Finite Group Databasebeta

← #14926342

Subgroups — #14926342

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×D4×Dic11C211yesmaximal, characteristic, complemented
3#13076939C212yesmaximal, complemented
4#13076910C212yesmaximal, complemented
5#13074399C212yesmaximal, complemented
6#13074392C212yesmaximal, complemented
7#13072364C214yesmaximal, complemented
8#13072349C214yesmaximal, complemented
9#13072091C214yesmaximal, complemented
10#13072076C214yesmaximal, complemented
11#13071230C211yesmaximal, characteristic, complemented
12#13071191C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622563C211yesmaximal, characteristic, complemented
15C11×#2308C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C2×#67006C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic, complemented
26#10623335—28no—
27C2×#66992C2212yes—
28C2×#66992C2212yes—
29C2×#66990C2212yes—
30C2×#66988C2212yes—
31C2×D4×Dic11—28no—
32C2×D4×Dic11C2214yes—
33C2×D4×Dic11C2214yescomplemented
34C2×#66982C2212yes—
35C22×(C2×D11)⋊C4C2212yescomplemented
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37C22×C4⋊Dic11C2212yescomplemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C2×#66939C2214yescomplemented
40C11×#386C2214yes—
41C11×#386C2214yescomplemented
42C11×#381C2212yescomplemented
43C11×#379C2212yescomplemented
44#10622826C2214yescomplemented
45#10622825C2214yescomplemented
46C2×C11⋊#95C2212yescomplemented
47C2×C11⋊#95C2212yescomplemented
48#10622574C2214yescomplemented
49#10622574C2214yescomplemented
50#10622571C2212yes—
51#10622571C2212yes—
52#10622571C2212yes—
53#10622571C2212yes—
54#10622571C2214yescomplemented
55#10622571C2214yescomplemented
56#10622568C2212yescomplemented
57#10622566C2214yescomplemented
58#10622566C2214yescomplemented
59#10622563C2212yescomplemented
60#10622563C2212yescomplemented
61#10622563C2212yescomplemented
62#10622563C2212yescomplemented
63#10622563C2212yescomplemented
64#10622563C2214yescomplemented
65#10622563C2214yescomplemented
66#10622563C2212yescomplemented
67#10622556C2212yescomplemented
68#10622556C2214yescomplemented
69#10622290C2214yescomplemented
70#10622287C2214yescomplemented
71#10622283C2214yescomplemented
72#10622283C2214yescomplemented
73#10622274C2214yescomplemented
74#10622272C2214yescomplemented
75#10622266C2214yescomplemented
76#10622266C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11D418yes—
83C22×D4×C11C2312yes—
84C22×D4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C23×C4×C11C2312yes—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2312yes—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—44no—
98C23×Dic11—44no—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2314yes—
102C23×Dic11C2312yes—
103C23×Dic11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117#67006—28no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128#66992—28no—
129#66992—28no—
130#66990—28no—
131#66988—28no—
132D4×Dic11—216no—
133D4×Dic11—216no—
134#66982—28no—
135C2×(C2×D11)⋊C4—44no—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11—44no—
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C2314yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×C4×Dic11—24no—
152C2×C4×Dic11C2314yes—
153#66939—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—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11C2×D414yes—
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—22no—
182C23×D11—42no—
183C23×D11—42no—
184C23×D11C2412yes—
185C2×D4×C11—232no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11C2×D418yes—
191C2×D4×C11C2×D418yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2414yes—
202C22×C4×C11C2414yes—
203C22×C4×C11C2412yes—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—416no—
215C22×Dic11—24no—
216C22×Dic11—28no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—28no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
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—416no—
240C22×Dic11—416no—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—44no—
253C11×C22⋊C4—44no—
254C22⋊Dic11—24no—
255C22⋊Dic11—28no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—28no—
268C4⋊Dic11—28no—
269C4⋊Dic11—44no—
270C4⋊Dic11—44no—
271C4⋊Dic11—44no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
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#2308D1111yescharacteristic, complemented
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—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—48no—
308C23×C11—48no—
309C23×C11#123116yescomplemented
310C23×C11C22×D414yes—
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—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—24no—
325C22×D11—24no—
326C22×D11—48no—
327C22×D11—44no—
328C22×D11—82no—
329C22×D11—82no—
330C22×D11—84no—
331D4×C11—216no—
332D4×C11—216no—
333C2×C4×C11—28no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—48no—
343C2×C4×C11—84no—
344C2×C4×C11C22×D414yes—
345C22⋊D11—48no—
346C22⋊D11—48no—
347C22⋊D11—84no—
348C22⋊D11—84no—
349C2×Dic11—28no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—24no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—48no—
367C2×Dic11—48no—
368C2×Dic11—416no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—82no—
374C2×Dic11—82no—
375C2×Dic11H(5,𝔽2)14yes—
376C23×D4—111no—
377C23×D4C2×D1111yescharacteristic
378C24×C4—111no—
379C24×C4—111no—
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—112no—
397C22×C22⋊C4C2×D1111yescharacteristic
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—114no—
413#386—112no—
414#386—112no—
415#386—112no—
416#386—114no—
417#386—112no—
418#386—114no—
419#386C2×D1114yes—
420#386C2×D1114yescomplemented
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—114no—
431#381C2×D1112yescomplemented
432#380—114no—
433#379—112no—
434#379C2×D1112yescomplemented
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×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—42no—
