic, complemented
218C2×C4×Dic11C2312yescomplemented
219#66947—44no—
220#66945—42no—
221#66939—24no—
222#66937—28no—
223#66936—28no—
224#66936—44no—
225#66935—24no—
226#66935—28no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11—24no—
229C22⋊C4×D11—28no—
230#66925—42no—
231C11×#95C2312yescomplemented
232C11⋊#95C2312yescomplemented
233C11⋊#95C2312yescomplemented
234C11⋊#95C2312yescomplemented
235C11⋊#95C2312yescomplemented
236C11⋊#95C2312yescomplemented
237C11⋊#95C2312yescomplemented
238C11⋊#95C2312yescomplemented
239#36714—111nomaximal, Sylow
240C24×C11—22no—
241C24×C11—24no—
242C24×C11—22no—
243C24×C11—42no—
244C24×C11—41no—
245C24×C11—41no—
246C24×C11—41no—
247C24×C11—41no—
248C24×C11—42no—
249C24×C11—42no—
250C24×C11C2412yes—
251C24×C11C2411yescharacteristic
252C24×C11C2411yescharacteristic
253C24×C11C2412yes—
254C23×D11—24no—
255C23×D11—24no—
256C23×D11—24no—
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—22no—
261C23×D11—22no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—24no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—41no—
273C23×D11—42no—
274C23×D11—41no—
275C23×D11—42no—
276C23×D11—42no—
277C23×D11—42no—
278C23×D11—42no—
279C23×D11—42no—
280C23×D11—42no—
281C23×D11—432no—
282C23×D11—416no—
283C23×D11—416no—
284C23×D11—432no—
285C23×D11—416no—
286C23×D11C2×D414yes—
287C23×D11C2×D414yes—
288C23×D11C2411yescharacteristic
289C23×D11C2411yescharacteristic
290C23×D11C2412yes—
291C23×D11C2411yescharacteristic
292C2×D4×C11—24no—
293C2×D4×C11—24no—
294C2×D4×C11—24no—
295C2×D4×C11—24no—
296C2×D4×C11—24no—
297C2×D4×C11—41no—
298C2×D4×C11—41no—
299C2×D4×C11—42no—
300C2×D4×C11—42no—
301C2×D4×C11—42no—
302C2×D4×C11—42no—
303C2×D4×C11—42no—
304C2×D4×C11—42no—
305C2×D4×C11—42no—
306C2×D4×C11C2×D414yes—
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2412yes—
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—24no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11—41no—
325C2×C22⋊D11—41no—
326C2×C22⋊D11—42no—
327C2×C22⋊D11—41no—
328C2×C22⋊D11—41no—
329C2×C22⋊D11—42no—
330C2×C22⋊D11—42no—
331C2×C22⋊D11—42no—
332C2×C22⋊D11—42no—
333C2×C22⋊D11—42no—
334C2×C22⋊D11—42no—
335C2×C22⋊D11—42no—
336C2×C22⋊D11—42no—
337C2×C22⋊D11—416no—
338C2×C22⋊D11C2×D414yes—
339C2×C22⋊D11C2×D414yes—
340C22×Dic11—22no—
341C22×Dic11—41no—
342C22×Dic11—41no—
343C22×Dic11C2412yes—
344C22×Dic11C2412yes—
345C22×Dic11C2412yes—
346C22×Dic11C2412yes—
347C22×Dic11C2412yes—
348C22×Dic11C2411yescharacteristic
349D4×D11—416no—
350D4×D11—432no—
351C2×D44—24no—
352C2×D44—24no—
353C2×D44—41no—
354C2×D44—41no—
355C2×D44—42no—
356C2×D44C2×D414yes—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11C2×D414yes—
366C11×C4⋊C4—41no—
367C11×C4⋊C4—42no—
368C11×C22⋊C4—22no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—24no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—24no—
373C11×C22⋊C4—42no—
374C11×C22⋊C4—42no—
375C11×C22⋊C4—42no—
376C11×C22⋊C4—42no—
377C11×C22⋊C4—42no—
378C42×C11—41no—
379C22⋊Dic11—24no—
