Finite Group Databasebeta

← #14960784

Subgroups — #14960784

Order 2816.

2970 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic, complemented
3#13076896C212yesmaximal, complemented
4#13075311C214yesmaximal, complemented
5#13075307C214yesmaximal, complemented
6#13074943C214yesmaximal, complemented
7#13074941C214yesmaximal, complemented
8#13074364C212yesmaximal, complemented
9#13073544C212yesmaximal, complemented
10#13073106C212yesmaximal, complemented
11#13071944C211yesmaximal, characteristic, complemented
12#13071939C211yesmaximal, characteristic, complemented
13#13071926C211yesmaximal, characteristic, complemented
14#13071212C211yesmaximal, characteristic, complemented
15C11×#2403C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic, complemented
20C2×C11×#120C2212yescomplemented
21C2×C11×#120C2212yescomplemented
22C2×#67006C2212yescomplemented
23C2×#67006C2212yescomplemented
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic, complemented
27#10623335—28no—
28C2×#66992C2212yes—
29C2×#66992C2212yes—
30C2×#66992C2214yescomplemented
31C2×#66990C2212yescomplemented
32C2×#66990C2212yescomplemented
33C2×#66988—28no—
34C2×#66988C2212yescomplemented
35C2×#66988C2214yescomplemented
36C2×#66988C2214yescomplemented
37C2×#66988C2212yescomplemented
38C2×#66982C2212yescomplemented
39C22×Dic11⋊C4C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41C2×#66939C2212yescomplemented
42C11×#392C2214yes—
43C11×#386C2212yescomplemented
44C11×#386C2212yescomplemented
45C11×#379C2211yescharacteristic
46#10622860C2211yescharacteristic
47#10622860C2212yescomplemented
48#10622836C2214yes—
49#10622836C2214yescomplemented
50#10622835C2214yescomplemented
51#10622834C2214yescomplemented
52#10622833C2212yescomplemented
53#10622833C2212yescomplemented
54#10622833C2214yescomplemented
55#10622826C2212yescomplemented
56#10622823C2212yescomplemented
57#10622574C2214yescomplemented
58#10622572C2214yescomplemented
59#10622571C2212yescomplemented
60#10622571C2214yescomplemented
61#10622570C2214yescomplemented
62#10622570C2214yescomplemented
63#10622568C2212yescomplemented
64#10622565C2214yescomplemented
65#10622563C2212yescomplemented
66#10622562C2214yescomplemented
67#10622561C2214yescomplemented
68#10622558C2214yescomplemented
69#10622557C2214yescomplemented
70#10622555C2214yescomplemented
71#10622555C2212yescomplemented
72C22⋊C4×Dic11C2212yescomplemented
73#10622289C2214yescomplemented
74#10622288C2214yescomplemented
75#10622270C2214yescomplemented
76#10622263C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—44no—
84C22×D4×C11—44no—
85C22×D4×C11C2312yes—
86C22×D4×C11C2312yes—
87C22×D4×C11C2312yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—24no—
93C22×C22⋊D11—44no—
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2314yes—
99C23×Dic11—24no—
100C23×Dic11—44no—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2314yes—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C11×#120—44no—
108C11×#120—44no—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114#67006—28no—
115#67006—44no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11D418yescomplemented
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2312yes—
131C2×C22⋊Dic11C2312yes—
132#66992—28no—
133#66992—28no—
134#66992—48no—
135#66990—28no—
136#66990—44no—
137#66988—216no—
138#66988—216no—
139#66988—28no—
140#66988—44no—
141#66982—28no—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×C4⋊Dic11C2314yes—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×C4×Dic11C2314yes—
157#66939—44no—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164#36721—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—24no—
167C24×C11—24no—
168C24×C11—24no—
169C24×C11—22no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11—42no—
176C24×C11C2×D414yes—
177C24×C11C2412yes—
178C24×C11C2411yescharacteristic
179C24×C11C2411yescharacteristic
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—42no—
184C23×D11—42no—
185C23×D11—42no—
186C23×D11C2412yes—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—28no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—416no—
203C2×D4×C11—416no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11C2414yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—42no—
219C2×C22⋊D11—42no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—416no—
225C22×Dic11—28no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—24no—
