Finite Group Databasebeta

← #14923628

Subgroups — #14923628

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13072931C211yesmaximal, characteristic, complemented
4#13072929C211yesmaximal, characteristic, complemented
5#13072922C211yesmaximal, characteristic, complemented
6#13072920C211yesmaximal, characteristic, complemented
7#13072914C211yesmaximal, characteristic, complemented
8#13072913C211yesmaximal, characteristic, complemented
9#13072907C211yesmaximal, characteristic, complemented
10#13072901C212yesmaximal, complemented
11#13072893C212yesmaximal, complemented
12#13072888C212yesmaximal, complemented
13#13071938C212yesmaximal
14#13071874C212yesmaximal, complemented
15#13071872C212yesmaximal, complemented
16#13071143C212yesmaximal, complemented
17#13071137C212yesmaximal, complemented
18#13071097C211yesmaximal, characteristic, complemented
19#13071097C211yesmaximal, characteristic, complemented
20#13070998C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22#13070998C211yesmaximal, characteristic, complemented
23C11×#2485C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×D4×Dic11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×#66979C2211yescharacteristic, complemented
33C4×D4×D11—28no—
34D11×#117—28no—
35C2×#66947C2212yes—
36C2×#66946C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic, complemented
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66936C2212yes—
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×#66930C2212yescomplemented
51C2×C4×D44C2211yescharacteristic
52C2×#66925C2212yes—
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2212yescomplemented
55C11×#397C2212yescomplemented
56C11×#394C2212yes—
57C11×#389C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#388C2212yescomplemented
60C11×#387C2212yescomplemented
61C11×#380C2211yescharacteristic, complemented
62C11×#380C2211yescharacteristic, complemented
63C11×#380C2211yescharacteristic, complemented
64#10622835C2212yes—
65#10622825C2211yescharacteristic, complemented
66#10622825C2211yescharacteristic, complemented
67#10622825C2211yescharacteristic, complemented
68#10622605C2212yescomplemented
69#10622602C2212yes—
70#10622602C2212yes—
71#10622602C2212yescomplemented
72#10622600C2211yescharacteristic, complemented
73#10622600C2211yescharacteristic, complemented
74#10622600C2211yescharacteristic, complemented
75#10622600C2211yescharacteristic, complemented
76#10622600C2211yescharacteristic, complemented
77#10622600C2211yescharacteristic, complemented
78#10622598C2211yescharacteristic, complemented
79#10622598C2211yescharacteristic, complemented
80#10622597C2212yescomplemented
81#10622591C2212yescomplemented
82C4⋊C4×Dic11C2212yescomplemented
83C4⋊C4×Dic11C2212yescomplemented
84#10622586C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622574C2212yes—
87#10622572C2212yes—
88#10622569C2212yes—
89#10622568C2212yes—
90#10622568C2212yes—
91#10622568C2212yes—
92#10622566C2212yescomplemented
93#10622565C2212yescomplemented
94#10622565C2212yescomplemented
95#10622565C2212yescomplemented
96#10622562C2212yescomplemented
97#10622557C2212yescomplemented
98C22⋊C4×Dic11C2212yescomplemented
99C22⋊C4×Dic11C2212yescomplemented
100C22⋊C4×Dic11C2212yescomplemented
101#10622553C2212yescomplemented
102#10622546C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622541C2211yescharacteristic, complemented
105#10622288C2212yescomplemented
106#10622283C2212yescomplemented
107#10622281C2212yes—
108#10622281C2212yes—
109#10622281C2212yescomplemented
110#10622279C2212yescomplemented
111#10622279C2212yescomplemented
112#10622279C2212yescomplemented
113#10622278C2212yes—
114#10622277C2212yes—
115#10622277C2212yes—
116#10622277C2212yes—
117#10622277C2212yescomplemented
118#10622277C2212yescomplemented
119#10622273C2212yescomplemented
120#10622271C2212yescomplemented
121#10622270C2212yescomplemented
122#10622266C2212yescomplemented
123#10622262C2212yescomplemented
124#10622262C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C2×D4×D11—24no—
135C2×D4×D11—24no—
136C2×D4×D11—24no—
137C22×D44C2311yescharacteristic
138C22×C4×D11—24no—
