Finite Group Databasebeta

← #14681400

Subgroups — #14681400

Order 2816.

1606 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×#10622553C211yesmaximal, characteristic
2C2×#10622546C211yesmaximal, characteristic, complemented
3C2×#10622602C211yesmaximal, characteristic
4C2×#10622277C211yesmaximal, characteristic
5C2×#10622280C211yesmaximal, characteristic
6#13066880C211yesmaximal, characteristic, complemented
7#13066876C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066867C211yesmaximal, characteristic, complemented
10#13066864C211yesmaximal, characteristic
11#13066862C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic
13#13066847C211yesmaximal, characteristic, complemented
14#13066845C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
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#10622602C418yescomplemented
52#10622553—24no—
53#10622546—24no—
54#10622280—24no—
55#10622277—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11C2×C414yes—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4C2×C414yes—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11—41no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4D414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4C2×C414yes—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—41no—
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—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yes—
138C11⋊#95C2×C414yes—
139C11⋊#95D414yes—
140#14381—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11C22×C412yes—
155C23×D11C2×D412yes—
156C23×D11#4112yes—
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×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
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—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11#4112yes—
255C2×C4×D11—28no—
256C2×C4×D11—28no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C11×C4⋊C4—44no—
263C42×C11—44no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—44no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C4×Dic11—44no—
276C2×#388—111no—
277C2×#387—111no—
278C2×#385—111no—
279C2×#381—111no—
280C2×#380—111no—
281#1444—111no—
282#1443—111no—
283#1442—111no—
284#1441—111no—
285#1440—111no—
286#1439—111no—
287#1437—111no—
288#1436—111no—
289#1436D1111yescharacteristic, complemented
290C4⋊#95—111no—
291C23×C11C23×C411yescharacteristic
292C23×C11C22×D411yescharacteristic
293C23×C11C22×D411yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4111yescharacteristic
297C23×C11C2×#4111yescharacteristic
298C23×C11H(5,𝔽2)11yescharacteristic
299C23×C11H(5,𝔽2)11yescharacteristic
300C23×C11H(5,𝔽2)11yescharacteristic
301C23×C11H(5,𝔽2)11yescharacteristic
302C23×C112−1+411yescharacteristic
303C23×C112−1+411yescharacteristic
304C23×C112−1+411yescharacteristic
305C23×C112−1+411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11C4×D414yes—
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—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
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×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11#11714yes—
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—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
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—41no—
438C2×Dic11C4×D414yes—
439C4×D11—416no—
440C24×C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4—111no—
446C22×C4⋊C4C2×D1111yescharacteristic
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C42—111no—
454C22×C42C2×D1111yescharacteristic
455#388—224no—
456#387—224no—
457#385—118no—
458#381—224no—
459#380—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×#95C2×D1111yescharacteristic
476C2×#95C2×D1111yescharacteristic
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C22×C11C2×#11711yescharacteristic
481C22×C11C2×C4×D411yescharacteristic
482C22×C11C2×C4×D411yescharacteristic
483C22×C11#51811yescharacteristic
484C22×C11#51911yescharacteristic
485C22×C11#52011yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11#53411yescharacteristic
488C22×C11#53611yescharacteristic
489C22×C11#53611yescharacteristic
490C22×C11#53711yescharacteristic
491C22×C11#53811yescharacteristic
492C22×C11#53811yescharacteristic
493C22×C11#53911yescharacteristic
494C22×C11#53911yescharacteristic
495C22×C11#53911yescharacteristic
496C22×C11#53911yescharacteristic
497C22×C11#54111yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11D4211yescharacteristic
500C22×C11#54611yescharacteristic
501C22×C11#54611yescharacteristic
502C22×C11#54711yescharacteristic
503C22×C11#54711yescharacteristic
504C22×C11#54711yescharacteristic
505C22×C11#55011yescharacteristic
506C22×C11#55111yescharacteristic
507C22×C11#55211yescharacteristic
508C22×C11#55211yescharacteristic
509C22×C11#55511yescharacteristic
510C22×C11#55611yescharacteristic
511C22×C11#56211yescharacteristic
512C22×C11#56211yescharacteristic
513C22×C11#56311yescharacteristic
514C22×C11#56311yescharacteristic
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C4×C11—24no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—81no—
536C4×C11—81no—
537Dic11—24no—
538Dic11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—81no—
543Dic11—81no—
544C25—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—114no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—222no—
554C23×C4—222no—
555C23×C4—222no—
556C23×C4—222no—
557C23×C4—441no—
558C23×C4—441no—
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—114no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—441no—
578C2×C4⋊C4—441no—
