Finite Group Databasebeta

← #14685011

Subgroups — #14685011

Order 2816.

2746 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×C4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622558C212yesmaximal, complemented
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622833C211yesmaximal, characteristic
5C2×#10622823C211yesmaximal, characteristic, complemented
6#13066853C212yesmaximal, complemented
7#13066851C212yesmaximal, 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⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11—24no—
25C22×C4×Dic11—28no—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2212yes—
28C11×#386—24no—
29C2×C11×#95C2212yes—
30#10622833—24no—
31#10622833C418yescomplemented
32#10622823—24no—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
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—24no—
55C23×C4×C11D414yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—24no—
64C23×Dic11—24no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11C2×C414yes—
68C23×Dic11D414yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—24no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11C2×C414yes—
93C2×C22⋊Dic11C2×C418yescomplemented
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×C4×Dic11—232no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11D418yescomplemented
104C11×#95—24no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95C2×C418yescomplemented
113#14696—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—22no—
123C24×C11—22no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—21no—
127C24×C11—21no—
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—28no—
145C22×C4×C11—216no—
146C22×C4×C11—28no—
147C22×C4×C11—28no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—216no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11#4114yes—
170C22×Dic11—28no—
171C22×Dic11—28no—
172C22×Dic11—216no—
173C22×Dic11—216no—
174C22×Dic11—216no—
175C22×Dic11—216no—
176C22×Dic11—28no—
177C22×Dic11—28no—
178C22×Dic11—28no—
179C22×Dic11—28no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
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—21no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11C22×C414yes—
207C22×Dic11C22×C414yes—
208C22×Dic11C2×D414yes—
209C22×Dic11C2×D412yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D412yes—
212C22×Dic11#4114yes—
213C22×Dic11#4114yes—
214C11×C22⋊C4—44no—
215C11×C22⋊C4—48no—
216C22⋊Dic11—216no—
217C22⋊Dic11—28no—
218C22⋊Dic11—44no—
219C22⋊Dic11—44no—
220C22⋊Dic11—44no—
221Dic11⋊C4—48no—
222C4×Dic11—216no—
223C4×Dic11—216no—
224C23×C42—111no—
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386D1111yescharacteristic
229C2×#385—111no—
230#1437—112no—
231#1436—112no—
232#1434—112no—
233C22⋊#95—111no—
234C22⋊#95—111no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—22no—
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—42no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—41no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
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×D411yescharacteristic
283C23×C11C22×D412yes—
284C23×C11C22×D411yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4112yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292D4×C11—416no—
293C2×C4×C11—232no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
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—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11#12118yes—
315C2×Dic11—232no—
316C2×Dic11—232no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
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—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—41no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—42no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11C4×D418yes—
349C2×Dic11#12014yes—
350C2×Dic11#12314yes—
351C23×D4C2×D1111yescharacteristic
352C24×C4—111no—
353C24×C4—111no—
354C24×C4C2×D1111yescharacteristic
355C22×C4⋊C4—112no—
356C22×C22⋊C4—111no—
357C22×C22⋊C4—112no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4C2×D1111yescharacteristic
362C22×C22⋊C4C2×D1112yes—
363C22×C42—112no—
364C22×C42—112no—
365C22×C42—228no—
366C22×C42—224no—
367#388—228no—
368#386—24no—
369#386—118no—
370#386—224no—
371#385—224no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95—111no—
378C2×#95—112no—
379C2×#95—111no—
380C2×#95C2×D1112yes—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—28no—
384C22×C11—28no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—28no—
388C22×C11—24no—
389C22×C11—28no—
390C22×C11—24no—
391C22×C11—42no—
392C22×C11—44no—
393C22×C11—42no—
394C22×C11—44no—
395C22×C11—42no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11#38818yescomplemented
403C22×C11C2×#11711yescharacteristic
404C22×C11C2×C4×D411yescharacteristic
405C22×C11C2×C4×D411yescharacteristic
406C22×C11C2×C4×D412yes—
407C22×C11C4×#4112yes—
408C22×C11C2×#12011yescharacteristic
409C22×C11C2×#12112yes—
410C22×C11C2×#12111yescharacteristic
411C22×C11C2×#12311yescharacteristic
412C22×C11C2×#12311yescharacteristic
413C22×C11#52512yes—
414C22×C11#52512yes—
415C22×C11#52511yescharacteristic
416C22×C11#52512yes—
417C22×C11#52512yes—
418C22×C11#52511yescharacteristic
419C22×C11C2×#12411yescharacteristic
