Finite Group Databasebeta

← #14925913

Subgroups — #14925913

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3#13074227C214yesmaximal, complemented
4#13074096C211yesmaximal, characteristic, complemented
5#13073797C212yesmaximal, complemented
6#13073775C211yesmaximal, characteristic, complemented
7#13073577C212yesmaximal, complemented
8#13073542C211yesmaximal, characteristic, complemented
9#13072010C212yesmaximal, complemented
10#13071988C212yesmaximal, complemented
11#13071880C212yesmaximal, complemented
12#13071834C212yesmaximal, complemented
13#13071135C212yesmaximal, complemented
14#13071124C214yesmaximal, complemented
15#13071117C212yesmaximal, complemented
16C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
17C11×#2583C211yesmaximal, characteristic, complemented
18C22×#4343C2211yescharacteristic, complemented
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C2×#66999C2211yescharacteristic, complemented
25C2×#66983C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29#10623158—28no—
30C2×#66948C2214yes—
31C2×#66948C2211yescharacteristic, complemented
32C2×#66947C2212yescomplemented
33C2×#66946—28no—
34C2×#66946C2212yes—
35C2×#66946C2212yes—
36C2×#66946C2212yes—
37C2×#66946C2212yes—
38C2×#66946C2212yescomplemented
39C2×#66946C2214yescomplemented
40C2×#66945C2211yescharacteristic, complemented
41C2×#66939C2212yes—
42C2×#66935C2212yes—
43C2×#66935C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×C22⋊C4×D11C2212yes—
46C2×C42×D11C2212yescomplemented
47C11×#398C2212yescomplemented
48C11×#395C2212yescomplemented
49C11×#389C2214yescomplemented
50C11×#385C2212yes—
51C11×#385C2212yes—
52C4×C11×C22⋊C4C2211yescharacteristic
53#10622844C2212yescomplemented
54#10622826C2212yes—
55#10622826C2212yes—
56C4×C22⋊Dic11C2211yescharacteristic
57#10622606C2212yescomplemented
58#10622604C2214yes—
59#10622604C2214yescomplemented
60#10622604C2212yescomplemented
61#10622603C2214yescomplemented
62#10622603C2214yescomplemented
63#10622603C2214yescomplemented
64#10622602C2214yescomplemented
65#10622600C2214yescomplemented
66#10622599C2212yescomplemented
67C4⋊C4×Dic11C2214yescomplemented
68#10622568C2212yes—
69#10622556C2212yes—
70C22⋊C4×Dic11C2212yes—
71#10622552C2214yescomplemented
72C4×(C2×D11)⋊C4C2212yescomplemented
73#10622290C2212yescomplemented
74#10622287C2214yescomplemented
75#10622284C2214yes—
76#10622284C2212yescomplemented
77#10622279C2214yescomplemented
78#10622279C2212yescomplemented
79#10622279C2214yescomplemented
80#10622278C2214yes—
81#10622278C2214yescomplemented
82#10622278C2214yescomplemented
83D11×#95C2212yescomplemented
84#10622267C2214yescomplemented
85C24×D11C2311yescharacteristic
86C24×D11C2311yescharacteristic
87C22×Q8×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11C2312yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C2×#4343—24no—
95C2×#4343—44no—
96C22×D44—24no—
97C22×D44—28no—
98C22×D44C2312yes—
99C22×D44C2312yes—
100C22×D44C2314yes—
101C22×D44C2312yes—
102C22×D44C2312yes—
103C22×D44C2311yescharacteristic
104C22×C4×D11—24no—
105C22×C4×D11—44no—
106C22×C4×D11—44no—
107C22×C4×D11D418yescomplemented
108C22×C4×D11C2312yes—
109C22×C4×D11C2312yes—
110C22×C4×D11C2314yes—
111C22×C4×D11C2311yescharacteristic
112C22×C4×D11C2311yescharacteristic
113C22×C4×D11C2312yes—
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2311yescharacteristic
116C11×C22⋊Q8—24no—
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2314yes—
123C2×C11×C4⋊C4C2314yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C42×C11C2312yes—
127C2×C22⋊Dic11C2312yes—
128#66999—24no—
129#66983—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4C2312yes—
150C2×C4×Dic11—24no—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2312yes—
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156#66948—216no—
157#66948—24no—
158#66947—28no—
159#66946—28no—
160#66946—28no—
161#66946—28no—
162#66946—28no—
163#66946—28no—
164#66946—48no—
165#66945—24no—
