Finite Group Databasebeta

← #14926335

Subgroups — #14926335

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
1C2×#10623335C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13076937C212yesmaximal, complemented
4#13076907C212yesmaximal, complemented
5#13074400C212yesmaximal, complemented
6#13074393C212yesmaximal, complemented
7#13072368C214yesmaximal, complemented
8#13072353C214yesmaximal, complemented
9#13072093C214yesmaximal, complemented
10#13072078C214yesmaximal, complemented
11#13071230C211yesmaximal, characteristic, complemented
12#13071194C211yesmaximal, characteristic, complemented
13#13071191C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yescomplemented
22C2×#67006C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26#10623335—28no—
27C2×#66992C2212yes—
28C2×#66992C2212yes—
29C2×#66990C2212yes—
30C2×#66988C2212yes—
31C2×#66982C2212yes—
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2214yes—
34C2×C4×C22⋊D11C2214yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
36C22×Dic11⋊C4C2211yescharacteristic, complemented
37C22×Dic11⋊C4C2212yescomplemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C2×#66936C2214yescomplemented
40C11×#386C2212yes—
41C11×#386C2212yes—
42C11×#386C2214yescomplemented
43C2×C11×#95C2212yescomplemented
44#10622860C2212yescomplemented
45#10622833C2212yes—
46#10622833C2212yes—
47#10622833C2214yescomplemented
48#10622826C2214yes—
49#10622825C2214yescomplemented
50#10622824C2212yescomplemented
51#10622823C2212yescomplemented
52#10622823C2214yescomplemented
53#10622823C2212yescomplemented
54C2×C11⋊#95C2212yescomplemented
55#10622574C2214yescomplemented
56#10622572C2214yescomplemented
57#10622571C2214yescomplemented
58#10622569C2214yescomplemented
59#10622568C2212yescomplemented
60#10622565C2214yescomplemented
61#10622564C2214yescomplemented
62#10622563C2212yescomplemented
63#10622563C2212yescomplemented
64#10622563C2212yescomplemented
65#10622563C2212yescomplemented
66#10622562C2214yescomplemented
67#10622558C2214yescomplemented
68#10622556C2212yescomplemented
69#10622288C2214yescomplemented
70#10622287C2214yescomplemented
71#10622281C2214yescomplemented
72#10622277C2214yescomplemented
73#10622271C2214yescomplemented
74#10622270C2214yescomplemented
75#10622267C2214yescomplemented
76#10622265C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11C2312yes—
84C22×D4×C11C2312yes—
85C23×C4×C11—24no—
86C23×C4×C11—44no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2312yes—
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2312yes—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11D418yes—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2312yes—
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—44no—
108C22×C4×D11C2314yes—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—44no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115#67006—28no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129#66992—28no—
130#66992—28no—
131#66990—28no—
132#66988—28no—
133#66982—28no—
134C4×C22⋊D11—216no—
135C4×C22⋊D11—216no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11C2314yes—
143C2×C4⋊Dic11C2314yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—44no—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×C4×Dic11—24no—
152C2×C4×Dic11C2314yes—
153#66936—48no—
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—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11C2×D414yes—
173C24×C11#4114yes—
174C24×C11#4114yes—
175C24×C11C2412yes—
176C24×C11C2411yescharacteristic
177C24×C11C2411yescharacteristic
178C24×C11C2411yescharacteristic
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—42no—
182C23×D11—42no—
183C23×D11C2×D414yes—
184C23×D11C2412yes—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—416no—
192C22×C4×C11—22no—
193C22×C4×C11—24no—
194C22×C4×C11—22no—
195C22×C4×C11—24no—
196C22×C4×C11—24no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—416no—
209C22×C4×C11C2412yes—
210C22×C4×C11C2414yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C2×C22⋊D11—232no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11C2×D418yes—
223C2×C22⋊D11C2×D418yes—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—24no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—42no—
234C22×Dic11—42no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11C2×D414yes—
238C22×Dic11C2414yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—44no—
247C2×C4×D11—416no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—44no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—44no—
268C4⋊Dic11—44no—
