Finite Group Databasebeta

← #14914180

Subgroups — #14914180

Order 2816.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#124C211yesmaximal, characteristic
2C2×#10623103C211yesmaximal, characteristic, complemented
3C2×#10623076C211yesmaximal, characteristic
4#13071692C211yesmaximal, characteristic, complemented
5#13071691C211yesmaximal, characteristic, complemented
6#13071689C211yesmaximal, characteristic, complemented
7#13071687C211yesmaximal, characteristic, complemented
8#13071686C211yesmaximal, characteristic, complemented
9#13071685C211yesmaximal, characteristic, complemented
10#13071683C211yesmaximal, characteristic, complemented
11#13071464C212yesmaximal, complemented
12#13071463C212yesmaximal, complemented
13#13071460C212yesmaximal, complemented
14#13071459C212yesmaximal, complemented
15#13071325C212yesmaximal, complemented
16#13071322C212yesmaximal, complemented
17#13071199C211yesmaximal, characteristic, complemented
18#13071195C211yesmaximal, characteristic
19#13071157C212yesmaximal, complemented
20C4×#66938C212yesmaximal, complemented
21#13071020C211yesmaximal, characteristic, complemented
22C4×#66945C211yesmaximal, characteristic, complemented
23C11×#2367C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C2×#67000C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66989C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C22×(C2×D11)⋊C4C2212yes—
35D11×#124C4116yescomplemented
36#10623103—28no—
37#10623076—28no—
38C2×#66946C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66945C2212yes—
41C2×#66945C2211yescharacteristic
42C2×#66940C2212yescomplemented
43C2×#66940C2211yescharacteristic, complemented
44C2×#66938C2212yes—
45C2×#66938C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×#66928C2211yescharacteristic
51C2×C4×D44C2211yescharacteristic
52C2×#66925C2211yescharacteristic
53C2×#66925C2211yescharacteristic
54C2×#66925C2212yes—
55C2×C42×D11C2211yescharacteristic
56C2×C4×Dic22C2212yescomplemented
57C2×C4×Dic22C2211yescharacteristic, complemented
58C11×#391C2211yescharacteristic, complemented
59C11×#390C2211yescharacteristic
60C11×#388C2212yescomplemented
61C11×#388C2212yescomplemented
62C11×#385C2212yescomplemented
63C4×C11×C4⋊C4C2211yescharacteristic, complemented
64C4×C11×C4⋊C4C2211yescharacteristic, complemented
65C4×C11×C22⋊C4C2212yescomplemented
66#10622843C2211yescharacteristic, complemented
67#10622834C2211yescharacteristic
68#10622823C2212yescomplemented
69C4×C22⋊Dic11C2212yescomplemented
70#10622603C2212yescomplemented
71#10622603C2212yescomplemented
72#10622602C2212yescomplemented
73#10622602C2212yescomplemented
74#10622601C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622600C2211yescharacteristic
77#10622589C2211yescharacteristic, complemented
78#10622589C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81#10622587C2211yescharacteristic, complemented
82#10622570C2212yes—
83#10622570C2212yes—
84#10622568C2212yes—
85#10622568C2212yes—
86#10622564C2212yescomplemented
87#10622564C2212yescomplemented
88#10622563C2212yescomplemented
89#10622559C2212yescomplemented
90#10622558C2212yescomplemented
91#10622558C2212yescomplemented
92#10622557C2212yescomplemented
93#10622557C2212yescomplemented
94C22⋊C4×Dic11C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96#10622553C2212yescomplemented
