Finite Group Databasebeta

← #14676291

Subgroups — #14676291

Order 2816.

4470 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13066855C214yesmaximal, complemented
8#13066838C214yesmaximal, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C23×C22⋊D11C2212yes—
12C24×Dic11C2212yes—
13C22×#4341—24no—
14C22×#4341—24no—
15C22×#4341—24no—
16C22×#4341—24no—
17C22×#4341—24no—
18C22×#4341—24no—
19C22×#4341C418yescomplemented
20C23×C4×D11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2214yes—
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2214yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C11×#390—24no—
31#10622834—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2214yes—
35C2×C11⋊#95C2214yes—
36#10622600—24no—
37#10622587—24no—
38C4×(C2×D11)⋊C4—24no—
39#10622542—24no—
40C25×C11C2312yes—
41C24×D11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11C2×C414yes—
47C22×D4×C11D414yes—
48C22×D4×C11D414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11—24no—
55C22×C22⋊D11—24no—
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11C2×C418yes—
59C23×Dic11—24no—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—24no—
65C23×Dic11C2×C418yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C2×#4341—232no—
71C2×#4341—232no—
72C2×#4341—232no—
73C2×#4341—232no—
74C2×#4341—232no—
75C2×#4341—232no—
76C2×#4341—232no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11C2×C414yes—
82C22×C4×D11D414yes—
83C22×C4×D11D414yes—
84C22×Dic22—22no—
85C22×Dic22—22no—
86C22×Dic22—22no—
87C22×Dic22—22no—
88C22×Dic22C2×C414yes—
89C22×Dic22D414yes—
90C22×Dic22D414yes—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C22⋊C4—28no—
95C2×C11×C22⋊C4—28no—
96C2×C11×C22⋊C4—44no—
97C2×C42×C11—22no—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×C22⋊Dic11—28no—
101C2×C22⋊Dic11—28no—
102C2×C22⋊Dic11—44no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—44no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C11⋊#95—28no—
115C11⋊#95—24no—
116C11⋊#95—28no—
117C11⋊#95—24no—
118#13937—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—24no—
127C24×C11C22×C414yes—
128C24×C11C2×D414yes—
129C24×C11C2×D414yes—
130C24×C11C2411yescharacteristic
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11C22×C412yes—
140C23×D11C2×D412yes—
141C23×D11C2×D412yes—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11C22⋊C4116yescomplemented
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4114yescomplemented
168C2×C22⋊D11—216no—
169C2×C22⋊D11—216no—
170C2×C22⋊D11—216no—
171C2×C22⋊D11—216no—
172C2×C22⋊D11—216no—
173C2×C22⋊D11—216no—
174C2×C22⋊D11—216no—
175C22×Dic11—216no—
176C22×Dic11—216no—
177C22×Dic11—216no—
178C22×Dic11—216no—
179C22×Dic11—216no—
180C22×Dic11—216no—
181C22×Dic11—216no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—24no—
198C22×Dic11—22no—
199C22×Dic11—24no—
200C22×Dic11—22no—
201C22×Dic11C22×C414yes—
202C22×Dic11C22×C412yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D412yes—
206C22×Dic11C2×D412yes—
207C22×Dic11#4114yescomplemented
208#4341—2256no—
209C2×C4×D11—28no—
210C2×C4×D11—28no—
211C2×C4×D11—28no—
212C2×C4×D11—28no—
213C2×C4×D11—28no—
214C2×C4×D11—28no—
215C2×C4×D11C22⋊C4116yescomplemented
216C2×Dic22—28no—
217C2×Dic22—28no—
218C2×Dic22—28no—
219C2×Dic22—28no—
220C2×Dic22—28no—
221C2×Dic22—28no—
222C2×Dic22C22⋊C4116yescomplemented
