Finite Group Databasebeta

← #14675668

Subgroups — #14675668

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C22×#66930C211yesmaximal, characteristic, complemented
3C2×#10622280C212yesmaximal, complemented
4C2×#10622555C211yesmaximal, characteristic, complemented
5#13066865C211yesmaximal, characteristic, complemented
6#13066855C211yesmaximal, characteristic
7#13066855C211yesmaximal, characteristic
8#13066852C212yesmaximal, complemented
9#13066847C212yesmaximal, complemented
10Dic11⋊#95C212yesmaximal, complemented
11C11×#1440C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×(C22⋊D11)⋊C4—24no—
29C2×(C22⋊D11)⋊C4—24no—
30C2×(C22⋊D11)⋊C4C418yescomplemented
31C2×#66930—24no—
32C2×#66930—28no—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622555—24no—
41#10622280—28no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11C2×C414yes—
53C23×Dic11—24no—
54C23×Dic11—24no—
55C23×Dic11C2×C414yes—
56C23×Dic11D414yes—
57C23×Dic11D414yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11C2×C414yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4C2×C414yes—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—42no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C414yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4C2×C414yes—
96C2×Dic11⋊C4D418yescomplemented
97C2×C4×Dic11—24no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11C2×C414yes—
103(C22⋊D11)⋊C4—232no—
104#66930—232no—
105C11×#95—24no—
106C11×#95—42no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—42no—
112#13871—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11C22×C412yes—
120C24×C11C2×D412yes—
121C24×C11C2×D412yes—
122C24×C11C2411yescharacteristic
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11C22×C412yes—
131C23×D11#4114yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
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—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D414yes—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—28no—
161C22×Dic11—216no—
162C22×Dic11—28no—
163C22×Dic11—216no—
164C22×Dic11—28no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11C22⋊C4116yescomplemented
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C2×D414yes—
188C22×Dic11C2×D412yes—
189C22×Dic11C2×D412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D414yes—
193C22×Dic11#4114yes—
194C22×Dic11#4114yes—
195C2×C4×D11—28no—
196C2×C4×D11—216no—
197C2×C4×D11—44no—
198C2×C4×D11—48no—
199C2×C4×D11—44no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—28no—
202C11×C22⋊C4—44no—
203C22⋊Dic11—28no—
204C22⋊Dic11—44no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208Dic11⋊C4—28no—
209Dic11⋊C4—216no—
210Dic11⋊C4—48no—
211C4×Dic11—216no—
212C4×Dic11—28no—
213C22×C4×D4—111no—
214C22×#117—111no—
215C2×#380—112no—
216C2×#380—111no—
217#1440—111no—
218#1440D1111yescharacteristic, complemented
219#1438—111no—
220#1438—111no—
221#1437—112no—
222#1436—112no—
223C4⋊#95—112no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—24no—
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×C11C2×C22⋊C414yes—
245C23×C11C23×C411yescharacteristic
246C23×C11C22×D411yescharacteristic
247C23×C11C22×D411yescharacteristic
248C23×C11C22×D412yes—
249C23×C11C2×#4112yes—
250C23×C11C2×#4112yes—
251C23×C11C2×#4112yes—
252C23×C11H(5,𝔽2)12yes—
253C23×C112−1+412yes—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—41no—
265C22×D11—42no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11#11714yescomplemented
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—41no—
283C2×C4×C11—42no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
