Finite Group Databasebeta

← #14925262

Subgroups — #14925262

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic, complemented
2C2×#10623053C211yesmaximal, characteristic, complemented
3#13074223C214yesmaximal, complemented
4#13074211C214yesmaximal, complemented
5#13073815C211yesmaximal, characteristic, complemented
6#13073804C211yesmaximal, characteristic, complemented
7#13073599C211yesmaximal, characteristic, complemented
8#13073589C211yesmaximal, characteristic, complemented
9#13073074C211yesmaximal, characteristic, complemented
10#13072245C211yesmaximal, characteristic, complemented
11#13072235C211yesmaximal, characteristic
12#13071853C214yesmaximal, complemented
13#13071185C211yesmaximal, characteristic, complemented
14#13071178C211yesmaximal, characteristic, complemented
15#13071159C211yesmaximal, characteristic, complemented
16#13071155C211yesmaximal, characteristic, complemented
17#13071054C214yesmaximal, complemented
18C4×#66930C211yesmaximal, characteristic, complemented
19C11×#2499C211yesmaximal, characteristic, complemented
20C22×#4339C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×#67000C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29#10623155—28no—
30#10623053—28no—
31C2×#66951C2212yes—
32C2×#66946C2211yescharacteristic
33C2×#66946C2211yescharacteristic
34C2×#66946C2214yes—
35C2×#66946C2211yescharacteristic
36C2×#66945C2212yes—
37C2×#66943C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66939C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×(C22⋊D11)⋊C4C2212yes—
43C2×(C22⋊D11)⋊C4C2212yes—
44C2×#66930C2212yes—
45C2×#66928C2211yescharacteristic
46C2×#66927C2211yescharacteristic
47C2×#66925C2212yes—
48C2×C42×D11C2212yes—
49C11×#397C2214yes—
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#387C2214yes—
53C11×#384C2211yescharacteristic
54C11×#382C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C22⋊Dic11C2211yescharacteristic
57#10622602C2214yes—
58#10622601C2214yes—
59#10622601C2211yescharacteristic
60#10622601C2211yescharacteristic
61#10622601C2211yescharacteristic
62#10622594C2214yes—
63#10622593C2214yes—
64#10622590C2211yescharacteristic
65#10622589C2211yescharacteristic
66#10622587C2211yescharacteristic
67#10622573C2214yes—
68#10622572C2214yes—
69#10622572C2214yes—
70C22⋊C4×Dic11C2212yes—
71#10622553C2214yes—
72#10622552C2211yescharacteristic
73C4×Dic11⋊C4C2211yescharacteristic
74C4×Dic11⋊C4C2211yescharacteristic
75C42×Dic11C2211yescharacteristic
76C42×Dic11C2211yescharacteristic
77#10622542C2211yescharacteristic
78#10622289C2214yes—
79#10622289C2214yes—
80#10622285C2214yes—
81#10622283C2214yes—
82#10622282C2214yes—
83#10622282C2214yes—
84#10622281C2214yes—
85#10622279C2214yes—
86#10622279C2214yes—
87#10622278C2214yes—
88#10622278C2214yes—
89#10622262C2212yes—
90#10622262C2214yes—
91#10622261C2212yes—
92#10622260C2214yes—
93C22×Q8×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2312yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C2×#4339—24no—
100C2×#4339—24no—
101C2×#4339—24no—
102C22×D44C2311yescharacteristic
103C22×D44C2314yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11C2312yes—
106C22×C4×D11C2312yes—
107C22×C4×D11C2312yes—
108C22×C4×D11C2312yes—
109C22×Dic22C2311yescharacteristic
110C11×C22⋊Q8—24no—
111C11×#117—24no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C42×C11C2312yes—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11C2312yes—
124#67000—24no—
125#67000—24no—
126Q8×Dic11—24no—
127#66997—24no—
128#66983—24no—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×C4×Dic11D418yescomplemented
152C2×C4×Dic11C2312yes—