223C11×C4⋊C4—44no—
224C11×C22⋊C4—416no—
225C42×C11—44no—
226C22⋊Dic11—416no—
227(C2×D11)⋊C4—216no—
228(C2×D11)⋊C4—48no—
229C4⋊Dic11—44no—
230C4×Dic11—44no—
231C23×#41—111no—
232C2×#391—111no—
233C2×#391—111no—
234C2×#390—111no—
235C2×#390D1111yescharacteristic, complemented
236C2×#380—111no—
237C2×C4×C22⋊C4—111no—
238#1438—114no—
239C22⋊#95—114no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—28no—
243C23×C11—28no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—28no—
249C23×C11—28no—
250C23×C11—28no—
251C23×C11—28no—
252C23×C11—44no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—44no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11—44no—
261C23×C11—44no—
262C23×C11C2×C22⋊C418yes—
263C23×C11C23×C411yescharacteristic
264C23×C11C22×D411yescharacteristic
265C23×C11C22×D411yescharacteristic
266C23×C11C22×D411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C2×#4112yes—
271C23×C11C2×#4112yes—
272C23×C11H(5,𝔽2)12yes—
273C23×C112−1+412yes—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—24no—
277C22×D11—24no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—24no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—24no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11C2×C22⋊C414yes—
297D4×C11—232no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
310C2×C4×C11C2×C22⋊C414yes—
311C2×C4×C11C2×C22⋊C414yes—
312C2×C4×C11C2×C22⋊C414yes—
313C2×C4×C11#12014yes—
314C2×C4×C11#12014yes—
315C2×C4×C11#12014yes—
316C2×C4×C11#12014yes—
317C22⋊D11—264no—
318C2×Dic11—264no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—44no—
342C2×Dic11—44no—
343C2×Dic11C2×C22⋊C418yes—
344C2×Dic11C2×C22⋊C414yes—
345C4×D11—232no—
346Dic22—232no—
347C22×#41—118no—
348C22×#41—224no—
349C22×#41—224no—
350C22×#41—224no—
351C22×#41—224no—
352C22×#41—224no—
353C22×#41—224no—
354C23×Q8—111no—
355C23×D4—112no—
356C23×D4C2×D1111yescharacteristic
357C24×C4—111no—
358C24×C4—112no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4C2×D1111yescharacteristic
361C22×C22⋊C4—112no—
362C22×C22⋊C4—114no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4C2×D1114yes—
365C22×C42—111no—
366C22×C42C2×D1111yescharacteristic
367#391—224no—
368#391—224no—
369#390—24no—
370#390—224no—
371#380—224no—
372C4×C22⋊C4—224no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—114no—
376C2×#95—114no—
377C22×C11—216no—
378C22×C11—28no—
379C22×C11—44no—
380C22×C11—48no—
381C22×C11—48no—
382C22×C11—48no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11C22×C22⋊C411yescharacteristic
389C22×C11C22×C22⋊C411yescharacteristic
390C22×C11C22×C22⋊C411yescharacteristic
391C22×C11C4×#4112yes—
392C22×C11#52012yes—
393C22×C11C2×#12011yescharacteristic
394C22×C11C2×#12011yescharacteristic
395C22×C11C2×#12011yescharacteristic
396C22×C11C2×#12011yescharacteristic
397C22×C11#52512yes—
398C22×C11#53211yescharacteristic
399C22×C11#53211yescharacteristic
400C22×C11#53511yescharacteristic
401C22×C11#53611yescharacteristic
402C22×C11#53712yes—
403C22×C11#54612yes—
404C22×C11#54612yes—
405C22×C11#54712yes—
406C22×C11#54712yes—
407C22×C11#54812yes—
408C22×C11#54812yes—
409C22×C11#55012yes—
410C22×C11#55012yes—
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—24no—
414C2×D11—44no—
415C2×D11—44no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C4×C11—44no—
423C4×C11—82no—
424C4×C11#37918yes—
425Dic11—28no—
426Dic11—24no—