97#10622553C2212yescomplemented
98#10622552C2211yescharacteristic
99C4×(C2×D11)⋊C4C2212yes—
100C4×(C2×D11)⋊C4C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×C4⋊Dic11C2211yescharacteristic, complemented
103C4×C4⋊Dic11C2211yescharacteristic, complemented
104C4×Dic11⋊C4C2211yescharacteristic, complemented
105C4×Dic11⋊C4C2211yescharacteristic, complemented
106C42×Dic11C2212yescomplemented
107#10622542C2211yescharacteristic, complemented
108#10622283C2212yescomplemented
109#10622283C2212yescomplemented
110#10622282C2212yescomplemented
111#10622282C2212yescomplemented
112#10622281C2212yescomplemented
113#10622281C2212yescomplemented
114#10622280C2211yescharacteristic
115#10622280C2211yescharacteristic
116#10622279C2212yes—
117#10622279C2212yescomplemented
118#10622279C2212yescomplemented
119#10622277C2212yes—
120#10622277C2212yes—
121#10622263C2211yescharacteristic, complemented
122#10622263C2211yescharacteristic, complemented
123#10622261C2212yescomplemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2312yes—
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C23×Dic11C2312yes—
132C2×Q8×D11—24no—
133C2×Q8×D11—24no—
134C2×Q8×D11C2×C418yescomplemented
135C2×D4×D11—24no—
136C2×D4×D11—24no—
137C2×D4×D11C2×C418yes—
138C22×D44C2311yescharacteristic
139C22×C4×D11C2312yes—
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×Dic22C2311yescharacteristic
146C22×Dic22C2312yes—
147C11×#124C2×C418yescomplemented
148C4×Q8×C11—24no—
149C4×D4×C11—24no—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2312yes—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2312yes—
164C2×C42×C11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170#67000C2×C418yescomplemented
171Q8×Dic11—24no—
172#66989C2×C418yescomplemented
173D4×Dic11—24no—
174C4×C22⋊D11—28no—
175C2×(C2×D11)⋊C4—28no—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2312yes—
192C2×C4⋊Dic11C2312yes—
193C2×C4⋊Dic11C2311yescharacteristic
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220#66946—24no—
221#66945—24no—
222#66945—28no—
223#66945D418yes—
224#66940—24no—
225#66940—28no—
226#66938C2×C4116yescomplemented
227#66938C2×C4116yescomplemented
228(C22⋊D11)⋊C4—28no—
229C22⋊C4×D11—28no—
230C22⋊C4×D11C2×C4116yescomplemented
231C22⋊C4×D11C2×C4116yescomplemented
232#66928C2×C418yescomplemented
233C4×D44—24no—
234#66925—24no—
235#66925—24no—
236#66925—28no—
237C42×D11C2×C418yescomplemented
238C4×Dic22—24no—
239C4×Dic22—28no—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2311yescharacteristic
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260#34211—111nomaximal, Sylow
261C24×C11C2412yes—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C22×C418yes—
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×Q8×C11—22no—
272C2×Q8×C11—22no—
273C2×Q8×C11C22×C414yes—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11C22×C414yes—
277C22×C4×C11—24no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—24no—
291C2×C22⋊D11—24no—
292C2×C22⋊D11C22×C418yes—
293C22×Dic11—24no—
294C22×Dic11—42no—
295C22×Dic11—42no—
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2412yes—
304C22×Dic11C2412yes—
305C22×Dic11C2411yescharacteristic
306Q8×D11—232no—
307D4×D11—232no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44C22×C414yes—
311C2×C4×D11—24no—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—41no—
