Finite Group Databasebeta

← #14684135

Subgroups — #14684135

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622286C211yesmaximal, characteristic
2#13066886C211yesmaximal, characteristic, complemented
3#13066886C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066862C211yesmaximal, characteristic
6#13066852C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic
8#13066850C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11#13066841C211yesmaximal, 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×Dic22C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
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#10622286C418yescomplemented
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11—41no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11—41no—
74C22×Dic22—41no—
75C22×Dic22—41no—
76C22×Dic22—41no—
77C22×Dic22—41no—
78C22×Dic22—41no—
79C22×Dic22—41no—
80C22×Dic22C2×C414yescomplemented
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4C2×C414yes—
96C2×(C2×D11)⋊C4C2×C414yes—
97C2×(C2×D11)⋊C4C2×C414yes—
98C2×(C2×D11)⋊C4Q814yescomplemented
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—41no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—41no—
105C2×C4×Dic11—41no—
106C2×C4×Dic11—41no—
107C2×C4×Dic11—41no—
108C11×#95—22no—
109C11×#95—22no—
110C11×#95—41no—
111C11×#95—41no—
112C11×#95—41no—
113C11×#95—41no—
114C11×#95C2×C414yescomplemented
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—41no—
118C11⋊#95—41no—
119C11⋊#95—41no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95C2×C414yescomplemented
131C11⋊#95C2×C414yescomplemented
132#14596—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11C22×C412yes—
147C23×D11C2×Q812yes—
148C23×D11#4112yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
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×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×Q812yes—
197C22×C4×C11#4112yes—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
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×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C2×Q812yes—
244C22×Dic11#4112yes—
245C22×Dic11#4112yes—
246C22×Dic11#4112yes—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×Dic22—44no—
255C2×Dic22—44no—
256C2×Dic22—44no—
257C2×Dic22—44no—
258C2×Dic22—44no—
259C2×Dic22—44no—
260C2×Dic22—44no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—44no—
268C4×Dic11—44no—
269C4×Dic11—44no—
270C2×#393—111no—
271#1446—111no—
272#1446—111no—
273#1443—111no—
274#1443D1111yescharacteristic, complemented
275#1439—111no—
276#1437—111no—
277#1437—111no—
278#1436—111no—
279#1436—111no—
280#1434—111no—
281#1434—111no—
282C22⋊#95—111no—
283C22⋊#95—111no—
284C22⋊#95—111no—
285C23×C11C23×C411yescharacteristic
286C23×C11C22×Q811yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4111yescharacteristic
291C23×C11C2×#4111yescharacteristic
292C23×C11H(5,𝔽2)11yescharacteristic
293C23×C11H(5,𝔽2)11yescharacteristic
294C23×C11H(5,𝔽2)11yescharacteristic
295C23×C11H(5,𝔽2)11yescharacteristic
296C23×C11H(5,𝔽2)11yescharacteristic
297C23×C11H(5,𝔽2)11yescharacteristic
298C23×C11H(5,𝔽2)11yescharacteristic
299C23×C112−1+411yescharacteristic
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11C4×Q814yes—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C4×D11—416no—
434Dic22—416no—
435C23×Q8—111no—
436C24×C4—111no—
437C22×C4⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C42—111no—
445C22×C42—111no—
446#393—118no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95C2×D1111yescharacteristic
465C2×#95C2×D1111yescharacteristic
466C2×#95C2×D1111yescharacteristic
467C2×#95C2×D1111yescharacteristic