427Dic11—44no—
428Dic11—82no—
429C25—111no—
430C25C22×D1112yes—
431C2×#41—2232no—
432C2×#41—2232no—
433C2×#41—2232no—
434C2×#41—2232no—
435C2×#41—2232no—
436C2×#41—2232no—
437C2×#41—2232no—
438C22×Q8—114no—
439C22×Q8—114no—
440C22×Q8—114no—
441C22×Q8—222no—
442C22×Q8—222no—
443C22×Q8—222no—
444C22×Q8—222no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—118no—
450C22×D4—224no—
451C22×D4—224no—
452C22×D4—224no—
453C22×D4—224no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4C4×D1114yes—
457C22×D4D4414yes—
458C22×D4C22⋊D1114yes—
459C23×C4—111no—
460C23×C4—112no—
461C23×C4—114no—
462C23×C4—114no—
463C23×C4—114no—
464C23×C4—118no—
465C23×C4—112no—
466C23×C4—112no—
467C23×C4—224no—
468C23×C4—224no—
469C23×C4—224no—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—224no—
473C23×C4—222no—
474C23×C4—222no—
475C23×C4—222no—
476C23×C4—222no—
477C23×C4C22×D1112yes—
478C23×C4C22×D1112yes—
479C23×C4C22×D1111yescharacteristic
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—44no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—228no—
494C2×C22⋊C4—228no—
495C2×C22⋊C4—444no—
496C2×C22⋊C4—444no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—222no—
503#95—224no—
504#95—224no—
505#95—228no—
506#95—228no—
507C2×C11—48no—
508C2×C11C2×#37911yescharacteristic
509C2×C11#229711yescharacteristic
510C2×C11#231111yescharacteristic
511C2×C11#233912yes—
512C2×C11#234112yes—
513C2×C11#240712yes—
514C2×C11#240712yes—
515C2×C11#243111yescharacteristic
516C2×C11#243111yescharacteristic
517C2×C11#243211yescharacteristic
518C2×C11#243211yescharacteristic
519D11—44no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—24no—
525C24—24no—
526C24—24no—
527C24—24no—
528C24—112no—
529C24—112no—
530C24—112no—
531C24—221no—
532C24—221no—
533C24—221no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—221no—
539C24C2×C4×D1114yes—
540C24C2×D4414yes—
541C24C2×C22⋊D1114yes—
542C24C23×D1111yescharacteristic
543#41—22256no—
544C2×Q8—1116no—
545C2×Q8—228no—
546C2×Q8—228no—
547C2×Q8—228no—
548C2×Q8—228no—
549C2×Q8—228no—
550C2×Q8—228no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—2216no—
558C2×D4—2216no—
559C2×D4—2216no—
560C2×D4—2216no—
561C2×D4—2216no—
562C2×D4—2216no—
563C2×D4—2216no—
564C2×D4(C2×D11)⋊C4116yescomplemented
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—112no—
577C22×C4—114no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—114no—
581C22×C4—114no—
582C22×C4—1116no—
583C22×C4—114no—
584C22×C4—2216no—
585C22×C4—2216no—
586C22×C4—2216no—
587C22×C4—2216no—
588C22×C4—2216no—
589C22×C4—2216no—
590C22×C4—2216no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—222no—
599C22×C4—228no—
600C22×C4—228no—
601C22×C4—228no—
602C22×C4—228no—
603C22×C4—228no—
604C22×C4—228no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4C2×C4×D1112yes—
617C22×C4C2×D4412yes—
618C22×C4D4×D1112yes—
619C22×C4D4×D1112yes—
620C22×C4D4×D1112yes—
621C22×C4D4×D1112yes—
622C22×C4#434114yescomplemented
623C22×C4C2×C22⋊D1112yes—
624C4⋊C4—44no—
625C4⋊C4—444no—
626C22⋊C4—416no—
627C22⋊C4—2216no—
628C22⋊C4—448no—
629C22⋊C4—4416no—
630C42—44no—
631C42—444no—
632C11#1393711yescharacteristic, complemented, Sylow
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—28no—
638C23—24no—
639C23—24no—
640C23—28no—
641C23—28no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—42no—