316C2×C4×D11—41no—
317C2×C4×D11—41no—
318C2×C4×D11—41no—
319C2×C4×D11—42no—
320C2×C4×D11—42no—
321C2×C4×D11—42no—
322C2×C4×D11—42no—
323C2×C4×D11C22×C418yes—
324C2×C4×D11C22×C414yes—
325C2×C4×D11C22×C414yes—
326C2×C4×D11C22×C414yes—
327C2×C4×D11C2×D414yes—
328C2×C4×D11#4114yes—
329C2×Dic22—24no—
330C2×Dic22—24no—
331C2×Dic22—22no—
332C2×Dic22—22no—
333C2×Dic22C22×C414yes—
334C2×Dic22C22×C418yes—
335C11×C4⋊C4—24no—
336C11×C4⋊C4—22no—
337C11×C4⋊C4—41no—
338C11×C4⋊C4—41no—
339C11×C4⋊C4C2×D414yes—
340C11×C22⋊C4—24no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4C22×C418yes—
344C11×C22⋊C4C22×C418yes—
345C42×C11—24no—
346C42×C11—22no—
347C42×C11—22no—
348C42×C11—42no—
349C42×C11C22×C414yes—
350C22⋊Dic11—24no—
351C22⋊Dic11—42no—
352C22⋊Dic11—42no—
353C22⋊Dic11C22×C418yes—
354C22⋊Dic11C22×C418yes—
355(C2×D11)⋊C4—24no—
356(C2×D11)⋊C4—22no—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4C22×C418yes—
367(C2×D11)⋊C4C22×C418yes—
368(C2×D11)⋊C4C22×C418yes—
369(C2×D11)⋊C4C22×C418yes—
370(C2×D11)⋊C4C2×D418yes—
371C4⋊Dic11—24no—
372C4⋊Dic11—22no—
373C4⋊Dic11—41no—
374C4⋊Dic11—41no—
375C4⋊Dic11C2×D414yes—
376Dic11⋊C4—24no—
377Dic11⋊C4—22no—
378Dic11⋊C4—22no—
379Dic11⋊C4—22no—
380Dic11⋊C4—22no—
381Dic11⋊C4—24no—
382Dic11⋊C4—41no—
383Dic11⋊C4—41no—
384Dic11⋊C4—41no—
385Dic11⋊C4—41no—
386C4×Dic11—24no—
387C4×Dic11—24no—
388C4×Dic11—24no—
389C4×Dic11—24no—
390C4×Dic11—22no—
391C4×Dic11—22no—
392C4×Dic11—42no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11C22×C414yes—
396C4×Dic11C22×C414yes—
397C4×Dic11C22×C414yes—
398C4×Dic11C2×D418yes—
399C22×#124—111no—
400C2×#519—111no—
401C2×#518—111no—
402#2367—111no—
403#2367—111no—
404#2367—111no—
405#2367—111no—
406#2367—111no—
407#2367—111no—
408#2367—111no—
409#2367D1111yescharacteristic, complemented
410#2342—112no—
411#2342—112no—
412#2342—112no—
413#2342—112no—
414#2326—112no—
415#2326—112no—
416#2310—111no—
417#2309—111no—
418C4×#124—112no—
419C4×#124—112no—
420#2285—111no—
421C4×#117—111no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11C23×C414yes—
429C23×C11C2511yescharacteristic
430C22×D11—21no—
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—216no—
441C22×D11—48no—
442C22×D11—48no—
443C22×D11—84no—
444C22×D11—84no—
445C22×D11—84no—
446C22×D11—84no—
447C22×D11C23×C414yes—
448C22×D11C23×C412yes—
449C22×D11C22×D412yes—
450C22×D11C2×#4112yes—
451Q8×C11—28no—
452D4×C11—28no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—84no—
477C2×C4×C11C23×C412yes—
478C2×C4×C11C23×C412yes—
479C2×C4×C11C23×C414yes—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C22×D414yes—
482C2×C4×C11C22×D412yes—
483C2×C4×C11C2×#4112yes—
484C22⋊D11—216no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—21no—
488C2×Dic11—21no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—84no—
509C2×Dic11C23×C412yes—
510C2×Dic11C23×C412yes—
511C2×Dic11C23×C414yes—
512C2×Dic11C23×C412yes—
513C2×Dic11C22×D414yes—
514C2×Dic11C22×D412yes—
515C2×Dic11C2×#4112yes—
516D44—28no—
517C4×D11—216no—
518C4×D11—44no—
519C4×D11—44no—
520C4×D11—84no—
521C4×D11—84no—
522C4×D11C4×D4116yes—
523Dic22—28no—
524Dic22—216no—
525C23×Q8—111no—
526C23×D4—111no—
527C2×#124—111no—
528C2×#124—111no—
529C2×#124—1116no—
530C2×#124—112no—
531C2×#124—112no—
532C2×#124—111no—
533C2×#124C2×D1111yescharacteristic
534#519—228no—
