Finite Group Databasebeta

← #14960800

Subgroups — #14960800

Order 2816.

2602 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623133C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3#13076904C211yesmaximal, characteristic, complemented
4#13076895C211yesmaximal, characteristic, complemented
5#13075321C214yesmaximal, complemented
6#13075295C214yesmaximal, complemented
7#13074983C214yesmaximal, complemented
8#13074967C214yesmaximal, complemented
9#13074421C211yesmaximal, characteristic, complemented
10#13073960C212yesmaximal, complemented
11#13072004C212yesmaximal, complemented
12#13071997C212yesmaximal, complemented
13#13071969C212yesmaximal, complemented
14#13071233C211yesmaximal, characteristic, complemented
15C11×#2617C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120C2212yes—
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66992C2214yes—
23C2×#66991C2212yescomplemented
24C2×#66990C2212yes—
25C2×#66988C2212yes—
26C2×#66988C2212yescomplemented
27C2×D4×Dic11C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32#10623133—28no—
33C2×#66950C2212yescomplemented
34C2×#66942C2212yescomplemented
35C2×#66936—28no—
36C2×#66936C2214yes—
37C2×#66936C2214yes—
38C2×#66932C2212yescomplemented
39C2×#66931C2212yescomplemented
40C2×#66930C2212yes—
41C11×#397C2212yescomplemented
42C11×#394C2214yescomplemented
43C11×#392C2212yescomplemented
44C11×#386C2212yes—
45C11×#380C2211yescharacteristic
46#10622860C2212yes—
47#10622836C2214yes—
48#10622835C2214yescomplemented
49#10622834C2214yescomplemented
50#10622833C2212yes—
51#10622825C2211yescharacteristic
52#10622823C2212yes—
53#10622600C2212yescomplemented
54#10622600C2212yescomplemented
55#10622585C2214yescomplemented
56#10622574C2214yes—
57#10622572C2214yescomplemented
58#10622570C2214yes—
59#10622570C2214yescomplemented
60#10622569C2214yescomplemented
61#10622568C2212yes—
62#10622563C2212yes—
63#10622563C2214yescomplemented
64#10622562C2212yescomplemented
65#10622561C2214yescomplemented
66#10622561C2214yescomplemented
67#10622561C2214yescomplemented
68#10622560C2212yescomplemented
69#10622557C2214yescomplemented
70#10622555C2212yes—
71#10622289C2214yescomplemented
72#10622282C2214yescomplemented
73#10622281C2214yescomplemented
74#10622274C2214yescomplemented
75#10622268C2214yescomplemented
76#10622260C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×D4×C11C2312yes—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—44no—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×C4×D11—24no—
93C22×C4×D11—44no—
94C22×C4×D11C2312yes—
95C22×C4×D11C2312yes—
96C22×Dic22C2311yescharacteristic
97C11×#121—24no—
98C11×#120—44no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2312yes—
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2312yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118#66992—48no—
119#66991—44no—
120#66990—44no—
121#66988—28no—
122#66988—28no—
123D4×Dic11—28no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×C4⋊Dic11—24no—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2314yes—
135#66977—24no—
136C2×Dic11⋊C4D418yescomplemented
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2314yes—
147#66950—44no—
148#66942—28no—
149#66936—216no—
150#66936—216no—
151#66932—28no—
152#66931—28no—
153#66930—44no—
154C11×#95C2312yes—
155C11×#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161#36722—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C23×D11—22no—
171C23×D11—24no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—42no—
175C23×D11C2412yes—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—22no—
180C2×D4×C11—42no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C22×C4×C11—22no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2414yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—28no—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11—44no—
199C2×C22⋊D11—416no—
200C22×Dic11—24no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206C22×Dic11—44no—
207C22×Dic11C2×D414yes—
208C22×Dic11C2×D414yes—
209C22×Dic11C2414yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—416no—
222C2×Dic22—22no—
223C2×Dic22—42no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—42no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—44no—
231C11×C22⋊C4—44no—
232C22⋊Dic11—24no—
233C22⋊Dic11—24no—
234C22⋊Dic11—24no—
235C22⋊Dic11—28no—
236C22⋊Dic11—24no—
237C22⋊Dic11—24no—
238C22⋊Dic11—44no—
239C22⋊Dic11—44no—
