Finite Group Databasebeta

← #14925905

Subgroups — #14925905

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074234C212yesmaximal, complemented
4#13074224C212yesmaximal, complemented
5#13074090C211yesmaximal, characteristic, complemented
6#13073990C211yesmaximal, characteristic, complemented
7#13073796C211yesmaximal, characteristic, complemented
8#13073792C211yesmaximal, characteristic, complemented
9#13073768C211yesmaximal, characteristic, complemented
10#13073578C211yesmaximal, characteristic, complemented
11#13073541C211yesmaximal, characteristic, complemented
12#13072011C212yesmaximal, complemented
13#13071987C212yesmaximal, complemented
14#13071880C211yesmaximal, characteristic, complemented
15#13071878C211yesmaximal, characteristic, complemented
16#13071830C211yesmaximal, characteristic, complemented
17#13071828C211yesmaximal, characteristic, complemented
18#13071143C212yesmaximal, complemented
19#121×Dic11C212yesmaximal, complemented
20#13071126C212yesmaximal, complemented
21#13071121C212yesmaximal, complemented
22C2×#10622279C211yesmaximal, characteristic, complemented
23C11×#2543C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#121C2212yes—
29C2×C11×#121C2211yescharacteristic, complemented
30C2×C4×D4×C11C2211yescharacteristic
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic
33C2×#66990C2212yes—
34C2×#66990C2212yes—
35C2×D4×Dic11C2211yescharacteristic
36C2×D4×Dic11C2212yescomplemented
37C2×D4×Dic11C2212yescomplemented
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2211yescharacteristic
40C22×(C2×D11)⋊C4C2212yes—
41C2×#66977C2211yescharacteristic, complemented
42C22×C4×Dic11C2212yescomplemented
43#10623137—28no—
44C4×D4×D11—28no—
45C2×#66950C2211yescharacteristic
46C2×#66946C2211yescharacteristic
47C2×#66945C2211yescharacteristic, complemented
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×#66936C2212yes—
50C2×#66936C2212yescomplemented
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2212yescomplemented
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C4×D44C2211yescharacteristic
58C2×C42×D11C2211yescharacteristic
59C11×#398C2211yescharacteristic, complemented
60C11×#397C2211yescharacteristic, complemented
61C11×#394C2211yescharacteristic, complemented
62C11×#392C2211yescharacteristic, complemented
63C11×#388C2212yescomplemented
64C11×#386C2212yescomplemented
65C11×#386C2212yescomplemented
66C2×C11×#95C2211yescharacteristic, complemented
67#10622836C2212yes—
68#10622836C2211yescharacteristic, complemented
69#10622835C2211yescharacteristic, complemented
70#10622834C2212yescomplemented
71#10622833C2212yes—
72#10622833C2212yescomplemented
73#10622826C2212yes—
74#10622825C2212yescomplemented
75#10622823C2212yescomplemented
76C2×C11⋊#95C2211yescharacteristic, complemented
77#10622606C2211yescharacteristic, complemented
78#10622604C2212yes—
79#10622602C2212yes—
80#10622599C2211yescharacteristic, complemented
81#10622598C2212yescomplemented
82#10622593C2211yescharacteristic, complemented
83#10622592C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2212yescomplemented
85#10622574C2212yescomplemented
86#10622573C2212yes—
87#10622572C2212yes—
88#10622572C2212yescomplemented
89#10622570C2212yescomplemented
90#10622569C2212yes—
91#10622569C2212yes—
92#10622569C2212yescomplemented
93#10622568C2212yes—
94#10622564C2212yescomplemented
95#10622564C2212yescomplemented
96#10622562C2211yescharacteristic, complemented
97#10622560C2211yescharacteristic, complemented
98#10622557C2212yescomplemented
99#10622557C2212yescomplemented
100#10622555C2212yescomplemented
101C22⋊C4×Dic11C2212yescomplemented
102C22⋊C4×Dic11C2212yescomplemented
103C22⋊C4×Dic11C2212yescomplemented
104#10622546C2212yescomplemented
105#10622290C2211yescharacteristic, complemented
106#10622288C2212yescomplemented
107#10622287C2212yescomplemented
108#10622286C2211yescharacteristic, complemented
109#10622283C2212yescomplemented
110#10622281C2212yes—
111#10622281C2212yescomplemented
112#10622279C2212yes—
113#10622279C2211yescharacteristic
114#10622279C2211yescharacteristic
115#10622279C2211yescharacteristic, complemented
116#10622279C2212yescomplemented
117#10622279C2211yescharacteristic, complemented
118#10622279C2212yescomplemented
119#10622277C2212yes—