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164C2×C4×Dic11C2312yes—
165#66951—28no—
166#66946—24no—
167#66946—24no—
168#66946—24no—
169#66946—216no—
170#66945—28no—
171#66943—24no—
172#66940—24no—
173#66940—24no—
174#66939—28no—
175(C22⋊D11)⋊C4—28no—
176(C22⋊D11)⋊C4—28no—
177(C22⋊D11)⋊C4—28no—
178#66930—28no—
179#66928—24no—
180#66927—24no—
181#66925—28no—
182C42×D11—28no—
183C11×#95C2314yes—
184C11×#95C2312yes—
185C11×#95C2314yes—
186C11×#95C2314yes—
187C11⋊#95C2314yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2314yes—
192C11⋊#95C2314yes—
193#34910—111nomaximal, Sylow
194C24×C11C2411yescharacteristic
195C23×D11C2412yes—
196C23×D11C2412yes—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—44no—
216C22×Dic11—24no—
217C22×Dic11—42no—
218C22×Dic11C2×D414yes—
219C22×Dic11C2×D414yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2411yescharacteristic
223C22×Dic11C2411yescharacteristic
224C22×Dic11C2411yescharacteristic
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2411yescharacteristic
228#4339—232no—
229C2×D44—28no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—28no—
236C2×D44—44no—
237C2×D44#4114yes—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—44no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22#4114yes—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—28no—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C42×C11—24no—
259C42×C11—22no—
260C42×C11—22no—
261C22⋊Dic11—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—22no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—28no—
282Dic11⋊C4—24no—
283Dic11⋊C4—44no—
284C4×Dic11—24no—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—22no—
289C4×Dic11—22no—
290C4×Dic11—42no—
291C4×Dic11—42no—
292C4×Dic11C2×D414yes—
293C4×Dic11C2×D414yes—
294C4×Dic11C2×D414yes—
295C4×Dic11C2×D414yes—
296C4×Dic11#4118yescomplemented
297C2×#529—111no—
298C2×C4×#41—111no—
299#2602—114no—
300#2601—114no—
301#2566—111no—
302#2565—111no—
303#2545—111no—
304#2544—111no—
305#2500—111no—
306#2499D1111yescharacteristic, complemented
307#2432—111no—
308#2431—111no—
309#2392—114no—
310C4×C4⋊Q8—111no—
311C4×#127—111no—
312C4×#124—111no—
313C4×#124—111no—
314#2290—114no—
315C4×#117—111no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11C22×D412yes—
321C23×C11C2511yescharacteristic
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—22no—
325C22×D11—24no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—24no—
331C22×D11C2×#4114yes—
332Q8×C11—44no—
333C2×C4×C11—22no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—28no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C2×#4114yes—
353C2×C4×C11C2×#4112yes—
354C2×C4×C11C2×#4112yes—
355C22⋊D11—216no—
356C22⋊D11—48no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—28no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—24no—
370C2×Dic11—44no—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375C2×Dic11C2×#4114yes—
376C2×Dic11C2×#4114yes—
377C2×Dic11C2×#4114yes—
378D44—28no—
379D44—416no—
380D44—44no—
381C4×D11—216no—
382C4×D11—48no—
383C4×D11—48no—
384C4×D11—48no—
385Dic22—28no—
386C22×#41—111no—
387C2×C4⋊Q8—111no—
388C2×#127—111no—
389#529—228no—
390C2×#126—112no—
391C2×#125—111no—
392C2×#124—111no—
393C2×#124—111no—
394C2×#124—111no—
395C2×#123—112no—
396C2×C22⋊Q8C2×D1111yescharacteristic
397C2×#121—111no—
398C4×#41—228no—
399C2×C4×Q8—111no—
400C2×C4×Q8—111no—
401C2×C4×Q8—111no—
402C2×C4×D4—114no—
403C2×C4×D4—111no—
404C2×C4×D4—111no—
405C2×C4×D4—111no—
406C2×C4×D4—112no—
407C2×C4×D4—112no—
408C2×C4×D4—112no—
409C2×#117—112no—
410C2×#117—112no—
411C2×#117—112no—
412C2×#117C2×D1111yescharacteristic
