Finite Group Databasebeta

← #14925258

Subgroups — #14925258

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×#10623211C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3#13074224C214yesmaximal, complemented
4#13074206C214yesmaximal, complemented
5#13073812C211yesmaximal, characteristic, complemented
6#13073807C211yesmaximal, characteristic, complemented
7#13073597C211yesmaximal, characteristic, complemented
8#13073077C211yesmaximal, characteristic, complemented
9#13073071C211yesmaximal, characteristic, complemented
10#13072247C211yesmaximal, characteristic, complemented
11#13072232C211yesmaximal, characteristic
12#13071855C214yesmaximal, complemented
13#13071185C211yesmaximal, characteristic, complemented
14#127×Dic11C211yesmaximal, characteristic, complemented
15#13071163C211yesmaximal, characteristic, complemented
16#124×Dic11C211yesmaximal, characteristic, complemented
17#13071056C214yesmaximal, complemented
18C4×#66945C211yesmaximal, characteristic, complemented
19C11×#2544C211yesmaximal, characteristic, complemented
20C22×#4341C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C2×#66991C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2214yes—
33C2×C4×C22⋊D11C2212yes—
34C22×C4×Dic11C2212yes—
35#10623211—28no—
36C4×#4341—28no—
37C2×#66945C2212yes—
38C2×#66945C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66936C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×(C22⋊D11)⋊C4C2212yes—
43C2×#66932C2212yes—
44C2×#66930C2212yes—
45C2×#66930C2212yes—
46C2×C42×D11C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48C2×C4×Dic22C2211yescharacteristic
49C11×#394C2214yes—
50C11×#391C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#386C2214yes—
53C4×C11×C4⋊C4C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622836C2214yes—
56#10622834C2214yes—
57#10622834C2211yescharacteristic
58#10622834C2211yescharacteristic
59#10622834C2211yescharacteristic
60#10622833C2214yes—
61#10622823C2214yes—
62#10622596C2214yes—
63#10622590C2211yescharacteristic
64#10622589C2211yescharacteristic
65C4⋊C4×Dic11C2212yes—
66#10622572C2214yes—
67#10622572C2214yes—
68#10622564C2214yes—
69#10622561C2214yes—
70#10622561C2214yes—
71#10622559C2214yes—
72#10622558C2214yes—
73#10622557C2214yes—
74#10622557C2214yes—
75C22⋊C4×Dic11C2214yes—
76C22⋊C4×Dic11C2214yes—
77C4×(C2×D11)⋊C4C2211yescharacteristic
78C4×(C2×D11)⋊C4C2211yescharacteristic
79#10622549C2211yescharacteristic
80#10622548C2211yescharacteristic
81C4×C4⋊Dic11C2211yescharacteristic
82C42×Dic11C2211yescharacteristic
83C42×Dic11C2211yescharacteristic
84#10622542C2211yescharacteristic
85#10622542C2211yescharacteristic
86#10622287C2214yes—
87#10622279C2212yes—
88#10622267C2214yes—
89#10622266C2214yes—
90#10622262C2214yes—
91#10622261C2212yes—
92#10622260C2214yes—
93C22×Q8×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2314yes—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C23×Dic11C2312yes—
101C23×Dic11C2312yes—
102C23×Dic11C2312yes—
103C2×#4341—24no—
104C2×#4341—24no—
105C2×#4341—24no—
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C11×#127—24no—
111C11×#124—24no—
112C11×#124—24no—
113C4×D4×C11—24no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131#66999—24no—
132Q8×Dic11—24no—
133#66997—24no—
134#66991—24no—
135#66989—24no—
136D4×Dic11—24no—
137D4×Dic11—24no—
138D4×Dic11—216no—
139C4×C22⋊D11—28no—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2314yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157C2×C4×Dic11—28no—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2311yescharacteristic
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2311yescharacteristic
168C2×C4×Dic11C2311yescharacteristic
169C2×C4×Dic11C2311yescharacteristic
170C2×C4×Dic11C2312yes—
171#66945—24no—
172#66945—28no—
173#66940—24no—
174#66936—28no—
175(C22⋊D11)⋊C4—28no—
176(C22⋊D11)⋊C4—28no—
177#66932—28no—
178#66930—28no—
179#66930—28no—
180C42×D11D418yescomplemented
181#66923—24no—
182C4×Dic22—24no—
183C11×#95C2314yes—
184C11×#95C2312yes—
185C11⋊#95C2314yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2314yes—
190C11⋊#95C2314yes—
191C11⋊#95C2314yes—
192C11⋊#95C2314yes—
193#34910—111nomaximal, Sylow
194C24×C11C2412yes—
195C24×C11C2412yes—
196C23×D11C2411yescharacteristic
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×D4×C11—28no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—28no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—44no—
208C2×D4×C11#4114yes—
209C22×C4×C11—24no—
210C22×C4×C11—44no—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—44no—
223C22×Dic11—24no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—28no—
228C22×Dic11—28no—
229C22×Dic11—24no—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2411yescharacteristic
