Finite Group Databasebeta

← #14677282

Subgroups — #14677282

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622265C211yesmaximal, characteristic, complemented
2C2×#10622823C211yesmaximal, characteristic
3C2×#10622555C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5C22×C11⋊#95C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic, complemented
7#13066876C211yesmaximal, characteristic, complemented
8#13066871C211yesmaximal, characteristic, complemented
9#13066867C211yesmaximal, characteristic, complemented
10#13066851C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066841C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic
14#13066838C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33#10622823—24no—
34C2×C11⋊#95—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622555C418yescomplemented
54C22⋊C4×Dic11—24no—
55#10622265—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—41no—
63C23×C4×C11—41no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—41no—
79C23×Dic11—41no—
80C23×Dic11—41no—
81C23×Dic11—41no—
82C23×Dic11C2×C414yes—
83C23×Dic11Q814yes—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4C2×C414yes—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11C2×C414yes—
103C2×C22⋊Dic11D414yes—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—41no—
111C2×Dic11⋊C4—41no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4C2×C414yescomplemented
115C2×Dic11⋊C4C2×C414yescomplemented
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11—41no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—41no—
125C11×#95—41no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95C2×C414yescomplemented
142C11⋊#95C2×C414yescomplemented
143C11⋊#95D414yes—
144#14028—111nomaximal, Sylow
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×C11C22×C412yes—
154C24×C11C2×D412yes—
155C24×C11C2×Q812yes—
156C24×C11#4112yes—
157C24×C11#4112yes—
158C24×C11#4112yes—
159C24×C11#4112yes—
160C24×C11C2411yescharacteristic
161C22×C4×C11—28no—
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—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—44no—
201C22×C4×C11—44no—
202C22×C4×C11—44no—
203C22×C4×C11—44no—
204C22×C4×C11—44no—
205C22×C4×C11—44no—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11#4112yes—
210C22×Dic11—28no—
211C22×Dic11—28no—
212C22×Dic11—28no—
213C22×Dic11—28no—
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—44no—
259C22×Dic11—44no—
260C22×Dic11—44no—
261C22×Dic11—44no—
262C22×Dic11—44no—
263C22×Dic11—44no—
264C22×Dic11—44no—
265C22×Dic11—44no—
266C22×Dic11—44no—
267C22×Dic11—44no—
268C22×Dic11C22×C412yes—
269C22×Dic11C22×C412yes—
270C22×Dic11C22×C412yes—
271C22×Dic11C22×C412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×D412yes—
276C22×Dic11C2×Q812yes—
277C22×Dic11C2×Q812yes—
278C22×Dic11#4112yes—
279C22×Dic11#4112yes—
280C11×C22⋊C4—28no—
281C11×C22⋊C4—44no—
282C22⋊Dic11—28no—
283C22⋊Dic11—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287Dic11⋊C4—44no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#387—111no—
291C2×#385—111no—
292C2×#380—111no—
293C2×C4×C22⋊C4—111no—
294C22×#95—111no—
295#1445—111no—
296#1443—111no—
297#1442—111no—
298#1441—111no—
299#1436—111no—
300#1436—111no—
301#1434—111no—
302C22⋊#95—111no—
303C22⋊#95—111no—
304C22⋊#95D1111yescharacteristic
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11#11714yes—
334C23×C11C4×D414yes—
335C23×C11C4×Q814yes—
336C23×C11C22⋊Q814yes—
337C23×C11#12314yes—
338C23×C11#12514yes—
339C23×C11#12614yes—
340C23×C11C23×C411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×Q811yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C112−1+411yescharacteristic
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—416no—
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×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×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—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—416no—
429C2×Dic11—416no—
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×Dic11C4×D414yes—
455C2×Dic11C22⋊Q814yes—
456C24×C4—111no—
457C24×C4—111no—
458C24×C4C2×D1111yescharacteristic
