Finite Group Databasebeta

← #14924699

Subgroups — #14924699

Order 2816.

1992 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074324C211yesmaximal, characteristic, complemented
2#13074303C212yesmaximal, complemented
3#13074106C211yesmaximal, characteristic, complemented
4#13073883C212yesmaximal, complemented
5#13073684C211yesmaximal, characteristic
6#13073460C212yesmaximal, complemented
7#13073430C212yesmaximal, complemented
8#13072799C212yesmaximal, complemented
9#13072769C212yesmaximal, complemented
10#13071908C211yesmaximal, characteristic, complemented
11#13071904C211yesmaximal, characteristic, complemented
12#13071861C212yesmaximal, complemented
13#13071157C212yesmaximal, complemented
14#13071155C211yesmaximal, characteristic, complemented
15#13071126C212yesmaximal, complemented
16#13071108C212yesmaximal, complemented
17#13071052C212yesmaximal, complemented
18#117×Dic11C212yesmaximal, complemented
19C11×#2609C211yesmaximal, characteristic, complemented
20C2×C11×#117C2212yes—
21C2×#66992C2212yes—
22C2×D4×Dic11C2211yescharacteristic
23C2×#66979C2212yes—
24C22×C4×Dic11C2212yes—
25C2×#66946C2211yescharacteristic
26C2×#66945C2212yes—
27C2×#66940C2211yescharacteristic
28C2×#66940C2211yescharacteristic
29C2×#66938C2212yes—
30C2×(C22⋊D11)⋊C4C2212yes—
31C2×(C22⋊D11)⋊C4C2212yes—
32C2×#66928C2211yescharacteristic
33C11×#398C2211yescharacteristic
34C11×#396C2212yes—
35C11×#394C2211yescharacteristic
36C11×#388C2212yes—
37C11×#387C2212yes—
38C11×#386C2212yes—
39C11×#385C2212yes—
40C11×#382C2211yescharacteristic
41#10622835C2211yescharacteristic
42#10622826C2212yes—
43#10622826C2212yes—
44#10622607C2212yes—
45#10622604C2212yes—
46#10622603C2212yes—
47#10622603C2212yes—
48#10622603C2212yes—
49#10622601C2211yescharacteristic
50#10622599C2211yescharacteristic
51#10622597C2212yes—
52#10622594C2212yes—
53#10622593C2211yescharacteristic
54#10622592C2211yescharacteristic
55#10622592C2212yes—
56#10622591C2212yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61#10622587C2211yescharacteristic
62#10622574C2212yes—
63#10622574C2212yes—
64#10622573C2212yes—
65#10622571C2212yes—
66#10622570C2212yes—
67#10622570C2212yes—
68#10622565C2212yes—
69#10622563C2212yes—
70#10622560C2212yes—
71#10622558C2212yes—
72#10622557C2212yes—
73#10622555C2212yes—
74C22⋊C4×Dic11C2212yes—
75C22⋊C4×Dic11C2212yes—
76C22⋊C4×Dic11C2212yes—
77C22⋊C4×Dic11C2212yes—
78C22⋊C4×Dic11C2212yes—
79#10622553C2212yes—
80#10622553C2212yes—
81#10622545C2212yes—
82#10622545C2212yes—
83C42×Dic11C2212yes—
84C42×Dic11C2211yescharacteristic
85#10622288C2212yes—
86#10622283C2212yes—
87#10622283C2212yes—
88#10622283C2212yes—
89#10622282C2212yes—
90#10622282C2212yes—
91#10622282C2212yes—
92#10622279C2212yes—
93#10622279C2212yes—
94#10622279C2212yes—
95#10622272C2211yescharacteristic
96#10622270C2212yes—
97#10622269C2211yescharacteristic
98#10622268C2212yes—
99#10622267C2212yes—
100#10622266C2212yes—
101#10622263C2212yes—
102#10622262C2212yes—
103#10622261C2211yescharacteristic
104#10622261C2211yescharacteristic
105#10622260C2212yes—
106#10622259C2212yes—
107C22×D4×C11C2311yescharacteristic
108C23×C4×C11C2312yes—
109C22×C22⋊D11C2312yes—
110C22×C22⋊D11C2312yes—
111C23×Dic11C2312yes—
112C23×Dic11C2312yes—
113C22×D44C2311yescharacteristic
114C22×C4×D11C2312yes—
115C22×Dic22C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C11×#117—28no—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C42×C11C2312yes—
130C2×C42×C11C2311yescharacteristic
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135#66992—28no—
136D4×Dic11—42no—
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)⋊C4C2312yes—
148#66979—28no—