465C2×D11—44no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—44no—
469C2×D11—88no—
470C4×C11—24no—
471C4×C11—44no—
472C4×C11—44no—
473Dic11—24no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25—111no—
481C25C22×D1111yescharacteristic
482C25C22×D1111yescharacteristic
483C22×D4—24no—
484C22×D4—24no—
485C22×D4—112no—
486C22×D4—112no—
487C22×D4—112no—
488C22×D4—112no—
489C22×D4—224no—
490C22×D4—224no—
491C22×D4—224no—
492C22×D4D4418yes—
493C22×D4C22×D1112yes—
494C22×D4C22×D1112yes—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—112no—
498C23×C4—112no—
499C23×C4—114no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—224no—
506C23×C4—224no—
507C23×C4—444no—
508C23×C4—444no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1112yes—
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—24no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
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—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
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×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—44no—
571C2×C11C22×#12311yescharacteristic
572C2×C11#345912yes—
573C2×C11#348411yescharacteristic
574C2×C11#348511yescharacteristic
575C2×C11#350512yes—
576D11—82no—
577C24—22no—
578C24—22no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—112no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—442no—
588C24—442no—
589C24C2×D4414yes—
590C24C2×D4414yes—
591C24#434114yes—
592C24#434114yes—
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—224no—
603C2×D4—224no—
604C2×D4—224no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—444no—
611C2×D4—444no—
612C2×D4—4416no—
613C2×D4C2×D4418yes—
614C2×D4C2×D4418yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
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—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—228no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—442no—
647C22×C4—444no—
648C22×C4—442no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—4416no—
655C22×C4—4416no—
656C22×C4C2×D4414yes—
657C22×C4C23×D1114yes—
658C22×C4C23×D1114yes—
659C22×C4C23×D1112yes—
660C4⋊C4—228no—
661C4⋊C4—228no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
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—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—48no—
704C23—48no—
705C23—48no—
706C23—48no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—224no—
711C23—224no—
712C23—448no—
713C23—444no—
714C23—884no—
715C23—882no—
716C23—882no—
717C23#66939116yescomplemented
718C23C22×D4414yes—
719C23C22×D4412yes—
720C23C22×D4412yes—
721C23C22×D4412yes—
722C23C2×#434112yes—
723C23C2×#434112yes—
724C23C2×#434112yes—
725C23C2×#434112yes—
726C23C2×#434112yes—
727C23C2×#434112yes—
728C23C24×D1111yescharacteristic
729D4—216no—
730D4—216no—
731D4—448no—
732D4—448no—
733D4—884no—
734D4—884no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—48no—
745C2×C4—84no—
746C2×C4—114no—
747C2×C4—228no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—448no—
765C2×C4—448no—
766C2×C4—4416no—
767C2×C4—444no—
768C2×C4—444no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4—882no—
772C2×C4—882no—
773C2×C4C22×D4414yes—
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—444no—
794C22—442no—
795C22—442no—
796C22—444no—
797C22—442no—
798C22—888no—
799C22C2×#6693914yes—
800C22C2×#6693914yes—
801C22C2×#6693914yes—
802C22C23×D4411yescharacteristic
803C22C22×#434111yescharacteristic
804C22C22×#434111yescharacteristic
805C22D11×H(5,𝔽2)12yes—
806C22#1062345512yes—
807C4—24no—
808C4—44no—
809C4—44no—
810C4—224no—
811C4—442no—
812C4—442no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4—442no—
817C2—24no—
818C2—24no—
819C2—24no—
820C2—44no—
821C2—882no—
822C2C22×#6693911yescharacteristic
823C2#1308202212yes—
824C2#1308225211yescharacteristic
825C2#1308226111yescharacteristic
826C2#1308245312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2308C2
prime radicalC2×#10623335C2
hypercenter#2308D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic11C2semidirect
3. #13076939C2semidirect
4. #13076910C2semidirect
5. #13074399C2semidirect
6. #13074392C2semidirect
7. #13072364C2semidirect
8. #13072349C2semidirect
9. #13072091C2semidirect
10. #13072076C2semidirect
11. #13071230C2semidirect
12. #13071191C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622563C2semidirect
15. C11×#2308C2semidirect
19. C24×Dic11C22semidirect
25. C22×C22⋊Dic11C22semidirect
33. C2×D4×Dic11C22semidirect
35. C22×(C2×D11)⋊C4C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×C4×Dic11C22semidirect
39. C2×#66939C22semidirect
41. C11×#386C22semidirect
42. C11×#381C22semidirect
43. C11×#379C22semidirect
44. #10622826C22semidirect
45. #10622825C22semidirect
46. C2×C11⋊#95C22semidirect
47. C2×C11⋊#95C22semidirect
48. #10622574C22semidirect
49. #10622574C22semidirect
54. #10622571C22semidirect
55. #10622571C22semidirect
56. #10622568C22semidirect
57. #10622566C22semidirect
58. #10622566C22semidirect
59. #10622563C22semidirect
60. #10622563C22semidirect
61. #10622563C22semidirect
62. #10622563C22semidirect
63. #10622563C22semidirect
64. #10622563C22semidirect
65. #10622563C22semidirect
66. #10622563C22semidirect
67. #10622556C22semidirect
68. #10622556C22semidirect
69. #10622290C22semidirect
70. #10622287C22semidirect
71. #10622283C22semidirect
72. #10622283C22semidirect
73. #10622274C22semidirect
74. #10622272C22semidirect
75. #10622266C22semidirect
76. #10622266C22semidirect
287. #2308D11semidirect
309. C23×C11#123semidirect
420. #386C2×D11semidirect
431. #381C2×D11semidirect
434. #379C2×D11semidirect
687. C11#34983semidirect
717. C23#66939semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C22×D4×Dic112
#130769392
#130769102
#130743992
#130743922
#130723642
#130723492
#130720912
#130720762
#130712302
#130711912
C2×#106225712
C2×#106225632
C11×#23082
#3498311