Finite Group Databasebeta

← #14927217

Subgroups — #14927217

Order 2816.

2966 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13076954C211yesmaximal, characteristic, complemented
4#13076949C211yesmaximal, characteristic, complemented
5#13076904C211yesmaximal, characteristic, complemented
6#13076899C211yesmaximal, characteristic, complemented
7#13074390C212yesmaximal, complemented
8#13074329C212yesmaximal, complemented
9#13074229C212yesmaximal, complemented
10#13074223C212yesmaximal, complemented
11#13074205C212yesmaximal, complemented
12#13074201C212yesmaximal, complemented
13#13072907C211yesmaximal, characteristic, complemented
14#13072047C211yesmaximal, characteristic, complemented
15#13072043C211yesmaximal, characteristic, complemented
16#13072036C211yesmaximal, characteristic, complemented
17#13072032C211yesmaximal, characteristic, complemented
18#13071962C211yesmaximal, characteristic, complemented
19#13071961C211yesmaximal, characteristic, complemented
20#13071289C212yesmaximal, complemented
21#13071278C212yesmaximal, complemented
22#13070998C211yesmaximal, characteristic, complemented
23C11×#2485C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic, complemented
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic
31C2×#66983C2211yescharacteristic, complemented
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66977C2211yescharacteristic, complemented
35C4×D4×D11—28no—
36#10623055—28no—
37C2×#66950C2211yescharacteristic
38C2×#66950C2211yescharacteristic, complemented
39C2×#66950C2211yescharacteristic, complemented
40C2×#66948C2211yescharacteristic
41C2×#66948C2211yescharacteristic, complemented
42C2×#66948C2211yescharacteristic, complemented
43C2×#66947C2212yes—
44C2×#66946C2211yescharacteristic
45C2×#66945C2211yescharacteristic, complemented
46C2×#66945C2211yescharacteristic, complemented
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×#66939C2212yescomplemented
49C2×#66935C2212yes—
50C2×#66935C2212yes—
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C4×D44C2212yes—
56C2×C4×D44C2211yescharacteristic
57C2×C4×D44C2212yescomplemented
58C2×C42×D11C2211yescharacteristic
59C11×#397C2212yescomplemented
60C11×#394C2212yes—
61C11×#389C2211yescharacteristic, complemented
62C11×#389C2211yescharacteristic, complemented
63C11×#388C2212yescomplemented
64C11×#387C2212yescomplemented
65C11×#380C2211yescharacteristic, complemented
66C11×#380C2211yescharacteristic, complemented
67C11×#380C2211yescharacteristic, complemented
68#10622836C2212yes—
69#10622825C2211yescharacteristic, complemented
70#10622604C2212yes—
71#10622604C2212yescomplemented
72#10622603C2212yescomplemented
73#10622602C2212yes—
74#10622602C2212yescomplemented
75#10622601C2212yescomplemented
76#10622601C2211yescharacteristic, complemented
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic, complemented
80#10622600C2211yescharacteristic, complemented
81#10622598C2212yescomplemented
82#10622594C2212yescomplemented
83#10622587C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622574C2212yescomplemented
87#10622573C2212yes—
88#10622573C2212yes—
89#10622572C2212yes—
90#10622572C2212yes—
91#10622572C2212yescomplemented
92#10622571C2212yescomplemented
93#10622570C2212yescomplemented
94#10622569C2212yescomplemented
