Finite Group Databasebeta

← #14677182

Subgroups — #14677182

Order 2816.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
2C2×#10622558C212yesmaximal, complemented
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622833C211yesmaximal, characteristic
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13066874C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066851C212yesmaximal, 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⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4—24no—
24C22×Dic11⋊C4—28no—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C11×#386—24no—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31#10622833—24no—
32#10622833C418yescomplemented
33C4×C22⋊Dic11—24no—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622558—28no—
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11C2×C414yes—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—24no—
54C23×C4×C11—42no—
55C23×C4×C11D414yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—24no—
64C23×Dic11—24no—
65C23×Dic11—22no—
66C23×Dic11—24no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—42no—
70C23×Dic11C2×C414yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—42no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—42no—
91C2×C22⋊Dic11C2×C414yes—
92C2×C22⋊Dic11C2×C418yescomplemented
93C2×C22⋊Dic11D414yes—
94C2×Dic11⋊C4—232no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4D418yescomplemented
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—42no—
104C11×#95—22no—
105C11×#95—22no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—42no—
112C11⋊#95C2×C418yescomplemented
113#14019—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11C22×C412yes—
129C24×C11C22×C412yes—
130C24×C11C2×D412yes—
131C24×C11C2×D412yes—
132C24×C11#4112yes—
133C24×C11#4112yes—
134C24×C11#4112yes—
135C24×C11#4112yes—
136C24×C11C2411yescharacteristic
137C2×D4×C11—28no—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—28no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—28no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—44no—
170C22×C4×C11—48no—
171C22×C4×C11—48no—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D412yes—
176C22×Dic11—28no—
177C22×Dic11—28no—
178C22×Dic11—216no—
179C22×Dic11—216no—
180C22×Dic11—28no—
181C22×Dic11—28no—
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—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—48no—
205C22×Dic11—48no—
206C22×Dic11—44no—
207C22×Dic11—44no—
208C22×Dic11C22×C414yes—
209C22×Dic11C22×C414yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D414yes—
213C22×Dic11#4114yes—
214C11×C22⋊C4—44no—
215C11×C22⋊C4—44no—
216C11×C22⋊C4—44no—
217C22⋊Dic11—216no—
218C22⋊Dic11—28no—
219C22⋊Dic11—28no—
220C22⋊Dic11—48no—
221Dic11⋊C4—216no—
222Dic11⋊C4—216no—
223C4×Dic11—48no—
224C23×C4⋊C4—111no—
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386D1111yescharacteristic
229C2×C4×C22⋊C4—111no—
230#1442—112no—
231#1439—112no—
232#1436—112no—
233C22⋊#95—111no—
234C22⋊#95—111no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—22no—
252C23×C11—24no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—24no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—42no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11#11714yes—
275C23×C11C4×D414yes—
276C23×C11C4×D414yes—
277C23×C11#12114yes—
278C23×C11#12314yes—
279C23×C11#12414yes—
280C23×C11#12614yes—
281C23×C11C23×C411yescharacteristic
282C23×C11C22×D412yes—
283C23×C11C22×D411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4112yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C112−1+412yes—
292D4×C11—416no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—416no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11#12014yes—
321C2×Dic11—232no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—416no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11C4×D418yes—
351C23×D4C2×D1111yescharacteristic
352C24×C4—111no—
353C24×C4—111no—
354C24×C4C2×D1111yescharacteristic
355C22×C4⋊C4—112no—
356C22×C4⋊C4—112no—
357C22×C4⋊C4—228no—
358C22×C4⋊C4—224no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4C2×D1111yescharacteristic
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1111yescharacteristic
366C22×C42—112no—
367#388—228no—
368#386—24no—
369#386—118no—
370#386—224no—
371C4×C22⋊C4—224no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95—112no—
379C2×#95C2×D1111yescharacteristic
380C2×#95C2×D1111yescharacteristic
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—28no—
384C22×C11—28no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—28no—
389C22×C11—28no—
390C22×C11—24no—
391C22×C11—42no—
392C22×C11—44no—
393C22×C11—44no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—82no—
401C22×C11—82no—
402C22×C11#38818yescomplemented
403C22×C11C2×#11711yescharacteristic
404C22×C11C2×C4×D411yescharacteristic
405C22×C11C2×C4×D411yescharacteristic
406C22×C11C2×C4×D412yes—
407C22×C11#52012yes—
408C22×C11C2×#12011yescharacteristic
409C22×C11C2×#12111yescharacteristic
410C22×C11C2×#12311yescharacteristic
411C22×C11#52512yes—
412C22×C11#52511yescharacteristic
413C22×C11C2×#12411yescharacteristic
414C22×C11C2×#12611yescharacteristic
415C22×C11#53411yescharacteristic
416C22×C11#53611yescharacteristic
417C22×C11#53912yes—
418C22×C11D4212yes—
419C22×C11#54612yes—
420C22×C11#54712yes—