269Dic11⋊C4—28no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—28no—
273Dic11⋊C4—44no—
274C4×Dic11—28no—
275C2×#534—111no—
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×#386D1111yescharacteristic, complemented
289C2×#385—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—48no—
304C23×C11—48no—
305C23×C11—48no—
306C23×C11—44no—
307C23×C11—82no—
308C23×C11—82no—
309C23×C11—84no—
310C23×C11#123116yescomplemented
311C23×C11C22×D412yes—
312C23×C11C22×D412yes—
313C23×C11C22×D412yes—
314C23×C11C2×#4112yes—
315C23×C11C2×#4112yes—
316C23×C11C2×#4112yes—
317C23×C11C2×#4112yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11C2511yescharacteristic
321C22×D11—28no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—24no—
325C22×D11—24no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—48no—
329C22×D11—48no—
330C22×D11C22×D414yes—
331D4×C11—48no—
332D4×C11—48no—
333C2×C4×C11—28no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—48no—
346C2×C4×C11—48no—
347C2×C4×C11—44no—
348C2×C4×C11—44no—
349C2×C4×C11—84no—
350C2×C4×C11H(5,𝔽2)14yes—
351C22⋊D11—216no—
352C22⋊D11—216no—
353C22⋊D11—84no—
354C22⋊D11—84no—
355C2×Dic11—28no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—24no—
368C2×Dic11—24no—
369C2×Dic11—44no—
370C2×Dic11—48no—
371C2×Dic11—44no—
372C2×Dic11—82no—
373C2×Dic11—82no—
374C2×Dic11C22×D414yes—
375C4×D11—416no—
376C23×D4—111no—
377C23×D4C2×D1111yescharacteristic
378C24×C4—111no—
379C24×C4C2×D1111yescharacteristic
380#534—228no—
381C2×#123—112no—
382C2×#123—112no—
383C2×#123—114no—
384C2×#121—112no—
385C2×#121—112no—
386C2×#120—112no—
387C2×#120—112no—
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⋊C4C2×D1111yescharacteristic
398C22×C22⋊C4C2×D1112yescomplemented
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—114no—
418#386C2×D1112yes—
419#386C2×D1112yes—
420#386C2×D1114yescomplemented
421#385—112no—
422#385—112no—
423#385—114no—
424#385—112no—
425#385—112no—
426#385—112no—
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×#95C2×D1112yescomplemented
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—416no—
450C22×C11—42no—
451C22×C11—44no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—44no—
455C22×C11—88no—
456C22×C11C2×#12314yes—
457C22×C11C2×#12314yes—
458C22×C11C2×#12314yes—
459C22×C11C23×D411yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C2×H(5,𝔽2)12yes—
463C22×C11#58512yes—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—416no—
468C2×D11—44no—
469C2×D11—44no—
470C4×C11—24no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—44no—
474Dic11—24no—
475Dic11—44no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25—111no—
481C25C22×D1111yescharacteristic
482C25C22×D1111yescharacteristic
483C22×D4—24no—
484C22×D4—24no—
485C22×D4—24no—
486C22×D4—118no—
487C22×D4—112no—
488C22×D4—112no—
489C22×D4—112no—
490C22×D4—112no—
491C22×D4—224no—
492C22×D4—224no—
493C22×D4C22×D1112yes—
494C22×D4C22×D1112yes—
495C23×C4—24no—
496C23×C4—44no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—112no—
502C23×C4—111no—
503C23×C4—114no—
504C23×C4—224no—
505C23×C4—444no—
506C23×C4C22×D1111yescharacteristic
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1112yes—
509C23×C4C22×D1112yes—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1112yes—
512#123—228no—
513#123—228no—
514#123—448no—
515#121—228no—
516#121—228no—
517#120—228no—
518#120—228no—
519C4×D4—2216no—
520C4×D4—2216no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—112no—
524C2×C4⋊C4—112no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—224no—
529C2×C4⋊C4—444no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—44no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—112no—
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—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—224no—
548C2×C22⋊C4—224no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C22⋊C4C22×D1112yes—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1114yes—
554C2×C22⋊C4C22×D1114yes—
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#95C22×D1114yes—
566#95C22×D1114yes—
567C2×C11—24no—
568C2×C11—24no—
569C2×C11—24no—
570C2×C11—82no—
571C2×C11C22×#12311yescharacteristic
572C2×C11#345912yes—
573C2×C11#348411yescharacteristic
574C2×C11#348511yescharacteristic
575C2×C11#350512yes—
576D11—44no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—112no—
585C24—114no—
586C24—222no—
587C24—222no—
588C24—442no—
589C24—442no—
590C24#433914yes—
591C24D4×D1114yes—
592C24#434114yes—
593C24C23×D1112yes—
594C24C23×D1111yescharacteristic
595C24C23×D1111yescharacteristic
596C24C23×D1111yescharacteristic