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2312yes—
151C2×C4⋊Dic11C2312yes—
152C2×C4⋊Dic11C2311yescharacteristic
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2311yescharacteristic
158C2×Dic11⋊C4C2311yescharacteristic
159C2×Dic11⋊C4C2312yes—
160C2×C4×Dic11—28no—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2311yescharacteristic
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2312yes—
173C2×C4×Dic11C2311yescharacteristic
174C2×C4×Dic11C2312yes—
175#66946—42no—
176#66945—28no—
177#66940—42no—
178#66940—42no—
179#66938—28no—
180(C22⋊D11)⋊C4—28no—
181(C22⋊D11)⋊C4—44no—
182#66928—24no—
183C11×#95C2312yes—
184C11×#95C2312yes—
185C11×#95C2311yescharacteristic
186C11×#95C2311yescharacteristic
187C11×#95C2312yes—
188C11×#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2311yescharacteristic
194C11⋊#95C2311yescharacteristic
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207#34874—111nomaximal, Sylow
208C24×C11C2412yes—
209C23×D11C2412yes—
210C2×D4×C11—24no—
211C2×D4×C11—41no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—24no—
215C22×C4×C11C2412yes—
216C22×C4×C11C2411yescharacteristic
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—42no—
228C2×C22⋊D11—42no—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11—24no—
234C22×Dic11—42no—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2411yescharacteristic
238C22×Dic11C2411yescharacteristic
239C22×Dic11C2411yescharacteristic
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2411yescharacteristic
244C2×D44—22no—
245C2×D44—41no—
246C2×D44—41no—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×C4×D11—24no—
250C2×Dic22—24no—
251C2×Dic22—22no—
252C2×Dic22—41no—
253C2×Dic22—41no—
254C2×Dic22—41no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—41no—
259C11×C4⋊C4—41no—
260C11×C4⋊C4—41no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—42no—
266C42×C11—24no—
267C42×C11#4114yes—
268C22⋊Dic11—24no—
269C22⋊Dic11—42no—
270C22⋊Dic11—42no—
271C22⋊Dic11#4118yes—
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—42no—
281(C2×D11)⋊C4—42no—
282(C2×D11)⋊C4—42no—
283C4⋊Dic11—24no—
284C4⋊Dic11—24no—
285C4⋊Dic11—24no—
286C4⋊Dic11—41no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—42no—
290Dic11⋊C4—41no—
291Dic11⋊C4—42no—
292Dic11⋊C4—41no—
293Dic11⋊C4—42no—
294C4×Dic11—24no—
295C4×Dic11—24no—
296C4×Dic11—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299C4×Dic11—24no—
300C4×Dic11—24no—
301C4×Dic11—22no—
302C4×Dic11—22no—
303C4×Dic11—22no—
304C4×Dic11—24no—
305C4×Dic11—41no—
306C4×Dic11—42no—
307C4×Dic11#4118yes—
308#2612—111no—
309#2610—112no—
310#2609D1111yescharacteristic, complemented
311#2593—111no—
312#2574—112no—
313#2555—111no—
314#2531—112no—
315#2529—112no—
316#2476—112no—
317#2474—112no—
318#2399—111no—
319#2398—111no—
320#2392—112no—
321C4×#124—112no—
322C4×#124—111no—
323C4×#121—112no—
324#2298—112no—
325#2290—112no—
326C4×#117—112no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11C2×#4114yes—
334C23×C11C2511yescharacteristic
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342D4×C11—44no—
343C2×C4×C11—216no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—21no—
359C2×C4×C11—22no—
360C2×C4×C11—21no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11C2×#4114yes—
364C2×C4×C11C2×#4112yes—
365C2×C4×C11C2×#4114yes—
366C22⋊D11—48no—
367C22⋊D11—48no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—21no—
380C2×Dic11—21no—
381C2×Dic11—21no—
382C2×Dic11—21no—
383C2×Dic11—21no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—48no—
389C2×Dic11—48no—
390C2×Dic11C2×#4114yes—
391C2×Dic11C2×#4114yes—
392C2×Dic11C2×#4114yes—