420C22×C11C2×#12611yescharacteristic
421C22×C11#52912yes—
422C22×C11#52912yes—
423C22×C11#52912yes—
424C22×C11#52912yes—
425C22×C11#53212yes—
426C4×C11—28no—
427C4×C11—42no—
428C4×C11—82no—
429Dic11—24no—
430Dic11—24no—
431Dic11—28no—
432Dic11—44no—
433Dic11—81no—
434Dic11—81no—
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—24no—
448C23×C4—112no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—114no—
452C23×C4—114no—
453C23×C4—112no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—224no—
460C23×C4—222no—
461C23×C4—222no—
462C23×C4—222no—
463C23×C4—222no—
464C23×C4C22⋊D1114yes—
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1112yes—
468C2×C4⋊C4—224no—
469C2×C4⋊C4—224no—
470C2×C4⋊C4—224no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—114no—
478C2×C22⋊C4—118no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—222no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C42—118no—
491C2×C42—224no—
492C2×C42—224no—
493C2×C42—224no—
494C2×C42—224no—
495C2×C42—2232no—
496C2×C42—224no—
497#95—24no—
498#95—118no—
499#95—224no—
500#95—224no—
501#95—222no—
502#95—222no—
503#95—224no—
504#95—224no—
505#95—224no—
506C2×C11—28no—
507C2×C11—82no—
508C2×C11C2×#38811yescharacteristic
509C2×C11#229012yes—
510C2×C11C4×#12011yescharacteristic
511C2×C11C4×#12112yes—
512C2×C11C4×#12311yescharacteristic
513C2×C11#284711yescharacteristic
514C2×C11#284911yescharacteristic
515C2×C11#285012yes—
516C2×C11#285212yes—
517C2×C11#285311yescharacteristic
518C2×C11#285411yescharacteristic
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—22no—
525C24—21no—
526C24—22no—
527C24—21no—
528C24—21no—
529C24—21no—
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—28no—
550C22×C4—216no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—216no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—114no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—114no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—228no—
580C22×C4—2216no—
581C22×C4—228no—
582C22×C4—228no—
583C22×C4—2216no—
584C22×C4—2216no—
585C22×C4—2216no—
586C22×C4—228no—
587C22×C4—228no—
588C22×C4—228no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—221no—
596C22×C4—221no—
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—221no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4C2×C4×D1112yes—
616C22×C4D4×D1114yes—
617C22×C4#434114yes—
618C22×C4C2×C22⋊D1114yes—
619C4⋊C4—448no—
620C22⋊C4—44no—
621C22⋊C4—48no—
622C22⋊C4—2216no—
623C22⋊C4—228no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C42—2216no—
628C42—2216no—
629C11#1469611yescharacteristic, complemented, Sylow
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
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
683C23C2×#434112yes—
684C23#41×D1112yes—
685C23#41×D1112yes—
686C23C22×C22⋊D1111yescharacteristic
687D4—416no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—118no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—2232no—
713C2×C4—2232no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—222no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—441no—
740C2×C4—442no—
741C2×C4—441no—
742C2×C4—442no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4#6699218yes—
746C22—24no—
747C22—28no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—28no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—81no—
762C22—81no—
763C22—82no—
764C22—82no—
765C22—81no—
766C22—81no—
767C22#1062255818yescomplemented
768C22C2×#6693011yescharacteristic
769C22C2×#6693211yescharacteristic
770C22C2×(C22⋊D11)⋊C411yescharacteristic
771C22C2×#6693611yescharacteristic
772C22C4×#434112yes—
773C22#1062306912yes—
774C22C4×D4×D1112yes—
775C22#1062307812yes—
776C22#1062311711yescharacteristic
777C22#1062311712yes—
778C22D11×#12011yescharacteristic
779C22#1062313112yes—
780C22#1062313112yes—
781C22#1062313712yes—
782C22#1062313712yes—
783C22#1062318012yes—
784C22D11×#12311yescharacteristic
785C22#1062318711yescharacteristic
786C22C2×C4×C22⋊D1111yescharacteristic
787C22C2×#6698911yescharacteristic
788C22C2×#6699212yes—
789C22C2×#6699211yescharacteristic
790C22#1062336312yes—
791C4—28no—
792C4—42no—
793C4—82no—
794C4—228no—
795C4—224no—
796C4—224no—
797C4—444no—
798C4—881no—
799C4—881no—
800C2—28no—
801C2—82no—
802C2C2×#1062255811yescharacteristic
803C2#1307105612yes—
804C2#1307112111yescharacteristic
805C2C4×#6699212yes—
806C2#1307114111yescharacteristic
807C2#1307689611yescharacteristic
808C2#1307690711yescharacteristic
809C2#1307691512yes—
810C2#1307692912yes—
811C2#1307693711yescharacteristic
812C2#1307694511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14696
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×C4×Dic11C2semidirect
2. C2×#10622558C2semidirect
5. C2×#10622823C2semidirect
6. #13066853C2semidirect
7. #13066851C2semidirect
8. #13066842C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
31. #10622833C4semidirect
93. C2×C22⋊Dic11C2×C4semidirect
103. C2×C4×Dic11D4semidirect
112. C11⋊#95C2×C4semidirect
402. C22×C11#388semidirect
629. C11#14696semidirect
767. C22#10622558semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
C2×#106225582
C2×#106228332
C2×#106228232
#130668532
#130668512
#130668422
#130668382
C2×C11×#3862
#1469611