Finite Group Databasebeta

← #14684139

Subgroups — #14684139

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#13066878C211yesmaximal, characteristic, complemented
5#13066877C211yesmaximal, characteristic, complemented
6#13066858C211yesmaximal, characteristic
7#13066854C211yesmaximal, characteristic
8#13066852C211yesmaximal, characteristic
9#13066848C211yesmaximal, characteristic, complemented
10#13066843C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
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×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—41no—
84C2×C42×C11—22no—
85C2×C42×C11—41no—
86C2×C42×C11—41no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4Q814yescomplemented
105C2×C4×Dic11—22no—
106C2×C4×Dic11—41no—
107C2×C4×Dic11—41no—
108C11×#95—22no—
109C11×#95—41no—
110C11×#95—41no—
111C11×#95—41no—
112C11×#95C2×C414yescomplemented
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—41no—
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×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×Q812yes—
195C22×C4×C11#4112yes—
196C22×C4×C11#4112yes—
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×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11C22×C412yes—
243C22×Dic11C22×C412yes—
244C22×Dic11C22×C412yes—
245C22×Dic11C2×Q812yes—
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—
261C11×C4⋊C4—44no—
262C42×C11—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4×Dic11—44no—
270C2×#393—111no—
271#1446—111no—
272#1446—111no—
273#1443—111no—
274#1443—111no—
275#1439—111no—
276#1437—111no—
277#1437—111no—
278#1436—111no—
279#1436D1111yescharacteristic, complemented
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—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
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—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
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⋊C4C2×D1111yescharacteristic
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×C42C2×D1111yescharacteristic
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×#95—111no—
465C2×#95—111no—
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—42no—
527C4×C11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—81no—
534Dic11—81no—
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—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—41no—
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—22no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—222no—
589C2×C42—441no—
590C2×C42—441no—
591#95—22no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—114no—
596#95—114no—
597#95—222no—
598#95—222no—
599#95—222no—
600#95—441no—
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—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
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—444no—
746C22×C4—444no—
747C22×C4—444no—
748C22×C4—444no—
749C22×C4—444no—
750C22×C4—444no—
751C22×C4—444no—
752C22×C4C2×C4×D1112yes—
753C22×C4C2×C4×D1112yes—
754C22×C4C2×C4×D1112yes—
755C22×C4#433912yes—
756C22×C4#433912yes—
757C22×C4#434112yes—
758C22×C4Q8×D1112yes—
759C4⋊C4—44no—
760C22⋊C4—444no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C42—44no—
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×#433911yescharacteristic
806C23C2×#433911yescharacteristic
807C23C2×#434111yescharacteristic
808C23#6703711yescharacteristic
809C23#6703711yescharacteristic
810C23#6703711yescharacteristic
811C23C2×Q8×D1111yescharacteristic
812C23#6704011yescharacteristic
813C23#41×D1111yescharacteristic
814C23#41×D1111yescharacteristic
815C23#6704211yescharacteristic
816C23#6704211yescharacteristic
817C23#6704211yescharacteristic
818C23#6704211yescharacteristic
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—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
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—4416no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
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—
934C22C4×#433911yescharacteristic
935C22#1062302611yescharacteristic
936C22#1062303511yescharacteristic
937C22#1062304211yescharacteristic
938C22#1062305211yescharacteristic
939C22#1062305811yescharacteristic
940C22#1062306311yescharacteristic
941C22C4×#434111yescharacteristic
942C22#1062307611yescharacteristic
943C22#1062307611yescharacteristic
944C22#1062308711yescharacteristic
945C22#1062308711yescharacteristic
946C22#1062309111yescharacteristic
947C22#1062309111yescharacteristic
948C22#1062309411yescharacteristic
949C22C4×Q8×D1111yescharacteristic
950C22#1062311011yescharacteristic
951C22#1062311311yescharacteristic
952C22#1062311311yescharacteristic
953C22#1062312411yescharacteristic
954C22#1062314411yescharacteristic
955C22#1062315111yescharacteristic
956C22#1062316511yescharacteristic
957C22#1062316611yescharacteristic
958C22#1062317111yescharacteristic
959C22#1062317411yescharacteristic
960C22#1062318811yescharacteristic
961C22#1062318911yescharacteristic
962C22#1062319711yescharacteristic
963C22#1062321411yescharacteristic
964C22#1062322111yescharacteristic
965C22#1062322311yescharacteristic
966C22#1062323611yescharacteristic
967C22#1062324211yescharacteristic
968C22#1062326011yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—442no—
977C4—442no—
978C4—442no—
979C4—442no—
980C4—442no—
981C4—881no—
982C4—881no—
983C2—444no—
984C2#1307135011yescharacteristic
985C2#1307142911yescharacteristic
986C2#1307143011yescharacteristic
987C2#1307169811yescharacteristic
988C2#1307170011yescharacteristic
989C2#1307172411yescharacteristic
990C2#1307175611yescharacteristic
991C2#1307566111yescharacteristic
992C2#1307566611yescharacteristic
993C2#1307567211yescharacteristic
994C2#1307574311yescharacteristic
995C2#1307599211yescharacteristic
996C2#1307602711yescharacteristic
997C2#1307631211yescharacteristic
998C2#1307631511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14596
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. #13066886C2semidirect
3. #13066886C2semidirect
4. #13066878C2semidirect
5. #13066877C2semidirect
9. #13066848C2semidirect
10. #13066843C2semidirect
11. #13066840C2semidirect
15. C11×#1436C2semidirect
51. #10622286C4semidirect
80. C22×Dic22C2×C4semidirect
104. C2×(C2×D11)⋊C4Q8semidirect
112. C11×#95C2×C4semidirect
130. C11⋊#95C2×C4semidirect
131. C11⋊#95C2×C4semidirect
279. #1436D11semidirect
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
#130668782
#130668772
#130668582
#130668542
#130668522
#130668482
#130668432
#130668402
(C2×D11)⋊#952
C11×#14362
#1459611