Finite Group Databasebeta

← #14926062

Subgroups — #14926062

Order 2816.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623180C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074241C212yesmaximal, complemented
4#13074239C212yesmaximal, complemented
5#13073811C212yesmaximal, complemented
6#13073582C212yesmaximal, complemented
7#13073106C211yesmaximal, characteristic, complemented
8#13073092C211yesmaximal, characteristic, complemented
9#13072265C211yesmaximal, characteristic, complemented
10#13072251C211yesmaximal, characteristic
11#13072002C211yesmaximal, characteristic, complemented
12#13072001C211yesmaximal, characteristic, complemented
13#13071995C211yesmaximal, characteristic, complemented
14#13071861C212yesmaximal, complemented
15#13071859C212yesmaximal, complemented
16#13071180C212yesmaximal, complemented
17#13071157C212yesmaximal, complemented
18#13071121C211yesmaximal, characteristic, complemented
19#120×Dic11C211yesmaximal, characteristic, complemented
20#13071117C211yesmaximal, characteristic, complemented
21#13071115C211yesmaximal, characteristic, complemented
22#117×Dic11C211yesmaximal, characteristic, complemented
23C11×#2411C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×#123C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C2×#67006C2211yescharacteristic
32C2×#66993C2212yes—
33C2×#66992C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C2×D4×Dic11C2212yescomplemented
37C2×#66982C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C2×#66979C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42#10623180—28no—
43C2×#66951C2211yescharacteristic, complemented
44C2×#66946C2212yescomplemented
45C2×#66945C2211yescharacteristic, complemented
46C2×#66942C2211yescharacteristic, complemented
47C2×#66940C2211yescharacteristic, complemented
48C2×#66938C2212yes—
49C2×#66938C2211yescharacteristic, complemented
50C2×#66935C2211yescharacteristic
51C2×(C22⋊D11)⋊C4—28no—
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×(C22⋊D11)⋊C4C2212yes—
56C2×(C22⋊D11)⋊C4C2212yes—
57C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
58C2×(C22⋊D11)⋊C4C2212yescomplemented
59C2×(C22⋊D11)⋊C4C2212yescomplemented
60C2×#66932C2211yescharacteristic, complemented
61C2×#66931C2211yescharacteristic
62C2×#66930C2211yescharacteristic, complemented
63C11×#396C2212yescomplemented
64C11×#394C2212yescomplemented
65C11×#390C2212yescomplemented
66C11×#388C2212yescomplemented
67C11×#386C2211yescharacteristic
68C11×#385C2211yescharacteristic
69C11×#379C2211yescharacteristic
70#10622860C2211yescharacteristic
71#10622836C2212yes—
72#10622833C2211yescharacteristic
73#10622833C2212yescomplemented
74#10622826C2211yescharacteristic
75#10622823C2211yescharacteristic
76#10622607C2212yescomplemented
77#10622607C2212yescomplemented
78#10622604C2212yescomplemented
79#10622603C2212yescomplemented
80#10622602C2212yescomplemented
81#10622597C2212yescomplemented
82#10622589C2212yescomplemented
83C4⋊C4×Dic11C2212yescomplemented
84C4⋊C4×Dic11C2212yescomplemented
85#10622574C2212yes—
86#10622574C2212yescomplemented
87#10622574C2212yescomplemented
88#10622573C2212yes—
89#10622572C2212yes—
90#10622571C2211yescharacteristic
91#10622571C2212yescomplemented
92#10622570C2212yes—
93#10622570C2212yes—
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622570C2212yescomplemented
97#10622569C2212yescomplemented
98#10622568C2211yescharacteristic
99#10622568C2211yescharacteristic
100#10622565C2212yescomplemented
101#10622563C2211yescharacteristic
102#10622563C2212yescomplemented
103#10622561C2212yescomplemented
104#10622559C2211yescharacteristic
105#10622559C2212yescomplemented
106#10622558C2212yescomplemented
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C22⋊C4×Dic11C2211yescharacteristic
110C22⋊C4×Dic11C2211yescharacteristic
111C22⋊C4×Dic11C2212yescomplemented
112C22⋊C4×Dic11C2212yescomplemented
113#10622553C2212yescomplemented
114#10622552C2212yescomplemented
115#10622545C2212yescomplemented
116C42×Dic11C2212yescomplemented
117#10622288C2212yescomplemented
118#10622281C2212yescomplemented
119#10622279C2212yescomplemented
120#10622279C2212yescomplemented
121#10622278C2212yescomplemented
122#10622270C2212yescomplemented
123#10622263C2212yescomplemented
124#10622259C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11—28no—
132C22×C22⋊D11—24no—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C23×Dic11—24no—
