Finite Group Databasebeta

← #14718688

Subgroups — #14718688

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 1102 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#13066871C211yesmaximal, characteristic, complemented
4#13066871C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic
13#13066855C211yesmaximal, characteristic
14#13066855C211yesmaximal, characteristic
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
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
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—41no—
63C22×C22⋊D11—41no—
64C22×C22⋊D11—41no—
65C22×C22⋊D11—41no—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—41no—
78C2×C11×C22⋊C4—41no—
79C2×C11×C22⋊C4—41no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—41no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11—41no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4—41no—
111C2×Dic11⋊C4—41no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C11×#95—41no—
116C11×#95—41no—
117C11×#95—41no—
118C11×#95—41no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135#17255—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
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#4112yes—
151C24×C11C2411yescharacteristic
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11#4112yes—
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×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
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×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11#4112yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C11×C22⋊C4—44no—
266C11×C22⋊C4—44no—
267C11×C22⋊C4—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4—44no—
277Dic11⋊C4—44no—
278Dic11⋊C4—44no—
279#1443—111no—
280#1443—111no—
281#1442—111no—
282#1442—111no—
283#1440—111no—
284#1440—111no—
285#1440—111no—
286#1440D1111yescharacteristic, complemented
287#1439—111no—
288#1439—111no—
289#1439—111no—
290#1439—111no—
291#1438—111no—
292#1438—111no—
293#1438—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
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×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C112−1+411yescharacteristic
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—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—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C22⋊D11—416no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C23×D4—111no—
472C22×C4⋊C4—111no—
473C22×C4⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4C2×D1111yescharacteristic
484C22×C22⋊C4C2×D1111yescharacteristic
485C22×C22⋊C4C2×D1111yescharacteristic
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95C2×D1111yescharacteristic
503C2×#95C2×D1111yescharacteristic
504C2×#95C2×D1111yescharacteristic
505C2×#95C2×D1111yescharacteristic
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—81no—
514C22×C11—81no—
515C22×C11—81no—
516C22×C11—81no—
517C22×C11—81no—
518C22×C11—81no—
519C22×C11—81no—
520C22×C11—81no—
521C22×C11#53811yescharacteristic
522C22×C11#53811yescharacteristic
523C22×C11#53811yescharacteristic
524C22×C11#53811yescharacteristic
525C22×C11#53811yescharacteristic
526C22×C11#53811yescharacteristic
527C22×C11#53811yescharacteristic
528C22×C11#53811yescharacteristic
529C22×C11#53811yescharacteristic
530C22×C11#53911yescharacteristic
531C22×C11#53911yescharacteristic
532C22×C11#54011yescharacteristic
533C22×C11#54011yescharacteristic
534C22×C11#54011yescharacteristic
535C22×C11#54211yescharacteristic
536C22×C11#55111yescharacteristic
537C22×C11#55111yescharacteristic
538C22×C11#55111yescharacteristic
539C22×C11#55111yescharacteristic
540C22×C11#55211yescharacteristic
541C22×C11#55311yescharacteristic