468C2×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C2×#95C2×D1111yescharacteristic
471C22×C11C2×C4×Q811yescharacteristic
472C22×C11C4×#4111yescharacteristic
473C22×C11C4×#4111yescharacteristic
474C22×C11#51811yescharacteristic
475C22×C11#51811yescharacteristic
476C22×C11#51811yescharacteristic
477C22×C11#52011yescharacteristic
478C22×C11#53811yescharacteristic
479C22×C11#53811yescharacteristic
480C22×C11#53811yescharacteristic
481C22×C11#53811yescharacteristic
482C22×C11#53811yescharacteristic
483C22×C11#53911yescharacteristic
484C22×C11#54211yescharacteristic
485C22×C11#54211yescharacteristic
486C22×C11#54211yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11#54311yescharacteristic
489C22×C11#54411yescharacteristic
490C22×C11#55111yescharacteristic
491C22×C11#55111yescharacteristic
492C22×C11#55111yescharacteristic
493C22×C11#55111yescharacteristic
494C22×C11#55111yescharacteristic
495C22×C11#55111yescharacteristic
496C22×C11#55411yescharacteristic
497C22×C11#55411yescharacteristic
498C22×C11#55411yescharacteristic
499C22×C11#55411yescharacteristic
500C22×C11#55511yescharacteristic
501C22×C11#55511yescharacteristic
502C22×C11#56011yescharacteristic
503C22×C11#56011yescharacteristic
504C22×C11#56011yescharacteristic
505C22×C11H(3,𝔽4)11yescharacteristic
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—81no—
527C4×C11—81no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—42no—
534Dic11—42no—
535C25—111no—
536C22×Q8—114no—
537C22×Q8—441no—
538C22×Q8—441no—
539C22×Q8—441no—
540C22×Q8—441no—
541C22×Q8—441no—
542C22×Q8—441no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—222no—
551C23×C4—222no—
552C23×C4—222no—
553C23×C4—441no—
554C23×C4—441no—
555C23×C4—441no—
556C23×C4—441no—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—441no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—222no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—441no—
576C2×C22⋊C4—441no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4—441no—
579C2×C22⋊C4—441no—
580C2×C22⋊C4—441no—
581C2×C22⋊C4—441no—
582C2×C22⋊C4—441no—
583C2×C22⋊C4—441no—
584C2×C22⋊C4—441no—
585C2×C42—222no—
586C2×C42—222no—
587C2×C42—441no—
588C2×C42—441no—
589C2×C42—441no—
590C2×C42—441no—
591#95—22no—
592#95—22no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—114no—
598#95—114no—
599#95—222no—
600#95—222no—
601#95—441no—
602#95—441no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95—441no—
614#95C4×D1114yescomplemented
615C2×C11#232911yescharacteristic
616C2×C11#233711yescharacteristic
617C2×C11#233711yescharacteristic
618C2×C11#236811yescharacteristic
619C2×C11#236811yescharacteristic
620C2×C11#237211yescharacteristic
621C2×C11#237511yescharacteristic
622C2×C11#273611yescharacteristic
623C2×C11#273711yescharacteristic
624C2×C11#273711yescharacteristic
625C2×C11#274211yescharacteristic
626C2×C11#276011yescharacteristic
627C2×C11#276311yescharacteristic
628C2×C11#278411yescharacteristic
629C2×C11#278411yescharacteristic
630D11—44no—
631C24—112no—
632C24—112no—
633C24—112no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24—221no—
641C24—221no—
642C24—221no—
643C24—221no—
644C24—221no—
645C24—221no—
646C24C23×D1111yescharacteristic
647C2×Q8—444no—
648C2×Q8—444no—
649C2×Q8—444no—
650C2×Q8—444no—
651C2×Q8—444no—
652C2×Q8—444no—
653C2×Q8—444no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—444no—
748C22×C4—444no—
749C22×C4—444no—
750C22×C4—444no—
751C22×C4—444no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4C2×C4×D1112yes—
755C22×C4C2×C4×D1112yes—
756C22×C4C2×C4×D1112yes—
757C22×C4#434112yes—
758C22×C4Q8×D1112yes—
759C4⋊C4—444no—
760C22⋊C4—444no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C42—444no—
