Finite Group Databasebeta

← #14676160

Subgroups — #14676160

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D11C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic, complemented
3C2×#10622542C211yesmaximal, characteristic, complemented
4C2×#10622587C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#13066886C214yesmaximal, complemented
8(C2×D11)⋊#95C214yesmaximal
9C2×C11×#391C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×Q8×D11—24no—
12C22×Q8×D11—24no—
13C22×Q8×D11—24no—
14C22×Q8×D11—24no—
15C22×Q8×D11—24no—
16C22×Q8×D11—24no—
17C22×Q8×D11C418yescomplemented
18C23×C4×D11C2212yes—
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2212yes—
21C23×Dic22C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C11×#391—24no—
29C2×C11×#95C2214yes—
30#10622843—24no—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2214yes—
33C2×C11⋊#95C2214yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622600—24no—
37#10622587—24no—
38C4×(C2×D11)⋊C4—24no—
39#10622542—24no—
40C24×D11C2311yescharacteristic
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11C2×C414yes—
46C22×Q8×C11D414yes—
47C22×Q8×C11D414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C2×Q8×D11—232no—
57C2×Q8×D11—232no—
58C2×Q8×D11—232no—
59C2×Q8×D11—232no—
60C2×Q8×D11—232no—
61C2×Q8×D11—232no—
62C2×Q8×D11—232no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—24no—
70C22×C4×D11—22no—
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11C2×C418yes—
74C22×C4×D11C2×C414yes—
75C22×C4×D11D414yes—
76C22×C4×D11D414yes—
77C22×Dic22—24no—
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—22no—
81C22×Dic22—24no—
82C22×Dic22—22no—
83C22×Dic22—24no—
84C22×Dic22—24no—
85C22×Dic22—24no—
86C22×Dic22—24no—
87C22×Dic22C2×C418yes—
88C22×Dic22C2×C414yes—
89C22×Dic22D414yes—
90C22×Dic22D414yes—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11—22no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—28no—
101C2×(C2×D11)⋊C4Q818yescomplemented
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C11×#95—28no—
109C11⋊#95—28no—
110C11⋊#95—28no—
111C11⋊#95—24no—
112C11⋊#95—28no—
113C11⋊#95—24no—
114#13922—111nomaximal, Sylow
115C24×C11C2411yescharacteristic
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11C22×C412yes—
123C23×D11C2×D412yes—
124C23×D11C2×D412yes—
125C23×D11C2×Q814yes—
126C23×D11#4114yes—
127C2×Q8×C11—28no—
128C2×Q8×C11—28no—
129C2×Q8×C11—28no—
130C2×Q8×C11—28no—
131C2×Q8×C11—28no—
132C2×Q8×C11—28no—
133C2×Q8×C11C22⋊C4116yescomplemented
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—24no—
148C22×C4×C11—24no—
149C22×C4×C11C22×C414yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×Q814yescomplemented
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11C22×C412yes—
180C22×Dic11C22×C414yes—
181C22×Dic11C2×D412yes—
182C22×Dic11C2×D412yes—
183C22×Dic11C2×D414yes—
184C22×Dic11C2×D414yes—
185C22×Dic11C2×Q814yescomplemented
186Q8×D11—2256no—
187C2×C4×D11—216no—
188C2×C4×D11—216no—
189C2×C4×D11—216no—
190C2×C4×D11—216no—
191C2×C4×D11—216no—
192C2×C4×D11—216no—
193C2×C4×D11—28no—
194C2×C4×D11—216no—
195C2×C4×D11—28no—
196C2×C4×D11—28no—
197C2×C4×D11—28no—
198C2×C4×D11—28no—
199C2×C4×D11—28no—
200C2×C4×D11C22⋊C4116yes—
201C2×Dic22—216no—
202C2×Dic22—216no—
