Finite Group Databasebeta

← #14718679

Subgroups — #14718679

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#13066878C211yesmaximal, characteristic, complemented
2#13066876C211yesmaximal, characteristic, complemented
3#13066874C211yesmaximal, characteristic, complemented
4#13066872C211yesmaximal, characteristic, complemented
5#13066865C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066859C211yesmaximal, characteristic, complemented
13#13066857C211yesmaximal, characteristic
14#13066857C211yesmaximal, characteristic
15C11×#1438C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
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
52C25×C11C2311yescharacteristic
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—41no—
57C22×D4×C11—41no—
58C22×D4×C11—41no—
59C22×D4×C11—41no—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
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×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C22⋊Dic11—41no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11—41no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C11×#95—22no—
116C11×#95—41no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
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—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11#4112yes—
165C24×C11#4112yes—
166C24×C11C2411yescharacteristic
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—44no—
171C2×D4×C11—44no—
172C2×D4×C11—44no—
173C2×D4×C11—44no—
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#4112yes—
208C22×C4×C11#4112yes—
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×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—21no—
263C22×Dic11—21no—
264C22×Dic11#4112yes—
265C11×C22⋊C4—44no—
266C11×C22⋊C4—44no—
267C11×C22⋊C4—44no—
268C11×C22⋊C4—44no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
271C22⋊Dic11—44no—
272C22⋊Dic11—44no—
273C22⋊Dic11—44no—
274C22⋊Dic11—44no—
275C22⋊Dic11—44no—
276C22⋊Dic11—44no—
277C4⋊Dic11—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#1440—111no—
287#1439—111no—
288#1439—111no—
289#1439—111no—
290#1439—111no—
291#1438—111no—
292#1438—111no—
293#1438D1111yescharacteristic
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
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×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11C2×#4111yescharacteristic
365C23×C11C2×#4111yescharacteristic
366C23×C11C2×#4111yescharacteristic
367C23×C11C2×#4111yescharacteristic
368C23×C11C2×#4111yescharacteristic
369C23×C11H(5,𝔽2)11yescharacteristic
370C23×C11H(5,𝔽2)11yescharacteristic
371C23×C11H(5,𝔽2)11yescharacteristic
372C23×C11H(5,𝔽2)11yescharacteristic
373C23×C11H(5,𝔽2)11yescharacteristic
374C23×C11H(5,𝔽2)11yescharacteristic
375C23×C11H(5,𝔽2)11yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C11H(5,𝔽2)11yescharacteristic
378C23×C112−1+411yescharacteristic
379D4×C11—416no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
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×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
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×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×D4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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×#95—111no—
503C2×#95—111no—
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—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—81no—
521C22×C11—81no—
522C22×C11—81no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—81no—
526C22×C11—81no—
527C22×C11—81no—
528C22×C11—81no—
529C22×C11—81no—
530C22×C11—81no—
531C22×C11—81no—
532C22×C11—81no—
533C22×C11—81no—
534C22×C11—81no—
535C22×C11—81no—
536C22×C11#53811yescharacteristic
537C22×C11#53811yescharacteristic
538C22×C11#53811yescharacteristic
539C22×C11#53811yescharacteristic
540C22×C11#53811yescharacteristic
541C22×C11#53811yescharacteristic
542C22×C11#53811yescharacteristic
543C22×C11#53811yescharacteristic
544C22×C11#53811yescharacteristic
545C22×C11#53911yescharacteristic
546C22×C11#53911yescharacteristic
547C22×C11#54011yescharacteristic
548C22×C11#54011yescharacteristic
549C22×C11#54011yescharacteristic
550C22×C11#54211yescharacteristic
551C22×C11#55111yescharacteristic
552C22×C11#55111yescharacteristic
553C22×C11#55111yescharacteristic
554C22×C11#55111yescharacteristic
555C22×C11#55211yescharacteristic
556C22×C11#55311yescharacteristic
557C22×C11#55311yescharacteristic
558C22×C11#55311yescharacteristic
559C22×C11#55511yescharacteristic
560C22×C11#55911yescharacteristic
561C22×C11#56011yescharacteristic
562C22×C11#56011yescharacteristic
563C22×C11#56011yescharacteristic
564C22×C11#56011yescharacteristic
565C22×C11#56011yescharacteristic
566C22×C11#56011yescharacteristic
567C22×C11H(3,𝔽4)11yescharacteristic
568C22×C11#56211yescharacteristic
569C22×C11#56211yescharacteristic
570C22×C11#56211yescharacteristic
571C4×C11—42no—
572C4×C11—42no—
573C4×C11—81no—
574C4×C11—81no—
575C4×C11—81no—
576Dic11—42no—
577Dic11—81no—
578Dic11—81no—
579Dic11—81no—
580Dic11—81no—
581Dic11—81no—
582Dic11—81no—
583Dic11—81no—
584C25C22×D1111yescharacteristic
585C25C22×D1111yescharacteristic
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—41no—
590C22×D4—41no—
591C22×D4—41no—
592C22×D4—41no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—111no—