393C2×Dic11C2×#4114yes—
394C2×Dic11H(5,𝔽2)12yes—
395D44—44no—
396C4×D11—48no—
397Dic22—44no—
398Dic22—44no—
399C2×#124—112no—
400C2×#124—111no—
401C2×#121—112no—
402C2×C4×Q8—111no—
403C2×C4×Q8—111no—
404C2×C4×D4—111no—
405C2×C4×D4—111no—
406C2×C4×D4—112no—
407C2×C4×D4—112no—
408C2×#117—112no—
409C2×#117—112no—
410C2×#117C2×D1112yes—
411C22×C42—112no—
412#400—111no—
413#400—111no—
414#398—112no—
415#398—111no—
416#398—112no—
417#398C2×D1111yescharacteristic
418#397—112no—
419#397—112no—
420#396—112no—
421#396C2×D1112yes—
422#395—112no—
423#395—111no—
424#395—111no—
425#394—111no—
426#394—112no—
427#394—112no—
428#394—112no—
429#394C2×D1111yescharacteristic
430#393—112no—
431#392—112no—
432#391—111no—
433#391—112no—
434#390—111no—
435#390—112no—
436#390—112no—
437#389—112no—
438#388—112no—
439#388—112no—
440#388—112no—
441#388—112no—
442#388—112no—
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#388C2×D1112yes—
452#387—112no—
453#387—112no—
454#387—112no—
455#387—112no—
456#387—112no—
457#387C2×D1112yes—
458#386—112no—
459#386—112no—
460#386—112no—
461#386C2×D1112yes—
462#385—112no—
463#385C2×D1112yes—
464#382—112no—
465#382C2×D1111yescharacteristic
466#380—112no—
467C4×C4⋊C4—112no—
468C4×C4⋊C4—112no—
469C4×C4⋊C4—112no—
470C4×C4⋊C4—112no—
471C4×C4⋊C4—112no—
472C4×C22⋊C4—112no—
473C4×C22⋊C4—112no—
474C4×C22⋊C4—112no—
475C4×C22⋊C4—112no—
476C4×C22⋊C4—112no—
477C4×C22⋊C4—112no—
478C4×C22⋊C4—112no—
479C4×C22⋊C4—112no—
480#376—112no—
481#376—112no—
482#376—111no—
483#376—111no—
484C43—111no—
485C43—112no—
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11C22×#4111yescharacteristic
494C22×C11C22×#4112yes—
495C22×C11C22×#4112yes—
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C22×C11#58511yescharacteristic
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C4×C11—24no—
506C4×C11—24no—
507C4×C11—22no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—41no—
512C4×C11—41no—
513Dic11—24no—
514Dic11—24no—
515Dic11—24no—
516Dic11—41no—
517Dic11—41no—
518Dic11—42no—
519Dic11—42no—
520Dic11—41no—
521Dic11#55514yes—
522C22×Q8—111no—
523C22×Q8—111no—
524C22×D4—112no—
525C22×D4—112no—
526C22×D4—111no—
527C22×D4C22×D1111yescharacteristic
528C23×C4—112no—
529C23×C4—112no—
530C23×C4—112no—
531C23×C4C22×D1112yes—
532#124—228no—
533#124—224no—
534#121—228no—
535C4×Q8—442no—
536C4×Q8—442no—
537C4×D4—228no—
538C4×D4—444no—
539C4×D4—442no—
540C4×D4—442no—
541#117—28no—
542#117—228no—
543#117—228no—
544C2×C4⋊C4—112no—
545C2×C4⋊C4—112no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—112no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—112no—
555C2×C4⋊C4C22×D1112yes—
556C2×C4⋊C4C22×D1112yes—
557C2×C4⋊C4C22×D1112yes—
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C4⋊C4C22×D1111yescharacteristic
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C22⋊C4—112no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4—112no—
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⋊C4C22×D1112yes—
577C2×C22⋊C4C22×D1112yes—
578C2×C22⋊C4C22×D1112yes—
579C2×C22⋊C4C22×D1112yes—
580C2×C22⋊C4C22×D1112yes—
581C2×C42—112no—
582C2×C42—112no—
583C2×C42—112no—
584C2×C42—112no—
585C2×C42—112no—
586C2×C42—111no—
587C2×C42—111no—
588C2×C42—111no—
589C2×C42—112no—
590C2×C42—112no—
591C2×C42—112no—
592C2×C42—112no—
593C2×C42—111no—
594C2×C42—112no—
595C2×C42—228no—
596C2×C42C22×D1112yes—
597C2×C42C22×D1111yescharacteristic
598#95—112no—
599#95—112no—
600#95—112no—
601#95—112no—
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×D1111yescharacteristic
617#95C22×D1111yescharacteristic
618#95C22×D1112yes—
619#95C22×D1112yes—
620#95C22×D1112yes—
621#95C22×D1112yes—
622C2×C11—44no—