140C23×Dic11—44no—
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2312yes—
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2312yes—
146C23×Dic11C2311yescharacteristic
147C22×D44C2312yes—
148C22×C4×D11—24no—
149C22×C4×D11—44no—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×Dic22C2311yescharacteristic
154C11×#123—24no—
155C11×#120—24no—
156C11×#117—24no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C22⋊C4—24no—
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C42×C11C2312yes—
174#67006—24no—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2311yescharacteristic
184#66993—28no—
185#66992—24no—
186#66990—24no—
187D4×Dic11—24no—
188D4×Dic11—44no—
189#66982—24no—
190C2×(C2×D11)⋊C4—24no—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205#66979—24no—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×Dic11⋊C4—24no—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×C4×Dic11D418yescomplemented
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233#66951—24no—
234#66946—44no—
235#66945—24no—
236#66942—24no—
237#66940—24no—
238#66938—28no—
239#66938—24no—
240#66935—24no—
241(C22⋊D11)⋊C4—24no—
242(C22⋊D11)⋊C4—28no—
243(C22⋊D11)⋊C4—28no—
244(C22⋊D11)⋊C4—28no—
245(C22⋊D11)⋊C4—28no—
246(C22⋊D11)⋊C4—24no—
247(C22⋊D11)⋊C4—44no—
248(C22⋊D11)⋊C4—44no—
249#66932—24no—
250#66931—24no—
251#66930—24no—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34965—111nomaximal, Sylow
265C24×C11—22no—
266C24×C11—24no—
267C24×C11—22no—
268C24×C11—22no—
269C24×C11—42no—
270C24×C11C2411yescharacteristic
271C24×C11C2412yes—
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—24no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—42no—
278C23×D11C2411yescharacteristic
279C23×D11C2412yes—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—24no—
283C2×D4×C11—22no—
284C2×D4×C11—24no—
285C2×D4×C11—42no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—42no—
290C22×C4×C11C2×D414yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C2×C22⋊D11—232no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11#4118yes—
317C22×Dic11—24no—
318C22×Dic11—24no—
319C22×Dic11—22no—
320C22×Dic11—24no—
321C22×Dic11—24no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—24no—
325C22×Dic11—22no—
326C22×Dic11—42no—
327C22×Dic11—42no—
328C22×Dic11—42no—
329C22×Dic11—416no—
330C22×Dic11C2×D414yes—
331C22×Dic11C2×D414yes—
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2412yes—
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2411yescharacteristic
342C2×D44—24no—
343C2×D44—24no—
344C2×D44—42no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—416no—
354C2×Dic22—22no—
355C2×Dic22—24no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—24no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4#4114yes—
371C42×C11—24no—
372C22⋊Dic11—22no—
373C22⋊Dic11—22no—
374C22⋊Dic11—24no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—22no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380C22⋊Dic11#4114yes—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—24no—
398C4⋊Dic11—42no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—42no—
408Dic11⋊C4—42no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—24no—
415C4×Dic11—24no—
416C4×Dic11C2×D414yes—
417C4×Dic11C2×D414yes—
418C4×Dic11C2×D414yes—
419C4×Dic11C2×D414yes—
420C2×#529—111no—
421C22×C4×D4—111no—
422#2603—112no—
423#2603—112no—
424#2566—112no—
425#2544—112no—
426#2504—111no—
427#2502—111no—
428#2435—111no—
429#2433—111no—
430#2411—111no—
431#2411—111no—
432#2411—111no—
433#2411D1111yescharacteristic, complemented
434#2392—112no—
435#2392—112no—
436C4×#127—112no—
437C4×#124—112no—
438C4×#120—111no—
439C4×#120—111no—
440C4×#120—111no—
441C4×#120—111no—
442C4×#117—111no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—28no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—21no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—48no—
458C23×C11—48no—
459C23×C11—44no—
460C23×C11—44no—
461C23×C11C22×D412yes—
462C23×C11C2×#4112yes—
463C23×C11C2×#4114yes—
464C23×C11C2×#4112yes—
465C23×C11C2511yescharacteristic
466C22×D11—28no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—22no—
476C22×D11—21no—
477C22×D11—22no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11C2×#4114yes—
483D4×C11—48no—
484D4×C11—44no—
485C2×C4×C11—28no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—44no—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C2×#4114yes—
