Finite Group Databasebeta

← #14914062

Subgroups — #14914062

Order 2816.

3118 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071657C212yesmaximal, complemented
5#13071655C212yesmaximal, complemented
6#13071640C212yesmaximal, complemented
7#13071638C212yesmaximal, complemented
8#13071566C211yesmaximal, characteristic, complemented
9#13071565C211yesmaximal, characteristic, complemented
10#13071563C211yesmaximal, characteristic, complemented
11#13071560C211yesmaximal, characteristic, complemented
12#13071542C211yesmaximal, characteristic, complemented
13#13071541C211yesmaximal, characteristic, complemented
14#13071538C211yesmaximal, characteristic, complemented
15#13071272C212yesmaximal, complemented
16#13071269C212yesmaximal, complemented
17#13071241C211yesmaximal, characteristic, complemented
18#13071205C211yesmaximal, characteristic, complemented
19#13071137C212yesmaximal, complemented
20C4×#66936C212yesmaximal, complemented
21#13070998C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2352C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2212yescomplemented
35C2×#66979C2211yescharacteristic
36C2×#66979C2211yescharacteristic, complemented
37#10623078C4116yescomplemented
38D11×#117—28no—
39C2×#66949C2211yescharacteristic
40C2×#66947C2211yescharacteristic
41#10623035—28no—
42C2×#66946C2212yes—
43C2×#66945C2211yescharacteristic
44C2×#66945C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×#66945C2211yescharacteristic, complemented
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×C4⋊C4×D11C2211yescharacteristic, complemented
51C2×#66940C2212yescomplemented
52C2×#66937C2211yescharacteristic
53C2×#66936C2211yescharacteristic
54C2×#66935C2211yescharacteristic
55C2×C22⋊C4×D11C2212yes—
56C2×#66931C2211yescharacteristic
57C2×#66930C2212yes—
58C2×C4×D44C2211yescharacteristic
59C2×#66925C2212yes—
60C2×#66925C2211yescharacteristic
61C2×C42×D11C2212yes—
62C11×#388C2212yes—
63C11×#387C2212yescomplemented
64C11×#386C2212yes—
65C11×#382C2211yescharacteristic, complemented
66C11×#380C2211yescharacteristic
67C11×#380C2211yescharacteristic, complemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69C4×C11×C22⋊C4C2212yescomplemented
70#10622834C2212yes—
71#10622826C2212yes—
72#10622825C2211yescharacteristic
73#10622825C2211yescharacteristic, complemented
74C4×C22⋊Dic11C2212yescomplemented
75#10622603C2212yes—
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic, complemented
79#10622600C2211yescharacteristic, complemented
80#10622591C2212yescomplemented
81#10622590C2211yescharacteristic, complemented
82#10622589C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2212yescomplemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85C4⋊C4×Dic11C2211yescharacteristic, complemented
86#10622570C2212yes—
87#10622570C2212yes—
88#10622570C2212yescomplemented
89#10622569C2212yes—
90#10622569C2212yes—
91#10622568C2212yes—
92#10622564C2212yes—
93#10622564C2212yescomplemented
94#10622558C2212yescomplemented
95#10622557C2212yes—
96#10622557C2212yes—
97C22⋊C4×Dic11C2212yes—
98#10622553C2212yescomplemented
99#10622552C2212yes—
100C4×(C2×D11)⋊C4C2212yes—
101#10622548C2211yescharacteristic, complemented
102C4×C4⋊Dic11C2212yescomplemented
103C4×C4⋊Dic11C2211yescharacteristic, complemented
104C4×Dic11⋊C4C2212yescomplemented
105C4×Dic11⋊C4C2212yescomplemented
106#10622283C2212yes—
107#10622283C2212yescomplemented
108#10622282C2212yes—
109#10622282C2212yes—
110#10622281C2212yes—
111#10622281C2212yes—
112#10622279C2212yes—