230C22×Dic11—28no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—44no—
234C22×Dic11—42no—
235C22×Dic11—42no—
236C22×Dic11—416no—
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D414yes—
239C22×Dic11C2414yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—42no—
247C11×C22⋊C4—42no—
248C11×C22⋊C4—44no—
249C11×C22⋊C4—44no—
250C22⋊Dic11—28no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—44no—
257C22⋊Dic11—42no—
258C22⋊Dic11—44no—
259C22⋊Dic11—42no—
260C22⋊Dic11—44no—
261C22⋊Dic11C2×D418yes—
262C22⋊Dic11C2×D418yes—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268C4⋊Dic11—44no—
269Dic11⋊C4—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C4×Dic11—44no—
276C2×#534—111no—
277C22×#123—111no—
278#2847—112no—
279#2706—114no—
280#2706—114no—
281#2678—114no—
282#2678—114no—
283#2618—112no—
284#2539—112no—
285#2504—112no—
286#2405—111no—
287#2405—111no—
288#2403—111no—
289#2403D1111yescharacteristic, complemented
290#2312—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—24no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—24no—
304C23×C11—28no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—24no—
308C23×C11—22no—
309C23×C11—24no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—416no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—88no—
317C23×C11—82no—
318C23×C11—82no—
319C23×C11—88no—
320C23×C11C22×D412yes—
321C23×C11C22×D412yes—
322C23×C11C22×D412yes—
323C23×C11H(5,𝔽2)14yes—
324C23×C11H(5,𝔽2)14yes—
325C23×C11C2511yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—24no—
331C22×D11—44no—
332C22×D11—82no—
333C22×D11—82no—
334C22×D11—88no—
335D4×C11—48no—
336D4×C11—48no—
337D4×C11—48no—
338D4×C11—48no—
339D4×C11—88no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—24no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
351C22⋊D11—48no—
352C22⋊D11—48no—
353C22⋊D11—84no—
354C22⋊D11—84no—
355C22⋊D11—88no—
356C2×Dic11—24no—
357C2×Dic11—24no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11—44no—
369C2×Dic11—44no—
370C2×Dic11—416no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11C22×D414yes—
375C2×Dic11C22×D414yes—
376C23×D4—111no—
377C23×D4C2×D1111yescharacteristic
378C23×D4C2×D1111yescharacteristic
379C24×C4—111no—
380#534—228no—
381C2×#123—114no—
382C2×#123—114no—
383C2×#123—112no—
384C2×#123—112no—
385C2×#123—112no—
386C2×#123—112no—
387C2×#123—228no—
388C2×#121—112no—
389C2×#121—112no—
390C2×#121—114no—
391C2×#120—112no—
392C2×#120—112no—
393C2×#120—112no—
394C2×#120—112no—
395C2×#120C2×D1112yescomplemented
396C2×#120C2×D1112yescomplemented
397C22×C4⋊C4—111no—
398C22×C4⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4—111no—
402#399—114no—
403#398—114no—
404#397—114no—
405#397—114no—
406#396—114no—
407#396—114no—
408#394—114no—
409#394—114no—
410#394—114no—
411#392—114no—
412#392—114no—
413#392C2×D1114yes—
414#390—114no—
415#390—114no—
416#390—114no—
417#388—114no—
418#388—114no—
419#386—112no—
420#386—114no—
421#386—112no—
422#386—112no—
423#386—112no—
424#386—114no—
425#386C2×D1112yescomplemented
426#386C2×D1112yescomplemented
427#385—112no—
428#385—112no—
429#382—114no—
430#380—112no—
431#380—114no—
432#379—111no—
433#379—112no—
434#379—112no—
435#379C2×D1111yescharacteristic
436C4×C22⋊C4—112no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—28no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—24no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—28no—
448C22×C11—416no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—44no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—44no—
458C22×C11—44no—
459C22×C11—88no—
460C22×C11—88no—
461C22×C11#53514yes—
462C22×C11C23×D411yescharacteristic
463C22×C11C2×H(5,𝔽2)12yes—
464C22×C11C2×H(5,𝔽2)12yes—
465C22×C11#58512yes—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—44no—
470C2×D11—44no—
471C2×D11—88no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—44no—
475Dic11—24no—
476Dic11—24no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480Dic11—44no—
481C25—111no—
482C25C22×D1111yescharacteristic
483C25C22×D1111yescharacteristic
484C25C22×D1111yescharacteristic
485C22×D4—24no—
486C22×D4—24no—
487C22×D4—44no—
488C22×D4—44no—
489C22×D4—112no—
490C22×D4—112no—
491C22×D4—114no—
492C22×D4—112no—
493C22×D4—112no—
494C22×D4—224no—
495C22×D4—444no—
496C22×D4C22×D1112yes—
497C22×D4C22×D1112yes—
498C22×D4C22×D1112yes—
499C22×D4C22×D1112yes—
