Finite Group Databasebeta

← #14926059

Subgroups — #14926059

Order 2816.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623059C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074246C211yesmaximal, characteristic, complemented
4#13074244C211yesmaximal, characteristic, complemented
5#13074238C211yesmaximal, characteristic, complemented
6#13074236C211yesmaximal, characteristic, complemented
7#13073811C212yesmaximal, complemented
8#13073582C212yesmaximal, complemented
9#13073103C211yesmaximal, characteristic, complemented
10#13073089C211yesmaximal, characteristic, complemented
11#13072262C211yesmaximal, characteristic, complemented
12#13072248C211yesmaximal, characteristic
13#13071996C212yesmaximal, complemented
14#13071994C212yesmaximal, complemented
15#13071856C211yesmaximal, characteristic, complemented
16#13071854C211yesmaximal, characteristic, complemented
17#13071852C211yesmaximal, characteristic, complemented
18C4×#66993C212yesmaximal, complemented
19C4×#66938C212yesmaximal, complemented
20C4×#66935C212yesmaximal, complemented
21C4×#66990C212yesmaximal, complemented
22C4×#66945C211yesmaximal, characteristic, complemented
23C11×#2392C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2212yescomplemented
28C2×C11×#117C2211yescharacteristic, complemented
29C2×#66993C2212yes—
30C2×#66990C2212yes—
31C2×D4×Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2212yescomplemented
36C2×C4×C22⋊D11C2212yescomplemented
37C4×D4×D11—28no—
38#10623059—28no—
39C2×#66951C2211yescharacteristic, complemented
40C2×#66949C2211yescharacteristic
41C2×#66947C2211yescharacteristic
42C2×#66946C2211yescharacteristic
43C2×#66945C2212yes—
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×#66942C2211yescharacteristic, complemented
46C2×#66938C2212yes—
47C2×#66938C2211yescharacteristic, complemented
48C2×#66937C2211yescharacteristic
49C2×#66936C2211yescharacteristic
50C2×#66935C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×#66932C2211yescharacteristic, complemented
54C2×C4×D44C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic
56C2×C4×D44C2212yescomplemented
57C2×#66925C2211yescharacteristic, complemented
58C2×C42×D11C2211yescharacteristic
59C2×C4×Dic22C2211yescharacteristic, complemented
60C11×#398C2211yescharacteristic, complemented
61C11×#397C2211yescharacteristic, complemented
62C11×#396C2212yescomplemented
63C11×#394C2211yescharacteristic
64C11×#394C2212yescomplemented
65C11×#392C2211yescharacteristic
66C4×C11×C4⋊C4C2211yescharacteristic, complemented
67C4×C11×C22⋊C4C2212yescomplemented
68#10622836C2211yescharacteristic
69#10622835C2211yescharacteristic
70#10622834C2212yescomplemented
71#10622833C2212yescomplemented
72C4×C22⋊Dic11C2212yescomplemented
73#10622607C2212yescomplemented
74#10622607C2212yescomplemented
75#10622606C2211yescharacteristic, complemented
76#10622604C2211yescharacteristic
77#10622604C2212yescomplemented
78#10622602C2212yes—
79#10622602C2212yescomplemented
80#10622601C2212yescomplemented
81#10622596C2211yescharacteristic, complemented
82#10622593C2211yescharacteristic, complemented
83#10622589C2212yescomplemented
84C4⋊C4×Dic11C2212yescomplemented
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622573C2211yescharacteristic
88#10622571C2212yescomplemented
89#10622570C2212yes—
90#10622570C2212yes—
91#10622570C2212yescomplemented
92#10622570C2212yescomplemented
93#10622570C2212yescomplemented
94#10622569C2212yes—
95#10622569C2212yescomplemented
96#10622568C2212yes—
97#10622568C2212yes—
98#10622566C2211yescharacteristic, complemented
