Finite Group Databasebeta

← #14926029

Subgroups — #14926029

Order 2816.

3270 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074184C211yesmaximal, characteristic, complemented
4#13074182C211yesmaximal, characteristic, complemented
5#13074176C211yesmaximal, characteristic, complemented
6#13073973C212yesmaximal, complemented
7#13073516C212yesmaximal, complemented
8#13072928C211yesmaximal, characteristic, complemented
9#13072926C211yesmaximal, characteristic, complemented
10#13072888C212yesmaximal, complemented
11#13071967C211yesmaximal, characteristic, complemented
12#13071965C211yesmaximal, characteristic, complemented
13#13071933C212yesmaximal, complemented
14#13071905C211yesmaximal, characteristic, complemented
15#13071904C211yesmaximal, characteristic, complemented
16#13071896C211yesmaximal, characteristic, complemented
17#13071894C211yesmaximal, characteristic, complemented
18#13071128C212yesmaximal, complemented
19#13071126C212yesmaximal, complemented
20#13071121C212yesmaximal, complemented
21#13071117C212yesmaximal, complemented
22#13071013C211yesmaximal, characteristic, complemented
23C11×#2598C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×#66992C2212yes—
30C2×#66990C2212yes—
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2212yescomplemented
33C2×C4×C22⋊D11C2212yes—
34C22×C4×Dic11C2211yescharacteristic, complemented
35C4×D4×D11—28no—
36#10623053—28no—
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic
39C2×#66946C2211yescharacteristic
40C2×#66946C2212yescomplemented
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66940C2211yescharacteristic, complemented
43C2×#66940C2211yescharacteristic, complemented
44C2×#66937C2212yes—
45C2×#66935C2212yes—
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
50C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
51C2×(C22⋊D11)⋊C4C2212yescomplemented
52C2×(C22⋊D11)⋊C4C2212yescomplemented
53C2×C22⋊C4×D11C2212yes—
54C2×C4×D44C2211yescharacteristic
55C2×#66925C2211yescharacteristic
56C2×#66925C2211yescharacteristic, complemented
57C2×C42×D11C2211yescharacteristic
58C2×C42×D11C2211yescharacteristic, complemented
59C11×#400C2211yescharacteristic, complemented
60C11×#399C2211yescharacteristic, complemented
61C11×#394C2211yescharacteristic
62C11×#392C2211yescharacteristic
63C11×#388C2212yescomplemented
64C11×#386C2212yescomplemented
65C11×#386C2212yescomplemented
66C11×#385C2212yescomplemented
67C11×#383C2211yescharacteristic, complemented
68#10622836C2211yescharacteristic
69#10622836C2212yescomplemented
70#10622835C2211yescharacteristic
71#10622826C2212yescomplemented
72#10622826C2212yescomplemented
73#10622823C2212yescomplemented
74#10622605C2211yescharacteristic, complemented
75#10622605C2212yescomplemented
76#10622604C2211yescharacteristic
77#10622602C2212yes—
78#10622602C2212yescomplemented
79#10622599C2211yescharacteristic, complemented
80#10622595C2211yescharacteristic, complemented
81#10622585C2212yescomplemented
82#10622573C2211yescharacteristic
83#10622573C2212yescomplemented
84#10622570C2212yes—
85#10622570C2212yes—
86#10622569C2212yes—
87#10622569C2212yescomplemented
88#10622569C2212yescomplemented
89#10622568C2212yes—
90#10622568C2212yes—
91#10622565C2212yescomplemented
92#10622562C2211yescharacteristic, complemented
93#10622562C2212yescomplemented
94#10622560C2212yescomplemented
95#10622557C2212yescomplemented
96#10622555C2212yescomplemented
97C22⋊C4×Dic11C2212yescomplemented
98C22⋊C4×Dic11C2212yescomplemented
99#10622553C2212yescomplemented
100#10622550C2211yescharacteristic, complemented
101#10622290C2211yescharacteristic, complemented
102#10622288C2212yescomplemented
103#10622286C2212yescomplemented
104#10622285C2211yescharacteristic
105#10622284C2211yescharacteristic
106#10622283C2212yescomplemented
107#10622281C2212yes—
108#10622281C2212yescomplemented
109#10622280C2211yescharacteristic
110#10622280C2211yescharacteristic
111#10622280C2212yescomplemented
112#10622279C2212yes—
113#10622279C2212yescomplemented
114#10622279C2212yescomplemented
115#10622278C2212yes—
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622277C2212yes—