120#10622272C2211yescharacteristic, complemented
121#10622269C2211yescharacteristic, complemented
122#10622266C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2312yes—
139C23×Dic11C2312yes—
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2312yes—
142C23×Dic11C2311yescharacteristic
143C2×#4341—24no—
144C2×#4341—44no—
145C2×D4×D11—24no—
146C2×D4×D11—24no—
147C2×D4×D11—24no—
148C22×D44C2311yescharacteristic
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11—44no—
152C22×C4×D11D418yescomplemented
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×Dic22C2311yescharacteristic
163C11×#121—28no—
164C11×#121—24no—
165C4×D4×C11—24no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C42×C11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186#66992—28no—
187#66991—24no—
188#66990—28no—
189#66990—28no—
190D4×Dic11—24no—
191D4×Dic11—28no—
192D4×Dic11—44no—
193C4×C22⋊D11—24no—
194C4×C22⋊D11—24no—
195C2×(C2×D11)⋊C4—28no—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2312yes—
214#66977—24no—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×C4×Dic11—44no—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230#66950—24no—
231#66946—24no—
232#66945—24no—
233C4⋊C4×D11—24no—
234#66936—28no—
235#66936—28no—
236(C22⋊D11)⋊C4—24no—
237(C22⋊D11)⋊C4—24no—
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—44no—
240C22⋊C4×D11—24no—
241C22⋊C4×D11—24no—
242C4×D44—24no—
243C42×D11—24no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2311yescharacteristic
248C11×#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262#34957—111nomaximal, Sylow
263C24×C11C2412yes—
264C24×C11C2411yescharacteristic
265C24×C11C2411yescharacteristic
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—24no—
271C23×D11—22no—
272C23×D11—24no—
273C23×D11—42no—
274C23×D11—42no—
275C23×D11C2×D414yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—24no—
285C2×D4×C11—22no—
286C2×D4×C11—24no—
287C2×D4×C11—42no—
288C2×D4×C11—42no—
289C2×D4×C11#4114yescomplemented
290C22×C4×C11—24no—
291C22×C4×C11—22no—
292C22×C4×C11—24no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11C2×D414yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2412yes—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11#4114yescomplemented
320C22×Dic11—24no—
321C22×Dic11—22no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—24no—
325C22×Dic11—24no—
326C22×Dic11—24no—
327C22×Dic11—24no—
328C22×Dic11—42no—
329C22×Dic11C2×D414yes—
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2412yes—
338C22×Dic11C2411yescharacteristic
339#4341—416no—
340D4×D11—232no—
341C2×D44—22no—
342C2×D44—22no—
343C2×D44—22no—
344C2×C4×D11—22no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—24no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—22no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—416no—
360C2×C4×D11—416no—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×Dic22—22no—
366C2×Dic22—42no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—24no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—42no—
377C42×C11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—24no—
380C22⋊Dic11—24no—
381C22⋊Dic11—24no—
382C22⋊Dic11—24no—
383C22⋊Dic11—22no—
384C22⋊Dic11—24no—
385C22⋊Dic11—42no—
386C22⋊Dic11—42no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4#4118yescomplemented
400C4⋊Dic11—22no—
401C4⋊Dic11—24no—
402C4⋊Dic11—22no—
403C4⋊Dic11—24no—
404C4⋊Dic11—42no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—22no—
410Dic11⋊C4—42no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—24no—
414C4×Dic11—24no—
415C4×Dic11—24no—
416C4×Dic11—22no—
417C4×Dic11—42no—
418C4×Dic11—42no—
419C2×#525—111no—
420C22×C4×D4—111no—
421#2602—112no—
422#2602—112no—
423#2591—111no—
424#2583—111no—
425#2564—111no—
426#2564—111no—
427#2561—111no—
428#2543—111no—
429#2543D1111yescharacteristic, complemented
430#2539—111no—
431#2412—112no—
432#2410—112no—
433#2395—111no—
434#2395—111no—
435#2388—111no—
436#2388—111no—
437C4×#123—112no—
438C4×#121—112no—
439C4×#121—112no—
440C4×#120—112no—
441C2×C4×C22⋊C4—111no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—21no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11C22×D412yes—
456C23×C11C2×#4112yes—
