Finite Group Databasebeta

← #14926736

Subgroups — #14926736

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623175C212yesmaximal, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076974C211yesmaximal, characteristic, complemented
4#13076962C211yesmaximal, characteristic, complemented
5#13076949C211yesmaximal, characteristic, complemented
6#13074760C212yesmaximal, complemented
7#13074749C212yesmaximal, complemented
8#13073691C212yesmaximal, complemented
9#13073679C212yesmaximal, complemented
10#13073198C211yesmaximal, characteristic, complemented
11#13072982C211yesmaximal, characteristic, complemented
12#13072749C212yesmaximal, complemented
13#13072383C211yesmaximal, characteristic, complemented
14#13072253C211yesmaximal, characteristic, complemented
15#13072202C211yesmaximal, characteristic, complemented
16#13072150C212yesmaximal, complemented
17#13072050C211yesmaximal, characteristic, complemented
18#13071973C211yesmaximal, characteristic, complemented
19#13071273C212yesmaximal, complemented
20#13071122C211yesmaximal, characteristic, complemented
21C2×#10622601C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2440C211yesmaximal, characteristic, complemented
24C23×D44C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×C22⋊Q8C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C2×#67000C2212yescomplemented
29C2×#67000C2212yescomplemented
30C2×#67000C2212yescomplemented
31C2×#66983C2211yescharacteristic
32C2×#66983C2212yes—
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yes—
35C22×(C2×D11)⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37#10623175—216no—
38C2×#66951C2212yescomplemented
39C2×#66951C2212yescomplemented
40C2×#66948C2211yescharacteristic
41C2×#66948C2211yescharacteristic
42C2×#66948C2212yescomplemented
43C2×#66948C2212yescomplemented
44C2×#66948C2212yescomplemented
45C2×#66948C2211yescharacteristic, complemented
46C2×#66947C2212yescomplemented
47C2×#66947C2212yescomplemented
48C2×#66946C2211yescharacteristic, complemented
49C2×#66935C2212yes—
50C2×#66935C2212yes—
51C2×#66935C2212yes—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2211yescharacteristic
55C2×#66927C2211yescharacteristic
56C2×#66927C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic, complemented
58C11×#398C2212yescomplemented
59C11×#395C2212yescomplemented
60C11×#389C2211yescharacteristic, complemented
61C11×#389C2211yescharacteristic, complemented
62C11×#385C2212yes—
63C11×#384C2211yescharacteristic, complemented
64C11×#380C2211yescharacteristic
65C4×C11×C22⋊C4C2211yescharacteristic
66#10622844C2212yescomplemented
67#10622826C2212yes—
68#10622607C2212yescomplemented
69#10622607C2212yescomplemented
70#10622606C2212yescomplemented
71#10622604C2212yescomplemented
72#10622604C2212yescomplemented
73#10622604C2212yescomplemented
74#10622604C2212yescomplemented
75#10622603C2212yescomplemented
76#10622603C2212yescomplemented
77#10622603C2212yescomplemented
78#10622603C2212yescomplemented
79#10622601C2212yes—
80#10622601C2211yescharacteristic
81#10622601C2211yescharacteristic
82#10622601C2212yes—
83#10622601C2211yescharacteristic
84#10622601C2211yescharacteristic
85#10622601C2211yescharacteristic
86#10622601C2211yescharacteristic
87#10622601C2212yescomplemented
88#10622601C2212yescomplemented
89#10622601C2211yescharacteristic, complemented
90#10622601C2212yescomplemented
91#10622601C2212yescomplemented
92#10622601C2211yescharacteristic, complemented
93#10622600C2211yescharacteristic, complemented
94#10622598C2211yescharacteristic, complemented
95C4⋊C4×Dic11C2211yescharacteristic, complemented
96#10622586C2211yescharacteristic, complemented
97#10622571C2212yes—
98#10622568C2212yes—
99C22⋊C4×Dic11C2211yescharacteristic
100C22⋊C4×Dic11C2211yescharacteristic
101#10622552C2211yescharacteristic
102#10622552C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
104C4×Dic11⋊C4C2211yescharacteristic, complemented
105C42×Dic11C2211yescharacteristic, complemented
106#10622285C2212yes—
107#10622285C2212yescomplemented
108#10622284C2212yes—
109#10622284C2212yes—
110#10622284C2212yes—
111#10622284C2212yescomplemented
112#10622283C2212yescomplemented
113#10622282C2212yescomplemented
114#10622282C2212yescomplemented
115#10622282C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2211yescharacteristic, complemented
118#10622279C2211yescharacteristic, complemented
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622262C2211yescharacteristic, complemented
123#10622262C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×Q8×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×D44—24no—
133C22×D44—42no—
134C22×D44—42no—
135C22×D44C2311yescharacteristic
136C22×D44C2311yescharacteristic
137C22×D44C2311yescharacteristic
138C22×D44C2312yes—
139C22×D44C2312yes—
140C22×D44C2312yes—
141C22×D44C2312yes—