95#10622568C2212yes—
96#10622568C2212yes—
97#10622565C2212yescomplemented
98#10622564C2212yescomplemented
99#10622563C2212yescomplemented
100C22⋊C4×Dic11C2212yescomplemented
101#10622553C2212yescomplemented
102#10622552C2211yescharacteristic, complemented
103#10622546C2212yescomplemented
104#10622542C2211yescharacteristic, complemented
105#10622288C2212yescomplemented
106#10622287C2212yescomplemented
107#10622285C2212yescomplemented
108#10622284C2212yes—
109#10622283C2212yescomplemented
110#10622283C2212yescomplemented
111#10622282C2212yescomplemented
112#10622282C2212yescomplemented
113#10622281C2212yes—
114#10622281C2212yescomplemented
115#10622281C2212yescomplemented
116#10622279C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622277C2212yes—
122#10622277C2212yescomplemented
123#10622268C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C2×D4×D11—24no—
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×#4339—24no—
140C2×#4339—42no—
141C2×#4339—42no—
142C22×D44C2312yes—
143C22×D44C2311yescharacteristic
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×D44C2312yes—
147C22×C4×D11—24no—
148C22×C4×D11—42no—
149C22×C4×D11—42no—
150C22×C4×D11—42no—
151C22×C4×D11—42no—
152C22×C4×D11D418yescomplemented
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×Dic22C2311yescharacteristic
164C4×D4×C11—24no—
165C11×#117—24no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C42×C11C2311yescharacteristic
180C2×C42×C11C2312yes—
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185D4×Dic11—24no—
186#66983—42no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—24no—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
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×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2312yes—
216#66977—42no—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2312yes—
227#66950—24no—
228#66950—24no—
229#66950—42no—
230#66948—24no—
231#66948—24no—
232#66948—42no—
233#66947—28no—
234#66946—24no—
235#66945—42no—
236#66945—42no—
237C4⋊C4×D11—24no—
238#66939—28no—
239#66935—28no—
240#66935—28no—
241(C22⋊D11)⋊C4—24no—
242(C22⋊D11)⋊C4—24no—
243C22⋊C4×D11—24no—
244C22⋊C4×D11—24no—
245C4×D44—28no—
246C4×D44—24no—
247C4×D44—28no—
248C42×D11—24no—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265#35031—111nomaximal, Sylow
266C24×C11C2411yescharacteristic
267C24×C11C2411yescharacteristic
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—41no—
273C23×D11—41no—
274C23×D11—41no—
275C23×D11—41no—
276C23×D11—41no—
277C23×D11—41no—
278C23×D11—41no—
279C23×D11—41no—
280C23×D11C2×D414yes—
281C23×D11#4114yescomplemented
282C23×D11C2412yes—
283C23×D11C2411yescharacteristic
284C23×D11C2411yescharacteristic
285C23×D11C2411yescharacteristic
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11C2×D414yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C22×Dic11—22no—
317C22×Dic11—41no—
318C22×Dic11—41no—
319C22×Dic11—41no—
320C22×Dic11—41no—
321C22×Dic11C2×D414yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2412yes—
325C22×Dic11C2412yes—
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330D4×D11—232no—
331#4339—416no—
332C2×D44—22no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44—22no—
336C2×D44—24no—
337C2×D44—24no—
338C2×D44—24no—