380C22⋊Dic11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—22no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—42no—
386C22⋊Dic11—42no—
387C22⋊Dic11—42no—
388C22⋊Dic11—42no—
389C22⋊Dic11—42no—
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—42no—
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—
409C4⋊Dic11—24no—
410C4⋊Dic11—42no—
411C4⋊Dic11—41no—
412Dic11⋊C4—24no—
413Dic11⋊C4—42no—
414Dic11⋊C4—42no—
415Dic11⋊C4—42no—
416C4×Dic11—41no—
417C4×Dic11—42no—
418C2×#534—111no—
419C22×#120—111no—
420#2846—112no—
421#2697—112no—
422#2697—111no—
423#2697—111no—
424#2679—112no—
425#2679—111no—
426#2679D1111yescharacteristic, complemented
427#2678—112no—
428#2678—112no—
429#2678—112no—
430#2678—112no—
431#2622—112no—
432#2411—112no—
433#2411—112no—
434#2405—112no—
435#2403—112no—
436#2309—111no—
437C23×C11—22no—
438C23×C11—22no—
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—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—48no—
459C23×C11—44no—
460C23×C11—44no—
461C23×C11—48no—
462C23×C11—44no—
463C23×C11—44no—
464C23×C11—84no—
465C23×C11—82no—
466C23×C11—84no—
467C23×C11—82no—
468C23×C11C22×D412yes—
469C23×C11C22×D412yes—
470C23×C11H(5,𝔽2)14yes—
471C23×C11C2511yescharacteristic
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—216no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—21no—
485C22×D11—21no—
486C22×D11—22no—
487C22×D11—21no—
488C22×D11—21no—
489C22×D11—28no—
490C22×D11—28no—
491C22×D11—48no—
492C22×D11—48no—
493C22×D11—48no—
494C22×D11—48no—
495C22×D11—44no—
496C22×D11—48no—
497C22×D11—48no—
498C22×D11—48no—
499C22×D11—48no—
500C22×D11—48no—
501C22×D11—48no—
502C22×D11—48no—
503C22×D11—44no—
504C22×D11—48no—
505C22×D11—44no—
506C22×D11—48no—
507C22×D11—48no—
508C22×D11—48no—
509C22×D11—44no—
510C22×D11—48no—
511C22×D11—4128no—
512C22×D11—44no—
513C22×D11—48no—
514C22×D11—48no—
515C22×D11—82no—
516C22×D11—84no—
517C22×D11—82no—
518C22×D11C22×D412yes—
519C22×D11C22×D412yes—
520C22×D11C22×D412yes—
521C22×D11H(5,𝔽2)14yes—
522C22×D11H(5,𝔽2)12yes—
523C22×D11H(5,𝔽2)12yes—
524D4×C11—44no—
525D4×C11—48no—
526D4×C11—84no—
527D4×C11—84no—
528D4×C11—84no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
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—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11C22×D412yes—
544C22⋊D11—44no—
545C22⋊D11—44no—
546C22⋊D11—48no—
547C22⋊D11—48no—
548C22⋊D11—48no—
549C22⋊D11—48no—
550C22⋊D11—84no—
551C22⋊D11—84no—
552C22⋊D11—84no—
553C2×Dic11—21no—
554C2×Dic11—21no—
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—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—22no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—44no—
571C2×Dic11C22×D412yes—
572D44—44no—
573D44—48no—
574C4×D11—28no—
575C4×D11—48no—
576C4×D11—84no—
577C26—111no—
578C23×D4—111no—
579C23×D4—111no—
580C23×D4—112no—
581#534—228no—
582C2×#123—111no—
583C2×#123—112no—
584C2×#123—112no—
585C2×#123—112no—
586C2×#123—111no—
587C2×#121—112no—
588C2×#121—112no—
589C2×#120—111no—
590C2×#120—111no—
591C2×#120—112no—
