Finite Group Databasebeta

← #14920613

Subgroups — #14920613

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074517C214yesmaximal, complemented
4#13074487C211yesmaximal, characteristic, complemented
5#13074484C211yesmaximal, characteristic, complemented
6#13074469C211yesmaximal, characteristic, complemented
7#13074420C212yesmaximal, complemented
8#13074395C212yesmaximal, complemented
9#13074349C212yesmaximal, complemented
10#13074327C212yesmaximal, complemented
11#13071898C212yesmaximal, complemented
12#13071894C212yesmaximal, complemented
13#13071853C212yesmaximal, complemented
14#13071851C212yesmaximal, complemented
15#13071121C214yesmaximal, complemented
16#13071013C211yesmaximal, characteristic, complemented
17C11×#2631C211yesmaximal, characteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C23×C4×D11C2212yes—
20C2×C11×#124C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic, complemented
24C2×#66991C2211yescharacteristic
25C2×#66990C2214yes—
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic, complemented
28C2×D4×Dic11C2214yescomplemented
29C2×C4×C22⋊D11C2212yes—
30#10623211—28no—
31C4×D4×D11—28no—
32C2×#66946C2211yescharacteristic
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×#66936C2212yes—
35C2×(C22⋊D11)⋊C4C2212yes—
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×(C22⋊D11)⋊C4C2214yescomplemented
38C2×C22⋊C4×D11C2212yes—
39C2×#66932C2212yescomplemented
40C2×#66930C2212yescomplemented
41C2×C4×D44C2211yescharacteristic
42C2×C42×D11C2211yescharacteristic
43C2×#66923C2211yescharacteristic, complemented
44C11×#397C2212yescomplemented
45C11×#393C2212yescomplemented
46C11×#392C2212yes—
47C11×#392C2212yescomplemented
48C11×#386C2214yescomplemented
49C11×#383C2211yescharacteristic, complemented
50#10622844C2212yescomplemented
51#10622836C2214yes—
52#10622836C2212yescomplemented
53#10622835C2212yes—
54#10622835C2214yescomplemented
55#10622823C2214yescomplemented
56#10622593C2212yescomplemented
57#10622574C2214yes—
58#10622573C2212yes—
59#10622572C2214yescomplemented
60#10622569C2214yes—
61#10622569C2214yescomplemented
62#10622568C2214yes—
63#10622566C2212yescomplemented
64#10622566C2212yescomplemented
65#10622562C2212yescomplemented
66#10622562C2214yescomplemented
67#10622561C2214yescomplemented
68C22⋊C4×Dic11C2214yescomplemented
69#10622550C2211yescharacteristic, complemented
70#10622290C2212yescomplemented
71#10622289C2214yescomplemented
72#10622287C2212yescomplemented
73#10622285C2212yes—
74#10622281C2214yes—
75#10622281C2214yescomplemented
76#10622280C2212yes—
77#10622279C2212yes—
78#10622279C2214yescomplemented
79#10622277C2212yes—
80#10622274C2212yescomplemented
81#10622273C2214yescomplemented
82#10622263C2212yescomplemented
83#10622262C2212yescomplemented
84#10622261C2212yescomplemented
85C24×D11C2312yes—
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2314yes—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2314yes—
94C23×Dic11C2312yes—
95C23×Dic11C2312yes—
96C2×D4×D11—28no—
97C2×D4×D11—24no—
98C22×D44C2311yescharacteristic
99C22×C4×D11—28no—
100C22×C4×D11—48no—
101C22×C4×D11C2312yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2312yes—
105C22×C4×D11C2312yes—
106C22×C4×D11C2311yescharacteristic
107C11×#124—24no—
108C4×D4×C11—24no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122#66999—24no—
123Q8×Dic11—24no—
124#66991—24no—
125#66990—216no—
126D4×Dic11—24no—
127D4×Dic11—24no—
128D4×Dic11—48no—
129C4×C22⋊D11—28no—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153#66946—24no—
154C4⋊C4×D11—24no—
155#66936—28no—
156(C22⋊D11)⋊C4—28no—
157(C22⋊D11)⋊C4—28no—
158(C22⋊D11)⋊C4—48no—
159C22⋊C4×D11—28no—
160#66932—28no—
161#66930—28no—
162C4×D44—24no—
163C42×D11D418yescomplemented
164#66923—24no—
165C11×#95C2312yes—
166C11×#95C2312yes—
167C11×#95C2312yes—