113#10622279C2212yes—
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622277C2212yes—
119#10622267C2212yescomplemented
120#10622265C2212yescomplemented
121#10622262C2212yescomplemented
122#10622262C2212yescomplemented
123#10622260C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C2×#4339—24no—
137C2×#4339—24no—
138C2×#4339C2×C418yes—
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×Dic22C2311yescharacteristic
153C4×D4×C11C2×C418yescomplemented
154C11×#117—24no—
155C2×C11×C4⋊C4—24no—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176#66992C2×C418yescomplemented
177#66990C2×C418yescomplemented
178C4×C22⋊D11—28no—
179C4×C22⋊D11—28no—
180C4×C22⋊D11C2×C418yescomplemented
181C4×C22⋊D11C2×C418yescomplemented
182C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197#66979—24no—
198#66979—24no—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226#66949C2×C418yescomplemented
227#66947C2×C418yescomplemented
228#66946—28no—
229#66945—24no—
230#66945—24no—
231#66945—24no—
232#66945—24no—
233#66945—24no—
234C4⋊C4×D11—24no—
235C4⋊C4×D11—24no—
236C4⋊C4×D11D418yescomplemented
237#66940—28no—
238#66937C2×C418yescomplemented
239#66936C2×C418yescomplemented
240#66935C2×C418yescomplemented
241C22⋊C4×D11—28no—
242#66931C2×C418yescomplemented
243#66930—28no—
244C4×D44C2×C418yescomplemented
245#66925—28no—
246#66925C2×C418yescomplemented
247C42×D11—28no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
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#34201—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—41no—
270C23×D11—41no—
271C23×D11—41no—
272C23×D11—41no—
273C23×D11C22×C414yes—
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C2×D4×C11—41no—
278C2×D4×C11—41no—
279C2×D4×C11C22×C414yes—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11C22×C414yes—
288C22×C4×C11C22×C414yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—41no—
303C2×C22⋊D11—41no—
304C2×C22⋊D11—41no—
305C2×C22⋊D11—41no—
306C2×C22⋊D11C22×C414yes—
307C2×C22⋊D11C22×C414yes—
308C2×C22⋊D11C22×C414yes—
309C2×C22⋊D11C22×C414yes—
310C22×Dic11—22no—
311C22×Dic11—22no—
312C22×Dic11C22×C414yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322#4339—232no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44—41no—
326C2×D44—41no—
327C2×D44C22×C414yes—
328C2×D44C22×C414yes—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—232no—
332C2×C4×D11—24no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11C22×C414yes—
347C2×C4×D11C22×C414yes—
348C2×C4×D11C22×C414yes—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C22×C414yes—
351C2×C4×D11C2×D418yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11#4114yes—
354C2×Dic22—22no—
355C2×Dic22—22no—
356C2×Dic22C22×C414yes—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4C22×C414yes—
362C11×C4⋊C4C2×D414yes—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4C22×C414yes—
367C11×C22⋊C4C22×C414yes—
368C42×C11—24no—
369C42×C11—42no—
370C42×C11C22×C414yes—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—42no—
374C22⋊Dic11—42no—
375C22⋊Dic11C22×C414yes—
376C22⋊Dic11C22×C414yes—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4C22×C414yes—
387(C2×D11)⋊C4C22×C414yes—
388(C2×D11)⋊C4C22×C414yes—
389(C2×D11)⋊C4C22×C414yes—
390(C2×D11)⋊C4C22×C414yes—
391(C2×D11)⋊C4C22×C414yes—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—42no—
396C4⋊Dic11—42no—
397C4⋊Dic11C22×C414yes—
398C4⋊Dic11C2×D414yes—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—42no—
