Finite Group Databasebeta

← #14680210

Subgroups — #14680210

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622281C211yesmaximal, characteristic
2C2×#10622602C211yesmaximal, characteristic
3C2×D11×#95C211yesmaximal, characteristic
4#13066882C211yesmaximal, characteristic, complemented
5#13066877C211yesmaximal, characteristic, complemented
6#13066876C211yesmaximal, characteristic, complemented
7#13066874C211yesmaximal, characteristic, complemented
8#13066871C211yesmaximal, characteristic, complemented
9#13066870C211yesmaximal, characteristic, complemented
10#13066869C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1445C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
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#10622602C418yescomplemented
52#10622281—24no—
53D11×#95—24no—
54C24×D11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11—41no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11C2×C414yes—
88C22×C4×D11D414yes—
89C22×C4×D11Q814yes—
90C2×C11×C4⋊C4—41no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4C2×C414yescomplemented
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4—41no—
111C2×Dic11⋊C4—41no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4C2×C414yescomplemented
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—41no—
117C11×#95—41no—
118C11×#95—41no—
119C11×#95—41no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
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—
135C11⋊#95—41no—
136C11⋊#95C2×C414yescomplemented
137C11⋊#95C2×C414yescomplemented
138#14265—111nomaximal, Sylow
139C24×C11C2411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11C22×C412yes—
149C23×D11C2×D412yes—
150C23×D11C2×Q812yes—
151C23×D11#4112yes—
152C23×D11#4112yes—
153C23×D11#4112yes—
154C23×D11#4112yes—
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—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×Q812yes—
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×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×Q812yes—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—28no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C11×C4⋊C4—44no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279C4⋊Dic11—44no—
280Dic11⋊C4—44no—
281Dic11⋊C4—44no—
282C2×#385—111no—
283C2×#385—111no—
284C22×#95—111no—
285#1445—111no—
286#1445D1111yescharacteristic, complemented
287#1443—111no—
288#1443—111no—
289#1442—111no—
290#1442—111no—
291#1441—111no—
292#1441—111no—
293C22⋊#95—111no—
294C22⋊#95—111no—
295C22⋊#95—111no—
296C22⋊#95—111no—
297C23×C11C23×C411yescharacteristic
298C23×C11C22×D411yescharacteristic
299C23×C11C22×Q811yescharacteristic
300C23×C11C2×#4111yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11H(5,𝔽2)11yescharacteristic
305C23×C11H(5,𝔽2)11yescharacteristic
306C23×C11H(5,𝔽2)11yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C112−1+411yescharacteristic
311C23×C112−1+411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11#11714yes—
341C22×D11C4×D414yes—
342C22×D11C4×Q814yes—
343C22×D11C22⋊Q814yes—
344C22×D11#12314yes—
345C22×D11#12514yes—
346C22×D11#12614yes—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
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—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×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×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—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
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×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—
445C4×D11—416no—
446C4×D11—416no—
447C4×D11—416no—
448C24×C4—111no—
449C24×C4—111no—
450C24×C4—111no—
451C22×C4⋊C4—111no—
452C22×C4⋊C4—111no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459#385—118no—
460#385—224no—
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×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—224no—
480C2×#95C2×D1111yescharacteristic
481C2×#95C2×D1111yescharacteristic
482C2×#95C2×D1111yescharacteristic
483C2×#95C2×D1111yescharacteristic
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11C2×#11711yescharacteristic
487C22×C11C2×C4×D411yescharacteristic
488C22×C11C2×C4×Q811yescharacteristic
489C22×C11#51811yescharacteristic
490C22×C11#51811yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11#52011yescharacteristic
493C22×C11C2×C22⋊Q811yescharacteristic
494C22×C11C2×#12311yescharacteristic
495C22×C11C2×#12511yescharacteristic
496C22×C11C2×#12611yescharacteristic
497C22×C11#53411yescharacteristic
498C22×C11#53411yescharacteristic
499C22×C11#53511yescharacteristic
500C22×C11#53611yescharacteristic
501C22×C11#53811yescharacteristic
502C22×C11#53811yescharacteristic
503C22×C11#53811yescharacteristic
504C22×C11#53811yescharacteristic
505C22×C11#53811yescharacteristic
506C22×C11#53811yescharacteristic
507C22×C11#53811yescharacteristic
508C22×C11#53811yescharacteristic
509C22×C11#53911yescharacteristic
510C22×C11#53911yescharacteristic
511C22×C11#53911yescharacteristic
512C22×C11#53911yescharacteristic
513C22×C11#53911yescharacteristic
514C22×C11#53911yescharacteristic
515C22×C11#53911yescharacteristic
516C22×C11#53911yescharacteristic
517C22×C11#54311yescharacteristic
518C22×C11#54311yescharacteristic
519C22×C11#54411yescharacteristic
520C22×C11#54411yescharacteristic
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11#38718yes—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—81no—
542C4×C11—81no—
543Dic11—42no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—81no—
549Dic11—81no—
550C25—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—114no—
557C23×C4—114no—
558C23×C4—114no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—222no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—441no—
568C23×C4—441no—
569C23×C4—441no—
570C23×C4—441no—
571C23×C4—441no—
572C23×C4—441no—
573C23×C4—441no—
574C23×C4—441no—