592C2×#120—112no—
593C2×#120—111no—
594C2×#120—112no—
595C2×#120—112no—
596C2×#120—112no—
597C2×#120—112no—
598C2×#120—112no—
599C2×#120—112no—
600C2×#120—111no—
601C2×#120—112no—
602C2×#120—228no—
603C2×#120C2×D1111yescharacteristic
604C2×#120C2×D1112yescomplemented
605C2×#120C2×D1111yescharacteristic, complemented
606C2×#120C2×D1112yescomplemented
607C2×#117—111no—
608C2×#117—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—112no—
611C22×C22⋊C4—111no—
612#397—112no—
613#397—112no—
614#397—112no—
615#397—112no—
616#396—112no—
617#396—112no—
618#396—112no—
619#396—112no—
620#394—112no—
621#394—112no—
622#394—112no—
623#394—112no—
624#394—112no—
625#394—112no—
626#394—112no—
627#394—112no—
628#394—112no—
629#394C2×D1112yescomplemented
630#394C2×D1112yescomplemented
631#394C2×D1112yescomplemented
632#392—112no—
633#392—112no—
634#392—112no—
635#392—112no—
636#390—111no—
637#390—112no—
638#390—111no—
639#390—112no—
640#390—112no—
641#390—112no—
642#390—112no—
643#390—111no—
644#390C2×D1111yescharacteristic, complemented
645#390C2×D1112yescomplemented
646#388—112no—
647#388—112no—
648#388—112no—
649#388—112no—
650#386—112no—
651#386—112no—
652#386—112no—
653#386—112no—
654#386—112no—
655#386—112no—
656#385—112no—
657#385—112no—
658#379—112no—
659#379—112no—
660#379—112no—
661#379—112no—
662#379—112no—
663#379—112no—
664#379—112no—
665#379—112no—
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—42no—
681C22×C11—41no—
682C22×C11—42no—
683C22×C11—41no—
684C22×C11—42no—
685C22×C11—42no—
686C22×C11—42no—
687C22×C11—42no—
688C22×C11—42no—
689C22×C11—42no—
690C22×C11—42no—
691C22×C11—88no—
692C22×C11C23×D411yescharacteristic
693C22×C11C2×H(5,𝔽2)12yes—
694C22×C11C2×H(5,𝔽2)11yescharacteristic
695C22×C11C2×H(5,𝔽2)11yescharacteristic
696C22×C11C2×H(5,𝔽2)12yes—
697C2×D11—24no—
698C2×D11—22no—
699C2×D11—24no—
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—22no—
703C2×D11—24no—
704C2×D11—24no—
705C2×D11—24no—
706C2×D11—24no—
707C2×D11—24no—
708C2×D11—432no—
709C2×D11—416no—
710C2×D11—432no—
711C2×D11—416no—
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—41no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—41no—
719C2×D11—41no—
720C2×D11—42no—
721C2×D11—41no—
722C2×D11—88no—
723C2×D11#53414yes—
724C4×C11—22no—
725C4×C11—42no—
726C4×C11—42no—
727C4×C11—42no—
728C4×C11—42no—
729Dic11—22no—
730Dic11—42no—
731Dic11—42no—
732Dic11—42no—
733Dic11—42no—
734Dic11—42no—
735C25—111no—
736C25—111no—
737C25—112no—
738C25—112no—
739C25—111no—
740C25—224no—
741C25—444no—
742C25—442no—
743C25—444no—
744C25—442no—
745C25C22×D1111yescharacteristic
746C25C22×D1111yescharacteristic, complemented
747C22×D4—111no—
748C22×D4—111no—
749C22×D4—118no—
750C22×D4—112no—
751C22×D4—112no—
752C22×D4—112no—
753C22×D4—112no—
754C22×D4—112no—
755C22×D4—112no—
756C22×D4—112no—
757C22×D4—111no—
758C22×D4—112no—
759C22×D4—228no—
760C22×D4—224no—
761C22×D4—442no—
762C22×D4—442no—
763C22×D4—444no—
764C22×D4—444no—
765C22×D4—442no—
766C22×D4—442no—
