Finite Group Databasebeta

← #14684437

Subgroups — #14684437

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622564C211yesmaximal, characteristic, complemented
4#13066875C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066862C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622601—24no—
36#10622573C418yescomplemented
37#10622564—24no—
38C25×C11C2311yescharacteristic
39C24×D11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—42no—
45C22×C22⋊D11—42no—
46C22×C22⋊D11—42no—
47C22×C22⋊D11—42no—
48C22×C22⋊D11—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11C2×C418yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—42no—
59C22×D44—42no—
60C22×D44C2×C414yes—
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×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C418yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—42no—
90C2×C4×Dic11—42no—
91C2×C4×Dic11D414yescomplemented
92C11×#95—22no—
93C11×#95—42no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95C2×C414yes—
101#14623—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—21no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11C22×C412yes—
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11C22×C414yes—
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×C11#4112yes—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11C22×C414yes—
185C22×Dic11C2×D412yes—
186C22×Dic11C2×D412yes—
187C2×D44—28no—
188C2×D44—48no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44—48no—
192C11×C4⋊C4—44no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—48no—
195C22⋊Dic11—44no—
196C22⋊Dic11—44no—
197(C2×D11)⋊C4—48no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202C4⋊Dic11—44no—
203C4×Dic11—44no—
204C2×#392—111no—
205C2×#390—111no—
206C2×#388—111no—
207#1442—111no—
208#1440—112no—
209#1439—112no—
210#1439D1111yescharacteristic, complemented
211#1438—111no—
212#1438—112no—
213#1438—112no—
214#1434—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11—41no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11C23×C411yescharacteristic
239C23×C11C22×D411yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11H(5,𝔽2)12yes—
242C23×C11H(5,𝔽2)12yes—
243C23×C11H(5,𝔽2)11yescharacteristic
244C23×C11H(5,𝔽2)12yes—
245C23×C11H(5,𝔽2)12yes—
246C23×C11H(5,𝔽2)11yescharacteristic
247C23×C11H(5,𝔽2)11yescharacteristic
248C23×C112−1+411yescharacteristic
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
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×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
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×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11C4×D414yes—
308C22⋊D11—432no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
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—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336D44—416no—
337C23×D4—112no—
338C23×D4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—112no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4C2×D1112yes—
350C22×C42—111no—
351#392—118no—
352#390—224no—
353#388—224no—
354C2×#95—111no—
355C2×#95—111no—
356C2×#95—111no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95C2×D1111yescharacteristic
362C2×#95C2×D1112yes—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—82no—
371C22×C11—82no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11C2×C4×D411yescharacteristic
375C22×C11#51811yescharacteristic
376C22×C11#51812yes—
377C22×C11#51812yes—
378C22×C11#52011yescharacteristic
379C22×C11#53411yescharacteristic
380C22×C11#53511yescharacteristic
381C22×C11#53511yescharacteristic
382C22×C11#53511yescharacteristic
383C22×C11#53511yescharacteristic
384C22×C11#53711yescharacteristic
385C22×C11#53812yes—
386C22×C11#54011yescharacteristic
387C22×C11#54012yes—
388C22×C11#54211yescharacteristic
389C22×C11#56012yes—
390C22×C11#56012yes—
391C22×C11#56012yes—
392C22×C11#56012yes—
393C22×C11#56012yes—
394C22×C11H(3,𝔽4)12yes—
395C22×C11#56212yes—
396C22×C11#56212yes—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—82no—
405C2×D11—82no—
406C2×D11—82no—
407C2×D11—82no—
408C2×D11—82no—
409C2×D11—82no—
410C2×D11—82no—
411C2×D11—82no—
412C4×C11—24no—
413C4×C11—42no—
414C4×C11—82no—
415C4×C11—82no—
416Dic11—44no—
417Dic11—42no—
418Dic11—42no—
419Dic11—81no—
420Dic11—81no—
421C25—112no—
422C25C22×D1111yescharacteristic
423C22×D4—118no—
424C22×D4—114no—
425C22×D4—222no—
426C22×D4—222no—
427C22×D4—442no—
428C22×D4—442no—
429C22×D4—442no—
430C22×D4—442no—
431C22×D4—442no—
432C22×D4—442no—
433C22×D4—442no—
434C22×D4—442no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—112no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4C22×D1112yes—
441C23×C4C22×D1112yes—
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—22no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—222no—
