Finite Group Databasebeta

← #14926348

Subgroups — #14926348

Order 2816.

3690 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C212yesmaximal, complemented
2C2×#10623136C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13076944C212yesmaximal, complemented
5#13076898C211yesmaximal, characteristic, complemented
6#13074361C211yesmaximal, characteristic, complemented
7#13074360C211yesmaximal, characteristic, complemented
8#13074354C212yesmaximal, complemented
9#13072166C214yesmaximal, complemented
10#13072164C214yesmaximal, complemented
11#13072151C214yesmaximal, complemented
12#13072149C214yesmaximal, complemented
13#13071229C211yesmaximal, characteristic, complemented
14D11×#386C212yesmaximal, complemented
15C11×#2847C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C22×D4×D11C2212yes—
19C23×C4×D11C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2212yescomplemented
22C2×C11×#120C2212yescomplemented
23C2×#67006C2212yescomplemented
24C22×C22⋊Dic11C2211yescharacteristic, complemented
25C2×#66992C2212yes—
26C2×#66991C2214yes—
27C2×#66990C2212yescomplemented
28C2×#66990C2214yescomplemented
29C2×#66988C2212yescomplemented
30C2×#66983C2211yescharacteristic
31C2×#66983C2212yescomplemented
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2214yescomplemented
34C2×C4×C22⋊D11C2214yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic, complemented
37C22×C4×Dic11C2211yescharacteristic, complemented
38#10623136—28no—
39#10623120—216no—
40C2×#66947C2212yescomplemented
41C2×#66939C2212yescomplemented
42C2×#66937C2214yes—
43C2×#66936C2214yescomplemented
44C2×#66936C2212yescomplemented
45C2×#66935C2212yescomplemented
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2214yescomplemented
48C11×#386C2214yescomplemented
49C11×#386C2212yescomplemented
50C11×#380C2212yescomplemented
51C11×#380C2211yescharacteristic, complemented
52#10622836C2214yescomplemented
53#10622835C2212yescomplemented
54#10622835C2214yescomplemented
55#10622833C2212yescomplemented
56#10622826C2214yescomplemented
57#10622826C2212yescomplemented
58#10622825C2212yescomplemented
59#10622825C2211yescharacteristic, complemented
60#10622607C2214yescomplemented
61#10622602C2214yescomplemented
62#10622593C2212yescomplemented
63#10622572C2214yescomplemented
64#10622571C2212yescomplemented
65#10622570C2214yescomplemented
66#10622569C2214yescomplemented
67#10622565C2214yescomplemented
68#10622564C2214yescomplemented
69#10622561C2214yescomplemented
70#10622555C2212yescomplemented
71#10622285C2212yescomplemented
72#10622282C2214yescomplemented
73#10622281C2214yescomplemented
74#10622278C2214yescomplemented
75D11×#95C2214yescomplemented
76#10622274C2212yescomplemented
77#10622260C2214yescomplemented
78C25×C11C2311yescharacteristic
79C24×D11C2312yes—
80C24×D11C2311yescharacteristic
81C22×D4×C11C2312yes—
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2314yes—
84C23×C4×C11—24no—
85C23×C4×C11—44no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C23×C4×C11C2312yes—
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11D418yescomplemented
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2314yes—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C2×D4×D11—28no—
102C2×D4×D11—28no—
103C2×D4×D11—28no—
104C22×D44C2312yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—44no—
108C22×C4×D11C2312yes—
109C22×C4×D11C2314yes—
110C22×C4×D11C2314yes—
111C11×#121—24no—
112C11×#121—44no—
113C11×#120—28no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2314yes—
