Finite Group Databasebeta

← #14680977

Subgroups — #14680977

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4#13066870C211yesmaximal, characteristic, complemented
5#13066866C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal
9#13066842C212yesmaximal, complemented
10#13066838C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×(C22⋊D11)⋊C4—24no—
26C2×(C22⋊D11)⋊C4—24no—
27C2×(C22⋊D11)⋊C4C418yescomplemented
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622277—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×C22⋊D11—22no—
52C22×C22⋊D11C2×C414yes—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—42no—
56C23×Dic11—42no—
57C23×Dic11C2×C414yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×C4×D11—42no—
64C22×C4×D11—42no—
65C22×C4×D11C2×C414yes—
66C22×C4×D11D414yes—
67C22×C4×D11D414yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—42no—
75C2×C11×C22⋊C4C2×C414yes—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C414yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—42no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4C2×C414yes—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11C2×C414yes—
96(C22⋊D11)⋊C4—232no—
97C11×#95—22no—
98C11×#95—42no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106C11⋊#95—42no—
107#14344—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11C22×C412yes—
117C24×C11#4112yes—
118C24×C11#4112yes—
119C24×C11C2411yescharacteristic
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11C22×C412yes—
129C23×D11C2×D412yes—
130C23×D11C2×D412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—28no—
162C22×Dic11—28no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—48no—
188C22×Dic11—44no—
189C22×Dic11—48no—
190C22×Dic11—44no—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11#4112yes—
197C22×Dic11#4112yes—
198C2×C4×D11—48no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—48no—
202C2×C4×D11C22⋊C4116yescomplemented
203C11×C4⋊C4—44no—
204C11×C22⋊C4—28no—
205C11×C22⋊C4—48no—
206C22⋊Dic11—48no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210C4⋊Dic11—44no—
211Dic11⋊C4—28no—
212C4×Dic11—28no—
213C22×C4×D4—111no—
214C2×#381—111no—
215C2×#380—111no—
216#1441—111no—
217#1441—111no—
218#1440—112no—
219#1439—111no—
220#1439D1111yescharacteristic, complemented
221#1438—112no—
222#1434—112no—
223C22⋊#95—112no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11#11714yes—
247C23×C11C23×C411yescharacteristic
248C23×C11C22×D411yescharacteristic
249C23×C11C22×D411yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C112−1+412yes—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—24no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—24no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11C2×C22⋊C414yes—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11C2×C22⋊C414yes—
305C22⋊D11—232no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—416no—
319C2×Dic11—41no—
320C2×Dic11—42no—
321C2×Dic11—41no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11C2×C22⋊C414yes—
337C2×Dic11#11714yes—
338C4×D11—416no—
339C23×D4—111no—
340C24×C4—111no—
341C24×C4—111no—
342C2×C4×D4—118no—
343C2×C4×D4—224no—
344C2×C4×D4—224no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4C2×D1111yescharacteristic
353C22×C22⋊C4C2×D1112yes—
354C22×C42—111no—
355#381—224no—
356#380—224no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—111no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95C2×D1111yescharacteristic
366C2×#95C2×D1112yes—
367C22×C11—28no—
368C22×C11—24no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11C22×C22⋊C411yescharacteristic
379C22×C11C2×#11711yescharacteristic
380C22×C11C2×#11711yescharacteristic
381C22×C11#51812yes—
382C22×C11#52012yes—
383C22×C11#52511yescharacteristic
384C22×C11#52511yescharacteristic
385C22×C11#52511yescharacteristic
386C22×C11#52511yescharacteristic
387C22×C11#53411yescharacteristic
388C22×C11#53412yes—
389C22×C11#53411yescharacteristic
390C22×C11#53511yescharacteristic
391C22×C11#53611yescharacteristic
392C22×C11#53712yes—
393C22×C11#53812yes—
394C22×C11#53812yes—
395C22×C11#53912yes—
396C22×C11#53912yes—
397C22×C11#54012yes—
398C22×C11#54012yes—
399C22×C11#54212yes—
400C22×C11#54212yes—
401C2×D11—24no—
402C2×D11—24no—
403C2×D11—24no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—44no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C4×C11—24no—
413C4×C11—42no—
414C4×C11—82no—
415C4×C11—82no—
416Dic11—24no—
417Dic11—24no—
418Dic11—42no—
419Dic11—82no—
420Dic11—82no—
421C25—111no—
422C25C22×D1111yescharacteristic
423C22×D4—114no—
424C22×D4—222no—
425C22×D4—222no—
426C22×D4—222no—
427C22×D4—222no—
428C22×D4—222no—
429C22×D4—222no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—114no—