339C2×D44—22no—
340C2×D44—22no—
341C2×D44—22no—
342C2×D44—22no—
343C2×D44—42no—
344C2×D44—42no—
345C2×D44—42no—
346C2×D44—42no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
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—22no—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—22no—
360C2×C4×D11—41no—
361C2×C4×D11—41no—
362C2×C4×D11—41no—
363C2×C4×D11—41no—
364C2×C4×D11—41no—
365C2×C4×D11—41no—
366C2×C4×D11—41no—
367C2×C4×D11—41no—
368C2×C4×D11—41no—
369C2×C4×D11—41no—
370C2×C4×D11—42no—
371C2×C4×D11—42no—
372C2×C4×D11—416no—
373C2×C4×D11—416no—
374C2×C4×D11C2×D414yes—
375C2×C4×D11C2×D414yes—
376C2×C4×D11C2×D414yes—
377C2×C4×D11C2×D414yes—
378C2×C4×D11#4114yescomplemented
379C2×Dic22—22no—
380C2×Dic22—22no—
381C2×Dic22—22no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—24no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—42no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—24no—
391C11×C22⋊C4—24no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—42no—
394C11×C22⋊C4—42no—
395C42×C11—22no—
396C42×C11—24no—
397C22⋊Dic11—22no—
398C22⋊Dic11—22no—
399C22⋊Dic11—42no—
400C22⋊Dic11—42no—
401(C2×D11)⋊C4—22no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—22no—
406(C2×D11)⋊C4—24no—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—22no—
409(C2×D11)⋊C4—24no—
410(C2×D11)⋊C4—24no—
411(C2×D11)⋊C4—24no—
412(C2×D11)⋊C4—22no—
413(C2×D11)⋊C4—24no—
414(C2×D11)⋊C4—42no—
415(C2×D11)⋊C4—42no—
416(C2×D11)⋊C4—42no—
417(C2×D11)⋊C4—42no—
418(C2×D11)⋊C4—42no—
419(C2×D11)⋊C4—42no—
420(C2×D11)⋊C4—42no—
421(C2×D11)⋊C4—42no—
422C4⋊Dic11—24no—
423C4⋊Dic11—24no—
424C4⋊Dic11—22no—
425C4⋊Dic11—22no—
426C4⋊Dic11—22no—
427C4⋊Dic11—42no—
428Dic11⋊C4—22no—
429Dic11⋊C4—24no—
430Dic11⋊C4—22no—
431Dic11⋊C4—42no—
432Dic11⋊C4—42no—
433C4×Dic11—22no—
434C4×Dic11—22no—
435C4×Dic11—22no—
436C4×Dic11—42no—
437C4×Dic11—42no—
438C2×#525—111no—
439C22×C4×D4—111no—
440#2855—111no—
441#2854—111no—
442#2848—111no—
443#2847—111no—
444#2622—112no—
445#2613—112no—
446#2602—112no—
447#2602—112no—
448#2600—112no—
449#2600—112no—
450#2485—111no—
451#2485D1111yescharacteristic, complemented
452#2415—111no—
453#2415—111no—
454#2414—111no—
455#2414—111no—
456#2407—111no—
457#2407—111no—
458#2322—112no—
459#2321—112no—
460#2280—111no—
461C23×C11—21no—
462C23×C11—21no—
463C23×C11—21no—
464C23×C11—21no—
465C23×C11—21no—
466C23×C11—21no—
467C23×C11—21no—
468C23×C11—21no—
469C23×C11—21no—
470C23×C11—21no—
471C23×C11—21no—
472C23×C11—21no—
473C23×C11C22×D412yes—
474C23×C11C2×#4112yes—
475C23×C11C2511yescharacteristic
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—21no—
479C22×D11—21no—
480C22×D11—21no—
481C22×D11—21no—
482C22×D11—21no—
483C22×D11—21no—
484C22×D11—21no—
485C22×D11—21no—
486C22×D11—21no—
487C22×D11—21no—
488C22×D11—21no—
489C22×D11—21no—
490C22×D11—21no—
491C22×D11—21no—
492C22×D11—28no—
493C22×D11—28no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—22no—
497C22×D11—22no—
498C22×D11—22no—
499C22×D11—22no—
500C22×D11—22no—
501C22×D11—44no—
502C22×D11—44no—
503C22×D11—44no—
504C22×D11—44no—
505C22×D11—44no—
506C22×D11—44no—
507C22×D11—44no—
508C22×D11—44no—
509C22×D11—44no—
510C22×D11—44no—
511C22×D11—44no—
512C22×D11—44no—
513C22×D11C22×D412yes—
514C22×D11C22×D412yes—
515C22×D11C2×#4112yes—