457C23×C11C2×#4112yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—21no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—28no—
474C22×D11—44no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11C22×D412yes—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4114yes—
485D4×C11—28no—
486D4×C11—48no—
487D4×C11—44no—
488D4×C11—48no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
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—22no—
505C2×C4×C11—44no—
506C2×C4×C11—48no—
507C2×C4×C11—44no—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C2×#4112yes—
511C2×C4×C11C2×#4114yes—
512C22⋊D11—28no—
513C22⋊D11—28no—
514C22⋊D11—48no—
515C22⋊D11—48no—
516C22⋊D11—48no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—28no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—48no—
537C2×Dic11—44no—
538C2×Dic11—48no—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C2×#4112yes—
542C2×Dic11C2×#4114yes—
543C2×Dic11H(5,𝔽2)14yes—
544D44—28no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—28no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11—44no—
554Dic22—44no—
555C22×#41—111no—
556C23×D4—111no—
557C24×C4—111no—
558C24×C4—111no—
559#525—228no—
560C2×#123—112no—
561C2×#123—112no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8—111no—
564C2×#121—111no—
565C2×#121—112no—
566C2×#121C2×D1112yes—
567C2×#121C2×D1111yescharacteristic, complemented
568C2×#120—112no—
569C2×#120—112no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—111no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C2×C4×D4—228no—
582C2×C4×D4C2×D1111yescharacteristic
583C2×#117—111no—
584C22×C4⋊C4—111no—
585C22×C22⋊C4—112no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C42—112no—
589C22×C42—111no—
590#400—111no—
591#400—111no—
592#399—111no—
593#399—111no—
594#398—111no—
595#398C2×D1111yescharacteristic, complemented
596#397—111no—
597#397—112no—
598#397—112no—
599#397C2×D1111yescharacteristic, complemented
600#395—111no—
601#395—111no—
602#394—111no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394C2×D1111yescharacteristic, complemented
608#393—111no—
609#393—111no—
610#392—112no—
611#392—111no—
612#392—112no—
613#392C2×D1111yescharacteristic, complemented
614#390—112no—
615#390—112no—
616#389—112no—
617#389—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388C2×D1112yescomplemented
624#387—112no—
625#387—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386C2×D1112yescomplemented
633#386C2×D1112yescomplemented
634#385—112no—
635#385—112no—
636#385—112no—
637#385—112no—
638#381—112no—
639#380—112no—
640#380—112no—
641#379—112no—
642C4×C4⋊C4—112no—
643C4×C4⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4—111no—
653C4×C22⋊C4—112no—
654C2×#95—111no—
655C2×#95C2×D1111yescharacteristic, complemented
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—22no—
661C22×C11—24no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11#52514yes—
673C22×C11C23×D411yescharacteristic
674C22×C11C22×#4111yescharacteristic
675C22×C11C22×#4111yescharacteristic
676C22×C11C22×#4112yes—
677C22×C11C2×H(5,𝔽2)12yes—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—24no—
681C2×D11—24no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—24no—
687C2×D11—416no—
688C2×D11—416no—
689C2×D11—41no—
690C2×D11—41no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11#53214yes—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—22no—
698C4×C11—24no—
699C4×C11—42no—
700C4×C11—41no—
701C4×C11—41no—
702C4×C11—42no—
703Dic11—22no—
704Dic11—22no—
705Dic11—24no—
706Dic11—41no—
707Dic11—42no—
708Dic11—42no—
709Dic11—41no—
710Dic11—42no—
711Dic11#53414yes—
712C25—111no—
713C25—111no—
714C2×#41—224no—
715C2×#41—444no—
716C22×Q8—111no—
717C22×D4—111no—
718C22×D4—111no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4—224no—
726C22×D4C22×D1112yes—
727C22×D4C22×D1112yes—
728C22×D4C22×D1111yescharacteristic
729C22×D4C22×D1111yescharacteristic
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—118no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—112no—
738C23×C4—112no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—224no—
745C23×C4—444no—
746C23×C4—444no—
747C23×C4C22×D1112yes—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic
750#123—228no—
751#123—228no—