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11D418yes—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C4×D4×C11—24no—
156C11×#117—24no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178D4×Dic11—24no—
179C4×C22⋊D11—24no—
180C4×C22⋊D11—24no—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
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—
195#66979—24no—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219#66947—28no—
220#66946—24no—
221#66945—24no—
222#66945—24no—
223#66945—24no—
224#66945—24no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—24no—
227C4⋊C4×D11—24no—
228#66936—28no—
229(C22⋊D11)⋊C4—24no—
230(C22⋊D11)⋊C4—24no—
231C22⋊C4×D11—28no—
232C22⋊C4×D11—24no—
233C22⋊C4×D11—24no—
234#66930—28no—
235C4×D44—24no—
236#66925—28no—
237C42×D11—24no—
238C42×D11—28no—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259#34809—111nomaximal, Sylow
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—41no—
272C23×D11—41no—
273C23×D11—41no—
274C23×D11—41no—
275C23×D11C2×D414yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11C2×D414yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11#4114yes—
303C22×Dic11—22no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11C2×D414yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318D4×D11—232no—
319C2×D44—22no—
320C2×D44—22no—
321C2×D44#4114yes—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—232no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—24no—
332C2×C4×D11—24no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—41no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—41no—
350C2×C4×D11—416no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11#4114yes—
356C2×C4×D11#4114yes—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—24no—
363C11×C4⋊C4—42no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—22no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C42×C11—24no—
371C42×C11—22no—
372C22⋊Dic11—22no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—24no—
376C22⋊Dic11—42no—
377C22⋊Dic11—42no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
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—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392C4⋊Dic11—22no—
393C4⋊Dic11—24no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407C4×Dic11—24no—
408C4×Dic11—24no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—22no—
415C22×C4×D4—111no—
416C22×#117—111no—
417#2487—111no—
418#2487—111no—
419#2486—111no—
420#2486—111no—
421#2485—111no—
422#2485—111no—
423#2485—111no—
424#2485D1111yescharacteristic, complemented
425#2484—112no—
426#2483—112no—
427#2482—112no—
428#2405—112no—
429#2395—112no—
430#2395—112no—
431C4×#123—112no—
432C4×#123—112no—
433#2296—111no—
434#2296—111no—
435#2280—111no—
436#2280—111no—
437#2280—111no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
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×C11C22×D412yes—
451C23×C11C2×#4112yes—
452C23×C11C2511yescharacteristic
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—28no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—28no—
469C22×D11—28no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—44no—
477C22×D11—44no—
478C22×D11—44no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11C22×D412yes—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485C22×D11C2×#4112yes—
486C22×D11C2×#4112yes—
487C22×D11C2×#4112yes—
488D4×C11—28no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—28no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
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—21no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—21no—
512C2×C4×C11—44no—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D412yes—
515C2×C4×C11C2×#4112yes—
516C2×C4×C11C2×#4112yes—
517C2×C4×C11C2×#4112yes—
518C22⋊D11—28no—
519C22⋊D11—28no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—28no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—22no—
543C2×Dic11—44no—
544C2×Dic11C22×D412yes—
545C2×Dic11C22×D412yes—
546C2×Dic11C2×#4112yes—
547C2×Dic11C2×#4112yes—
548C2×Dic11C2×#4112yes—
549D44—28no—
550C4×D11—28no—