646C23—42no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—42no—
653C23—42no—
654C23—44no—
655C23—114no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—224no—
663C23—222no—
664C23—222no—
665C23—224no—
666C23—224no—
667C23—224no—
668C23—222no—
669C23—222no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23C2×(C2×D11)⋊C418yes—
679C23C22×C4×D1111yescharacteristic
680C23C22×D4411yescharacteristic
681C23C2×D4×D1111yescharacteristic
682C23C2×D4×D1111yescharacteristic
683C23C2×D4×D1111yescharacteristic
684C23C2×D4×D1111yescharacteristic
685C23C2×#434112yes—
686C23#6703712yes—
687C23#41×D1112yes—
688C23#6704312yes—
689C23C22×C22⋊D1111yescharacteristic
690Q8—2232no—
691D4—232no—
692D4—2264no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—114no—
706C2×C4—118no—
707C2×C4—2264no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—222no—
715C2×C4—224no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—2232no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—444no—
731C2×C4—444no—
732C2×C4—442no—
733C2×C4C22⋊C4×D1114yes—
734C2×C4C22⋊C4×D1114yes—
735C2×C4#6693514yes—
736C2×C4#6693514yes—
737C2×C4C2×(C2×D11)⋊C414yes—
738C2×C4#6699014yes—
739C2×C4#6699014yes—
740C22—216no—
741C22—28no—
742C22—48no—
743C22—48no—
744C22—48no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—224no—
752C22—224no—
753C22—224no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22C2×C22⋊C4×D1111yescharacteristic
763C22C2×C22⋊C4×D1111yescharacteristic
764C22C2×#6693511yescharacteristic
765C22C2×#6693511yescharacteristic
766C22C4×#434112yes—
767C22#1062307712yes—
768C22#1062308512yes—
769C22#1062308612yes—
770C22#1062312912yes—
771C22#1062313012yes—
772C22#1062313712yes—
773C22#1062313912yes—
774C22#1062319911yescharacteristic
775C22#1062320611yescharacteristic
776C22#1062320812yes—
777C22#1062324611yescharacteristic
778C22#1062324711yescharacteristic
779C22#1062324912yes—
780C22C22×(C2×D11)⋊C411yescharacteristic
781C22C2×#6699011yescharacteristic
782C22C2×#6699011yescharacteristic
783C22#1062333712yes—
784C22#1062335512yes—
785C4—44no—
786C4—82no—
787C4—224no—
788C4—228no—
789C4—444no—
790C4—882no—
791C4#1062256818yes—
792C2—48no—
793C2—444no—
794C2C2×#1062256811yescharacteristic
795C2#1307110311yescharacteristic
796C2#1307120611yescharacteristic
797C2#1307144112yes—
798C2#1307145512yes—
799C2#1307195712yes—
800C2#1307195912yes—
801C2#1307223211yescharacteristic
802C2#1307223411yescharacteristic
803C2#1307224611yescharacteristic
804C2#1307224711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×#4341C2
hypercenterC2×#390D11
hypocenterC11#13937
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. C2×#10622587C2semidirect
4. C2×#10622834C2semidirect
5. C2×#10622600C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. #13066855C2semidirect
8. #13066838C2semidirect
9. C2×C11×#390C2semidirect
19. C22×#4341C4semidirect
148. C2×D4×C11C22⋊C4semidirect
167. C22×C4×C11#41semidirect
207. C22×Dic11#41semidirect
215. C2×C4×D11C22⋊C4semidirect
222. C2×Dic22C22⋊C4semidirect
235. C2×#390D11semidirect
564. C2×D4(C2×D11)⋊C4semidirect
622. C22×C4#4341semidirect
632. C11#13937semidirect

Maximal subgroups

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

subgroupindex
C23×#43412
C2×#106225422
C2×#106225872
C2×#106228342
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668552
#130668382
C2×C11×#3902
#1393711