542C22×C11#55311yescharacteristic
543C22×C11#55311yescharacteristic
544C22×C11#55511yescharacteristic
545C22×C11#55911yescharacteristic
546C22×C11#56011yescharacteristic
547C22×C11#56011yescharacteristic
548C22×C11#56011yescharacteristic
549C22×C11#56011yescharacteristic
550C22×C11#56011yescharacteristic
551C22×C11#56011yescharacteristic
552C22×C11H(3,𝔽4)11yescharacteristic
553C22×C11#56211yescharacteristic
554C22×C11#56211yescharacteristic
555C22×C11#56211yescharacteristic
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—81no—
564C2×D11—81no—
565C2×D11—81no—
566C2×D11—81no—
567C2×D11—81no—
568C2×D11—81no—
569C2×D11—81no—
570C2×D11—81no—
571C4×C11—81no—
572C4×C11—81no—
573C4×C11—81no—
574C4×C11—81no—
575C4×C11—81no—
576C4×C11—81no—
577Dic11—42no—
578Dic11—42no—
579Dic11—42no—
580Dic11—81no—
581Dic11—81no—
582Dic11—81no—
583Dic11—81no—
584C25—111no—
585C25C22×D1111yescharacteristic
586C22×D4—222no—
587C22×D4—222no—
588C22×D4—222no—
589C22×D4—441no—
590C22×D4—441no—
591C22×D4—441no—
592C22×D4—441no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—111no—
597C23×C4—111no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C2×C4⋊C4—441no—
607C2×C4⋊C4—441no—
608C2×C4⋊C4—441no—
609C2×C4⋊C4—441no—
610C2×C4⋊C4—441no—
611C2×C4⋊C4—441no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—441no—
629C2×C22⋊C4—441no—
630C2×C22⋊C4—441no—
631C2×C22⋊C4—441no—
632C2×C22⋊C4—441no—
633C2×C22⋊C4—441no—
634C2×C22⋊C4—441no—
635C2×C22⋊C4—441no—
636C2×C22⋊C4—441no—
637C2×C22⋊C4—441no—
638C2×C22⋊C4—441no—
639C2×C22⋊C4—441no—
640C2×C22⋊C4—441no—
641C2×C22⋊C4—441no—
642C2×C22⋊C4—441no—
643C2×C22⋊C4—441no—
644C2×C22⋊C4—441no—
645C2×C22⋊C4—441no—
646C2×C22⋊C4—441no—
647C2×C22⋊C4—441no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—222no—
653#95—222no—
654#95—222no—
655#95—222no—
656#95—441no—
657#95—441no—
658#95—441no—
659#95—441no—
660#95—441no—
661#95—441no—
662#95—441no—
663#95—441no—
664#95—441no—
665#95—441no—
666#95—441no—
667#95—441no—
668C2×C11—82no—
669C2×C11#273611yescharacteristic
670C2×C11#274311yescharacteristic
671C2×C11#274911yescharacteristic
672C2×C11#275611yescharacteristic
673C2×C11#276111yescharacteristic
674C2×C11#277811yescharacteristic
675C2×C11#278111yescharacteristic
676C2×C11#279611yescharacteristic
677C2×C11#279711yescharacteristic
678C2×C11#280311yescharacteristic
679C2×C11#282411yescharacteristic
680C2×C11#282511yescharacteristic
681C2×C11#282611yescharacteristic
682C2×C11#282811yescharacteristic
683C2×C11#282911yescharacteristic
684D11—82no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—112no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24—221no—
704C24—221no—
705C24—221no—
706C24—221no—
707C24—221no—
708C24—221no—
709C24—221no—
710C24—221no—
711C24—221no—
712C24—221no—
713C24—221no—
714C24#433912yes—
715C24C23×D1111yescharacteristic
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—444no—
719C2×D4—444no—
720C2×D4—444no—
721C2×D4—444no—
722C2×D4—444no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—112no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C4⋊C4—444no—
815C4⋊C4—444no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—444no—
820C22⋊C4—444no—
821C22⋊C4—444no—
822C22⋊C4—444no—
823C22⋊C4—444no—
824C22⋊C4—444no—
825C22⋊C4—444no—
826C22⋊C4—444no—
827C22⋊C4—444no—
828C11#1725511yescharacteristic, complemented, Sylow
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—441no—
872C23—441no—
873C23—441no—
874C23—441no—
875C23—441no—
876C23—441no—
877C23—441no—
878C23—441no—
879C23—441no—
880C23—441no—
881C23—441no—
882C23—441no—
883C23—441no—
884C23—441no—
885C23—441no—
886C23—441no—
887C23—441no—
888C23—441no—
889C23—441no—
890C23—441no—
891C23—441no—
892C23—441no—
