Finite Group Databasebeta

← #14685005

Subgroups — #14685005

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×#10622603C212yesmaximal, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622571C211yesmaximal, characteristic
6#13066852C212yesmaximal, complemented
7#13066848C212yesmaximal, complemented
8#13066842C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4×Dic11—24no—
25C22×C4×Dic11—28no—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2212yes—
28C11×#385—24no—
29C2×C11×#95C2212yes—
30#10622826—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39#10622603—28no—
40#10622571—24no—
41#10622571C418yescomplemented
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11D414yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11C2×C414yes—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—24no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—24no—
68C23×Dic11C2×C414yes—
69C23×Dic11D414yes—
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4C2×C414yes—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4C2×C418yescomplemented
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—22no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—24no—
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×C11C22×C412yes—
119C24×C11C2×D412yes—
120C24×C11C2×D412yes—
121C24×C11#4112yes—
122C24×C11#4112yes—
123C24×C11#4112yes—
124C24×C11#4112yes—
125C24×C11C2411yescharacteristic
126C23×D11—22no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11C22×C412yes—
137C22×C4×C11—28no—
138C22×C4×C11—216no—
139C22×C4×C11—28no—
140C22×C4×C11—28no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—216no—
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—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11C22×C414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11#4114yes—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—44no—
170C2×C22⋊D11—44no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11—44no—
173C22×Dic11—28no—
174C22×Dic11—28no—
175C22×Dic11—216no—
176C22×Dic11—216no—
177C22×Dic11—216no—
178C22×Dic11—216no—
179C22×Dic11—28no—
180C22×Dic11—28no—
181C22×Dic11—28no—
182C22×Dic11—28no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11C22×C412yes—
207C22×Dic11C22×C414yes—
208C22×Dic11C2×D414yes—
209C22×Dic11C2×D412yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D412yes—
212C22×Dic11#4114yes—
213C22×Dic11#4114yes—
214C11×C4⋊C4—48no—
215C11×C22⋊C4—28no—
216C11×C22⋊C4—44no—
217C22⋊Dic11—44no—
218(C2×D11)⋊C4—216no—
219(C2×D11)⋊C4—44no—
220(C2×D11)⋊C4—44no—
221(C2×D11)⋊C4—48no—
222C4×Dic11—216no—
223C4×Dic11—216no—
224C23×C42—111no—
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386—111no—
229C2×#385D1111yescharacteristic, complemented
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#11714yes—
252C23×C11C4×D414yes—
253C23×C11C4×D414yes—
254C23×C11#12114yes—
255C23×C11#12314yes—
256C23×C11#12414yes—
257C23×C11#12614yes—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D412yes—
261C23×C11C22×D411yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4112yes—
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4112yes—
268C23×C11C2×#4112yes—
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—24no—
274C22×D11—41no—
275C22×D11—42no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—41no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C2×C4×C11—232no—
293C2×C4×C11—24no—
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—24no—
301C2×C4×C11—24no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11#12118yes—
317C22⋊D11—416no—
318C2×Dic11—232no—
319C2×Dic11—232no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11C4×D418yes—
349C2×Dic11#12014yes—
350C2×Dic11#12314yes—
351C23×D4—111no—
352C24×C4—111no—
353C24×C4—111no—
354C24×C4C2×D1111yescharacteristic
355C22×C4⋊C4C2×D1112yes—
356C22×C22⋊C4—112no—
357C22×C22⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4C2×D1111yescharacteristic
362C22×C22⋊C4C2×D1111yescharacteristic
363C22×C42—112no—
364C22×C42—112no—
365C22×C42—228no—
366C22×C42—224no—
367#388—228no—
368#386—118no—
369#386—224no—
370#386—224no—
371#385—24no—
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#38818yescomplemented
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C2×C4×D412yes—
396C22×C11C4×#4112yes—
397C22×C11C2×#12011yescharacteristic
398C22×C11C2×#12112yes—
399C22×C11C2×#12111yescharacteristic
400C22×C11C2×#12311yescharacteristic
401C22×C11C2×#12311yescharacteristic
402C22×C11#52512yes—
403C22×C11#52512yes—
404C22×C11#52511yescharacteristic
405C22×C11#52512yes—
406C22×C11#52512yes—
407C22×C11#52511yescharacteristic
408C22×C11C2×#12411yescharacteristic
409C22×C11C2×#12611yescharacteristic
410C22×C11#52912yes—
411C22×C11#52912yes—
412C22×C11#52912yes—
413C22×C11#52912yes—
414C22×C11#53212yes—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—42no—
418C2×D11—44no—
419C2×D11—42no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—82no—
423C2×D11—82no—
424C2×D11—81no—
425C2×D11—81no—
426C4×C11—28no—
427C4×C11—44no—
428C4×C11—81no—
429C4×C11—81no—
430Dic11—24no—
431Dic11—24no—
432Dic11—28no—
433Dic11—42no—
434Dic11—82no—
435C25—111no—
436C25C22×D1111yescharacteristic
437C22×D4—114no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—222no—