752C22⋊Q8—224no—
753C22⋊Q8—224no—
754#121—28no—
755#121—24no—
756#121—224no—
757#121—228no—
758#120—228no—
759#120—228no—
760C4×D4—24no—
761C4×D4—224no—
762C4×D4—224no—
763C4×D4—224no—
764C4×D4—228no—
765C4×D4—224no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—228no—
769C4×D4—224no—
770C4×D4—444no—
771C4×D4—444no—
772#117—224no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—224no—
785C2×C4⋊C4C22×D1111yescharacteristic
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1112yes—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—224no—
811C2×C22⋊C4—224no—
812C2×C22⋊C4—228no—
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C42—112no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—224no—
829C2×C42—444no—
830C2×C42C22×D1111yescharacteristic
831#95—112no—
832#95—111no—
833#95—111no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95C22×D1112yes—
845#95C22×D1111yescharacteristic
846#95C22×D1111yescharacteristic
847#95C22×D1112yes—
848#95C22×D1112yes—
849C2×C11—24no—
850C2×C11—42no—
851C2×C11—82no—
852C2×C11C2×#52511yescharacteristic
853C2×C11C2×#53211yescharacteristic
854C2×C11C2×#53411yescharacteristic
855C2×C11#348112yes—
856C2×C11#348112yes—
857D11—24no—
858D11—42no—
859D11—42no—
860C24—111no—
861C24—111no—
862C24—111no—
863C24—114no—
864C24—222no—
865C24—224no—
866C24—222no—
867C24—224no—
868C24—222no—
869C24—222no—
870C24—222no—
871C24—442no—
872C24—442no—
873C24C23×D1112yes—
874C24C23×D1111yescharacteristic
875C24C23×D1111yescharacteristic
876#41—4416no—
877C2×Q8—222no—
878C2×Q8—442no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—22no—
886C2×D4—24no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—114no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—224no—
894C2×D4—2232no—
895C2×D4—222no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—222no—
905C2×D4—442no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4#434114yescomplemented
909C22×C4—24no—
910C22×C4—22no—
911C22×C4—24no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—111no—
916C22×C4—114no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—112no—
925C22×C4—111no—
926C22×C4—112no—
927C22×C4—111no—
928C22×C4—112no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—224no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—222no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—224no—
947C22×C4—222no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—4416no—
953C22×C4—4416no—
954C22×C4—442no—
955C22×C4D4×D1114yes—
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1112yes—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—24no—
967C4⋊C4—222no—
968C4⋊C4—222no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—224no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—442no—
977C4⋊C4—442no—
978C22⋊C4—22no—
979C22⋊C4—24no—
980C22⋊C4—22no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—42no—
985C22⋊C4—118no—
986C22⋊C4—222no—
987C22⋊C4—224no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C42—22no—
1008C42—222no—
1009C42—222no—
1010C42—224no—
1011C42—224no—
1012C42—224no—
1013C42—222no—
1014C42—442no—
1015C42—442no—
1016C11#3495711yescharacteristic, complemented, Sylow
1017C23—22no—
1018C23—22no—
1019C23—21no—
1020C23—22no—
1021C23—21no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—112no—
1031C23—114no—
1032C23—112no—
1033C23—112no—
1034C23—228no—
1035C23—228no—
1036C23—221no—
1037C23—221no—
1038C23—222no—
1039C23—228no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—222no—
1044C23—222no—
1045C23—221no—
1046C23—222no—
1047C23—222no—
1048C23—444no—
1049C23—448no—
1050C23—448no—
1051C23—448no—
1052C23—444no—
1053C23—448no—
1054C23—444no—
1055C23C2×D4×D1112yes—
1056C23C2×#434112yes—
1057C23C2×#434112yes—
1058C23#41×D1112yes—
1059C23C24×D1111yescharacteristic
1060Q8—444no—
1061D4—28no—
1062D4—48no—
1063D4—44no—
1064D4—48no—
1065D4—228no—
1066D4—228no—
1067D4—228no—
1068D4—448no—
1069D4—448no—
1070D4—448no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—44no—
1088C2×C4—48no—
1089C2×C4—44no—
1090C2×C4—112no—
1091C2×C4—114no—
1092C2×C4—112no—
1093C2×C4—114no—
1094C2×C4—112no—
1095C2×C4—228no—
1096C2×C4—228no—
1097C2×C4—228no—
1098C2×C4—228no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—444no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—448no—