99#10622564C2212yescomplemented
100#10622563C2212yescomplemented
101#10622561C2212yescomplemented
102#10622559C2212yescomplemented
103#10622557C2212yescomplemented
104C4×(C2×D11)⋊C4C2212yes—
105C4×(C2×D11)⋊C4C2212yescomplemented
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108C42×Dic11C2212yescomplemented
109#10622287C2211yescharacteristic, complemented
110#10622285C2211yescharacteristic
111#10622284C2211yescharacteristic
112#10622283C2212yescomplemented
113#10622282C2212yescomplemented
114#10622281C2212yes—
115#10622281C2212yescomplemented
116#10622279C2211yescharacteristic
117#10622279C2211yescharacteristic
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622274C2211yescharacteristic, complemented
121#10622263C2212yescomplemented
122#10622261C2211yescharacteristic, complemented
123#10622261C2211yescharacteristic, complemented
124#10622259C2212yescomplemented
125C24×D11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C23×Dic11C2312yes—
136C2×D4×D11—28no—
137C2×D4×D11—24no—
138C22×D44C2311yescharacteristic
139C22×D44C2311yescharacteristic
140C22×D44C2312yes—
141C22×C4×D11—28no—
142C22×C4×D11—44no—
143C22×C4×D11—44no—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C4×D4×C11—24no—
153C4×D4×C11—44no—
154C11×#117—24no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177#66993—28no—
178#66990—28no—
179D4×Dic11—24no—
180C4×C22⋊D11—24no—
181C4×C22⋊D11—24no—
182C4×C22⋊D11—28no—
183C4×C22⋊D11—44no—
184C4×C22⋊D11—44no—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226#66951—24no—
227#66949—24no—
228#66947—24no—
229#66946—24no—
230#66945—28no—
231C4⋊C4×D11—24no—
232#66942—24no—
233#66938—28no—
234#66938—24no—
235#66937—24no—
236#66936—24no—
237#66935—28no—
238(C22⋊D11)⋊C4—28no—
239C22⋊C4×D11—28no—
240#66932—24no—
241C4×D44—24no—
242C4×D44—24no—
243C4×D44—44no—
244#66925—24no—
245C42×D11D418yescomplemented
246C4×Dic22—24no—
247C11×#95C2312yes—
248C11×#95C2311yescharacteristic
249C11×#95C2311yescharacteristic
250C11×#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#34965—111nomaximal, Sylow
262C24×C11C2411yescharacteristic
263C24×C11C2412yes—
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—24no—
268C23×D11—24no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11C2411yescharacteristic
272C23×D11C2412yes—
273C23×D11C2411yescharacteristic
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—22no—
277C2×D4×C11—24no—
278C2×D4×C11—42no—
279C22×C4×C11—22no—
280C22×C4×C11—24no—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C2×C22⋊D11—24no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11#4118yes—
307C22×Dic11—24no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319D4×D11—232no—
320C2×D44—22no—
321C2×D44—24no—
322C2×D44—24no—
323C2×D44—24no—
324C2×D44—22no—
325C2×D44—24no—
326C2×D44—42no—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—432no—
344C2×C4×D11C2×D414yes—
345C2×C4×D11C2×D414yes—
346C2×C4×D11C2×D414yes—
347C2×Dic22—22no—
348C2×Dic22—24no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—22no—
351C11×C4⋊C4—22no—
352C11×C4⋊C4—24no—
353C11×C4⋊C4—42no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—24no—
357C11×C22⋊C4—22no—
358C11×C22⋊C4—24no—
359C11×C22⋊C4—42no—
360C11×C22⋊C4—42no—
361C42×C11—22no—
362C42×C11—24no—
363C42×C11C2×D414yes—
364C22⋊Dic11—22no—
365C22⋊Dic11—22no—
366C22⋊Dic11—24no—
367C22⋊Dic11—24no—
368C22⋊Dic11—24no—
369C22⋊Dic11—42no—
370C22⋊Dic11—42no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4#4118yes—
389C4⋊Dic11—22no—
390C4⋊Dic11—22no—
391C4⋊Dic11—24no—
