Finite Group Databasebeta

← #14719305

Subgroups — #14719305

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066881C211yesmaximal, characteristic, complemented
2#13066877C211yesmaximal, characteristic, complemented
3#13066874C211yesmaximal, characteristic, complemented
4#13066873C211yesmaximal, characteristic, complemented
5#13066872C211yesmaximal, characteristic, complemented
6#13066868C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic
10#13066861C211yesmaximal, characteristic
11#13066861C211yesmaximal, characteristic
12#13066861C211yesmaximal, characteristic
13#13066859C211yesmaximal, characteristic
14#13066859C211yesmaximal, characteristic
15C11×#1440C211yesmaximal, characteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
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×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—41no—
69C2×C11×C22⋊C4—41no—
70C2×C11×C22⋊C4—41no—
71C2×C11×C22⋊C4—41no—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4Q814yes—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—41no—
78C2×C22⋊Dic11—41no—
79C2×C22⋊Dic11—41no—
80C2×C22⋊Dic11—41no—
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×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11—41no—
98C2×C4⋊Dic11—41no—
99C2×Dic11⋊C4—41no—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4—41no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95—41no—
108C11×#95—41no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
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—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127#17303—111nomaximal, Sylow
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—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11C2×Q812yes—
143C24×C11C2411yescharacteristic
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×C11C2×Q812yes—
183C22×C4×C11C2×Q812yes—
184C22×C4×C11#4112yes—
185C22×C4×C11#4112yes—
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—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11#4112yes—
241C22×Dic11#4112yes—
242C11×C22⋊C4—44no—
243C11×C22⋊C4—44no—
244C11×C22⋊C4—44no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247C22⋊Dic11—44no—
248C22⋊Dic11—44no—
249C4⋊Dic11—44no—
250C4⋊Dic11—44no—
251C4⋊Dic11—44no—
252C4⋊Dic11—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255#1444—111no—
256#1443—111no—
257#1442—111no—
258#1442—111no—
259#1442—111no—
260#1441—111no—
261#1441—111no—
262#1441—111no—
263#1440D1111yescharacteristic
264#1439—111no—
265#1439—111no—
266#1439—111no—
267#1439—111no—
268#1439—111no—
269#1439—111no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
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×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11C22×Q811yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C11H(5,𝔽2)11yescharacteristic
315C23×C11H(5,𝔽2)11yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C112−1+411yescharacteristic
319C23×C112−1+411yescharacteristic
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
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×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
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—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4C2×D1111yescharacteristic
429C22×C22⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4C2×D1111yescharacteristic
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×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95C2×D1111yescharacteristic
450C2×#95C2×D1111yescharacteristic
451C2×#95C2×D1111yescharacteristic
452C2×#95C2×D1111yescharacteristic
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11#53811yescharacteristic
469C22×C11#53811yescharacteristic
470C22×C11#53811yescharacteristic
471C22×C11#53811yescharacteristic
472C22×C11#53811yescharacteristic
473C22×C11#53811yescharacteristic
474C22×C11#53811yescharacteristic
475C22×C11#53911yescharacteristic
476C22×C11#53911yescharacteristic
477C22×C11#53911yescharacteristic
478C22×C11#54011yescharacteristic
479C22×C11#54211yescharacteristic
480C22×C11#54311yescharacteristic
481C22×C11#54411yescharacteristic
482C22×C11#54411yescharacteristic
483C22×C11#55211yescharacteristic
484C22×C11#55311yescharacteristic
485C22×C11#55411yescharacteristic
486C22×C11#55411yescharacteristic
487C22×C11#55411yescharacteristic
488C22×C11#55411yescharacteristic
489C22×C11#55511yescharacteristic
490C22×C11#55511yescharacteristic
491C22×C11#55611yescharacteristic
492C22×C11#55911yescharacteristic
493C22×C11#56011yescharacteristic
494C22×C11#56011yescharacteristic
495C22×C11#56011yescharacteristic
496C22×C11#56011yescharacteristic
497C22×C11#56011yescharacteristic
498C22×C11#56211yescharacteristic
499C22×C11#56211yescharacteristic
500C22×C11#56211yescharacteristic
501C22×C11#56211yescharacteristic
502C22×C11#56311yescharacteristic
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—81no—
508C4×C11—81no—
509Dic11—42no—
510Dic11—42no—
511Dic11—81no—
512Dic11—81no—
513Dic11—81no—
514Dic11—81no—
515Dic11—81no—
516Dic11—81no—
517C25C22×D1111yescharacteristic
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C2×C4⋊C4—222no—
533C2×C4⋊C4—222no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—441no—
536C2×C4⋊C4—441no—
537C2×C4⋊C4—441no—
538C2×C4⋊C4—441no—
539C2×C4⋊C4—441no—
