Finite Group Databasebeta

← #14677192

Subgroups — #14677192

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×#10622826C211yesmaximal, characteristic
3C2×#10622826C211yesmaximal, characteristic
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13066877C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066852C212yesmaximal, complemented
8#13066842C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C22×C11×#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C2×C11×#95—24no—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27#10622826—24no—
28#10622826—24no—
29#10622826C418yescomplemented
30C4×C22⋊Dic11—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—24no—
48C23×C4×C11—24no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—42no—
52C23×C4×C11—42no—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11C2×C414yes—
56C23×C4×C11D414yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—22no—
62C22×C22⋊D11—22no—
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11C2×C414yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11C2×C414yes—
81C2×C22⋊Dic11D414yes—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
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—24no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—24no—
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—28no—
135C22×C4×C11—28no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
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—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—28no—
153C22×C4×C11—48no—
154C22×C4×C11—44no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11—44no—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11—48no—
163C22×C4×C11—44no—
164C22×C4×C11C22×C414yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4114yes—
168C22×C4×C11#4114yes—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—44no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—44no—
175C2×C22⋊D11—44no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11C22×C412yes—
205C22×Dic11C22×C414yes—
206C22×Dic11C2×D414yes—
207C22⋊Dic11—28no—
208C22⋊Dic11—28no—
209C22⋊Dic11—44no—
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×#95D1111yescharacteristic, complemented
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×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11C2×#4111yescharacteristic
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4111yescharacteristic
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—22no—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—416no—
297C2×C4×C11—416no—
298C2×C4×C11—416no—
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—42no—
308C2×C4×C11—42no—
309C2×C4×C11#12314yes—
310C22⋊D11—416no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
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—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×C4C2×D1111yescharacteristic
344C24×C4C2×D1111yescharacteristic
345C24×C4C2×D1111yescharacteristic
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—111no—
353C22×C42—112no—
354#386—118no—
355#386—224no—
356#386—224no—
357C4×C22⋊C4—224no—
358C2×#95—24no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—111no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—111no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
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—24no—
416C4×C11—44no—
417C4×C11—44no—
418C4×C11—42no—
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—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4—112no—
447C23×C4—112no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4C4×D1114yes—
452C23×C4C22⋊D1114yes—
453C23×C4C22×D1112yes—
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C2×C22⋊C4—114no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—118no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—222no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C22⋊C4—442no—
476C2×C42—224no—
477C2×C42—224no—
478C2×C42—442no—
479#95—24no—
480#95—24no—
481#95—118no—
482#95—224no—
483#95—224no—
484#95—224no—
485#95—222no—
486#95—222no—
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—222no—
509C24—222no—
510C24—221no—
511C24—221no—
512C24—221no—
513C24—222no—
514C24—222no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24C2×C4×D1112yes—
519C24#433912yes—
520C24D4×D1112yes—
521C24#434112yes—
522C24#434312yes—
523C24#434312yes—
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—21no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
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—28no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—112no—
568C22×C4—114no—
569C22×C4—114no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4C2×C4×D1114yes—
599C22×C4#433914yes—
600C22×C4#433914yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C22⋊C4—228no—
604C22⋊C4—228no—
605C22⋊C4—448no—
606C22⋊C4—448no—
607C22⋊C4—444no—
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—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—224no—
629C23—224no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
639C23—441no—
640C23—441no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23#6694514yes—
652C23#6694614yes—
653C23#6694714yes—
654C23#6695114yes—
655C23C4×C22⋊D1114yes—
656C23#6699214yes—
657C23#6700014yes—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433912yes—
660C23C2×#433912yes—
661C23C2×#433911yescharacteristic
662C23C2×D4×D1111yescharacteristic
663C23C2×#434111yescharacteristic
664C23#6703712yes—
665C23#6703712yes—
666C23C2×#434311yescharacteristic
667C23C2×#434311yescharacteristic
668C23C22×C22⋊D1111yescharacteristic
669D4—4416no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—416no—
685C2×C4—416no—
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—42no—
695C2×C4—42no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—222no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4#6698214yes—
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#1062260318yes—
750C22C4×#433912yes—
751C22#1062301012yes—
752C22#1062301712yes—
753C22#1062302112yes—
754C22#1062302112yes—
755C22#1062302512yes—
756C22#1062302612yes—
757C22#1062302612yes—
758C22C2×#6694511yescharacteristic
759C22C2×#6694611yescharacteristic
760C22C2×#6694711yescharacteristic
761C22C2×#6695111yescharacteristic
762C22#1062304512yes—
763C22#1062304512yes—
764C22#1062304512yes—
765C22#1062304512yes—
766C22C2×C4×C22⋊D1111yescharacteristic
767C22C2×#6698211yescharacteristic
768C22#1062332211yescharacteristic
769C22C2×#6699211yescharacteristic
770C22#1062333511yescharacteristic
771C22#1062333611yescharacteristic
772C22C2×#6700011yescharacteristic
773C4—24no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—444no—
778C4—442no—
779C4—444no—
780C4—881no—
781C4—881no—
782C2—28no—
783C2—882no—
784C2C2×#1062260311yescharacteristic
785C2C4×#6698211yescharacteristic
786C2#1307127411yescharacteristic
787C2#1307155212yes—
788C2#1307166312yes—
789C2#1307200111yescharacteristic
790C2#1307201211yescharacteristic
791C2#1307236612yes—
792C2#1307310411yescharacteristic
793C2#1307317612yes—
794C2#1307409611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#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×C4×C22⋊Dic11C2semidirect
5. #13066877C2semidirect
6. #13066864C2semidirect
7. #13066852C2semidirect
8. #13066842C2semidirect
9. #13066839C2semidirect
10. #13066839C2semidirect
11. C22×C11×#95C2semidirect
29. #10622826C4semidirect
91. C2×(C2×D11)⋊C4C2×C4semidirect
105. C11⋊#95C2×C4semidirect
219. 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×C4×C22⋊Dic112
#130668772
#130668642
#130668522
#130668422
#130668392
C22×C11×#952
#1402011