203C2×Dic22—216no—
204C2×Dic22—216no—
205C2×Dic22—216no—
206C2×Dic22—216no—
207C2×Dic22—28no—
208C2×Dic22—216no—
209C2×Dic22—28no—
210C2×Dic22—28no—
211C2×Dic22—28no—
212C2×Dic22—28no—
213C2×Dic22—28no—
214C2×Dic22C22⋊C4116yescomplemented
215C11×C4⋊C4—44no—
216C42×C11—44no—
217(C2×D11)⋊C4—216no—
218(C2×D11)⋊C4—48no—
219C4⋊Dic11—44no—
220C4×Dic11—44no—
221C24×Q8—111no—
222C2×#391—111no—
223C2×#391—111no—
224C2×#391—111no—
225C2×#391D1111yescharacteristic, complemented
226C2×#380—111no—
227C2×C4×C22⋊C4—111no—
228#1446—114no—
229C22⋊#95—114no—
230C23×C11C23×C411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D411yescharacteristic
237C23×C11C22×Q812yes—
238C23×C11C2×#4112yes—
239C23×C112−1+412yes—
240C23×C112−1+412yes—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—24no—
250C22×D11—22no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11C2×C22⋊C414yes—
260C22×D11C4×Q818yes—
261C22×D11C22⋊Q818yes—
262C22×D11#12414yes—
263C22×D11C4⋊Q814yes—
264Q8×C11—232no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—44no—
282C2×C4×C11—44no—
283C2×C4×C11C2×C22⋊C414yes—
284C2×C4×C11C2×C22⋊C414yes—
285C2×C4×C11C2×C22⋊C418yes—
286C2×C4×C11C2×C22⋊C414yes—
287C2×C4×C11#12014yes—
288C2×C4×C11#12014yes—
289C2×C4×C11#12014yes—
290C2×C4×C11#12014yes—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—44no—
314C2×Dic11—44no—
315C2×Dic11C2×C22⋊C414yes—
316C2×Dic11C2×C22⋊C418yes—
317C4×D11—264no—
318C4×D11—232no—
319Dic22—264no—
320Dic22—232no—
321C23×Q8—118no—
322C23×Q8—111no—
323C23×Q8—112no—
324C23×Q8—224no—
325C23×Q8—224no—
326C23×Q8—224no—
327C23×Q8—224no—
328C23×Q8—224no—
329C23×Q8—224no—
330C23×Q8C2×D1111yescharacteristic
331C24×C4—111no—
332C24×C4—112no—
333C22×C4⋊C4—111no—
334C22×C4⋊C4C2×D1111yescharacteristic
335C22×C22⋊C4—112no—
336C22×C22⋊C4—112no—
337C22×C42—111no—
338C22×C42C2×D1111yescharacteristic
339#391—24no—
340#391—224no—
341#391—224no—
342#391—224no—
343#380—224no—
344C4×C22⋊C4—224no—
345C2×#95—114no—
346C2×#95—114no—
347C2×#95—114no—
348C2×#95—112no—
349C2×#95—112no—
350C2×#95C2×D1114yes—
351C22×C11C22×C22⋊C411yescharacteristic
352C22×C11C22×C22⋊C411yescharacteristic
353C22×C11C22×C22⋊C411yescharacteristic
354C22×C11C2×C4×Q812yes—
355C22×C11#51912yes—
356C22×C11C2×#12011yescharacteristic
357C22×C11C2×#12011yescharacteristic
358C22×C11C2×#12011yescharacteristic
359C22×C11C2×#12011yescharacteristic
360C22×C11C2×C22⋊Q812yes—
361C22×C11C2×#12411yescharacteristic
362C22×C11C2×C4⋊Q811yescharacteristic
363C22×C11#53611yescharacteristic
364C22×C11#53612yes—
365C22×C11#53611yescharacteristic
366C22×C11#54812yes—
367C22×C11#54812yes—
368C22×C11#54812yes—
369C22×C11#54812yes—
370C22×C11D4×Q812yes—
371C22×C11D4×Q812yes—
372C22×C11D4×Q812yes—
373C22×C11D4×Q812yes—
374C2×D11—24no—
375C2×D11—28no—
376C2×D11—28no—
377C2×D11—28no—
378C2×D11—28no—
379C2×D11—24no—
380C2×D11—24no—
381C2×D11—24no—
382C2×D11—24no—
383C2×D11—24no—
384C2×D11#39118yescomplemented
385C4×C11—28no—
386C4×C11—44no—
387C4×C11—82no—
388C4×C11#37918yes—
389Dic11—24no—
390Dic11—28no—
391Dic11—44no—
392Dic11—82no—
393C25—111no—
394C22×Q8—22no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—114no—
399C22×Q8—118no—
400C22×Q8—114no—
401C22×Q8—114no—
402C22×Q8—224no—
403C22×Q8—224no—
404C22×Q8—224no—
