Finite Group Databasebeta

← #14677195

Subgroups — #14677195

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622826C211yesmaximal, characteristic
2C2×#10622571C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C22×C11⋊#95C211yesmaximal, characteristic, complemented
6#13066877C212yesmaximal, complemented
7#13066864C212yesmaximal, complemented
8#13066852C212yesmaximal, complemented
9#13066841C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26#10622826—24no—
27C2×C11⋊#95—24no—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622571—24no—
38#10622571C418yescomplemented
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C22×C22⋊D11—22no—
52C22×C22⋊D11—22no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11C2×C414yes—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—42no—
64C23×Dic11—42no—
65C23×Dic11—42no—
66C23×Dic11C2×C414yes—
67C23×Dic11D414yes—
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11D414yes—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4C2×C418yescomplemented
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—42no—
95C11×#95—24no—
96C11×#95—42no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95C2×C418yescomplemented
106#14020—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11C22×C412yes—
112C24×C11C2×D412yes—
113C24×C11C2×D412yes—
114C24×C11#4112yes—
115C24×C11#4112yes—
116C24×C11#4112yes—
117C24×C11#4112yes—
118C24×C11C2411yescharacteristic
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11C22×C412yes—
130C22×C4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
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—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11C22×C414yes—
158C22×C4×C11#4114yes—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—44no—
163C2×C22⋊D11—44no—
164C2×C22⋊D11—44no—
165C2×C22⋊D11—44no—
166C22×Dic11—28no—
167C22×Dic11—28no—
168C22×Dic11—28no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—48no—
195C22×Dic11—44no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—44no—
199C22×Dic11—44no—
200C22×Dic11—48no—
201C22×Dic11C22×C412yes—
202C22×Dic11C22×C414yes—
203C22×Dic11C2×D412yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D412yes—
206C22×Dic11#4114yes—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—44no—
209C22⋊Dic11—28no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—44no—
213(C2×D11)⋊C4—44no—
214C4×Dic11—48no—
215C2×#386—111no—
216C2×#386—111no—
217C2×#386—111no—
218C2×C4×C22⋊C4—111no—
219C22×#95—111no—
220#1443—112no—
221#1440—112no—
222#1437—112no—
223#1434—112no—
224C22⋊#95—111no—
225C22⋊#95D1111yescharacteristic, complemented
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11#11714yes—
243C23×C11C4×D414yes—
244C23×C11C4×D414yes—
245C23×C11#12114yes—
246C23×C11#12314yes—
247C23×C11#12414yes—
248C23×C11#12614yes—
249C23×C11C23×C411yescharacteristic
250C23×C11C22×D411yescharacteristic
251C23×C11C22×D411yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11C2×#4111yescharacteristic
255C23×C11C2×#4112yes—
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4112yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)12yes—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—42no—
272C22×D11—41no—
273C22×D11—41no—
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—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—416no—
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—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C22⋊D11—416no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—416no—
326C2×Dic11—416no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11#12314yes—
342C23×D4—111no—
343C24×C4—111no—
344C24×C4—111no—
345C24×C4C2×D1111yescharacteristic
346C22×C22⋊C4—111no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4C2×D1111yescharacteristic
353C22×C42—112no—
354#386—118no—
355#386—224no—
356#386—224no—
357C4×C22⋊C4—224no—
358C2×#95—112no—
359C2×#95—111no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—111no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—224no—
368C2×#95C2×D1112yes—
369C2×#95C2×D1112yes—
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—28no—
373C22×C11—28no—
374C22×C11—24no—
375C22×C11—24no—
376C22×C11—28no—
377C22×C11—24no—
378C22×C11—28no—
379C22×C11—24no—
380C22×C11#38818yes—
381C22×C11C2×#11711yescharacteristic
382C22×C11C2×C4×D411yescharacteristic
383C22×C11C2×C4×D411yescharacteristic
384C22×C11C4×#4112yes—
385C22×C11#51812yes—
386C22×C11C2×#12111yescharacteristic
387C22×C11C2×#12311yescharacteristic
388C22×C11C2×#12311yescharacteristic
389C22×C11#52511yescharacteristic
390C22×C11C2×#12411yescharacteristic
391C22×C11C2×#12611yescharacteristic
392C22×C11#52912yes—
393C22×C11#53411yescharacteristic
394C22×C11#53511yescharacteristic
395C22×C11#53812yes—
396C22×C11#54612yes—
397C22×C11#54612yes—
398C22×C11#55112yes—
399C22×C11#55112yes—
400C22×C11#55312yes—
401C22×C11#55312yes—
402C22×C11#55312yes—
403C22×C11#55312yes—
404C2×D11—42no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—82no—
413C2×D11—81no—
414C2×D11—82no—
415C4×C11—44no—
416C4×C11—44no—
417C4×C11—81no—
418C4×C11—81no—
419Dic11—24no—
420Dic11—44no—
421Dic11—42no—
422Dic11—44no—
423Dic11—42no—
424C25—111no—
425C25C22×D1111yescharacteristic
426C22×D4—114no—
427C22×D4—222no—
428C22×D4—222no—
429C22×D4—222no—
430C22×D4—222no—
431C22×D4—222no—
432C22×D4—222no—
433C23×C4—22no—
434C23×C4—24no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—42no—
