Finite Group Databasebeta

← #14924651

Subgroups — #14924651

Order 2816.

2040 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074297C212yesmaximal, complemented
2#13074293C211yesmaximal, characteristic, complemented
3#13074028C211yesmaximal, characteristic, complemented
4#13073866C211yesmaximal, characteristic, complemented
5#13073679C212yesmaximal, complemented
6#13073485C212yesmaximal, complemented
7#13073395C212yesmaximal, complemented
8#13072854C212yesmaximal, complemented
9#13072734C212yesmaximal, complemented
10#13071893C212yesmaximal, complemented
11#13071882C211yesmaximal, characteristic, complemented
12#13071834C211yesmaximal, characteristic
13#13071166C212yesmaximal, complemented
14#13071155C211yesmaximal, characteristic, complemented
15#13071137C212yesmaximal, complemented
16#13071105C212yesmaximal, complemented
17#13071074C212yesmaximal, complemented
18#13070955C212yesmaximal, complemented
19C11×#2612C211yesmaximal, characteristic, complemented
20C22×#4343C2211yescharacteristic
21C2×#66951C2212yes—
22C2×#66947C2212yes—
23C2×#66946C2212yes—
24C2×#66946C2211yescharacteristic
25C2×#66945C2212yes—
26C2×#66945C2211yescharacteristic
27C2×#66940C2211yescharacteristic
28C2×#66928C2211yescharacteristic
29C2×#66925C2212yes—
30C2×#66925C2212yes—
31C2×C42×D11C2212yes—
32C11×#400C2211yescharacteristic
33C11×#398C2212yes—
34C11×#395C2211yescharacteristic
35C11×#391C2212yes—
36C11×#389C2212yes—
37C11×#387C2212yes—
38C11×#387C2212yes—
39C11×#382C2211yescharacteristic
40C11×#376C2212yes—
41#10622844C2211yescharacteristic
42#10622843C2212yes—
43#10622607C2212yes—
44#10622607C2212yes—
45#10622605C2211yescharacteristic
46#10622605C2212yes—
47#10622604C2211yescharacteristic
48#10622604C2212yes—
49#10622603C2212yes—
50#10622603C2212yes—
51#10622603C2212yes—
52#10622601C2212yes—
53#10622601C2211yescharacteristic
54#10622601C2212yes—
55#10622598C2212yes—
56#10622597C2212yes—
57#10622596C2211yescharacteristic
58#10622591C2212yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61#10622587C2211yescharacteristic
62#10622553C2212yes—
63#10622553C2212yes—
64#10622552C2212yes—
65#10622552C2212yes—
66#10622545C2212yes—
67C42×Dic11C2211yescharacteristic
68C42×Dic11C2212yes—
69#10622288C2212yes—
70#10622287C2211yescharacteristic
71#10622286C2212yes—
72#10622285C2212yes—
73#10622284C2212yes—
74#10622284C2211yescharacteristic
75#10622283C2212yes—
76#10622283C2212yes—
77#10622283C2212yes—
78#10622283C2212yes—
79#10622282C2212yes—
80#10622282C2212yes—
81#10622281C2212yes—
82#10622279C2212yes—
83#10622279C2212yes—
84#10622279C2212yes—
85#10622279C2212yes—
86#10622279C2211yescharacteristic
87#10622279C2212yes—
88#10622279C2212yes—
89#10622279C2212yes—
90#10622279C2211yescharacteristic
91#10622279C2212yes—
92#10622278C2212yes—
93#10622278C2212yes—
94#10622278C2212yes—
95#10622278C2212yes—
96#10622278C2212yes—
97#10622277C2212yes—
98#10622273C2212yes—
99#10622269C2212yes—
100#10622268C2212yes—
101#10622266C2212yes—
102#10622264C2212yes—
103#10622262C2212yes—
104#10622262C2212yes—
105#10622262C2212yes—
106#10622262C2212yes—
107C22×Q8×C11C2311yescharacteristic
