Finite Group Databasebeta

← #14682701

Subgroups — #14682701

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622282C211yesmaximal, characteristic
2#13066882C211yesmaximal, characteristic, complemented
3#13066876C211yesmaximal, characteristic, complemented
4#13066870C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic
8#13066850C211yesmaximal, characteristic, complemented
9#13066841C211yesmaximal, characteristic, complemented
10#13066841C211yesmaximal, 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
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
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#10622282C418yescomplemented
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—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—41no—
82C2×(C2×D11)⋊C4—41no—
83C2×(C2×D11)⋊C4—41no—
84C2×(C2×D11)⋊C4—41no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4C2×C414yes—
90C2×(C2×D11)⋊C4C2×C414yes—
91C2×(C2×D11)⋊C4C2×C414yes—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11—41no—
95C2×Dic11⋊C4—41no—
96C2×Dic11⋊C4—41no—
97C2×Dic11⋊C4C2×C414yescomplemented
98C2×C4×Dic11—22no—
99C2×C4×Dic11—41no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11—41no—
103C2×C4×Dic11C2×C414yescomplemented
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—41no—
107C11×#95—41no—
108C11×#95—41no—
109C11×#95—41no—
110C11×#95C2×C414yescomplemented
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—41no—
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⋊#95C2×C414yescomplemented
128#14484—111nomaximal, Sylow
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
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×D11C22×C412yes—
143C23×D11#4112yes—
144C23×D11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
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×C11C22×C412yes—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11#4112yes—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
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×Dic11C22×C412yes—
238C22×Dic11C22×C412yes—
239C22×Dic11C22×C412yes—
240C22×Dic11#4112yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C2×C4×D11—44no—
244C2×C4×D11—44no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250(C2×D11)⋊C4—28no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256C4⋊Dic11—44no—
257Dic11⋊C4—44no—
258C4×Dic11—44no—
259C4×Dic11—44no—
260C2×#388—111no—
261#1445—111no—
262#1443—111no—
263#1443D1111yescharacteristic, complemented
264#1441—111no—
265#1440—111no—
266#1439—111no—
267#1437—111no—
268#1436—111no—
269#1434—111no—
270#1434—111no—
271#1434—111no—
272C22⋊#95—111no—
273C22⋊#95—111no—
274C22⋊#95—111no—
275C23×C11C23×C411yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4111yescharacteristic
280C23×C11C2×#4111yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C11H(5,𝔽2)11yescharacteristic
284C23×C11H(5,𝔽2)11yescharacteristic
285C23×C11H(5,𝔽2)11yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C11H(5,𝔽2)11yescharacteristic
288C23×C112−1+411yescharacteristic
289C23×C112−1+411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
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—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11#11714yes—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
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×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
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—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
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—
423C4×D11—416no—
424C24×C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C42—111no—
434C22×C42—111no—
435#388—118no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95C2×D1111yescharacteristic
454C2×#95C2×D1111yescharacteristic
455C2×#95C2×D1111yescharacteristic
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C22×C11C2×#11711yescharacteristic
461C22×C11C4×#4111yescharacteristic
462C22×C11C4×#4111yescharacteristic
463C22×C11#51811yescharacteristic
464C22×C11#51811yescharacteristic
465C22×C11#52011yescharacteristic
466C22×C11#52011yescharacteristic
467C22×C11#53811yescharacteristic
468C22×C11#53811yescharacteristic
469C22×C11#53811yescharacteristic
470C22×C11#53811yescharacteristic
471C22×C11#53811yescharacteristic
472C22×C11#53811yescharacteristic
473C22×C11#53911yescharacteristic
474C22×C11#53911yescharacteristic
475C22×C11#54011yescharacteristic
476C22×C11#54011yescharacteristic
477C22×C11#54211yescharacteristic
478C22×C11#54211yescharacteristic
479C22×C11#55111yescharacteristic
480C22×C11#55111yescharacteristic
481C22×C11#55111yescharacteristic
482C22×C11#55111yescharacteristic
483C22×C11#55111yescharacteristic
484C22×C11#55211yescharacteristic
485C22×C11#55211yescharacteristic
486C22×C11#55211yescharacteristic
487C22×C11#55311yescharacteristic
488C22×C11#55311yescharacteristic
489C22×C11#55311yescharacteristic
490C22×C11#55611yescharacteristic
491C22×C11#56011yescharacteristic
492C22×C11#56211yescharacteristic
493C22×C11#56211yescharacteristic
494C22×C11#56311yescharacteristic
495C2×D11—24no—
496C2×D11—24no—
497C2×D11—24no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—81no—
515C4×C11—81no—
516C4×C11—81no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520Dic11—42no—
521Dic11—42no—
522Dic11—42no—
523Dic11—81no—
524C25—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—222no—
533C23×C4—222no—
534C23×C4—222no—
535C23×C4—441no—
536C23×C4—441no—
537C23×C4—441no—
538C23×C4—441no—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C2×C4⋊C4—114no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—441no—
549C2×C4⋊C4—441no—
550C2×C4⋊C4—441no—
551C2×C4⋊C4—441no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—222no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—222no—
