Finite Group Databasebeta

← #14684790

Subgroups — #14684790

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4#13066870C211yesmaximal, characteristic, complemented
5#13066868C212yesmaximal, complemented
6#13066866C211yesmaximal, characteristic, complemented
7#13066864C212yesmaximal, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066859C212yesmaximal, complemented
10#13066855C212yesmaximal
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C2×#66936—24no—
27C2×#66936—24no—
28C2×#66936C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622280—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—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11C2×C414yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D414yes—
60C22×C4×D11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4C2×C414yes—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C414yes—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4C2×C414yes—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—42no—
88C2×C4⋊Dic11C2×C414yes—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—42no—
93C2×Dic11⋊C4—42no—
94C2×Dic11⋊C4C2×C414yes—
95#66936—232no—
96C11×#95—22no—
97C11×#95—42no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14658—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—22no—
116C24×C11C22×C412yes—
117C24×C11C2411yescharacteristic
118C23×D11—21no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—22no—
126C23×D11C22×C412yes—
127C23×D11C2×D412yes—
128C23×D11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
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×C11C22×C412yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—44no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—44no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
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—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C2×D412yes—
188C22×Dic11C2×D412yes—
189C2×C4×D11—48no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—48no—
193C2×C4×D11C22⋊C4116yescomplemented
194C11×C4⋊C4—44no—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—48no—
197C22⋊Dic11—28no—
198C22⋊Dic11—48no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202C4⋊Dic11—28no—
203C4⋊Dic11—44no—
204Dic11⋊C4—28no—
205Dic11⋊C4—48no—
206C22×#123—111no—
207C2×#380—111no—
208C2×#380—111no—
209#1441—112no—
210#1441—111no—
211#1441—111no—
212#1440—112no—
213#1439—112no—
214#1439—111no—
215#1439D1111yescharacteristic, complemented
216#1438—112no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—42no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C23×C411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C22×D411yescharacteristic
243C23×C11H(5,𝔽2)12yes—
244C23×C11H(5,𝔽2)12yes—
245C23×C11H(5,𝔽2)11yescharacteristic
246C23×C11H(5,𝔽2)12yes—
247C23×C11H(5,𝔽2)11yescharacteristic
248C23×C112−1+411yescharacteristic
249C23×C112−1+411yescharacteristic
250C23×C112−1+412yes—
251C22×D11—24no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—24no—
255C22×D11—22no—
256C22×D11—24no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—22no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11C2×C22⋊C414yes—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
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×C11C2×C22⋊C414yes—
298C22⋊D11—416no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—41no—
309C2×Dic11—42no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11C2×C22⋊C414yes—
330C4×D11—416no—
331C23×D4—111no—
332C24×C4—111no—
333C2×#123—118no—
334C2×#123—224no—
335C2×#123—224no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—112no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4C2×D1111yescharacteristic
347C22×C22⋊C4C2×D1112yes—
348#380—224no—
349#380—224no—
350C2×#95—112no—
351C2×#95—111no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95C2×D1111yescharacteristic
358C2×#95C2×D1112yes—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—44no—
363C22×C11—44no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—82no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—82no—
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11#51812yes—
372C22×C11#52011yescharacteristic
373C22×C11#52011yescharacteristic
374C22×C11#52012yes—
375C22×C11#53411yescharacteristic
376C22×C11#53412yes—
377C22×C11#53411yescharacteristic
378C22×C11#53511yescharacteristic
379C22×C11#53511yescharacteristic
380C22×C11#53611yescharacteristic
381C22×C11#53611yescharacteristic
382C22×C11#53711yescharacteristic
383C22×C11#53712yes—
384C22×C11#53711yescharacteristic
385C22×C11#56012yes—
386C22×C11#56012yes—
387C22×C11#56212yes—
388C22×C11#56212yes—
389C22×C11#56212yes—
390C22×C11#56212yes—
391C22×C11#56312yes—
392C22×C11#56312yes—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—42no—
399C2×D11—42no—
400C2×D11—44no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—44no—
404C4×C11—24no—
405C4×C11—42no—
406C4×C11—82no—
407C4×C11—82no—
408Dic11—24no—
409Dic11—42no—
410Dic11—42no—
411Dic11—82no—
412Dic11—82no—
413C25—111no—