235C22×Dic11C2411yescharacteristic
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2411yescharacteristic
239#4341—232no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—42no—
244C2×C4×D11C2×D414yes—
245C2×C4×D11C2×D414yes—
246C2×C4×D11C2×D414yes—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22#4114yes—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—24no—
252C11×C22⋊C4—28no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—44no—
257C42×C11—22no—
258C42×C11—22no—
259C42×C11C2×D414yes—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—44no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271C4⋊Dic11—24no—
272C4⋊Dic11—24no—
273C4⋊Dic11—22no—
274C4⋊Dic11—22no—
275C4⋊Dic11—22no—
276C4⋊Dic11—28no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—28no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—44no—
284C4×Dic11—24no—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C4×Dic11—22no—
290C4×Dic11—22no—
291C4×Dic11—42no—
292C4×Dic11—42no—
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#2544D1111yescharacteristic, complemented
305#2500—111no—
306#2499—111no—
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—24no—
318C23×C11—22no—
319C23×C11—24no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—24no—
323C23×C11—22no—
324C23×C11—24no—
325C23×C11C2×#4114yes—
326C23×C11C2511yescharacteristic
327C22×D11—22no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—22no—
331C22×D11C22×D412yes—
332Q8×C11—44no—
333D4×C11—28no—
334D4×C11—416no—
335D4×C11—44no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
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—22no—
347C2×C4×C11—24no—
348C2×C4×C11—48no—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C2×#4112yes—
353C2×C4×C11C2×#4114yes—
354C2×C4×C11C2×#4112yes—
355C22⋊D11—216no—
356C22⋊D11—48no—
357C2×Dic11—216no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—24no—
371C2×Dic11—24no—
372C2×Dic11—22no—
373C2×Dic11—24no—
374C2×Dic11—48no—
375C2×Dic11—48no—
376C2×Dic11C22×D412yes—
377C2×Dic11C22×D412yes—
378C2×Dic11C22×D412yes—
379C2×Dic11C2×#4114yes—
380C2×Dic11C2×#4114yes—
381C2×Dic11C2×#4114yes—
382C4×D11—28no—
383C4×D11—28no—
384C4×D11—44no—
385Dic22—28no—
386C22×#41—111no—
387C2×C4⋊Q8—111no—
388C2×#127C2×D1111yescharacteristic
389#529—228no—
390C2×#126—112no—
391C2×#125—111no—
392C2×#124—111no—
393C2×#124C2×D1111yescharacteristic
394C2×#124C2×D1111yescharacteristic
395C2×#123—112no—
396C2×C22⋊Q8—111no—
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—112no—
406C2×C4×D4—112no—
407C2×C4×D4—112no—
408C2×C4×D4C2×D1111yescharacteristic
409C2×#117—112no—
410C2×#117—111no—
411C2×#117—112no—
412C2×#117—112no—
413C22×C42—111no—
414C22×C42—112no—
415#398—114no—
416#397—114no—
417#396—114no—
418#396—114no—
419#394—114no—
420#394—114no—
421#394C2×D1114yes—
422#392—114no—
423#391—111no—
424#391—111no—
425#391—111no—
426#391C2×D1111yescharacteristic
427#390—111no—
428#390—114no—
429#390—111no—
430#390—111no—
431#390C2×D1111yescharacteristic
432#389—114no—
433#388—114no—
434#388—114no—
435#388—114no—
436#388—114no—
437#387—114no—
438#387—114no—
439#386—114no—
440#386C2×D1114yes—
441#385—114no—
442#385—114no—
443#384—111no—
444#384—111no—
445#382—111no—
446#382—111no—
447C4×C4⋊C4—112no—
448C4×C4⋊C4—111no—
449C4×C4⋊C4—114no—
450C4×C4⋊C4C2×D1111yescharacteristic
451C4×C22⋊C4—114no—
452C4×C22⋊C4—114no—
453C4×C22⋊C4—111no—
454C4×C22⋊C4—111no—
455C4×C22⋊C4—112no—
456#376—112no—
457C43—111no—
458C43—111no—
459C22×C11—24no—
460C22×C11—28no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—44no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—44no—
468C22×C11—44no—
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4112yes—
473C22×C11#58512yes—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—42no—
478C2×D11—42no—
479C4×C11—22no—
480C4×C11—22no—
481C4×C11—24no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11#52514yes—
486Dic11—24no—
487Dic11—22no—
488Dic11—22no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
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×D4C22×D1111yescharacteristic
503C22×D4C22×D1114yes—
504C22×D4C22×D1111yescharacteristic
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—112no—
509C23×C4—112no—
510C23×C4—112no—
511C23×C4C22×D1112yes—
512C4⋊Q8—224no—
513#127—24no—
514#126—228no—
515#125—224no—
516#124—24no—
517#124—24no—
518#124—224no—
519#123—228no—
520C22⋊Q8—224no—
521#121—224no—
522C4×Q8—224no—
523C4×Q8—224no—
524C4×Q8—224no—
525C4×D4—24no—
526C4×D4—224no—
527C4×D4—224no—
528C4×D4—2216no—
529C4×D4—228no—
530C4×D4—228no—
531C4×D4—228no—
532#117—228no—
533#117—228no—
534#117—228no—
535#117—224no—
536C2×C4⋊C4—111no—
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—111no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1112yes—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4C22×D1112yes—