535#518—228no—
536C2×C4×Q8—111no—
537C2×C4×Q8—112no—
538C2×C4×Q8—111no—
539C2×C4×Q8—112no—
540C2×C4×Q8—111no—
541C2×C4×Q8C2×D1111yescharacteristic, complemented
542C2×C4×D4—111no—
543C2×C4×D4—112no—
544C2×C4×D4—111no—
545C2×C4×D4—112no—
546C2×C4×D4—111no—
547C2×C4×D4C2×D1111yescharacteristic
548C2×#117—111no—
549C2×#117—111no—
550C2×#117—112no—
551C2×#117—111no—
552C2×#117—111no—
553C2×#117—112no—
554C22×C22⋊C4—112no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557C22×C22⋊C4—112no—
558C22×C42—111no—
559#391—111no—
560#391—111no—
561#391—111no—
562#391—112no—
563#391—112no—
564#391C2×D1111yescharacteristic, complemented
565#390—111no—
566#390—111no—
567#390—112no—
568#390—112no—
569#390—111no—
570#390C2×D1111yescharacteristic
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388C2×D1112yescomplemented
586#388C2×D1112yescomplemented
587#385—112no—
588#385—112no—
589#385—112no—
590#385—112no—
591#385—112no—
592#385—112no—
593#385—112no—
594#385C2×D1112yescomplemented
595#384—111no—
596#384—111no—
597#382—111no—
598#382—111no—
599#381—112no—
600#381—112no—
601#380—111no—
602#380—111no—
603#380—111no—
604#380—111no—
605#379—112no—
606#379—112no—
607C4×C4⋊C4—111no—
608C4×C4⋊C4—111no—
609C4×C4⋊C4—111no—
610C4×C4⋊C4—111no—
611C4×C4⋊C4—111no—
612C4×C4⋊C4—111no—
613C4×C4⋊C4C2×D1111yescharacteristic, complemented
614C4×C4⋊C4C2×D1111yescharacteristic, complemented
615C4×C22⋊C4—112no—
616C4×C22⋊C4—112no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—112no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4C2×D1112yescomplemented
625#376—112no—
626C43—112no—
627C22×C11—24no—
628C22×C11—24no—
629C22×C11—24no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11C24×C411yescharacteristic
635C22×C11C23×D411yescharacteristic
636C22×C11C22×#4111yescharacteristic
637C22×C11#58511yescharacteristic
638C22×C11#58511yescharacteristic
639C22×C11#58511yescharacteristic
640C22×C11#58511yescharacteristic
641C2×D11—22no—
642C2×D11—22no—
643C2×D11—22no—
644C2×D11—22no—
645C2×D11—22no—
646C2×D11—22no—
647C2×D11—24no—
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—42no—
654C2×D11—816no—
655C2×D11C2×C4×D414yes—
656C4×C11—24no—
657C4×C11—22no—
658C4×C11—22no—
659C4×C11—24no—
660C4×C11—41no—
661C4×C11—41no—
662C4×C11—41no—
663C4×C11—41no—
664C4×C11—42no—
665C4×C11C2×C4×D414yes—
666Dic11—24no—
667Dic11—22no—
668Dic11—22no—
669Dic11—24no—
670Dic11—41no—
671Dic11—41no—
672Dic11—41no—
673Dic11—41no—
674Dic11—42no—
675Dic11C2×C4×D414yes—
676C25—112no—
677C22×Q8—118no—
678C22×Q8—112no—
679C22×Q8—111no—
680C22×Q8—224no—
681C22×Q8—224no—
682C22×Q8C22×D1111yescharacteristic
683C22×D4—112no—
684C22×D4—118no—
685C22×D4—111no—
686C22×D4—224no—
687C22×D4—224no—
688C22×D4C22×D1111yescharacteristic
689C23×C4—111no—
690C23×C4—112no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—112no—
694C23×C4—112no—
695C23×C4—112no—
696C23×C4C22×D1112yes—
697#124—118no—
698#124—118no—
699#124—1116no—
700#124—1116no—
701#124—118no—
702#124C4×D1118yescomplemented
703C4×Q8—24no—
704C4×Q8—228no—
705C4×Q8—224no—
706C4×Q8—228no—
707C4×Q8—224no—
708C4×Q8—224no—
709C4×D4—24no—
710C4×D4—224no—
711C4×D4—228no—
712C4×D4—228no—
713C4×D4—224no—
714C4×D4—224no—
715#117—118no—
716#117—228no—
717#117—224no—
718#117—224no—
719#117—228no—
720#117—224no—
721C2×C4⋊C4—111no—
722C2×C4⋊C4—111no—