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—118no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—442no—
459C2×C22⋊C4—442no—
460C2×C22⋊C4—442no—
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⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4C4×D1114yes—
473C2×C42—114no—
474C2×C42—442no—
475#95—22no—
476#95—42no—
477#95—114no—
478#95—222no—
479#95—222no—
480#95—442no—
481#95—442no—
482#95—442no—
483#95—442no—
484C2×C11—82no—
485C2×C11#232111yescharacteristic
486C2×C11#232411yescharacteristic
487C2×C11#232811yescharacteristic
488C2×C11#237512yes—
489C2×C11#237712yes—
490C2×C11#281311yescharacteristic
491C2×C11#281511yescharacteristic
492C2×C11#281811yescharacteristic
493C2×C11#281911yescharacteristic
494C2×C11#282812yes—
495C2×C11#282912yes—
496D11—84no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—114no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24—222no—
512C24—222no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—222no—
522C24C2×C4×D1112yes—
523C24C23×D1111yescharacteristic
524C2×D4—228no—
525C2×D4—448no—
526C2×D4—444no—
527C2×D4—448no—
528C2×D4—444no—
529C2×D4—448no—
530C2×D4—448no—
531C2×D4—448no—
532C2×D4—448no—
533C2×D4—448no—
534C2×D4—448no—
535C2×D4—448no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
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—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—114no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—221no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—222no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4C2×C4×D1112yes—
584C22×C4C2×C4×D1112yes—
585C22×C4D4×D1112yes—
586C22×C4#434112yes—
587C4⋊C4—44no—
588C4⋊C4—444no—
589C22⋊C4—28no—
590C22⋊C4—48no—
591C22⋊C4—448no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C22⋊C4—444no—
597C22⋊C4—444no—
598C42—444no—
599C11#1462311yescharacteristic, complemented, Sylow
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—42no—
623C23—224no—
624C23—224no—
625C23—224no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—224no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C22×C4×D1111yescharacteristic
659C23C2×D4×D1111yescharacteristic
660C23C2×#434111yescharacteristic
661C23#6703712yes—
662C23#6703711yescharacteristic
663C23#6703712yes—
664C23#6704011yescharacteristic
665C23#6704211yescharacteristic
666C23#6704212yes—
667C23#6704212yes—
668C23#6704211yescharacteristic
669D4—4416no—
670D4—4432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
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—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—222no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—442no—
716C2×C4—441no—
717C2×C4—442no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—442no—
721C2×C4(C22⋊D11)⋊C414yes—
722C22—44no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—82no—
728C22—82no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—444no—
734C22—444no—
735C22—444no—
736C22—444no—
737C22—444no—
738C22—444no—
739C22—444no—
740C22—882no—
741C22—882no—
742C22—882no—
743C22—882no—
744C22—882no—
745C22—882no—
746C22—882no—
747C22—882no—
748C22C2×(C22⋊D11)⋊C411yescharacteristic
749C22#1062303511yescharacteristic
750C22#1062305211yescharacteristic
751C22#1062307612yes—
752C22#1062307612yes—
753C22#1062312311yescharacteristic
754C22#1062312612yes—
755C22#1062313811yescharacteristic
756C22#1062314812yes—
757C22#1062315011yescharacteristic
758C22#1062315012yes—
759C22#1062315112yes—
760C22#1062316011yescharacteristic
761C22#1062317411yescharacteristic
762C22#1062317812yes—
763C22#1062317812yes—
764C22#1062318411yescharacteristic
765C22#1062319712yes—
766C22#1062319712yes—
767C22#1062320511yescharacteristic
768C22#1062321412yes—
769C22#1062324212yes—
770C22#1062324611yescharacteristic
771C4—24no—
772C4—42no—
773C4—82no—
774C4—82no—
775C4—442no—
776C4—444no—
777C4—442no—
778C4—881no—
779C4—881no—
780C2—82no—
781C2—884no—
782C2#1307127911yescharacteristic
783C2#1307130511yescharacteristic
784C2#1307134011yescharacteristic
785C2#1307175612yes—
786C2#1307177212yes—
787C2#1307661911yescharacteristic
788C2#1307663911yescharacteristic
789C2#1307665511yescharacteristic
790C2#1307666411yescharacteristic
791C2#1307673912yes—
792C2#1307675012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622564C2semidirect
4. #13066875C2semidirect
5. #13066864C2semidirect
6. #13066862C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066841C2semidirect
11. C11×#1439C2semidirect
36. #10622573C4semidirect
91. C2×C4×Dic11D4semidirect
210. #1439D11semidirect
599. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106226012
C2×#106225642
#130668752
#130668642
#130668622
#130668562
#130668552
#130668412
C11×#14392
#1462311