Finite Group Databasebeta

← #14719140

Subgroups — #14719140

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066883C211yesmaximal, characteristic, complemented
2#13066879C211yesmaximal, characteristic, complemented
3#13066878C211yesmaximal, characteristic, complemented
4#13066877C211yesmaximal, characteristic, complemented
5#13066876C211yesmaximal, characteristic, complemented
6#13066875C211yesmaximal, characteristic, complemented
7#13066874C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066865C211yesmaximal, characteristic
10#13066865C211yesmaximal, characteristic
11#13066863C211yesmaximal, characteristic
12#13066861C211yesmaximal, characteristic
13#13066859C211yesmaximal, characteristic
14#13066859C211yesmaximal, characteristic
15C11×#1439C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
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
51C25×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×C11×C4⋊C4—41no—
67C2×C11×C4⋊C4—41no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—41no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—41no—
82C2×C22⋊Dic11—41no—
83C2×C22⋊Dic11—41no—
84C2×C22⋊Dic11—41no—
85C2×C22⋊Dic11—41no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11—41no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—41no—
93C2×Dic11⋊C4—41no—
94C2×Dic11⋊C4—41no—
95C2×Dic11⋊C4—41no—
96C2×Dic11⋊C4—41no—
97C2×Dic11⋊C4—41no—
98C2×Dic11⋊C4—41no—
99C11×#95—22no—
100C11×#95—41no—
101C11×#95—41no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C11⋊#95—41no—
108C11⋊#95—41no—
109C11⋊#95—41no—
110C11⋊#95—41no—
111C11⋊#95—41no—
112C11⋊#95—41no—
113C11⋊#95—41no—
114C11⋊#95—41no—
115C11⋊#95—41no—
116C11⋊#95—41no—
117C11⋊#95—41no—
118C11⋊#95—41no—
119C11⋊#95—41no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123#17290—111nomaximal, Sylow
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11#4112yes—
139C24×C11C2411yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
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#4112yes—
181C22×C4×C11#4112yes—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
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#4112yes—
237C22×Dic11#4112yes—
238C11×C4⋊C4—44no—
239C11×C22⋊C4—44no—
240C11×C22⋊C4—44no—
241C11×C22⋊C4—44no—
242C22⋊Dic11—44no—
243C22⋊Dic11—44no—
244C22⋊Dic11—44no—
245C22⋊Dic11—44no—
246C4⋊Dic11—44no—
247Dic11⋊C4—44no—
248Dic11⋊C4—44no—
249#1445—111no—
250#1444—111no—
251#1443—111no—
252#1443—111no—
253#1443—111no—
254#1442—111no—
255#1442—111no—
256#1441—111no—
257#1440—111no—
258#1440—111no—
259#1440—111no—
260#1439—111no—
261#1439—111no—
262#1439—111no—
263#1439D1111yescharacteristic
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11C2×#4111yescharacteristic
300C23×C11C2×#4111yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11H(5,𝔽2)11yescharacteristic
305C23×C11H(5,𝔽2)11yescharacteristic
306C23×C11H(5,𝔽2)11yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C112−1+411yescharacteristic
312C23×C112−1+411yescharacteristic
313C23×C112−1+411yescharacteristic
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C22×C4⋊C4—111no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—111no—
415C22×C4⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4C2×D1111yescharacteristic
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95—111no—
428C2×#95—111no—
429C2×#95—111no—
430C2×#95—111no—
431C2×#95—111no—
432C2×#95—111no—
433C2×#95—111no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11#53811yescharacteristic
463C22×C11#53811yescharacteristic
464C22×C11#53811yescharacteristic
465C22×C11#53811yescharacteristic
466C22×C11#53811yescharacteristic
467C22×C11#53911yescharacteristic
468C22×C11#53911yescharacteristic
469C22×C11#53911yescharacteristic
470C22×C11#53911yescharacteristic
471C22×C11#54011yescharacteristic
472C22×C11#54211yescharacteristic
473C22×C11#54211yescharacteristic
474C22×C11#54211yescharacteristic
475C22×C11#54211yescharacteristic
476C22×C11#54211yescharacteristic
477C22×C11#55111yescharacteristic
478C22×C11#55111yescharacteristic
479C22×C11#55211yescharacteristic
480C22×C11#55211yescharacteristic
481C22×C11#55211yescharacteristic
482C22×C11#55311yescharacteristic
483C22×C11#55311yescharacteristic
484C22×C11#55311yescharacteristic
485C22×C11#55511yescharacteristic
486C22×C11#55911yescharacteristic
487C22×C11#56011yescharacteristic
488C22×C11#56011yescharacteristic
489C22×C11#56011yescharacteristic
490C22×C11#56011yescharacteristic
491C22×C11#56211yescharacteristic
492C22×C11#56211yescharacteristic
493C22×C11#56211yescharacteristic
494C22×C11#56311yescharacteristic
495C22×C11#56311yescharacteristic
496C22×C11#56311yescharacteristic
497C4×C11—42no—
498C4×C11—42no—
499C4×C11—81no—
500C4×C11—81no—
501C4×C11—81no—
502C4×C11—81no—
503Dic11—42no—
504Dic11—42no—
505Dic11—81no—
506Dic11—81no—
507Dic11—81no—
508Dic11—81no—
509Dic11—81no—
510Dic11—81no—
511C25C22×D1111yescharacteristic
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—441no—
532C2×C4⋊C4—441no—
533C2×C4⋊C4—441no—
534C2×C4⋊C4—441no—
535C2×C4⋊C4—441no—
536C2×C4⋊C4—441no—