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4C2×D1111yescharacteristic
466C22×C22⋊C4C2×D1111yescharacteristic
467C22×C42—111no—
468C22×C42—111no—
469#387—224no—
470#385—224no—
471#380—118no—
472C4×C22⋊C4—224no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—224no—
492C2×#95C2×D1111yescharacteristic
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—24no—
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—24no—
509C22×C11—24no—
510C22×C11#38718yescomplemented
511C22×C11C2×#11711yescharacteristic
512C22×C11C2×C4×D411yescharacteristic
513C22×C11C2×C4×D411yescharacteristic
514C22×C11C2×C4×Q811yescharacteristic
515C22×C11C4×#4111yescharacteristic
516C22×C11#51811yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11C2×C22⋊Q811yescharacteristic
519C22×C11C2×C22⋊Q811yescharacteristic
520C22×C11C2×#12311yescharacteristic
521C22×C11#52511yescharacteristic
522C22×C11C2×#12511yescharacteristic
523C22×C11C2×#12611yescharacteristic
524C22×C11#52911yescharacteristic
525C22×C11#53311yescharacteristic
526C22×C11#53811yescharacteristic
527C22×C11#53911yescharacteristic
528C22×C11#54311yescharacteristic
529C22×C11#54411yescharacteristic
530C22×C11D4211yescharacteristic
531C22×C11#54611yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54611yescharacteristic
534C22×C11#54611yescharacteristic
535C22×C11#54711yescharacteristic
536C22×C11#54811yescharacteristic
537C22×C11#55111yescharacteristic
538C22×C11#55111yescharacteristic
539C22×C11#55111yescharacteristic
540C22×C11#55111yescharacteristic
541C22×C11#55211yescharacteristic
542C22×C11#55211yescharacteristic
543C22×C11#55311yescharacteristic
544C22×C11#55311yescharacteristic
545C22×C11#55311yescharacteristic
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—81no—
552Dic11—24no—
553Dic11—24no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25C22×D1111yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—114no—
577C23×C4—114no—
578C23×C4—222no—
579C23×C4—222no—
580C23×C4—222no—
581C23×C4—222no—
582C23×C4—222no—
583C23×C4—222no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—441no—
587C23×C4—441no—
588C23×C4—441no—
589C23×C4—441no—
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595C23×C4C22×D1111yescharacteristic
596C2×C4⋊C4—114no—
597C2×C4⋊C4—114no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—441no—
605C2×C4⋊C4—441no—
606C2×C4⋊C4—441no—
607C2×C4⋊C4—441no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—114no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—222no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4C4×D1114yes—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624C2×C42—441no—
625C2×C42—441no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—114no—
631#95—114no—
632#95—114no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—222no—
639#95—222no—
640#95—222no—
641#95—222no—
642#95—222no—
643#95—222no—
644#95—441no—
645#95—441no—
646#95—441no—
647#95—441no—
648C2×C11—28no—
649C2×C11C2×#38711yescharacteristic
650C2×C11C4×C22⋊Q811yescharacteristic
651C2×C11#232911yescharacteristic
652C2×C11#234211yescharacteristic
653C2×C11#234311yescharacteristic
654C2×C11#236111yescharacteristic
655C2×C11#236411yescharacteristic
656C2×C11#241811yescharacteristic
657C2×C11#241911yescharacteristic
658C2×C11#243711yescharacteristic
659C2×C11#243811yescharacteristic
660C2×C11#244211yescharacteristic
661C2×C11#248111yescharacteristic
662C2×C11#251011yescharacteristic
663C2×C11#256911yescharacteristic
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C2×C4×D1112yes—
673C24#433912yes—
674C24#433912yes—
675C24D4×D1112yes—
676C24#434112yes—
677C24#434112yes—
678C24Q8×D1112yes—
679C24C23×D1111yescharacteristic
680C22×C4—28no—
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—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—228no—
738C22×C4—228no—
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—228no—
748C22×C4—228no—
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×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—444no—
786C22×C4—444no—
787C22×C4—444no—
788C22×C4—444no—
789C22×C4—444no—
790C22×C4—444no—
791C22×C4—444no—
792C22×C4—444no—
