Finite Group Databasebeta

← #14680893

Subgroups — #14680893

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622565C211yesmaximal, characteristic
2#13066877C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066875C211yesmaximal, characteristic, complemented
5#13066867C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic
7#13066859C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066851C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
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
51#10622565C418yescomplemented
52C25×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
66C23×Dic11C2311yescharacteristic
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4—41no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—41no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—41no—
84C2×C22⋊Dic11—41no—
85C2×C22⋊Dic11—41no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11C2×C414yes—
90C2×C22⋊Dic11C2×C414yes—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—41no—
93C2×Dic11⋊C4—41no—
94C2×Dic11⋊C4—41no—
95C2×Dic11⋊C4—41no—
96C2×Dic11⋊C4C2×C414yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11—41no—
103C2×C4×Dic11—41no—
104C2×C4×Dic11—41no—
105C2×C4×Dic11—41no—
106C11×#95—22no—
107C11×#95—41no—
108C11×#95—41no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
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⋊#95C2×C414yes—
126C11⋊#95C2×C414yes—
127C11⋊#95C2×C414yes—
128#14332—111nomaximal, Sylow
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×C11—21no—
143C24×C11C22×C412yes—
144C24×C11C2411yescharacteristic
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×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
236C22×Dic11C22×C412yes—
237C22×Dic11C22×C412yes—
238C22×Dic11C22×C412yes—
239C22×Dic11#4112yes—
240C22×Dic11#4112yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C11×C4⋊C4—44no—
244C11×C22⋊C4—44no—
245C11×C22⋊C4—44no—
246C11×C22⋊C4—44no—
247C22⋊Dic11—44no—
248C22⋊Dic11—44no—
249C22⋊Dic11—44no—
250C22⋊Dic11—44no—
251Dic11⋊C4—44no—
252Dic11⋊C4—44no—
253C4×Dic11—44no—
254C4×Dic11—44no—
255C4×Dic11—44no—
256C2×#397—111no—
257#1443—111no—
258#1443—111no—
259#1442—111no—
260#1441—111no—
261#1440—111no—
262#1439—111no—
263#1439D1111yescharacteristic
264#1437—111no—
265#1437—111no—
266#1437—111no—
267#1436—111no—
268#1436—111no—
269#1436—111no—
270C4×#95—111no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
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×C11—41no—
306C23×C11C23×C411yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
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×C11H(5,𝔽2)11yescharacteristic
319C23×C112−1+411yescharacteristic
320C23×C112−1+411yescharacteristic
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—22no—
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—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
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—
418C2×Dic11#12614yes—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4C2×D1111yescharacteristic
427C22×C22⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4C2×D1111yescharacteristic
429C22×C42—111no—
430C22×C42—111no—
431C22×C42—111no—
432#397—118no—
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×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95C2×D1111yescharacteristic
453C2×#95C2×D1111yescharacteristic
454C2×#95C2×D1111yescharacteristic
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11C4×#4111yescharacteristic
471C22×C11C4×#4111yescharacteristic
472C22×C11C4×#4111yescharacteristic
473C22×C11#51811yescharacteristic
474C22×C11#51811yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11#52011yescharacteristic
477C22×C11C2×#12611yescharacteristic
478C22×C11#52911yescharacteristic
479C22×C11#52911yescharacteristic
480C22×C11#52911yescharacteristic
481C22×C11#53811yescharacteristic
482C22×C11#53811yescharacteristic
483C22×C11#53811yescharacteristic
484C22×C11#53811yescharacteristic
485C22×C11#53811yescharacteristic
486C22×C11#53811yescharacteristic
487C22×C11#53811yescharacteristic
488C22×C11#53811yescharacteristic
489C22×C11#53911yescharacteristic
490C22×C11#53911yescharacteristic
491C22×C11#53911yescharacteristic
492C22×C11#53911yescharacteristic
493C22×C11#54011yescharacteristic
494C22×C11#54011yescharacteristic
495C22×C11#54011yescharacteristic
496C22×C11#54011yescharacteristic
497C22×C11#54011yescharacteristic
498C22×C11#54111yescharacteristic
499C22×C11#54211yescharacteristic
500C22×C11#54211yescharacteristic
501C22×C11#54211yescharacteristic
502C22×C11#54211yescharacteristic
503C22×C11#54211yescharacteristic
504C22×C11#54211yescharacteristic
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—81no—
510C4×C11—81no—
511Dic11—24no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11—81no—
518Dic11—81no—
519C25C22×D1111yescharacteristic
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C2×C4⋊C4—22no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—441no—
540C2×C4⋊C4—441no—
541C2×C4⋊C4—441no—
542C2×C4⋊C4—441no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—222no—
554C2×C22⋊C4—222no—