723C2×C4⋊C4—111no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—111no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—112no—
728C2×C4⋊C4—112no—
729C2×C4⋊C4—111no—
730C2×C4⋊C4—111no—
731C2×C4⋊C4—111no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4C22×D1112yes—
737C2×C4⋊C4C22×D1111yescharacteristic
738C2×C4⋊C4C22×D1111yescharacteristic
739C2×C4⋊C4C22×D1111yescharacteristic
740C2×C4⋊C4C22×D1111yescharacteristic
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—112no—
746C2×C22⋊C4—112no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—1116no—
749C2×C22⋊C4—1116no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—111no—
752C2×C22⋊C4—111no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—111no—
756C2×C22⋊C4—111no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—228no—
765C2×C22⋊C4—228no—
766C2×C22⋊C4C22×D1112yes—
767C2×C22⋊C4C22×D1112yes—
768C2×C22⋊C4C22×D1112yes—
769C2×C22⋊C4C22×D1112yes—
770C2×C22⋊C4C22×D1112yes—
771C2×C42—112no—
772C2×C42—111no—
773C2×C42—111no—
774C2×C42—111no—
775C2×C42—118no—
776C2×C42—111no—
777C2×C42—112no—
778C2×C42—112no—
779C2×C42—112no—
780C2×C42—111no—
781C2×C42—112no—
782C2×C42—112no—
783C2×C42—112no—
784C2×C42—112no—
785C2×C42C22×D1111yescharacteristic
786C2×C42C22×D1112yes—
787C2×C42C22×D1111yescharacteristic
788C2×C42C22×D1112yes—
789C2×C42C22×D1111yescharacteristic
790#95—112no—
791#95—112no—
792#95—112no—
793#95—111no—
794#95—111no—
795#95—111no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95C22×D1112yes—
806#95C22×D1111yescharacteristic
807#95C22×D1112yes—
808#95C22×D1111yescharacteristic
809#95C22×D1112yes—
810C2×C11—44no—
811C2×C11C22×C4×D411yescharacteristic
812C2×C11#342811yescharacteristic
813C2×C11#342811yescharacteristic
814C2×C11#350011yescharacteristic
815C2×C11#350011yescharacteristic
816C2×C11#351011yescharacteristic
817C2×C11#351011yescharacteristic
818D11—24no—
819D11—44no—
820C24—111no—
821C24—112no—
822C24—118no—
823C24—224no—
824C24—224no—
825C24—442no—
826C24—442no—
827C24—442no—
828C24—442no—
829C24C23×D1112yes—
830C2×Q8—22no—
831C2×Q8—22no—
832C2×Q8—118no—
833C2×Q8—114no—
834C2×Q8—224no—
835C2×Q8—224no—
836C2×Q8—2232no—
837C2×Q8—222no—
838C2×Q8—222no—
839C2×Q8C2×C4×D1114yes—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—118no—
843C2×D4—114no—
844C2×D4—2232no—
845C2×D4—224no—
846C2×D4—224no—
847C2×D4—222no—
848C2×D4—222no—
849C2×D4C2×C4×D1114yes—
850C22×C4—24no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—111no—
854C22×C4—114no—
855C22×C4—114no—
856C22×C4—114no—
857C22×C4—111no—
858C22×C4—111no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—118no—
862C22×C4—114no—
863C22×C4—114no—
864C22×C4—112no—
865C22×C4—111no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—111no—
869C22×C4—224no—
870C22×C4—224no—
871C22×C4—224no—
872C22×C4—224no—
873C22×C4—224no—
874C22×C4—441no—
875C22×C4—441no—
876C22×C4—441no—
877C22×C4—441no—
878C22×C4—442no—
879C22×C4—442no—
880C22×C4—442no—
881C22×C4—442no—
882C22×C4—442no—
883C22×C4—442no—
884C22×C4C23×D1112yes—
885C22×C4C23×D1111yescharacteristic
886C22×C4C23×D1111yescharacteristic
887C22×C4C23×D1111yescharacteristic
888C22×C4C23×D1111yescharacteristic
889C22×C4C23×D1111yescharacteristic
890C22×C4C23×D1111yescharacteristic
891C22×C4C23×D1112yes—
892C22×C4C23×D1112yes—
893C22×C4C23×D1111yescharacteristic