516C22×D11C2×#4112yes—
517C22×D11C2×#4112yes—
518D4×C11—28no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—28no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—21no—
542C2×C4×C11—44no—
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D412yes—
545C2×C4×C11C2×#4112yes—
546C2×C4×C11H(5,𝔽2)12yes—
547C2×C4×C11H(5,𝔽2)12yes—
548C22⋊D11—28no—
549C22⋊D11—28no—
550C22⋊D11—48no—
551C22⋊D11—84no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—21no—
556C2×Dic11—21no—
557C2×Dic11—21no—
558C2×Dic11—21no—
559C2×Dic11—21no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—21no—
567C2×Dic11—22no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—21no—
573C2×Dic11—44no—
574C2×Dic11—44no—
575C2×Dic11C22×D412yes—
576C2×Dic11C22×D412yes—
577C2×Dic11C2×#4112yes—
578D44—28no—
579D44—48no—
580D44—48no—
581D44—44no—
582D44—84no—
583C4×D11—28no—
584C4×D11—28no—
585C4×D11—28no—
586C4×D11—44no—
587C4×D11—44no—
588C4×D11—44no—
589C4×D11—48no—
590C4×D11—44no—
591C4×D11—44no—
592C4×D11—44no—
593Dic22—44no—
594C22×#41—111no—
595C23×D4—111no—
596C24×C4—111no—
597C24×C4—111no—
598#525—228no—
599C2×#123—112no—
600C2×#123—112no—
601C2×C22⋊Q8—111no—
602C2×C22⋊Q8—111no—
603C2×C22⋊Q8—111no—
604C2×C22⋊Q8—111no—
605C2×#121—111no—
606C2×#121—111no—
607C2×#121—111no—
608C2×#121—111no—
609C2×#120—112no—
610C2×#120—112no—
611C2×C4×D4—111no—
612C2×C4×D4—111no—
613C2×C4×D4—111no—
614C2×C4×D4—111no—
615C2×C4×D4—111no—
616C2×C4×D4—111no—
617C2×C4×D4—112no—
618C2×C4×D4—111no—
619C2×C4×D4—112no—
620C2×C4×D4—228no—
621C2×C4×D4C2×D1111yescharacteristic
622C2×#117—111no—
623C2×#117—111no—
624C2×#117C2×D1111yescharacteristic, complemented
625C22×C4⋊C4—111no—
626C22×C22⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C42—111no—
629#397—112no—
630#397—112no—
631#397—112no—
632#397C2×D1112yescomplemented
633#394—112no—
634#394—112no—
635#394—112no—
636#394—112no—
637#394—112no—
638#394—112no—
639#394—112no—
640#394C2×D1112yes—
641#392—112no—
642#392—112no—
643#392—112no—
644#392—112no—
645#391—111no—
646#391—111no—
647#390—112no—
648#390—111no—
649#390—112no—
650#390—111no—
651#389—112no—
652#389—111no—
653#389—111no—
654#389—112no—
655#389C2×D1111yescharacteristic, complemented
656#389C2×D1111yescharacteristic, complemented
657#388—112no—
658#388—112no—
659#388—112no—
660#388—112no—
661#388—112no—
662#388—112no—
663#388—112no—
664#388C2×D1112yescomplemented
665#387—112no—
666#387—112no—
667#387—112no—
668#387C2×D1112yescomplemented
669#386—112no—
670#386—112no—
671#386—112no—
672#386—112no—
673#386—112no—
674#386—112no—
675#385—112no—
676#385—112no—
677#385—112no—
678#385—112no—
679#385—112no—
680#385—112no—
681#381—112no—
682#381—112no—
683#380—111no—
684#380—111no—
685#380—111no—
686#380—111no—
687#380—111no—
688#380C2×D1111yescharacteristic, complemented
689#380C2×D1111yescharacteristic, complemented
690#380C2×D1111yescharacteristic, complemented
691#379—112no—
692#379—112no—
693C4×C22⋊C4—112no—
694C4×C22⋊C4—112no—
695C22×C11—22no—
696C22×C11—22no—
697C22×C11—22no—
698C22×C11—22no—
699C22×C11—22no—
700C22×C11—22no—
701C22×C11—41no—
702C22×C11—41no—
703C22×C11—41no—
704C22×C11—41no—
705C22×C11—41no—
706C22×C11—41no—
707C22×C11—41no—
708C22×C11—41no—
709C22×C11C23×D411yescharacteristic
710C22×C11C22×#4111yescharacteristic
