Finite Group Databasebeta

← #14677193

Subgroups — #14677193

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×#10622833C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066876C212yesmaximal, complemented
6#13066863C212yesmaximal, complemented
7#13066853C212yesmaximal, complemented
8#13066842C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#386C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C4×Dic11C2212yes—
24C11×#386—24no—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27#10622833—24no—
28#10622833C418yescomplemented
29C4×C22⋊Dic11—24no—
30C2×C11⋊#95—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—24no—
52C23×C4×C11—42no—
53C23×C4×C11D414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—42no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11C2×C414yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
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⋊C4—22no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—42no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11—42no—
88C2×C22⋊Dic11—42no—
89C2×C22⋊Dic11C2×C414yes—
90C2×C22⋊Dic11C2×C418yescomplemented
91C2×C22⋊Dic11D414yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—42no—
95C11×#95—22no—
96C11×#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
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×C11—21no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C22×C412yes—
122C24×C11C22×C412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D412yes—
125C24×C11#4112yes—
126C24×C11#4112yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11C2411yescharacteristic
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—44no—
163C22×C4×C11—48no—
164C22×C4×C11—48no—
165C22×C4×C11C22×C412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11#4114yes—
169C22×Dic11—28no—
170C22×Dic11—28no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
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—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—48no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—44no—
199C22×Dic11—44no—
200C22×Dic11—44no—
201C22×Dic11—48no—
202C22×Dic11—44no—
203C22×Dic11C22×C414yes—
204C22×Dic11C22×C414yes—
205C22×Dic11C2×D414yes—
206C22×Dic11#4114yes—
207C11×C22⋊C4—44no—
208C11×C22⋊C4—44no—
209C11×C22⋊C4—44no—
210C22⋊Dic11—28no—
211C22⋊Dic11—28no—
212C22⋊Dic11—48no—
213C22⋊Dic11—48no—
214C4×Dic11—48no—
215C2×#386—111no—
216C2×#386—111no—
217C2×#386D1111yescharacteristic
218C2×C4×C22⋊C4—111no—
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—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—42no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11#11714yes—
266C23×C11C4×D414yes—
267C23×C11C4×D414yes—
268C23×C11#12114yes—
269C23×C11#12314yes—
270C23×C11#12414yes—
271C23×C11#12614yes—
272C23×C11C23×C411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4112yes—
280C23×C11C2×#4112yes—
281C23×C11H(5,𝔽2)12yes—
282C23×C11H(5,𝔽2)12yes—
283D4×C11—416no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—416no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11#12314yes—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—416no—
325C2×Dic11—416no—
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—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C23×D4C2×D1111yescharacteristic
343C24×C4—111no—
344C24×C4—111no—
345C24×C4C2×D1111yescharacteristic
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4C2×D1111yescharacteristic
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4C2×D1111yescharacteristic
353C22×C42—112no—
354#386—24no—
355#386—118no—
356#386—224no—
357C4×C22⋊C4—224no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—224no—
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1111yescharacteristic
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—42no—
381C22×C11—44no—
382C22×C11—44no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—82no—
389C22×C11—81no—
390C22×C11—82no—
391C22×C11#38818yes—
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C4×#4112yes—
396C22×C11#51812yes—
397C22×C11C2×#12111yescharacteristic
398C22×C11C2×#12311yescharacteristic
399C22×C11C2×#12311yescharacteristic
400C22×C11#52511yescharacteristic
401C22×C11C2×#12411yescharacteristic
402C22×C11C2×#12611yescharacteristic
403C22×C11#52912yes—
404C22×C11#53411yescharacteristic
405C22×C11#53511yescharacteristic
406C22×C11#53812yes—
407C22×C11#54612yes—
408C22×C11#54612yes—
409C22×C11#55112yes—
410C22×C11#55112yes—
411C22×C11#55312yes—
412C22×C11#55312yes—
413C22×C11#55312yes—
414C22×C11#55312yes—
415C4×C11—24no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—81no—
419C4×C11—81no—
420Dic11—44no—
421Dic11—44no—
