Finite Group Databasebeta

← #14719141

Subgroups — #14719141

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#13066882C211yesmaximal, characteristic, complemented
2#13066880C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066872C211yesmaximal, characteristic, complemented
6#13066871C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic
9#13066864C211yesmaximal, characteristic
10#13066864C211yesmaximal, characteristic
11#13066862C211yesmaximal, characteristic
12#13066860C211yesmaximal, characteristic
13#13066860C211yesmaximal, characteristic
14#13066860C211yesmaximal, characteristic
15C11×#1443C211yesmaximal, characteristic, complemented
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
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
51C24×D11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—41no—
74C2×(C2×D11)⋊C4—41no—
75C2×(C2×D11)⋊C4—41no—
76C2×(C2×D11)⋊C4—41no—
77C2×(C2×D11)⋊C4—41no—
78C2×(C2×D11)⋊C4—41no—
79C2×(C2×D11)⋊C4—41no—
80C2×(C2×D11)⋊C4—41no—
81C2×(C2×D11)⋊C4—41no—
82C2×(C2×D11)⋊C4—41no—
83C2×(C2×D11)⋊C4—41no—
84C2×(C2×D11)⋊C4—41no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
87C2×C4⋊Dic11—41no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11—41no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—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—41no—
103C11×#95—41no—
104C11×#95—41no—
105C11×#95—41no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—22no—
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×C11C2411yescharacteristic
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—21no—
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11#4112yes—
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—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#4112yes—
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#4112yes—
236C22×Dic11#4112yes—
237C22×Dic11#4112yes—
238(C2×D11)⋊C4—44no—
239(C2×D11)⋊C4—44no—
240(C2×D11)⋊C4—44no—
241(C2×D11)⋊C4—44no—
242(C2×D11)⋊C4—44no—
243(C2×D11)⋊C4—44no—
244(C2×D11)⋊C4—44no—
245C4⋊Dic11—44no—
246Dic11⋊C4—44no—
247Dic11⋊C4—44no—
248Dic11⋊C4—44no—
249#1445—111no—
250#1444—111no—
251#1443—111no—
252#1443—111no—
253#1443D1111yescharacteristic, complemented
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#1439—111no—
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11H(5,𝔽2)11yescharacteristic
270C23×C11H(5,𝔽2)11yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C11H(5,𝔽2)11yescharacteristic
273C23×C11H(5,𝔽2)11yescharacteristic
274C23×C11H(5,𝔽2)11yescharacteristic
275C23×C11H(5,𝔽2)11yescharacteristic
276C23×C112−1+411yescharacteristic
277C23×C112−1+411yescharacteristic
278C23×C112−1+411yescharacteristic
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
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×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×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
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⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
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×#95C2×D1111yescharacteristic
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11#53811yescharacteristic
448C22×C11#53811yescharacteristic
449C22×C11#53811yescharacteristic
450C22×C11#53811yescharacteristic
451C22×C11#53811yescharacteristic
452C22×C11#53911yescharacteristic
453C22×C11#53911yescharacteristic
454C22×C11#53911yescharacteristic
455C22×C11#53911yescharacteristic
456C22×C11#54011yescharacteristic
457C22×C11#54211yescharacteristic
458C22×C11#54211yescharacteristic
459C22×C11#54211yescharacteristic
460C22×C11#54211yescharacteristic
461C22×C11#54211yescharacteristic
462C22×C11#55111yescharacteristic
463C22×C11#55111yescharacteristic
464C22×C11#55211yescharacteristic
465C22×C11#55211yescharacteristic
466C22×C11#55211yescharacteristic
467C22×C11#55311yescharacteristic
468C22×C11#55311yescharacteristic
469C22×C11#55311yescharacteristic
470C22×C11#55511yescharacteristic
471C22×C11#55911yescharacteristic
472C22×C11#56011yescharacteristic
473C22×C11#56011yescharacteristic
474C22×C11#56011yescharacteristic
475C22×C11#56011yescharacteristic
476C22×C11#56211yescharacteristic
477C22×C11#56211yescharacteristic
478C22×C11#56211yescharacteristic
479C22×C11#56311yescharacteristic
480C22×C11#56311yescharacteristic
481C22×C11#56311yescharacteristic
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—81no—
490C2×D11—81no—
491C2×D11—81no—
492C2×D11—81no—
493C2×D11—81no—
494C2×D11—81no—
495C2×D11—81no—
496C2×D11—81no—
497C4×C11—42no—
498C4×C11—81no—
499C4×C11—81no—
500C4×C11—81no—
501C4×C11—81no—
502C4×C11—81no—
503C4×C11—81no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507Dic11—81no—
508Dic11—81no—
509Dic11—81no—
510Dic11—81no—
511C25—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C2×C4⋊C4—222no—
527C2×C4⋊C4—222no—
528C2×C4⋊C4—441no—
529C2×C4⋊C4—441no—
530C2×C4⋊C4—441no—
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—222no—
539C2×C22⋊C4—222no—
540C2×C22⋊C4—222no—
541C2×C22⋊C4—222no—
542C2×C22⋊C4—222no—
543C2×C22⋊C4—222no—
544C2×C22⋊C4—222no—
545C2×C22⋊C4—441no—