402Dic11⋊C4—42no—
403Dic11⋊C4C22×C414yes—
404Dic11⋊C4C22×C414yes—
405Dic11⋊C4C22×C414yes—
406Dic11⋊C4C22×C414yes—
407Dic11⋊C4C2×D418yes—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—24no—
415C4×Dic11—42no—
416C4×Dic11—42no—
417C4×Dic11—42no—
418C4×Dic11C22×C414yes—
419C2×#525—111no—
420C2×#520—111no—
421C22×#117—111no—
422#2363—112no—
423#2363—112no—
424#2362—112no—
425#2362—112no—
426#2354—111no—
427#2354—111no—
428#2354—111no—
429#2354—111no—
430#2352—111no—
431#2352—111no—
432#2352—111no—
433#2352D1111yescharacteristic, complemented
434#2321—112no—
435#2321—112no—
436#2317—111no—
437#2311—111no—
438C4×#123—112no—
439C4×#123—112no—
440#2280—111no—
441#2274—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—21no—
454C23×C11C23×C412yes—
455C23×C11C23×C412yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—28no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—44no—
477C22×D11—44no—
478C22×D11—44no—
479C22×D11—44no—
480C22×D11C23×C412yes—
481C22×D11C23×C412yes—
482C22×D11C23×C412yes—
483C22×D11C22×D412yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
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—28no—
497C2×C4×C11—28no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—84no—
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C412yes—
510C2×C4×C11C23×C412yes—
511C2×C4×C11C23×C412yes—
512C2×C4×C11C23×C412yes—
513C2×C4×C11C22×D414yes—
514C2×C4×C11C22×D412yes—
515C2×C4×C11C2×#4112yes—
516C22⋊D11—28no—
517C22⋊D11—28no—
518C22⋊D11—44no—
519C22⋊D11—44no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—28no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C412yes—
543C2×Dic11C23×C412yes—
544C2×Dic11C23×C412yes—
545C2×Dic11C22×D414yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C2×#4112yes—
548D44—28no—
549D44—44no—
550C4×D11—28no—
551C4×D11—28no—
552C4×D11—28no—
553C4×D11—28no—
554C4×D11—48no—
555C4×D11—48no—
556C4×D11—84no—
557C4×D11C4×D4116yes—
558Dic22—28no—
559C22×#41—111no—
560C24×C4—111no—
561#525—1116no—
562C2×#123—111no—
563C2×#123—111no—
564C2×C22⋊Q8—111no—
565C2×C22⋊Q8—111no—
566C2×#121—111no—
567C2×#121—111no—
568C2×#120—111no—
569C2×#120—111no—
570#520—228no—
571C2×C4×Q8—112no—
572C2×C4×D4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4—111no—
578C2×C4×D4C2×D1111yescharacteristic
579C2×#117—111no—
580C2×#117—111no—
581C2×#117—111no—
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—111no—
585C2×#117—111no—
586C2×#117—112no—
587C2×#117—111no—
588C2×#117—112no—
589C2×#117—228no—
590C2×#117C2×D1111yescharacteristic
591C22×C4⋊C4—111no—
592C22×C4⋊C4—111no—
593C22×C4⋊C4—111no—
594C22×C4⋊C4C2×D1111yescharacteristic, complemented
595C22×C22⋊C4—112no—
596C22×C42—112no—
597#391—112no—
598#390—112no—
599#390—112no—
600#390—112no—
601#390—112no—
602#390—112no—
603#389—112no—
604#389—112no—
605#388—112no—
606#388—112no—
607#388—112no—
608#388—112no—
609#388—112no—
610#388—112no—
611#388—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388C2×D1112yes—
617#387—112no—
618#387—112no—
619#387—112no—
620#387C2×D1112yescomplemented
621#386—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386C2×D1112yes—
627#385—112no—
628#385—112no—
629#384—111no—
630#384—111no—
631#382—111no—
632#382C2×D1111yescharacteristic, complemented
633#381—112no—
634#380—111no—
635#380—111no—
636#380—111no—
637#380—111no—
638#380—111no—
639#380—111no—
640#380C2×D1111yescharacteristic
641#380C2×D1111yescharacteristic, complemented
642#379—112no—
643C4×C4⋊C4—111no—
644C4×C4⋊C4—111no—