551C4×D11—28no—
552C4×D11—28no—
553C4×D11—28no—
554C4×D11—44no—
555C4×D11—48no—
556C4×D11—44no—
557C4×D11—48no—
558C4×D11—44no—
559C4×D11—44no—
560C4×D11#123116yescomplemented
561C23×D4—111no—
562C24×C4—111no—
563C24×C4—111no—
564C2×#123—112no—
565C2×#123—112no—
566C2×C4×D4—111no—
567C2×C4×D4—111no—
568C2×C4×D4—111no—
569C2×C4×D4—111no—
570C2×C4×D4—111no—
571C2×C4×D4—111no—
572C2×C4×D4—111no—
573C2×C4×D4—228no—
574C2×C4×D4C2×D1111yescharacteristic
575C2×#117—111no—
576C2×#117—111no—
577C2×#117—111no—
578C2×#117—111no—
579C2×#117—111no—
580C2×#117—112no—
581C2×#117—112no—
582C2×#117—228no—
583C2×#117C2×D1111yescharacteristic, complemented
584C22×C4⋊C4—111no—
585C22×C4⋊C4—111no—
586C22×C4⋊C4—111no—
587C22×C22⋊C4—112no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C42—111no—
591C22×C42—112no—
592#400—112no—
593#400—112no—
594#399—112no—
595#399—112no—
596#398—112no—
597#398—112no—
598#397—112no—
599#397—112no—
600#397—112no—
601#397—112no—
602#397—112no—
603#397C2×D1112yescomplemented
604#394—112no—
605#394—112no—
606#394—112no—
607#394C2×D1112yes—
608#389—111no—
609#389—111no—
610#389—111no—
611#389—111no—
612#389—111no—
613#389—111no—
614#389C2×D1111yescharacteristic, complemented
615#389C2×D1111yescharacteristic, complemented
616#388—112no—
617#388—112no—
618#388—112no—
619#388C2×D1112yescomplemented
620#387—112no—
621#387—112no—
622#387—112no—
623#387C2×D1112yescomplemented
624#386—112no—
625#386—112no—
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#385—112no—
631#385—112no—
632#381—112no—
633#381—112no—
634#381—112no—
635#381—112no—
636#381—112no—
637#380—111no—
638#380—111no—
639#380—111no—
640#380—111no—
641#380—111no—
642#380—111no—
643#380—111no—
644#380—111no—
645#380—111no—
646#380C2×D1111yescharacteristic, complemented
647#380C2×D1111yescharacteristic, complemented
648#380C2×D1111yescharacteristic, complemented
649#379—112no—
650#379—112no—
651#379—112no—
652C4×C4⋊C4—112no—
653C4×C4⋊C4—112no—
654C4×C4⋊C4—112no—
655C4×C4⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4—112no—
659C4×C22⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4—112no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—41no—
669C22×C11—41no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—41no—
676C22×C11C23×D411yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C22×#4111yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C22×#4111yescharacteristic
681C22×C11#58511yescharacteristic
682C22×C11#58511yescharacteristic
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—22no—
695C2×D11—22no—
696C2×D11—22no—
697C2×D11—22no—
698C2×D11—416no—
699C2×D11—416no—
700C2×D11—41no—
701C2×D11—41no—
702C2×D11—41no—
703C2×D11—41no—
704C2×D11C2×#12314yes—
705C2×D11#52514yes—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11—42no—
713C4×C11—42no—
714C4×C11C2×#12314yes—
715Dic11—22no—
716Dic11—22no—
717Dic11—41no—
718Dic11—42no—
719Dic11—42no—
720Dic11—41no—
721Dic11—42no—
722Dic11—42no—
723Dic11C2×#12314yes—
724C25—111no—
725C25—111no—
726C22×D4—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—224no—
730C22×D4—224no—
731C22×D4—224no—
732C22×D4C22×D1111yescharacteristic
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—118no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—112no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—224no—
748C23×C4—224no—
749C23×C4—224no—
750C23×C4—224no—
751C23×C4—224no—
752C23×C4C22×D1111yescharacteristic
753C23×C4C22×D1111yescharacteristic
754#123—228no—
755#123—228no—
756C4×D4—24no—
757C4×D4—224no—
758C4×D4—224no—
759C4×D4—224no—
760C4×D4—224no—
761C4×D4—224no—
762C4×D4—224no—
763C4×D4—224no—
764#117—24no—
765#117—228no—
766#117—228no—
767#117—224no—
768#117—224no—
769#117—224no—
770#117—224no—
771#117—224no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C4⋊C4C22×D1111yescharacteristic
793C2×C4⋊C4C22×D1111yescharacteristic
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1112yes—
796C2×C4⋊C4C22×D1112yes—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
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—224no—
818C2×C22⋊C4—228no—