414C25C22×D1111yescharacteristic
415C22×D4—114no—
416C22×D4—222no—
417C22×D4—222no—
418C22×D4—442no—
419C22×D4—442no—
420C23×C4—111no—
421C23×C4—114no—
422C23×C4—114no—
423C23×C4—114no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—112no—
427C23×C4—112no—
428C23×C4—442no—
429C23×C4—442no—
430C23×C4C22×D1112yes—
431C23×C4C22×D1112yes—
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434#123—2232no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—224no—
444C2×C4⋊C4—222no—
445C2×C4⋊C4—442no—
446C2×C4⋊C4—442no—
447C2×C4⋊C4—442no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—222no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4C4×D1114yes—
469#95—22no—
470#95—42no—
471#95—224no—
472#95—222no—
473#95—442no—
474#95—442no—
475#95—442no—
476#95—442no—
477#95—442no—
478C2×C11—82no—
479C2×C11#230811yescharacteristic
480C2×C11#231111yescharacteristic
481C2×C11#231111yescharacteristic
482C2×C11#237612yes—
483C2×C11#237612yes—
484C2×C11#281311yescharacteristic
485C2×C11#281311yescharacteristic
486C2×C11#281312yes—
487C2×C11#281411yescharacteristic
488C2×C11#281411yescharacteristic
489C2×C11#281412yes—
490D11—44no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—22no—
501C24—112no—
502C24—112no—
503C24—112no—
504C24—222no—
505C24—221no—
506C24—222no—
507C24—221no—
508C24—221no—
509C24—222no—
510C24—221no—
511C24—222no—
512C24C2×C4×D1112yes—
513C24C23×D1111yescharacteristic
514C2×D4—228no—
515C2×D4—448no—
516C2×D4—444no—
517C2×D4—448no—
518C2×D4—444no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—1116no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—222no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—448no—
572C22×C4—444no—
573C22×C4—448no—
574C22×C4—444no—
575C22×C4C2×C4×D1112yes—
576C22×C4C2×C4×D1112yes—
577C22×C4D4×D1112yes—
578C22×C4D4×D1112yes—
579C4⋊C4—44no—
580C4⋊C4—228no—
581C4⋊C4—228no—
582C4⋊C4—444no—
583C4⋊C4—448no—
584C22⋊C4—28no—
585C22⋊C4—48no—
586C22⋊C4—228no—
587C22⋊C4—228no—
588C22⋊C4—448no—
589C22⋊C4—448no—
590C22⋊C4—448no—
591C11#1465811yescharacteristic, complemented, Sylow
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—42no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—42no—
615C23—114no—
616C23—222no—
617C23—222no—
618C23—222no—
619C23—224no—
620C23—224no—
621C23—222no—
622C23—224no—
623C23—222no—
624C23—222no—
625C23—224no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23C22×C4×D1111yescharacteristic
639C23C2×D4×D1111yescharacteristic
640C23C2×D4×D1111yescharacteristic
641C23#6703712yes—
642C23#6703711yescharacteristic
643C23#6703712yes—
644C23#6704011yescharacteristic
645C23#6704212yes—
646C23#6704211yescharacteristic
647C23#6704311yescharacteristic
648C23#6704312yes—
649D4—4416no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—114no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—224no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—224no—
683C2×C4—4416no—
684C2×C4—441no—
685C2×C4—442no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4C22⋊C4×D1114yes—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—44no—
710C22—44no—
711C22—81no—
712C22—81no—
713C22—82no—
714C22—81no—
715C22—81no—
716C22—82no—
717C22—224no—
718C22—224no—
719C22—224no—
720C22—442no—
721C22—442no—
722C22—444no—
723C22—444no—
724C22—442no—
725C22—444no—
726C22—442no—
727C22—444no—
728C22C2×C22⋊C4×D1111yescharacteristic
729C22#1062303511yescharacteristic
730C22#1062305411yescharacteristic
731C22#1062307612yes—
732C22#1062307712yes—
733C22#1062312011yescharacteristic
734C22#1062312612yes—
735C22#1062313612yes—
736C22#1062313811yescharacteristic
737C22#1062313911yescharacteristic
738C22#1062313912yes—
739C22#1062315212yes—
740C22#1062315911yescharacteristic
741C22#1062316011yescharacteristic
742C22#1062317712yes—
743C22#1062317812yes—
744C22#1062318411yescharacteristic
745C22#1062319712yes—
746C22#1062319812yes—
747C22#1062320611yescharacteristic
748C22#1062321512yes—
749C22#1062324312yes—
750C22#1062324611yescharacteristic
751C4—24no—
752C4—42no—
753C4—82no—
754C4—82no—
755C4—224no—
756C4—442no—
757C4—442no—
758C4—882no—
759C4—882no—
760C2—82no—
761C2—444no—
762C2#1307119011yescharacteristic
763C2#1307120511yescharacteristic
764C2#1307120611yescharacteristic
765C2#1307175812yes—
766C2#1307176512yes—
767C2#1307661511yescharacteristic
768C2#1307661911yescharacteristic
769C2#1307662312yes—
770C2#1307662611yescharacteristic
771C2#1307663011yescharacteristic
772C2#1307663412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14658
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622280C2semidirect
3. C2×#10622600C2semidirect
4. #13066870C2semidirect
5. #13066868C2semidirect
6. #13066866C2semidirect
7. #13066864C2semidirect
8. #13066861C2semidirect
9. #13066859C2semidirect
11. C11×#1439C2semidirect
28. C2×#66936C4semidirect
193. C2×C4×D11C22⋊C4semidirect
215. #1439D11semidirect
591. C11#14658semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
C2×#106222802
C2×#106226002
#130668702
#130668682
#130668662
#130668642
#130668612
#130668592
#130668552
C11×#14392
#1465811