Finite Group Databasebeta

← #14926333

Subgroups — #14926333

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic, complemented
2#13076935C212yesmaximal, complemented
3#13076906C212yesmaximal, complemented
4#13074398C212yesmaximal, complemented
5#13074391C212yesmaximal, complemented
6#13072362C214yesmaximal, complemented
7#13072347C214yesmaximal, complemented
8#13072089C214yesmaximal, complemented
9#13072074C214yesmaximal, complemented
10#13071228C211yesmaximal, characteristic, complemented
11#13071194C211yesmaximal, characteristic, complemented
12#13071194C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622559C211yesmaximal, characteristic, complemented
15C2×C11×#534C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic, complemented
20C11×#534—28no—
21C2×C11×#123C2212yes—
22C2×C11×#123C2212yes—
23C2×C11×#121C2212yes—
24C2×C11×#121C2212yes—
25C2×C11×#120C2212yes—
26C2×C11×#120C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic, complemented
32C22×C22⋊Dic11C2212yescomplemented
33C2×#66988C2214yescomplemented
34C2×D4×Dic11—28no—
35C2×D4×Dic11C2214yes—
36C2×D4×Dic11C2214yescomplemented
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C22×Dic11⋊C4C2212yescomplemented
39C22×C4×Dic11C2211yescharacteristic, complemented
40#10622860C2212yescomplemented
41#10622860C2212yescomplemented
42#10622835C2214yescomplemented
43#10622835C2214yescomplemented
44#10622833C2212yes—
45#10622833C2212yes—
46#10622833C2214yes—
47#10622833C2212yes—
48#10622833C2212yes—
49#10622833C2214yescomplemented
50#10622833C2214yescomplemented
51#10622833C2214yescomplemented
52#10622833C2214yescomplemented
53#10622824C2212yescomplemented
54#10622824C2212yescomplemented
55#10622823C2212yescomplemented
56#10622823C2212yescomplemented
57C2×C11⋊#95C2212yescomplemented
58C2×C11⋊#95C2212yescomplemented
59#10622599C2214yescomplemented
60#10622596C2214yescomplemented
61#10622591C2214yescomplemented
62#10622591C2214yescomplemented
63#10622566C2214yescomplemented
64#10622565C2214yescomplemented
65#10622565C2214yescomplemented
66#10622562C2214yescomplemented
67#10622559C2212yescomplemented
68#10622559C2212yescomplemented
69#10622559C2212yescomplemented
70#10622559C2214yescomplemented
71#10622559C2214yescomplemented
72#10622559C2212yescomplemented
73#10622557C2214yescomplemented
74#10622557C2214yescomplemented
75#10622556C2214yescomplemented
76#10622555C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11D418yes—
86C22×D4×C11C2312yes—
87C22×D4×C11C2312yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2312yes—
90C22×D4×C11C2312yes—
91C22×D4×C11C2312yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11—44no—
99C23×Dic11—44no—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2312yes—
102C23×Dic11C2314yes—
103C23×Dic11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2312yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2312yes—
109C11×#123—28no—
110C11×#123—28no—
111C11×#121—28no—
112C11×#121—28no—
113C11×#120—28no—
114C11×#120—28no—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C11×C22⋊C4C2312yes—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—44no—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142#66988—48no—
143D4×Dic11—216no—
144D4×Dic11—216no—
145C2×C4⋊Dic11—24no—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—44no—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164#34983—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
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×C11C2×D414yes—
178C24×C11#4114yes—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2411yescharacteristic
183C24×C11C2411yescharacteristic
184C24×C11C2411yescharacteristic
185C2×D4×C11—232no—
186C2×D4×C11—24no—
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—24no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—44no—
199C2×D4×C11—44no—
200C2×D4×C11—416no—
201C2×D4×C11C2×D418yes—
202C2×D4×C11C2×D418yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—28no—
220C22×Dic11—24no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—28no—
226C22×Dic11—24no—
227C22×Dic11—24no—
228C22×Dic11—24no—
229C22×Dic11—24no—
230C22×Dic11—42no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—42no—
234C22×Dic11—42no—
235C22×Dic11—44no—
236C22×Dic11—42no—
237C22×Dic11—42no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—416no—
241C22×Dic11—416no—
242C22×Dic11C2414yes—
243C22×Dic11C2414yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C22⋊Dic11—28no—
257C22⋊Dic11—28no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C4⋊Dic11—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—44no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274C4×Dic11—28no—
275C2×#534D1111yescharacteristic
276C22×C4×D4—111no—