142C22×D44C2312yes—
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×D44C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C11×C4⋊Q8—42no—
151C11×C22⋊Q8—28no—
152C2×C11×C4⋊C4—42no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169#67000—28no—
170#67000—28no—
171#67000—44no—
172#66983—24no—
173#66983—28no—
174C4×C22⋊D11—24no—
175C2×(C2×D11)⋊C4—28no—
176C2×(C2×D11)⋊C4—44no—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×C4×Dic11—42no—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225#66951—28no—
226#66951—28no—
227#66948—28no—
228#66948—28no—
229#66948—44no—
230#66948—42no—
231#66948—42no—
232#66948—42no—
233#66947—28no—
234#66947—28no—
235#66946—42no—
236#66935—28no—
237#66935—28no—
238#66935—28no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—24no—
241(C22⋊D11)⋊C4D418yescomplemented
242#66927—42no—
243#66927—42no—
244C42×D11—42no—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2411yescharacteristic
260C23×D11—24no—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11C2412yes—
268C23×D11C2412yes—
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×Q8×C11—24no—
272C2×Q8×C11—42no—
273C2×Q8×C11—42no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—24no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11#4114yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—24no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—22no—
293C2×C22⋊D11—24no—
294C2×C22⋊D11—24no—
295C2×C22⋊D11C2×D414yes—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—41no—
299C22×Dic11—41no—
300C22×Dic11—41no—
301C22×Dic11C2×D414yes—
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C2×D44—24no—
311C2×D44—24no—
312C2×D44—24no—
313C2×D44—24no—
314C2×D44—24no—
315C2×D44—22no—
316C2×D44—24no—
317C2×D44—22no—
318C2×D44—22no—
319C2×D44—24no—
320C2×D44—24no—
321C2×D44—22no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—42no—
328C2×D44—42no—
329C2×D44—42no—
330C2×D44—42no—
331C2×D44—42no—
332C2×D44—42no—
333C2×D44—42no—
334C2×D44—42no—
335C2×D44—42no—
336C2×D44—42no—
337C2×D44—42no—
338C2×D44—42no—
339C2×D44—42no—
340C2×D44—42no—
341C2×D44—42no—
342C2×D44—42no—
343C2×D44—416no—
344C2×C4×D11—22no—
345C2×C4×D11—24no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—22no—
350C2×C4×D11—41no—
351C2×C4×D11—41no—
352C2×C4×D11—41no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11C2×D414yescomplemented
356C11×C4⋊C4—24no—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—24no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—42no—
364C11×C4⋊C4—42no—
365C11×C4⋊C4—42no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4C2×D414yes—
368C11×C22⋊C4#4114yes—
369C42×C11—22no—
370C42×C11—22no—
371C22⋊Dic11—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—42no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4C2×D414yescomplemented
401C4⋊Dic11—24no—
402C4⋊Dic11—22no—
403Dic11⋊C4—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4C2×D414yescomplemented
407C4×Dic11—24no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—41no—
414C4×Dic11—41no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
421#2858—111no—
422#2856—111no—
423#2854—111no—
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491—111no—
430#2472—112no—
431#2445—111no—
432#2440D1111yescharacteristic, complemented
433#2433—111no—
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408—111no—
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11C22×D412yes—
447C23×C11C2×#4112yes—
448C23×C11C2×#4112yes—
449C23×C11C2511yescharacteristic
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11—84no—
483C22×D11—84no—
484C22×D11C22×D412yes—
485Q8×C11—84no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—28no—
497C2×C4×C11—22no—
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—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—84no—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C2×#4112yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11C2×#4112yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C2×C4×C11H(5,𝔽2)12yes—
518C22⋊D11—28no—
519C22⋊D11—48no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—44no—
541C2×Dic11—44no—
542C2×Dic11C22×D412yes—
543C2×Dic11C22×D412yes—
544C2×Dic11C22×D412yes—
545C2×Dic11H(5,𝔽2)12yes—
546D44—48no—
547D44—44no—
548D44—44no—
549D44—44no—
550D44—84no—
551D44—84no—
552D44—84no—
553D44—84no—
554D44—84no—
555D44—84no—
556D44—84no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—44no—
560C4×D11—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8C2×D1111yescharacteristic, complemented
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8C2×D1112yes—
574C2×#121—112no—
575C2×#121—111no—
576C2×#121—112no—
577C2×#121—112no—
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—111no—
581C2×#121—112no—
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4—111no—
