Finite Group Databasebeta

← #14683046

Subgroups — #14683046

Order 2816.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622558C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic
4#13066874C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066867C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic
9#13066859C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35#10622823C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52#10622558—24no—
53#10622557—24no—
54C25×C11C2311yescharacteristic
55C23×C4×C11—41no—
56C23×C4×C11—41no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11C2×C414yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
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—22no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11C2×C414yes—
91C2×C22⋊Dic11C2×C414yes—
92C2×C22⋊Dic11D414yes—
93C2×C22⋊Dic11Q814yes—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4—41no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4C2×C414yes—
111C2×Dic11⋊C4C2×C414yes—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C11×#95—41no—
119C11×#95—41no—
120C11×#95—41no—
121C11×#95—41no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95C2×C414yes—
137C11⋊#95C2×C414yes—
138#14514—111nomaximal, Sylow
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×C11C22×C412yes—
152C24×C11C2×D412yes—
153C24×C11C2×Q812yes—
154C24×C11C2411yescharacteristic
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—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11#4112yes—
203C22×C4×C11#4112yes—
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—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×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×Q812yes—
257C22×Dic11C2×Q812yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C11×C22⋊C4—44no—
261C11×C22⋊C4—44no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11C4⋊C4116yescomplemented
266Dic11⋊C4—44no—
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270Dic11⋊C4—44no—
271Dic11⋊C4—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C2×#388—111no—
275C2×#388—111no—
276C2×#385—111no—
277#1442—111no—
278#1442—111no—
279#1441—111no—
280#1441—111no—
281#1439—111no—
282#1439—111no—
283#1436—111no—
284#1436—111no—
285C4⋊#95—111no—
286C4⋊#95—111no—
287C22⋊#95—111no—
288C22⋊#95D1111yescharacteristic
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
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—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×C11C2×C4⋊C414yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×Q811yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C112−1+411yescharacteristic
338C23×C112−1+411yescharacteristic
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—416no—
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×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
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—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×Dic11C2×C4⋊C414yes—
437C2×Dic11C2×C4⋊C414yes—
438C24×C4C2×D1111yescharacteristic
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4C2×D1111yescharacteristic
450C22×C22⋊C4C2×D1111yescharacteristic
451C22×C42—111no—
452C22×C42—111no—
453#388—224no—
454#388—224no—
455#385—118no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95C2×D1111yescharacteristic
473C2×#95C2×D1111yescharacteristic
474C2×#95C2×D1111yescharacteristic
475C2×#95C2×D1111yescharacteristic
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11C22×C4⋊C411yescharacteristic
492C22×C11C4×#4111yescharacteristic
493C22×C11C4×#4111yescharacteristic
494C22×C11#51811yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#51811yescharacteristic
497C22×C11#51911yescharacteristic
498C22×C11#53711yescharacteristic
499C22×C11#53711yescharacteristic
500C22×C11#53911yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#53911yescharacteristic
504C22×C11#54211yescharacteristic
505C22×C11#54211yescharacteristic
506C22×C11#54211yescharacteristic
507C22×C11#54211yescharacteristic
508C22×C11#54411yescharacteristic
509C22×C11#54411yescharacteristic
510C22×C11#54611yescharacteristic
511C22×C11#54611yescharacteristic
512C22×C11#54611yescharacteristic
513C22×C11#54611yescharacteristic
514C22×C11#55111yescharacteristic
515C22×C11#55311yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55411yescharacteristic
518C22×C11#55411yescharacteristic
519C22×C11#55411yescharacteristic
520C22×C11#55411yescharacteristic
521C22×C11#55911yescharacteristic
522C22×C11#56011yescharacteristic
523C22×C11#56011yescharacteristic
524C22×C11#56011yescharacteristic
525C22×C11H(3,𝔽4)11yescharacteristic
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—81no—
531C4×C11—81no—
532Dic11—24no—
533Dic11—24no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—81no—
539Dic11—81no—
540C25C22×D1111yescharacteristic
541C23×C4—41no—
542C23×C4—41no—
543C23×C4—41no—
544C23×C4—41no—
545C23×C4—41no—
546C23×C4—41no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4C4×D1114yes—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—441no—
571C2×C4⋊C4—441no—
572C2×C4⋊C4—441no—