819C2×C22⋊C4—224no—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1111yescharacteristic
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—228no—
835C2×C42—224no—
836C2×C42C22×D1112yes—
837C2×C42C22×D1111yescharacteristic
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
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#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856#95C22×D1112yes—
857#95C22×D1112yes—
858C2×C11—42no—
859C2×C11—42no—
860C2×C11C22×#12311yescharacteristic
861C2×C11C2×#52511yescharacteristic
862C2×C11#344911yescharacteristic
863C2×C11#347511yescharacteristic
864C2×C11#347511yescharacteristic
865C2×C11#347511yescharacteristic
866C2×C11#347511yescharacteristic
867D11—24no—
868D11—24no—
869D11—42no—
870C24—111no—
871C24—111no—
872C24—111no—
873C24—114no—
874C24—222no—
875C24—222no—
876C24—222no—
877C24—222no—
878C24—222no—
879C24—222no—
880C24—222no—
881C24—222no—
882C24—222no—
883C24—441no—
884C24—441no—
885C24—441no—
886C24—441no—
887C24C23×D1111yescharacteristic
888C24C23×D1111yescharacteristic
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—114no—
893C2×D4—114no—
894C2×D4—222no—
895C2×D4—222no—
896C2×D4—222no—
897C2×D4—2232no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—222no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—111no—
908C22×C4—114no—
909C22×C4—114no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—111no—
913C22×C4—111no—
914C22×C4—114no—
915C22×C4—114no—
916C22×C4—114no—
917C22×C4—111no—
918C22×C4—112no—
919C22×C4—112no—
920C22×C4—111no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—2232no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—222no—
950C22×C4—222no—
951C22×C4—222no—
952C22×C4—442no—
953C22×C4—441no—
954C22×C4—442no—
955C22×C4—441no—
956C22×C4—4416no—
957C22×C4D4×D1114yes—
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1112yes—
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1112yes—
964C22×C4C23×D1111yescharacteristic
965C22×C4C23×D1111yescharacteristic
966C22×C4C23×D1111yescharacteristic
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—24no—
973C4⋊C4—42no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—224no—
979C4⋊C4—224no—
980C4⋊C4—222no—
981C4⋊C4—222no—
982C4⋊C4—222no—
983C4⋊C4—222no—
984C4⋊C4—222no—
985C4⋊C4—224no—
986C4⋊C4—442no—
987C4⋊C4—442no—
988C4⋊C4—442no—
989C22⋊C4—24no—
990C22⋊C4—22no—
991C22⋊C4—24no—
992C22⋊C4—22no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—222no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—222no—
1007C22⋊C4—224no—
1008C22⋊C4—222no—
1009C22⋊C4—224no—
1010C22⋊C4—222no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4—442no—
1014C22⋊C4—442no—
1015C42—24no—
1016C42—22no—
1017C42—224no—
1018C42—224no—
1019C42—222no—
1020C42—222no—
1021C42—224no—
1022C42—224no—
1023C42—224no—
1024C42—222no—
1025C11#3480911yescharacteristic, complemented, Sylow
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—112no—
1039C23—112no—
1040C23—112no—
1041C23—112no—
1042C23—112no—
1043C23—112no—
1044C23—112no—
1045C23—228no—
1046C23—228no—
1047C23—228no—
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—221no—
1062C23—444no—
1063C23—444no—
1064C23—444no—
1065C23—444no—
1066C23—444no—
1067C23—444no—
1068C23—444no—
1069C23—444no—
1070C23—444no—
1071C23—444no—
1072C23—444no—
1073C23C2×D4×D1112yes—
1074C23#41×D1112yes—
1075C23C24×D1111yescharacteristic
1076D4—28no—
1077D4—228no—
1078D4—228no—
1079D4—228no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—28no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—44no—
1104C2×C4—112no—
1105C2×C4—112no—
1106C2×C4—112no—
1107C2×C4—1116no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—228no—
1111C2×C4—228no—
1112C2×C4—228no—
1113C2×C4—228no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—228no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—221no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—448no—
1140C2×C4—448no—
1141C2×C4—444no—
1142C2×C4—444no—
1143C2×C4—444no—
1144C2×C4C2×D4×D1112yes—
1145C2×C4C2×D4×D1112yes—
1146C2×C4#41×D1112yes—
1147C2×C4#41×D1112yes—
1148C2×C4#41×D1112yes—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—114no—