405C22×Q8—224no—
406C22×Q8—2232no—
407C22×Q8—2232no—
408C22×Q8—2232no—
409C22×Q8—2232no—
410C22×Q8—2232no—
411C22×Q8—2232no—
412C22×Q8—2232no—
413C22×Q8—224no—
414C22×Q8—222no—
415C22×Q8—222no—
416C22×Q8—222no—
417C22×Q8—224no—
418C22×Q8—222no—
419C22×Q8C4×D1114yes—
420C22×Q8D4414yes—
421C22×Q8C22⋊D1114yes—
422C23×C4—111no—
423C23×C4—112no—
424C23×C4—114no—
425C23×C4—114no—
426C23×C4—114no—
427C23×C4—112no—
428C23×C4—118no—
429C23×C4—112no—
430C23×C4—224no—
431C23×C4—224no—
432C23×C4—224no—
433C23×C4—224no—
434C23×C4—224no—
435C23×C4—222no—
436C23×C4—222no—
437C23×C4—222no—
438C23×C4—224no—
439C23×C4—222no—
440C23×C4C22×D1112yes—
441C23×C4C22×D1112yes—
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—222no—
448C2×C4⋊C4—222no—
449C2×C4⋊C4—222no—
450C2×C22⋊C4—118no—
451C2×C22⋊C4—224no—
452C2×C22⋊C4—224no—
453C2×C22⋊C4—224no—
454C2×C22⋊C4—228no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—222no—
459C2×C42—222no—
460C2×C42—222no—
461#95—28no—
462#95—224no—
463#95—224no—
464#95—228no—
465#95—228no—
466#95—228no—
467C2×C11C2×#37911yescharacteristic
468C2×C11C2×#39111yescharacteristic
469C2×C11#231011yescharacteristic
470C2×C11Q8×C22⋊C412yes—
471C2×C11Q8×C22⋊C412yes—
472C2×C11#240912yes—
473C2×C11#240912yes—
474C2×C11#243411yescharacteristic
475C2×C11#243411yescharacteristic
476C2×C11#243611yescharacteristic
477C2×C11#243611yescharacteristic
478D11—28no—
479C24—112no—
480C24—112no—
481C24—112no—
482C24—114no—
483C24—114no—
484C24—221no—
485C24—221no—
486C24—221no—
487C24—222no—
488C24—222no—
489C24—221no—
490C24C23×D1111yescharacteristic
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—28no—
497C2×Q8—1116no—
498C2×Q8—2216no—
499C2×Q8—2216no—
500C2×Q8—2216no—
501C2×Q8—2216no—
502C2×Q8—2216no—
503C2×Q8—2216no—
504C2×Q8—22256no—
505C2×Q8—228no—
506C2×Q8—228no—
507C2×Q8—228no—
508C2×Q8—2216no—
509C2×Q8—228no—
510C2×Q8—228no—
511C2×Q8—228no—
512C2×Q8(C2×D11)⋊C4116yescomplemented
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—112no—
529C22×C4—114no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—114no—
533C22×C4—114no—
534C22×C4—1116no—
535C22×C4—114no—
536C22×C4—2216no—
537C22×C4—2216no—
538C22×C4—2216no—
539C22×C4—2216no—
540C22×C4—2216no—
541C22×C4—2216no—
542C22×C4—221no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—221no—
546C22×C4—222no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—222no—
550C22×C4—228no—
551C22×C4—228no—
552C22×C4—228no—
553C22×C4—2216no—
554C22×C4—228no—
555C22×C4—228no—
556C22×C4—228no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—224no—
567C22×C4—224no—
568C22×C4C2×C4×D1114yes—
569C22×C4C2×C4×D1112yes—
570C22×C4C2×D4414yes—
571C22×C4C2×D4412yes—
572C22×C4D4×D1112yes—
573C22×C4D4×D1112yes—
574C22×C4D4×D1112yes—
575C22×C4D4×D1112yes—
576C22×C4Q8×D1114yescomplemented
577C22×C4C2×C22⋊D1114yes—
578C22×C4C2×C22⋊D1112yes—
579C4⋊C4—44no—
580C4⋊C4—444no—
581C22⋊C4—2216no—
582C22⋊C4—448no—
583C42—44no—
584C42—444no—
585C11#1392211yescharacteristic, complemented, Sylow
586C23—114no—
587C23—114no—
588C23—118no—
589C23—118no—
590C23—114no—
591C23—222no—
592C23—224no—
593C23—222no—
594C23—222no—
595C23—222no—
596C23—222no—
597C23—222no—
598C23—222no—
599C23—224no—
600C23—224no—
601C23—224no—
602C23—224no—
603C23—224no—