438C23×C4—111no—
439C23×C4—112no—
440C23×C4—112no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—114no—
444C23×C4—114no—
445C23×C4—224no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—222no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4—442no—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1112yes—
456C23×C4C22×D1112yes—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—118no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C22⋊C4C4×D1114yes—
476C2×C42—224no—
477C2×C42—224no—
478C2×C42—442no—
479#95—24no—
480#95—42no—
481#95—118no—
482#95—224no—
483#95—224no—
484#95—224no—
485#95—224no—
486#95—222no—
487#95—222no—
488#95—442no—
489#95—442no—
490C2×C11—28no—
491C2×C11C2×#38811yescharacteristic
492C2×C11C4×#12311yescharacteristic
493C2×C11#232111yescharacteristic
494C2×C11#235312yes—
495C2×C11#236412yes—
496C2×C11#241111yescharacteristic
497C2×C11#241211yescharacteristic
498C2×C11#244412yes—
499C2×C11#250411yescharacteristic
500C2×C11#251012yes—
501C2×C11#259111yescharacteristic
502D11—82no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—112no—
508C24—221no—
509C24—221no—
510C24—221no—
511C24—221no—
512C24—222no—
513C24—221no—
514C24—222no—
515C24—221no—
516C24—222no—
517C24—222no—
518C24C2×C4×D1112yes—
519C24#433912yes—
520C24#433912yes—
521C24D4×D1112yes—
522C24D4×D1112yes—
523C24#434112yes—
524C24#434312yes—
525C24C23×D1111yescharacteristic
526C2×D4—228no—
527C2×D4—228no—
528C2×D4—228no—
529C2×D4—444no—
530C2×D4—444no—
531C2×D4—444no—
532C2×D4—444no—
533C22×C4—28no—
534C22×C4—22no—
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—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—112no—
561C22×C4—114no—
562C22×C4—112no—
563C22×C4—114no—
564C22×C4—112no—
565C22×C4—114no—
566C22×C4—228no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—228no—
571C22×C4—228no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—444no—
595C22×C4—448no—
596C22×C4—448no—
597C22×C4—448no—
598C22×C4—444no—
599C22×C4—448no—
600C22×C4—444no—
601C22×C4C2×C4×D1114yes—
602C22×C4#434114yes—
603C22⋊C4—28no—
604C22⋊C4—44no—
605C22⋊C4—228no—
606C22⋊C4—448no—
607C22⋊C4—448no—
608C22⋊C4—444no—
609C22⋊C4—444no—
610C42—448no—
611C11#1402011yescharacteristic, complemented, Sylow
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—224no—
632C23—224no—
633C23—441no—
634C23—441no—
635C23—442no—
636C23—441no—
637C23—441no—
638C23—442no—
639C23—442no—
640C23—442no—
641C23—441no—
642C23—442no—
643C23—441no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—441no—
649C23—441no—
650C23—442no—
651C23#6692514yes—
652C23(C22⋊D11)⋊C414yes—
653C23#6693714yes—
654C23#6693814yes—
655C23#6694614yes—
656C23#6694714yes—
657C23#6695114yes—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433911yescharacteristic
660C23C2×#433911yescharacteristic
661C23C2×D4×D1111yescharacteristic
662C23C2×D4×D1111yescharacteristic
663C23C2×#434111yescharacteristic
664C23C2×#434112yes—
665C23#6703712yes—
666C23C2×#434311yescharacteristic
667C23#41×D1112yes—
668C23#6704212yes—
669D4—4416no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—416no—
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—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—114no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—4416no—
713C2×C4—4416no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C22—28no—
729C22—24no—
730C22—28no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—24no—
737C22—28no—
738C22—442no—
739C22—444no—
740C22—442no—
741C22—444no—
742C22—442no—
743C22—882no—
744C22—881no—
745C22—881no—
746C22—881no—
747C22—881no—
748C22—882no—
749C22#1062228218yes—
750C22C2×#6692511yescharacteristic
751C22C2×(C22⋊D11)⋊C411yescharacteristic
752C22C2×#6693711yescharacteristic
753C22C2×#6693811yescharacteristic
754C22#1062302612yes—
755C22C2×#6694611yescharacteristic
756C22C2×#6694711yescharacteristic
757C22C2×#6695111yescharacteristic
758C22#1062305812yes—
759C22C4×#434112yes—
760C22#1062307112yes—
761C22#1062307612yes—
762C22#1062309612yes—
763C22#1062311711yescharacteristic
764C22#1062312212yes—
765C22#1062312311yescharacteristic
766C22#1062313212yes—
767C22#1062314912yes—
768C22#1062315512yes—
769C22#1062317512yes—
770C22D11×#12311yescharacteristic
771C22#1062318411yescharacteristic
772C22#1062318512yes—
773C4—44no—
774C4—44no—
775C4—81no—
776C4—81no—
777C4—224no—
778C4—442no—
779C4—444no—
780C4—442no—
781C4—444no—
782C2—28no—
783C2—882no—
784C2C2×#1062228211yescharacteristic
785C2#1307113511yescharacteristic
786C2#1307127311yescharacteristic
787C2#1307155012yes—
788C2#1307166412yes—
789C2#1307200311yescharacteristic
790C2#1307201411yescharacteristic
791C2#1307237012yes—
792C2#1307310611yescharacteristic
793C2#1307317212yes—
794C2#1307409311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14020
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic11C2semidirect
5. C22×C11⋊#95C2semidirect
6. #13066877C2semidirect
7. #13066864C2semidirect
8. #13066852C2semidirect
9. #13066841C2semidirect
10. #13066838C2semidirect
11. C11×C22⋊#95C2semidirect
38. #10622571C4semidirect
91. C2×(C2×D11)⋊C4C2×C4semidirect
105. C11⋊#95C2×C4semidirect
225. C22⋊#95D11semidirect
611. C11#14020semidirect

Maximal subgroups

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

subgroupindex
C2×#106228262
C2×#106225712
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668772
#130668642
#130668522
#130668412
#130668382
C11×C22⋊#952
#1402011