120#67006—28no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128#66992—28no—
129#66991—216no—
130#66990—216no—
131#66990—28no—
132#66988—28no—
133#66983—24no—
134#66983—44no—
135C4×C22⋊D11—216no—
136C4×C22⋊D11—216no—
137C2×(C2×D11)⋊C4D418yescomplemented
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2312yes—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C2312yes—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2314yes—
157#66947—28no—
158#66939—28no—
159#66937—216no—
160#66936—216no—
161#66936—28no—
162#66935—28no—
163C22⋊C4×D11—28no—
164C22⋊C4×D11—48no—
165C11×#95C2314yes—
166C11×#95C2312yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2312yes—
172#34984—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—42no—
176C24×C11—42no—
177C24×C11C2×D414yes—
178C24×C11C2412yes—
179C24×C11C2412yes—
180C24×C11C2411yescharacteristic
181C23×D11—24no—
182C23×D11—24no—
183C23×D11—24no—
184C23×D11—42no—
185C23×D11—42no—
186C23×D11—44no—
187C23×D11—44no—
188C23×D11C2×D414yes—
189C23×D11C2×D414yes—
190C23×D11#4114yes—
191C23×D11C2412yes—
192C23×D11C2412yes—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—28no—
197C2×D4×C11—22no—
198C2×D4×C11—42no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C22×C4×C11—22no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—42no—
210C22×C4×C11—416no—
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2414yes—
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2412yes—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—232no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11C2×D4116yes—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D414yes—
239C22×Dic11C2414yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244D4×D11—432no—
245C2×D44—24no—
246C2×D44—24no—
247C2×D44—24no—
248C2×D44—22no—
249C2×D44—42no—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—28no—
253C2×C4×D11—28no—
254C2×C4×D11—24no—
255C2×C4×D11—28no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—416no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—42no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—28no—
266C22⋊Dic11—24no—
267C22⋊Dic11—28no—
268C22⋊Dic11—28no—
269C22⋊Dic11—24no—
270C22⋊Dic11—28no—
271C22⋊Dic11—44no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4C2×D418yes—
279(C2×D11)⋊C4C2×D418yes—
280C4⋊Dic11—28no—
281C4⋊Dic11—22no—
282C4⋊Dic11—42no—
283Dic11⋊C4—28no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—44no—
288C4×Dic11—28no—
289C2×#534—111no—
290C2×#534—112no—
291C22×C4×D4—111no—
292#2854—112no—
293#2847—111no—
294#2847D1111yescharacteristic, complemented
295#2618—111no—
296#2618—111no—
297#2617—112no—
298#2425—114no—
299#2425—114no—
300#2424—114no—
301#2424—114no—
302#2315—111no—
303C2×#386—112no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—28no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—24no—
317C23×C11—24no—
318C23×C11—48no—
319C23×C11—44no—
320C23×C11—48no—
321C23×C11—44no—
322C23×C11C22×D414yes—
323C23×C11C22×D412yes—
324C23×C11C22×D412yes—
325C23×C11C2×#4112yes—
326C23×C11C2511yescharacteristic
327C22×D11—24no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—24no—
333C22×D11—24no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—48no—
337C22×D11—48no—
338C22×D11—416no—
339C22×D11—48no—
340C22×D11—84no—
341C22×D11—84no—
342C22×D11—88no—
343C22×D11#121116yescomplemented
344C22×D11C22×D414yes—
345C22×D11C22×D414yes—
346C22×D11C2×#4114yes—
347D4×C11—48no—
348D4×C11—82no—
349D4×C11—88no—
350C2×C4×C11—28no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—44no—