413C22×C42—111no—
414C22×C42—112no—
415#398—114no—
416#397C2×D1114yes—
417#396—114no—
418#396—114no—
419#394—114no—
420#394—114no—
421#394—114no—
422#392—114no—
423#391—111no—
424#391—111no—
425#391C2×D1111yescharacteristic
426#391C2×D1111yescharacteristic
427#390—111no—
428#390—114no—
429#390—111no—
430#390—111no—
431#390—111no—
432#389—114no—
433#388—114no—
434#388—114no—
435#388—114no—
436#388—114no—
437#387—114no—
438#387C2×D1114yes—
439#386—114no—
440#386—114no—
441#385—114no—
442#385—114no—
443#384—111no—
444#384C2×D1111yescharacteristic
445#382—111no—
446#382C2×D1111yescharacteristic
447C4×C4⋊C4—111no—
448C4×C4⋊C4—111no—
449C4×C4⋊C4—114no—
450C4×C4⋊C4—112no—
451C4×C22⋊C4—111no—
452C4×C22⋊C4—112no—
453C4×C22⋊C4—114no—
454C4×C22⋊C4—114no—
455C4×C22⋊C4C2×D1111yescharacteristic
456#376—112no—
457C43—111no—
458C43—111no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11C23×D411yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C22×#4112yes—
468C22×C11#58512yes—
469C2×D11—24no—
470C2×D11—28no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—44no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—44no—
478C2×D11—44no—
479C4×C11—22no—
480C4×C11—24no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11#52514yes—
487Dic11—24no—
488Dic11—22no—
489Dic11—22no—
490Dic11—22no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11#53214yes—
495C2×#41—224no—
496C2×#41—224no—
497C2×#41—224no—
498C22×Q8—111no—
499C22×Q8C22×D1111yescharacteristic
500C22×D4—112no—
501C22×D4—112no—
502C22×D4—111no—
503C22×D4—111no—
504C22×D4—114no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—112no—
508C23×C4—112no—
509C23×C4—112no—
510C23×C4—112no—
511C23×C4C22×D1111yescharacteristic
512C4⋊Q8—224no—
513#127—224no—
514#126—228no—
515#125—224no—
516#124—224no—
517#124—224no—
518#124—224no—
519#123—228no—
520C22⋊Q8—24no—
521#121—224no—
522C4×Q8—224no—
523C4×Q8—224no—
524C4×Q8—224no—
525C4×D4—224no—
526C4×D4—224no—
527C4×D4—224no—
528C4×D4—2216no—
529C4×D4—228no—
530C4×D4—228no—
531C4×D4—228no—
532#117—24no—
533#117—228no—
534#117—228no—
535#117—228no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4C22×D1112yes—
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1114yes—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4C22×D1112yes—
565C2×C22⋊C4C22×D1112yes—
566C2×C22⋊C4C22×D1112yes—
567C2×C42—118no—
568C2×C42—111no—
569C2×C42—111no—
570C2×C42—112no—
571C2×C42—111no—
572C2×C42—111no—
573C2×C42—112no—
574C2×C42—112no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—111no—
578C2×C42—111no—
579C2×C42—112no—
580C2×C42—112no—
581C2×C42—228no—
582C2×C42C22×D1112yes—
583C2×C42C22×D1111yescharacteristic
584C2×C42C22×D1111yescharacteristic
585#95—112no—
586#95—112no—
587#95—112no—
588#95—114no—
589#95—114no—
590#95—114no—
591#95C22×D1112yes—
592#95C22×D1114yes—
593#95C22×D1114yes—
594#95C22×D1114yes—
595C2×C11—42no—
596C2×C11C2×#52511yescharacteristic
597C2×C11C2×#53211yescharacteristic
598C2×C11#344911yescharacteristic
599C2×C11#347512yes—
600C2×C11#348012yes—
601D11—44no—
602D11—82no—
603C24—112no—
604C24—112no—
605C24C23×D1111yescharacteristic
606#41—2232no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—114no—
611C2×Q8—222no—
612C2×Q8—222no—
613C2×D4—114no—
614C2×D4—228no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—222no—
620C2×D4—222no—
621C2×D4—222no—
622C2×D4—228no—
623C2×D4—222no—
624C2×D4—222no—
625C2×D4—444no—
626C2×D4—444no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—111no—
630C22×C4—114no—
631C22×C4—111no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—114no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—228no—