590C22×C4⋊C4C2×D1111yescharacteristic
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42—111no—
595#398C2×D1112yescomplemented
596#397—112no—
597#396—112no—
598#396—112no—
599#395C2×D1112yescomplemented
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—112no—
612#390—112no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—112no—
617#390—111no—
618#390—111no—
619#390—112no—
620#390—111no—
621#390—112no—
622#390—111no—
623#390—111no—
624#390—112no—
625#390—111no—
626#390—111no—
627#389—111no—
628#389—111no—
629#389C2×D1111yescharacteristic, complemented
630#389C2×D1111yescharacteristic, complemented
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—112no—
644#385C2×D1112yes—
645#384C2×D1111yescharacteristic, complemented
646#380—111no—
647#380C2×D1111yescharacteristic
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—112no—
659C4×C22⋊C4C2×D1111yescharacteristic
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11#53214yes—
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11C2×H(5,𝔽2)11yescharacteristic
674C22×C11#58511yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—816no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—22no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—42no—
712C4×C11—42no—
713C4×C11#53814yescomplemented
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—42no—
719Dic11—41no—
720Dic11—41no—
721Dic11—41no—
722C25—112no—
723C22×Q8C22×D1112yes—
724C22×D4—111no—
725C22×D4—112no—
726C22×D4—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—112no—
736C22×D4—112no—
737C22×D4—224no—
738C22×D4—442no—
739C22×D4—442no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—112no—
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1112yes—
748C4⋊Q8—42no—
749#127—442no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—28no—
759#121—228no—
760#121—228no—
761#121—228no—
762#121—224no—
763#121—444no—
764#121—442no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—118no—
771C4×D4—228no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—42no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4C22×D1111yescharacteristic
783C2×C4⋊C4C22×D1111yescharacteristic
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1112yes—
786C2×C4⋊C4C22×D1112yes—
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1112yes—
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
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—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—228no—
823C2×C22⋊C4—444no—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1111yescharacteristic
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C42—111no—
828C2×C42—112no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—111no—
839C2×C42—442no—
840C2×C42—442no—
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95C22×D1111yescharacteristic
852#95C22×D1111yescharacteristic
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—24no—
857C2×C11C2×#53211yescharacteristic
858C2×C11C2×#53811yescharacteristic
859C2×C11#346011yescharacteristic
860C2×C11#349611yescharacteristic
861C2×C11#349811yescharacteristic
862C2×C11#351411yescharacteristic
863C2×C11#351911yescharacteristic
864D11—42no—
865D11—82no—
866D11—82no—
867D11—82no—
868C24—111no—
869C24—112no—
870C24—112no—
871C24—112no—
872C24—224no—
873C24—224no—
874C24—224no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24—442no—
879C24C23×D1111yescharacteristic
880C2×Q8—24no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×D4—114no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—222no—
888C2×D4—222no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—222no—
895C2×D4—222no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—224no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—4416no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—442no—
913C2×D4—442no—
914C2×D4—442no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—24no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—111no—
937C22×C4—112no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—441no—
952C22×C4—441no—
953C22×C4—441no—
954C22×C4#434314yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1112yes—
957C22×C4C23×D1112yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—114no—
976C4⋊C4—224no—
977C4⋊C4—224no—
978C4⋊C4—222no—
979C4⋊C4—222no—
980C4⋊C4—222no—
981C22⋊C4—24no—
982C22⋊C4—114no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—222no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4D4×D1114yes—
1013C22⋊C4#434314yes—
1014C42—22no—
1015C42—22no—
1016C42—114no—
1017C42—224no—
1018C42—222no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—112no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—448no—
1062C23—448no—
1063C23—448no—
1064C23—884no—
1065C23—884no—
1066C23—884no—
1067C23—884no—