362C2×C4×C11—48no—
363C2×C4×C11—48no—
364C2×C4×C11C22×D412yes—
365C2×C4×C11C22×D412yes—
366C2×C4×C11H(5,𝔽2)14yes—
367C22⋊D11—232no—
368C22⋊D11—48no—
369C22⋊D11—48no—
370C22⋊D11—84no—
371C22⋊D11—88no—
372C2×Dic11—28no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—24no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—24no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—24no—
382C2×Dic11—24no—
383C2×Dic11—24no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11C22×D414yes—
387C2×Dic11C22×D414yes—
388D44—48no—
389D44—82no—
390C4×D11—416no—
391C4×D11—48no—
392C4×D11—88no—
393C23×D4—111no—
394C23×D4—112no—
395C24×C4—111no—
396C24×C4C2×D1111yescharacteristic, complemented
397#534—228no—
398#534—2216no—
399C2×#123—112no—
400C2×#123—112no—
401C2×#123—112no—
402C2×#123—112no—
403C2×#123—114no—
404C2×#121—112no—
405C2×#121—114no—
406C2×#121—111no—
407C2×#121—112no—
408C2×#121—114no—
409C2×#121C2×D1111yescharacteristic
410C2×#121C2×D1112yescomplemented
411C2×#120—112no—
412C2×#120—112no—
413C2×#120—114no—
414C2×#120—112no—
415C2×#120C2×D1112yescomplemented
416C2×C4×D4—114no—
417C2×C4×D4—114no—
418C2×C4×D4—228no—
419C22×C4⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—112no—
423C22×C22⋊C4—114no—
424C22×C42—111no—
425#398—112no—
426#398—112no—
427#397—114no—
428#396—114no—
429#396—114no—
430#394—114no—
431#394—112no—
432#394—114no—
433#394—112no—
434#392—114no—
435#390—114no—
436#389—114no—
437#388—114no—
438#388—114no—
439#386—112no—
440#386—112no—
441#386—114no—
442#386—112no—
443#386—114no—
444#386—114no—
445#386C2×D1112yescomplemented
446#386C2×D1114yescomplemented
447#385—114no—
448#385—114no—
449#380—111no—
450#380—112no—
451#380—112no—
452#380C2×D1111yescharacteristic, complemented
453#380C2×D1112yescomplemented
454C2×#95—114no—
455C22×C11—24no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—416no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—44no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—44no—
472C22×C11C2×#12114yes—
473C22×C11C23×D411yescharacteristic
474C22×C11C23×D411yescharacteristic
475C22×C11C22×#4111yescharacteristic
476C22×C11C2×H(5,𝔽2)12yes—
477C22×C11#58512yes—
478C2×D11—28no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—28no—
482C2×D11—416no—
483C2×D11—42no—
484C2×D11—44no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—44no—
488C2×D11—816no—
489C2×D11C2×#12118yes—
490C4×C11—24no—
491C4×C11—22no—
492C4×C11—22no—
493C4×C11—42no—
494C4×C11—44no—
495Dic11—24no—
496Dic11—24no—
497Dic11—42no—
498Dic11—42no—
499Dic11—44no—
500C25—111no—
501C25—112no—
502C25C22×D1111yescharacteristic
503C22×D4—118no—
504C22×D4—114no—
505C22×D4—112no—
506C22×D4—112no—
507C22×D4—114no—
508C22×D4—112no—
509C22×D4—112no—
510C22×D4—111no—
511C22×D4—228no—
512C22×D4—228no—
513C22×D4—228no—
514C22×D4—224no—
515C22×D4—224no—
516C22×D4C22×D1112yes—
517C22×D4C22×D1111yescharacteristic
518C22×D4C22×D1114yes—
519C23×C4—24no—
520C23×C4—44no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—112no—
525C23×C4—114no—
526C23×C4—114no—
527C23×C4—224no—
528C23×C4—444no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1112yes—
531C23×C4C22×D1112yes—
532C23×C4C22×D1111yescharacteristic
533#123—228no—
534#123—228no—
535#123—2216no—
536#123—228no—
537#123—228no—
538#121—24no—
539#121—44no—
540#121—2216no—
541#121—228no—
542#121—2216no—
543#121—224no—
544#121—444no—
545#120—28no—
546#120—228no—
547#120—228no—
548#120—2216no—
549#120—228no—
550C4×D4—2216no—
551C4×D4—2216no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—112no—
