Finite Group Databasebeta

← #14690491

Subgroups — #14690491

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622286C212yesmaximal, complemented
3C2×#10622560C212yesmaximal, complemented
4C2×#10622570C212yesmaximal
5C2×#10622570C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9Dic11⋊#95C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×Dic22C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×#66941—28no—
29C2×#66941—24no—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622570—28no—
38#10622570—24no—
39#10622560—28no—
40#10622286—28no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—24no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11Q814yescomplemented
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C22×Dic22—24no—
58C22×Dic22—24no—
59C22×Dic22—24no—
60C22×Dic22—24no—
61C22×Dic22—24no—
62C22×Dic22—42no—
63C22×Dic22—42no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—42no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—42no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4D418yes—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11D414yes—
100#66941—232no—
101C11×#95—24no—
102C11×#95—22no—
103C11⋊#95—24no—
104C11⋊#95—22no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95D418yescomplemented
108#15144—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—22no—
119C24×C11C2×Q812yes—
120C24×C11C2411yescharacteristic
121C23×D11—22no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—22no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—21no—
130C23×D11—22no—
131C23×D11C2×Q812yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—44no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11C2×D414yes—
182C22×Dic11C2×D414yes—
183C22×Dic11C2×D414yes—
184C22×Dic11C2×D412yes—
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D412yes—
187C22×Dic11C2×Q812yes—
188C22×Dic11#4112yes—
189C22×Dic11#4114yes—
190C2×Dic22—216no—
191C2×Dic22—48no—
192C2×Dic22—48no—
193C2×Dic22—48no—
194C2×Dic22—48no—
195C2×Dic22—48no—
196C2×Dic22—48no—
197C11×C4⋊C4—28no—
198C11×C22⋊C4—48no—
199C11×C22⋊C4—44no—
200C22⋊Dic11—48no—
201C22⋊Dic11—44no—
202(C2×D11)⋊C4—48no—
203(C2×D11)⋊C4—48no—
204(C2×D11)⋊C4—44no—
205(C2×D11)⋊C4—44no—
206C4⋊Dic11—28no—
207Dic11⋊C4—216no—
208Dic11⋊C4—44no—
209C4×Dic11—28no—
210C4×Dic11—48no—
211C22×C4⋊Q8—111no—
212C2×#393—112no—
213C2×#393—112no—
214C2×#390—111no—
215C2×#390—112no—
216#1439—111no—
217#1439—111no—
218#1439—111no—
219#1439D1111yescharacteristic, complemented
220C4⋊#95—112no—
221C4×#95—111no—
222C23×C11—22no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—42no—
231C23×C11—41no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246C23×C11C22×D412yes—
247C23×C11C22×D412yes—
248C23×C11C22×Q811yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4112yes—
252C23×C11C2×#4111yescharacteristic
253C23×C11H(5,𝔽2)11yescharacteristic
254C23×C11H(5,𝔽2)11yescharacteristic
255C23×C112−1+412yes—
256C22×D11—22no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—42no—
265C22×D11—41no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—41no—
278C22×D11—41no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
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—42no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11#12414yes—
303C22⋊D11—416no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11#12014yes—
328C2×Dic11C22⋊Q814yes—
329C2×Dic11C22⋊Q818yes—
330C2×Dic11#12418yes—
331C2×Dic11#12414yes—
332C2×Dic11#12714yes—
333Dic22—432no—
334C23×Q8—112no—
335C23×D4—111no—
336C2×C4⋊Q8—224no—
337C2×C4⋊Q8—228no—
338C22×C4⋊C4—112no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4C2×D1111yescharacteristic
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4C2×D1112yes—
350C22×C42—111no—
351C22×C42—112no—
352#393—228no—
353#393—228no—
354#390—224no—
355#390—228no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95C2×D1112yes—
362C2×#95C2×D1111yescharacteristic
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—42no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11C2×#12011yescharacteristic
375C22×C11C2×C22⋊Q811yescharacteristic
376C22×C11C2×C22⋊Q812yes—
377C22×C11C2×#12411yescharacteristic
378C22×C11C2×#12411yescharacteristic
379C22×C11C2×#12412yes—
380C22×C11C2×#12711yescharacteristic
381C22×C11#53212yes—
382C22×C11#53212yes—
383C22×C11#53511yescharacteristic
384C22×C11#53611yescharacteristic
385C22×C11#54212yes—
386C22×C11#54212yes—
387C22×C11D4212yes—
388C22×C11D4212yes—
389C22×C11#54712yes—
390C22×C11#54812yes—
391C22×C11#54812yes—
392C22×C11D4×Q812yes—
393C22×C11#55411yescharacteristic
394C22×C11#55411yescharacteristic
395C22×C11#55511yescharacteristic
396C22×C11#55511yescharacteristic
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—42no—
402C2×D11—81no—
403C2×D11—81no—
404C2×D11—81no—
405C2×D11—81no—
406C2×D11—82no—
407C2×D11—82no—
408C4×C11—24no—
409C4×C11—44no—
410C4×C11—44no—
411C4×C11—81no—
412Dic11—24no—
413Dic11—44no—
414Dic11—44no—
415Dic11—81no—
416Dic11#39318yescomplemented
417C25—111no—
418C25C22×D1111yescharacteristic
419C22×Q8—224no—
420C22×Q8—224no—
421C22×Q8—224no—
422C22×Q8—224no—
423C22×Q8—224no—
424C22×Q8—442no—
425C22×Q8—442no—