1068C23C2×D4×D1112yes—
1069C23C2×#434312yes—
1070C23C2×#434312yes—
1071C23C24×D1111yescharacteristic
1072Q8—84no—
1073D4—228no—
1074D4—448no—
1075D4—448no—
1076D4—444no—
1077D4—444no—
1078D4—444no—
1079D4—884no—
1080D4—884no—
1081D4—884no—
1082D4—884no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—28no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—84no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—112no—
1113C2×C4—112no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—222no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—222no—
1126C2×C4—221no—
1127C2×C4—221no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—444no—
1135C2×C4—444no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—884no—
1140C2×C4C2×D4×D1112yes—
1141C2×C4C2×D4×D1112yes—
1142C2×C4#6703712yes—
1143C2×C4C2×#434312yes—
1144C2×C4C2×#434312yes—
1145C2×C4C2×#434312yes—
1146C2×C4C2×#434312yes—
1147C2×C4#6704212yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—222no—
1155C22—222no—
1156C22—222no—
1157C22—441no—
1158C22—441no—
1159C22—441no—
1160C22—441no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22—442no—
1170C22—442no—
1171C22—442no—
1172C22—442no—
1173C22—442no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—8816no—
1183C22#1062325614yes—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C22×#434311yescharacteristic
1187C22C22×#434311yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345711yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—441no—
1205C4—442no—
1206C4—441no—
1207C4—441no—
1208C4#1062317514yescomplemented
1209C2—24no—
1210C2—442no—
1211C2—882no—
1212C2—882no—
1213C2—882no—
1214C2C2×#1062325611yescharacteristic
1215C2C2×#1062317511yescharacteristic
1216C2#1308203911yescharacteristic
1217C2#1308237411yescharacteristic
1218C2#1308238811yescharacteristic
1219C2#1308257811yescharacteristic
1220C2#1308264911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2440C2
hypercenter#2440D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#10623175C2semidirect
2. #13076984C2semidirect
3. #13076974C2semidirect
4. #13076962C2semidirect
5. #13076949C2semidirect
6. #13074760C2semidirect
7. #13074749C2semidirect
8. #13073691C2semidirect
9. #13073679C2semidirect
10. #13073198C2semidirect
11. #13072982C2semidirect
12. #13072749C2semidirect
13. #13072383C2semidirect
14. #13072253C2semidirect
15. #13072202C2semidirect
16. #13072150C2semidirect
17. #13072050C2semidirect
18. #13071973C2semidirect
19. #13071273C2semidirect
20. #13071122C2semidirect
21. C2×#10622601C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2440C2semidirect
25. C2×C11×C4⋊Q8C22semidirect
28. C2×#67000C22semidirect
29. C2×#67000C22semidirect
30. C2×#67000C22semidirect
38. C2×#66951C22semidirect
39. C2×#66951C22semidirect
42. C2×#66948C22semidirect
43. C2×#66948C22semidirect
44. C2×#66948C22semidirect
45. C2×#66948C22semidirect
46. C2×#66947C22semidirect
47. C2×#66947C22semidirect
48. C2×#66946C22semidirect
57. C2×C42×D11C22semidirect
58. C11×#398C22semidirect
59. C11×#395C22semidirect
60. C11×#389C22semidirect
61. C11×#389C22semidirect
63. C11×#384C22semidirect
66. #10622844C22semidirect
68. #10622607C22semidirect
69. #10622607C22semidirect
70. #10622606C22semidirect
71. #10622604C22semidirect
72. #10622604C22semidirect
73. #10622604C22semidirect
74. #10622604C22semidirect
75. #10622603C22semidirect
76. #10622603C22semidirect
77. #10622603C22semidirect
78. #10622603C22semidirect
87. #10622601C22semidirect
88. #10622601C22semidirect
89. #10622601C22semidirect
90. #10622601C22semidirect
91. #10622601C22semidirect
92. #10622601C22semidirect
93. #10622600C22semidirect
94. #10622598C22semidirect
95. C4⋊C4×Dic11C22semidirect
96. #10622586C22semidirect
103. C4×(C2×D11)⋊C4C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. C42×Dic11C22semidirect
107. #10622285C22semidirect
111. #10622284C22semidirect
112. #10622283C22semidirect
113. #10622282C22semidirect
114. #10622282C22semidirect
115. #10622282C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
241. (C22⋊D11)⋊C4D4semidirect
355. C2×C4×D11C2×D4semidirect
400. (C2×D11)⋊C4C2×D4semidirect
406. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
432. #2440D11semidirect
563. C2×C4⋊Q8C2×D11semidirect
595. #398C2×D11semidirect
599. #395C2×D11semidirect
629. #389C2×D11semidirect
630. #389C2×D11semidirect
645. #384C2×D11semidirect
713. C4×C11#538semidirect
1028. C11#35007semidirect
1208. C4#10623175semidirect

Maximal subgroups

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

subgroupindex
C2×#106231752
#130769842
#130769742
#130769622
#130769492
#130747602
#130747492
#130736912
#130736792
#130731982
#130729822
#130727492
#130723832
#130722532
#130722022
#130721502
#130720502
#130719732
#130712732
#130711222
C2×#106226012
C4×(C22⋊D11)⋊C42
C11×#24402
#3500711