168C11×#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2312yes—
171C11⋊#95C2312yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176#34593—111nomaximal, Sylow
177C24×C11C2412yes—
178C24×C11C2412yes—
179C23×D11—24no—
180C23×D11—24no—
181C23×D11—44no—
182C23×D11—44no—
183C23×D11#4118yes—
184C23×D11C2412yes—
185C23×D11C2411yescharacteristic
186C2×Q8×C11—22no—
187C2×Q8×C11—42no—
188C2×D4×C11—24no—
189C2×D4×C11—28no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—44no—
193C2×D4×C11—42no—
194C2×D4×C11—44no—
195C22×C4×C11—24no—
196C22×C4×C11—44no—
197C22×C4×C11C2414yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—28no—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—28no—
216C22×Dic11C2414yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2411yescharacteristic
222C22×Dic11C2411yescharacteristic
223D4×D11—232no—
224C2×D44—24no—
225C2×D44—22no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—28no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—44no—
233C2×C4×D11—44no—
234C2×C4×D11—42no—
235C2×C4×D11—432no—
236C2×C4×D11C2×D414yes—
237C2×C4×D11C2×D414yes—
238C2×C4×D11C2×D414yes—
239C11×C4⋊C4—22no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—44no—
244C11×C22⋊C4—44no—
245C42×C11C2×D414yes—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—28no—
250C22⋊Dic11—44no—
251C22⋊Dic11—44no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—44no—
258(C2×D11)⋊C4—44no—
259C4⋊Dic11—24no—
260C4⋊Dic11—22no—
261C4⋊Dic11—22no—
262C4⋊Dic11—22no—
263C4⋊Dic11—44no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270C4×Dic11—24no—
271C4×Dic11—28no—
272C4×Dic11C2×D414yes—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D414yes—
275C2×#529—111no—
276C22×C4×D4—111no—
277#2636—114no—
278#2633—111no—
279#2633—111no—
280#2631—111no—
281#2631D1111yescharacteristic, complemented
282#2626—112no—
283#2623—112no—
284#2617—112no—
285#2613—112no—
286#2398—112no—
287#2397—112no—
288#2392—112no—
289#2392—112no—
290C4×#120—114no—
291#2283—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—22no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—24no—
301C23×C11C2×#4114yes—
302C23×C11C2511yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—24no—
308C22×D11—24no—
309C22×D11—216no—
310C22×D11—416no—
311C22×D11—48no—
312C22×D11—48no—
313C22×D11—416no—
314C22×D11C22×D412yes—
315C22×D11C2×#4114yes—
316C22×D11C2×#4114yes—
317Q8×C11—44no—
318D4×C11—28no—
319D4×C11—44no—
320D4×C11—416no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—24no—
331C2×C4×C11—48no—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C22⋊D11—216no—
336C22⋊D11—416no—
337C22⋊D11—48no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—48no—
351C2×Dic11—48no—
352C2×Dic11C22×D412yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355C2×Dic11H(5,𝔽2)14yes—
356D44—28no—
357C4×D11—28no—
358C4×D11—28no—
359C4×D11—44no—
360C4×D11—48no—
361C4×D11—48no—
362C4×D11—48no—
363C23×D4—111no—
364C24×C4—112no—
365#529—228no—
366C2×#126—112no—
367C2×#125—111no—
368C2×#124C2×D1111yescharacteristic, complemented
369C2×#123—112no—
370C2×C22⋊Q8—111no—
371C2×#121—111no—
372C2×#120—114no—
373C2×C4×Q8—111no—
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—112no—
377C2×C4×D4—114no—
378C2×C4×D4—111no—
379C2×C4×D4—112no—
380C2×C4×D4—112no—
381C2×C4×D4—114no—
382C2×C4×D4—111no—
383C2×C4×D4—228no—
384C2×C4×D4C2×D1111yescharacteristic
385C2×#117—112no—
386C22×C4⋊C4—111no—
387C22×C22⋊C4—112no—
388C22×C42—111no—
389#400—114no—
390#399—114no—
391#399—112no—
392#399—112no—
393#398—112no—
394#398—112no—
395#397—112no—
396#397—112no—
397#397—112no—
398#397C2×D1112yescomplemented
399#396—114no—
400#396—114no—
401#394—112no—
402#394—114no—
403#394—114no—
404#394—114no—
405#394—112no—
406#393—112no—
407#393C2×D1112yescomplemented
408#392—114no—
409#392—112no—
410#392—112no—
411#392C2×D1112yes—