767C22×D4C22×D1112yes—
768C22×D4C22×D1112yes—
769C22×D4C22×D1112yes—
770C22×D4C22×D1112yes—
771C22×D4C22×D1111yescharacteristic
772C23×C4—111no—
773C23×C4—111no—
774C23×C4—112no—
775C23×C4—112no—
776#123—228no—
777#123—224no—
778#123—224no—
779#123—444no—
780#123—444no—
781#121—228no—
782#121—228no—
783#120—24no—
784#120—24no—
785#120—44no—
786#120—44no—
787#120—224no—
788#120—228no—
789#120—228no—
790#120—228no—
791#120—224no—
792#120—224no—
793#120—224no—
794#120—444no—
795#120—444no—
796#120—444no—
797#120—444no—
798#120—444no—
799#120—444no—
800#117—442no—
801#117—442no—
802C2×C4⋊C4—112no—
803C2×C4⋊C4—112no—
804C2×C4⋊C4—112no—
805C2×C4⋊C4—111no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—112no—
808C2×C4⋊C4—112no—
809C2×C4⋊C4C22×D1111yescharacteristic, complemented
810C2×C4⋊C4C22×D1112yescomplemented
811C2×C22⋊C4—112no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—111no—
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—112no—
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—112no—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—112no—
841C2×C22⋊C4—228no—
842C2×C22⋊C4—224no—
843C2×C22⋊C4—224no—
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1111yescharacteristic
846C2×C22⋊C4C22×D1112yes—
847C2×C22⋊C4C22×D1112yes—
848C2×C22⋊C4C22×D1112yes—
849C2×C22⋊C4C22×D1111yescharacteristic, complemented
850C2×C22⋊C4C22×D1112yescomplemented
851C2×C22⋊C4C22×D1112yescomplemented
852C2×C22⋊C4C22×D1112yescomplemented
853C2×C22⋊C4C22×D1112yescomplemented
854C2×C42—112no—
855C2×C42—111no—
856C2×C42C22×D1111yescharacteristic, complemented
857#95—112no—
858#95—112no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95—112no—
863#95—112no—
864#95C22×D1112yescomplemented
865C2×C11—42no—
866C2×C11—44no—
867C2×C11—42no—
868C2×C11—82no—
869C2×C11C2×#53411yescharacteristic
870C2×C11#348412yes—
871C2×C11#353211yescharacteristic
872C2×C11#353212yes—
873C2×C11#353211yescharacteristic
874D11—24no—
875D11—42no—
876D11—44no—
877D11—42no—
878C24—22no—
879C24—24no—
880C24—22no—
881C24—42no—
882C24—41no—
883C24—41no—
884C24—41no—
885C24—41no—
886C24—42no—
887C24—42no—
888C24—111no—
889C24—111no—
890C24—112no—
891C24—111no—
892C24—114no—
893C24—114no—
894C24—224no—
895C24—222no—
896C24—222no—
897C24—224no—
898C24—222no—
899C24—222no—
900C24—224no—
901C24—224no—
902C24—224no—
903C24—224no—
904C24—224no—
905C24—224no—
906C24—222no—
907C24—224no—
908C24—442no—
909C24—442no—
910C24—442no—
911C24—442no—
912C24—442no—
913C24—442no—
914C24—442no—
915C24—442no—
916C24—442no—
917C24—441no—
918C24—441no—
919C24—442no—
920C24—442no—
921C24—4432no—
922C24—4416no—
923C24—4416no—
924C24—4432no—
925C24—4416no—
926C24C23×D1112yes—
927C24C23×D1111yescharacteristic
928C24C23×D1111yescharacteristic
929C24C23×D1112yes—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—24no—
935C2×D4—41no—
936C2×D4—41no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—114no—
945C2×D4—114no—
946C2×D4—114no—
947C2×D4—224no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—224no—