509C22⋊D11—216no—
510C22⋊D11—216no—
511C22⋊D11—48no—
512C22⋊D11—48no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—28no—
520C2×Dic11—28no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—48no—
535C2×Dic11—44no—
536C2×Dic11—44no—
537C2×Dic11—48no—
538C2×Dic11C22×D412yes—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C22×D412yes—
542C2×Dic11C2×#4114yes—
543C2×Dic11C2×#4114yes—
544C2×Dic11H(5,𝔽2)14yes—
545D44—48no—
546C4×D11—48no—
547C4×D11—44no—
548C4×D11—48no—
549Dic22—44no—
550C23×D4—111no—
551C24×C4—111no—
552C24×C4—111no—
553C2×#127—112no—
554#529—228no—
555C2×#126—111no—
556C2×#126—111no—
557C2×#125—111no—
558C2×#124—112no—
559C2×#124—111no—
560C2×#123—111no—
561C2×#123C2×D1111yescharacteristic
562C2×C22⋊Q8—111no—
563C2×#121—111no—
564C2×#120—111no—
565C2×#120—111no—
566C2×#120—111no—
567C2×#120C2×D1111yescharacteristic
568C2×C4×Q8—111no—
569C2×C4×D4—111no—
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—228no—
581C2×#117—111no—
582C2×#117—111no—
583C2×#117—111no—
584C2×#117C2×D1111yescharacteristic
585C22×C4⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4C2×D1111yescharacteristic
588C22×C42—111no—
589#398—112no—
590#398—112no—
591#397—112no—
592#397—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#396C2×D1112yescomplemented
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394C2×D1112yescomplemented
603#392—112no—
604#392—112no—
605#391—112no—
606#390—112no—
607#390—112no—
608#390—112no—
609#390—112no—
610#390—112no—
611#390—112no—
612#390C2×D1112yescomplemented
613#388—112no—
614#388—112no—
615#388—112no—
616#388C2×D1112yescomplemented
617#386—112no—
618#386—111no—
619#386—111no—
620#386—112no—
621#386—112no—
622#386—111no—
623#386—112no—
624#386C2×D1111yescharacteristic
625#385—111no—
626#385—112no—
627#385—112no—
628#385—112no—
629#385—111no—
630#385—111no—
631#385—112no—
632#385C2×D1111yescharacteristic
633#384—112no—
634#382—112no—
635#379—111no—
636#379—111no—
637#379—111no—
638#379C2×D1111yescharacteristic
639C4×C4⋊C4—112no—
640C4×C4⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649#376—112no—
650C43—112no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—416no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11#53214yes—
669C22×C11C23×D411yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C22×#4112yes—
672C22×C11C22×#4111yescharacteristic
673C22×C11C2×H(5,𝔽2)12yes—
674C2×D11—24no—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—416no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—42no—
686C2×D11—42no—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—24no—
690C4×C11—41no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—41no—
694C4×C11—42no—
695Dic11—22no—
696Dic11—22no—
697Dic11—24no—
698Dic11—41no—
699Dic11—41no—
700Dic11—41no—
701Dic11—42no—
702Dic11—42no—
703Dic11#52514yes—
704Dic11#53514yes—
705C25—111no—
706C25C22×D1111yescharacteristic
707C22×Q8—111no—
708C22×D4—112no—
709C22×D4—112no—
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—112no—
713C22×D4—112no—
714C22×D4—112no—
715C22×D4—224no—
716C22×D4—228no—
717C22×D4C22×D1111yescharacteristic
718C22×D4C22×D1112yes—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—112no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—111no—
726C23×C4—112no—
727C23×C4—112no—
728C23×C4—224no—
729C23×C4—224no—
730C23×C4—444no—
731C23×C4—444no—
732C23×C4C22×D1111yescharacteristic
733C23×C4C22×D1111yescharacteristic
734#127—228no—
735#126—224no—
736#126—224no—
737#125—224no—
738#124—224no—
739#124—228no—
740#123—24no—
741#123—224no—
742C22⋊Q8—224no—
743#121—224no—
744#120—24no—
745#120—224no—
746#120—224no—
747#120—224no—
748C4×Q8—224no—
749C4×D4—228no—
750C4×D4—228no—
751C4×D4—228no—
752C4×D4—228no—
753C4×D4—224no—
754C4×D4—224no—
755C4×D4—224no—
756C4×D4—444no—
757C4×D4—444no—
758C4×D4—444no—
759C4×D4—444no—
760#117—24no—
761#117—224no—
762#117—224no—
763#117—224no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—224no—
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1112yes—
781C2×C4⋊C4C22×D1111yescharacteristic
782C2×C4⋊C4C22×D1112yes—
783C2×C22⋊C4—24no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—224no—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1111yescharacteristic
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4C22×D1112yes—
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1111yescharacteristic