392C4⋊Dic11—22no—
393C4⋊Dic11—42no—
394Dic11⋊C4—22no—
395Dic11⋊C4—22no—
396Dic11⋊C4—24no—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—42no—
402Dic11⋊C4—42no—
403C4×Dic11—24no—
404C4×Dic11—24no—
405C4×Dic11—24no—
406C4×Dic11—22no—
407C4×Dic11—24no—
408C4×Dic11—24no—
409C4×Dic11C2×D414yes—
410C4×Dic11C2×D414yes—
411C4×Dic11C2×D414yes—
412C2×#529—111no—
413C22×C4×D4—111no—
414#2603—111no—
415#2603—111no—
416#2603—111no—
417#2603—111no—
418#2566—112no—
419#2544—112no—
420#2504—111no—
421#2502—111no—
422#2435—111no—
423#2433—111no—
424#2411—112no—
425#2411—112no—
426#2392—111no—
427#2392—111no—
428#2392—111no—
429#2392D1111yescharacteristic, complemented
430C4×#127—112no—
431C4×#124—112no—
432C4×#120—112no—
433C4×#120—112no—
434C4×#117—111no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11C2×#4114yes—
447C23×C11C2511yescharacteristic
448C22×D11—22no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—216no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—48no—
464C22×D11—48no—
465C22×D11—48no—
466C22×D11—48no—
467C22×D11—48no—
468C22×D11—48no—
469C22×D11C22×D412yes—
470C22×D11C2×#4114yes—
471C22×D11C2×#4114yes—
472D4×C11—28no—
473D4×C11—48no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—48no—
492C2×C4×C11—44no—
493C2×C4×C11C22×D412yes—
494C2×C4×C11C22×D412yes—
495C2×C4×C11C22×D412yes—
496C2×C4×C11C2×#4114yes—
497C2×C4×C11H(5,𝔽2)12yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C22⋊D11—216no—
500C22⋊D11—48no—
501C22⋊D11—48no—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—48no—
523C2×Dic11C22×D412yes—
524C2×Dic11C22×D412yes—
525C2×Dic11C22×D412yes—
526C2×Dic11C2×#4114yes—
527C2×Dic11C2×#4114yes—
528D44—28no—
529D44—48no—
530D44—44no—
531C4×D11—28no—
532C4×D11—28no—
533C4×D11—28no—
534C4×D11—48no—
535C4×D11—48no—
536C4×D11—44no—
537C4×D11—48no—
538Dic22—44no—
539C23×D4—111no—
540C24×C4—112no—
541C2×#127—112no—
542#529—228no—
543C2×#126—111no—
544C2×#126—111no—
545C2×#125—111no—
546C2×#124—112no—
547C2×#124—111no—
548C2×#123—111no—
549C2×#123—111no—
550C2×C22⋊Q8—111no—
551C2×#121—111no—
552C2×#120—112no—
553C2×#120—112no—
554C2×C4×Q8—111no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—112no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—112no—
561C2×C4×D4—111no—
562C2×C4×D4—112no—
563C2×C4×D4—111no—
564C2×C4×D4—111no—
565C2×C4×D4—112no—
566C2×C4×D4—228no—
567C2×C4×D4C2×D1111yescharacteristic
568C2×C4×D4C2×D1112yescomplemented
569C2×#117—112no—
570C2×#117—111no—
571C2×#117C2×D1111yescharacteristic, complemented
572C22×C4⋊C4—111no—
573C22×C22⋊C4—112no—
574C22×C42—111no—
575#398—111no—
576#398—111no—
577#398—111no—
578#398C2×D1111yescharacteristic, complemented
579#397—111no—
580#397—111no—
581#397—111no—
582#397C2×D1111yescharacteristic, complemented
583#396—112no—
584#396—112no—
585#396—112no—
586#396C2×D1112yescomplemented
587#394—111no—
588#394—111no—
589#394—112no—
590#394—112no—
591#394—112no—
592#394—111no—
593#394C2×D1111yescharacteristic
594#394C2×D1112yescomplemented
595#392—111no—
596#392—111no—
597#392—111no—
598#392C2×D1111yescharacteristic
599#391—112no—
600#390—112no—
601#390—112no—
602#390—112no—
603#390—112no—
604#390—112no—
605#390—112no—
606#390—112no—
607#388—112no—
608#388—112no—
609#388—112no—
610#388—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#385—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#384—112no—
624#382—112no—
625#379—112no—
626#379—112no—
627C4×C4⋊C4—112no—
628C4×C4⋊C4—111no—
629C4×C4⋊C4C2×D1111yescharacteristic, complemented
