Finite Group Databasebeta

← #14677279

Subgroups — #14677279

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×#10622281C211yesmaximal, characteristic
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5C2×D11×#95C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic, complemented
7#13066874C211yesmaximal, characteristic, complemented
8#13066870C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
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
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#10622281—24no—
52#10622280C418yescomplemented
53#10622279—24no—
54D11×#95—24no—
55#10622265—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11C2×C414yes—
91C22×C4×D11Q814yes—
92C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4D414yes—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
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—22no—
125C11×#95—22no—
126C11×#95—41no—
127C11×#95—41no—
128C11×#95C2×C414yescomplemented
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—22no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95C2×C414yescomplemented
143C11⋊#95D414yes—
144#14028—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11C22×C412yes—
155C23×D11C2×D412yes—
156C23×D11C2×Q812yes—
157C23×D11#4112yes—
158C23×D11#4112yes—
159C23×D11#4112yes—
160C23×D11#4112yes—
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×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×Q812yes—
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×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×Q812yes—
256C22×Dic11#4112yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
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—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4—28no—
282(C2×D11)⋊C4—28no—
283(C2×D11)⋊C4—44no—
284C4⋊Dic11—44no—
285Dic11⋊C4—28no—
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#1443D1111yescharacteristic, complemented
297#1442—111no—
298#1441—111no—
299#1436—111no—
300#1436—111no—
301#1434—111no—
302C22⋊#95—111no—
303C22⋊#95—111no—
304C22⋊#95—111no—
305C23×C11C23×C411yescharacteristic
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×Q811yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C112−1+411yescharacteristic
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—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11#11714yes—
349C22×D11C4×D414yes—
350C22×D11C4×Q814yes—
351C22×D11C22⋊Q814yes—
352C22×D11#12314yes—
353C22×D11#12514yes—
354C22×D11#12614yes—
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—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
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×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
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—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—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11C4×D414yes—
452C2×Dic11C22⋊Q814yes—
453C4×D11—416no—
454C4×D11—416no—
455C4×D11—416no—
456C24×C4—111no—
457C24×C4—111no—
458C24×C4—111no—
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⋊C4—111no—
466C22×C22⋊C4—111no—
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—224no—
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C2×#95C2×D1111yescharacteristic
492C2×#95C2×D1111yescharacteristic
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11C2×#11711yescharacteristic
497C22×C11C2×C4×D411yescharacteristic
498C22×C11C2×C4×D411yescharacteristic
499C22×C11C2×C4×Q811yescharacteristic
500C22×C11C4×#4111yescharacteristic
501C22×C11#51811yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11C2×C22⋊Q811yescharacteristic
504C22×C11C2×C22⋊Q811yescharacteristic
505C22×C11C2×#12311yescharacteristic
506C22×C11#52511yescharacteristic
507C22×C11C2×#12511yescharacteristic
508C22×C11C2×#12611yescharacteristic
509C22×C11#52911yescharacteristic
510C22×C11#53311yescharacteristic
511C22×C11#53811yescharacteristic
512C22×C11#53911yescharacteristic
513C22×C11#54311yescharacteristic
514C22×C11#54411yescharacteristic
515C22×C11D4211yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54611yescharacteristic
520C22×C11#54711yescharacteristic
521C22×C11#54811yescharacteristic
522C22×C11#55111yescharacteristic
523C22×C11#55111yescharacteristic
524C22×C11#55111yescharacteristic
525C22×C11#55111yescharacteristic
526C22×C11#55211yescharacteristic
527C22×C11#55211yescharacteristic
528C22×C11#55311yescharacteristic
529C22×C11#55311yescharacteristic
530C22×C11#55311yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—24no—
541C2×D11—24no—
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11#38718yescomplemented
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—81no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—81no—
560C25—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—114no—
568C23×C4—114no—
569C23×C4—111no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—222no—
575C23×C4—222no—
576C23×C4—222no—
577C23×C4—222no—
578C23×C4—222no—
579C23×C4—222no—
580C23×C4—222no—
581C23×C4—222no—
582C23×C4—222no—
583C23×C4—441no—
584C23×C4—441no—
585C23×C4—441no—
586C23×C4—441no—
587C23×C4—441no—
588C23×C4—441no—
589C23×C4C22×D1111yescharacteristic
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—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—114no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—222no—
614C2×C22⋊C4—222no—
615C2×C22⋊C4—222no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—222no—
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—22no—
629#95—22no—
630#95—41no—
631#95—41no—
632#95—114no—
633#95—114no—
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—441no—