819C2×C42—118no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—111no—
825C2×C42—111no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42C22×D1112yes—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95C22×D1112yes—
843#95C22×D1112yes—
844C2×C11—24no—
845C2×C11—44no—
846C2×C11—81no—
847C2×C11C2×#52511yescharacteristic
848C2×C11C2×#53211yescharacteristic
849C2×C11C2×#53511yescharacteristic
850C2×C11#348112yes—
851C2×C11#348112yes—
852D11—44no—
853D11—81no—
854C24—22no—
855C24—24no—
856C24—22no—
857C24—22no—
858C24—42no—
859C24—112no—
860C24—111no—
861C24—224no—
862C24—222no—
863C24—222no—
864C24—222no—
865C24—442no—
866C24C23×D1111yescharacteristic
867C24C23×D1112yes—
868C24C23×D1111yescharacteristic
869C2×Q8—222no—
870C2×Q8—224no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—42no—
877C2×D4—118no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—222no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—2232no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—42no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—112no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—112no—
913C22×C4—111no—
914C22×C4—222no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—4416no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—4416no—
936C22×C4D4×D1114yes—
937C22×C4C23×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1112yes—
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1112yes—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—24no—
948C4⋊C4—42no—
949C4⋊C4—224no—
950C4⋊C4—224no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—224no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—222no—
958C4⋊C4—222no—
959C4⋊C4—222no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—114no—
974C22⋊C4—222no—
975C22⋊C4—222no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—224no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4#434114yes—
997C42—24no—
998C42—114no—
999C42—114no—
1000C42—114no—
1001C42—114no—
1002C42—222no—
1003C42—222no—
1004C42—224no—
1005C42—224no—
1006C42—224no—
1007C42—224no—
1008C42—224no—
1009C11#3496511yescharacteristic, complemented, Sylow
1010C23—22no—
1011C23—22no—
1012C23—28no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—22no—
1023C23—22no—
1024C23—48no—
1025C23—48no—
1026C23—44no—
1027C23—44no—
1028C23—114no—
1029C23—228no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—222no—
1040C23—222no—
1041C23—448no—
1042C23—448no—
1043C23—444no—
1044C23—444no—
1045C23C2×D4×D1112yes—
1046C23C2×#434112yes—
1047C23#41×D1114yes—
1048C23#41×D1112yes—
1049C23C24×D1111yescharacteristic
1050Q8—444no—
1051D4—48no—
1052D4—44no—
1053D4—2216no—
1054D4—2216no—
1055D4—448no—
1056D4—444no—
1057D4—448no—
1058D4—448no—
1059D4—444no—
1060C2×C4—28no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—44no—
1081C2×C4—112no—
1082C2×C4—112no—
1083C2×C4—114no—
1084C2×C4—114no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—114no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—448no—
1108C2×C4—444no—
1109C2×C4—448no—
1110C2×C4—448no—
1111C2×C4—444no—
1112C2×C4—448no—
1113C2×C4—444no—
1114C2×C4C2×D4×D1112yes—
1115C2×C4C2×D4×D1112yes—
1116C2×C4C2×#434114yes—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—416no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—41no—
1130C22—41no—
1131C22—42no—
1132C22—42no—
1133C22—41no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—4416no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—441no—
1143C22—441no—
1144C22—442no—
1145C22—442no—
1146C22—441no—
1147C22#1062312714yes—
1148C22C22×D4×D1111yescharacteristic
1149C22C22×#434111yescharacteristic
1150C22C2×#41×D1111yescharacteristic
1151C22C2×#41×D1112yes—
1152C22D11×H(5,𝔽2)12yes—
1153C4—22no—
1154C4—22no—
1155C4—24no—
1156C4—41no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—114no—
1162C4—114no—
1163C4—222no—
1164C4—224no—
1165C4—222no—
1166C4—441no—
1167C4—442no—
1168C4—441no—
1169C4—442no—
1170C4—441no—
1171C2—24no—
1172C2—44no—
1173C2—81no—
1174C2—444no—
1175C2—881no—
1176C2D11×#52511yescharacteristic
1177C2C2×#1062312711yescharacteristic
1178C2D11×#53511yescharacteristic
1179C2#1308221912yes—
1180C2#1308222112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2411C2
prime radical#13072251C2
hypercenter#2411D11
hypocenterC11#34965
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2411