558C2×C22⋊C4—222no—
559C2×C22⋊C4—222no—
560C2×C22⋊C4—222no—
561C2×C22⋊C4—222no—
562C2×C22⋊C4—441no—
563C2×C22⋊C4—441no—
564C2×C22⋊C4—441no—
565C2×C22⋊C4—441no—
566C2×C22⋊C4—441no—
567C2×C22⋊C4—441no—
568C2×C22⋊C4—441no—
569C2×C22⋊C4—441no—
570C2×C42—114no—
571C2×C42—222no—
572C2×C42—441no—
573C2×C42—441no—
574C2×C42—441no—
575C2×C42—441no—
576#95—22no—
577#95—22no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—41no—
582#95—114no—
583#95—222no—
584#95—222no—
585#95—222no—
586#95—222no—
587#95—441no—
588#95—441no—
589#95—441no—
590#95—441no—
591#95—441no—
592#95—441no—
593#95—441no—
594#95—441no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95—441no—
599#95C4×D1114yescomplemented
600C2×C11#231811yescharacteristic
601C2×C11#233311yescharacteristic
602C2×C11#233711yescharacteristic
603C2×C11#234311yescharacteristic
604C2×C11#235311yescharacteristic
605C2×C11#237311yescharacteristic
606C2×C11#237611yescharacteristic
607C2×C11#273511yescharacteristic
608C2×C11#274111yescharacteristic
609C2×C11#274311yescharacteristic
610C2×C11#274511yescharacteristic
611C2×C11#276111yescharacteristic
612C2×C11#277011yescharacteristic
613C2×C11#277811yescharacteristic
614C2×C11#278611yescharacteristic
615D11—44no—
616C24—112no—
617C24—112no—
618C24—112no—
619C24—221no—
620C24—221no—
621C24—221no—
622C24—221no—
623C24—221no—
624C24—221no—
625C24—221no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—221no—
630C24—221no—
631C24C23×D1111yescharacteristic
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
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—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
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—444no—
727C22×C4—444no—
728C22×C4—444no—
729C22×C4—444no—
730C22×C4—444no—
731C22×C4—444no—
732C22×C4—444no—
733C22×C4C2×C4×D1112yes—
734C22×C4C2×C4×D1112yes—
735C22×C4C2×C4×D1112yes—
736C22×C4#434112yes—
737C4⋊C4—444no—
738C4⋊C4—444no—
739C22⋊C4—228no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C22⋊C4—444no—
744C22⋊C4—444no—
745C42—444no—
746C42—444no—
747C11#1448411yescharacteristic, complemented, Sylow
748C23—114no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—441no—
768C23—441no—
769C23—441no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23C22×C4×D1111yescharacteristic
784C23C2×#434111yescharacteristic
785C23#6703711yescharacteristic
786C23#6703711yescharacteristic
787C23#6704011yescharacteristic
788C23#41×D1111yescharacteristic
789C23#41×D1111yescharacteristic
790C23#41×D1111yescharacteristic
791C23#41×D1111yescharacteristic
792C23#41×D1111yescharacteristic
793C23#6704211yescharacteristic
794C23#6704211yescharacteristic
795C23#6704211yescharacteristic
796C23#6704211yescharacteristic
797C23#6704311yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
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—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—4416no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
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—
897C22—224no—
898C22—224no—
899C22—224no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22D11×#11711yescharacteristic
913C22#1062305311yescharacteristic
914C22#1062305411yescharacteristic
915C22C4×#434111yescharacteristic
916C22#1062307611yescharacteristic
917C22#1062307611yescharacteristic
918C22#1062310511yescharacteristic
919C22#1062314511yescharacteristic
920C22#1062314611yescharacteristic
921C22#1062314811yescharacteristic
922C22#1062316911yescharacteristic
923C22#1062317211yescharacteristic
924C22#1062317811yescharacteristic
925C22#1062318811yescharacteristic
926C22#1062318911yescharacteristic
927C22#1062318911yescharacteristic
928C22#1062319311yescharacteristic
929C22#1062319411yescharacteristic
930C22#1062319811yescharacteristic
931C22#1062320911yescharacteristic
932C22#1062321011yescharacteristic
933C22#1062321311yescharacteristic
934C22#1062322311yescharacteristic
935C22#1062322411yescharacteristic
936C22#1062323011yescharacteristic
937C22#1062323511yescharacteristic
938C22#1062323511yescharacteristic
939C22#1062323511yescharacteristic
940C22#1062323611yescharacteristic
941C22#1062323611yescharacteristic
942C22#1062323911yescharacteristic
943C22#1062323911yescharacteristic
944C22#1062324011yescharacteristic
945C22#1062324011yescharacteristic
946C22#1062324211yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—442no—
955C4—442no—
956C4—442no—
957C4—442no—
958C4—442no—
959C4—442no—
960C4—881no—
961C2—444no—
962C2#1307124811yescharacteristic
963C2#1307137911yescharacteristic
964C2#1307142311yescharacteristic
965C2#1307147311yescharacteristic
966C2#1307155111yescharacteristic
967C2#1307172911yescharacteristic
968C2#1307176311yescharacteristic
969C2#1307565611yescharacteristic
970C2#1307573311yescharacteristic
971C2#1307574811yescharacteristic
972C2#1307579211yescharacteristic
973C2#1307601011yescharacteristic
974C2#1307611311yescharacteristic
975C2#1307624111yescharacteristic
976C2#1307633411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#14484
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #13066882C2semidirect
3. #13066876C2semidirect
4. #13066870C2semidirect
8. #13066850C2semidirect
9. #13066841C2semidirect
10. #13066841C2semidirect
11. #13066840C2semidirect
15. C11×#1443C2semidirect
51. #10622282C4semidirect
97. C2×Dic11⋊C4C2×C4semidirect
103. C2×C4×Dic11C2×C4semidirect
110. C11×#95C2×C4semidirect
127. C11⋊#95C2×C4semidirect
263. #1443D11semidirect
599. #95C4×D11semidirect
747. C11#14484semidirect

Maximal subgroups

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

subgroupindex
C2×#106222822
#130668822
#130668762
#130668702
#130668642
#130668622
#130668522
#130668502
#130668412
#130668402
(C2×D11)⋊#952
C11×#14432
#1448411