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—114no—
899C4⋊C4—222no—
900C4⋊C4—222no—
901C4⋊C4—222no—
902C4⋊C4—224no—
903C4⋊C4—222no—
904C4⋊C4—224no—
905C4⋊C4—224no—
906C4⋊C4—222no—
907C4⋊C4—441no—
908C4⋊C4—441no—
909C4⋊C4—441no—
910C4⋊C4—441no—
911C4⋊C4—441no—
912C4⋊C4—441no—
913C4⋊C4D4×D1114yes—
914C22⋊C4—24no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—118no—
918C22⋊C4—118no—
919C22⋊C4—118no—
920C22⋊C4—118no—
921C22⋊C4—118no—
922C22⋊C4—118no—
923C22⋊C4—118no—
924C22⋊C4—224no—
925C22⋊C4—222no—
926C22⋊C4—222no—
927C22⋊C4—222no—
928C22⋊C4—222no—
929C22⋊C4—224no—
930C22⋊C4—224no—
931C22⋊C4—224no—
932C22⋊C4—442no—
933C22⋊C4—442no—
934C22⋊C4—442no—
935C22⋊C4—442no—
936C22⋊C4—442no—
937C22⋊C4—442no—
938C22⋊C4C2×C4×D1118yes—
939C22⋊C4C2×C4×D1118yes—
940C42—22no—
941C42—24no—
942C42—22no—
943C42—42no—
944C42—114no—
945C42—114no—
946C42—114no—
947C42—118no—
948C42—224no—
949C42—224no—
950C42—224no—
951C42—222no—
952C42—224no—
953C42—222no—
954C42—442no—
955C42—442no—
956C42—442no—
957C42C2×C4×D1114yes—
958C11#3421111yescharacteristic, complemented, Sylow
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—112no—
966C23—112no—
967C23—112no—
968C23—114no—
969C23—2216no—
970C23—221no—
971C23—221no—
972C23—221no—
973C23—221no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—448no—
981C23—448no—
982C23—884no—
983C23—884no—
984C23—884no—
985C23—884no—
986C23C22×C4×D1114yes—
987C23C24×D1111yescharacteristic
988Q8—28no—
989Q8—2216no—
990Q8—228no—
991D4—28no—
992D4—2216no—
993D4—228no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—84no—
1018C2×C4—112no—
1019C2×C4—112no—
1020C2×C4—112no—
1021C2×C4—1116no—
1022C2×C4—112no—
1023C2×C4—112no—
1024C2×C4—114no—
1025C2×C4—114no—
1026C2×C4—2216no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—221no—
1030C2×C4—221no—
1031C2×C4—222no—
1032C2×C4—221no—
1033C2×C4—222no—
1034C2×C4—221no—
1035C2×C4—221no—
1036C2×C4—221no—
1037C2×C4—221no—
1038C2×C4—221no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—221no—
1042C2×C4—221no—
1043C2×C4—221no—
1044C2×C4—221no—
1045C2×C4—221no—
1046C2×C4—221no—
1047C2×C4—222no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—444no—
1051C2×C4—444no—
1052C2×C4—884no—
1053C2×C4—884no—
1054C2×C4—884no—
1055C2×C4C22×C4×D1112yes—
1056C2×C4C22×C4×D1112yes—
1057C2×C4C22×C4×D1114yes—
1058C2×C4C22×C4×D1112yes—
1059C2×C4C2×D4×D1114yes—
1060C2×C4C2×D4×D1112yes—
1061C2×C4#41×D1112yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—114no—
1070C22—222no—
1071C22—222no—
1072C22—222no—
1073C22—222no—
1074C22—222no—
1075C22—222no—
1076C22—224no—
1077C22—224no—
1078C22—224no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—8816no—
1084C22C23×C4×D1111yescharacteristic
1085C22C22×D4×D1111yescharacteristic
1086C22C2×#41×D1111yescharacteristic
1087C22#1062345311yescharacteristic
1088C22#1062345311yescharacteristic
1089C22#1062345511yescharacteristic
1090C22#1062345711yescharacteristic
1091C4—24no—
1092C4—24no—
1093C4—22no—
1094C4—22no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—42no—
1100C4—114no—
1101C4—224no—
1102C4—224no—
1103C4—222no—
1104C4—222no—
1105C4—441no—
1106C4—441no—
1107C4—441no—
1108C4—441no—
1109C4—442no—
1110C4C4×D4×D1114yes—
1111C2—44no—
1112C2—224no—
1113C2—444no—
1114C2C2×C4×D4×D1111yescharacteristic
1115C2#1308181511yescharacteristic