893C23—441no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23C2×#433911yescharacteristic
900C23#6703711yescharacteristic
901C23#6703711yescharacteristic
902C23#6703711yescharacteristic
903C23#6703711yescharacteristic
904C23#6703711yescharacteristic
905C23#6703711yescharacteristic
906C23#41×D1111yescharacteristic
907C23#41×D1111yescharacteristic
908C23#41×D1111yescharacteristic
909C23#41×D1111yescharacteristic
910C23#6704211yescharacteristic
911C23#6704211yescharacteristic
912C23#6704211yescharacteristic
913C23#6704311yescharacteristic
914D4—4416no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
1003C2×C4—441no—
1004C2×C4—441no—
1005C2×C4—441no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—81no—
1014C22—81no—
1015C22—81no—
1016C22—81no—
1017C22—81no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22—442no—
1022C22—442no—
1023C22—442no—
1024C22—442no—
1025C22—442no—
1026C22—442no—
1027C22—442no—
1028C22—881no—
1029C22—881no—
1030C22—881no—
1031C22—881no—
1032C22—881no—
1033C22—881no—
1034C22—881no—
1035C22—881no—
1036C22#1062302511yescharacteristic
1037C22#1062305811yescharacteristic
1038C22#1062306211yescharacteristic
1039C22#1062307111yescharacteristic
1040C22#1062308711yescharacteristic
1041C22#1062309111yescharacteristic
1042C22#1062309111yescharacteristic
1043C22#1062312611yescharacteristic
1044C22#1062312611yescharacteristic
1045C22#1062314411yescharacteristic
1046C22#1062314411yescharacteristic
1047C22#1062314611yescharacteristic
1048C22#1062314611yescharacteristic
1049C22#1062315111yescharacteristic
1050C22#1062315111yescharacteristic
1051C22#1062315111yescharacteristic
1052C22#1062315211yescharacteristic
1053C22#1062318811yescharacteristic
1054C22#1062318811yescharacteristic
1055C22#1062319011yescharacteristic
1056C22#1062319111yescharacteristic
1057C22#1062319211yescharacteristic
1058C22#1062319411yescharacteristic
1059C22#1062319511yescharacteristic
1060C22#1062319711yescharacteristic
1061C22#1062319811yescharacteristic
1062C22#1062319811yescharacteristic
1063C22#1062320011yescharacteristic
1064C22#1062320111yescharacteristic
1065C22#1062320911yescharacteristic
1066C22#1062321411yescharacteristic
1067C22#1062323511yescharacteristic
1068C22#1062323611yescharacteristic
1069C22#1062323811yescharacteristic
1070C22#1062324011yescharacteristic
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—442no—
1078C4—442no—
1079C4—442no—
1080C4—881no—
1081C4—881no—
1082C4—881no—
1083C4—881no—
1084C2—82no—
1085C2—882no—
1086C2#1307566111yescharacteristic
1087C2#1307575211yescharacteristic
1088C2#1307584411yescharacteristic
1089C2#1307594311yescharacteristic
1090C2#1307600111yescharacteristic
1091C2#1307623111yescharacteristic
1092C2#1307627411yescharacteristic
1093C2#1307646311yescharacteristic
1094C2#1307646911yescharacteristic
1095C2#1307655411yescharacteristic
1096C2#1307669411yescharacteristic
1097C2#1307670211yescharacteristic
1098C2#1307671211yescharacteristic
1099C2#1307673211yescharacteristic
1100C2#1307674111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1440C2
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#17255
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
1. #13066877C2semidirect
2. #13066877C2semidirect
3. #13066871C2semidirect
4. #13066871C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066863C2semidirect
8. #13066860C2semidirect
9. #13066860C2semidirect
10. #13066859C2semidirect
11. #13066859C2semidirect
15. C11×#1440C2semidirect
286. #1440D11semidirect
828. C11#17255semidirect

Maximal subgroups

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

subgroupindex
#130668772
#130668712
#130668642
#130668632
#130668602
#130668592
#130668552
C11×#14402
#1725511