546C2×C22⋊C4—441no—
547C2×C22⋊C4—441no—
548C2×C22⋊C4—441no—
549C2×C22⋊C4—441no—
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—41no—
563#95—41no—
564#95—41no—
565#95—41no—
566#95—222no—
567#95—222no—
568#95—222no—
569#95—222no—
570#95—222no—
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#273711yescharacteristic
584C2×C11#274111yescharacteristic
585C2×C11#276411yescharacteristic
586C2×C11#276511yescharacteristic
587C2×C11#277111yescharacteristic
588C2×C11#277911yescharacteristic
589C2×C11#278111yescharacteristic
590C2×C11#279511yescharacteristic
591C2×C11#279611yescharacteristic
592C2×C11#279711yescharacteristic
593C2×C11#282511yescharacteristic
594C2×C11#282711yescharacteristic
595C2×C11#283011yescharacteristic
596C2×C11#283711yescharacteristic
597C2×C11#283811yescharacteristic
598D11—82no—
599C24—112no—
600C24—221no—
601C24—221no—
602C24—221no—
603C24—221no—
604C24—221no—
605C24—221no—
606C24—221no—
607C24—221no—
608C24—221no—
609C24—221no—
610C24—221no—
611C24—221no—
612C24—221no—
613C24—221no—
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—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—112no—
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—221no—
712C22×C4#433912yes—
713C4⋊C4—444no—
714C4⋊C4—444no—
715C4⋊C4—444no—
716C4⋊C4—444no—
717C22⋊C4—444no—
718C22⋊C4—444no—
719C22⋊C4—444no—
720C22⋊C4—444no—
721C22⋊C4—444no—
722C22⋊C4—444no—
723C22⋊C4—444no—
724C11#1729011yescharacteristic, complemented, Sylow
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—441no—
733C23—441no—
734C23—441no—
735C23—441no—
736C23—441no—
737C23—441no—
738C23—441no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23C2×#433911yescharacteristic
761C23#6703711yescharacteristic
762C23#6703711yescharacteristic
763C23#6703711yescharacteristic
764C23#6704011yescharacteristic
765C23#41×D1111yescharacteristic
766C23#41×D1111yescharacteristic
767C23#41×D1111yescharacteristic
768C23#41×D1111yescharacteristic
769C23#6704211yescharacteristic
770C23#6704211yescharacteristic
771C23#6704211yescharacteristic
772C23#6704211yescharacteristic
773C23#6704311yescharacteristic
774C23#6704311yescharacteristic
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
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—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
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—442no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—881no—
881C22—881no—
882C22—881no—
883C22—881no—
884C22—881no—
885C22—881no—
886C22—881no—
887C22—881no—
888C22#1062305811yescharacteristic
889C22#1062306311yescharacteristic
890C22#1062306511yescharacteristic
891C22#1062307111yescharacteristic
892C22#1062308911yescharacteristic
893C22#1062309511yescharacteristic
894C22#1062311311yescharacteristic
895C22#1062314411yescharacteristic
896C22#1062315111yescharacteristic
897C22#1062315211yescharacteristic
898C22#1062317111yescharacteristic
899C22#1062317711yescharacteristic
900C22#1062317811yescharacteristic
901C22#1062318811yescharacteristic
902C22#1062319411yescharacteristic
903C22#1062319511yescharacteristic
904C22#1062319711yescharacteristic
905C22#1062319711yescharacteristic
906C22#1062319811yescharacteristic
907C22#1062320011yescharacteristic
908C22#1062320911yescharacteristic
909C22#1062320911yescharacteristic
910C22#1062322311yescharacteristic
911C22#1062322411yescharacteristic
912C22#1062323011yescharacteristic
913C22#1062323511yescharacteristic
914C22#1062323611yescharacteristic
915C22#1062323811yescharacteristic
916C22#1062323811yescharacteristic
917C22#1062323911yescharacteristic
918C22#1062323911yescharacteristic
919C22#1062324011yescharacteristic
920C22#1062324111yescharacteristic
921C22#1062324211yescharacteristic
922C22#1062324311yescharacteristic
923C4—42no—
924C4—81no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—81no—
929C4—81no—
930C4—442no—
931C4—442no—
932C4—442no—
933C4—881no—
934C4—881no—
935C4—881no—
936C4—881no—
937C2—882no—
938C2#1307566811yescharacteristic
939C2#1307572511yescharacteristic
940C2#1307604011yescharacteristic
941C2#1307605811yescharacteristic
942C2#1307612811yescharacteristic
943C2#1307625211yescharacteristic
944C2#1307627711yescharacteristic
945C2#1307644411yescharacteristic
946C2#1307645611yescharacteristic
947C2#1307647811yescharacteristic
948C2#1307670611yescharacteristic
949C2#1307672711yescharacteristic
950C2#1307675811yescharacteristic
951C2#1307683111yescharacteristic
952C2#1307683911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1443C2
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#17290
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. #13066882C2semidirect
2. #13066880C2semidirect
3. #13066877C2semidirect
4. #13066876C2semidirect
5. #13066872C2semidirect
6. #13066871C2semidirect
7. #13066867C2semidirect
15. C11×#1443C2semidirect
253. #1443D11semidirect
724. C11#17290semidirect

Maximal subgroups

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

subgroupindex
#130668822
#130668802
#130668772
#130668762
#130668722
#130668712
#130668672
#130668642
#130668622
#130668602
C11×#14432
#1729011