412#392C2×D1112yescomplemented
413#386—114no—
414#386—114no—
415#386C2×D1114yescomplemented
416#385—114no—
417#385—114no—
418#385—114no—
419#383—111no—
420#383C2×D1111yescharacteristic, complemented
421#382—112no—
422#381—112no—
423#380—112no—
424#379—114no—
425C4×C4⋊C4—112no—
426C4×C22⋊C4—114no—
427C4×C22⋊C4—112no—
428C4×C22⋊C4—114no—
429#376—112no—
430C22×C11—24no—
431C22×C11—28no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—44no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—44no—
439C22×C11—44no—
440C22×C11C23×D411yescharacteristic
441C22×C11C22×#4112yes—
442C22×C11C2×H(5,𝔽2)12yes—
443C22×C11#58512yes—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—28no—
447C2×D11—24no—
448C2×D11—28no—
449C2×D11—432no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—44no—
453C2×D11#52514yes—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—22no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11—44no—
460Dic11—22no—
461Dic11—22no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11—44no—
466Dic11#53514yes—
467C25—112no—
468C22×Q8C22×D1111yescharacteristic
469C22×D4—112no—
470C22×D4—112no—
471C22×D4—114no—
472C22×D4—111no—
473C22×D4—224no—
474C22×D4—228no—
475C22×D4C22×D1111yescharacteristic
476C22×D4C22×D1114yes—
477C22×D4C22×D1111yescharacteristic
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—112no—
482C23×C4—112no—
483C23×C4—112no—
484C23×C4—112no—
485C23×C4—112no—
486C23×C4—228no—
487C23×C4—448no—
488C23×C4C22×D1112yes—
489#126—228no—
490#125—224no—
491#124—24no—
492#123—228no—
493C22⋊Q8—224no—
494#121—224no—
495#120—2216no—
496C4×Q8—224no—
497C4×D4—24no—
498C4×D4—228no—
499C4×D4—224no—
500C4×D4—228no—
501C4×D4—224no—
502C4×D4—224no—
503C4×D4—228no—
504C4×D4—224no—
505C4×D4—448no—
506C4×D4—448no—
507#117—228no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—112no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—224no—
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—228no—
535C2×C22⋊C4C22×D1112yes—
536C2×C22⋊C4C22×D1112yes—
537C2×C22⋊C4C22×D1112yes—
538C2×C22⋊C4C22×D1114yes—
539C2×C22⋊C4C22×D1114yes—
540C2×C42—111no—
541C2×C42—111no—
542C2×C42—111no—
543C2×C42—118no—
544C2×C42—112no—
545C2×C42—114no—
546C2×C42C22×D1111yescharacteristic
547#95—112no—
548#95—114no—
549#95—112no—
550#95—114no—
551#95—114no—
552#95—114no—
553#95—112no—
554#95C22×D1112yes—
555#95C22×D1112yes—
556#95C22×D1114yes—
557#95C22×D1112yes—
558C2×C11—44no—
559C2×C11—82no—
560C2×C11C2×#52511yescharacteristic
561C2×C11C2×#53511yescharacteristic
562C2×C11#344911yescharacteristic
563C2×C11#345914yes—
564D11—24no—
565D11—44no—
566C24—111no—
567C24—112no—
568C24—118no—
569C24—224no—
570C24—224no—
571C24—444no—
572C24—444no—
573C24C23×D1112yes—
574C24C23×D1112yes—
575C2×Q8—22no—
576C2×Q8—42no—
577C2×D4—24no—
578C2×D4—28no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—44no—
584C2×D4—224no—
585C2×D4—224no—
586C2×D4—2232no—
587C2×D4—224no—
588C2×D4—224no—
589C2×D4—224no—
590C2×D4—228no—
591C2×D4—228no—
592C2×D4—222no—
593C2×D4—444no—
594C2×D4—444no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—114no—
601C22×C4—114no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—112no—
607C22×C4—224no—
608C22×C4—224no—
609C22×C4—228no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—228no—
617C22×C4—224no—
618C22×C4—444no—
619C22×C4—444no—
620C22×C4—442no—
621C22×C4—4432no—
622C22×C4C23×D1114yes—
623C22×C4C23×D1112yes—
624C22×C4C23×D1112yes—
625C22×C4C23×D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627C22×C4C23×D1111yescharacteristic
628C4⋊C4—22no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—222no—
633C4⋊C4—224no—
634C4⋊C4—222no—
635C4⋊C4—224no—
636C4⋊C4—222no—
637C4⋊C4—444no—
638C4⋊C4—444no—
639C4⋊C4—444no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—228no—
648C22⋊C4—228no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—228no—