166#66939—28no—
167#66935—28no—
168#66935—28no—
169(C22⋊D11)⋊C4—28no—
170C22⋊C4×D11—28no—
171C42×D11—44no—
172C11×#95C2314yes—
173C11×#95C2312yes—
174C11×#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2312yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181#34957—111nomaximal, Sylow
182C24×C11C2411yescharacteristic
183C23×D11—22no—
184C23×D11—24no—
185C23×D11—24no—
186C23×D11—24no—
187C23×D11—24no—
188C23×D11—42no—
189C23×D11—42no—
190C23×D11C2×D414yes—
191C23×D11C2412yes—
192C23×D11C2411yescharacteristic
193C23×D11C2412yes—
194C23×D11C2411yescharacteristic
195C2×Q8×C11—22no—
196C2×Q8×C11—42no—
197C22×C4×C11—22no—
198C22×C4×C11—24no—
199C22×C4×C11—22no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2412yes—
209C22×C4×C11C2414yes—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C22×Dic11—24no—
214C22×Dic11—22no—
215C22×Dic11—24no—
216C22×Dic11C2×D414yes—
217C22×Dic11C2414yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2411yescharacteristic
222#4343—416no—
223C2×D44—232no—
224C2×D44—24no—
225C2×D44—24no—
226C2×D44—24no—
227C2×D44—24no—
228C2×D44—24no—
229C2×D44—24no—
230C2×D44—28no—
231C2×D44—28no—
232C2×D44—22no—
233C2×D44—24no—
234C2×D44—28no—
235C2×D44—44no—
236C2×D44—42no—
237C2×D44—44no—
238C2×D44#4118yescomplemented
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—44no—
249C2×C4×D11—42no—
250C2×C4×D11—42no—
251C2×C4×D11—44no—
252C2×C4×D11—416no—
253C2×C4×D11—416no—
254C2×C4×D11C2×D414yes—
255C2×C4×D11C2×D414yes—
256C2×C4×D11C2×D414yes—
257C2×C4×D11C2×D414yes—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—28no—
263C11×C4⋊C4—44no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4#4118yescomplemented
266C42×C11—42no—
267C22⋊Dic11—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—28no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283C4⋊Dic11—22no—
284C4⋊Dic11—28no—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C4×Dic11—28no—
290C4×Dic11—42no—
291C2×#525—111no—
292C22×C4×D4—111no—
293#2602—114no—
294#2591—111no—
295#2583D1111yescharacteristic, complemented
296#2564—112no—
297#2561—111no—
298#2543—112no—
299#2539—111no—
300#2412—112no—
301#2410—112no—
302#2395—112no—
303#2388—112no—
304C4×#123—112no—
305C4×#121—114no—
306C4×#120—112no—
307C2×C4×C22⋊C4—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11C22×D412yes—
311C23×C11C2×#4114yes—
312C23×C11C2511yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—24no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—24no—
323C22×D11—22no—
324C22×D11—28no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—24no—
328C22×D11—22no—
329C22×D11—24no—
330C22×D11—44no—
331C22×D11—416no—
332C22×D11—416no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11C22×D412yes—
336C22×D11C22×D412yes—
337C22×D11C2×#4114yes—
338C22×D11C2×#4114yes—
339Q8×C11—44no—
340C2×C4×C11—28no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—44no—
354C2×C4×C11—44no—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C2×#4118yes—
358C2×C4×C11C2×#4114yes—
359C22⋊D11—48no—
360C2×Dic11—22no—
361C2×Dic11—28no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—22no—
368C2×Dic11—24no—
369C2×Dic11—24no—
370C2×Dic11—44no—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373C2×Dic11H(5,𝔽2)14yes—
374D44—216no—
375D44—216no—
376D44—416no—
377D44—44no—
378D44—48no—
379D44—48no—
380C4×D11—28no—
381C4×D11—28no—
382C4×D11—44no—
383C4×D11—44no—
384C4×D11—48no—
385C4×D11—416no—
386C4×D11—48no—
387C4×D11—48no—
388C22×#41—111no—
389C23×D4—111no—
390C24×C4—111no—
391C24×C4—111no—
392#525—228no—
393C2×#123—112no—
394C2×#123—112no—
395C2×C22⋊Q8—111no—
396C2×C22⋊Q8C2×D1111yescharacteristic
397C2×#121—111no—
398C2×#121—114no—
399C2×#121—111no—
400C2×#120—112no—
401C2×#120—112no—
402C2×C4×D4—112no—
403C2×C4×D4—112no—
404C2×C4×D4—112no—
405C2×C4×D4—112no—
406C2×C4×D4—112no—
407C2×C4×D4—114no—
408C2×C4×D4—112no—
409C2×C4×D4—228no—
410C2×#117—111no—
411C22×C4⋊C4C2×D1111yescharacteristic