793C22×C4—444no—
794C22×C4—444no—
795C22×C4C2×C4×D1112yes—
796C22×C4C2×C4×D1112yes—
797C22×C4D4×D1112yes—
798C22×C4#434112yes—
799C4⋊C4—228no—
800C4⋊C4—444no—
801C4⋊C4—444no—
802C4⋊C4—444no—
803C22⋊C4—28no—
804C22⋊C4—44no—
805C22⋊C4—228no—
806C22⋊C4—228no—
807C42—444no—
808C42—444no—
809C11#1402811yescharacteristic, complemented, Sylow
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23#6692514yes—
839C23#6693214yes—
840C23(C22⋊D11)⋊C414yes—
841C23#6693614yes—
842C23#6694014yes—
843C23#6694214yes—
844C23#6694914yes—
845C23C22×C4×D1111yescharacteristic
846C23C2×#433911yescharacteristic
847C23C2×#433911yescharacteristic
848C23C2×D4×D1111yescharacteristic
849C23C2×D4×D1111yescharacteristic
850C23C2×#434111yescharacteristic
851C23C2×#434111yescharacteristic
852C23C2×#434111yescharacteristic
853C23#6703711yescharacteristic
854C23#6703711yescharacteristic
855C23C2×Q8×D1111yescharacteristic
856C23#41×D1111yescharacteristic
857C23#41×D1111yescharacteristic
858C23#6704211yescharacteristic
859C23#6704311yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—416no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—114no—
904C2×C4—114no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—4416no—
936C2×C4—4416no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22#1062226518yescomplemented
976C22C2×#6692511yescharacteristic
977C22C2×#6693211yescharacteristic
978C22C2×(C22⋊D11)⋊C411yescharacteristic
979C22C2×#6693611yescharacteristic
980C22#1062302111yescharacteristic
981C22#1062302611yescharacteristic
982C22C2×#6694011yescharacteristic
983C22C2×#6694211yescharacteristic
984C22C2×#6694911yescharacteristic
985C22#1062305811yescharacteristic
986C22#1062306211yescharacteristic
987C22C4×#434111yescharacteristic
988C22#1062307211yescharacteristic
989C22C4×D4×D1111yescharacteristic
990C22#1062307611yescharacteristic
991C22#1062307711yescharacteristic
992C22#1062308111yescharacteristic
993C22#1062308711yescharacteristic
994C22#1062308711yescharacteristic
995C22#1062311711yescharacteristic
996C22#1062312111yescharacteristic
997C22#1062312211yescharacteristic
998C22#1062312411yescharacteristic
999C22#1062312911yescharacteristic
1000C22#1062313211yescharacteristic
1001C22#1062313211yescharacteristic
1002C22#1062314911yescharacteristic
1003C22#1062315311yescharacteristic
1004C22#1062315411yescharacteristic
1005C22D11×C22⋊Q811yescharacteristic
1006C22#1062316511yescharacteristic
1007C22#1062318011yescharacteristic
1008C22#1062318511yescharacteristic
1009C22#1062318611yescharacteristic
1010C22#1062319611yescharacteristic
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—81no—
1016C4—81no—
1017C4—224no—
1018C4—224no—
1019C4—442no—
1020C4—442no—
1021C4—442no—
1022C4—442no—
1023C4—442no—
1024C4—442no—
1025C2—28no—
1026C2C2×#1062226511yescharacteristic
1027C2#1307114811yescharacteristic
1028C2#1307134711yescharacteristic
1029C2#1307145911yescharacteristic
1030C2#1307147011yescharacteristic
1031C2#1307162711yescharacteristic
1032C2#1307166411yescharacteristic
1033C2#1307208211yescharacteristic
1034C2#1307209711yescharacteristic
1035C2#1307228111yescharacteristic
1036C2#1307229611yescharacteristic
1037C2#1307233711yescharacteristic
1038C2#1307287611yescharacteristic
1039C2#1307317411yescharacteristic
1040C2#1307383711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14028
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#10622265C2semidirect
6. #13066882C2semidirect
7. #13066876C2semidirect
8. #13066871C2semidirect
9. #13066867C2semidirect
10. #13066851C2semidirect
11. #13066847C2semidirect
12. #13066841C2semidirect
53. #10622555C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
115. C2×Dic11⋊C4C2×C4semidirect
141. C11⋊#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
510. C22×C11#387semidirect
809. C11#14028semidirect
975. C22#10622265semidirect

Maximal subgroups

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

subgroupindex
C2×#106222652
C2×#106228232
C2×#106225552
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668822
#130668762
#130668712
#130668672
#130668512
#130668472
#130668412
#130668382
C11×C22⋊#952
#1402811