558C2×C4⋊C4—112no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C4⋊C4C22×D1112yes—
563C2×C22⋊C4—118no—
564C2×C22⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—112no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—112no—
574C2×C22⋊C4—112no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—228no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—448no—
581C2×C22⋊C4C22×D1112yes—
582C2×C22⋊C4C22×D1114yes—
583C2×C22⋊C4C22×D1112yes—
584C2×C22⋊C4C22×D1114yes—
585C2×C42—114no—
586C2×C42—224no—
587#95—114no—
588#95—114no—
589#95—114no—
590#95—112no—
591#95—114no—
592#95C22×D1114yes—
593#95C22×D1112yes—
594C2×C11—24no—
595C2×C11—44no—
596C2×C11—82no—
597C2×C11C22×#12111yescharacteristic
598C2×C11#345912yes—
599C2×C11#348411yescharacteristic
600C2×C11#348511yescharacteristic
601C2×C11#349612yes—
602D11—28no—
603D11—82no—
604C24—22no—
605C24—22no—
606C24—42no—
607C24—42no—
608C24—112no—
609C24—114no—
610C24—114no—
611C24—114no—
612C24—112no—
613C24—224no—
614C24—224no—
615C24—224no—
616C24—442no—
617C24—442no—
618C24—444no—
619C24—444no—
620C24D4×D1114yes—
621C24C23×D1112yes—
622C24C23×D1112yes—
623C24C23×D1111yescharacteristic
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—28no—
628C2×D4—22no—
629C2×D4—42no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—1116no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—228no—
638C2×D4—2232no—
639C2×D4—228no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—228no—
647C2×D4—222no—
648C2×D4—442no—
649C2×D4—444no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—4432no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—416no—
663C22×C4—114no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—114no—
667C22×C4—114no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—228no—
671C22×C4—224no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—228no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—228no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—444no—
682C22×C4—4416no—
683C22×C4—442no—
684C22×C4—442no—
685C22×C4D4×D1114yes—
686C22×C4C23×D1114yes—
687C22×C4C23×D1112yes—
688C22×C4C23×D1111yescharacteristic
689C22×C4C23×D1111yescharacteristic
690C22×C4C23×D1112yes—
691C4⋊C4—22no—
692C4⋊C4—42no—
693C4⋊C4—228no—
694C4⋊C4—224no—
695C4⋊C4—228no—
696C4⋊C4—224no—
697C4⋊C4—224no—
698C4⋊C4—222no—
699C4⋊C4—442no—
700C4⋊C4—444no—
701C22⋊C4—24no—
702C22⋊C4—28no—
703C22⋊C4—24no—
704C22⋊C4—28no—
705C22⋊C4—118no—
706C22⋊C4—118no—
707C22⋊C4—228no—
708C22⋊C4—224no—
709C22⋊C4—228no—
710C22⋊C4—228no—
711C22⋊C4—224no—
712C22⋊C4—228no—
713C22⋊C4—224no—
714C22⋊C4—228no—
715C22⋊C4—224no—
716C22⋊C4—228no—
717C22⋊C4—444no—
718C22⋊C4—444no—
719C42—228no—
720C11#3498411yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—28no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—24no—
733C23—22no—
734C23—24no—
735C23—48no—
736C23—44no—
737C23—44no—
738C23—48no—
739C23—114no—
740C23—114no—
741C23—114no—
742C23—1116no—
743C23—224no—
744C23—224no—
745C23—222no—
746C23—222no—
747C23—224no—
748C23—222no—
749C23—224no—
750C23—444no—
751C23—448no—
752C23—444no—
753C23—448no—
754C23—448no—
755C23—4416no—
756C23—888no—
757C23—884no—
758C23—884no—
759C23C2×D4×D1114yes—
760C23C2×D4×D1112yes—
761C23C2×D4×D1112yes—
762C23#41×D1112yes—
763C23C24×D1111yescharacteristic
764D4—48no—
765D4—82no—
766D4—88no—
767D4—2232no—
768D4—448no—
769D4—448no—
770D4—448no—
771D4—882no—
772D4—884no—
773D4—888no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—44no—