555C2×C22⋊C4—222no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—441no—
558C2×C22⋊C4—441no—
559C2×C22⋊C4—441no—
560C2×C22⋊C4—441no—
561C2×C22⋊C4—441no—
562C2×C22⋊C4—441no—
563C2×C22⋊C4C4×D1114yes—
564C2×C42—222no—
565C2×C42—222no—
566C2×C42—222no—
567C2×C42—441no—
568C2×C42—441no—
569C2×C42—441no—
570C2×C42—441no—
571C2×C42—441no—
572C2×C42—441no—
573#95—22no—
574#95—41no—
575#95—41no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—222no—
580#95—222no—
581#95—222no—
582#95—222no—
583#95—222no—
584#95—222no—
585#95—441no—
586#95—441no—
587#95—441no—
588#95—441no—
589#95—441no—
590#95—441no—
591#95—441no—
592#95—441no—
593#95—441no—
594#95—441no—
595C2×C11—82no—
596C2×C11C4×#12611yescharacteristic
597C2×C11#233311yescharacteristic
598C2×C11#233411yescharacteristic
599C2×C11#233511yescharacteristic
600C2×C11#233511yescharacteristic
601C2×C11#233511yescharacteristic
602C2×C11#233711yescharacteristic
603C2×C11#264311yescharacteristic
604C2×C11#264411yescharacteristic
605C2×C11#264811yescharacteristic
606C2×C11#264811yescharacteristic
607C2×C11#265011yescharacteristic
608C2×C11#265111yescharacteristic
609C2×C11#265311yescharacteristic
610C2×C11#265411yescharacteristic
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C2×C4×D1112yes—
626C24C23×D1111yescharacteristic
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—21no—
664C22×C4—21no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—112no—
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×C4—221no—
720C22×C4—221no—
721C22×C4C2×C4×D1112yes—
722C22×C4C2×C4×D1112yes—
723C22×C4#434112yes—
724C22×C4#434112yes—
725C4⋊C4—44no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C42—444no—
736C42—444no—
737C42—444no—
738C11#1433211yescharacteristic, complemented, Sylow
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
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—
772C23—41no—
773C23—41no—
774C23C22×C4×D1111yescharacteristic
775C23C2×#434111yescharacteristic
776C23C2×#434111yescharacteristic
777C23#6703711yescharacteristic
778C23#6703711yescharacteristic
779C23#6703711yescharacteristic
780C23#6703711yescharacteristic
781C23#6703711yescharacteristic
782C23#6704011yescharacteristic
783C23#41×D1111yescharacteristic
784C23#41×D1111yescharacteristic
785C23#41×D1111yescharacteristic
786C23#41×D1111yescharacteristic
787C23#6704211yescharacteristic
788C23#6704311yescharacteristic
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—22no—
800C2×C4—22no—
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—41no—
830C2×C4—41no—
831C2×C4—114no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
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—
885C2×C4—441no—
886C2×C4—441no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22#1062301711yescharacteristic
903C22#1062303511yescharacteristic
904C22#1062305311yescharacteristic
905C22C4×#434111yescharacteristic
906C22C4×#434111yescharacteristic
907C22#1062307611yescharacteristic
908C22#1062307711yescharacteristic
909C22#1062312411yescharacteristic
910C22#1062312411yescharacteristic
911C22#1062312411yescharacteristic
912C22#1062313111yescharacteristic
913C22#1062313411yescharacteristic
914C22#1062314411yescharacteristic
915C22#1062314611yescharacteristic
916C22#1062314611yescharacteristic
917C22#1062314611yescharacteristic
918C22#1062314611yescharacteristic
919C22#1062314811yescharacteristic
920C22#1062315611yescharacteristic
921C22#1062316911yescharacteristic
922C22#1062317111yescharacteristic
923C22#1062317111yescharacteristic
924C22#1062317111yescharacteristic
925C22#1062317411yescharacteristic
926C22#1062318011yescharacteristic
927C22#1062318811yescharacteristic
928C22#1062319111yescharacteristic
929C22#1062319111yescharacteristic
930C22#1062319311yescharacteristic
931C22#1062320911yescharacteristic
932C22#1062320911yescharacteristic
933C22#1062321111yescharacteristic
934C22D11×#12611yescharacteristic
935C22#1062323811yescharacteristic
936C22#1062325011yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4—224no—
944C4—442no—
945C4—442no—
946C4—442no—
947C4—442no—
948C4—442no—
949C4—881no—
950C4—881no—
951C2—82no—
952C2#1307117011yescharacteristic
953C2#1307137511yescharacteristic
954C2#1307138611yescharacteristic
955C2#1307140211yescharacteristic
956C2#1307140411yescharacteristic
957C2#1307140711yescharacteristic
958C2#1307143011yescharacteristic
959C2#1307456811yescharacteristic
960C2#1307457811yescharacteristic
961C2#1307459711yescharacteristic
962C2#1307460511yescharacteristic
963C2#1307463511yescharacteristic
964C2#1307464611yescharacteristic
965C2#1307467611yescharacteristic
966C2#1307468911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14332
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066877C2semidirect
4. #13066875C2semidirect
5. #13066867C2semidirect
11. #13066851C2semidirect
12. #13066851C2semidirect
13. #13066848C2semidirect
14. #95×Dic11C2semidirect
51. #10622565C4semidirect
738. C11#14332semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
#130668772
#130668752
#130668672
#130668632
#130668592
#130668532
#130668512
#130668482
#95×Dic112
C11×#14392
#1433211