653C22⋊C4—224no—
654C22⋊C4—444no—
655C22⋊C4—444no—
656C22⋊C4—444no—
657C22⋊C4—444no—
658C42—114no—
659C42—114no—
660C42—114no—
661C42—224no—
662C42—228no—
663C42D4×D1114yes—
664C11#3459311yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—112no—
675C23—114no—
676C23—114no—
677C23—2216no—
678C23—222no—
679C23—222no—
680C23—222no—
681C23—222no—
682C23—224no—
683C23—224no—
684C23—4416no—
685C23—448no—
686C23—448no—
687C23—4416no—
688C23#41×D1114yes—
689C23C24×D1111yescharacteristic
690Q8—44no—
691D4—28no—
692D4—44no—
693D4—416no—
694D4—228no—
695D4—2216no—
696D4—448no—
697D4—4416no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—48no—
709C2×C4—112no—
710C2×C4—114no—
711C2×C4—112no—
712C2×C4—112no—
713C2×C4—228no—
714C2×C4—228no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—444no—
728C2×C4—448no—
729C2×C4—448no—
730C2×C4—448no—
731C2×C4—448no—
732C2×C4—448no—
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1112yes—
735C2×C4C2×D4×D1112yes—
736C22—28no—
737C22—24no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—114no—
747C22—222no—
748C22—222no—
749C22—228no—
750C22—228no—
751C22—224no—
752C22—4432no—
753C22—442no—
754C22—442no—
755C22—444no—
756C22C22×D4×D1111yescharacteristic
757C22C2×#41×D1112yes—
758C22D11×H(5,𝔽2)12yes—
759C22#1062345512yes—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—44no—
766C4—114no—
767C4—222no—
768C4—222no—
769C4—442no—
770C4—442no—
771C4—444no—
772C4—442no—
773C2—44no—
774C2—82no—
775C2—224no—
776C2—444no—
777C2D11×#52511yescharacteristic
778C2D11×#53511yescharacteristic
779C2#1308194711yescharacteristic
780C2#1308202714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2631C2
hypercenter#2631D11
hypocenterC11#34593
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2631

Complements

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

NH ≅ G/Ntype
1. C2×#10623211C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074517C2semidirect
4. #13074487C2semidirect
5. #13074484C2semidirect
6. #13074469C2semidirect
7. #13074420C2semidirect
8. #13074395C2semidirect
9. #13074349C2semidirect
10. #13074327C2semidirect
11. #13071898C2semidirect
12. #13071894C2semidirect
13. #13071853C2semidirect
14. #13071851C2semidirect
15. #13071121C2semidirect
16. #13071013C2semidirect
17. C11×#2631C2semidirect
20. C2×C11×#124C22semidirect
23. C2×Q8×Dic11C22semidirect
27. C2×D4×Dic11C22semidirect
28. C2×D4×Dic11C22semidirect
37. C2×(C22⋊D11)⋊C4C22semidirect
39. C2×#66932C22semidirect
40. C2×#66930C22semidirect
43. C2×#66923C22semidirect
44. C11×#397C22semidirect
45. C11×#393C22semidirect
47. C11×#392C22semidirect
48. C11×#386C22semidirect
49. C11×#383C22semidirect
50. #10622844C22semidirect
52. #10622836C22semidirect
54. #10622835C22semidirect
55. #10622823C22semidirect
56. #10622593C22semidirect
59. #10622572C22semidirect
61. #10622569C22semidirect
63. #10622566C22semidirect
64. #10622566C22semidirect
65. #10622562C22semidirect
66. #10622562C22semidirect
67. #10622561C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. #10622550C22semidirect
70. #10622290C22semidirect
71. #10622289C22semidirect
72. #10622287C22semidirect
75. #10622281C22semidirect
78. #10622279C22semidirect
80. #10622274C22semidirect
81. #10622273C22semidirect
82. #10622263C22semidirect
83. #10622262C22semidirect
84. #10622261C22semidirect
163. C42×D11D4semidirect
281. #2631D11semidirect
368. C2×#124C2×D11semidirect
398. #397C2×D11semidirect
407. #393C2×D11semidirect
412. #392C2×D11semidirect
415. #386C2×D11semidirect
420. #383C2×D11semidirect
664. C11#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×C4×D4×D112
#130745172
#130744872
#130744842
#130744692
#130744202
#130743952
#130743492
#130743272
#130718982
#130718942
#130718532
#130718512
#130711212
#130710132
C11×#26312
#3459311