644C22×C4—228no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—444no—
649C22×C4—442no—
650C22×C4D4×D1114yes—
651C22×C4C23×D1112yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1111yescharacteristic
657C22×C4C23×D1112yes—
658C22×C4C23×D1111yescharacteristic
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—24no—
662C4⋊C4—22no—
663C4⋊C4—28no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—228no—
671C4⋊C4—222no—
672C4⋊C4—224no—
673C4⋊C4—444no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—228no—
683C22⋊C4—228no—
684C22⋊C4—228no—
685C22⋊C4—228no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—444no—
689C22⋊C4—444no—
690C42—24no—
691C42—22no—
692C42—22no—
693C42—114no—
694C42—114no—
695C42—114no—
696C42—114no—
697C42—118no—
698C42—224no—
699C42—224no—
700C42—224no—
701C42—224no—
702C42—222no—
703C42—222no—
704C42—442no—
705C42—442no—
706C11#3491011yescharacteristic, complemented, Sylow
707C23—22no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—114no—
712C23—222no—
713C23—224no—
714C23—222no—
715C23—224no—
716C23—222no—
717C23—222no—
718C23—224no—
719C23—222no—
720C23—224no—
721C23C2×D4×D1112yes—
722C23C24×D1111yescharacteristic
723Q8—44no—
724Q8—228no—
725D4—2216no—
726D4—228no—
727D4—4416no—
728D4—448no—
729D4—444no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—112no—
748C2×C4—114no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—112no—
752C2×C4—114no—
753C2×C4—114no—
754C2×C4—2216no—
755C2×C4—228no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—224no—
768C2×C4—448no—
769C2×C4—448no—
770C2×C4—448no—
771C2×C4—444no—
772C2×C4C2×D4×D1112yes—
773C2×C4C2×D4×D1112yes—
774C2×C4#41×D1114yes—
775C2×C4#41×D1112yes—
776C2×C4#41×D1112yes—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—228no—
783C22—224no—
784C22—442no—
785C22—442no—
786C22—444no—
787C22—442no—
788C22—444no—
789C22—442no—
790C22—444no—
791C22—442no—
792C22C22×D4×D1111yescharacteristic
793C22C2×#41×D1112yes—
794C22C2×#41×D1111yescharacteristic
795C22C2×#41×D1111yescharacteristic
796C22#1062345712yes—
797C4—24no—
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—114no—
805C4—222no—
806C4—222no—
807C4—222no—
808C4—224no—
809C4—224no—
810C4—442no—
811C4—442no—
812C4#1062318714yes—
813C2—42no—
814C2—444no—
815C2—882no—
816C2C2×#1062318711yescharacteristic
817C2D11×#53211yescharacteristic
818C2#1308194811yescharacteristic
819C2#1308218112yes—
820C2#1308220812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2499C2
prime radical#13072235C2
hypercenter#2499D11
hypocenterC11#34910
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2499

Complements

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

NH ≅ G/Ntype
1. C2×#10623155C2semidirect
2. C2×#10623053C2semidirect
3. #13074223C2semidirect
4. #13074211C2semidirect
5. #13073815C2semidirect
6. #13073804C2semidirect
7. #13073599C2semidirect
8. #13073589C2semidirect
9. #13073074C2semidirect
10. #13072245C2semidirect
12. #13071853C2semidirect
13. #13071185C2semidirect
14. #13071178C2semidirect
15. #13071159C2semidirect
16. #13071155C2semidirect
17. #13071054C2semidirect
18. C4×#66930C2semidirect
19. C11×#2499C2semidirect
151. C2×C4×Dic11D4semidirect
296. C4×Dic11#41semidirect
306. #2499D11semidirect
706. C11#34910semidirect

Maximal subgroups

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

subgroupindex
C2×#106231552
C2×#106230532
#130742232
#130742112
#130738152
#130738042
#130735992
#130735892
#130730742
#130722452
#130722352
#130718532
#130711852
#130711782
#130711592
#130711552
#130710542
C4×#669302
C11×#24992
#3491011