604C23—224no—
605C23—224no—
606C23—224no—
607C23—222no—
608C23—224no—
609C23C22×C4×D1111yescharacteristic
610C23C22×D4411yescharacteristic
611C23C2×D4×D1111yescharacteristic
612C23C2×D4×D1111yescharacteristic
613C23C2×D4×D1111yescharacteristic
614C23C2×D4×D1111yescharacteristic
615C23C2×Q8×D1112yes—
616C23#6704012yes—
617C23#41×D1112yes—
618C23#6704312yes—
619C23C22×C22⋊D1111yescharacteristic
620Q8—232no—
621Q8—2264no—
622Q8—2232no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—114no—
642C2×C4—118no—
643C2×C4—2264no—
644C2×C4—222no—
645C2×C4—224no—
646C2×C4—222no—
647C2×C4—224no—
648C2×C4—222no—
649C2×C4—224no—
650C2×C4—222no—
651C2×C4—224no—
652C2×C4—222no—
653C2×C4—224no—
654C2×C4—222no—
655C2×C4—224no—
656C2×C4—2232no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—224no—
660C2×C4—442no—
661C2×C4—442no—
662C2×C4—442no—
663C2×C4—442no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—444no—
667C2×C4—444no—
668C2×C4—442no—
669C2×C4C22⋊C4×D1114yes—
670C2×C4C22⋊C4×D1114yes—
671C2×C4#6693514yes—
672C2×C4#6693514yes—
673C2×C4C2×(C2×D11)⋊C418yes—
674C2×C4C2×(C2×D11)⋊C414yes—
675C2×C4#6699014yes—
676C2×C4#6699014yes—
677C22—118no—
678C22—228no—
679C22—228no—
680C22—224no—
681C22—228no—
682C22—228no—
683C22—224no—
684C22—224no—
685C22—224no—
686C22—224no—
687C22—224no—
688C22C2×C22⋊C4×D1111yescharacteristic
689C22C2×C22⋊C4×D1111yescharacteristic
690C22C2×#6693511yescharacteristic
691C22C2×#6693511yescharacteristic
692C22C4×Q8×D1112yes—
693C22#1062310312yes—
694C22Q8×D4412yes—
695C22#1062310712yes—
696C22D11×C22⋊Q812yes—
697C22#1062315912yes—
698C22#1062316312yes—
699C22#1062316412yes—
700C22D11×#12411yescharacteristic
701C22#1062320611yescharacteristic
702C22#1062320812yes—
703C22D11×C4⋊Q811yescharacteristic
704C22#1062325511yescharacteristic
705C22#1062325812yes—
706C22C22×(C2×D11)⋊C411yescharacteristic
707C22C2×#6699011yescharacteristic
708C22C2×#6699011yescharacteristic
709C22Q8×C22⋊D1112yes—
710C22#1062336212yes—
711C4—28no—
712C4—44no—
713C4—82no—
714C4—224no—
715C4—228no—
716C4—444no—
717C4—882no—
718C4#1062256818yes—
719C2—228no—
720C2C2×#1062256811yescharacteristic
721C2D11×#39111yescharacteristic
722C2#1307119911yescharacteristic
723C2Q8×(C2×D11)⋊C412yes—
724C2#1307145012yes—
725C2#1307197712yes—
726C2#1307197912yes—
727C2#1307225711yescharacteristic
728C2#1307225911yescharacteristic
729C2#1307227111yescharacteristic
730C2#1307227311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#391D11
hypocenterC11#13922
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#10622843C2semidirect
3. C2×#10622542C2semidirect
4. C2×#10622587C2semidirect
7. #13066886C2semidirect
9. C2×C11×#391C2semidirect
17. C22×Q8×D11C4semidirect
101. C2×(C2×D11)⋊C4Q8semidirect
133. C2×Q8×C11C22⋊C4semidirect
159. C22×C4×C11C2×Q8semidirect
185. C22×Dic11C2×Q8semidirect
214. C2×Dic22C22⋊C4semidirect
225. C2×#391D11semidirect
384. C2×D11#391semidirect
512. C2×Q8(C2×D11)⋊C4semidirect
576. C22×C4Q8×D11semidirect
585. C11#13922semidirect

Maximal subgroups

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

subgroupindex
C23×Q8×D112
C2×#106228432
C2×#106225422
C2×#106225872
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668862
(C2×D11)⋊#952
C2×C11×#3912
#1392211