Complements

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

NH ≅ G/Ntype
1. C2×#10623180C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074241C2semidirect
4. #13074239C2semidirect
5. #13073811C2semidirect
6. #13073582C2semidirect
7. #13073106C2semidirect
8. #13073092C2semidirect
9. #13072265C2semidirect
11. #13072002C2semidirect
12. #13072001C2semidirect
13. #13071995C2semidirect
14. #13071861C2semidirect
15. #13071859C2semidirect
16. #13071180C2semidirect
17. #13071157C2semidirect
18. #13071121C2semidirect
19. #120×Dic11C2semidirect
20. #13071117C2semidirect
21. #13071115C2semidirect
22. #117×Dic11C2semidirect
23. C11×#2411C2semidirect
36. C2×D4×Dic11C22semidirect
43. C2×#66951C22semidirect
44. C2×#66946C22semidirect
45. C2×#66945C22semidirect
46. C2×#66942C22semidirect
47. C2×#66940C22semidirect
49. C2×#66938C22semidirect
57. C2×(C22⋊D11)⋊C4C22semidirect
58. C2×(C22⋊D11)⋊C4C22semidirect
59. C2×(C22⋊D11)⋊C4C22semidirect
60. C2×#66932C22semidirect
62. C2×#66930C22semidirect
63. C11×#396C22semidirect
64. C11×#394C22semidirect
65. C11×#390C22semidirect
66. C11×#388C22semidirect
73. #10622833C22semidirect
76. #10622607C22semidirect
77. #10622607C22semidirect
78. #10622604C22semidirect
79. #10622603C22semidirect
80. #10622602C22semidirect
81. #10622597C22semidirect
82. #10622589C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. C4⋊C4×Dic11C22semidirect
86. #10622574C22semidirect
87. #10622574C22semidirect
91. #10622571C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
96. #10622570C22semidirect
97. #10622569C22semidirect
100. #10622565C22semidirect
102. #10622563C22semidirect
103. #10622561C22semidirect
105. #10622559C22semidirect
106. #10622558C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. C22⋊C4×Dic11C22semidirect
113. #10622553C22semidirect
114. #10622552C22semidirect
115. #10622545C22semidirect
116. C42×Dic11C22semidirect
117. #10622288C22semidirect
118. #10622281C22semidirect
119. #10622279C22semidirect
120. #10622279C22semidirect
121. #10622278C22semidirect
122. #10622270C22semidirect
123. #10622263C22semidirect
124. #10622259C22semidirect
221. C2×C4×Dic11D4semidirect
433. #2411D11semidirect
596. #396C2×D11semidirect
602. #394C2×D11semidirect
612. #390C2×D11semidirect
616. #388C2×D11semidirect
1009. C11#34965semidirect

Maximal subgroups

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

subgroupindex
C2×#106231802
C22×(C22⋊D11)⋊C42
#130742412
#130742392
#130738112
#130735822
#130731062
#130730922
#130722652
#130722512
#130720022
#130720012
#130719952
#130718612
#130718592
#130711802
#130711572
#130711212
#120×Dic112
#130711172
#130711152
#117×Dic112
C11×#24112
#3496511