Finite Group Databasebeta

← #14690444

Subgroups — #14690444

Order 2816.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622565C212yesmaximal, complemented
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622834C211yesmaximal, characteristic
4C2×#10622541C211yesmaximal, characteristic, complemented
5#13066865C212yesmaximal, complemented
6#13066863C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#390—24no—
27#10622834—24no—
28#10622834—24no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622565—28no—
39#10622541—24no—
40C25×C11C2312yes—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11D414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11D414yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C11⋊#95—22no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95D414yescomplemented
106#15138—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C2×D414yes—
122C24×C11C2411yescharacteristic
123C2×D4×C11—28no—
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
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×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D412yes—
197C22×Dic11C2×D414yes—
198C22×Dic11#4112yes—
199C22×Dic11#4112yes—
200C11×C4⋊C4—44no—
201C11×C22⋊C4—48no—
202C11×C22⋊C4—48no—
203C42×C11—44no—
204C22⋊Dic11—48no—
205C22⋊Dic11—48no—
206C22⋊Dic11—48no—
207C22⋊Dic11—48no—
208C4⋊Dic11—28no—
209C4⋊Dic11—44no—
210Dic11⋊C4—48no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C2×#397—112no—
214C2×#390—111no—
215C2×#390—111no—
216C2×#390D1111yescharacteristic
217C2×#389—111no—
218#1440—112no—
219#1440—112no—
220#1439—112no—
221C4⋊#95—111no—
222C4⋊#95—111no—
223C4×#95—111no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11H(5,𝔽2)11yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C11H(5,𝔽2)11yescharacteristic
273C23×C112−1+411yescharacteristic
274D4×C11—416no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11#12114yes—
297C2×C4×C11#12314yes—
298C2×C4×C11#12314yes—
299C2×C4×C11#12314yes—
300C2×C4×C11#12414yes—
301C2×C4×C11#12614yes—
302C2×C4×C11#12614yes—
303C2×Dic11—24no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—42no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—42no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—42no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C23×D4C2×D1111yescharacteristic
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4C2×D1112yes—
355C22×C22⋊C4C2×D1112yes—
356C22×C42—111no—
357C22×C42—111no—
358C22×C42C2×D1111yescharacteristic
359#397—228no—
360#390—24no—
361#390—224no—
362#390—224no—
363#389—224no—
364C2×#95—111no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—82no—
381C22×C11—82no—
382C22×C11—82no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—82no—
386C22×C11—82no—
387C22×C11—82no—
388C22×C11C2×#12111yescharacteristic
389C22×C11C2×#12311yescharacteristic
390C22×C11C2×#12311yescharacteristic
391C22×C11C2×#12311yescharacteristic
392C22×C11C2×#12411yescharacteristic
393C22×C11C2×#12611yescharacteristic
394C22×C11C2×#12611yescharacteristic
395C22×C11#52911yescharacteristic
396C22×C11#52911yescharacteristic
397C22×C11#52911yescharacteristic
398C22×C11#53211yescharacteristic
399C22×C11#53211yescharacteristic
400C22×C11#53211yescharacteristic
401C22×C11#54011yescharacteristic
402C22×C11#54011yescharacteristic
403C22×C11#54011yescharacteristic
404C22×C11#54211yescharacteristic
405C22×C11#54211yescharacteristic
406C22×C11#54211yescharacteristic
407C22×C11D4211yescharacteristic
408C22×C11D4211yescharacteristic
409C22×C11#54611yescharacteristic
410C22×C11#54611yescharacteristic
411C22×C11#54611yescharacteristic
412C22×C11#54711yescharacteristic
413C22×C11#54711yescharacteristic
414C22×C11#54811yescharacteristic
415C22×C11#55011yescharacteristic
416C22×C11#55011yescharacteristic
417C22×C11#55311yescharacteristic
418C22×C11#55311yescharacteristic
419C22×C11#55511yescharacteristic
420C22×C11#55611yescharacteristic
421C22×C11#55911yescharacteristic
422C22×C11#55911yescharacteristic
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—82no—
426C4×C11#39718yescomplemented
427Dic11—42no—
428Dic11—42no—
429Dic11—44no—
430Dic11—42no—
431Dic11—42no—
432Dic11—82no—
433C25C22×D1112yes—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4C22⋊D1114yes—
441C23×C4—112no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—112no—
447C23×C4C22×D1112yes—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—442no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4—442no—
480C2×C22⋊C4—442no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—222no—
485C2×C42—222no—
486C2×C42—222no—
487C2×C42—222no—
488C2×C42—222no—
489C2×C42—222no—
490#95—114no—
491#95—222no—
492#95—222no—
493#95—224no—
494#95—224no—
495#95—224no—
496#95—222no—
497#95—442no—
498#95—442no—
499C2×C11—84no—
500C2×C11C2×#39711yescharacteristic