563C2×C22⋊C4C22×D1112yes—
564C2×C22⋊C4C22×D1112yes—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C42—111no—
568C2×C42—111no—
569C2×C42—112no—
570C2×C42—111no—
571C2×C42—118no—
572C2×C42—112no—
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×D1111yescharacteristic
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#95—114no—
592#95—114no—
593#95C22×D1112yes—
594#95C22×D1114yes—
595C2×C11—44no—
596C2×C11—82no—
597C2×C11C2×#52511yescharacteristic
598C2×C11C2×#53211yescharacteristic
599C2×C11#344911yescharacteristic
600C2×C11#347512yes—
601C2×C11#348012yes—
602D11—42no—
603C24—111no—
604C24C23×D1112yes—
605C24C23×D1112yes—
606#41—2232no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—114no—
611C2×Q8—222no—
612C2×Q8—222no—
613C2×D4—28no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—28no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—444no—
626C2×D4#434114yes—
627C22×C4—24no—
628C22×C4—44no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—111no—
634C22×C4—114no—
635C22×C4—114no—
636C22×C4—114no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—228no—
647C22×C4—228no—
648C22×C4—224no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—442no—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1111yescharacteristic
656C22×C4C23×D1111yescharacteristic
657C22×C4C23×D1112yes—
658C22×C4C23×D1111yescharacteristic
659C4⋊C4—22no—
660C4⋊C4—24no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—228no—
666C4⋊C4—224no—
667C4⋊C4—222no—
668C4⋊C4—224no—
669C4⋊C4—222no—
670C4⋊C4—224no—
671C4⋊C4—222no—
672C4⋊C4—228no—
673C4⋊C4—444no—
674C22⋊C4—28no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—44no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—228no—
686C22⋊C4—228no—
687C22⋊C4—228no—
688C22⋊C4—224no—
689C22⋊C4—444no—
690C42—22no—
691C42—22no—
692C42—114no—
693C42—114no—
694C42—114no—
695C42—118no—
696C42—224no—
697C42—224no—
698C42—224no—
699C42—224no—
700C42—224no—
701C42—222no—
702C42—222no—
703C42—442no—
704C42—442no—
705C42D4×D1114yes—
706C11#3491011yescharacteristic, complemented, Sylow
707C23—22no—
708C23—24no—
709C23—22no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—112no—
717C23—221no—
718C23—222no—
719C23—221no—
720C23—222no—
721C23C2×#434114yes—
722C23C24×D1111yescharacteristic
723Q8—44no—
724Q8—228no—
725D4—28no—
726D4—416no—
727D4—44no—
728D4—2216no—
729D4—448no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—48no—
743C2×C4—112no—
744C2×C4—114no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—114no—
748C2×C4—114no—
749C2×C4—228no—
750C2×C4—2216no—
751C2×C4—222no—
752C2×C4—221no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—221no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—228no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—222no—
767C2×C4—224no—
768C2×C4—444no—
769C2×C4—448no—
770C2×C4—448no—
771C2×C4C2×D4×D1112yes—
772C2×C4C2×D4×D1112yes—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×#434112yes—
775C2×C4#41×D1114yes—
776C2×C4#41×D1112yes—
777C22—24no—
778C22—28no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—442no—
791C22—442no—
792C22C22×D4×D1111yescharacteristic
793C22C22×#434111yescharacteristic
794C22C2×#41×D1111yescharacteristic
795C22C2×#41×D1112yes—
796C22#1062345512yes—
797C4—22no—
798C4—24no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—114no—
804C4—222no—
805C4—224no—
806C4—222no—
807C4—224no—
808C4—442no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062313714yes—
813C2—44no—
814C2—82no—
815C2—442no—
816C2C2×#1062313711yescharacteristic
817C2D11×#53211yescharacteristic
818C2#1308194711yescharacteristic
819C2#1308216712yes—
820C2#1308221212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2544C2
prime radical#13072232C2
hypercenter#2544D11
hypocenterC11#34910
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. C2×#10623211C2semidirect
2. C2×C4×#4341C2semidirect
3. #13074224C2semidirect
4. #13074206C2semidirect
5. #13073812C2semidirect
6. #13073807C2semidirect
7. #13073597C2semidirect
8. #13073077C2semidirect
9. #13073071C2semidirect
10. #13072247C2semidirect
12. #13071855C2semidirect
13. #13071185C2semidirect
14. #127×Dic11C2semidirect
15. #13071163C2semidirect
16. #124×Dic11C2semidirect
17. #13071056C2semidirect
18. C4×#66945C2semidirect
19. C11×#2544C2semidirect
180. C42×D11D4semidirect
296. C4×Dic11#41semidirect
304. #2544D11semidirect
706. C11#34910semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×C4×#43412
#130742242
#130742062
#130738122
#130738072
#130735972
#130730772
#130730712
#130722472
#130722322
#130718552
#130711852
#127×Dic112
#130711632
#124×Dic112
#130710562
C4×#669452
C11×#25442
#3491011