108C2×#4343—28no—
109C2×#4343—42no—
110C22×D44C2312yes—
111C22×D44C2311yescharacteristic
112C22×D44C2312yes—
113C22×D44C2311yescharacteristic
114C22×C4×D11C2312yes—
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2312yes—
118C22×C4×D11C2312yes—
119C22×Dic22C2311yescharacteristic
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2312yes—
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C42×C11C2312yes—
128C2×C42×C11C2312yes—
129C2×C42×C11C2311yescharacteristic
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2312yes—
146C2×(C2×D11)⋊C4C2312yes—
147C2×(C2×D11)⋊C4C2311yescharacteristic
148C2×(C2×D11)⋊C4C2311yescharacteristic
149C2×(C2×D11)⋊C4C2312yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×C4⋊Dic11C2312yes—
152C2×C4⋊Dic11C2312yes—
153C2×C4⋊Dic11C2311yescharacteristic
154C2×C4⋊Dic11C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×Dic11⋊C4C2312yes—
159C2×Dic11⋊C4C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2311yescharacteristic
171C2×C4×Dic11C2312yes—
172#66951—28no—
173#66947—28no—
174#66946—28no—
175#66946—42no—
176#66945—44no—
177#66945—42no—
178#66940—42no—
179#66928—24no—
180#66925—28no—
181#66925—28no—
182C42×D11—28no—
183C11×#95C2312yes—
184C11×#95C2312yes—
185C11×#95C2312yes—
186C11×#95C2312yes—
187C11×#95C2312yes—
188C11×#95C2312yes—
189C11×#95C2311yescharacteristic
190C11×#95C2312yes—
191C11×#95C2311yescharacteristic
192C11×#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2311yescharacteristic
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2311yescharacteristic
207#34871—111nomaximal, Sylow
208C23×D11C2411yescharacteristic
209C23×D11C2411yescharacteristic
210C23×D11C2412yes—
211C2×Q8×C11—24no—
212C2×Q8×C11—41no—
213C22×C4×C11C2411yescharacteristic
214C22×C4×C11C2412yes—
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2411yescharacteristic
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2411yescharacteristic
229#4343—416no—
230C2×D44—24no—
231C2×D44—24no—
232C2×D44—24no—
233C2×D44—22no—
234C2×D44—24no—
235C2×D44—24no—
236C2×D44—41no—
237C2×D44—42no—
238C2×D44—41no—
239C2×D44—42no—
240C2×D44—41no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—42no—
253C2×C4×D11#4118yes—
254C2×Dic22—22no—
255C2×Dic22—41no—
256C2×Dic22—41no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—41no—
261C11×C4⋊C4—42no—
262C11×C4⋊C4—41no—
263C11×C4⋊C4—41no—
264C42×C11—24no—
265C42×C11—24no—
266C42×C11#4114yescomplemented
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—42no—
282(C2×D11)⋊C4—42no—
283(C2×D11)⋊C4—42no—
284(C2×D11)⋊C4—41no—
285(C2×D11)⋊C4—41no—
286(C2×D11)⋊C4—42no—
287(C2×D11)⋊C4—42no—
288C4⋊Dic11—24no—
289C4⋊Dic11—42no—
290C4⋊Dic11—41no—
291C4⋊Dic11—42no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295Dic11⋊C4—42no—
296Dic11⋊C4#4118yescomplemented
297C4×Dic11—24no—
298C4×Dic11—24no—
299C4×Dic11—24no—
300C4×Dic11—24no—
301C4×Dic11—24no—
302C4×Dic11—24no—
303C4×Dic11—22no—
304C4×Dic11—24no—
305C4×Dic11—24no—
306C4×Dic11—24no—
307C4×Dic11—42no—
308C4×Dic11—41no—
309#2612D1111yescharacteristic, complemented
310#2610—112no—
311#2609—111no—
312#2586—111no—
313#2572—111no—
314#2554—112no—