119#10622272C2211yescharacteristic, complemented
120#10622263C2212yescomplemented
121#10622262C2212yescomplemented
122#10622261C2211yescharacteristic, complemented
123#10622261C2211yescharacteristic, complemented
124#10622260C2212yescomplemented
125C24×D11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2312yes—
138C2×D4×D11—28no—
139C2×D4×D11—24no—
140C2×#4339—24no—
141C2×#4339—24no—
142C2×#4339—24no—
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×C4×D11—28no—
147C22×C4×D11—44no—
148C22×C4×D11—44no—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2312yes—
158C22×Dic22C2311yescharacteristic
159C4×D4×C11—24no—
160C11×#117—24no—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#66992—28no—
180#66990—28no—
181D4×Dic11—24no—
182D4×Dic11—44no—
183C4×C22⋊D11—28no—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
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—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×C4×Dic11—24no—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222#66946—24no—
223#66946—24no—
224#66946—24no—
225#66946—44no—
226C4⋊C4×D11—24no—
227#66940—24no—
228#66940—24no—
229#66937—28no—
230#66935—28no—
231(C22⋊D11)⋊C4—24no—
232(C22⋊D11)⋊C4—24no—
233(C22⋊D11)⋊C4—28no—
234(C22⋊D11)⋊C4—24no—
235(C22⋊D11)⋊C4—24no—
236(C22⋊D11)⋊C4—44no—
237(C22⋊D11)⋊C4—44no—
238C22⋊C4×D11—28no—
239C4×D44—24no—
240#66925—24no—
241#66925—24no—
242C42×D11—24no—
243C42×D11D418yescomplemented
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262#34963—111nomaximal, Sylow
263C24×C11C2412yes—
264C24×C11C2411yescharacteristic
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—24no—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11C2412yes—
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×D4×C11—24no—
276C2×D4×C11—24no—
277C2×D4×C11—24no—
278C2×D4×C11—22no—
279C2×D4×C11—42no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—22no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11#4114yes—
309C2×C22⋊D11#4118yescomplemented
310C22×Dic11—22no—
311C22×Dic11—22no—
312C22×Dic11—24no—
313C22×Dic11—24no—
314C22×Dic11—24no—
315C22×Dic11—24no—
316C22×Dic11—24no—
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326D4×D11—232no—
327#4339—232no—
328C2×D44—22no—
329C2×D44—22no—
330C2×D44—24no—
331C2×D44—24no—
332C2×D44—24no—
333C2×D44—22no—
334C2×D44—42no—
335C2×D44#4114yes—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—24no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—432no—
357C2×C4×D11C2×D414yes—
358C2×C4×D11C2×D414yes—
359C2×C4×D11C2×D414yes—
360C2×Dic22—22no—
361C2×Dic22—22no—
362C2×Dic22—22no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—42no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—42no—
373C11×C22⋊C4—42no—
374C42×C11—22no—
375C42×C11C2×D414yes—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
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—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—22no—
415C4×Dic11C2×D414yes—
416C4×Dic11C2×D414yes—
417C4×Dic11C2×D414yes—
418C2×C4×#41—111no—
419C22×C4×D4—111no—
420#2598—111no—
421#2598—111no—
422#2598—111no—
423#2598D1111yescharacteristic, complemented
424#2580—112no—
425#2535—112no—
426#2487—111no—
427#2487—111no—
428#2482—112no—
429#2408—111no—
430#2408—111no—
431#2404—112no—
432#2398—111no—
433#2398—111no—
434#2397—111no—
435#2397—111no—
436C4×#121—112no—
437C4×#121—112no—
438C4×#120—112no—
439C4×#120—112no—
440#2283—111no—
441C23×C11—22no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11C2×#4114yes—
452C23×C11C2×#4112yes—
453C23×C11C2511yescharacteristic
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—216no—
457C22×D11—21no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—48no—
468C22×D11—48no—
469C22×D11—48no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11C22×D412yes—
474C22×D11C2×#4114yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477C22×D11C2×#4112yes—
478D4×C11—28no—
479D4×C11—48no—
480C2×C4×C11—28no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—48no—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C22⋊D11—28no—
506C22⋊D11—28no—
507C22⋊D11—216no—
508C22⋊D11—48no—
509C22⋊D11—48no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—44no—