711C22×C11C22×#4111yescharacteristic
712C22×C11C2×H(5,𝔽2)11yescharacteristic
713C22×C11C2×H(5,𝔽2)11yescharacteristic
714C22×C11#58511yescharacteristic
715C22×C11#58511yescharacteristic
716C2×D11—22no—
717C2×D11—22no—
718C2×D11—22no—
719C2×D11—22no—
720C2×D11—22no—
721C2×D11—22no—
722C2×D11—22no—
723C2×D11—22no—
724C2×D11—22no—
725C2×D11—22no—
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—416no—
729C2×D11—416no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—41no—
734C2×D11—41no—
735C2×D11—41no—
736C2×D11—41no—
737C2×D11—41no—
738C2×D11—42no—
739C2×D11—42no—
740C2×D11—42no—
741C2×D11—42no—
742C2×D11—42no—
743C2×D11—42no—
744C2×D11—42no—
745C2×D11#52514yes—
746C4×C11—22no—
747C4×C11—22no—
748C4×C11—42no—
749C4×C11—41no—
750C4×C11—41no—
751C4×C11—42no—
752C4×C11—42no—
753C4×C11—42no—
754C4×C11#53414yes—
755Dic11—22no—
756Dic11—22no—
757Dic11—22no—
758Dic11—42no—
759Dic11—41no—
760Dic11—41no—
761Dic11—42no—
762Dic11—42no—
763C25—111no—
764C25—111no—
765C2×#41—224no—
766C2×#41—442no—
767C2×#41—442no—
768C22×Q8—111no—
769C22×D4—111no—
770C22×D4—111no—
771C22×D4—112no—
772C22×D4—112no—
773C22×D4—111no—
774C22×D4—112no—
775C22×D4—111no—
776C22×D4—112no—
777C22×D4—112no—
778C22×D4—224no—
779C22×D4—224no—
780C22×D4—224no—
781C22×D4C22×D1111yescharacteristic
782C23×C4—111no—
783C23×C4—111no—
784C23×C4—111no—
785C23×C4—111no—
786C23×C4—118no—
787C23×C4—111no—
788C23×C4—111no—
789C23×C4—111no—
790C23×C4—111no—
791C23×C4—111no—
792C23×C4—111no—
793C23×C4—111no—
794C23×C4—112no—
795C23×C4—224no—
796C23×C4—442no—
797C23×C4—442no—
798C23×C4—442no—
799C23×C4—442no—
800C23×C4C22×D1111yescharacteristic
801C23×C4C22×D1111yescharacteristic
802#123—228no—
803#123—228no—
804C22⋊Q8—224no—
805C22⋊Q8—224no—
806C22⋊Q8—442no—
807C22⋊Q8—442no—
808#121—224no—
809#121—224no—
810#121—442no—
811#121—442no—
812#120—228no—
813#120—228no—
814C4×D4—24no—
815C4×D4—224no—
816C4×D4—228no—
817C4×D4—228no—
818C4×D4—224no—
819C4×D4—224no—
820C4×D4—224no—
821C4×D4—224no—
822C4×D4—224no—
823C4×D4—224no—
824#117—24no—
825#117—442no—
826#117—442no—
827C2×C4⋊C4—111no—
828C2×C4⋊C4—111no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—112no—
833C2×C4⋊C4—112no—
834C2×C4⋊C4—112no—
835C2×C4⋊C4—112no—
836C2×C4⋊C4—112no—
837C2×C4⋊C4—112no—
838C2×C4⋊C4—224no—
839C2×C4⋊C4C22×D1111yescharacteristic
840C2×C4⋊C4C22×D1111yescharacteristic
841C2×C4⋊C4C22×D1111yescharacteristic
842C2×C4⋊C4C22×D1111yescharacteristic
843C2×C4⋊C4C22×D1111yescharacteristic
844C2×C4⋊C4C22×D1112yes—
845C2×C4⋊C4C22×D1112yes—
846C2×C22⋊C4—111no—
847C2×C22⋊C4—111no—
848C2×C22⋊C4—111no—
849C2×C22⋊C4—111no—
850C2×C22⋊C4—111no—
851C2×C22⋊C4—111no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—112no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—112no—
862C2×C22⋊C4—112no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—112no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—224no—
872C2×C22⋊C4—224no—
873C2×C22⋊C4C22×D1111yescharacteristic
874C2×C22⋊C4C22×D1111yescharacteristic
875C2×C22⋊C4C22×D1112yes—
876C2×C22⋊C4C22×D1112yes—
877C2×C22⋊C4C22×D1112yes—
878C2×C22⋊C4C22×D1112yes—
879C2×C42—111no—
880C2×C42—111no—
881C2×C42—111no—
882C2×C42—112no—
883C2×C42—112no—
884C2×C42—224no—
885C2×C42C22×D1112yes—
886C2×C42C22×D1111yescharacteristic