579C2×C4⋊C4—441no—
580C2×C4⋊C4—441no—
581C2×C4⋊C4—441no—
582C2×C4⋊C4—441no—
583C2×C4⋊C4C4×D1114yes—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—222no—
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—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4—441no—
598C2×C22⋊C4—441no—
599C2×C22⋊C4—441no—
600C2×C22⋊C4—441no—
601C2×C22⋊C4—441no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—222no—
606C2×C42—441no—
607C2×C42—441no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—114no—
614#95—114no—
615#95—114no—
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—441no—
625#95—441no—
626#95—441no—
627#95—441no—
628C2×C11#231811yescharacteristic
629C2×C11#232211yescharacteristic
630C2×C11#232311yescharacteristic
631C2×C11#234411yescharacteristic
632C2×C11#235411yescharacteristic
633C2×C11#235811yescharacteristic
634C2×C11#237811yescharacteristic
635C2×C11#268011yescharacteristic
636C2×C11#268211yescharacteristic
637C2×C11#268611yescharacteristic
638C2×C11#268911yescharacteristic
639C2×C11#269411yescharacteristic
640C2×C11#269511yescharacteristic
641C2×C11#274411yescharacteristic
642C2×C11#274511yescharacteristic
643D11—44no—
644C24—112no—
645C24—112no—
646C24—112no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24—221no—
658C24—221no—
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—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—228no—
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—221no—
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—444no—
754C22×C4—444no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4—444no—
758C22×C4C2×C4×D1112yes—
759C22×C4C2×C4×D1112yes—
760C22×C4C2×C4×D1112yes—
761C22×C4#433912yes—
762C22×C4#433912yes—
763C22×C4D4×D1112yes—
764C22×C4D4×D1112yes—
765C4⋊C4—44no—
766C4⋊C4—228no—
767C4⋊C4—444no—
768C4⋊C4—444no—
769C4⋊C4—444no—
770C4⋊C4—444no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—444no—
774C22⋊C4—444no—
775C22⋊C4—444no—
776C22⋊C4—444no—
777C42—44no—
778C42—444no—
779C11#1438111yescharacteristic, complemented, Sylow
780C23—114no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23C22×C4×D1111yescharacteristic
816C23C2×#433911yescharacteristic
817C23C2×#433911yescharacteristic
818C23C2×D4×D1111yescharacteristic
819C23C2×D4×D1111yescharacteristic
820C23#6703711yescharacteristic
821C23#6703711yescharacteristic
822C23#6704011yescharacteristic
823C23#6704011yescharacteristic
824C23#41×D1111yescharacteristic
825C23#41×D1111yescharacteristic
826C23#6704211yescharacteristic
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—22no—
846C2×C4—22no—
847C2×C4—22no—
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—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—114no—
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—4416no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
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#6692514yes—
929C22—224no—
930C22—224no—
931C22—224no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22C2×#6692511yescharacteristic
945C22#1062301711yescharacteristic
946C22#1062303811yescharacteristic
947C22#1062303811yescharacteristic
948C22#1062305411yescharacteristic
949C22#1062306011yescharacteristic
950C22#1062306311yescharacteristic
951C22C4×D4×D1111yescharacteristic
952C22C4×D4×D1111yescharacteristic
953C22#1062308211yescharacteristic
954C22#1062308411yescharacteristic
955C22#1062309111yescharacteristic
956C22#1062309111yescharacteristic
957C22#1062309511yescharacteristic
958C22#1062309511yescharacteristic
959C22#1062309911yescharacteristic
960C22#1062310311yescharacteristic
961C22#1062310511yescharacteristic
962C22#1062311211yescharacteristic
963C22#1062312111yescharacteristic
964C22#1062314311yescharacteristic
965C22#1062314311yescharacteristic
966C22#1062315911yescharacteristic
967C22#1062316011yescharacteristic
968C22#1062317711yescharacteristic
969C22#1062317811yescharacteristic
970C22#1062317911yescharacteristic
971C22#1062318411yescharacteristic
972C22#1062319011yescharacteristic
973C22#1062321511yescharacteristic
974C22#1062322311yescharacteristic
975C22#1062322711yescharacteristic
976C22#1062323811yescharacteristic
977C22#1062324111yescharacteristic
978C22#1062326611yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—81no—
986C4—224no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C4—881no—
992C4—881no—
993C2—444no—
994C2#1307124311yescharacteristic
995C2#1307128911yescharacteristic
996C2#1307129711yescharacteristic
997C2#1307148111yescharacteristic
998C2#1307156111yescharacteristic
999C2#1307159911yescharacteristic
1000C2#1307177711yescharacteristic
1001C2#1307495811yescharacteristic
1002C2#1307498211yescharacteristic
1003C2#1307502311yescharacteristic
1004C2#1307506811yescharacteristic
1005C2#1307513711yescharacteristic
1006C2#1307515211yescharacteristic
1007C2#1307576711yescharacteristic
1008C2#1307578211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14381
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622546C2semidirect
6. #13066880C2semidirect
7. #13066876C2semidirect
8. #13066874C2semidirect
9. #13066867C2semidirect
13. #13066847C2semidirect
14. #13066845C2semidirect
15. C11×#1436C2semidirect
51. #10622602C4semidirect
289. #1436D11semidirect
779. C11#14381semidirect

Maximal subgroups

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

subgroupindex
C2×#106225532
C2×#106225462
C2×#106226022
C2×#106222772
C2×#106222802
#130668802
#130668762
#130668742
#130668672
#130668642
#130668622
#130668522
#130668472
#130668452
C11×#14362
#1438111