528C2×Dic11—48no—
529C2×Dic11—44no—
530C2×Dic11C22×D412yes—
531C2×Dic11C22×D412yes—
532C2×Dic11C22×D412yes—
533C2×Dic11C2×#4112yes—
534C2×Dic11C2×#4114yes—
535C2×Dic11H(5,𝔽2)14yes—
536D44—28no—
537D44—28no—
538D44—48no—
539C4×D11—28no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—28no—
543C4×D11—48no—
544C4×D11—48no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—48no—
548Dic22—28no—
549C22×#41—111no—
550C23×D4—111no—
551C24×C4—112no—
552C2×#121—112no—
553C2×#121—112no—
554C2×#120—112no—
555C2×#120—112no—
556C4×#41—228no—
557C2×C4×Q8—111no—
558C2×C4×Q8—111no—
559C2×C4×D4—111no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4—111no—
564C2×C4×D4—111no—
565C2×C4×D4—112no—
566C2×C4×D4—112no—
567C2×C4×D4—111no—
568C2×C4×D4—111no—
569C2×C4×D4—111no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—112no—
573C2×C4×D4—111no—
574C2×C4×D4—228no—
575C2×C4×D4C2×D1111yescharacteristic
576C2×#117—111no—
577C2×#117—111no—
578C2×#117C2×D1111yescharacteristic, complemented
579C22×C4⋊C4—111no—
580C22×C22⋊C4—112no—
581C22×C42—111no—
582C22×C42—111no—
583C22×C42—111no—
584#400—111no—
585#400—111no—
586#400—111no—
587#400C2×D1111yescharacteristic, complemented
588#399—112no—
589#399—111no—
590#399—112no—
591#399—111no—
592#399—111no—
593#399C2×D1111yescharacteristic, complemented
594#397—112no—
595#397—112no—
596#394—111no—
597#394—111no—
598#394—111no—
599#394C2×D1111yescharacteristic
600#393—112no—
601#393—112no—
602#392—111no—
603#392—112no—
604#392—111no—
605#392—112no—
606#392—111no—
607#392C2×D1111yescharacteristic
608#390—112no—
609#390—112no—
610#389—112no—
611#389—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388C2×D1112yescomplemented
616#386—112no—
617#386—112no—
618#386—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#386—112no—
624#386C2×D1112yescomplemented
625#386C2×D1112yescomplemented
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#385—112no—
631#385C2×D1112yescomplemented
632#383—111no—
633#383C2×D1111yescharacteristic, complemented
634#382—112no—
635#381—112no—
636#380—112no—
637#380—111no—
638#380—111no—
639#380—112no—
640#379—112no—
641#379—112no—
642C4×C4⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—112no—
648#376—111no—
649#376—111no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—42no—
656C22×C11—41no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11C23×D411yescharacteristic
663C22×C11C22×#4111yescharacteristic
664C22×C11C22×#4112yes—
665C22×C11C22×#4111yescharacteristic
666C22×C11C2×H(5,𝔽2)12yes—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—24no—
672C2×D11—22no—
673C2×D11—24no—
674C2×D11—24no—
675C2×D11—24no—
676C2×D11—432no—
677C2×D11—42no—
678C2×D11—41no—
679C2×D11—42no—
680C2×D11—41no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11#52514yes—
685C4×C11—22no—
686C4×C11—22no—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—41no—
690C4×C11—42no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—42no—
694Dic11—22no—
695Dic11—22no—
696Dic11—41no—
697Dic11—42no—
698Dic11—41no—
699Dic11—42no—
700Dic11—42no—
701Dic11#52514yes—
702Dic11#53514yes—
703C25—112no—
704C2×#41—224no—
705C2×#41—224no—
706C2×#41—224no—
707C22×Q8—111no—
708C22×D4—111no—
709C22×D4—112no—
710C22×D4—111no—
711C22×D4—112no—
712C22×D4—112no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—224no—
717C22×D4—228no—
718C22×D4C22×D1111yescharacteristic
719C22×D4C22×D1112yes—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—112no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—228no—
733C23×C4—444no—
734C23×C4—444no—
735C23×C4C22×D1111yescharacteristic
736C23×C4C22×D1112yes—
737#121—228no—
738#121—228no—
739#120—228no—
740#120—228no—
741C4×Q8—224no—
742C4×Q8—224no—
743C4×D4—24no—
744C4×D4—228no—
745C4×D4—224no—
746C4×D4—224no—
747C4×D4—224no—
748C4×D4—228no—
749C4×D4—224no—
750C4×D4—224no—
751C4×D4—224no—
752C4×D4—224no—
753C4×D4—224no—
754C4×D4—224no—
755C4×D4—444no—
756C4×D4—444no—
757C4×D4—444no—
758C4×D4—444no—
759#117—24no—
760#117—224no—
761#117—224no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—224no—