887#95—112no—
888#95—112no—
889#95—112no—
890#95—112no—
891#95—112no—
892#95—112no—
893#95—112no—
894#95—112no—
895#95—112no—
896#95—112no—
897#95—112no—
898#95C22×D1112yes—
899#95C22×D1112yes—
900#95C22×D1112yes—
901#95C22×D1112yes—
902#95C22×D1112yes—
903C2×C11—42no—
904C2×C11—42no—
905C2×C11C2×#52511yescharacteristic
906C2×C11C2×#53411yescharacteristic
907C2×C11#344911yescharacteristic
908C2×C11#350511yescharacteristic
909C2×C11#350511yescharacteristic
910C2×C11#350611yescharacteristic
911C2×C11#350611yescharacteristic
912D11—24no—
913D11—42no—
914D11—42no—
915D11—82no—
916C24—111no—
917C24—111no—
918C24—111no—
919C24—114no—
920C24—114no—
921C24—112no—
922C24—222no—
923C24—222no—
924C24—222no—
925C24—222no—
926C24—441no—
927C24—441no—
928C24—441no—
929C24—441no—
930C24—441no—
931C24—441no—
932C24—441no—
933C24—441no—
934C24C23×D1111yescharacteristic
935C24C23×D1111yescharacteristic
936#41—4416no—
937C2×Q8—222no—
938C2×Q8—222no—
939C2×Q8—222no—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—22no—
943C2×D4—222no—
944C2×D4—222no—
945C2×D4—224no—
946C2×D4—224no—
947C2×D4—224no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—222no—
951C2×D4—222no—
952C2×D4—2232no—
953C2×D4—222no—
954C2×D4—222no—
955C2×D4—222no—
956C2×D4—222no—
957C2×D4—224no—
958C2×D4—224no—
959C2×D4—222no—
960C2×D4—222no—
961C2×D4—222no—
962C2×D4—222no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—442no—
966C2×D4—442no—
967C2×D4—442no—
968C2×D4—442no—
969C2×D4—442no—
970C2×D4—442no—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—111no—
977C22×C4—111no—
978C22×C4—111no—
979C22×C4—114no—
980C22×C4—114no—
981C22×C4—114no—
982C22×C4—114no—
983C22×C4—114no—
984C22×C4—114no—
985C22×C4—112no—
986C22×C4—111no—
987C22×C4—112no—
988C22×C4—111no—
989C22×C4—112no—
990C22×C4—222no—
991C22×C4—222no—
992C22×C4—222no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—222no—
1001C22×C4—224no—
1002C22×C4—222no—
1003C22×C4—222no—
1004C22×C4—4416no—
1005C22×C4—441no—
1006C22×C4—441no—
1007C22×C4—441no—
1008C22×C4—441no—
1009C22×C4—441no—
1010C22×C4—441no—
1011C22×C4—441no—
1012C22×C4—441no—
1013C22×C4—442no—
1014C22×C4—442no—
1015C22×C4—441no—
1016C22×C4—441no—
1017C22×C4—4416no—
1018C22×C4—441no—
1019C22×C4—441no—
1020C22×C4—441no—
1021C22×C4—441no—
1022C22×C4D4×D1114yes—
1023C22×C4C23×D1112yes—
1024C22×C4C23×D1111yescharacteristic
1025C22×C4C23×D1112yes—
1026C22×C4C23×D1112yes—
1027C22×C4C23×D1112yes—
1028C22×C4C23×D1111yescharacteristic
1029C22×C4C23×D1111yescharacteristic
1030C22×C4C23×D1111yescharacteristic
1031C22×C4C23×D1111yescharacteristic
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—24no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—42no—
1039C4⋊C4—222no—
1040C4⋊C4—222no—
1041C4⋊C4—224no—
1042C4⋊C4—224no—
1043C4⋊C4—224no—
1044C4⋊C4—222no—
1045C4⋊C4—222no—
1046C4⋊C4—222no—
1047C4⋊C4—442no—
1048C4⋊C4—442no—
1049C4⋊C4—442no—
1050C22⋊C4—22no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—22no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—222no—
1057C22⋊C4—224no—
1058C22⋊C4—224no—
1059C22⋊C4—224no—
1060C22⋊C4—222no—
1061C22⋊C4—222no—
1062C22⋊C4—224no—
1063C22⋊C4—224no—
1064C22⋊C4—224no—
1065C22⋊C4—224no—
1066C22⋊C4—224no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—224no—