623C2×C11#344412yes—
624C2×C11#346011yescharacteristic
625C2×C11C2×#55511yescharacteristic
626C2×C11#347512yes—
627C2×C11#348111yescharacteristic
628D11—82no—
629C24—112no—
630C24C23×D1112yes—
631C2×Q8—224no—
632C2×Q8—222no—
633C2×Q8—441no—
634C2×Q8—441no—
635C2×Q8—441no—
636C2×D4—24no—
637C2×D4—41no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—222no—
643C2×D4—441no—
644C2×D4—441no—
645C2×D4—442no—
646C2×D4—442no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—111no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—224no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—224no—
667C22×C4—442no—
668C22×C4C23×D1112yes—
669C22×C4C23×D1111yescharacteristic
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1112yes—
675C22×C4C23×D1112yes—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—442no—
688C4⋊C4—441no—
689C4⋊C4—442no—
690C4⋊C4—441no—
691C4⋊C4—441no—
692C4⋊C4—442no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—118no—
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—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C42—24no—
714C42—118no—
715C42—224no—
716C42—224no—
717C42—224no—
718C42—224no—
719C42—224no—
720C42—222no—
721C42—224no—
722C42—222no—
723C42—222no—
724C42—224no—
725C42—224no—
726C42—441no—
727C42—442no—
728C42#434114yes—
729C11#3487411yescharacteristic, complemented, Sylow
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23#41×D1114yes—
744C23C24×D1111yescharacteristic
745Q8—444no—
746Q8—444no—
747D4—44no—
748D4—444no—
749D4—448no—
750D4—448no—
751C2×C4—216no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—114no—
772C2×C4—112no—
773C2×C4—114no—
774C2×C4—114no—
775C2×C4—114no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—221no—
783C2×C4—221no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—221no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—448no—
797C2×C4—448no—
798C2×C4—448no—
799C2×C4C2×#434114yes—
800C2×C4C2×#434112yes—
801C2×C4#41×D1114yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22C22×#434111yescharacteristic
817C22C2×#41×D1112yes—
818C22C2×#41×D1112yes—
819C22D11×H(5,𝔽2)11yescharacteristic
820C22#1062345711yescharacteristic
821C4—24no—
822C4—24no—
823C4—22no—
824C4—42no—
825C4—42no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—114no—
830C4—224no—
831C4—224no—
832C4—224no—
833C4—442no—
834C4—442no—
835C4—441no—
836C4—441no—
837C4—441no—
838C2—44no—
839C2—882no—
840C2#1308190812yes—
841C2#1308203311yescharacteristic
842C2D11×#55511yescharacteristic
843C2#1308216912yes—
844C2#1308221911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2609C2
prime radical#13073684C2
hypercenter#2609D11
hypocenterC11#34874
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2609

Complements

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

NH ≅ G/Ntype
1. #13074324C2semidirect
2. #13074303C2semidirect
3. #13074106C2semidirect
4. #13073883C2semidirect
6. #13073460C2semidirect
7. #13073430C2semidirect
8. #13072799C2semidirect
9. #13072769C2semidirect
10. #13071908C2semidirect
11. #13071904C2semidirect
12. #13071861C2semidirect
13. #13071157C2semidirect
14. #13071155C2semidirect
15. #13071126C2semidirect
16. #13071108C2semidirect
17. #13071052C2semidirect
18. #117×Dic11C2semidirect
19. C11×#2609C2semidirect
310. #2609D11semidirect
729. C11#34874semidirect

Maximal subgroups

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

subgroupindex
#130743242
#130743032
#130741062
#130738832
#130736842
#130734602
#130734302
#130727992
#130727692
#130719082
#130719042
#130718612
#130711572
#130711552
#130711262
#130711082
#130710522
#117×Dic112
C11×#26092
#3487411