645C4×C4⋊C4—112no—
646C4×C4⋊C4—111no—
647C4×C4⋊C4—112no—
648C4×C4⋊C4—112no—
649C4×C4⋊C4—112no—
650C4×C4⋊C4—112no—
651C4×C4⋊C4—112no—
652C4×C4⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4—112no—
659C4×C22⋊C4—112no—
660C4×C22⋊C4C2×D1112yescomplemented
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—41no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11C24×C411yescharacteristic
676C22×C11C23×D411yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11#58511yescharacteristic
679C22×C11#58511yescharacteristic
680C22×C11#58511yescharacteristic
681C22×C11#58511yescharacteristic
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—416no—
695C2×D11—41no—
696C2×D11—41no—
697C2×D11—41no—
698C2×D11—41no—
699C2×D11—41no—
700C2×D11—41no—
701C2×D11—41no—
702C2×D11—41no—
703C2×D11C2×C4×D414yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—24no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—42no—
712C4×C11C2×C4×D414yes—
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—24no—
718Dic11—42no—
719Dic11—42no—
720Dic11—42no—
721Dic11C2×C4×D414yes—
722C25—111no—
723C2×#41—118no—
724C2×#41—224no—
725C2×#41—224no—
726C22×Q8—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—111no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—111no—
733C22×D4C22×D1111yescharacteristic
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—118no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4—224no—
745C23×C4—224no—
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1112yes—
749#123—118no—
750#123—118no—
751C22⋊Q8—118no—
752C22⋊Q8—118no—
753#121—118no—
754#121—118no—
755#120—118no—
756#120—118no—
757C4×Q8—228no—
758C4×D4—118no—
759C4×D4—118no—
760C4×D4—118no—
761C4×D4—228no—
762C4×D4—228no—
763C4×D4—228no—
764C4×D4C4×D1118yescomplemented
765#117—24no—
766#117—118no—
767#117—228no—
768#117—228no—
769#117—224no—
770#117—224no—
771#117—224no—
772#117—224no—
773#117—224no—
774#117—224no—
775#117—224no—
776C2×C4⋊C4—24no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—118no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—224no—
795C2×C4⋊C4—224no—
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C4⋊C4C22×D1112yes—
799C2×C4⋊C4C22×D1111yescharacteristic
800C2×C4⋊C4C22×D1111yescharacteristic
801C2×C4⋊C4C22×D1111yescharacteristic
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—112no—
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—112no—
823C2×C22⋊C4—228no—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
827C2×C22⋊C4C22×D1111yescharacteristic
828C2×C22⋊C4C22×D1111yescharacteristic
829C2×C42—111no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—112no—
834C2×C42—112no—
835C2×C42—112no—
836C2×C42—112no—
837C2×C42—112no—
838C2×C42—112no—
839C2×C42—112no—
840C2×C42—228no—
841C2×C42C22×D1112yes—
842C2×C42C22×D1112yes—
843C2×C42C22×D1111yescharacteristic
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95C22×D1112yes—
856#95C22×D1112yes—
857#95C22×D1112yes—
858#95C22×D1112yes—
859#95C22×D1112yes—
860C2×C11—42no—
861C2×C11—42no—
862C2×C11C22×C4×D411yescharacteristic
863C2×C11#342811yescharacteristic
864C2×C11#342811yescharacteristic
865C2×C11#348511yescharacteristic
866C2×C11#348711yescharacteristic
867C2×C11#349311yescharacteristic
868C2×C11#349311yescharacteristic
869D11—24no—
870D11—42no—
871D11—42no—
872C24—111no—
873C24—111no—
874C24—111no—
875C24—114no—
876C24—222no—
877C24—222no—
878C24—441no—
879C24—441no—
880C24—441no—
881C24—441no—
882C24C23×D1111yescharacteristic