767C42—444no—
768C11#1459611yescharacteristic, complemented, Sylow
769C23—114no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—441no—
789C23—441no—
790C23—441no—
791C23—441no—
792C23—441no—
793C23—441no—
794C23—441no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23C22×C4×D1111yescharacteristic
805C23C2×#434111yescharacteristic
806C23#6703711yescharacteristic
807C23#6703711yescharacteristic
808C23C2×Q8×D1111yescharacteristic
809C23#41×D1111yescharacteristic
810C23#41×D1111yescharacteristic
811C23#41×D1111yescharacteristic
812C23#41×D1111yescharacteristic
813C23#6704211yescharacteristic
814C23#6704211yescharacteristic
815C23#6704211yescharacteristic
816C23#6704211yescharacteristic
817C23#6704211yescharacteristic
818C23#6704311yescharacteristic
819Q8—4416no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—4416no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C22—224no—
920C22—224no—
921C22—224no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—442no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22#1062305211yescharacteristic
935C22#1062305311yescharacteristic
936C22#1062305411yescharacteristic
937C22C4×#434111yescharacteristic
938C22#1062307611yescharacteristic
939C22#1062307611yescharacteristic
940C22C4×Q8×D1111yescharacteristic
941C22#1062314711yescharacteristic
942C22#1062314811yescharacteristic
943C22#1062315111yescharacteristic
944C22#1062316511yescharacteristic
945C22#1062316611yescharacteristic
946C22#1062316711yescharacteristic
947C22#1062318911yescharacteristic
948C22#1062318911yescharacteristic
949C22#1062319011yescharacteristic
950C22#1062319111yescharacteristic
951C22#1062319311yescharacteristic
952C22#1062319711yescharacteristic
953C22#1062320111yescharacteristic
954C22#1062321311yescharacteristic
955C22#1062321411yescharacteristic
956C22#1062322011yescharacteristic
957C22#1062322111yescharacteristic
958C22#1062322111yescharacteristic
959C22#1062323511yescharacteristic
960C22#1062323511yescharacteristic
961C22#1062323511yescharacteristic
962C22#1062323511yescharacteristic
963C22#1062323611yescharacteristic
964C22#1062323611yescharacteristic
965C22#1062323611yescharacteristic
966C22#1062324111yescharacteristic
967C22#1062324111yescharacteristic
968C22#1062324211yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—442no—
977C4—442no—
978C4—442no—
979C4—442no—
980C4—442no—
981C4—442no—
982C4—442no—
983C2—444no—
984C2#1307134311yescharacteristic
985C2#1307142311yescharacteristic
986C2#1307142611yescharacteristic
987C2#1307169311yescharacteristic
988C2#1307169811yescharacteristic
989C2#1307172311yescharacteristic
990C2#1307175611yescharacteristic
991C2#1307566311yescharacteristic
992C2#1307567011yescharacteristic
993C2#1307567611yescharacteristic
994C2#1307574411yescharacteristic
995C2#1307599411yescharacteristic
996C2#1307603111yescharacteristic
997C2#1307631611yescharacteristic
998C2#1307631811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#14596
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #13066886C2semidirect
3. #13066886C2semidirect
4. #13066876C2semidirect
8. #13066850C2semidirect
9. #13066850C2semidirect
10. #13066842C2semidirect
11. #13066841C2semidirect
15. C11×#1443C2semidirect
51. #10622286C4semidirect
80. C22×Dic22C2×C4semidirect
98. C2×(C2×D11)⋊C4Q8semidirect
114. C11×#95C2×C4semidirect
130. C11⋊#95C2×C4semidirect
131. C11⋊#95C2×C4semidirect
274. #1443D11semidirect
614. #95C4×D11semidirect
768. C11#14596semidirect

Maximal subgroups

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

subgroupindex
C2×#106222862
#130668862
#130668762
#130668622
#130668522
#130668502
#130668422
#130668412
(C2×D11)⋊#952
C11×#14432
#1459611