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—416no—
604C2×D4—118no—
605C2×D4—118no—
606C2×D4—2232no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—224no—
613C2×D4—444no—
614C2×D4—444no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—416no—
632C22×C4—114no—
633C22×C4—112no—
634C22×C4—114no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—228no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—228no—
648C22×C4—444no—
649C22×C4—4416no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—442no—
655C22×C4—442no—
656C22×C4C23×D1112yes—
657C22×C4C23×D1114yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—228no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—228no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—28no—
670C22⋊C4—44no—
671C22⋊C4—228no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
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—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—44no—
700C23—48no—
701C23—44no—
702C23—48no—
703C23—48no—
704C23—44no—
705C23—84no—
706C23—82no—
707C23—82no—
708C23—114no—
709C23—228no—
710C23—222no—
711C23—222no—
712C23—224no—
713C23—224no—
714C23—444no—
715C23—444no—
716C23—448no—
717C23—448no—
718C23#66936116yescomplemented
719C23C2×#433912yes—
720C23C2×#433912yes—
721C23C2×#433912yes—
722C23C2×D4×D1112yes—
723C23C2×D4×D1112yes—
724C23C2×D4×D1112yes—
725C23C2×#434112yes—
726C23C2×#434112yes—
727C23C2×#434112yes—
728C23C24×D1111yescharacteristic
729D4—48no—
730D4—48no—
731D4—2216no—
732D4—2216no—
733D4—884no—
734D4—884no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—84no—
752C2×C4—114no—
753C2×C4—228no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—4416no—
768C2×C4—444no—
769C2×C4—444no—
770C2×C4—448no—
771C2×C4—882no—
772C2×C4—882no—
773C2×C4#6703714yes—
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—416no—
787C22—44no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—42no—
792C22—88no—
793C22—224no—
794C22—224no—
795C22—224no—
796C22—4416no—
797C22—444no—
798C22—444no—
799C22C2×#6693614yes—
800C22C2×#6693614yes—
801C22C2×#6693614yes—
802C22C22×#433911yescharacteristic
803C22C22×D4×D1111yescharacteristic
804C22C22×#434111yescharacteristic
805C22C2×#6703712yes—
806C22#1062345312yes—
807C4—24no—
808C4—44no—
809C4—42no—
810C4—42no—
811C4—224no—
812C4—442no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4—444no—
817C2—24no—
818C2—24no—
819C2—24no—
820C2—82no—
821C2—444no—
822C2C22×#6693611yescharacteristic
823C2#1308202512yes—
824C2#1308224511yescharacteristic
825C2#1308225411yescharacteristic
826C2#1308245012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#386C2
prime radicalC2×#10623335C2
hypercenterC2×#386D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. #13076937C2semidirect
4. #13076907C2semidirect
5. #13074400C2semidirect
6. #13074393C2semidirect
7. #13072368C2semidirect
8. #13072353C2semidirect
9. #13072093C2semidirect
10. #13072078C2semidirect
11. #13071230C2semidirect
12. #13071194C2semidirect
13. #13071191C2semidirect
14. C2×#10622823C2semidirect
15. C2×C11×#386C2semidirect
19. C23×C4×D11C22semidirect
21. C22×C11×C22⋊C4C22semidirect
34. C2×C4×C22⋊D11C22semidirect
35. C22×(C2×D11)⋊C4C22semidirect
36. C22×Dic11⋊C4C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. C22×C4×Dic11C22semidirect
39. C2×#66936C22semidirect
42. C11×#386C22semidirect
43. C2×C11×#95C22semidirect
44. #10622860C22semidirect
47. #10622833C22semidirect
49. #10622825C22semidirect
50. #10622824C22semidirect
51. #10622823C22semidirect
52. #10622823C22semidirect
53. #10622823C22semidirect
54. C2×C11⋊#95C22semidirect
55. #10622574C22semidirect
56. #10622572C22semidirect
57. #10622571C22semidirect
58. #10622569C22semidirect
59. #10622568C22semidirect
60. #10622565C22semidirect
61. #10622564C22semidirect
62. #10622563C22semidirect
63. #10622563C22semidirect
64. #10622563C22semidirect
65. #10622563C22semidirect
66. #10622562C22semidirect
67. #10622558C22semidirect
68. #10622556C22semidirect
69. #10622288C22semidirect
70. #10622287C22semidirect
71. #10622281C22semidirect
72. #10622277C22semidirect
73. #10622271C22semidirect
74. #10622270C22semidirect
75. #10622267C22semidirect
76. #10622265C22semidirect
288. C2×#386D11semidirect
310. C23×C11#123semidirect
398. C22×C22⋊C4C2×D11semidirect
420. #386C2×D11semidirect
436. C2×#95C2×D11semidirect
687. C11#34983semidirect
718. C23#66936semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C22×C4×C22⋊D112
#130769372
#130769072
#130744002
#130743932
#130723682
#130723532
#130720932
#130720782
#130712302
#130711942
#130711912
C2×#106228232
C2×C11×#3862
#3498311