630C4×C22⋊C4—112no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4C2×D1112yescomplemented
637#376—111no—
638#376—111no—
639C43—112no—
640C22×C11—24no—
641C22×C11—24no—
642C22×C11—24no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—41no—
648C22×C11—41no—
649C22×C11—41no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11C23×D411yescharacteristic
653C22×C11C22×#4112yes—
654C22×C11C22×#4112yes—
655C22×C11C2×H(5,𝔽2)11yescharacteristic
656C22×C11C2×H(5,𝔽2)11yescharacteristic
657C2×D11—22no—
658C2×D11—22no—
659C2×D11—24no—
660C2×D11—24no—
661C2×D11—24no—
662C2×D11—24no—
663C2×D11—24no—
664C2×D11—432no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11—41no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11#53214yes—
675C4×C11—22no—
676C4×C11—22no—
677C4×C11—24no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11—41no—
681C4×C11—42no—
682C4×C11—42no—
683C4×C11#53514yes—
684Dic11—22no—
685Dic11—22no—
686Dic11—24no—
687Dic11—41no—
688Dic11—41no—
689Dic11—42no—
690Dic11—41no—
691Dic11—42no—
692Dic11#52514yes—
693C25—112no—
694C22×Q8—111no—
695C22×D4—112no—
696C22×D4—111no—
697C22×D4—111no—
698C22×D4—112no—
699C22×D4—112no—
700C22×D4—111no—
701C22×D4—111no—
702C22×D4—112no—
703C22×D4—224no—
704C22×D4—228no—
705C22×D4C22×D1111yescharacteristic
706C22×D4C22×D1112yes—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—112no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—112no—
714C23×C4—112no—
715C23×C4—228no—
716C23×C4—444no—
717C23×C4—444no—
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1112yes—
720#127—228no—
721#126—224no—
722#126—224no—
723#125—224no—
724#124—224no—
725#124—228no—
726#123—224no—
727#123—224no—
728C22⋊Q8—224no—
729#121—224no—
730#120—228no—
731#120—228no—
732C4×Q8—224no—
733C4×D4—24no—
734C4×D4—44no—
735C4×D4—224no—
736C4×D4—228no—
737C4×D4—224no—
738C4×D4—228no—
739C4×D4—224no—
740C4×D4—224no—
741C4×D4—224no—
742C4×D4—224no—
743C4×D4—444no—
744C4×D4—444no—
745C4×D4—444no—
746#117—24no—
747#117—228no—
748#117—224no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—224no—
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C4⋊C4C22×D1112yes—
766C2×C4⋊C4C22×D1111yescharacteristic
767C2×C4⋊C4C22×D1111yescharacteristic
768C2×C4⋊C4C22×D1112yes—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—228no—
795C2×C22⋊C4C22×D1112yes—
796C2×C22⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—118no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—111no—
811C2×C42—112no—
812C2×C42C22×D1111yescharacteristic
813C2×C42C22×D1112yes—
814C2×C42C22×D1111yescharacteristic
815#95—112no—
816#95—112no—
817#95—111no—
818#95—111no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95C22×D1111yescharacteristic
826#95C22×D1111yescharacteristic
827#95C22×D1112yes—
828#95C22×D1112yes—
829C2×C11—44no—
830C2×C11—81no—
831C2×C11C2×#52511yescharacteristic
832C2×C11C2×#53211yescharacteristic
833C2×C11C2×#53511yescharacteristic
834C2×C11#348112yes—
835C2×C11#348112yes—
836D11—24no—
837D11—44no—
838D11—81no—
839C24—111no—
840C24—112no—
841C24—111no—
842C24—224no—
843C24—224no—
844C24—224no—
845C24—224no—
846C24—224no—
847C24—442no—
848C24—442no—
849C24C23×D1111yescharacteristic
850C24C23×D1112yes—
851C2×Q8—222no—
852C2×Q8—224no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—42no—
858C2×D4—118no—
859C2×D4—224no—
860C2×D4—222no—
861C2×D4—224no—
862C2×D4—224no—
863C2×D4—224no—
864C2×D4—224no—
865C2×D4—222no—
866C2×D4—224no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—2232no—
870C2×D4—222no—
871C2×D4—224no—
872C2×D4—224no—
873C2×D4—224no—