1164C22—114no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—222no—
1173C22—222no—
1174C22—222no—
1175C22—222no—
1176C22—222no—
1177C22—222no—
1178C22—222no—
1179C22—222no—
1180C22—4416no—
1181C22—4416no—
1182C22—441no—
1183C22—441no—
1184C22—441no—
1185C22—441no—
1186C22C22×D4×D1111yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#41×D1111yescharacteristic
1189C22C2×#41×D1111yescharacteristic
1190C22C2×#41×D1111yescharacteristic
1191C22#1062345511yescharacteristic
1192C22#1062345711yescharacteristic
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—42no—
1197C4—41no—
1198C4—42no—
1199C4—41no—
1200C4—42no—
1201C4—114no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—442no—
1206C4—441no—
1207C4—442no—
1208C4—441no—
1209C4—442no—
1210C4D11×#12314yes—
1211C2—42no—
1212C2—42no—
1213C2—224no—
1214C2—224no—
1215C2—442no—
1216C2C2×D11×#12311yescharacteristic
1217C2D11×#52511yescharacteristic
1218C2#1308194411yescharacteristic
1219C2#1308216911yescharacteristic
1220C2#1308217311yescharacteristic
1221C2#1308217511yescharacteristic
1222C2#1308217711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2485C2
prime radicalC22×D4×D11C22
hypercenter#2485D11
hypocenterC11#34809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2485

Complements

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

NH ≅ G/Ntype
2. C2×D11×#117C2semidirect
3. #13072931C2semidirect
4. #13072929C2semidirect
5. #13072922C2semidirect
6. #13072920C2semidirect
7. #13072914C2semidirect
8. #13072913C2semidirect
9. #13072907C2semidirect
10. #13072901C2semidirect
11. #13072893C2semidirect
12. #13072888C2semidirect
14. #13071874C2semidirect
15. #13071872C2semidirect
16. #13071143C2semidirect
17. #13071137C2semidirect
18. #13071097C2semidirect
19. #13071097C2semidirect
20. #13070998C2semidirect
21. #13070998C2semidirect
22. #13070998C2semidirect
23. C11×#2485C2semidirect
28. C2×C11×#117C22semidirect
32. C2×#66979C22semidirect
42. C2×C4⋊C4×D11C22semidirect
43. C2×C4⋊C4×D11C22semidirect
50. C2×#66930C22semidirect
54. C2×C42×D11C22semidirect
55. C11×#397C22semidirect
57. C11×#389C22semidirect
58. C11×#389C22semidirect
59. C11×#388C22semidirect
60. C11×#387C22semidirect
61. C11×#380C22semidirect
62. C11×#380C22semidirect
63. C11×#380C22semidirect
65. #10622825C22semidirect
66. #10622825C22semidirect
67. #10622825C22semidirect
68. #10622605C22semidirect
71. #10622602C22semidirect
72. #10622600C22semidirect
73. #10622600C22semidirect
74. #10622600C22semidirect
75. #10622600C22semidirect
76. #10622600C22semidirect
77. #10622600C22semidirect
78. #10622598C22semidirect
79. #10622598C22semidirect
80. #10622597C22semidirect
81. #10622591C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622586C22semidirect
85. #10622586C22semidirect
92. #10622566C22semidirect
93. #10622565C22semidirect
94. #10622565C22semidirect
95. #10622565C22semidirect
96. #10622562C22semidirect
97. #10622557C22semidirect
98. C22⋊C4×Dic11C22semidirect
99. C22⋊C4×Dic11C22semidirect
100. C22⋊C4×Dic11C22semidirect
101. #10622553C22semidirect
102. #10622546C22semidirect
103. #10622541C22semidirect
104. #10622541C22semidirect
105. #10622288C22semidirect
106. #10622283C22semidirect
109. #10622281C22semidirect
110. #10622279C22semidirect
111. #10622279C22semidirect
112. #10622279C22semidirect
117. #10622277C22semidirect
118. #10622277C22semidirect
119. #10622273C22semidirect
120. #10622271C22semidirect
121. #10622270C22semidirect
122. #10622266C22semidirect
123. #10622262C22semidirect
124. #10622262C22semidirect
424. #2485D11semidirect
560. C4×D11#123semidirect
583. C2×#117C2×D11semidirect
603. #397C2×D11semidirect
614. #389C2×D11semidirect
615. #389C2×D11semidirect
619. #388C2×D11semidirect
623. #387C2×D11semidirect
646. #380C2×D11semidirect
647. #380C2×D11semidirect
648. #380C2×D11semidirect
1025. C11#34809semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C2×D11×#1172
#130729312
#130729292
#130729222
#130729202
#130729142
#130729132
#130729072
#130729012
#130728932
#130728882
#130719382
#130718742
#130718722
#130711432
#130711372
#130710972
#130709982
C11×#24852
#3480911