433C23×C4—114no—
434C23×C4—114no—
435C23×C4—111no—
436C23×C4—114no—
437C23×C4—112no—
438C23×C4—112no—
439C23×C4—222no—
440C23×C4—222no—
441C23×C4—442no—
442C23×C4—442no—
443C23×C4—442no—
444C23×C4—442no—
445C23×C4C22×D1112yes—
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C4×D4—2232no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—442no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4C4×D1114yes—
475C2×C42—114no—
476C2×C42—222no—
477C2×C42—222no—
478#95—22no—
479#95—42no—
480#95—224no—
481#95—224no—
482#95—224no—
483#95—224no—
484#95—222no—
485#95—442no—
486#95—442no—
487#95—442no—
488C2×C11—44no—
489C2×C11#228011yescharacteristic
490C2×C11#230811yescharacteristic
491C2×C11#231111yescharacteristic
492C2×C11#231812yes—
493C2×C11#231912yes—
494C2×C11#263012yes—
495C2×C11#263012yes—
496C2×C11#263511yescharacteristic
497C2×C11#263511yescharacteristic
498C2×C11#263811yescharacteristic
499C2×C11#263811yescharacteristic
500D11—44no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—112no—
510C24—112no—
511C24—112no—
512C24—221no—
513C24—222no—
514C24—222no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—222no—
519C24—222no—
520C24C2×C4×D1112yes—
521C24#434112yes—
522C24#434312yes—
523C24C23×D1111yescharacteristic
524C2×D4—228no—
525C2×D4—228no—
526C2×D4—228no—
527C2×D4—228no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—228no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—1116no—
558C22×C4—112no—
559C22×C4—228no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—448no—
585C22×C4—444no—
586C22×C4—448no—
587C22×C4—444no—
588C22×C4—448no—
589C22×C4—444no—
590C22×C4—448no—
591C22×C4—444no—
592C22×C4C2×C4×D1112yes—
593C22×C4C2×C4×D1112yes—
594C22×C4D4×D1112yes—
595C22×C4D4×D1112yes—
596C4⋊C4—44no—
597C4⋊C4—228no—
598C4⋊C4—444no—
599C22⋊C4—28no—
600C22⋊C4—48no—
601C22⋊C4—228no—
602C22⋊C4—448no—
603C22⋊C4—448no—
604C22⋊C4—448no—
605C42—228no—
606C11#1434411yescharacteristic, complemented, Sylow
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23—114no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—224no—
634C23—224no—
635C23—222no—
636C23—224no—
637C23—222no—
638C23—222no—
639C23—224no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23#6694514yes—
653C23C22×C4×D1111yescharacteristic
654C23C2×D4×D1111yescharacteristic
655C23C2×D4×D1111yescharacteristic
656C23C2×#434111yescharacteristic
657C23#6703712yes—
658C23#6703712yes—
659C23C2×#434311yescharacteristic
660C23#41×D1111yescharacteristic
661C23#41×D1111yescharacteristic
662C23#6704212yes—
663C23#6704312yes—
664D4—2232no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—114no—
689C2×C4—114no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—4416no—
703C2×C4—4416no—
704C2×C4—441no—
705C2×C4—442no—
706C2×C4—441no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4C22⋊C4×D1114yes—
722C22—28no—
723C22—24no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—44no—
733C22—224no—
734C22—224no—
735C22—224no—
736C22—444no—
737C22—444no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—444no—
743C22—444no—
744C22C2×C22⋊C4×D1111yescharacteristic
745C22C2×#6694511yescharacteristic
746C22D11×#11711yescharacteristic
747C22#1062307612yes—
748C22#1062307712yes—
749C22#1062312011yescharacteristic
750C22#1062312412yes—
751C22#1062313612yes—
752C22#1062313711yescharacteristic
753C22#1062313711yescharacteristic
754C22#1062313912yes—
755C22#1062314612yes—
756C22#1062315811yescharacteristic
757C22#1062315811yescharacteristic
758C22#1062317512yes—
759C22#1062317612yes—
760C22#1062318411yescharacteristic
761C22#1062319412yes—
762C22#1062319612yes—
763C22#1062320012yes—
764C22#1062320611yescharacteristic
765C22#1062324112yes—
766C22#1062324611yescharacteristic
767C4—24no—
768C4—42no—
769C4—82no—
770C4—82no—
771C4—224no—
772C4—224no—
773C4—442no—
774C4—882no—
775C4—882no—
776C2—44no—
777C2—444no—
778C2#1307099811yescharacteristic
779C2#1307119011yescharacteristic
780C2#1307120611yescharacteristic
781C2#1307124412yes—
782C2#1307125712yes—
783C2#1307446012yes—
784C2#1307446212yes—
785C2#1307450511yescharacteristic
786C2#1307450611yescharacteristic
787C2#1307453811yescharacteristic
788C2#1307453911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622600C2semidirect
4. #13066870C2semidirect
5. #13066866C2semidirect
6. #13066864C2semidirect
7. #13066861C2semidirect
9. #13066842C2semidirect
10. #13066838C2semidirect
11. C11×#1439C2semidirect
27. C2×(C22⋊D11)⋊C4C4semidirect
202. C2×C4×D11C22⋊C4semidirect
220. #1439D11semidirect
606. C11#14344semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106222772
C2×#106226002
#130668702
#130668662
#130668642
#130668612
#130668552
#130668422
#130668382
C11×#14392
#1434411