Finite Group Databasebeta

← #14684438

Subgroups — #14684438

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×#10622836C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic, complemented
4#13066872C211yesmaximal, characteristic, complemented
5#13066863C212yesmaximal, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066859C212yesmaximal, complemented
8#13066855C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28#10622836C418yescomplemented
29#10622834—24no—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622282—24no—
38C25×C11C2312yes—
39C24×D11C2311yescharacteristic
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11C2×C414yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—42no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11—42no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11C2×C418yes—
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4—42no—
63C2×C11×C22⋊C4—42no—
64C2×C11×C22⋊C4—42no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11C2×C418yes—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—42no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—42no—
90C2×C4×Dic11—42no—
91C2×C4×Dic11D414yescomplemented
92C11×#95—22no—
93C11×#95—22no—
94C11⋊#95—22no—
95C11⋊#95—42no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95C2×C414yes—
101#14623—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11C22×C414yes—
117C24×C11C2411yescharacteristic
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11C22×C412yes—
129C2×D4×C11—28no—
130C2×D4×C11—48no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—48no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
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—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
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—21no—
177C22×Dic11—22no—
178C22×Dic11—21no—
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—21no—
188C22×Dic11C22×C414yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×D412yes—
192C11×C22⋊C4—48no—
193C11×C22⋊C4—48no—
194C22⋊Dic11—48no—
195C22⋊Dic11—48no—
196C22⋊Dic11—48no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4—44no—
200(C2×D11)⋊C4—48no—
201C4⋊Dic11—44no—
202Dic11⋊C4—44no—
203C4×Dic11—44no—
204C2×#392—111no—
205C2×#390—111no—
206C2×#388—111no—
207#1442—111no—
208#1440—112no—
209#1439—111no—
210#1439—112no—
211#1438—112no—
212#1438—112no—
213#1438D1111yescharacteristic, complemented
214#1434—111no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
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×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11C23×C411yescharacteristic
251C23×C11C22×D411yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11H(5,𝔽2)12yes—
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)11yescharacteristic
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C112−1+411yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—22no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—41no—
274C22×D11—42no—
275C22×D11—41no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284D4×C11—416no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
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×C11C4×D414yes—
307C22⋊D11—432no—
308C2×Dic11—22no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
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×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C23×D4—112no—
338C23×D4C2×D1111yescharacteristic
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4C2×D1112yes—
349C22×C22⋊C4C2×D1112yes—
350C22×C42—111no—
351#392—118no—
352#390—224no—
353#388—224no—
354C2×#95—111no—
355C2×#95—111no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95C2×D1111yescharacteristic
362C2×#95C2×D1111yescharacteristic
363C22×C11—44no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—82no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#51812yes—
380C22×C11#51811yescharacteristic
381C22×C11#51812yes—
382C22×C11#52011yescharacteristic
383C22×C11#53411yescharacteristic
384C22×C11#53511yescharacteristic
385C22×C11#53511yescharacteristic
386C22×C11#53511yescharacteristic
387C22×C11#53511yescharacteristic
388C22×C11#53711yescharacteristic
389C22×C11#53812yes—
390C22×C11#54011yescharacteristic
391C22×C11#54012yes—
392C22×C11#54211yescharacteristic
393C22×C11#56012yes—
394C22×C11#56012yes—
395C22×C11#56012yes—
396C22×C11#56012yes—
397C22×C11#56012yes—
398C22×C11H(3,𝔽4)12yes—
399C22×C11#56212yes—
400C22×C11#56212yes—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—82no—
409C2×D11—82no—
410C2×D11—81no—
411C2×D11—81no—
412C4×C11—24no—
