Finite Group Databasebeta

← #14677443

Subgroups — #14677443

Order 2816.

1862 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×#10622279C211yesmaximal, characteristic
3C2×D11×#95C211yesmaximal, characteristic
4#13066883C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066877C211yesmaximal, characteristic, complemented
7#13066850C211yesmaximal, characteristic, complemented
8#13066847C211yesmaximal, characteristic, complemented
9#13066841C211yesmaximal, characteristic, complemented
10#13066841C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic
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×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
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#10622281C418yescomplemented
52#10622279—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—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
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×D11—41no—
88C22×C4×D11C2×C414yes—
89C22×C4×D11D414yes—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4Q814yes—
102C2×C4⋊Dic11—41no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11C2×C414yescomplemented
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4C2×C414yescomplemented
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11—41no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—41no—
119C11×#95—41no—
120C11×#95C2×C414yescomplemented
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yescomplemented
138#14040—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×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×Q812yes—
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×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C2×D412yes—
249C22×Dic11C2×Q812yes—
250C22×Dic11#4112yes—
251C22×Dic11#4112yes—
252C22×Dic11#4112yes—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—28no—
256C2×C4×D11—28no—
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—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—44no—
278C4⋊Dic11—44no—
279Dic11⋊C4—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#385—111no—
283C2×C4×C22⋊C4—111no—
284C22×#95—111no—
285#1445—111no—
286#1445—111no—
287#1443—111no—
288#1443D1111yescharacteristic, complemented
289#1436—111no—
290#1436—111no—
291#1434—111no—
292#1434—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×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
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—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
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#12314yes—
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×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C42—111no—
458C22×C42—111no—
459#385—118no—
460C4×C22⋊C4—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—224no—
479C2×#95C2×D1111yescharacteristic
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×C11C4×#4111yescharacteristic
490C22×C11C4×#4111yescharacteristic
491C22×C11#51811yescharacteristic
492C22×C11#51811yescharacteristic
493C22×C11C2×C22⋊Q811yescharacteristic
494C22×C11C2×#12311yescharacteristic
495C22×C11C2×#12311yescharacteristic
496C22×C11#52511yescharacteristic
497C22×C11C2×#12511yescharacteristic
498C22×C11C2×#12611yescharacteristic
499C22×C11#52911yescharacteristic
500C22×C11#52911yescharacteristic
501C22×C11#53411yescharacteristic
502C22×C11#53511yescharacteristic
503C22×C11#53811yescharacteristic
504C22×C11#53811yescharacteristic
505C22×C11#55111yescharacteristic
506C22×C11#55111yescharacteristic
507C22×C11#55111yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55111yescharacteristic
512C22×C11#55111yescharacteristic
513C22×C11#55311yescharacteristic
514C22×C11#55311yescharacteristic
515C22×C11#55311yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55411yescharacteristic
518C22×C11#55411yescharacteristic
519C22×C11#55411yescharacteristic
520C22×C11#55411yescharacteristic
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—42no—
542C4×C11—81no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—81no—
550C25—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—114no—
558C23×C4—114no—
559C23×C4—111no—
560C23×C4—222no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—222no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4—222no—
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—114no—
587C2×C4⋊C4—114no—
588C2×C4⋊C4—441no—
589C2×C4⋊C4—441no—
590C2×C4⋊C4—441no—
591C2×C4⋊C4—441no—
592C2×C22⋊C4—114no—
593C2×C22⋊C4—114no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—222no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—222no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C42—222no—
605C2×C42—222no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—441no—