500C22×D4C22×D1114yes—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—114no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—224no—
508C23×C4—444no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511#123—228no—
512#123—2216no—
513#123—2216no—
514#123—228no—
515#123—444no—
516#123—444no—
517#121—228no—
518#121—228no—
519#121—448no—
520#120—44no—
521#120—44no—
522#120—228no—
523#120—228no—
524#120—444no—
525#120—444no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—224no—
534C2×C4⋊C4—224no—
535C2×C22⋊C4—118no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—112no—
546C2×C22⋊C4—112no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1112yes—
558C2×C22⋊C4C22×D1114yes—
559C2×C22⋊C4C22×D1114yes—
560C2×C22⋊C4C22×D1112yes—
561C2×C42—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95—114no—
567#95C22×D1114yes—
568C2×C11—24no—
569C2×C11—42no—
570C2×C11—44no—
571C2×C11—42no—
572C2×C11—82no—
573C2×C11C2×#53511yescharacteristic
574C2×C11#348411yescharacteristic
575C2×C11#348511yescharacteristic
576C2×C11#353414yes—
577D11—82no—
578C24—22no—
579C24—24no—
580C24—24no—
581C24—24no—
582C24—22no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—42no—
589C24—112no—
590C24—222no—
591C24—442no—
592C24—442no—
593C24—442no—
594C24D4×D1114yes—
595C24C23×D1112yes—
596C24C23×D1111yescharacteristic
597C24C23×D1111yescharacteristic
598C24C23×D1112yes—
599C24C23×D1111yescharacteristic
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—28no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—416no—
616C2×D4—416no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—228no—
624C2×D4—442no—
625C2×D4—442no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—4416no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—114no—
638C22×C4—114no—
639C22×C4—114no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—228no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—228no—
648C22×C4—224no—
649C22×C4—442no—
650C22×C4—444no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—4416no—
655C22×C4C23×D1114yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C4⋊C4—228no—
659C4⋊C4—228no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—444no—
663C4⋊C4—444no—
664C4⋊C4—444no—
665C22⋊C4—24no—
666C22⋊C4—44no—
667C22⋊C4—42no—
668C22⋊C4—44no—
669C22⋊C4—42no—
670C22⋊C4—118no—
671C22⋊C4—118no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—228no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—442no—
685C22⋊C4—444no—
686C22⋊C4—444no—
687C22⋊C4—442no—
688C42—444no—
689C11#3672111yescharacteristic, complemented, Sylow
690C23—22no—
691C23—22no—
692C23—28no—
693C23—22no—
694C23—24no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—28no—
704C23—22no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—44no—
710C23—44no—
711C23—416no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—88no—
716C23—82no—
717C23—82no—
718C23—88no—
719C23—222no—
720C23—222no—
721C23—224no—
722C23—222no—
723C23—224no—
724C23—444no—
725C23—882no—
726C23—882no—
727C23—888no—
728C23C2×D4×D1112yes—
729C23C2×D4×D1112yes—
730C23C2×D4×D1112yes—
731C23#6703714yes—
732C23#6703714yes—
733C23C24×D1111yescharacteristic
734D4—48no—
735D4—48no—
736D4—48no—
737D4—48no—
738D4—88no—
739D4—448no—
740D4—448no—
741D4—884no—
742D4—884no—
743D4—888no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—114no—
756C2×C4—114no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—224no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4—4416no—
772C2×C4—444no—
773C2×C4—444no—
774C2×C4—444no—
775C22—22no—
776C22—22no—
777C22—28no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—28no—
786C22—416no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—88no—
798C22—88no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—444no—
803C22—444no—
804C22—888no—
805C22#1062312314yes—
806C22C22×D4×D1111yescharacteristic
807C22C2×#6703712yes—
808C22C2×#6703712yes—
809C22#1062345512yes—
810C4—42no—
811C4—42no—
812C4—44no—
813C4—224no—
814C4—224no—
815C4—442no—
816C4—442no—
817C4—442no—
818C4—444no—
819C2—24no—
820C2—44no—
821C2—42no—
822C2—42no—
823C2—82no—
824C2—882no—
825C2C2×#1062312311yescharacteristic
826C2#1308224511yescharacteristic
827C2#1308225711yescharacteristic
828C2#1308279414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2403C2
hypercenter#2403D11
hypocenterC11#36721
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2403