277#2853—112no—
278#2849—112no—
279#2623—112no—
280#2622—112no—
281#2444—114no—
282#2443—114no—
283#2419—114no—
284#2418—114no—
285#2315—111no—
286#2308—111no—
287#2308—111no—
288C2×#386—111no—
289C2×#385—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—28no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11—24no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—48no—
311C23×C11—48no—
312C23×C11—48no—
313C23×C11—48no—
314C23×C11—48no—
315C23×C11—44no—
316C23×C11—82no—
317C23×C11—82no—
318C23×C11—84no—
319C23×C11#123116yescomplemented
320C23×C11C22×D414yes—
321C23×C11C22×D412yes—
322C23×C11C22×D412yes—
323C23×C11C22×D412yes—
324C23×C11C2×#4112yes—
325C23×C11C2×#4112yes—
326C23×C11C2×#4112yes—
327C23×C11C2×#4112yes—
328C23×C11C2×#4112yes—
329C23×C11C2×#4112yes—
330C23×C11C2511yescharacteristic
331D4×C11—216no—
332D4×C11—216no—
333D4×C11—48no—
334D4×C11—48no—
335D4×C11—84no—
336D4×C11—84no—
337C2×C4×C11—28no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—44no—
348C2×C4×C11—82no—
349C2×C4×C11—82no—
350C2×C4×C11C22×D414yes—
351C2×Dic11—28no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—24no—
358C2×Dic11—24no—
359C2×Dic11—24no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—48no—
368C2×Dic11—48no—
369C2×Dic11—416no—
370C2×Dic11—48no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—84no—
375C2×Dic11H(5,𝔽2)14yes—
376C23×D4C2×D1111yescharacteristic
377C23×D4C2×D1111yescharacteristic
378C24×C4—111no—
379C24×C4—111no—
380#534—28no—
381C2×#123—114no—
382C2×#123C2×D1112yes—
383C2×#123C2×D1112yes—
384C2×#121C2×D1112yes—
385C2×#121C2×D1112yes—
386C2×#120C2×D1112yes—
387C2×#120C2×D1112yes—
388C2×C4×D4—114no—
389C2×C4×D4—114no—
390C2×C4×D4—228no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—112no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—112no—
398C22×C22⋊C4C2×D1111yescharacteristic
399C22×C42—111no—
400#400—114no—
401#399—114no—
402#398—114no—
403#397—114no—
404#397—114no—
405#397—114no—
406#394—114no—
407#394—114no—
408#388—114no—
409#388—114no—
410#387—114no—
411#387—114no—
412#386—112no—
413#386—112no—
414#386—114no—
415#386—114no—
416#386—114no—
417#386—112no—
418#386—114no—
419#386—112no—
420#386—114no—
421#385—112no—
422#385—112no—
423#385—112no—
424#385—112no—
425#385—112no—
426#385—114no—
427#385—112no—
428#385—114no—
429#381—112no—
430#381—112no—
431#381—114no—
432#380—114no—
433#379—112no—
434#379—112no—
435C2×#95—112no—
436C2×#95—112no—
437C22×C11—24no—
438C22×C11—24no—
439C22×C11—24no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—416no—
453C22×C11—416no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11—42no—
457C22×C11—44no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—44no—
461C22×C11—88no—
462C22×C11C2×#12314yes—
463C22×C11C2×#12314yes—
464C22×C11C2×#12314yes—
465C22×C11C23×D411yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C22×#4111yescharacteristic
468C22×C11C2×H(5,𝔽2)12yes—
469C22×C11#58512yes—
470C4×C11—24no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474Dic11—24no—
475Dic11—44no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—44no—
480C25C22×D1111yescharacteristic
481C25C22×D1111yescharacteristic
482C25C22×D1111yescharacteristic
483C22×D4—24no—
484C22×D4—24no—
485C22×D4—24no—
486C22×D4—24no—
487C22×D4—24no—
488C22×D4C22⋊D1118yes—
489C22×D4C22×D1112yes—
490C22×D4C22×D1112yes—
491C22×D4C22×D1112yes—
492C22×D4C22×D1112yes—
493C22×D4C22×D1112yes—
494C22×D4C22×D1112yes—
495C23×C4—111no—
496C23×C4—112no—
497C23×C4—112no—
498C23×C4—114no—
499C23×C4—112no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—112no—
504C23×C4—224no—
505C23×C4—224no—
506C23×C4—444no—
507C23×C4—444no—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512#123—28no—
513#123—28no—
514#123—448no—
515#121—28no—
516#121—28no—
517#120—28no—
518#120—28no—
519C4×D4—2216no—
520C4×D4—2216no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—444no—
528C2×C4⋊C4C22×D1112yes—
529C2×C4⋊C4C22×D1112yes—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—112no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—224no—
545C2×C22⋊C4—224no—
546C2×C22⋊C4—224no—
547C2×C22⋊C4—224no—
548C2×C22⋊C4—444no—
549C2×C22⋊C4C22×D1112yes—
550C2×C22⋊C4C22×D1112yes—
551C2×C22⋊C4C22×D1112yes—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1112yes—
554C2×C22⋊C4C22×D1112yes—
555C2×C42—114no—
556C2×C42—224no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95—114no—
567C2×C11—24no—
568C2×C11—24no—
569C2×C11—24no—
570C2×C11—44no—
571C2×C11—82no—
572C2×C11C22×#12311yescharacteristic
573C2×C11#345912yes—
574C2×C11#348411yescharacteristic
575C2×C11#348511yescharacteristic
576C2×C11#350512yes—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24#434114yes—