1071C22⋊C4—442no—
1072C22⋊C4—442no—
1073C22⋊C4—442no—
1074C22⋊C4—442no—
1075C22⋊C4—442no—
1076C22⋊C4—442no—
1077C22⋊C4—442no—
1078C22⋊C4—442no—
1079C22⋊C4—442no—
1080C22⋊C4—442no—
1081C42—22no—
1082C42—24no—
1083C42—222no—
1084C42—222no—
1085C42—222no—
1086C42—442no—
1087C42—442no—
1088C11#3503111yescharacteristic, complemented, Sylow
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—112no—
1102C23—112no—
1103C23—112no—
1104C23—112no—
1105C23—112no—
1106C23—228no—
1107C23—228no—
1108C23—221no—
1109C23—221no—
1110C23—221no—
1111C23—221no—
1112C23—221no—
1113C23—221no—
1114C23—221no—
1115C23—221no—
1116C23—221no—
1117C23—221no—
1118C23—221no—
1119C23—221no—
1120C23—221no—
1121C23—221no—
1122C23—221no—
1123C23—221no—
1124C23—222no—
1125C23—222no—
1126C23—222no—
1127C23—222no—
1128C23—222no—
1129C23—222no—
1130C23—222no—
1131C23—444no—
1132C23—444no—
1133C23—444no—
1134C23—444no—
1135C23—444no—
1136C23—444no—
1137C23—444no—
1138C23—444no—
1139C23—444no—
1140C23—444no—
1141C23—444no—
1142C23—444no—
1143C23C2×D4×D1112yes—
1144C23#41×D1112yes—
1145C23C24×D1111yescharacteristic
1146Q8—444no—
1147D4—28no—
1148D4—228no—
1149D4—228no—
1150D4—228no—
1151D4—448no—
1152D4—448no—
1153D4—448no—
1154D4—444no—
1155D4—884no—
1156D4—884no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—28no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—44no—
1181C2×C4—112no—
1182C2×C4—112no—
1183C2×C4—112no—
1184C2×C4—228no—
1185C2×C4—221no—
1186C2×C4—221no—
1187C2×C4—221no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—221no—
1191C2×C4—228no—
1192C2×C4—228no—
1193C2×C4—221no—
1194C2×C4—221no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—221no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—221no—
1204C2×C4—221no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—221no—
1208C2×C4—444no—
1209C2×C4—444no—
1210C2×C4—448no—
1211C2×C4—444no—
1212C2×C4—444no—
1213C2×C4—444no—
1214C2×C4—444no—
1215C2×C4—444no—
1216C2×C4—444no—
1217C2×C4C2×D4×D1112yes—
1218C2×C4C2×D4×D1112yes—
1219C2×C4#41×D1112yes—
1220C2×C4#6704212yes—
1221C2×C4#6704212yes—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—114no—
1237C22—222no—
1238C22—222no—
1239C22—222no—
1240C22—222no—
1241C22—222no—
1242C22—222no—
1243C22—222no—
1244C22—222no—
1245C22—222no—
1246C22—222no—
1247C22—222no—
1248C22—222no—
1249C22—4416no—
1250C22—4416no—
1251C22—441no—
1252C22—441no—
1253C22—441no—
1254C22—441no—
1255C22—441no—
1256C22—441no—
1257C22—441no—
1258C22—441no—
1259C22—442no—
1260C22—442no—
1261C22—442no—
1262C22—442no—
1263C22—442no—
1264C22—442no—
1265C22—442no—
1266C22C22×D4×D1111yescharacteristic
1267C22C2×#41×D1111yescharacteristic
1268C22C2×#41×D1111yescharacteristic
1269C22C2×#6704211yescharacteristic
1270C22C2×#6704211yescharacteristic
1271C22#1062345511yescharacteristic
1272C22#1062345711yescharacteristic
1273C4—22no—
1274C4—22no—
1275C4—41no—
1276C4—42no—
1277C4—41no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—222no—
1282C4—222no—
1283C4—222no—
1284C4—441no—
1285C4—442no—
1286C4—441no—
1287C4—442no—
1288C4—442no—
1289C4#1062318414yes—
1290C2—42no—
1291C2—42no—
1292C2—224no—
1293C2—442no—
1294C2—442no—
1295C2—882no—
1296C2D11×#52511yescharacteristic
1297C2C2×#1062318411yescharacteristic
1298C2#1308194411yescharacteristic