240C22⋊Dic11—44no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—44no—
244(C2×D11)⋊C4—44no—
245C4⋊Dic11—24no—
246C4⋊Dic11—28no—
247C4⋊Dic11—22no—
248C4⋊Dic11—44no—
249C4⋊Dic11—42no—
250Dic11⋊C4—24no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256Dic11⋊C4C2×D418yes—
257Dic11⋊C4C2×D418yes—
258C4×Dic11—24no—
259C4×Dic11—44no—
260C2×#539—111no—
261C22×#123—111no—
262#2848—111no—
263#2847—111no—
264#2707—114no—
265#2705—114no—
266#2682—114no—
267#2681—114no—
268#2626—111no—
269#2617D1111yescharacteristic, complemented
270#2579—112no—
271#2411—112no—
272#2411—112no—
273#2408—112no—
274#2316—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—24no—
286C23×C11—24no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11C22×D412yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C112−1+412yes—
295C23×C11C2511yescharacteristic
296C22×D11—28no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—48no—
304C22×D11—48no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11H(5,𝔽2)14yes—
308D4×C11—48no—
309D4×C11—82no—
310D4×C11—88no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C22⋊D11—416no—
326C22⋊D11—88no—
327C2×Dic11—28no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—44no—
342C2×Dic11—44no—
343C2×Dic11—84no—
344C2×Dic11C22×D414yes—
345C2×Dic11C22×D414yes—
346C4×D11—48no—
347C4×D11—48no—
348Dic22—82no—
349C23×D4—111no—
350C24×C4—111no—
351#539—228no—
352C2×#126—112no—
353C2×#125—112no—
354C2×#123—112no—
355C2×#123—112no—
356C2×#123—114no—
357C2×#123—114no—
358C2×#123—228no—
359C2×C22⋊Q8—111no—
360C2×C22⋊Q8—112no—
361C2×C22⋊Q8—112no—
362C2×#121—112no—
363C2×#121—114no—
364C2×#121C2×D1111yescharacteristic
365C2×#120—112no—
366C2×#120C2×D1112yes—
367C2×C4×D4—112no—
368C2×#117—112no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4C2×D1111yescharacteristic
374#399—112no—
375#398—114no—
376#397C2×D1112yescomplemented
377#396—114no—
378#396—114no—
379#396—114no—
380#396—114no—
381#394—114no—
382#394—114no—
383#394—114no—
384#394C2×D1114yescomplemented
385#393—112no—
386#392—114no—
387#392C2×D1112yescomplemented
388#390—114no—
389#390—114no—
390#390—114no—
391#389—114no—
392#389—114no—
393#388—114no—
394#388—114no—
395#387—114no—
396#386—112no—
397#386—114no—
398#386C2×D1112yes—
399#385—112no—
400#385—112no—
401#385—114no—
402#385—114no—
403#380—111no—
404#380—112no—
405#380—112no—
406#380—112no—
407#380C2×D1111yescharacteristic
408#379—112no—
409#379—112no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—44no—
421C22×C11—44no—
422C22×C11—44no—
423C22×C11—44no—
424C22×C11—88no—
425C22×C11#53714yes—
426C22×C11C23×D411yescharacteristic
427C22×C11C2×H(5,𝔽2)11yescharacteristic
428C22×C11C2×H(5,𝔽2)12yes—
429C22×C11C2×2−1+411yescharacteristic
430C22×C11#58512yes—
431C2×D11—24no—
432C2×D11—24no—
433C2×D11—24no—
434C2×D11—416no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—44no—
444Dic11—24no—
445Dic11—24no—
446Dic11—42no—
447Dic11—42no—
448Dic11—42no—
449Dic11—44no—
450C25—111no—
451C25C22×D1111yescharacteristic
452C22×Q8—111no—
453C22×D4—114no—
454C22×D4—114no—
455C22×D4—224no—
456C22×D4—444no—
457C22×D4C22×D1112yes—
458C22×D4C22×D1111yescharacteristic
459C22×D4C22×D1114yes—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—112no—
464C23×C4—112no—
465C23×C4—112no—
466C23×C4—224no—
467C23×C4—444no—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470#126—228no—
471#125—228no—
472#123—2216no—
473#123—2216no—
474#123—228no—
475#123—228no—
476C22⋊Q8—228no—
477C22⋊Q8—224no—
478C22⋊Q8—444no—
479#121—24no—
480#121—448no—
481#121—444no—
482#120—44no—
483#120—444no—
484C4×D4—228no—
485#117—444no—
486C2×C4⋊C4—118no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1112yes—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4C22×D1112yes—
520C2×C22⋊C4C22×D1112yes—
521C2×C22⋊C4C22×D1112yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—112no—
526C2×C42—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—112no—
531#95—114no—
532#95C22×D1112yes—
533#95C22×D1114yes—
534C2×C11—24no—
535C2×C11—82no—
536C2×C11—82no—
537C2×C11C2×#53711yescharacteristic
538C2×C11#348411yescharacteristic
539C2×C11#348711yescharacteristic
540C2×C11#353412yes—
541C2×C11#353512yes—
542D11—44no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—42no—
547C24—42no—
548C24—112no—
549C24—224no—
550C24—222no—
551C24—222no—
552C24—222no—
553C24—442no—
554C24C23×D1112yes—
555C24C23×D1112yes—
556C24C23×D1111yescharacteristic