597C23×C4—111no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—111no—
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—22no—
614C2×C22⋊C4—22no—
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—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
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—22no—
649#95—41no—
650#95—222no—
651#95—222no—
652#95—222no—
653#95—441no—
654#95—441no—
655#95—441no—
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—82no—
670C2×C11#273611yescharacteristic
671C2×C11#274311yescharacteristic
672C2×C11#274911yescharacteristic
673C2×C11#275611yescharacteristic
674C2×C11#276111yescharacteristic
675C2×C11#277811yescharacteristic
676C2×C11#278111yescharacteristic
677C2×C11#279611yescharacteristic
678C2×C11#279711yescharacteristic
679C2×C11#280311yescharacteristic
680C2×C11#282411yescharacteristic
681C2×C11#282511yescharacteristic
682C2×C11#282611yescharacteristic
683C2×C11#282811yescharacteristic
684C2×C11#282911yescharacteristic
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—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24#433912yes—
714C24#434112yes—
715C24C23×D1111yescharacteristic
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
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—112no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
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#434112yes—
813C22×C4#434112yes—
814C4⋊C4—444no—
815C4⋊C4—444no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
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—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
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—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23C2×#433911yescharacteristic
900C23C2×#434111yescharacteristic
901C23C2×#434111yescharacteristic
902C23C2×#434111yescharacteristic
903C23#6703711yescharacteristic
904C23#6703711yescharacteristic
905C23#6703711yescharacteristic
906C23#6703711yescharacteristic
907C23#6703711yescharacteristic
908C23#6703711yescharacteristic
909C23#6703711yescharacteristic
910C23#41×D1111yescharacteristic
911C23#6704211yescharacteristic
912C23#6704211yescharacteristic
913C23#6704311yescharacteristic
914D4—416no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
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—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
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—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—81no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—81no—
1036C22#1062302511yescharacteristic
1037C22#1062302611yescharacteristic
1038C22#1062302611yescharacteristic
1039C22#1062308711yescharacteristic
1040C22#1062309111yescharacteristic
1041C22#1062309511yescharacteristic
1042C22#1062309611yescharacteristic
1043C22#1062311811yescharacteristic
1044C22#1062312411yescharacteristic
1045C22#1062312411yescharacteristic
1046C22#1062312411yescharacteristic
1047C22#1062312411yescharacteristic
1048C22#1062312411yescharacteristic
1049C22#1062312511yescharacteristic
1050C22#1062312611yescharacteristic
1051C22#1062313311yescharacteristic
1052C22#1062314511yescharacteristic
1053C22#1062314611yescharacteristic
1054C22#1062314711yescharacteristic
1055C22#1062314811yescharacteristic
1056C22#1062314911yescharacteristic
1057C22#1062315011yescharacteristic
1058C22#1062315111yescharacteristic
1059C22#1062315111yescharacteristic
1060C22#1062315111yescharacteristic
1061C22#1062315211yescharacteristic
1062C22#1062315211yescharacteristic
1063C22#1062318111yescharacteristic
1064C22#1062319411yescharacteristic
1065C22#1062319711yescharacteristic
1066C22#1062319811yescharacteristic
1067C22#1062320911yescharacteristic
1068C22#1062321311yescharacteristic
1069C22#1062324411yescharacteristic
1070C22#1062325111yescharacteristic
1071C4—42no—
1072C4—42no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—442no—
1077C4—881no—
1078C4—881no—
1079C4—881no—
1080C4—881no—
1081C4—881no—
1082C4—881no—
1083C4—881no—
1084C2—82no—
1085C2—82no—
1086C2#1307566211yescharacteristic
1087C2#1307575311yescharacteristic
1088C2#1307583711yescharacteristic
1089C2#1307594111yescharacteristic
1090C2#1307600511yescharacteristic
1091C2#1307623411yescharacteristic
1092C2#1307628111yescharacteristic
1093C2#1307645211yescharacteristic
1094C2#1307647511yescharacteristic
1095C2#1307655511yescharacteristic
1096C2#1307669811yescharacteristic
1097C2#1307670411yescharacteristic
1098C2#1307671111yescharacteristic
1099C2#1307673611yescharacteristic
1100C2#1307675211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1438C2
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#17255
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13066878C2semidirect
2. #13066876C2semidirect
3. #13066874C2semidirect
4. #13066872C2semidirect
5. #13066865C2semidirect
6. #13066863C2semidirect
7. #13066863C2semidirect
8. #13066863C2semidirect
9. #13066861C2semidirect
10. #13066861C2semidirect
11. #13066859C2semidirect
12. #13066859C2semidirect
828. C11#17255semidirect

Maximal subgroups

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

subgroupindex
#130668782
#130668762
#130668742
#130668722
#130668652
#130668632
#130668612
#130668592
#130668572
C11×#14382
#1725511