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C4⋊C4C22×D1112yes—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
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—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—228no—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1111yescharacteristic
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C22⋊C4C22×D1112yes—
804C2×C22⋊C4C22×D1112yes—
805C2×C22⋊C4C22×D1112yes—
806C2×C22⋊C4C22×D1112yes—
807C2×C42—111no—
808C2×C42—111no—
809C2×C42—111no—
810C2×C42—118no—
811C2×C42—111no—
812C2×C42—112no—
813C2×C42—112no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—224no—
819C2×C42—224no—
820C2×C42C22×D1111yescharacteristic
821C2×C42C22×D1111yescharacteristic
822#95—111no—
823#95—111no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95C22×D1111yescharacteristic
835#95C22×D1111yescharacteristic
836#95C22×D1112yes—
837#95C22×D1112yes—
838#95C22×D1112yes—
839#95C22×D1112yes—
840C2×C11—44no—
841C2×C11—42no—
842C2×C11C2×#52511yescharacteristic
843C2×C11C2×#52511yescharacteristic
844C2×C11C2×#53511yescharacteristic
845C2×C11#348112yes—
846C2×C11#348112yes—
847D11—24no—
848D11—42no—
849D11—44no—
850C24—111no—
851C24—112no—
852C24—111no—
853C24—224no—
854C24—224no—
855C24—224no—
856C24—224no—
857C24—224no—
858C24—442no—
859C24—442no—
860C24C23×D1112yes—
861C24C23×D1111yescharacteristic
862#41—2232no—
863C2×Q8—222no—
864C2×Q8—222no—
865C2×Q8—222no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—22no—
870C2×D4—42no—
871C2×D4—114no—
872C2×D4—118no—
873C2×D4—114no—
874C2×D4—222no—
875C2×D4—224no—
876C2×D4—222no—
877C2×D4—224no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—222no—
881C2×D4—224no—
882C2×D4—2232no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—222no—
892C2×D4—442no—
893C2×D4—442no—
894C2×D4—442no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—112no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—111no—
913C22×C4—224no—
914C22×C4—224no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—222no—
935C22×C4—224no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—4432no—
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1112yes—
944C22×C4C23×D1112yes—
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C22×C4C23×D1111yescharacteristic
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—42no—
954C4⋊C4—224no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—222no—
960C4⋊C4—222no—
961C4⋊C4—222no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C4⋊C4—442no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—24no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—222no—
975C22⋊C4—222no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—224no—
982C22⋊C4—224no—
983C22⋊C4—224no—
984C22⋊C4—222no—
985C22⋊C4—222no—
986C22⋊C4—224no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C42—22no—
994C42—114no—
995C42—114no—
996C42—114no—
997C42—222no—
998C42—222no—
999C42—222no—
1000C42—222no—
1001C42—224no—
1002C42—224no—
1003C42—222no—
1004C42D4×D1114yes—
1005C11#3496311yescharacteristic, complemented, Sylow
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—21no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—112no—
1017C23—112no—
1018C23—112no—
1019C23—114no—
1020C23—112no—
1021C23—2216no—
1022C23—222no—
1023C23—222no—
1024C23—221no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—221no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—448no—
1035C23—448no—
1036C23—448no—
1037C23—448no—
1038C23—448no—
1039C23—448no—
1040C23#41×D1114yes—
1041C23#41×D1112yes—
1042C23C24×D1111yescharacteristic
1043Q8—228no—
1044D4—28no—
1045D4—48no—
1046D4—228no—
1047D4—228no—
1048D4—2216no—
1049D4—228no—
1050D4—228no—
1051D4—448no—
1052D4—448no—
1053D4—448no—
1054C2×C4—28no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—48no—
1075C2×C4—112no—
1076C2×C4—112no—
1077C2×C4—114no—
1078C2×C4—114no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—228no—
1082C2×C4—228no—
1083C2×C4—228no—
1084C2×C4—228no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—221no—
1089C2×C4—221no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—448no—
1103C2×C4—448no—
1104C2×C4—444no—
1105C2×C4—444no—