315#2532—112no—
316#2526—112no—
317#2479—112no—
318#2471—112no—
319#2396—112no—
320#2395—111no—
321#2388—111no—
322C4×#126—112no—
323C4×#124—111no—
324C4×#123—112no—
325#2297—112no—
326#2293—112no—
327C4×#117—112no—
328C23×C11C2511yescharacteristic
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—21no—
337C22×D11—21no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—21no—
342C22×D11—21no—
343C22×D11—21no—
344C22×D11—21no—
345C22×D11C2×#4114yes—
346Q8×C11—44no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11C2×#4114yes—
369C2×C4×C11C2×#4112yes—
370C2×C4×C11C2×#4114yes—
371C2×C4×C11C2×#4114yes—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—21no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11C2×#4114yes—
388C2×Dic11C2×#4114yes—
389C2×Dic11C2×#4114yes—
390C2×Dic11H(5,𝔽2)12yes—
391D44—48no—
392D44—48no—
393D44—44no—
394D44—44no—
395C4×D11—216no—
396C4×D11—216no—
397C4×D11—48no—
398C4×D11—44no—
399C4×D11—44no—
400Dic22—44no—
401C22×#41—111no—
402C2×#126—112no—
403C2×#124—111no—
404C2×#123—112no—
405C2×C4×Q8—111no—
406C2×C4×D4—112no—
407C2×C4×D4—111no—
408C2×#117—111no—
409C2×#117—112no—
410C2×#117—112no—
411C2×#117—112no—
412C22×C42—112no—
413#400—112no—
414#400C2×D1111yescharacteristic
415#399—111no—
416#399—112no—
417#398—111no—
418#398—112no—
419#398C2×D1112yes—
420#397—111no—
421#397—112no—
422#396—112no—
423#396—112no—
424#395—112no—
425#395C2×D1111yescharacteristic
426#394—111no—
427#394—112no—
428#394—112no—
429#393—111no—
430#393—112no—
431#392—112no—
432#392—111no—
433#391—112no—
434#391—111no—
435#391C2×D1112yes—
436#390—112no—
437#390—112no—
438#390—111no—
439#390—112no—
440#390—112no—
441#389—112no—
442#389C2×D1112yes—
443#388—112no—
444#388—112no—
445#388—112no—
446#388—112no—
447#388—112no—
448#388—112no—
449#388—112no—
450#388—112no—
451#388—112no—
452#388—112no—
453#388—112no—
454#387—112no—
455#387—112no—
456#387—112no—
457#387C2×D1112yes—
458#387C2×D1112yes—
459#386—112no—
460#386—112no—
461#386—112no—
462#386—112no—
463#386—112no—
464#385—112no—
465#383—112no—
466#382C2×D1111yescharacteristic
467#381—112no—
468C4×C4⋊C4—112no—
469C4×C4⋊C4—112no—
470C4×C4⋊C4—112no—
471C4×C4⋊C4—112no—
472C4×C4⋊C4—112no—
473C4×C4⋊C4—112no—
474C4×C22⋊C4—111no—
475C4×C22⋊C4—112no—
476C4×C22⋊C4—112no—
477C4×C22⋊C4—112no—
478C4×C22⋊C4—112no—
479C4×C22⋊C4—111no—
480C4×C22⋊C4—112no—
481C4×C22⋊C4—112no—
482C4×C22⋊C4—112no—
483C4×C22⋊C4—112no—
484#376—112no—
485#376C2×D1112yes—
486C43—112no—
487C43—111no—
488C22×C11C22×#4111yescharacteristic
489C22×C11C22×#4112yes—
490C22×C11C22×#4112yes—
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11#58511yescharacteristic
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—41no—
503C2×D11—41no—
504C2×D11—41no—
505C2×D11—41no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—41no—
509C2×D11—41no—
510C4×C11—24no—
511C4×C11—22no—
512C4×C11—24no—
513C4×C11—24no—
514C4×C11—41no—
515C4×C11—41no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519Dic11—24no—
520Dic11—24no—
521Dic11—42no—
522Dic11—42no—
523Dic11—42no—
524Dic11—41no—
525Dic11#55114yes—
526C2×#41—228no—
527C2×#41—442no—