609C2×C42—441no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—41no—
615#95—41no—
616#95—114no—
617#95—222no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95—222no—
623#95—222no—
624#95—222no—
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#95C4×D1114yescomplemented
634C2×C11C2×#38711yescharacteristic
635C2×C11C4×#12311yescharacteristic
636C2×C11#232111yescharacteristic
637C2×C11#235311yescharacteristic
638C2×C11#235311yescharacteristic
639C2×C11#236811yescharacteristic
640C2×C11#236811yescharacteristic
641C2×C11#248211yescharacteristic
642C2×C11#248311yescharacteristic
643C2×C11#248711yescharacteristic
644C2×C11#250511yescharacteristic
645C2×C11#250511yescharacteristic
646C2×C11#251011yescharacteristic
647C2×C11#251011yescharacteristic
648C2×C11#257911yescharacteristic
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—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—228no—
718C22×C4—228no—
719C22×C4—228no—
720C22×C4—228no—
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×C4C2×C4×D1112yes—
780C22×C4C2×C4×D1112yes—
781C22×C4C2×C4×D1112yes—
782C22×C4D4×D1112yes—
783C22×C4#434112yes—
784C22×C4Q8×D1112yes—
785C4⋊C4—444no—
786C4⋊C4—444no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—444no—
791C42—444no—
792C42—444no—
793C11#1404011yescharacteristic, 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
831C23C2×#434111yescharacteristic
832C23#6703711yescharacteristic
833C23C2×Q8×D1111yescharacteristic
834C23#41×D1111yescharacteristic
835C23#41×D1111yescharacteristic
836C23#41×D1111yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#6704211yescharacteristic
842C23#6704211yescharacteristic
843C23#6704211yescharacteristic
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—22no—
860C2×C4—22no—
861C2×C4—22no—
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—114no—
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—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—4416no—
916C2×C4—4416no—
917C2×C4—4416no—
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—
960C22D11×#11711yescharacteristic
961C22#1062305211yescharacteristic
962C22#1062305311yescharacteristic
963C22C4×#434111yescharacteristic
964C22C4×D4×D1111yescharacteristic
965C22#1062307611yescharacteristic
966C22C4×Q8×D1111yescharacteristic
967C22#1062313611yescharacteristic
968C22#1062313711yescharacteristic
969C22#1062314511yescharacteristic
970C22D11×C22⋊Q811yescharacteristic
971C22#1062316611yescharacteristic
972C22#1062316711yescharacteristic
973C22D11×#12311yescharacteristic
974C22D11×#12311yescharacteristic
975C22#1062318811yescharacteristic
976C22#1062318911yescharacteristic
977C22#1062318911yescharacteristic
978C22#1062319011yescharacteristic
979C22#1062320511yescharacteristic
980C22#1062321011yescharacteristic
981C22#1062321111yescharacteristic
982C22D11×#12511yescharacteristic
983C22#1062322111yescharacteristic
984C22#1062322111yescharacteristic
985C22D11×#12611yescharacteristic
986C22#1062323511yescharacteristic
987C22#1062323611yescharacteristic
988C22#1062323611yescharacteristic
989C22#1062323611yescharacteristic
990C22#1062323611yescharacteristic
991C22#1062323711yescharacteristic
992C22#1062324011yescharacteristic
993C22#1062324011yescharacteristic
994C22#1062324011yescharacteristic
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—224no—
1003C4—442no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C4—442no—
1008C4—881no—
1009C2—228no—
1010C2D11×#38711yescharacteristic
1011C2#1307114311yescharacteristic
1012C2#1307126911yescharacteristic
1013C2#1307154911yescharacteristic
1014C2#1307155111yescharacteristic
1015C2#1307169311yescharacteristic
1016C2#1307169811yescharacteristic
1017C2#1307288511yescharacteristic
1018C2#1307289311yescharacteristic
1019C2#1307292811yescharacteristic
1020C2#1307311011yescharacteristic
1021C2#1307311211yescharacteristic
1022C2#1307316911yescharacteristic
1023C2#1307317111yescharacteristic
1024C2#1307395811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#14040
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
4. #13066883C2semidirect
5. #13066882C2semidirect
6. #13066877C2semidirect
7. #13066850C2semidirect
8. #13066847C2semidirect
9. #13066841C2semidirect
10. #13066841C2semidirect
15. C11×#1443C2semidirect
51. #10622281C4semidirect
104. C2×C4⋊Dic11C2×C4semidirect
107. C2×Dic11⋊C4C2×C4semidirect
120. C11×#95C2×C4semidirect
137. C11⋊#95C2×C4semidirect
288. #1443D11semidirect
633. #95C4×D11semidirect
793. C11#14040semidirect

Maximal subgroups

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

subgroupindex
C2×#106222812
C2×#106222792
C2×D11×#952
#130668832
#130668822
#130668772
#130668502
#130668472
#130668412
(C2×D11)⋊#952
C11×#14432
#1404011