413C4×C11—81no—
414C4×C11—82no—
415C4×C11—81no—
416Dic11—42no—
417Dic11—44no—
418Dic11—42no—
419Dic11—42no—
420Dic11—82no—
421C25—111no—
422C25C22×D1112yes—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—42no—
426C22×D4—42no—
427C22×D4—118no—
428C22×D4—442no—
429C22×D4—442no—
430C22×D4—442no—
431C22×D4—442no—
432C22×D4—442no—
433C22×D4—442no—
434C22×D4C4×D1114yes—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—112no—
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—222no—
445C2×C4⋊C4—222no—
446C2×C4⋊C4—442no—
447C2×C4⋊C4—442no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—118no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—224no—
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⋊C4—442no—
473C2×C42—114no—
474C2×C42—442no—
475#95—22no—
476#95—22no—
477#95—114no—
478#95—222no—
479#95—442no—
480#95—442no—
481#95—442no—
482#95—442no—
483#95—442no—
484C2×C11—84no—
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—82no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—112no—
512C24—221no—
513C24—221no—
514C24—221no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—221no—
519C24—222no—
520C24—221no—
521C24—221no—
522C24C2×C4×D1114yes—
523C24C23×D1111yescharacteristic
524C2×D4—28no—
525C2×D4—48no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—48no—
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—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—114no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—221no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4C2×C4×D1112yes—
585C22×C4D4×D1112yes—
586C22×C4#434112yes—
587C4⋊C4—444no—
588C4⋊C4—444no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—228no—
592C22⋊C4—444no—
593C22⋊C4—444no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C22⋊C4—448no—
597C22⋊C4—448no—
598C42—444no—
599C11#1462311yescharacteristic, complemented, Sylow
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—222no—
636C23—224no—
637C23—222no—
638C23—224no—
639C23—222no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—441no—
648C23—441no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—441no—
657C23—441no—
658C23C22×C4×D1111yescharacteristic
659C23C2×D4×D1111yescharacteristic
660C23C2×#434111yescharacteristic
661C23#6703712yes—
662C23#6703711yescharacteristic
663C23#6703711yescharacteristic
664C23#6703712yes—
665C23#6703712yes—
666C23#6704211yescharacteristic
667C23#6704212yes—
668C23#6704311yescharacteristic
669D4—416no—
670D4—4432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—224no—
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—441no—
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—442no—
713C2×C4—441no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4(C22⋊D11)⋊C414yes—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—444no—
738C22—444no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—882no—
743C22—882no—
744C22—881no—
745C22—881no—
746C22—881no—
747C22—881no—
748C22C2×(C22⋊D11)⋊C411yescharacteristic
749C22#1062301712yes—
750C22#1062307611yescharacteristic
751C22#1062307612yes—
752C22#1062307711yescharacteristic
753C22#1062312011yescharacteristic
754C22#1062312311yescharacteristic
755C22#1062312412yes—
756C22#1062312512yes—
757C22#1062312612yes—
758C22#1062313811yescharacteristic
759C22#1062313911yescharacteristic
760C22#1062315012yes—
761C22#1062315112yes—
762C22#1062315112yes—
763C22#1062315112yes—
764C22#1062315212yes—
765C22#1062319712yes—
766C22#1062319812yes—
767C22#1062320511yescharacteristic
768C22#1062321311yescharacteristic
769C22#1062324611yescharacteristic
770C22#1062325011yescharacteristic
771C4—24no—
772C4—82no—
773C4—81no—
774C4—81no—
775C4—442no—
776C4—444no—
777C4—442no—
778C4—442no—
779C4—882no—
780C2—84no—
781C2—882no—
782C2#1307127111yescharacteristic
783C2#1307131211yescharacteristic
784C2#1307134011yescharacteristic
785C2#1307175412yes—
786C2#1307177412yes—
787C2#1307661711yescharacteristic
788C2#1307663711yescharacteristic
789C2#1307665811yescharacteristic
790C2#1307666311yescharacteristic
791C2#1307673812yes—
792C2#1307675212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622282C2semidirect
4. #13066872C2semidirect
5. #13066863C2semidirect
6. #13066862C2semidirect
7. #13066859C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066841C2semidirect
11. C11×#1438C2semidirect
28. #10622836C4semidirect
91. C2×C4×Dic11D4semidirect
213. #1438D11semidirect
599. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106228342
C2×#106222822
#130668722
#130668632
#130668622
#130668592
#130668552
#130668412
C11×#14382
#1462311