1106C2×C4—448no—
1107C2×C4—448no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4C2×D4×D1112yes—
1111C2×C4C2×D4×D1112yes—
1112C2×C4C2×D4×D1112yes—
1113C2×C4#41×D1112yes—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—22no—
1118C22—24no—
1119C22—42no—
1120C22—41no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—41no—
1125C22—42no—
1126C22—114no—
1127C22—222no—
1128C22—224no—
1129C22—224no—
1130C22—222no—
1131C22—224no—
1132C22—224no—
1133C22—224no—
1134C22—222no—
1135C22—224no—
1136C22—4432no—
1137C22—442no—
1138C22—441no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—441no—
1143C22—442no—
1144C22C22×D4×D1111yescharacteristic
1145C22C2×#41×D1111yescharacteristic
1146C22C2×#41×D1112yes—
1147C22C2×#41×D1111yescharacteristic
1148C22D11×H(5,𝔽2)12yes—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—22no—
1153C4—42no—
1154C4—41no—
1155C4—42no—
1156C4—42no—
1157C4—41no—
1158C4—114no—
1159C4—114no—
1160C4—222no—
1161C4—222no—
1162C4—442no—
1163C4—441no—
1164C4—442no—
1165C4—442no—
1166C4—441no—
1167C2—44no—
1168C2—42no—
1169C2—224no—
1170C2—444no—
1171C2—442no—
1172C2D11×#52511yescharacteristic
1173C2D11×#52511yescharacteristic
1174C2D11×#53511yescharacteristic
1175C2#1308221912yes—
1176C2#1308222312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2598C2
hypercenter#2598D11
hypocenterC11#34963
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. C2×#10623053C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074184C2semidirect
4. #13074182C2semidirect
5. #13074176C2semidirect
6. #13073973C2semidirect
7. #13073516C2semidirect
8. #13072928C2semidirect
9. #13072926C2semidirect
10. #13072888C2semidirect
11. #13071967C2semidirect
12. #13071965C2semidirect
13. #13071933C2semidirect
14. #13071905C2semidirect
15. #13071904C2semidirect
16. #13071896C2semidirect
17. #13071894C2semidirect
18. #13071128C2semidirect
19. #13071126C2semidirect
20. #13071121C2semidirect
21. #13071117C2semidirect
22. #13071013C2semidirect
23. C11×#2598C2semidirect
28. C2×C11×#117C22semidirect
32. C2×D4×Dic11C22semidirect
34. C22×C4×Dic11C22semidirect
40. C2×#66946C22semidirect
42. C2×#66940C22semidirect
43. C2×#66940C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
56. C2×#66925C22semidirect
58. C2×C42×D11C22semidirect
59. C11×#400C22semidirect
60. C11×#399C22semidirect
63. C11×#388C22semidirect
64. C11×#386C22semidirect
65. C11×#386C22semidirect
66. C11×#385C22semidirect
67. C11×#383C22semidirect
69. #10622836C22semidirect
71. #10622826C22semidirect
72. #10622826C22semidirect
73. #10622823C22semidirect
74. #10622605C22semidirect
75. #10622605C22semidirect
78. #10622602C22semidirect
79. #10622599C22semidirect
80. #10622595C22semidirect
81. #10622585C22semidirect
83. #10622573C22semidirect
87. #10622569C22semidirect
88. #10622569C22semidirect
91. #10622565C22semidirect
92. #10622562C22semidirect
93. #10622562C22semidirect
94. #10622560C22semidirect
95. #10622557C22semidirect
96. #10622555C22semidirect
97. C22⋊C4×Dic11C22semidirect
98. C22⋊C4×Dic11C22semidirect
99. #10622553C22semidirect
100. #10622550C22semidirect
101. #10622290C22semidirect
102. #10622288C22semidirect
103. #10622286C22semidirect
106. #10622283C22semidirect
108. #10622281C22semidirect
111. #10622280C22semidirect
113. #10622279C22semidirect
114. #10622279C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
119. #10622272C22semidirect
120. #10622263C22semidirect
121. #10622262C22semidirect
122. #10622261C22semidirect
123. #10622261C22semidirect
124. #10622260C22semidirect
243. C42×D11D4semidirect
309. C2×C22⋊D11#41semidirect
423. #2598D11semidirect
578. C2×#117C2×D11semidirect
587. #400C2×D11semidirect
593. #399C2×D11semidirect
615. #388C2×D11semidirect
624. #386C2×D11semidirect
625. #386C2×D11semidirect
631. #385C2×D11semidirect
633. #383C2×D11semidirect
1005. C11#34963semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
C2×C4×D4×D112
#130741842
#130741822
#130741762
#130739732
#130735162
#130729282
#130729262
#130728882
#130719672
#130719652
#130719332
#130719052
#130719042
#130718962
#130718942
#130711282
#130711262
#130711212
#130711172
#130710132
C11×#25982
#3496311