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—42no—
298C2×C4×C11—42no—
299C22⋊D11—232no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—232no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—42no—
313C2×Dic11—42no—
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—42no—
323C2×Dic11C2×C22⋊C414yes—
324C2×Dic11C2×C22⋊C414yes—
325C2×Dic11#11714yescomplemented
326C2×Dic11C4×D418yes—
327C2×Dic11#12014yes—
328C2×Dic11#12118yes—
329C2×Dic11#12314yes—
330C4×D11—416no—
331C23×D4—111no—
332C24×C4—111no—
333C24×C4—111no—
334C2×C4×D4—118no—
335C2×C4×D4—224no—
336C2×C4×D4—224no—
337C2×#117—228no—
338C2×#117—224no—
339C22×C4⋊C4—112no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—112no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4C2×D1111yescharacteristic
350C22×C42—111no—
351C22×C42—112no—
352#380—228no—
353#380—224no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95C2×D1112yes—
360C2×#95C2×D1112yes—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—24no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11C2×#11711yescharacteristic
372C22×C11C2×#11711yescharacteristic
373C22×C11C2×C4×D412yes—
374C22×C11#52012yes—
375C22×C11C2×#12011yescharacteristic
376C22×C11C2×#12112yes—
377C22×C11C2×#12311yescharacteristic
378C22×C11#52512yes—
379C22×C11#52512yes—
380C22×C11#53511yescharacteristic
381C22×C11#53611yescharacteristic
382C22×C11#53712yes—
383C22×C11#54612yes—
384C22×C11#54712yes—
385C22×C11#54812yes—
386C22×C11#55012yes—
387C22×C11#55212yes—
388C22×C11#55312yes—
389C22×C11#55512yes—
390C22×C11#55612yes—
391C2×D11—28no—
392C2×D11—24no—
393C2×D11—42no—
394C2×D11—44no—
395C2×D11—44no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—42no—
400C4×C11—42no—
401C4×C11—44no—
402C4×C11—42no—
403C4×C11—82no—
404Dic11—24no—
405Dic11—24no—
406Dic11—44no—
407Dic11—82no—
408Dic11#38618yes—
409C25—111no—
410C25C22×D1111yescharacteristic
411C22×D4—114no—
412C22×D4—224no—
413C22×D4—224no—
414C22×D4—222no—
415C22×D4—222no—
416C23×C4—111no—
417C23×C4—114no—
418C23×C4—114no—
419C23×C4—114no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—112no—
423C23×C4—114no—
424C23×C4—112no—
425C23×C4—222no—
426C23×C4—222no—
427C23×C4—224no—
428C23×C4—224no—
429C23×C4—224no—
430C23×C4—224no—
431C23×C4C22×D1112yes—
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C23×C4C22×D1112yes—
435C4×D4—2232no—
436#117—2232no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—118no—
439C2×C4⋊C4—224no—
440C2×C4⋊C4—224no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—224no—
444C2×C4⋊C4—224no—
445C2×C4⋊C4—224no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—222no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4C4×D1114yes—
466C2×C42—114no—
467C2×C42—224no—
468C2×C42—224no—
469C2×C42—222no—
470C2×C42—222no—
471C2×C42—224no—
472#95—24no—
473#95—42no—
474#95—224no—
475#95—224no—
476#95—224no—
477#95—224no—
478#95—442no—
479C2×C11—44no—
480C2×C11#228011yescharacteristic
481C2×C11C2×#38611yescharacteristic
482C2×C11#231111yescharacteristic
483C2×C11#235212yes—
484C2×C11#235412yes—
485C2×C11#240712yes—
486C2×C11#241412yes—
487C2×C11#241512yes—
488C2×C11#248512yes—
489D11—44no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—112no—
497C24—114no—
498C24—222no—
499C24—221no—
500C24—221no—
501C24—222no—
502C24—222no—
503C24—222no—
504C24—222no—
505C24C2×C4×D1112yes—
506C24D4×D1112yes—
507C24D4×D1112yes—
508C24C23×D1111yescharacteristic
509C2×D4—228no—
510C2×D4—228no—
511C2×D4—2216no—
512C2×D4—2216no—
513C2×D4—228no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—114no—