421C22×C11#54812yes—
422C22×C11#54812yes—
423C22×C11#55212yes—
424C22×C11#55312yes—
425C22×C11#55312yes—
426C4×C11—24no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—81no—
430C4×C11—81no—
431Dic11—28no—
432Dic11—44no—
433Dic11—44no—
434Dic11—44no—
435C25C22×D1111yescharacteristic
436C25C22×D1111yescharacteristic
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4C4×D1114yes—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—24no—
447C23×C4—42no—
448C23×C4—112no—
449C23×C4—114no—
450C23×C4—112no—
451C23×C4—112no—
452C23×C4—112no—
453C23×C4—224no—
454C23×C4—224no—
455C23×C4—224no—
456C23×C4—222no—
457C23×C4—222no—
458C23×C4—222no—
459C23×C4—222no—
460C23×C4—222no—
461C23×C4—442no—
462C23×C4C22⋊D1114yes—
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C2×C4⋊C4—118no—
469C2×C4⋊C4—224no—
470C2×C4⋊C4—224no—
471C2×C4⋊C4—2232no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—224no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—118no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C22⋊C4—222no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—442no—
494C2×C42—224no—
495C2×C42—224no—
496C2×C42—442no—
497#95—22no—
498#95—22no—
499#95—118no—
500#95—224no—
501#95—224no—
502#95—224no—
503#95—224no—
504#95—224no—
505#95—442no—
506C2×C11—28no—
507C2×C11—82no—
508C2×C11C2×#38811yescharacteristic
509C2×C11C4×#12011yescharacteristic
510C2×C11#232211yescharacteristic
511C2×C11#235212yes—
512C2×C11#236112yes—
513C2×C11#241011yescharacteristic
514C2×C11#241311yescharacteristic
515C2×C11#243611yescharacteristic
516C2×C11#244312yes—
517C2×C11#248112yes—
518C2×C11#259111yescharacteristic
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24C2×C4×D1112yes—
534C24C2×C4×D1112yes—
535C24#433912yes—
536C24D4×D1112yes—
537C24#434112yes—
538C24#434112yes—
539C24#434112yes—
540C24C2×C22⋊D1112yes—
541C24C23×D1111yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—114no—
580C22×C4—114no—
581C22×C4—114no—
582C22×C4—114no—
583C22×C4—2216no—
584C22×C4—228no—
585C22×C4—2216no—
586C22×C4—228no—
587C22×C4—228no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—228no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—448no—
612C22×C4—448no—
613C22×C4—444no—
614C22×C4—444no—
615C22×C4C2×C4×D1112yes—
616C22×C4D4×D1114yes—
617C22×C4C2×C22⋊D1112yes—
618C22×C4C2×C22⋊D1112yes—
619C4⋊C4—2216no—
620C4⋊C4—2216no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—2216no—
625C22⋊C4—228no—
626C22⋊C4—228no—
627C22⋊C4—448no—
628C42—448no—
629C11#1401911yescharacteristic, complemented, Sylow
630C23—22no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—41no—
658C23—42no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23#6693014yes—
670C23#6693214yes—
671C23(C22⋊D11)⋊C414yes—
672C23#6693614yes—
673C23C4×C22⋊D1114yes—
674C23#6698914yes—
675C23#6699214yes—
676C23C22×C4×D1111yescharacteristic
677C23C2×#433911yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×D4×D1112yes—
680C23C2×#434111yescharacteristic
681C23C2×#434111yescharacteristic
682C23C2×#434111yescharacteristic
683C23#6703712yes—
684C23#41×D1112yes—
685C23#6704312yes—
686C23C22×C22⋊D1111yescharacteristic
687D4—416no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—416no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—118no—
716C2×C4—2232no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—4416no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4#6699014yes—
746C22—28no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—28no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22#1062255818yescomplemented
768C22C2×#6693011yescharacteristic
769C22C2×#6693211yescharacteristic
770C22C2×(C22⋊D11)⋊C411yescharacteristic
771C22C2×#6693611yescharacteristic
772C22C4×D4×D1112yes—
773C22#1062307712yes—
774C22#1062307812yes—
775C22#1062309512yes—
776C22#1062312112yes—
777C22#1062312212yes—
778C22#1062312912yes—
779C22#1062312912yes—
780C22#1062313212yes—
781C22#1062313212yes—
782C22#1062318112yes—
783C22#1062318612yes—
784C22C2×C4×C22⋊D1111yescharacteristic
785C22C2×#6698911yescharacteristic
786C22C2×#6699011yescharacteristic
787C22C2×#6699211yescharacteristic
788C22#1062333511yescharacteristic
789C22#1062335611yescharacteristic
790C22#1062335911yescharacteristic
791C4—24no—
792C4—42no—
793C4—42no—
794C4—81no—
795C4—81no—
796C4—228no—
797C4—444no—
798C4—444no—
799C4—444no—
800C2—28no—
801C2—82no—
802C2C2×#1062255811yescharacteristic
803C2C4×#6699011yescharacteristic
804C2#1307128111yescharacteristic
805C2#1307154312yes—
806C2#1307162712yes—
807C2#1307199111yescharacteristic
808C2#1307202411yescharacteristic
809C2#1307227511yescharacteristic
810C2#1307235312yes—
811C2#1307287912yes—
812C2#1307409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14019
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×Dic11⋊C4C2semidirect
2. C2×#10622558C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. #13066874C2semidirect
7. #13066859C2semidirect
8. #13066851C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
32. #10622833C4semidirect
92. C2×C22⋊Dic11C2×C4semidirect
100. C2×Dic11⋊C4D4semidirect
112. C11⋊#95C2×C4semidirect
402. C22×C11#388semidirect
629. C11#14019semidirect
767. C22#10622558semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106225582
C2×#106228332
C2×C4×C22⋊Dic112
#130668742
#130668592
#130668512
#130668382
C2×C11×#3862
#1401911