1125C2×C4—448no—
1126C2×C4C2×D4×D1112yes—
1127C2×C4C2×D4×D1112yes—
1128C2×C4C2×#434112yes—
1129C2×C4#41×D1114yes—
1130C22—22no—
1131C22—22no—
1132C22—24no—
1133C22—24no—
1134C22—22no—
1135C22—24no—
1136C22—41no—
1137C22—41no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—114no—
1147C22—222no—
1148C22—222no—
1149C22—224no—
1150C22—224no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—224no—
1156C22—4416no—
1157C22—4416no—
1158C22—441no—
1159C22—441no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22#1062313714yes—
1164C22C22×D4×D1111yescharacteristic
1165C22C22×#434111yescharacteristic
1166C22C2×#41×D1111yescharacteristic
1167C22C2×#41×D1112yes—
1168C22D11×H(5,𝔽2)12yes—
1169C4—22no—
1170C4—22no—
1171C4—22no—
1172C4—24no—
1173C4—42no—
1174C4—41no—
1175C4—41no—
1176C4—42no—
1177C4—114no—
1178C4—222no—
1179C4—222no—
1180C4—224no—
1181C4—441no—
1182C4—442no—
1183C4—441no—
1184C4—442no—
1185C4—442no—
1186C2—24no—
1187C2—42no—
1188C2—82no—
1189C2—224no—
1190C2—442no—
1191C2—442no—
1192C2C2×#1062313711yescharacteristic
1193C2D11×#53211yescharacteristic
1194C2D11×#53411yescharacteristic
1195C2#1308222112yes—
1196C2#1308222312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2543C2
hypercenter#2543D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. C2×#10623137C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074234C2semidirect
4. #13074224C2semidirect
5. #13074090C2semidirect
6. #13073990C2semidirect
7. #13073796C2semidirect
8. #13073792C2semidirect
9. #13073768C2semidirect
10. #13073578C2semidirect
11. #13073541C2semidirect
12. #13072011C2semidirect
13. #13071987C2semidirect
14. #13071880C2semidirect
15. #13071878C2semidirect
16. #13071830C2semidirect
17. #13071828C2semidirect
18. #13071143C2semidirect
19. #121×Dic11C2semidirect
20. #13071126C2semidirect
21. #13071121C2semidirect
22. C2×#10622279C2semidirect
23. C11×#2543C2semidirect
24. C22×#4341C22semidirect
29. C2×C11×#121C22semidirect
36. C2×D4×Dic11C22semidirect
37. C2×D4×Dic11C22semidirect
41. C2×#66977C22semidirect
42. C22×C4×Dic11C22semidirect
47. C2×#66945C22semidirect
50. C2×#66936C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
59. C11×#398C22semidirect
60. C11×#397C22semidirect
61. C11×#394C22semidirect
62. C11×#392C22semidirect
63. C11×#388C22semidirect
64. C11×#386C22semidirect
65. C11×#386C22semidirect
66. C2×C11×#95C22semidirect
68. #10622836C22semidirect
69. #10622835C22semidirect
70. #10622834C22semidirect
72. #10622833C22semidirect
74. #10622825C22semidirect
75. #10622823C22semidirect
76. C2×C11⋊#95C22semidirect
77. #10622606C22semidirect
80. #10622599C22semidirect
81. #10622598C22semidirect
82. #10622593C22semidirect
83. #10622592C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622574C22semidirect
88. #10622572C22semidirect
89. #10622570C22semidirect
92. #10622569C22semidirect
94. #10622564C22semidirect
95. #10622564C22semidirect
96. #10622562C22semidirect
97. #10622560C22semidirect
98. #10622557C22semidirect
99. #10622557C22semidirect
100. #10622555C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. C22⋊C4×Dic11C22semidirect
104. #10622546C22semidirect
105. #10622290C22semidirect
106. #10622288C22semidirect
107. #10622287C22semidirect
108. #10622286C22semidirect
109. #10622283C22semidirect
111. #10622281C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
120. #10622272C22semidirect
121. #10622269C22semidirect
122. #10622266C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
152. C22×C4×D11D4semidirect
289. C2×D4×C11#41semidirect
319. C2×C22⋊D11#41semidirect
399. (C2×D11)⋊C4#41semidirect
429. #2543D11semidirect
567. C2×#121C2×D11semidirect
595. #398C2×D11semidirect
599. #397C2×D11semidirect
607. #394C2×D11semidirect
613. #392C2×D11semidirect
623. #388C2×D11semidirect
632. #386C2×D11semidirect
633. #386C2×D11semidirect
655. C2×#95C2×D11semidirect
908. C2×D4#4341semidirect
1016. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×C4×D4×D112
#130742342
#130742242
#130740902
#130739902
#130737962
#130737922
#130737682
#130735782
#130735412
#130720112
#130719872
#130718802
#130718782
#130718302
#130718282
#130711432
#121×Dic112
#130711262
#130711212
C2×#106222792
C11×#25432
#3495711