1299C2#1308244511yescharacteristic
1300C2#1308245611yescharacteristic
1301C2#1308245811yescharacteristic
1302C2#1308246911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2485C2
hypercenter#2485D11
hypocenterC11#35031
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2485

Complements

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

NH ≅ G/Ntype
1. C2×#10623055C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13076954C2semidirect
4. #13076949C2semidirect
5. #13076904C2semidirect
6. #13076899C2semidirect
7. #13074390C2semidirect
8. #13074329C2semidirect
9. #13074229C2semidirect
10. #13074223C2semidirect
11. #13074205C2semidirect
12. #13074201C2semidirect
13. #13072907C2semidirect
14. #13072047C2semidirect
15. #13072043C2semidirect
16. #13072036C2semidirect
17. #13072032C2semidirect
18. #13071962C2semidirect
19. #13071961C2semidirect
20. #13071289C2semidirect
21. #13071278C2semidirect
22. #13070998C2semidirect
23. C11×#2485C2semidirect
25. C22×#4339C22semidirect
29. C2×C11×#117C22semidirect
31. C2×#66983C22semidirect
34. C2×#66977C22semidirect
38. C2×#66950C22semidirect
39. C2×#66950C22semidirect
41. C2×#66948C22semidirect
42. C2×#66948C22semidirect
45. C2×#66945C22semidirect
46. C2×#66945C22semidirect
48. C2×#66939C22semidirect
57. C2×C4×D44C22semidirect
59. C11×#397C22semidirect
61. C11×#389C22semidirect
62. C11×#389C22semidirect
63. C11×#388C22semidirect
64. C11×#387C22semidirect
65. C11×#380C22semidirect
66. C11×#380C22semidirect
67. C11×#380C22semidirect
69. #10622825C22semidirect
71. #10622604C22semidirect
72. #10622603C22semidirect
74. #10622602C22semidirect
75. #10622601C22semidirect
76. #10622601C22semidirect
79. #10622600C22semidirect
80. #10622600C22semidirect
81. #10622598C22semidirect
82. #10622594C22semidirect
83. #10622587C22semidirect
84. #10622586C22semidirect
85. #10622586C22semidirect
86. #10622574C22semidirect
91. #10622572C22semidirect
92. #10622571C22semidirect
93. #10622570C22semidirect
94. #10622569C22semidirect
97. #10622565C22semidirect
98. #10622564C22semidirect
99. #10622563C22semidirect
100. C22⋊C4×Dic11C22semidirect
101. #10622553C22semidirect
102. #10622552C22semidirect
103. #10622546C22semidirect
104. #10622542C22semidirect
105. #10622288C22semidirect
106. #10622287C22semidirect
107. #10622285C22semidirect
109. #10622283C22semidirect
110. #10622283C22semidirect
111. #10622282C22semidirect
112. #10622282C22semidirect
114. #10622281C22semidirect
115. #10622281C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
122. #10622277C22semidirect
123. #10622268C22semidirect
124. #10622260C22semidirect
152. C22×C4×D11D4semidirect
281. C23×D11#41semidirect
378. C2×C4×D11#41semidirect
451. #2485D11semidirect
624. C2×#117C2×D11semidirect
632. #397C2×D11semidirect
655. #389C2×D11semidirect
656. #389C2×D11semidirect
664. #388C2×D11semidirect
668. #387C2×D11semidirect
688. #380C2×D11semidirect
689. #380C2×D11semidirect
690. #380C2×D11semidirect
1088. C11#35031semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×C4×D4×D112
#130769542
#130769492
#130769042
#130768992
#130743902
#130743292
#130742292
#130742232
#130742052
#130742012
#130729072
#130720472
#130720432
#130720362
#130720322
#130719622
#130719612
#130712892
#130712782
#130709982
C11×#24852
#3503111