539C22×C4—114no—
540C22×C4—1116no—
541C22×C4—112no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—114no—
546C22×C4—114no—
547C22×C4—228no—
548C22×C4—2216no—
549C22×C4—228no—
550C22×C4—2216no—
551C22×C4—2216no—
552C22×C4—228no—
553C22×C4—222no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—222no—
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—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—444no—
572C22×C4—448no—
573C22×C4—444no—
574C22×C4C2×C4×D1112yes—
575C22×C4C2×C4×D1112yes—
576C22×C4D4×D1114yes—
577C4⋊C4—2216no—
578C4⋊C4—228no—
579C4⋊C4—448no—
580C22⋊C4—28no—
581C22⋊C4—28no—
582C22⋊C4—44no—
583C22⋊C4—228no—
584C22⋊C4—228no—
585C22⋊C4—448no—
586C22⋊C4—448no—
587C22⋊C4—444no—
588C42—228no—
589C42—2216no—
590C11#1387111yescharacteristic, complemented, Sylow
591C23—22no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—114no—
612C23—224no—
613C23—222no—
614C23—222no—
615C23—224no—
616C23—224no—
617C23—224no—
618C23—224no—
619C23—224no—
620C23—224no—
621C23—224no—
622C23—442no—
623C23—441no—
624C23—441no—
625C23—442no—
626C23—442no—
627C23—442no—
628C23—441no—
629C23—441no—
630C23—442no—
631C23—442no—
632C23C22⋊C4×D1114yes—
633C23C22×C4×D1111yescharacteristic
634C23C2×D4×D1111yescharacteristic
635C23C2×D4×D1111yescharacteristic
636C23C2×D4×D1112yes—
637C23#6703712yes—
638C23#41×D1112yes—
639C23#41×D1112yes—
640C23#41×D1112yes—
641C23#6704312yes—
642D4—2232no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—114no—
668C2×C4—118no—
669C2×C4—114no—
670C2×C4—118no—
671C2×C4—114no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—2232no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—224no—
678C2×C4—222no—
679C2×C4—224no—
680C2×C4—222no—
681C2×C4—224no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—4416no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—224no—
708C22—228no—
709C22—444no—
710C22—444no—
711C22—442no—
712C22—444no—
713C22—444no—
714C22—442no—
715C22—444no—
716C22C2×C22⋊C4×D1111yescharacteristic
717C22D11×#11711yescharacteristic
718C22D11×#11711yescharacteristic
719C22C4×D4×D1112yes—
720C22#1062307712yes—
721C22D11×#12011yescharacteristic
722C22#1062312311yescharacteristic
723C22#1062312812yes—
724C22#1062313012yes—
725C22D11×#12112yes—
726C22#1062314112yes—
727C22#1062317911yescharacteristic
728C22D11×#12311yescharacteristic
729C22#1062318612yes—
730C22#1062318712yes—
731C22#1062318712yes—
732C22#1062319212yes—
733C22#1062320112yes—
734C22#1062320812yes—
735C22#1062323312yes—
736C22#1062323912yes—
737C4—44no—
738C4—42no—
739C4—42no—
740C4—82no—
741C4—118no—
742C4—224no—
743C4—224no—
744C4—444no—
745C4—882no—
746C2—44no—
747C2—444no—
748C2#1307099611yescharacteristic
749C2D11×#38611yescharacteristic
750C2#1307120311yescharacteristic
751C2#1307154412yes—
752C2#1307156212yes—
753C2#1307195612yes—
754C2#1307202912yes—
755C2#1307204012yes—
756C2#1307290812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#13871
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C22×#66930C2semidirect
3. C2×#10622280C2semidirect
4. C2×#10622555C2semidirect
5. #13066865C2semidirect
8. #13066852C2semidirect
9. #13066847C2semidirect
10. Dic11⋊#95C2semidirect
11. C11×#1440C2semidirect
30. C2×(C22⋊D11)⋊C4C4semidirect
96. C2×Dic11⋊C4D4semidirect
183. C22×Dic11C22⋊C4semidirect
218. #1440D11semidirect
274. C22×D11#117semidirect
325. C2×Dic11#117semidirect
590. C11#13871semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C22×#669302
C2×#106222802
C2×#106225552
#130668652
#130668552
#130668522
#130668472
Dic11⋊#952
C11×#14402
#1387111