951C2×D4—224no—
952C2×D4—224no—
953C2×D4—224no—
954C2×D4—224no—
955C2×D4—224no—
956C2×D4—224no—
957C2×D4—224no—
958C2×D4—224no—
959C2×D4—224no—
960C2×D4—441no—
961C2×D4—441no—
962C2×D4—442no—
963C2×D4—4416no—
964C2×D4—441no—
965C2×D4—441no—
966C2×D4—441no—
967C2×D4—441no—
968C2×D4—442no—
969C2×D4—442no—
970C2×D4—442no—
971C2×D4—442no—
972C2×D4—442no—
973C2×D4—442no—
974C2×D4—442no—
975C2×D4—442no—
976C2×D4—442no—
977C2×D4—442no—
978C2×D4—4432no—
979C2×D4—4416no—
980C2×D4D4×D1114yes—
981C22×C4—111no—
982C22×C4—114no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—222no—
989C22×C4—222no—
990C22×C4—224no—
991C22×C4—224no—
992C22×C4—222no—
993C22×C4—442no—
994C22×C4—442no—
995C22×C4—442no—
996C22×C4—442no—
997C22×C4—441no—
998C22×C4—441no—
999C22×C4C23×D1112yes—
1000C22×C4C23×D1112yes—
1001C22×C4C23×D1112yes—
1002C22×C4C23×D1112yes—
1003C22×C4C23×D1111yescharacteristic
1004C4⋊C4—41no—
1005C4⋊C4—42no—
1006C4⋊C4—224no—
1007C4⋊C4—224no—
1008C4⋊C4—442no—
1009C4⋊C4—441no—
1010C4⋊C4—442no—
1011C4⋊C4—442no—
1012C4⋊C4—442no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—224no—
1024C22⋊C4—224no—
1025C22⋊C4—224no—
1026C22⋊C4—224no—
1027C22⋊C4—224no—
1028C22⋊C4—224no—
1029C22⋊C4—224no—
1030C22⋊C4—224no—
1031C22⋊C4—224no—
1032C22⋊C4—224no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—224no—
1036C22⋊C4—224no—
1037C22⋊C4—224no—
1038C22⋊C4—442no—
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—442no—
1051C22⋊C4—442no—
1052C22⋊C4—442no—
1053C42—41no—
1054C42—441no—
1055C42—442no—
1056C11#3671411yescharacteristic, complemented, Sylow
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—48no—
1079C23—44no—
1080C23—44no—
1081C23—48no—
1082C23—44no—
1083C23—44no—
1084C23—84no—
1085C23—82no—
1086C23—84no—
1087C23—82no—
1088C23—112no—
1089C23—112no—
1090C23—112no—
1091C23—112no—
1092C23—112no—
1093C23—114no—
1094C23—228no—
1095C23—228no—
1096C23—2216no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—221no—
1110C23—221no—
1111C23—221no—
1112C23—221no—
1113C23—448no—
1114C23—448no—
1115C23—448no—
1116C23—448no—
1117C23—448no—
1118C23—448no—
1119C23—448no—
1120C23—444no—
1121C23—448no—
1122C23—448no—
1123C23—448no—
1124C23—448no—
1125C23—448no—
1126C23—444no—
1127C23—448no—
1128C23—448no—
1129C23—444no—
1130C23—448no—
1131C23—448no—
1132C23—444no—
1133C23—448no—
1134C23—44128no—
1135C23—444no—
1136C23—448no—
1137C23—882no—
1138C23—884no—
1139C23—882no—
1140C23C2×D4×D1112yes—
1141C23C2×D4×D1112yes—
1142C23#6703714yes—
1143C23C24×D1111yescharacteristic
1144D4—44no—
1145D4—48no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—444no—
1150D4—448no—
1151D4—444no—
1152D4—444no—
1153D4—448no—
1154D4—448no—
1155D4—448no—
1156D4—448no—
1157D4—884no—
1158D4—884no—
1159D4—884no—
1160C2×C4—21no—
1161C2×C4—21no—
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—112no—
1175C2×C4—228no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—222no—
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—222no—
1192C2×C4—222no—