528C22×Q8—111no—
529C22×Q8C22×D1111yescharacteristic
530C22×D4—112no—
531C22×D4—111no—
532C22×D4—112no—
533C22×D4—111no—
534C23×C4—112no—
535C23×C4—112no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—112no—
539#126—228no—
540#124—224no—
541#123—228no—
542C4×Q8—442no—
543C4×D4—228no—
544C4×D4—442no—
545#117—228no—
546#117—228no—
547#117—442no—
548#117—444no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—112no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—112no—
556C2×C4⋊C4—112no—
557C2×C4⋊C4—112no—
558C2×C4⋊C4C22×D1112yes—
559C2×C4⋊C4C22×D1112yes—
560C2×C4⋊C4C22×D1112yes—
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C4⋊C4C22×D1112yes—
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C4⋊C4C22×D1111yescharacteristic
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—112no—
569C2×C22⋊C4—112no—
570C2×C22⋊C4—112no—
571C2×C22⋊C4—112no—
572C2×C22⋊C4—112no—
573C2×C22⋊C4—112no—
574C2×C22⋊C4—112no—
575C2×C22⋊C4—112no—
576C2×C22⋊C4—112no—
577C2×C22⋊C4—112no—
578C2×C22⋊C4—112no—
579C2×C22⋊C4—112no—
580C2×C22⋊C4—112no—
581C2×C22⋊C4—112no—
582C2×C22⋊C4—111no—
583C2×C22⋊C4—111no—
584C2×C22⋊C4—112no—
585C2×C22⋊C4—112no—
586C2×C42—112no—
587C2×C42—112no—
588C2×C42—112no—
589C2×C42—112no—
590C2×C42—111no—
591C2×C42—112no—
592C2×C42—112no—
593C2×C42—112no—
594C2×C42—112no—
595C2×C42—112no—
596C2×C42—111no—
597C2×C42—112no—
598C2×C42—228no—
599C2×C42C22×D1112yes—
600C2×C42C22×D1112yes—
601C2×C42C22×D1111yescharacteristic
602#95—112no—
603#95—112no—
604#95—112no—
605#95—112no—
606#95—112no—
607#95—111no—
608#95—112no—
609#95—111no—
610#95—112no—
611#95—112no—
612#95—112no—
613#95—112no—
614#95—112no—
615#95—112no—
616#95C22×D1112yes—
617#95C22×D1112yes—
618#95C22×D1112yes—
619#95C22×D1112yes—
620#95C22×D1111yescharacteristic
621#95C22×D1112yes—
622#95C22×D1112yes—
623#95C22×D1112yes—
624#95C22×D1112yes—
625#95C22×D1111yescharacteristic
626C2×C11#344412yes—
627C2×C11#346011yescharacteristic
628C2×C11C2×#55111yescharacteristic
629C2×C11#347512yes—
630C2×C11#348311yescharacteristic
631D11—44no—
632D11—81no—
633D11—81no—
634C24—112no—
635C24—111no—
636C24—111no—
637#41—4416no—
638C2×Q8—24no—
639C2×Q8—41no—
640C2×Q8—222no—
641C2×Q8—441no—
642C2×Q8—441no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—222no—
647C2×D4—224no—
648C2×D4—224no—
649C2×D4—441no—
650C2×D4—442no—
651C2×D4—441no—
652C2×D4—442no—
653C2×D4—441no—
654C22×C4—111no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—118no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—111no—
662C22×C4—224no—
663C22×C4—224no—
664C22×C4—224no—
665C22×C4—222no—
666C22×C4—224no—
667C22×C4—222no—
668C22×C4—224no—
669C22×C4—224no—
670C22×C4—224no—
671C22×C4—224no—
672C22×C4—224no—
673C22×C4—442no—
674C22×C4C23×D1111yescharacteristic
675C22×C4C23×D1112yes—
676C22×C4C23×D1111yescharacteristic
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1111yescharacteristic
681C22×C4C23×D1112yes—
682C22×C4C23×D1112yes—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—42no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4—118no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—442no—