540C2×C4⋊C4—441no—
541C2×C4⋊C4—441no—
542C2×C4⋊C4—441no—
543C2×C4⋊C4—441no—
544C2×C4⋊C4—441no—
545C2×C4⋊C4—441no—
546C2×C4⋊C4—441no—
547C2×C4⋊C4—441no—
548C2×C4⋊C4—441no—
549C2×C4⋊C4—441no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—222no—
559C2×C22⋊C4—222no—
560C2×C22⋊C4—441no—
561C2×C22⋊C4—441no—
562C2×C22⋊C4—441no—
563C2×C22⋊C4—441no—
564C2×C22⋊C4—441no—
565C2×C22⋊C4—441no—
566C2×C22⋊C4—441no—
567C2×C22⋊C4—441no—
568C2×C22⋊C4—441no—
569C2×C22⋊C4—441no—
570C2×C22⋊C4Dic2214yes—
571#95—22no—
572#95—22no—
573#95—41no—
574#95—41no—
575#95—222no—
576#95—222no—
577#95—222no—
578#95—441no—
579#95—441no—
580#95—441no—
581#95—441no—
582#95—441no—
583#95—441no—
584#95—441no—
585#95—441no—
586#95—441no—
587#95—441no—
588#95—441no—
589#95—441no—
590#95—441no—
591#95—441no—
592#95—441no—
593C2×C11—82no—
594C2×C11#276811yescharacteristic
595C2×C11#277511yescharacteristic
596C2×C11#278111yescharacteristic
597C2×C11#278411yescharacteristic
598C2×C11#278411yescharacteristic
599C2×C11#278811yescharacteristic
600C2×C11#279011yescharacteristic
601C2×C11#280311yescharacteristic
602C2×C11#280711yescharacteristic
603C2×C11#280811yescharacteristic
604C2×C11#282511yescharacteristic
605C2×C11#282611yescharacteristic
606C2×C11#282711yescharacteristic
607C2×C11#282911yescharacteristic
608C2×C11#284111yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24C2×Dic2212yes—
624C24C23×D1111yescharacteristic
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—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—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4C2×Dic2212yes—
720C22×C4C2×Dic2212yes—
721C22×C4#434112yes—
722C22×C4#434112yes—
723C4⋊C4—444no—
724C4⋊C4—444no—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C4⋊C4—444no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C11#1730311yescharacteristic, complemented, Sylow
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
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—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23C22×Dic2211yescharacteristic
773C23C2×#434111yescharacteristic
774C23C2×#434111yescharacteristic
775C23#6703711yescharacteristic
776C23#6703711yescharacteristic
777C23#6703711yescharacteristic
778C23#6703711yescharacteristic
779C23#41×D1111yescharacteristic
780C23#41×D1111yescharacteristic
781C23#6704211yescharacteristic
782C23#6704211yescharacteristic
783C23#6704211yescharacteristic
784C23#6704211yescharacteristic
785C23#6704311yescharacteristic
786C23#6704311yescharacteristic
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
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—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
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—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22#1062301411yescharacteristic
901C22#1062305011yescharacteristic
902C22#1062305011yescharacteristic
903C22#1062307011yescharacteristic
904C22#1062307011yescharacteristic
905C22#1062307411yescharacteristic
906C22#1062307411yescharacteristic
907C22#1062312411yescharacteristic
908C22#1062312411yescharacteristic
909C22#1062313311yescharacteristic
910C22#1062314711yescharacteristic
911C22#1062314711yescharacteristic
912C22#1062314911yescharacteristic
913C22#1062315011yescharacteristic
914C22#1062315111yescharacteristic
915C22#1062315111yescharacteristic
916C22#1062315211yescharacteristic
917C22#1062318111yescharacteristic
918C22#1062318211yescharacteristic
919C22#1062318811yescharacteristic
920C22#1062318811yescharacteristic
921C22#1062318811yescharacteristic
922C22#1062319611yescharacteristic
923C22#1062319711yescharacteristic
924C22#1062319711yescharacteristic
925C22#1062319811yescharacteristic
926C22#1062319811yescharacteristic
927C22#1062320911yescharacteristic
928C22#1062321211yescharacteristic
929C22#1062321311yescharacteristic
930C22#1062321511yescharacteristic
931C22#1062323311yescharacteristic
932C22#1062323511yescharacteristic
933C22#1062323811yescharacteristic
934C22#1062324211yescharacteristic
935C4—42no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—442no—
942C4—442no—
943C4—881no—
944C4—881no—
945C4—881no—
946C4—881no—
947C4—881no—
948C4—881no—
949C2—82no—
950C2#1307610011yescharacteristic
951C2#1307619111yescharacteristic
952C2#1307628111yescharacteristic
953C2#1307631411yescharacteristic
954C2#1307631411yescharacteristic
955C2#1307636311yescharacteristic
956C2#1307638611yescharacteristic
957C2#1307655111yescharacteristic
958C2#1307658311yescharacteristic
959C2#1307659711yescharacteristic
960C2#1307670611yescharacteristic
961C2#1307670811yescharacteristic
962C2#1307672411yescharacteristic
963C2#1307675211yescharacteristic
964C2#1307687311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1440C2
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11#17303
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
1. #13066881C2semidirect
2. #13066877C2semidirect
3. #13066874C2semidirect
4. #13066873C2semidirect
5. #13066872C2semidirect
6. #13066868C2semidirect
7. #13066868C2semidirect
8. #13066868C2semidirect
736. C11#17303semidirect

Maximal subgroups

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

subgroupindex
#130668812
#130668772
#130668742
#130668732
#130668722
#130668682
#130668612
#130668592
C11×#14402
#1730311