426C22×D4—114no—
427C22×D4—222no—
428C22×D4—224no—
429C22×D4—222no—
430C22×D4—224no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—112no—
434C23×C4—112no—
435C23×C4—111no—
436C23×C4C22×D1111yescharacteristic
437C23×C4C22×D1112yes—
438C23×C4C22×D1112yes—
439C23×C4C22×D1111yescharacteristic
440C4⋊Q8—2232no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—118no—
444C2×C4⋊C4—224no—
445C2×C4⋊C4—224no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—222no—
448C2×C4⋊C4—222no—
449C2×C4⋊C4—224no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C42—114no—
473C2×C42—224no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42—224no—
477#95—24no—
478#95—22no—
479#95—118no—
480#95—224no—
481#95—224no—
482#95—222no—
483#95—224no—
484C2×C11—82no—
485C2×C11C2×#39311yescharacteristic
486C2×C11#243311yescharacteristic
487C2×C11#243611yescharacteristic
488C2×C11#245212yes—
489C2×C11#245212yes—
490C2×C11#249112yes—
491C2×C11#249112yes—
492C2×C11#254211yescharacteristic
493C2×C11#256311yescharacteristic
494C2×C11#264011yescharacteristic
495C2×C11#285811yescharacteristic
496D11—82no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—112no—
508C24—221no—
509C24—222no—
510C24—221no—
511C24—222no—
512C24—221no—
513C24—221no—
514C24—222no—
515C24—221no—
516C24—221no—
517C24—222no—
518C24Q8×D1112yes—
519C24C23×D1111yescharacteristic
520C2×Q8—2216no—
521C2×Q8—448no—
522C2×Q8—448no—
523C2×Q8—448no—
524C2×Q8—448no—
525C2×Q8—448no—
526C2×Q8—448no—
527C2×D4—2216no—
528C2×D4—228no—
529C2×D4—444no—
530C2×D4—448no—
531C2×D4—444no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—112no—
552C22×C4—114no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—114no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—114no—
560C22×C4—222no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4#433912yes—
581C22×C4D4×D1114yes—
582C22×C4D4×D1114yes—
583C22×C4D4×D1112yes—
584C22×C4#434112yes—
585C4⋊C4—28no—
586C4⋊C4—2216no—
587C4⋊C4—228no—
588C4⋊C4—444no—
589C22⋊C4—48no—
590C22⋊C4—44no—
591C22⋊C4—448no—
592C22⋊C4—448no—
593C22⋊C4—444no—
594C22⋊C4—444no—
595C22⋊C4—448no—
596C22⋊C4—444no—
597C42—228no—
598C42—448no—
599C11#1514411yescharacteristic, complemented, Sylow
600C23—22no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—222no—
624C23—224no—
625C23—222no—
626C23—224no—
627C23—222no—
628C23—442no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—442no—
633C23—442no—
634C23—441no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—441no—
639C23—442no—
640C23—441no—
641C23—441no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—441no—
646C23C2×#433911yescharacteristic
647C23C2×D4×D1111yescharacteristic
648C23C2×D4×D1112yes—
649C23C2×D4×D1112yes—
650C23C2×#434111yescharacteristic
651C23#6703711yescharacteristic
652C23C2×Q8×D1111yescharacteristic
653C23#41×D1112yes—
654C23#41×D1111yescharacteristic
655C23#6704211yescharacteristic
656C23#6704312yes—
657Q8—4432no—
658D4—4416no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—114no—
683C2×C4—118no—
684C2×C4—114no—
685C2×C4—118no—
686C2×C4—114no—
687C2×C4—114no—
688C2×C4—222no—
689C2×C4—224no—
690C2×C4—222no—
691C2×C4—224no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—441no—
711C2×C4#6693814yes—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—444no—
724C22—444no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—882no—
729C22—882no—
730C22—881no—
731C22—881no—
732C22—881no—
733C22—881no—
734C22C2×#6693811yescharacteristic
735C22#1062304211yescharacteristic
736C22#1062306311yescharacteristic
737C22#1062307912yes—
738C22#1062308312yes—
739C22D11×#12011yescharacteristic
740C22#1062312112yes—
741C22#1062312712yes—
742C22#1062312912yes—
743C22#1062313811yescharacteristic
744C22#1062314012yes—
745C22#1062314711yescharacteristic
746C22D11×C22⋊Q812yes—
747C22D11×C22⋊Q811yescharacteristic
748C22#1062316312yes—
749C22#1062316611yescharacteristic
750C22#1062317911yescharacteristic
751C22#1062318612yes—
752C22#1062319312yes—
753C22D11×#12412yes—
754C22D11×#12411yescharacteristic
755C22#1062324112yes—
756C22D11×#12711yescharacteristic
757C4—24no—
758C4—44no—
759C4—44no—
760C4—81no—
761C4—118no—
762C4—224no—
763C4—444no—
764C4—444no—
765C4—881no—
766C2—82no—
767C2—882no—
768C2D11×#39311yescharacteristic
769C2#1307224811yescharacteristic
770C2#1307227211yescharacteristic
771C2#1307245912yes—
772C2#1307246312yes—
773C2#1307297212yes—
774C2#1307297812yes—
775C2#1307356411yescharacteristic
776C2#1307378611yescharacteristic
777C2#1307455111yescharacteristic
778C2#1307697011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1439C2
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#15144
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622286C2semidirect
3. C2×#10622560C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066858C2semidirect
9. Dic11⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1439C2semidirect
51. C22×C22⋊D11Q8semidirect
107. C11⋊#95D4semidirect
219. #1439D11semidirect
416. Dic11#393semidirect
599. C11#15144semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106222862
C2×#106225602
C2×#106225702
#130668622
#130668612
#130668582
Dic11⋊#952
#95×Dic112
C11×#14392
#1514411