441C22×D4—222no—
442C22×D4—222no—
443C22×D4—222no—
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—111no—
454C23×C4—112no—
455C23×C4—224no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—222no—
460C23×C4—222no—
461C23×C4—222no—
462C23×C4—222no—
463C23×C4C22⋊D1114yes—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1112yes—
467C23×C4C22×D1112yes—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—118no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—222no—
480C2×C22⋊C4—222no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4C4×D1114yes—
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×C11C2×#38811yescharacteristic
508C2×C11#229012yes—
509C2×C11C4×#12011yescharacteristic
510C2×C11C4×#12112yes—
511C2×C11C4×#12311yescharacteristic
512C2×C11#284711yescharacteristic
513C2×C11#284911yescharacteristic
514C2×C11#285012yes—
515C2×C11#285212yes—
516C2×C11#285311yescharacteristic
517C2×C11#285411yescharacteristic
518D11—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—112no—
524C24—221no—
525C24—222no—
526C24—221no—
527C24—222no—
528C24—221no—
529C24—221no—
530C24—221no—
531C24—222no—
532C24—222no—
533C24—221no—
534C24C2×C4×D1112yes—
535C24#433912yes—
536C24D4×D1112yes—
537C24#434112yes—
538C24#434312yes—
539C24#434312yes—
540C24C2×C22⋊D1112yes—
541C24C23×D1111yescharacteristic
542C2×D4—228no—
543C2×D4—228no—
544C2×D4—228no—
545C2×D4—444no—
546C2×D4—444no—
547C2×D4—444no—
548C2×D4—444no—
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—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—114no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—114no—
580C22×C4—114no—
581C22×C4—112no—
582C22×C4—228no—
583C22×C4—2216no—
584C22×C4—228no—
585C22×C4—228no—
586C22×C4—2216no—
587C22×C4—2216no—
588C22×C4—2216no—
589C22×C4—228no—
590C22×C4—228no—
591C22×C4—228no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4C2×C4×D1114yes—
616C22×C4D4×D1114yes—
617C22×C4#434114yes—
618C22×C4C2×C22⋊D1114yes—
619C4⋊C4—48no—
620C22⋊C4—28no—
621C22⋊C4—44no—
622C22⋊C4—2216no—
623C22⋊C4—444no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C22⋊C4—448no—
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—222no—
647C23—222no—
648C23—222no—
649C23—224no—
650C23—224no—
651C23—441no—
652C23—441no—
653C23—442no—
654C23—442no—
655C23—441no—
656C23—442no—
657C23—441no—
658C23—442no—
659C23—441no—
660C23—442no—
661C23—441no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—441no—
668C23—441no—
669C23#6694514yes—
670C23#6694614yes—
671C23#6694714yes—
672C23#6695114yes—
673C23C4×C22⋊D1114yes—
674C23#6699214yes—
675C23#6700014yes—
676C23C22×C4×D1111yescharacteristic
677C23C2×#433911yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×D4×D1112yes—
680C23C2×#434111yescharacteristic
681C23C2×#434112yes—
682C23C2×#434311yescharacteristic
683C23C2×#434311yescharacteristic
684C23#41×D1112yes—
685C23#41×D1112yes—
686C23C22×C22⋊D1111yescharacteristic
687D4—4416no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—118no—
713C2×C4—114no—
714C2×C4—114no—
715C2×C4—2232no—
716C2×C4—2232no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4#6699218yes—
746C22—24no—
747C22—28no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—28no—
752C22—28no—
753C22—28no—
754C22—24no—
755C22—24no—
756C22—442no—
757C22—444no—
758C22—442no—
759C22—442no—
760C22—444no—
761C22—881no—
762C22—881no—
763C22—882no—
764C22—882no—
765C22—881no—
766C22—881no—
767C22#1062260318yescomplemented
768C22C2×#6694511yescharacteristic
769C22C2×#6694611yescharacteristic
770C22C2×#6694711yescharacteristic
771C22C2×#6695111yescharacteristic
772C22C4×#434112yes—
773C22#1062306912yes—
774C22C4×D4×D1112yes—
775C22#1062307812yes—
776C22#1062311711yescharacteristic
777C22#1062311712yes—
778C22D11×#12011yescharacteristic
779C22#1062315512yes—
780C22#1062315512yes—
781C22#1062315812yes—
782C22#1062315812yes—
783C22#1062318012yes—
784C22D11×#12311yescharacteristic
785C22#1062318711yescharacteristic
786C22C2×C4×C22⋊D1111yescharacteristic
787C22C2×#6699212yes—
788C22C2×#6699211yescharacteristic
789C22C2×#6700011yescharacteristic
790C22#1062336312yes—
791C4—28no—
792C4—44no—
793C4—81no—
794C4—81no—
795C4—228no—
796C4—224no—
797C4—224no—
798C4—442no—
799C4—882no—
800C2—28no—
801C2—882no—
802C2C2×#1062260311yescharacteristic
803C2#1307105212yes—
804C2#1307111711yescharacteristic
805C2C4×#6699212yes—
806C2#1307113511yescharacteristic
807C2#1307689611yescharacteristic
808C2#1307691111yescharacteristic
809C2#1307691912yes—
810C2#1307693312yes—
811C2#1307694111yescharacteristic
812C2#1307694511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#14696
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C23×C4×Dic11C2semidirect
2. C2×#10622603C2semidirect
6. #13066852C2semidirect
7. #13066848C2semidirect
8. #13066842C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
11. C2×C11×#385C2semidirect
41. #10622571C4semidirect
96. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×C4×Dic11D4semidirect
112. C11⋊#95C2×C4semidirect
229. C2×#385D11semidirect
391. C22×C11#388semidirect
629. C11#14696semidirect
767. C22#10622603semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
C2×#106226032
C2×#106228262
C2×#106225712
#130668522
#130668482
#130668422
#130668382
C2×C11×#3852
#1469611