1116C2#1308181611yescharacteristic
1117C2#1308240211yescharacteristic
1118C2#1308240711yescharacteristic
1119C2#1308250611yescharacteristic
1120C2#1308250911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2367D11
hypocenterC11#34211
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×#10623103C2semidirect
4. #13071692C2semidirect
5. #13071691C2semidirect
6. #13071689C2semidirect
7. #13071687C2semidirect
8. #13071686C2semidirect
9. #13071685C2semidirect
10. #13071683C2semidirect
11. #13071464C2semidirect
12. #13071463C2semidirect
13. #13071460C2semidirect
14. #13071459C2semidirect
15. #13071325C2semidirect
16. #13071322C2semidirect
17. #13071199C2semidirect
19. #13071157C2semidirect
20. C4×#66938C2semidirect
21. #13071020C2semidirect
22. C4×#66945C2semidirect
23. C11×#2367C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
35. D11×#124C4semidirect
42. C2×#66940C22semidirect
43. C2×#66940C22semidirect
56. C2×C4×Dic22C22semidirect
57. C2×C4×Dic22C22semidirect
58. C11×#391C22semidirect
60. C11×#388C22semidirect
61. C11×#388C22semidirect
62. C11×#385C22semidirect
63. C4×C11×C4⋊C4C22semidirect
64. C4×C11×C4⋊C4C22semidirect
65. C4×C11×C22⋊C4C22semidirect
66. #10622843C22semidirect
68. #10622823C22semidirect
69. C4×C22⋊Dic11C22semidirect
70. #10622603C22semidirect
71. #10622603C22semidirect
72. #10622602C22semidirect
73. #10622602C22semidirect
77. #10622589C22semidirect
78. #10622589C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622587C22semidirect
86. #10622564C22semidirect
87. #10622564C22semidirect
88. #10622563C22semidirect
89. #10622559C22semidirect
90. #10622558C22semidirect
91. #10622558C22semidirect
92. #10622557C22semidirect
93. #10622557C22semidirect
94. C22⋊C4×Dic11C22semidirect
95. C22⋊C4×Dic11C22semidirect
96. #10622553C22semidirect
97. #10622553C22semidirect
100. C4×(C2×D11)⋊C4C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. C4×C4⋊Dic11C22semidirect
103. C4×C4⋊Dic11C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. C4×Dic11⋊C4C22semidirect
106. C42×Dic11C22semidirect
107. #10622542C22semidirect
108. #10622283C22semidirect
109. #10622283C22semidirect
110. #10622282C22semidirect
111. #10622282C22semidirect
112. #10622281C22semidirect
113. #10622281C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
121. #10622263C22semidirect
122. #10622263C22semidirect
123. #10622261C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
134. C2×Q8×D11C2×C4semidirect
147. C11×#124C2×C4semidirect
170. #67000C2×C4semidirect
172. #66989C2×C4semidirect
226. #66938C2×C4semidirect
227. #66938C2×C4semidirect
230. C22⋊C4×D11C2×C4semidirect
231. C22⋊C4×D11C2×C4semidirect
232. #66928C2×C4semidirect
237. C42×D11C2×C4semidirect
409. #2367D11semidirect
541. C2×C4×Q8C2×D11semidirect
564. #391C2×D11semidirect
585. #388C2×D11semidirect
586. #388C2×D11semidirect
594. #385C2×D11semidirect
613. C4×C4⋊C4C2×D11semidirect
614. C4×C4⋊C4C2×D11semidirect
624. C4×C22⋊C4C2×D11semidirect
702. #124C4×D11semidirect
958. C11#34211semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1242
C2×#106231032
C2×#106230762
#130716922
#130716912
#130716892
#130716872
#130716862
#130716852
#130716832
#130714642
#130714632
#130714602
#130714592
#130713252
#130713222
#130711992
#130711952
#130711572
C4×#669382
#130710202
C4×#669452
C11×#23672
#3421111