575C23×C4—441no—
576C23×C4—441no—
577C23×C4—441no—
578C23×C4—441no—
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C23×C4C22×D1111yescharacteristic
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—441no—
592C2×C4⋊C4—441no—
593C2×C4⋊C4—441no—
594C2×C4⋊C4—441no—
595C2×C4⋊C4—441no—
596C2×C4⋊C4—441no—
597C2×C4⋊C4C4×D1114yescomplemented
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—114no—
617#95—114no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95—441no—
623#95—441no—
624#95—441no—
625#95—441no—
626#95—441no—
627#95—441no—
628#95—441no—
629#95—441no—
630#95—441no—
631#95—441no—
632#95—441no—
633#95—441no—
634C2×C11C2×#38711yescharacteristic
635C2×C11#231811yescharacteristic
636C2×C11#231811yescharacteristic
637C2×C11#232111yescharacteristic
638C2×C11#232211yescharacteristic
639C2×C11#232911yescharacteristic
640C2×C11#232911yescharacteristic
641C2×C11#262211yescharacteristic
642C2×C11#262311yescharacteristic
643C2×C11#262611yescharacteristic
644C2×C11#262711yescharacteristic
645C2×C11#264311yescharacteristic
646C2×C11#264311yescharacteristic
647C2×C11#264611yescharacteristic
648C2×C11#264611yescharacteristic
649D11—28no—
650C24—112no—
651C24—112no—
652C24—112no—
653C24—112no—
654C24—112no—
655C24—112no—
656C24—112no—
657C24—221no—
658C24—221no—
659C24—221no—
660C24—221no—
661C24—221no—
662C24—221no—
663C24—221no—
664C24—221no—
665C24C23×D1111yescharacteristic
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—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—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—228no—
716C22×C4—228no—
717C22×C4—228no—
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×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4—444no—
769C22×C4—444no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—444no—
774C22×C4—444no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4C2×C4×D1112yes—
781C22×C4C2×C4×D1112yes—
782C22×C4C2×C4×D1112yes—
783C22×C4D4×D1112yes—
784C22×C4Q8×D1112yes—
785C4⋊C4—44no—
786C4⋊C4—444no—
787C4⋊C4—444no—
788C4⋊C4—444no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C11#1426511yescharacteristic, complemented, Sylow
794C23—114no—
795C23—114no—
796C23—114no—
797C23—114no—
798C23—114no—
799C23—114no—
800C23—114no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23C22×C4×D1111yescharacteristic
830C23C2×D4×D1111yescharacteristic
831C23#6703711yescharacteristic
832C23#6703711yescharacteristic
833C23#6703711yescharacteristic
834C23C2×Q8×D1111yescharacteristic
835C23#6704011yescharacteristic
836C23#41×D1111yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#6704211yescharacteristic
841C23#6704211yescharacteristic
842C23#6704211yescharacteristic
843C23#6704311yescharacteristic
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
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—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—4416no—
909C2×C4—4416no—
910C2×C4—4416no—
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—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C22—118no—
946C22—224no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—224no—
954C22—224no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22#1062301711yescharacteristic
961C22D11×#11711yescharacteristic
962C22#1062305411yescharacteristic
963C22C4×D4×D1111yescharacteristic
964C22#1062307611yescharacteristic
965C22C4×Q8×D1111yescharacteristic
966C22#1062310511yescharacteristic
967C22#1062313611yescharacteristic
968C22#1062314411yescharacteristic
969C22D11×C22⋊Q811yescharacteristic
970C22#1062315911yescharacteristic
971C22#1062316511yescharacteristic
972C22#1062316511yescharacteristic
973C22#1062316911yescharacteristic
974C22#1062316911yescharacteristic
975C22D11×#12311yescharacteristic
976C22#1062318411yescharacteristic
977C22#1062318811yescharacteristic
978C22#1062318811yescharacteristic
979C22#1062318811yescharacteristic
980C22#1062319111yescharacteristic
981C22#1062319111yescharacteristic
982C22#1062319111yescharacteristic
983C22#1062320911yescharacteristic
984C22#1062320911yescharacteristic
985C22D11×#12511yescharacteristic
986C22#1062322011yescharacteristic
987C22#1062322311yescharacteristic
988C22#1062322311yescharacteristic
989C22D11×#12611yescharacteristic
990C22#1062323511yescharacteristic
991C22#1062323511yescharacteristic
992C22#1062323811yescharacteristic
993C22#1062324611yescharacteristic
994C22#1062326011yescharacteristic
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—81no—
1001C4—81no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C4—881no—
1008C4—881no—
1009C2—228no—
1010C2D11×#38711yescharacteristic
1011C2#1307124511yescharacteristic
1012C2#1307124811yescharacteristic
1013C2#1307127511yescharacteristic
1014C2#1307128911yescharacteristic
1015C2#1307134311yescharacteristic
1016C2#1307134811yescharacteristic
1017C2#1307439011yescharacteristic
1018C2#1307440111yescharacteristic
1019C2#1307442211yescharacteristic
1020C2#1307443411yescharacteristic
1021C2#1307456811yescharacteristic
1022C2#1307457011yescharacteristic
1023C2#1307458511yescharacteristic
1024C2#1307458711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#14265
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. #13066882C2semidirect
5. #13066877C2semidirect
6. #13066876C2semidirect
7. #13066874C2semidirect
8. #13066871C2semidirect
9. #13066870C2semidirect
10. #13066869C2semidirect
15. C11×#1445C2semidirect
51. #10622602C4semidirect
92. C2×C11×C4⋊C4C2×C4semidirect
113. C2×Dic11⋊C4C2×C4semidirect
136. C11⋊#95C2×C4semidirect
137. C11⋊#95C2×C4semidirect
286. #1445D11semidirect
597. C2×C4⋊C4C4×D11semidirect
793. C11#14265semidirect

Maximal subgroups

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

subgroupindex
C2×#106222812
C2×#106226022
C2×D11×#952
#130668822
#130668772
#130668762
#130668742
#130668712
#130668702
#130668692
(C2×D11)⋊#952
C11×#14452
#1426511