883C24C23×D1111yescharacteristic
884#41—2232no—
885C2×Q8—114no—
886C2×Q8—222no—
887C2×Q8—222no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—114no—
891C2×D4—114no—
892C2×D4—114no—
893C2×D4—114no—
894C2×D4—114no—
895C2×D4—114no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—222no—
902C2×D4—441no—
903C2×D4—441no—
904C2×D4—441no—
905C2×D4—441no—
906C2×D4—441no—
907C2×D4—441no—
908C2×D4C2×C4×D1114yes—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—111no—
917C22×C4—114no—
918C22×C4—114no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—112no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—118no—
931C22×C4—112no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—2232no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4C2×C4×D1114yes—
954C22×C4C2×C4×D1114yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1112yes—
957C22×C4C23×D1112yes—
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C4⋊C4—22no—
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—114no—
969C4⋊C4—114no—
970C4⋊C4—114no—
971C4⋊C4—114no—
972C4⋊C4—114no—
973C4⋊C4—114no—
974C4⋊C4—118no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—222no—
980C4⋊C4—442no—
981C4⋊C4—442no—
982C4⋊C4—442no—
983C4⋊C4—442no—
984C4⋊C4C2×C4×D1114yes—
985C4⋊C4D4×D1114yes—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—114no—
990C22⋊C4—114no—
991C22⋊C4—114no—
992C22⋊C4—114no—
993C22⋊C4—114no—
994C22⋊C4—114no—
995C22⋊C4—114no—
996C22⋊C4—114no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4C2×C4×D1114yes—
1011C22⋊C4C2×C4×D1114yes—
1012C42—24no—
1013C42—42no—
1014C42—114no—
1015C42—224no—
1016C42—224no—
1017C42—224no—
1018C42—224no—
1019C42—224no—
1020C42—224no—
1021C42—224no—
1022C42—442no—
1023C42—442no—
1024C42—442no—
1025C42C2×C4×D1114yes—
1026C11#3420111yescharacteristic, complemented, Sylow
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—112no—
1040C23—112no—
1041C23—112no—
1042C23—112no—
1043C23—112no—
1044C23—228no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—221no—
1052C23—221no—
1053C23—221no—
1054C23—221no—
1055C23—221no—
1056C23—221no—
1057C23—221no—
1058C23—221no—
1059C23—221no—
1060C23—221no—
1061C23—444no—
1062C23—444no—
1063C23—444no—
1064C23—444no—
1065C23—444no—
1066C23—444no—
1067C23C22×C4×D1112yes—
1068C23C22×C4×D1112yes—
1069C23C24×D1111yescharacteristic
1070Q8—228no—
1071D4—44no—
1072D4—228no—
1073D4—228no—
1074D4—228no—
1075D4—444no—
1076D4—444no—
1077D4—444no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—28no—
1089C2×C4—28no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—84no—
1100C2×C4—112no—
1101C2×C4—112no—
1102C2×C4—112no—
1103C2×C4—1116no—
1104C2×C4—112no—
1105C2×C4—112no—
1106C2×C4—112no—
1107C2×C4—112no—
1108C2×C4—114no—
1109C2×C4—228no—
1110C2×C4—228no—
1111C2×C4—228no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—221no—
1122C2×C4—228no—
1123C2×C4—228no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—448no—
1134C2×C4—448no—
1135C2×C4—884no—
1136C2×C4C22×C4×D1112yes—
1137C2×C4C22×C4×D1112yes—
1138C2×C4C22×C4×D1112yes—
1139C2×C4C22×C4×D1112yes—
1140C2×C4C22×C4×D1112yes—
1141C2×C4C2×D4×D1114yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4#41×D1112yes—
1144C22—22no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—114no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—222no—
1170C22—222no—
1171C22—4416no—
1172C22—441no—
1173C22—441no—
1174C22—441no—
1175C22—441no—
1176C22—441no—
1177C22—441no—
1178C22—441no—
1179C22—441no—
1180C22C23×C4×D1111yescharacteristic
