Finite Group Databasebeta

← #14677186

Subgroups — #14677186

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
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066876C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066854C212yesmaximal, complemented
8#13066843C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C42×C11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C4×C11×C22⋊C4—24no—
25C2×C11×#95C2212yes—
26#10622826—24no—
27C2×C11⋊#95—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622571—24no—
39#10622571C418yescomplemented
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—24no—
45C23×C4×C11—42no—
46C23×C4×C11D414yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
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—24no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—42no—
65C23×Dic11—42no—
66C23×Dic11—42no—
67C23×Dic11C2×C414yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4C2×C414yes—
78C2×C11×C22⋊C4D414yes—
79C2×C42×C11—24no—
80C2×C42×C11—24no—
81C2×C42×C11—42no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4C2×C418yescomplemented
95C11×#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
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—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—28no—
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—21no—
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—28no—
151C22×C4×C11—44no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
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—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—48no—
199C22×Dic11—44no—
200C22×Dic11—44no—
201C22×Dic11—44no—
202C22×Dic11—48no—
203C22×Dic11—44no—
204C22×Dic11C22×C412yes—
205C22×Dic11C22×C414yes—
206C22×Dic11#4114yes—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—28no—
209C42×C11—48no—
210C22⋊Dic11—44no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—48no—
213(C2×D11)⋊C4—44no—
214(C2×D11)⋊C4—44no—
215C2×#386—111no—
216C2×#386—111no—
217C2×#386—111no—
218C2×C4×C22⋊C4D1111yescharacteristic, complemented
219C22×#95—111no—
220#1443—112no—
221#1440—112no—
222#1437—112no—
223#1434—112no—
224C22⋊#95—111no—
225C22⋊#95—111no—
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×#4111yescharacteristic
256C23×C11C2×#4112yes—
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—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—416no—
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×C11#12314yes—
308C22⋊D11—416no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—416no—
319C2×Dic11—416no—
320C2×Dic11—42no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C23×D4—111no—
343C24×C4—111no—
344C24×C4—111no—
345C24×C4C2×D1111yescharacteristic
346C22×C22⋊C4—112no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4C2×D1111yescharacteristic
353C22×C42C2×D1112yes—
354#386—118no—
355#386—224no—
356#386—224no—
357C4×C22⋊C4—24no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—111no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—224no—
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—24no—
416C4×C11—44no—
417C4×C11—42no—
418C4×C11—44no—
419Dic11—44no—
420Dic11—44no—
421Dic11—42no—
422Dic11—81no—
423Dic11—81no—
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—22no—
435C23×C4—24no—
436C23×C4—42no—
437C23×C4—112no—
438C23×C4—112no—
439C23×C4—111no—
440C23×C4—114no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—224no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4D4414yes—
453C23×C4C22×D1112yes—
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1112yes—
456C23×C4C22×D1111yescharacteristic
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—118no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4C4×D1114yes—
475C2×C22⋊C4C22⋊D1114yes—
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—42no—
479#95—24no—
480#95—118no—
481#95—224no—
482#95—224no—
483#95—224no—
484#95—222no—
485#95—222no—
486#95—224no—
487#95—442no—
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—221no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—221no—
518C24C2×C4×D1112yes—
519C24C2×D4412yes—
520C24#433912yes—
521C24#433912yes—
522C24#433912yes—
523C24#433912yes—
524C24C2×C22⋊D1112yes—
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—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—28no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
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—21no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—114no—
560C22×C4—228no—
561C22×C4—228no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4—444no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4—448no—
597C22×C4—444no—
598C22×C4C2×C4×D1114yes—
599C22×C4C2×D4412yes—
600C22×C4C2×D4412yes—
601C22×C4#434114yes—
602C22×C4C2×C22⋊D1114yes—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—448no—
606C22⋊C4—448no—
607C22⋊C4—444no—
608C22⋊C4—444no—
609C22⋊C4—444no—
610C42—48no—
611C11#1402011yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—224no—
632C23—224no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—442no—
638C23—441no—
639C23—441no—
640C23—442no—
641C23—441no—
642C23—441no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23#6692514yes—
652C23C4×D4414yes—
653C23#6692814yes—
654C23#6692914yes—
655C23C4×C22⋊D1114yes—
656C23#6698214yes—
657C23#6698314yes—
658C23C22×C4×D1111yescharacteristic
659C23C22×D4411yescharacteristic
660C23C2×#433911yescharacteristic
661C23C2×#433911yescharacteristic
662C23C2×#433911yescharacteristic
663C23C2×#433911yescharacteristic
664C23C2×#434112yes—
665C23#6703712yes—
666C23#41×D1112yes—
667C23#6704212yes—
668C23C22×C22⋊D1111yescharacteristic
669D4—4416no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—416no—
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—222no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—222no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—4416no—
704C2×C4—4416no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—441no—
712C2×C4—442no—
713C2×C4—441no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4#6693914yes—
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#1062255318yes—
750C22C2×#6692511yescharacteristic
751C22C2×C4×D4411yescharacteristic
752C22C2×#6692811yescharacteristic
753C22C2×#6692911yescharacteristic
754C22C2×#6693911yescharacteristic
755C22#1062302411yescharacteristic
756C22#1062302612yes—
757C22#1062305511yescharacteristic
758C22#1062305611yescharacteristic
759C22#1062305812yes—
760C22C4×#434112yes—
761C22#1062306912yes—
762C22#1062307112yes—
763C22#1062307112yes—
764C22#1062307612yes—
765C22#1062309112yes—
766C22#1062309612yes—
767C22#1062309612yes—
768C22C2×C4×C22⋊D1111yescharacteristic
769C22C2×#6698211yescharacteristic
770C22C2×#6698311yescharacteristic
771C22#1062333712yes—
772C22#1062336012yes—
773C4—24no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—444no—
778C4—444no—
779C4—442no—
780C4—881no—
781C4—881no—
782C2—28no—
783C2—882no—
784C2C2×#1062255311yescharacteristic
785C2C4×#6693911yescharacteristic
786C2#1307127611yescharacteristic
787C2#1307155012yes—
788C2#1307166112yes—
789C2#1307199511yescharacteristic
790C2#1307200611yescharacteristic
791C2#1307236012yes—
792C2#1307310811yescharacteristic
793C2#1307317012yes—
794C2#1307409111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14020
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×C11⋊#95C2semidirect
5. #13066876C2semidirect
6. #13066864C2semidirect
7. #13066854C2semidirect
8. #13066843C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
39. #10622571C4semidirect
94. C2×(C2×D11)⋊C4C2×C4semidirect
105. C11⋊#95C2×C4semidirect
218. C2×C4×C22⋊C4D11semidirect
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
C22×C11⋊#952
#130668762
#130668642
#130668542
#130668432
#130668382
C2×C4×C11×C22⋊C42
#1402011