644#95—441no—
645#95—441no—
646#95—441no—
647#95C4×D1114yescomplemented
648C2×C11C2×#38711yescharacteristic
649C2×C11C4×C22⋊Q811yescharacteristic
650C2×C11#232911yescharacteristic
651C2×C11#234211yescharacteristic
652C2×C11#234311yescharacteristic
653C2×C11#236111yescharacteristic
654C2×C11#236411yescharacteristic
655C2×C11#241811yescharacteristic
656C2×C11#241911yescharacteristic
657C2×C11#243711yescharacteristic
658C2×C11#243811yescharacteristic
659C2×C11#244211yescharacteristic
660C2×C11#248111yescharacteristic
661C2×C11#251011yescharacteristic
662C2×C11#256911yescharacteristic
663D11—28no—
664C24—112no—
665C24—112no—
666C24—112no—
667C24—112no—
668C24—112no—
669C24—112no—
670C24—112no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24—221no—
677C24—221no—
678C24—221no—
679C24C23×D1111yescharacteristic
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—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—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—112no—
724C22×C4—112no—
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—228no—
734C22×C4—228no—
735C22×C4—228no—
736C22×C4—228no—
737C22×C4—228no—
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—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—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4—444no—
784C22×C4—444no—
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×C4C2×C4×D1112yes—
794C22×C4C2×C4×D1112yes—
795C22×C4C2×C4×D1112yes—
796C22×C4D4×D1112yes—
797C22×C4D4×D1112yes—
798C22×C4Q8×D1112yes—
799C4⋊C4—228no—
800C4⋊C4—444no—
801C4⋊C4—444no—
802C4⋊C4—444no—
803C22⋊C4—228no—
804C22⋊C4—228no—
805C22⋊C4—228no—
806C22⋊C4—444no—
807C42—444no—
808C42—444no—
809C11#1402811yescharacteristic, complemented, Sylow
810C23—114no—
811C23—114no—
812C23—114no—
813C23—114no—
814C23—114no—
815C23—114no—
816C23—114no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23C22×C4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23C2×D4×D1111yescharacteristic
848C23#6703711yescharacteristic
849C23C2×Q8×D1111yescharacteristic
850C23#41×D1111yescharacteristic
851C23#41×D1111yescharacteristic
852C23#41×D1111yescharacteristic
853C23#41×D1111yescharacteristic
854C23#41×D1111yescharacteristic
855C23#41×D1111yescharacteristic
856C23#41×D1111yescharacteristic
857C23#6704211yescharacteristic
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—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
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—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—114no—
910C2×C4—114no—
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—4416no—
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—118no—
962C22—224no—
963C22—224no—
964C22—224no—
965C22—224no—
966C22—224no—
967C22—224no—
968C22—224no—
969C22—224no—
970C22—224no—
971C22—224no—
972C22—224no—
973C22—224no—
974C22—224no—
975C22—224no—
976C22D11×#11711yescharacteristic
977C22#1062305311yescharacteristic
978C22#1062305411yescharacteristic
979C22C4×D4×D1111yescharacteristic
980C22C4×D4×D1111yescharacteristic
981C22#1062307611yescharacteristic
982C22C4×Q8×D1111yescharacteristic
983C22#1062314011yescharacteristic
984C22#1062314111yescharacteristic
985C22#1062314311yescharacteristic
986C22D11×C22⋊Q811yescharacteristic
987C22D11×C22⋊Q811yescharacteristic
988C22#1062316511yescharacteristic
989C22D11×#12311yescharacteristic
990C22#1062318511yescharacteristic
991C22#1062318611yescharacteristic
992C22#1062318711yescharacteristic
993C22#1062319111yescharacteristic
994C22#1062319211yescharacteristic
995C22#1062320711yescharacteristic
996C22#1062320811yescharacteristic
997C22#1062321011yescharacteristic
998C22D11×#12511yescharacteristic
999C22#1062321911yescharacteristic
1000C22#1062322011yescharacteristic
1001C22D11×#12611yescharacteristic
1002C22#1062323511yescharacteristic
1003C22#1062323611yescharacteristic
1004C22#1062323611yescharacteristic
1005C22#1062323611yescharacteristic
1006C22#1062323711yescharacteristic
1007C22#1062323911yescharacteristic
1008C22#1062323911yescharacteristic
1009C22#1062324011yescharacteristic
1010C22#1062324011yescharacteristic
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—224no—
1019C4—224no—
1020C4—442no—
1021C4—442no—
1022C4—442no—
1023C4—442no—
1024C4—881no—
1025C2—228no—
1026C2D11×#38711yescharacteristic
1027C2#1307115011yescharacteristic
1028C2#1307134311yescharacteristic
1029C2#1307146011yescharacteristic
1030C2#1307147311yescharacteristic
1031C2#1307162911yescharacteristic
1032C2#1307166011yescharacteristic
1033C2#1307207911yescharacteristic
1034C2#1307208811yescharacteristic
1035C2#1307227811yescharacteristic
1036C2#1307229511yescharacteristic
1037C2#1307233311yescharacteristic
1038C2#1307287211yescharacteristic
1039C2#1307317111yescharacteristic
1040C2#1307383611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#14028
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#10622265C2semidirect
6. #13066882C2semidirect
7. #13066874C2semidirect
8. #13066870C2semidirect
9. #13066850C2semidirect
10. #13066847C2semidirect
11. #13066840C2semidirect
15. C11×#1443C2semidirect
52. #10622280C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
115. C2×Dic11⋊C4C2×C4semidirect
128. C11×#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
296. #1443D11semidirect
545. C2×D11#387semidirect
647. #95C4×D11semidirect
809. C11#14028semidirect

Maximal subgroups

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

subgroupindex
C2×#106222652
C2×#106222812
C2×#106222802
C2×#106222792
C2×D11×#952
#130668822
#130668742
#130668702
#130668502
#130668472
#130668402
(C2×D11)⋊#952
C11×#14432
#1402811