Finite Group Databasebeta

← #14677025

Subgroups — #14677025

Order 2816.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C211yesmaximal, characteristic
2C2×#10622268C211yesmaximal, characteristic, complemented
3C2×#10622559C211yesmaximal, characteristic
4C2×#10622556C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic
6#13066876C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13#13066841C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622564—24no—
52#10622559C418yescomplemented
53#10622556—24no—
54C22⋊C4×Dic11—24no—
55#10622268—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—41no—
68C23×Dic11—41no—
69C23×Dic11C2×C414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11C2×C414yes—
95C2×C22⋊Dic11D414yes—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—41no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4C2×C414yes—
107C2×Dic11⋊C4C2×C414yes—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—41no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95C2×C414yes—
138C11⋊#95C2×C414yes—
139C11⋊#95D414yes—
140#14008—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11C22×C412yes—
154C24×C11C2×D412yes—
155C24×C11#4112yes—
156C24×C11C2411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11#4112yes—
198C22×C4×C11#4112yes—
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11—44no—
248C22×Dic11—44no—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—44no—
265C22⋊Dic11—28no—
266C22⋊Dic11—28no—
267C22⋊Dic11—44no—
268C4⋊Dic11—44no—
269Dic11⋊C4—28no—
270Dic11⋊C4—44no—
271Dic11⋊C4—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C4×Dic11—44no—
275C4×Dic11—44no—
276C2×#388—111no—
277C2×#387—111no—
278C2×#385—111no—
279C2×#381—111no—
280C2×C4×C22⋊C4—111no—
281#1443—111no—
282#1441—111no—
283#1440D1111yescharacteristic
284#1439—111no—
285#1437—111no—
286#1436—111no—
287#1436—111no—
288C4⋊#95—111no—
289#1434—111no—
290C4×#95—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11C4×D414yes—
326C23×C11C23×C411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
339C23×C112−1+411yescharacteristic
340C23×C112−1+411yescharacteristic
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—416no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11#11714yes—
438C2×Dic11C4×D414yes—
439C2×Dic11#12314yes—
440C24×C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4C2×D1111yescharacteristic
449C22×C22⋊C4C2×D1111yescharacteristic
450C22×C22⋊C4C2×D1111yescharacteristic
451C22×C42—111no—
452C22×C42—111no—
453C22×C42—111no—
454C22×C42—111no—
455#388—224no—
456#387—224no—
457#385—118no—
458#381—224no—
459C4×C22⋊C4—224no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95C2×D1111yescharacteristic
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11C2×#11711yescharacteristic
496C22×C11C2×C4×D411yescharacteristic
497C22×C11C2×C4×D411yescharacteristic
498C22×C11C4×#4111yescharacteristic
499C22×C11C4×#4111yescharacteristic
500C22×C11#51811yescharacteristic
501C22×C11#51911yescharacteristic
502C22×C11C2×#12311yescharacteristic
503C22×C11#52511yescharacteristic
504C22×C11#52911yescharacteristic
505C22×C11#52911yescharacteristic
506C22×C11#52911yescharacteristic
507C22×C11#52911yescharacteristic
508C22×C11#53211yescharacteristic
509C22×C11#53211yescharacteristic
510C22×C11#53911yescharacteristic
511C22×C11#53911yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11D4211yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54711yescharacteristic
518C22×C11#54711yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54811yescharacteristic
521C22×C11#55111yescharacteristic
522C22×C11#55111yescharacteristic
523C22×C11#55111yescharacteristic
524C22×C11#55211yescharacteristic
525C22×C11#55211yescharacteristic
526C22×C11#55211yescharacteristic
527C22×C11#55311yescharacteristic
528C22×C11#55311yescharacteristic
529C22×C11#55611yescharacteristic
530C4×C11—42no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—81no—
536Dic11—24no—
537Dic11—24no—
538Dic11—24no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—42no—
543Dic11—81no—
544C25C22×D1111yescharacteristic
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—114no—
553C23×C4—111no—
554C23×C4—222no—
555C23×C4—222no—
556C23×C4—222no—
557C23×C4—222no—
558C23×C4—441no—
559C23×C4—441no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—441no—
575C2×C4⋊C4—441no—
576C2×C4⋊C4—441no—
577C2×C4⋊C4—441no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4C4×D1114yes—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42—222no—
604C2×C42—222no—
605C2×C42—441no—
606C2×C42—441no—
607C2×C42—441no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—114no—