589C24#434114yes—
590C24C2×C22⋊D1114yes—
591C24C2×C22⋊D1114yes—
592C24C23×D1112yes—
593C24C23×D1112yes—
594C24C23×D1111yescharacteristic
595C24C23×D1111yescharacteristic
596C24C23×D1111yescharacteristic
597C2×D4—232no—
598C2×D4—24no—
599C2×D4—24no—
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—24no—
609C2×D4—24no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4C2×C22⋊D1118yes—
614C2×D4C2×C22⋊D1118yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—112no—
625C22×C4—114no—
626C22×C4—114no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—228no—
634C22×C4—222no—
635C22×C4—224no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—228no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—444no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4—442no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—4416no—
654C22×C4—4416no—
655C22×C4C2×C22⋊D1114yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—228no—
663C4⋊C4—228no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—228no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—228no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C42—228no—
687C11#3498311yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—28no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—22no—
704C23—44no—
705C23—44no—
706C23—48no—
707C23—48no—
708C23—44no—
709C23—44no—
710C23—48no—
711C23—48no—
712C23—48no—
713C23—44no—
714C23—84no—
715C23—82no—
716C23—82no—
717C23#66988116yescomplemented
718C23C2×#434112yes—
719C23C2×#434112yes—
720C23C2×#434112yes—
721C23C2×#434112yes—
722C23C2×#434112yes—
723C23C2×#434112yes—
724C23C22×C22⋊D1114yes—
725C23C22×C22⋊D1112yes—
726C23C22×C22⋊D1112yes—
727C23C22×C22⋊D1112yes—
728C23C24×D1111yescharacteristic
729D4—216no—
730D4—216no—
731D4—48no—
732D4—48no—
733D4—84no—
734D4—84no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—114no—
749C2×C4—228no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—224no—
758C2×C4—222no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—448no—
766C2×C4—448no—
767C2×C4—4416no—
768C2×C4—444no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4—448no—
772C2×C4—884no—
773C2×C4C22×C22⋊D1114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—416no—
790C22—416no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—88no—
799C22C2×#6698814yes—
800C22C2×#6698814yes—
801C22C2×#6698814yes—
802C22C22×#434111yescharacteristic
803C22C22×#434111yescharacteristic
804C22D11×H(5,𝔽2)12yes—
805C22#1062345512yes—
806C22C23×C22⋊D1111yescharacteristic
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—224no—
812C4—444no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4—444no—
817C2—24no—
818C2—24no—
819C2—24no—
820C2—44no—
821C2—82no—
822C2C22×#6698811yescharacteristic
823C2#1308202212yes—
824C2#1308224711yescharacteristic
825C2#1308225611yescharacteristic
826C2#1308245312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC2×C11×#534C2
hypercenterC2×#534D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. #13076935C2semidirect
3. #13076906C2semidirect
4. #13074398C2semidirect
5. #13074391C2semidirect
6. #13072362C2semidirect
7. #13072347C2semidirect
8. #13072089C2semidirect
9. #13072074C2semidirect
10. #13071228C2semidirect
11. #13071194C2semidirect
12. #13071194C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622559C2semidirect
19. C24×Dic11C22semidirect
31. C22×C22⋊Dic11C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C2×#66988C22semidirect
36. C2×D4×Dic11C22semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×Dic11⋊C4C22semidirect
39. C22×C4×Dic11C22semidirect
40. #10622860C22semidirect
41. #10622860C22semidirect
42. #10622835C22semidirect
43. #10622835C22semidirect
49. #10622833C22semidirect
50. #10622833C22semidirect
51. #10622833C22semidirect
52. #10622833C22semidirect
53. #10622824C22semidirect
54. #10622824C22semidirect
55. #10622823C22semidirect
56. #10622823C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. #10622599C22semidirect
60. #10622596C22semidirect
61. #10622591C22semidirect
62. #10622591C22semidirect
63. #10622566C22semidirect
64. #10622565C22semidirect
65. #10622565C22semidirect
66. #10622562C22semidirect
67. #10622559C22semidirect
68. #10622559C22semidirect
69. #10622559C22semidirect
70. #10622559C22semidirect
71. #10622559C22semidirect
72. #10622559C22semidirect
73. #10622557C22semidirect
74. #10622557C22semidirect
75. #10622556C22semidirect
76. #10622555C22semidirect
319. C23×C11#123semidirect
687. C11#34983semidirect
717. C23#66988semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
#130769352
#130769062
#130743982
#130743912
#130723622
#130723472
#130720892
#130720742
#130712282
#130711942
C2×#106228332
C2×#106225592
C2×C11×#5342
#3498311