1193C2×C4—448no—
1194C2×C4—444no—
1195C2×C4—884no—
1196C2×C4C2×D4×D1112yes—
1197C22—22no—
1198C22—22no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—416no—
1205C22—42no—
1206C22—42no—
1207C22—41no—
1208C22—41no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—41no—
1213C22—42no—
1214C22—41no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—88no—
1223C22—114no—
1224C22—224no—
1225C22—222no—
1226C22—224no—
1227C22—222no—
1228C22—222no—
1229C22—222no—
1230C22—224no—
1231C22—224no—
1232C22—224no—
1233C22—224no—
1234C22—224no—
1235C22—4416no—
1236C22—4432no—
1237C22—4416no—
1238C22—4432no—
1239C22—442no—
1240C22—442no—
1241C22—441no—
1242C22—442no—
1243C22—441no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—441no—
1248C22—441no—
1249C22—888no—
1250C22C22×D4×D1111yescharacteristic
1251C22C2×#6703712yes—
1252C22D11×H(5,𝔽2)11yescharacteristic
1253C22D11×H(5,𝔽2)11yescharacteristic
1254C22D11×H(5,𝔽2)12yes—
1255C4—22no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—222no—
1261C4—442no—
1262C4—442no—
1263C4—442no—
1264C4—442no—
1265C4—442no—
1266C2—42no—
1267C2—44no—
1268C2—42no—
1269C2—82no—
1270C2—224no—
1271C2—442no—
1272C2—444no—
1273C2—442no—
1274C2D11×#53411yescharacteristic
1275C2#1308224412yes—
1276C2#1308276611yescharacteristic
1277C2#1308276812yes—
1278C2#1308277311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2679C2
hypercenter#2679D11
hypocenterC11#36714
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. C2×#10623120C2semidirect
2. C2×D11×#120C2semidirect
3. #13076892C2semidirect
4. #13075182C2semidirect
5. #13075178C2semidirect
6. #13075177C2semidirect
7. #13074950C2semidirect
8. #13074950C2semidirect
9. #13074948C2semidirect
10. #13074947C2semidirect
11. #13074938C2semidirect
12. #13074937C2semidirect
13. #13074388C2semidirect
14. #13071998C2semidirect
15. #13071994C2semidirect
16. #13071938C2semidirect
17. #13071927C2semidirect
18. #13071195C2semidirect
19. C11×#2679C2semidirect
20. C25×D11C22semidirect
21. C23×C22⋊D11C22semidirect
25. C2×C11×#120C22semidirect
26. C2×C11×#120C22semidirect
27. C2×C11×#120C22semidirect
28. C2×#67006C22semidirect
29. C2×#67006C22semidirect
30. C2×#67006C22semidirect
31. C2×#66991C22semidirect
37. C2×#66990C22semidirect
38. C2×#66990C22semidirect
39. C2×#66990C22semidirect
40. C2×#66988C22semidirect
43. C2×#66947C22semidirect
44. C2×#66945C22semidirect
45. C2×#66939C22semidirect
46. C2×#66937C22semidirect
47. C2×#66936C22semidirect
48. C2×#66936C22semidirect
49. C2×#66935C22semidirect
50. C2×#66935C22semidirect
51. C2×C22⋊C4×D11C22semidirect
52. C2×C22⋊C4×D11C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C2×#66925C22semidirect
55. C11×#394C22semidirect
56. C11×#394C22semidirect
57. C11×#394C22semidirect
58. C11×#390C22semidirect
59. C11×#390C22semidirect
60. #10622860C22semidirect
61. #10622836C22semidirect
62. #10622836C22semidirect
63. #10622835C22semidirect
64. #10622835C22semidirect
65. #10622835C22semidirect
66. #10622834C22semidirect
67. #10622834C22semidirect