501C2×C11#242011yescharacteristic
502C2×C11#242211yescharacteristic
503C2×C11#242711yescharacteristic
504C2×C11#242811yescharacteristic
505C2×C11#244511yescharacteristic
506C2×C11#244511yescharacteristic
507C2×C11#244711yescharacteristic
508C2×C11#244811yescharacteristic
509C2×C11#249011yescharacteristic
510C2×C11#249111yescharacteristic
511C2×C11#251211yescharacteristic
512C2×C11#251311yescharacteristic
513C2×C11#264411yescharacteristic
514C2×C11#286011yescharacteristic
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24C2×C22⋊D1114yes—
530C24C23×D1111yescharacteristic
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—28no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—114no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4#433912yes—
600C22×C4#433912yes—
601C22×C4D4×D1112yes—
602C22×C4D4×D1112yes—
603C22×C4#434112yes—
604C22×C4#434112yes—
605C22×C4#434112yes—
606C22×C4#434112yes—
607C22×C4C2×C22⋊D1112yes—
608C4⋊C4—44no—
609C4⋊C4—228no—
610C4⋊C4—448no—
611C4⋊C4—444no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C22⋊C4—448no—
617C22⋊C4—448no—
618C42—44no—
619C42—444no—
620C42—444no—
621C11#1513811yescharacteristic, complemented, Sylow
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×#433911yescharacteristic
658C23C2×#433911yescharacteristic
659C23C2×D4×D1111yescharacteristic
660C23C2×D4×D1111yescharacteristic
661C23C2×#434111yescharacteristic
662C23C2×#434111yescharacteristic
663C23C2×#434111yescharacteristic
664C23C2×#434111yescharacteristic
665C23#6703711yescharacteristic
666C23#6703711yescharacteristic
667C23#41×D1111yescharacteristic
668C23#41×D1111yescharacteristic
669C23#6704211yescharacteristic
670C23#6704311yescharacteristic
671C23C22×C22⋊D1111yescharacteristic
672D4—416no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—222no—
695C2×C4—224no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—222no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—442no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—442no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—442no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—442no—
728C2×C4—441no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4#6693214yes—
737C2×C4#6693214yes—
738C2×C4#6693614yes—
739C2×C4#6693814yes—
740C2×C4#6698214yes—
741C2×C4#6698814yes—
742C2×C4#6699214yes—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22C2×#6693211yescharacteristic
759C22C2×#6693211yescharacteristic
760C22C2×#6693611yescharacteristic
761C22C2×#6693811yescharacteristic
762C22#1062307911yescharacteristic
763C22#1062308211yescharacteristic
764C22#1062308811yescharacteristic
765C22#1062308911yescharacteristic
766C22#1062308911yescharacteristic
767C22#1062309211yescharacteristic
768C22#1062309311yescharacteristic
769C22#1062309411yescharacteristic
770C22#1062312711yescharacteristic
771C22#1062312911yescharacteristic
772C22#1062313011yescharacteristic
773C22#1062313111yescharacteristic
774C22#1062313411yescharacteristic
775C22#1062314011yescharacteristic
776C22#1062314311yescharacteristic
777C22#1062315011yescharacteristic
778C22#1062320211yescharacteristic
779C22#1062321111yescharacteristic
780C22#1062321211yescharacteristic
781C22#1062321311yescharacteristic
782C22#1062324411yescharacteristic
783C22#1062324711yescharacteristic
784C22#1062324911yescharacteristic
785C22#1062325011yescharacteristic
786C22C2×#6698211yescharacteristic
787C22C2×#6698811yescharacteristic
788C22D4×C22⋊D1111yescharacteristic
789C22C2×#6699211yescharacteristic
790C22#1062333711yescharacteristic
791C22#1062335511yescharacteristic
792C22#1062336011yescharacteristic
793C4—42no—
794C4—42no—
795C4—82no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4—444no—
801C4—882no—
802C4#1062256518yescomplemented
803C2—84no—
804C2C2×#1062256511yescharacteristic
805C2#1307210211yescharacteristic
806C2#1307212411yescharacteristic
807C2#1307219511yescharacteristic
808C2#1307220611yescharacteristic
809C2#1307237711yescharacteristic
810C2#1307238211yescharacteristic
811C2#1307239911yescharacteristic
812C2#1307241511yescharacteristic
813C2#1307296611yescharacteristic
814C2#1307297711yescharacteristic
815C2#1307320011yescharacteristic
816C2#1307321111yescharacteristic
817C2#1307457711yescharacteristic
818C2#1307698011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#390C2
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#15138
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10622565C2semidirect
4. C2×#10622541C2semidirect
5. #13066865C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. C4×C11⋊#95C2semidirect
105. C11⋊#95D4semidirect
426. C4×C11#397semidirect
621. C11#15138semidirect
802. C4#10622565semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
C2×#106228342
C2×#106225412
#130668652
#130668632
#130668592
#130668452
C4×C11⋊#952
C2×C11×#3902
#1513811