422Dic11—44no—
423Dic11—44no—
424C25C22×D1111yescharacteristic
425C25C22×D1111yescharacteristic
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4C4×D1114yes—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—24no—
436C23×C4—42no—
437C23×C4—112no—
438C23×C4—112no—
439C23×C4—112no—
440C23×C4—112no—
441C23×C4—114no—
442C23×C4—224no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—442no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4C22⋊D1114yes—
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—118no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C22⋊C4—442no—
476C2×C42—224no—
477C2×C42—224no—
478C2×C42—442no—
479#95—22no—
480#95—22no—
481#95—118no—
482#95—224no—
483#95—224no—
484#95—224no—
485#95—224no—
486#95—224no—
487#95—442no—
488#95—442no—
489#95—442no—
490C2×C11—28no—
491C2×C11—82no—
492C2×C11C2×#38811yescharacteristic
493C2×C11C4×#12311yescharacteristic
494C2×C11#232111yescharacteristic
495C2×C11#235312yes—
496C2×C11#236412yes—
497C2×C11#241111yescharacteristic
498C2×C11#241211yescharacteristic
499C2×C11#244412yes—
500C2×C11#250411yescharacteristic
501C2×C11#251012yes—
502C2×C11#259111yescharacteristic
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—21no—
517C24C2×C4×D1112yes—
518C24C2×C4×D1112yes—
519C24#433912yes—
520C24D4×D1112yes—
521C24#434112yes—
522C24#434112yes—
523C24#434112yes—
524C24C2×C22⋊D1112yes—
525C24C23×D1111yescharacteristic
526C2×D4—28no—
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—114no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—114no—
565C22×C4—228no—
566C22×C4—228no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4—448no—
594C22×C4—444no—
595C22×C4—448no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4C2×C4×D1112yes—
600C22×C4#434114yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—228no—
607C22⋊C4—228no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—448no—
611C11#1402011yescharacteristic, complemented, Sylow
612C23—24no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#6693014yes—
652C23#6693214yes—
653C23(C22⋊D11)⋊C414yes—
654C23#6693614yes—
655C23C4×C22⋊D1114yes—
656C23#6698914yes—
657C23#6699214yes—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433911yescharacteristic
660C23C2×D4×D1111yescharacteristic
661C23C2×#434111yescharacteristic
662C23C2×#434111yescharacteristic
663C23C2×#434111yescharacteristic
664C23C2×#434112yes—
665C23#6703712yes—
666C23#41×D1112yes—
667C23#6704212yes—
668C23C22×C22⋊D1111yescharacteristic
669D4—416no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—416no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—4416no—
710C2×C4—4416no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
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#6698814yes—
728C22—28no—
729C22—24no—
730C22—28no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—24no—
737C22—28no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—82no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—82no—
749C22#1062255818yes—
750C22C2×#6693011yescharacteristic
751C22C2×#6693211yescharacteristic
752C22C2×(C22⋊D11)⋊C411yescharacteristic
753C22C2×#6693611yescharacteristic
754C22C4×#434112yes—
755C22#1062306912yes—
756C22#1062307612yes—
757C22#1062309112yes—
758C22#1062311812yes—
759C22#1062312212yes—
760C22#1062313212yes—
761C22#1062313212yes—
762C22#1062314912yes—
763C22#1062314912yes—
764C22#1062318512yes—
765C22#1062318912yes—
766C22C2×C4×C22⋊D1111yescharacteristic
767C22C2×#6698811yescharacteristic
768C22C2×#6698911yescharacteristic
769C22C2×#6699211yescharacteristic
770C22#1062333511yescharacteristic
771C22#1062335911yescharacteristic
772C22#1062336111yescharacteristic
773C4—24no—
774C4—42no—
775C4—42no—
776C4—81no—
777C4—81no—
778C4—444no—
779C4—444no—
780C4—444no—
781C4—444no—
782C2—28no—
783C2—82no—
784C2C2×#1062255811yescharacteristic
785C2C4×#6698811yescharacteristic
786C2#1307127011yescharacteristic
787C2#1307155412yes—
788C2#1307166412yes—
789C2#1307200211yescharacteristic
790C2#1307201311yescharacteristic
791C2#1307236812yes—
792C2#1307310911yescharacteristic
793C2#1307317812yes—
794C2#1307409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14020
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic11C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066876C2semidirect
6. #13066863C2semidirect
7. #13066853C2semidirect
8. #13066842C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
28. #10622833C4semidirect
90. C2×C22⋊Dic11C2×C4semidirect
105. C11⋊#95C2×C4semidirect
611. C11#14020semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×C4×C22⋊Dic112
C22×C11⋊#952
#130668762
#130668632
#130668532
#130668422
#130668382
C2×C11×#3862
#1402011