68. #10622833C22semidirect
69. #10622607C22semidirect
70. #10622607C22semidirect
71. #10622606C22semidirect
72. #10622602C22semidirect
73. #10622601C22semidirect
74. #10622574C22semidirect
75. #10622574C22semidirect
76. #10622574C22semidirect
77. #10622573C22semidirect
78. #10622573C22semidirect
79. #10622572C22semidirect
80. #10622572C22semidirect
81. #10622572C22semidirect
82. #10622571C22semidirect
83. #10622570C22semidirect
84. #10622570C22semidirect
85. #10622570C22semidirect
86. #10622570C22semidirect
87. #10622569C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622568C22semidirect
91. #10622568C22semidirect
92. #10622568C22semidirect
93. #10622568C22semidirect
94. #10622568C22semidirect
95. #10622568C22semidirect
96. #10622568C22semidirect
97. #10622566C22semidirect
98. #10622565C22semidirect
99. #10622564C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622558C22semidirect
103. #10622553C22semidirect
104. #10622552C22semidirect
105. #10622288C22semidirect
106. #10622283C22semidirect
107. #10622281C22semidirect
108. #10622278C22semidirect
110. C25×C11C23semidirect
137. C22×C22⋊D11C23semidirect
138. C23×Dic11C23semidirect
144. C2×D4×D11D4semidirect
149. C22×C4×D11C23semidirect
154. C2×C11×C4⋊C4C23semidirect
155. C2×C11×C4⋊C4C23semidirect
161. C2×C11×C22⋊C4C23semidirect
162. C2×C11×C22⋊C4C23semidirect
163. C2×C11×C22⋊C4C23semidirect
164. C2×C11×C22⋊C4C23semidirect
165. C2×C11×C22⋊C4C23semidirect
166. C2×C42×C11C23semidirect
178. C2×C22⋊Dic11C23semidirect
179. C2×C22⋊Dic11C23semidirect
180. C2×C22⋊Dic11C23semidirect
181. C2×C22⋊Dic11C23semidirect
182. C2×C22⋊Dic11C23semidirect
208. C2×(C2×D11)⋊C4C23semidirect
209. C2×(C2×D11)⋊C4C23semidirect
210. C2×C4⋊Dic11C23semidirect
211. C2×C4⋊Dic11C23semidirect
212. C2×C4⋊Dic11C23semidirect
213. C2×Dic11⋊C4C23semidirect
214. C2×Dic11⋊C4C23semidirect
215. C2×Dic11⋊C4C23semidirect
216. C2×Dic11⋊C4C23semidirect
217. C2×C4×Dic11C23semidirect
218. C2×C4×Dic11C23semidirect
231. C11×#95C23semidirect
232. C11⋊#95C23semidirect
233. C11⋊#95C23semidirect
234. C11⋊#95C23semidirect
235. C11⋊#95C23semidirect
236. C11⋊#95C23semidirect
237. C11⋊#95C23semidirect
238. C11⋊#95C23semidirect
426. #2679D11semidirect
604. C2×#120C2×D11semidirect
605. C2×#120C2×D11semidirect
606. C2×#120C2×D11semidirect
629. #394C2×D11semidirect
630. #394C2×D11semidirect
631. #394C2×D11semidirect
644. #390C2×D11semidirect
645. #390C2×D11semidirect
746. C25C22×D11semidirect
809. C2×C4⋊C4C22×D11semidirect
810. C2×C4⋊C4C22×D11semidirect
849. C2×C22⋊C4C22×D11semidirect
850. C2×C22⋊C4C22×D11semidirect
851. C2×C22⋊C4C22×D11semidirect
852. C2×C22⋊C4C22×D11semidirect
853. C2×C22⋊C4C22×D11semidirect
856. C2×C42C22×D11semidirect
864. #95C22×D11semidirect
1056. C11#36714semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C2×D11×#1202
#130768922
#130751822
#130751782
#130751772
#130749502
#130749482
#130749472
#130749382
#130749372
#130743882
#130719982
#130719942
#130719382
#130719272
#130711952
C11×#26792
#3671411