573C2×C4⋊C4—441no—
574C2×C4⋊C4—441no—
575C2×C4⋊C4—441no—
576C2×C4⋊C4—441no—
577C2×C4⋊C4—441no—
578C2×C4⋊C4—441no—
579C2×C4⋊C4—441no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—114no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4—441no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—222no—
602C2×C42—441no—
603C2×C42—441no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—114no—
609#95—114no—
610#95—222no—
611#95—222no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—441no—
617#95—441no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95—441no—
623#95—441no—
624C2×C11—44no—
625C2×C11#231611yescharacteristic
626C2×C11#233211yescharacteristic
627C2×C11#233211yescharacteristic
628C2×C11#234911yescharacteristic
629C2×C11#234911yescharacteristic
630C2×C11#237411yescharacteristic
631C2×C11#237511yescharacteristic
632C2×C11#269111yescharacteristic
633C2×C11#269111yescharacteristic
634C2×C11#269311yescharacteristic
635C2×C11#271211yescharacteristic
636C2×C11#276311yescharacteristic
637C2×C11#279011yescharacteristic
638C2×C11#279011yescharacteristic
639C2×C11#280711yescharacteristic
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24C2×C4×D1112yes—
653C24D4×D1112yes—
654C24Q8×D1112yes—
655C24C23×D1111yescharacteristic
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—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
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×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4C2×C4×D1112yes—
758C22×C4C2×C4×D1112yes—
759C22×C4#433912yes—
760C22×C4#433912yes—
761C4⋊C4—444no—
762C4⋊C4—444no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C4⋊C4—444no—
766C4⋊C4—444no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—1116no—
770C22⋊C4—444no—
771C22⋊C4—444no—
772C22⋊C4—444no—
773C42—444no—
774C42—444no—
775C11#1451411yescharacteristic, complemented, Sylow
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C4⋊C4×D1114yes—
811C23C22×C4×D1111yescharacteristic
812C23C2×#433911yescharacteristic
813C23C2×#433911yescharacteristic
814C23C2×D4×D1111yescharacteristic
815C23#6703711yescharacteristic
816C23#6703711yescharacteristic
817C23#6703711yescharacteristic
818C23#6703711yescharacteristic
819C23#6703711yescharacteristic
820C23#6703711yescharacteristic
821C23C2×Q8×D1111yescharacteristic
822C23#41×D1111yescharacteristic
823C23#41×D1111yescharacteristic
824C23#6704311yescharacteristic
825C23#6704311yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—416no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—114no—
870C2×C4—114no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C4×#433911yescharacteristic
941C22#1062301711yescharacteristic
942C22#1062301711yescharacteristic
943C22#1062301711yescharacteristic
944C22#1062302111yescharacteristic
945C22#1062302111yescharacteristic
946C22C2×C4⋊C4×D1111yescharacteristic
947C22#1062304211yescharacteristic
948C22#1062304211yescharacteristic
949C22#1062304711yescharacteristic
950C22#1062305311yescharacteristic
951C22#1062307111yescharacteristic
952C22#1062308711yescharacteristic
953C22#1062308911yescharacteristic
954C22#1062309011yescharacteristic
955C22#1062309211yescharacteristic
956C22#1062309211yescharacteristic
957C22#1062309511yescharacteristic
958C22#1062309511yescharacteristic
959C22#1062312511yescharacteristic
960C22#1062312611yescharacteristic
961C22#1062312611yescharacteristic
962C22#1062312611yescharacteristic
963C22#1062312811yescharacteristic
964C22#1062312811yescharacteristic
965C22#1062314111yescharacteristic
966C22#1062314111yescharacteristic
967C22#1062315411yescharacteristic
968C22#1062315411yescharacteristic
969C22#1062316711yescharacteristic
970C22#1062316711yescharacteristic
971C22#1062319111yescharacteristic
972C22#1062319111yescharacteristic
973C22#1062319311yescharacteristic
974C22#1062319311yescharacteristic
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—224no—
982C4—224no—
983C4—442no—
984C4—442no—
985C4—442no—
986C4—442no—
987C4—881no—
988C4—881no—
989C2—44no—
990C2#1307123311yescharacteristic
991C2#1307136911yescharacteristic
992C2#1307137211yescharacteristic
993C2#1307152011yescharacteristic
994C2#1307152311yescharacteristic
995C2#1307174711yescharacteristic
996C2#1307175511yescharacteristic
997C2#1307509211yescharacteristic
998C2#1307509411yescharacteristic
999C2#1307512211yescharacteristic
1000C2#1307538311yescharacteristic
1001C2#1307602811yescharacteristic
1002C2#1307638011yescharacteristic
1003C2#1307638711yescharacteristic
1004C2#1307658211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14514
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #13066874C2semidirect
5. #13066871C2semidirect
6. #13066867C2semidirect
7. #13066867C2semidirect
10. #13066851C2semidirect
11. #13066847C2semidirect
12. Dic11⋊#95C2semidirect
13. Dic11⋊#95C2semidirect
35. #10622823C4semidirect
265. C22⋊Dic11C4⋊C4semidirect
775. C11#14514semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106225572
C2×#106228232
#130668742
#130668712
#130668672
#130668592
#130668512
#130668472
Dic11⋊#952
#130668392
C11×C22⋊#952
#1451411