696C4⋊C4—441no—
697C4⋊C4—442no—
698C4⋊C4—442no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C22⋊C4—224no—
711C22⋊C4—224no—
712C22⋊C4—224no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—442no—
716C22⋊C4—441no—
717C22⋊C4—441no—
718C22⋊C4—442no—
719C22⋊C4—442no—
720C42—24no—
721C42—24no—
722C42—224no—
723C42—224no—
724C42—224no—
725C42—224no—
726C42—224no—
727C42—224no—
728C42—222no—
729C42—224no—
730C42—224no—
731C42—224no—
732C42—442no—
733C42—441no—
734C42#434314yescomplemented
735C11#3487111yescharacteristic, complemented, Sylow
736C23—114no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—221no—
744C23—221no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—221no—
750C23—221no—
751C23—221no—
752C23—221no—
753C23C24×D1111yescharacteristic
754Q8—44no—
755Q8—444no—
756D4—448no—
757D4—448no—
758D4—444no—
759D4—444no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—114no—
782C2×C4—112no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—2216no—
786C2×C4—2216no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—221no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—444no—
803C2×C4—444no—
804C2×C4—448no—
805C2×C4C2×#434314yes—
806C2×C4C2×#434312yes—
807C2×C4#41×D1114yes—
808C2×C4#41×D1114yes—
809C22—224no—
810C22—224no—
811C22—224no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—441no—
821C22—441no—
822C22—441no—
823C22—441no—
824C22—441no—
825C22—441no—
826C22C22×#434311yescharacteristic
827C22C2×#41×D1112yes—
828C22C2×#41×D1112yes—
829C22D11×H(5,𝔽2)11yescharacteristic
830C22#1062345711yescharacteristic
831C4—24no—
832C4—24no—
833C4—22no—
834C4—24no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—41no—
839C4—41no—
840C4—114no—
841C4—224no—
842C4—224no—
843C4—442no—
844C4—441no—
845C4—442no—
846C4—442no—
847C2—444no—
848C2—881no—
849C2—881no—
850C2#1308191312yes—
851C2#1308203911yescharacteristic
852C2D11×#55111yescharacteristic
853C2#1308216912yes—
854C2#1308224111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2612C2
prime radical#13071834C2
hypercenter#2612D11
hypocenterC11#34871
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2612

Complements

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

NH ≅ G/Ntype
1. #13074297C2semidirect
2. #13074293C2semidirect
3. #13074028C2semidirect
4. #13073866C2semidirect
5. #13073679C2semidirect
6. #13073485C2semidirect
7. #13073395C2semidirect
8. #13072854C2semidirect
9. #13072734C2semidirect
10. #13071893C2semidirect
11. #13071882C2semidirect
13. #13071166C2semidirect
14. #13071155C2semidirect
15. #13071137C2semidirect
16. #13071105C2semidirect
17. #13071074C2semidirect
18. #13070955C2semidirect
19. C11×#2612C2semidirect
266. C42×C11#41semidirect
296. Dic11⋊C4#41semidirect
309. #2612D11semidirect
734. C42#4343semidirect
735. C11#34871semidirect

Maximal subgroups

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

subgroupindex
#130742972
#130742932
#130740282
#130738662
#130736792
#130734852
#130733952
#130728542
#130727342
#130718932
#130718822
#130718342
#130711662
#130711552
#130711372
#130711052
#130710742
#130709552
C11×#26122
#3487111