786C2×C4—48no—
787C2×C4—48no—
788C2×C4—114no—
789C2×C4—114no—
790C2×C4—228no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—224no—
799C2×C4—224no—
800C2×C4—222no—
801C2×C4—224no—
802C2×C4—4416no—
803C2×C4—448no—
804C2×C4—444no—
805C2×C4—444no—
806C2×C4—888no—
807C2×C4C2×D4×D1112yes—
808C2×C4C2×D4×D1112yes—
809C2×C4#6703714yes—
810C22—24no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—42no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—118no—
828C22—228no—
829C22—224no—
830C22—224no—
831C22—228no—
832C22—4416no—
833C22—444no—
834C22—442no—
835C22—442no—
836C22—444no—
837C22—442no—
838C22—8816no—
839C22D11×#12114yes—
840C22C22×D4×D1111yescharacteristic
841C22C22×D4×D1111yescharacteristic
842C22C2×#6703712yes—
843C22C2×#41×D1111yescharacteristic
844C22#1062345312yes—
845C4—24no—
846C4—22no—
847C4—22no—
848C4—44no—
849C4—42no—
850C4—224no—
851C4—224no—
852C4—444no—
853C4—442no—
854C4—442no—
855C2—24no—
856C2—44no—
857C2—82no—
858C2—228no—
859C2—882no—
860C2C2×D11×#12111yescharacteristic
861C2#1308202312yes—
862C2#1308224511yescharacteristic
863C2#1308225811yescharacteristic
864C2#1308237312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2847C2
hypercenter#2847D11
hypocenterC11#34984
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#10623120C2semidirect
2. C2×#10623136C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13076944C2semidirect
5. #13076898C2semidirect
6. #13074361C2semidirect
7. #13074360C2semidirect
8. #13074354C2semidirect
9. #13072166C2semidirect
10. #13072164C2semidirect
11. #13072151C2semidirect
12. #13072149C2semidirect
13. #13071229C2semidirect
14. D11×#386C2semidirect
15. C11×#2847C2semidirect
16. C24×C4×C11C22semidirect
21. C2×C11×#121C22semidirect
22. C2×C11×#120C22semidirect
23. C2×#67006C22semidirect
24. C22×C22⋊Dic11C22semidirect
27. C2×#66990C22semidirect
28. C2×#66990C22semidirect
29. C2×#66988C22semidirect
31. C2×#66983C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
36. C22×Dic11⋊C4C22semidirect
37. C22×C4×Dic11C22semidirect
40. C2×#66947C22semidirect
41. C2×#66939C22semidirect
43. C2×#66936C22semidirect
44. C2×#66936C22semidirect
45. C2×#66935C22semidirect
47. C2×C22⋊C4×D11C22semidirect
48. C11×#386C22semidirect
49. C11×#386C22semidirect
50. C11×#380C22semidirect
51. C11×#380C22semidirect
52. #10622836C22semidirect
53. #10622835C22semidirect
54. #10622835C22semidirect
55. #10622833C22semidirect
56. #10622826C22semidirect
57. #10622826C22semidirect
58. #10622825C22semidirect
59. #10622825C22semidirect
60. #10622607C22semidirect
61. #10622602C22semidirect
62. #10622593C22semidirect
63. #10622572C22semidirect
64. #10622571C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622565C22semidirect
68. #10622564C22semidirect
69. #10622561C22semidirect
70. #10622555C22semidirect
71. #10622285C22semidirect
72. #10622282C22semidirect
73. #10622281C22semidirect
74. #10622278C22semidirect
75. D11×#95C22semidirect
76. #10622274C22semidirect
77. #10622260C22semidirect
92. C22×C22⋊D11D4semidirect
137. C2×(C2×D11)⋊C4D4semidirect
294. #2847D11semidirect
343. C22×D11#121semidirect
396. C24×C4C2×D11semidirect
410. C2×#121C2×D11semidirect
415. C2×#120C2×D11semidirect
445. #386C2×D11semidirect
446. #386C2×D11semidirect
452. #380C2×D11semidirect
453. #380C2×D11semidirect
720. C11#34984semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C2×#106231362
C22×C4×C22⋊D112
#130769442
#130768982
#130743612
#130743602
#130743542
#130721662
#130721642
#130721512
#130721492
#130712292
D11×#3862
C11×#28472
#3498411