874C2×D4—222no—
875C2×D4—224no—
876C2×D4—442no—
877C2×D4—442no—
878C2×D4—442no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—22no—
882C22×C4—24no—
883C22×C4—22no—
884C22×C4—24no—
885C22×C4—111no—
886C22×C4—112no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—114no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—112no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—112no—
896C22×C4—111no—
897C22×C4—224no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—224no—
906C22×C4—222no—
907C22×C4—224no—
908C22×C4—222no—
909C22×C4—224no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—4432no—
915C22×C4—442no—
916C22×C4—442no—
917C22×C4C23×D1112yes—
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1112yes—
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C22×C4C23×D1111yescharacteristic
924C22×C4C23×D1112yes—
925C22×C4C23×D1111yescharacteristic
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—24no—
930C4⋊C4—42no—
931C4⋊C4—224no—
932C4⋊C4—224no—
933C4⋊C4—222no—
934C4⋊C4—222no—
935C4⋊C4—222no—
936C4⋊C4—222no—
937C4⋊C4—222no—
938C4⋊C4—222no—
939C4⋊C4—222no—
940C4⋊C4—222no—
941C4⋊C4—222no—
942C4⋊C4—442no—
943C4⋊C4—442no—
944C4⋊C4—442no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—24no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—118no—
953C22⋊C4—224no—
954C22⋊C4—222no—
955C22⋊C4—222no—
956C22⋊C4—224no—
957C22⋊C4—224no—
958C22⋊C4—222no—
959C22⋊C4—222no—
960C22⋊C4—224no—
961C22⋊C4—224no—
962C22⋊C4—224no—
963C22⋊C4—222no—
964C22⋊C4—222no—
965C22⋊C4—224no—
966C22⋊C4—224no—
967C22⋊C4—224no—
968C22⋊C4—222no—
969C22⋊C4—222no—
970C22⋊C4—224no—
971C22⋊C4—442no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C42—22no—
978C42—24no—
979C42—114no—
980C42—114no—
981C42—114no—
982C42—224no—
983C42—224no—
984C42—224no—
985C42—222no—
986C42—224no—
987C42—224no—
988C42D4×D1114yes—
989C11#3496511yescharacteristic, complemented, Sylow
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—21no—
997C23—21no—
998C23—22no—
999C23—22no—
1000C23—21no—
1001C23—112no—
1002C23—114no—
1003C23—114no—
1004C23—2216no—
1005C23—221no—
1006C23—222no—
1007C23—221no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—221no—
1015C23—221no—
1016C23—222no—
1017C23—222no—
1018C23—221no—
1019C23—448no—
1020C23—448no—
1021C23—448no—
1022C23—448no—
1023C23—448no—
1024C23—448no—
1025C23#41×D1114yes—
1026C23C24×D1111yescharacteristic
1027Q8—444no—
1028D4—28no—
1029D4—48no—
1030D4—228no—
1031D4—2216no—
1032D4—448no—
1033D4—444no—
1034D4—444no—
1035D4—448no—
1036D4—448no—
1037D4—444no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—112no—
1058C2×C4—114no—
1059C2×C4—112no—
1060C2×C4—112no—
1061C2×C4—114no—
1062C2×C4—228no—
1063C2×C4—228no—
1064C2×C4—221no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—228no—
1070C2×C4—221no—
1071C2×C4—221no—
1072C2×C4—221no—
1073C2×C4—222no—
1074C2×C4—221no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—448no—
1084C2×C4—448no—
1085C2×C4—448no—
1086C2×C4—448no—
1087C2×C4—444no—
1088C2×C4C2×D4×D1112yes—
1089C2×C4C2×D4×D1112yes—
1090C2×C4C2×D4×D1112yes—
1091C2×C4#6703712yes—
1092C2×C4#41×D1114yes—
1093C2×C4#6704212yes—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—41no—
1102C22—41no—
1103C22—42no—
1104C22—42no—
1105C22—41no—
1106C22—114no—
1107C22—222no—
1108C22—224no—
1109C22—224no—
1110C22—222no—
1111C22—224no—
1112C22—224no—
1113C22—224no—
1114C22—4432no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—441no—
1120C22—441no—
1121C22—442no—
1122C22—442no—
1123C22—441no—