Complements

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

NH ≅ G/Ntype
1. C2×#10623335C2semidirect
2. C22×#66988C2semidirect
3. #13076896C2semidirect
4. #13075311C2semidirect
5. #13075307C2semidirect
6. #13074943C2semidirect
7. #13074941C2semidirect
8. #13074364C2semidirect
9. #13073544C2semidirect
10. #13073106C2semidirect
11. #13071944C2semidirect
12. #13071939C2semidirect
13. #13071926C2semidirect
14. #13071212C2semidirect
15. C11×#2403C2semidirect
19. C24×Dic11C22semidirect
20. C2×C11×#120C22semidirect
21. C2×C11×#120C22semidirect
22. C2×#67006C22semidirect
23. C2×#67006C22semidirect
26. C22×C22⋊Dic11C22semidirect
30. C2×#66992C22semidirect
31. C2×#66990C22semidirect
32. C2×#66990C22semidirect
34. C2×#66988C22semidirect
35. C2×#66988C22semidirect
36. C2×#66988C22semidirect
37. C2×#66988C22semidirect
38. C2×#66982C22semidirect
39. C22×Dic11⋊C4C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C2×#66939C22semidirect
43. C11×#386C22semidirect
44. C11×#386C22semidirect
47. #10622860C22semidirect
49. #10622836C22semidirect
50. #10622835C22semidirect
51. #10622834C22semidirect
52. #10622833C22semidirect
53. #10622833C22semidirect
54. #10622833C22semidirect
55. #10622826C22semidirect
56. #10622823C22semidirect
57. #10622574C22semidirect
58. #10622572C22semidirect
59. #10622571C22semidirect
60. #10622571C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622568C22semidirect
64. #10622565C22semidirect
65. #10622563C22semidirect
66. #10622562C22semidirect
67. #10622561C22semidirect
68. #10622558C22semidirect
69. #10622557C22semidirect
70. #10622555C22semidirect
71. #10622555C22semidirect
72. C22⋊C4×Dic11C22semidirect
73. #10622289C22semidirect
74. #10622288C22semidirect
75. #10622270C22semidirect
76. #10622263C22semidirect
118. C2×C22⋊Dic11D4semidirect
289. #2403D11semidirect
395. C2×#120C2×D11semidirect
396. C2×#120C2×D11semidirect
425. #386C2×D11semidirect
426. #386C2×D11semidirect
689. C11#36721semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C22×#669882
#130768962
#130753112
#130753072
#130749432
#130749412
#130743642
#130735442
#130731062
#130719442
#130719392
#130719262
#130712122
C11×#24032
#3672111