537C2×C4⋊C4—441no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—222no—
548C2×C22⋊C4—222no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—441no—
551C2×C22⋊C4—441no—
552C2×C22⋊C4—441no—
553C2×C22⋊C4—441no—
554C2×C22⋊C4—441no—
555C2×C22⋊C4—441no—
556C2×C22⋊C4—441no—
557C2×C22⋊C4—441no—
558C2×C22⋊C4—441no—
559#95—22no—
560#95—41no—
561#95—41no—
562#95—222no—
563#95—222no—
564#95—222no—
565#95—222no—
566#95—222no—
567#95—441no—
568#95—441no—
569#95—441no—
570#95—441no—
571#95—441no—
572#95—441no—
573#95—441no—
574#95—441no—
575#95—441no—
576#95—441no—
577#95—441no—
578#95—441no—
579#95—441no—
580#95—441no—
581#95—441no—
582#95—441no—
583C2×C11—82no—
584C2×C11#273711yescharacteristic
585C2×C11#274111yescharacteristic
586C2×C11#276411yescharacteristic
587C2×C11#276511yescharacteristic
588C2×C11#277111yescharacteristic
589C2×C11#277911yescharacteristic
590C2×C11#278111yescharacteristic
591C2×C11#279511yescharacteristic
592C2×C11#279611yescharacteristic
593C2×C11#279711yescharacteristic
594C2×C11#282511yescharacteristic
595C2×C11#282711yescharacteristic
596C2×C11#283011yescharacteristic
597C2×C11#283711yescharacteristic
598C2×C11#283811yescharacteristic
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24#434112yes—
614C24C23×D1111yescharacteristic
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4#433912yes—
712C22×C4#434112yes—
713C4⋊C4—44no—
714C4⋊C4—444no—
715C4⋊C4—444no—
716C4⋊C4—444no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—444no—
721C22⋊C4—444no—
722C22⋊C4—444no—
723C22⋊C4—444no—
724C11#1729011yescharacteristic, complemented, Sylow
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23C2×#433911yescharacteristic
761C23C2×#434111yescharacteristic
762C23C2×#434111yescharacteristic
763C23#6703711yescharacteristic
764C23#6703711yescharacteristic
765C23#6703711yescharacteristic
766C23#6703711yescharacteristic
767C23#6703711yescharacteristic
768C23#6704011yescharacteristic
769C23#41×D1111yescharacteristic
770C23#41×D1111yescharacteristic
771C23#6704211yescharacteristic
772C23#6704211yescharacteristic
773C23#6704311yescharacteristic
774C23#6704311yescharacteristic
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4—441no—
830C2×C4—441no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—441no—
837C2×C4—441no—
838C2×C4—441no—
839C2×C4—441no—
840C2×C4—441no—
841C2×C4—441no—
842C2×C4—441no—
843C2×C4—441no—
844C2×C4—441no—
845C2×C4—441no—
846C2×C4—441no—
847C2×C4—441no—
848C2×C4—441no—
849C2×C4—441no—
850C2×C4—441no—
851C2×C4—441no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22#1062302611yescharacteristic
889C22#1062304411yescharacteristic
890C22#1062306611yescharacteristic
891C22#1062308711yescharacteristic
892C22#1062309011yescharacteristic
893C22#1062309211yescharacteristic
894C22#1062309511yescharacteristic
895C22#1062312411yescharacteristic
896C22#1062312411yescharacteristic
897C22#1062312611yescharacteristic
898C22#1062313211yescharacteristic
899C22#1062313311yescharacteristic
900C22#1062313411yescharacteristic
901C22#1062314711yescharacteristic
902C22#1062314811yescharacteristic
903C22#1062314911yescharacteristic
904C22#1062315111yescharacteristic
905C22#1062315111yescharacteristic
906C22#1062316911yescharacteristic
907C22#1062317111yescharacteristic
908C22#1062317411yescharacteristic
909C22#1062317711yescharacteristic
910C22#1062317711yescharacteristic
911C22#1062317811yescharacteristic
912C22#1062318111yescharacteristic
913C22#1062318111yescharacteristic
914C22#1062318811yescharacteristic
915C22#1062319111yescharacteristic
916C22#1062319811yescharacteristic
917C22#1062320011yescharacteristic
918C22#1062320911yescharacteristic
919C22#1062321511yescharacteristic
920C22#1062324011yescharacteristic
921C22#1062324311yescharacteristic
922C22#1062325111yescharacteristic
923C4—42no—
924C4—42no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—81no—
929C4—442no—
930C4—442no—
931C4—881no—
932C4—881no—
933C4—881no—
934C4—881no—
935C4—881no—
936C4—881no—
937C2—82no—
938C2#1307566911yescharacteristic
939C2#1307573111yescharacteristic
940C2#1307603711yescharacteristic
941C2#1307605311yescharacteristic
942C2#1307613411yescharacteristic
943C2#1307624211yescharacteristic
944C2#1307628111yescharacteristic
945C2#1307644211yescharacteristic
946C2#1307645811yescharacteristic
947C2#1307647611yescharacteristic
948C2#1307670411yescharacteristic
949C2#1307671711yescharacteristic
950C2#1307676011yescharacteristic
951C2#1307682811yescharacteristic
952C2#1307684711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1439C2
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#17290
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. #13066883C2semidirect
2. #13066879C2semidirect
3. #13066878C2semidirect
4. #13066877C2semidirect
5. #13066876C2semidirect
6. #13066875C2semidirect
7. #13066874C2semidirect
8. #13066868C2semidirect
724. C11#17290semidirect

Maximal subgroups

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

subgroupindex
#130668832
#130668792
#130668782
#130668772
#130668762
#130668752
#130668742
#130668682
#130668652
#130668632
#130668612
#130668592
C11×#14392
#1729011