613#95—114no—
614#95—114no—
615#95—222no—
616#95—222no—
617#95—222no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95—222no—
623#95—222no—
624#95—222no—
625#95—222no—
626#95—222no—
627#95—222no—
628C2×C11—44no—
629C2×C11#229311yescharacteristic
630C2×C11C4×#12311yescharacteristic
631C2×C11#233211yescharacteristic
632C2×C11#234411yescharacteristic
633C2×C11#235311yescharacteristic
634C2×C11#235811yescharacteristic
635C2×C11#236211yescharacteristic
636C2×C11#241911yescharacteristic
637C2×C11#242211yescharacteristic
638C2×C11#246111yescharacteristic
639C2×C11#246611yescharacteristic
640C2×C11#251511yescharacteristic
641C2×C11#252711yescharacteristic
642C2×C11#255311yescharacteristic
643C2×C11#255811yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D1112yes—
657C24D4×D1112yes—
658C24#434112yes—
659C24C23×D1111yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—228no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—228no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4—444no—
758C22×C4—444no—
759C22×C4—444no—
760C22×C4C2×C4×D1112yes—
761C22×C4C2×C4×D1112yes—
762C22×C4D4×D1112yes—
763C22×C4#434112yes—
764C22×C4#434112yes—
765C4⋊C4—228no—
766C4⋊C4—444no—
767C4⋊C4—444no—
768C4⋊C4—444no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—44no—
772C22⋊C4—228no—
773C22⋊C4—228no—
774C22⋊C4—444no—
775C42—444no—
776C42—444no—
777C42—444no—
778C42—444no—
779C11#1400811yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23(C22⋊D11)⋊C414yes—
815C23C22×C4×D1111yescharacteristic
816C23C2×D4×D1111yescharacteristic
817C23C2×D4×D1111yescharacteristic
818C23C2×#434111yescharacteristic
819C23C2×#434111yescharacteristic
820C23C2×#434111yescharacteristic
821C23#6703711yescharacteristic
822C23#41×D1111yescharacteristic
823C23#41×D1111yescharacteristic
824C23#41×D1111yescharacteristic
825C23#41×D1111yescharacteristic
826C23#41×D1111yescharacteristic
827C23#6704211yescharacteristic
828C23#6704311yescharacteristic
829C23#6704311yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—114no—
873C2×C4—114no—
874C2×C4—114no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—4416no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×(C22⋊D11)⋊C411yescharacteristic
945C22#1062304711yescharacteristic
946C22D11×#11711yescharacteristic
947C22C4×#434111yescharacteristic
948C22C4×#434111yescharacteristic
949C22C4×D4×D1111yescharacteristic
950C22#1062307611yescharacteristic
951C22#1062311711yescharacteristic
952C22#1062312211yescharacteristic
953C22#1062312711yescharacteristic
954C22#1062312911yescharacteristic
955C22#1062313111yescharacteristic
956C22#1062313111yescharacteristic
957C22#1062313311yescharacteristic
958C22#1062314011yescharacteristic
959C22#1062314111yescharacteristic
960C22#1062314511yescharacteristic
961C22#1062318011yescharacteristic
962C22#1062318111yescharacteristic
963C22#1062318111yescharacteristic
964C22D11×#12311yescharacteristic
965C22#1062318611yescharacteristic
966C22#1062318611yescharacteristic
967C22#1062318611yescharacteristic
968C22#1062318911yescharacteristic
969C22#1062318911yescharacteristic
970C22#1062319111yescharacteristic
971C22#1062319911yescharacteristic
972C22#1062320211yescharacteristic
973C22#1062321011yescharacteristic
974C22#1062321311yescharacteristic
975C22#1062323711yescharacteristic
976C22#1062323911yescharacteristic
977C22#1062324011yescharacteristic
978C22#1062324111yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—224no—
986C4—224no—
987C4—224no—
988C4—442no—
989C4—442no—
990C4—442no—
991C4—442no—
992C4—881no—
993C2—44no—
994C2#1307107611yescharacteristic
995C2#1307114111yescharacteristic
996C2#1307136611yescharacteristic
997C2#1307148011yescharacteristic
998C2#1307155111yescharacteristic
999C2#1307159611yescharacteristic
1000C2#1307164611yescharacteristic
1001C2#1307208811yescharacteristic
1002C2#1307212511yescharacteristic
1003C2#1307257611yescharacteristic
1004C2#1307264511yescharacteristic
1005C2#1307322811yescharacteristic
1006C2#1307340411yescharacteristic
1007C2#1307365411yescharacteristic
1008C2#1307373111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11#14008
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#10622268C2semidirect
6. #13066876C2semidirect
7. #13066870C2semidirect
10. #13066851C2semidirect
11. #13066847C2semidirect
12. Dic11⋊#95C2semidirect
13. #13066841C2semidirect
14. #95×Dic11C2semidirect
52. #10622559C4semidirect
779. C11#14008semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106222682
C2×#106225592
C2×#106225562
C2×C22⋊C4×Dic112
#130668762
#130668702
#130668592
#130668532
#130668512
#130668472
Dic11⋊#952
#130668412
#95×Dic112
C11×#14402
#1400811