1124C22C22×D4×D1111yescharacteristic
1125C22C2×#6703711yescharacteristic
1126C22C2×#41×D1112yes—
1127C22C2×#41×D1112yes—
1128C22C2×#6704211yescharacteristic
1129C4—22no—
1130C4—24no—
1131C4—22no—
1132C4—41no—
1133C4—42no—
1134C4—41no—
1135C4—42no—
1136C4—41no—
1137C4—114no—
1138C4—222no—
1139C4—222no—
1140C4—224no—
1141C4—441no—
1142C4—442no—
1143C4—441no—
1144C4—442no—
1145C4—441no—
1146C4#1062313814yes—
1147C2—44no—
1148C2—81no—
1149C2—224no—
1150C2—444no—
1151C2—881no—
1152C2D11×#52511yescharacteristic
1153C2D11×#53211yescharacteristic
1154C2C2×#1062313811yescharacteristic
1155C2#1308221812yes—
1156C2#1308222212yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2392C2
prime radical#13072248C2
hypercenter#2392D11
hypocenterC11#34965
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C2×#10623059C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074246C2semidirect
4. #13074244C2semidirect
5. #13074238C2semidirect
6. #13074236C2semidirect
7. #13073811C2semidirect
8. #13073582C2semidirect
9. #13073103C2semidirect
10. #13073089C2semidirect
11. #13072262C2semidirect
13. #13071996C2semidirect
14. #13071994C2semidirect
15. #13071856C2semidirect
16. #13071854C2semidirect
17. #13071852C2semidirect
18. C4×#66993C2semidirect
19. C4×#66938C2semidirect
20. C4×#66935C2semidirect
21. C4×#66990C2semidirect
22. C4×#66945C2semidirect
23. C11×#2392C2semidirect
27. C2×C4×D4×C11C22semidirect
28. C2×C11×#117C22semidirect
34. C2×C4×C22⋊D11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
39. C2×#66951C22semidirect
45. C2×#66942C22semidirect
47. C2×#66938C22semidirect
53. C2×#66932C22semidirect
56. C2×C4×D44C22semidirect
57. C2×#66925C22semidirect
59. C2×C4×Dic22C22semidirect
60. C11×#398C22semidirect
61. C11×#397C22semidirect
62. C11×#396C22semidirect
64. C11×#394C22semidirect
66. C4×C11×C4⋊C4C22semidirect
67. C4×C11×C22⋊C4C22semidirect
70. #10622834C22semidirect
71. #10622833C22semidirect
72. C4×C22⋊Dic11C22semidirect
73. #10622607C22semidirect
74. #10622607C22semidirect
75. #10622606C22semidirect
77. #10622604C22semidirect
79. #10622602C22semidirect
80. #10622601C22semidirect
81. #10622596C22semidirect
82. #10622593C22semidirect
83. #10622589C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
88. #10622571C22semidirect
91. #10622570C22semidirect
92. #10622570C22semidirect
93. #10622570C22semidirect
95. #10622569C22semidirect
98. #10622566C22semidirect
99. #10622564C22semidirect
100. #10622563C22semidirect
101. #10622561C22semidirect
102. #10622559C22semidirect
103. #10622557C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C42×Dic11C22semidirect
109. #10622287C22semidirect
112. #10622283C22semidirect
113. #10622282C22semidirect
115. #10622281C22semidirect
119. #10622278C22semidirect
120. #10622274C22semidirect
121. #10622263C22semidirect
122. #10622261C22semidirect
123. #10622261C22semidirect
124. #10622259C22semidirect
245. C42×D11D4semidirect
429. #2392D11semidirect
568. C2×C4×D4C2×D11semidirect
571. C2×#117C2×D11semidirect
578. #398C2×D11semidirect
582. #397C2×D11semidirect
586. #396C2×D11semidirect
594. #394C2×D11semidirect
629. C4×C4⋊C4C2×D11semidirect
636. C4×C22⋊C4C2×D11semidirect
989. C11#34965semidirect

Maximal subgroups

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

subgroupindex
C2×#106230592
C2×C4×D4×D112
#130742462
#130742442
#130742382
#130742362
#130738112
#130735822
#130731032
#130730892
#130722622
#130722482
#130719962
#130719942
#130718562
#130718542
#130718522
C4×#669932
C4×#669382
C4×#669352
C4×#669902
C4×#669452
C11×#23922
#3496511