557C2×Q8—222no—
558C2×Q8—442no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—44no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—228no—
568C2×D4—228no—
569C2×D4—228no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—4416no—
574C22×C4—22no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—114no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—114no—
581C22×C4—114no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—442no—
594C22×C4—442no—
595C22×C4—4416no—
596C22×C4—442no—
597C22×C4—442no—
598C22×C4—444no—
599C22×C4D4×D1114yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1114yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1111yescharacteristic
604C22×C4C23×D1111yescharacteristic
605C4⋊C4—22no—
606C4⋊C4—42no—
607C4⋊C4—118no—
608C4⋊C4—118no—
609C4⋊C4—228no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—222no—
615C4⋊C4—444no—
616C4⋊C4—444no—
617C4⋊C4—442no—
618C4⋊C4—444no—
619C4⋊C4—444no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—228no—
627C22⋊C4—228no—
628C22⋊C4—228no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—444no—
635C22⋊C4—444no—
636C22⋊C4—444no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C42—224no—
640C42—444no—
641C11#3672211yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—84no—
658C23—84no—
659C23—114no—
660C23—228no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—448no—
668C23—448no—
669C23—444no—
670C23—444no—
671C23C2×D4×D1112yes—
672C23#6703712yes—
673C23#6704312yes—
674C23C24×D1111yescharacteristic
675Q8—882no—
676D4—48no—
677D4—82no—
678D4—88no—
679D4—4416no—
680D4—888no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—114no—
694C2×C4—114no—
695C2×C4—228no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—224no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—448no—
710C2×C4—448no—
711C2×C4—444no—
712C2×C4—444no—
713C2×C4—884no—
714C2×C4C2×D4×D1112yes—
715C2×C4C2×D4×D1112yes—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—88no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—4416no—
735C22—442no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22#1062313914yes—
740C22C22×D4×D1111yescharacteristic
741C22C2×#6703711yescharacteristic
742C22C2×#6704311yescharacteristic
743C22D11×H(5,𝔽2)12yes—
744C22#1062345512yes—
745C4—22no—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—44no—
750C4—224no—
751C4—224no—
752C4—442no—
753C4—442no—
754C4—442no—
755C4—444no—
756C2—24no—
757C2—82no—
758C2—82no—
759C2—444no—
760C2C2×#1062313911yescharacteristic
761C2#1308224811yescharacteristic
762C2#1308227211yescharacteristic
763C2#1308280312yes—
764C2#1308281412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2617C2
hypercenter#2617D11
hypocenterC11#36722
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#10623133C2semidirect
2. C22×#66936C2semidirect
3. #13076904C2semidirect
4. #13076895C2semidirect
5. #13075321C2semidirect
6. #13075295C2semidirect
7. #13074983C2semidirect
8. #13074967C2semidirect
9. #13074421C2semidirect
10. #13073960C2semidirect
11. #13072004C2semidirect
12. #13071997C2semidirect
13. #13071969C2semidirect
14. #13071233C2semidirect
15. C11×#2617C2semidirect
23. C2×#66991C22semidirect
26. C2×#66988C22semidirect
33. C2×#66950C22semidirect
34. C2×#66942C22semidirect
38. C2×#66932C22semidirect
39. C2×#66931C22semidirect
41. C11×#397C22semidirect
42. C11×#394C22semidirect
43. C11×#392C22semidirect
48. #10622835C22semidirect
49. #10622834C22semidirect
53. #10622600C22semidirect
54. #10622600C22semidirect
55. #10622585C22semidirect
57. #10622572C22semidirect
59. #10622570C22semidirect
60. #10622569C22semidirect
63. #10622563C22semidirect
64. #10622562C22semidirect
65. #10622561C22semidirect
66. #10622561C22semidirect
67. #10622561C22semidirect
68. #10622560C22semidirect
69. #10622557C22semidirect
71. #10622289C22semidirect
72. #10622282C22semidirect
73. #10622281C22semidirect
74. #10622274C22semidirect
75. #10622268C22semidirect
76. #10622260C22semidirect
136. C2×Dic11⋊C4D4semidirect
269. #2617D11semidirect
376. #397C2×D11semidirect
384. #394C2×D11semidirect
387. #392C2×D11semidirect
641. C11#36722semidirect

Maximal subgroups

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

subgroupindex
C2×#106231332
C22×#669362
#130769042
#130768952
#130753212
#130752952
#130749832
#130749672
#130744212
#130739602
#130720042
#130719972
#130719692
#130712332
C11×#26172
#3672211