1181C22C22×D4×D1111yescharacteristic
1182C22C2×#41×D1111yescharacteristic
1183C22#1062345311yescharacteristic
1184C22#1062345311yescharacteristic
1185C22#1062345511yescharacteristic
1186C22#1062345711yescharacteristic
1187C4—24no—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—114no—
1196C4—224no—
1197C4—222no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—442no—
1202C4—442no—
1203C4—442no—
1204C4C4×D4×D1114yes—
1205C2—42no—
1206C2—42no—
1207C2—224no—
1208C2—442no—
1209C2—442no—
1210C2C2×C4×D4×D1111yescharacteristic
1211C2#1308181611yescharacteristic
1212C2#1308181711yescharacteristic
1213C2#1308225311yescharacteristic
1214C2#1308227311yescharacteristic
1215C2#1308233211yescharacteristic
1216C2#1308233411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2352C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2352D11
hypocenterC11#34201
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×D11×#117C2semidirect
4. #13071657C2semidirect
5. #13071655C2semidirect
6. #13071640C2semidirect
7. #13071638C2semidirect
8. #13071566C2semidirect
9. #13071565C2semidirect
10. #13071563C2semidirect
11. #13071560C2semidirect
12. #13071542C2semidirect
13. #13071541C2semidirect
14. #13071538C2semidirect
15. #13071272C2semidirect
16. #13071269C2semidirect
17. #13071241C2semidirect
18. #13071205C2semidirect
19. #13071137C2semidirect
20. C4×#66936C2semidirect
21. #13070998C2semidirect
22. #13070970C2semidirect
23. C11×#2352C2semidirect
28. C22×C11×C4⋊C4C22semidirect
34. C2×C4×C22⋊D11C22semidirect
36. C2×#66979C22semidirect
37. #10623078C4semidirect
47. C2×#66945C22semidirect
50. C2×C4⋊C4×D11C22semidirect
51. C2×#66940C22semidirect
63. C11×#387C22semidirect
65. C11×#382C22semidirect
67. C11×#380C22semidirect
68. C4×C11×C4⋊C4C22semidirect
69. C4×C11×C22⋊C4C22semidirect
73. #10622825C22semidirect
74. C4×C22⋊Dic11C22semidirect
78. #10622600C22semidirect
79. #10622600C22semidirect
80. #10622591C22semidirect
81. #10622590C22semidirect
82. #10622589C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. C4⋊C4×Dic11C22semidirect
88. #10622570C22semidirect
93. #10622564C22semidirect
94. #10622558C22semidirect
98. #10622553C22semidirect
101. #10622548C22semidirect
102. C4×C4⋊Dic11C22semidirect
103. C4×C4⋊Dic11C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. C4×Dic11⋊C4C22semidirect
107. #10622283C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
119. #10622267C22semidirect
120. #10622265C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
143. C22×C4×D11C2×C4semidirect
153. C4×D4×C11C2×C4semidirect
176. #66992C2×C4semidirect
177. #66990C2×C4semidirect
180. C4×C22⋊D11C2×C4semidirect
181. C4×C22⋊D11C2×C4semidirect
226. #66949C2×C4semidirect
227. #66947C2×C4semidirect
236. C4⋊C4×D11D4semidirect
238. #66937C2×C4semidirect
239. #66936C2×C4semidirect
240. #66935C2×C4semidirect
242. #66931C2×C4semidirect
244. C4×D44C2×C4semidirect
246. #66925C2×C4semidirect
433. #2352D11semidirect
594. C22×C4⋊C4C2×D11semidirect
620. #387C2×D11semidirect
632. #382C2×D11semidirect
641. #380C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
660. C4×C22⋊C4C2×D11semidirect
764. C4×D4C4×D11semidirect
1026. C11#34201semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×#106230352
C2×D11×#1172
#130716572
#130716552
#130716402
#130716382
#130715662
#130715652
#130715632
#130715602
#130715422
#130715412
#130715382
#130712722
#130712692
#130712412
#130712052
#130711372
C4×#669362
#130709982
#130709702
C11×#23522
#3420111