Finite Group Databasebeta

← #14719166

Subgroups — #14719166

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#13066877C211yesmaximal, characteristic, complemented
2#13066877C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066871C211yesmaximal, characteristic, complemented
5#13066868C211yesmaximal, characteristic, complemented
6#13066868C211yesmaximal, characteristic, complemented
7#13066866C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic
9#13066864C211yesmaximal, characteristic
10#13066864C211yesmaximal, characteristic
11#13066862C211yesmaximal, characteristic
12#13066860C211yesmaximal, characteristic
13#13066860C211yesmaximal, characteristic
14#13066858C211yesmaximal, characteristic
15C11×#1442C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊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×(C2×D11)⋊C4C2211yescharacteristic
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
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×C11×C4⋊C4—41no—
67C2×C11×C4⋊C4—41no—
68C2×C11×C4⋊C4—41no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
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×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—41no—
93C2×Dic11⋊C4—22no—
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—22no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—22no—
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#17291—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#4112yes—
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—21no—
236C22×Dic11#4112yes—
237C22×Dic11#4112yes—
238C11×C4⋊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—
245(C2×D11)⋊C4—44no—
246C4⋊Dic11—44no—
247Dic11⋊C4—44no—
248Dic11⋊C4—44no—
249#1443—111no—
250#1443—111no—
251#1443—111no—
252#1442—111no—
253#1442D1111yescharacteristic, complemented
254#1441—111no—
255#1441—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—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×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—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⋊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×#95—111no—
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#53811yescharacteristic
453C22×C11#53911yescharacteristic
454C22×C11#54011yescharacteristic
455C22×C11#54111yescharacteristic
456C22×C11#54211yescharacteristic
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#55311yescharacteristic
471C22×C11#55311yescharacteristic
472C22×C11#56011yescharacteristic
473C22×C11#56011yescharacteristic
474C22×C11#56011yescharacteristic
475C22×C11#56211yescharacteristic
476C22×C11#56211yescharacteristic
477C22×C11#56211yescharacteristic
478C22×C11#56211yescharacteristic
479C22×C11#56211yescharacteristic
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—42no—
499C4×C11—81no—
500C4×C11—81no—
501C4×C11—81no—
502C4×C11—81no—
503C4×C11—81no—
504Dic11—42no—
505Dic11—42no—
506Dic11—81no—
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—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
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—222no—
566#95—222no—
567#95—222no—
568#95—222no—
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#273911yescharacteristic
584C2×C11#274111yescharacteristic
585C2×C11#276111yescharacteristic
586C2×C11#276411yescharacteristic
587C2×C11#277011yescharacteristic
588C2×C11#277211yescharacteristic
589C2×C11#277811yescharacteristic
590C2×C11#277811yescharacteristic
591C2×C11#277911yescharacteristic
592C2×C11#280111yescharacteristic
593C2×C11#282611yescharacteristic
594C2×C11#282911yescharacteristic
595C2×C11#283011yescharacteristic
596C2×C11#283011yescharacteristic
597C2×C11#283111yescharacteristic
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—112no—
663C22×C4—112no—
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#434312yes—
713C4⋊C4—44no—
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#1729111yescharacteristic, 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#6703711yescharacteristic
765C23C2×#434311yescharacteristic
766C23#6704011yescharacteristic
767C23#41×D1111yescharacteristic
768C23#41×D1111yescharacteristic
769C23#41×D1111yescharacteristic
770C23#6704211yescharacteristic
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—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—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—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#1062304511yescharacteristic
889C22#1062306211yescharacteristic
890C22#1062306511yescharacteristic
891C22#1062307111yescharacteristic
892C22#1062308911yescharacteristic
893C22#1062309111yescharacteristic
894C22#1062311311yescharacteristic
895C22#1062312611yescharacteristic
896C22#1062314611yescharacteristic
897C22#1062315111yescharacteristic
898C22#1062315211yescharacteristic
899C22#1062316811yescharacteristic
900C22#1062317111yescharacteristic
901C22#1062317511yescharacteristic
902C22#1062317711yescharacteristic
903C22#1062317811yescharacteristic
904C22#1062318811yescharacteristic
905C22#1062318811yescharacteristic
906C22#1062318811yescharacteristic
907C22#1062319811yescharacteristic
908C22#1062319811yescharacteristic
909C22#1062320011yescharacteristic
910C22#1062320011yescharacteristic
911C22#1062320911yescharacteristic
912C22#1062321511yescharacteristic
913C22#1062322411yescharacteristic
914C22#1062322611yescharacteristic
915C22#1062322611yescharacteristic
916C22#1062322811yescharacteristic
917C22#1062323011yescharacteristic
918C22#1062323611yescharacteristic
919C22#1062323811yescharacteristic
920C22#1062323911yescharacteristic
921C22#1062324211yescharacteristic
922C22#1062326411yescharacteristic
923C4—42no—
924C4—42no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—81no—
929C4—81no—
930C4—442no—
931C4—442no—
932C4—881no—
933C4—881no—
934C4—881no—
935C4—881no—
936C4—881no—
937C2—882no—
938C2#1307570811yescharacteristic
939C2#1307573211yescharacteristic
940C2#1307599611yescharacteristic
941C2#1307604011yescharacteristic
942C2#1307611411yescharacteristic
943C2#1307614011yescharacteristic
944C2#1307622811yescharacteristic
945C2#1307624011yescharacteristic
946C2#1307625211yescharacteristic
947C2#1307652111yescharacteristic
948C2#1307670811yescharacteristic
949C2#1307674111yescharacteristic
950C2#1307675711yescharacteristic
951C2#1307676011yescharacteristic
952C2#1307677811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1442C2
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#17291
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. #13066877C2semidirect
2. #13066877C2semidirect
3. #13066877C2semidirect
4. #13066871C2semidirect
5. #13066868C2semidirect
6. #13066868C2semidirect
7. #13066866C2semidirect
15. C11×#1442C2semidirect
253. #1442D11semidirect
724. C11#17291semidirect

Maximal subgroups

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

subgroupindex
#130668772
#130668712
#130668682
#130668662
#130668642
#130668622
#130668602
#130668582
C11×#14422
#1729111