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—112no—
415C22×C42—111no—
416C22×C42—112no—
417#400—112no—
418#399—112no—
419#398C2×D1112yescomplemented
420#397—112no—
421#397—114no—
422#395C2×D1112yescomplemented
423#394—112no—
424#394—114no—
425#394—114no—
426#393—112no—
427#392—114no—
428#392—112no—
429#390—114no—
430#389C2×D1114yescomplemented
431#388—114no—
432#388—114no—
433#388—114no—
434#387—114no—
435#386—112no—
436#386—112no—
437#386—114no—
438#386—114no—
439#386—114no—
440#385—114no—
441#385C2×D1112yes—
442#385C2×D1112yes—
443#381—112no—
444#380—114no—
445#379—112no—
446C4×C4⋊C4—114no—
447C4×C22⋊C4—111no—
448C4×C22⋊C4—112no—
449C4×C22⋊C4—112no—
450C4×C22⋊C4—112no—
451C4×C22⋊C4—114no—
452C4×C22⋊C4—114no—
453C4×C22⋊C4C2×D1111yescharacteristic
454C2×#95—112no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—28no—
458C22×C11#53214yes—
459C22×C11C23×D411yescharacteristic
460C22×C11C22×#4112yes—
461C22×C11C22×#4112yes—
462C22×C11C2×H(5,𝔽2)12yes—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—28no—
466C2×D11—22no—
467C2×D11—24no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—28no—
471C2×D11—416no—
472C2×D11—416no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—44no—
476C2×D11—44no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—44no—
481C2×D11—44no—
482C2×D11#52514yes—
483C4×C11—24no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—28no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490Dic11—22no—
491Dic11—42no—
492Dic11—42no—
493Dic11—44no—
494Dic11#53414yes—
495C25—111no—
496C25—111no—
497C2×#41—224no—
498C2×#41—444no—
499C22×Q8C22×D1111yescharacteristic
500C22×D4—112no—
501C22×D4—112no—
502C22×D4—112no—
503C22×D4—112no—
504C22×D4—114no—
505C22×D4—112no—
506C22×D4—111no—
507C22×D4—228no—
508C22×D4—224no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—118no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—112no—
517C23×C4—112no—
518C23×C4—114no—
519C23×C4—112no—
520C23×C4—224no—
521C23×C4—444no—
522C23×C4—444no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526#123—228no—
527#123—228no—
528C22⋊Q8—24no—
529C22⋊Q8—224no—
530#121—224no—
531#121—2216no—
532#121—224no—
533#120—228no—
534#120—228no—
535C4×D4—228no—
536C4×D4—228no—
537C4×D4—228no—
538C4×D4—228no—
539C4×D4—228no—
540C4×D4—228no—
541C4×D4—448no—
542#117—224no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—112no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4C22×D1112yes—
548C2×C4⋊C4C22×D1112yes—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1112yes—
551C2×C4⋊C4C22×D1114yes—
552C2×C4⋊C4C22×D1114yes—
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—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—114no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—224no—
570C2×C22⋊C4—224no—
571C2×C22⋊C4—228no—
572C2×C22⋊C4C22×D1112yes—
573C2×C22⋊C4C22×D1112yes—
574C2×C42—112no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—114no—
578C2×C42—112no—
579C2×C42—224no—
580C2×C42—444no—
581C2×C42C22×D1112yes—
582#95—114no—
583#95—112no—
584#95—114no—
585#95—114no—
586#95—114no—
587#95—114no—
588#95C22×D1112yes—
589#95C22×D1114yes—
590#95C22×D1114yes—
591C2×C11—24no—
592C2×C11C2×#52511yescharacteristic
593C2×C11C2×#53211yescharacteristic
594C2×C11C2×#53411yescharacteristic
595C2×C11#348114yes—
596D11—24no—
597D11—42no—
598D11—44no—
599D11—82no—
600C24—111no—
601C24—111no—
602C24—112no—
603C24—114no—
604C24—112no—
605C24—224no—
606C24—224no—
607C24—222no—
608C24—224no—
609C24—224no—
610C24—442no—
611C24—442no—
612C24C23×D1111yescharacteristic
613#41—4416no—
614C2×Q8—22no—
615C2×Q8—42no—
616C2×D4—118no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—2232no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—222no—
630C2×D4—228no—
631C2×D4—224no—
632C2×D4—444no—
633C2×D4—442no—
634C2×D4—444no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—22no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—111no—
641C22×C4—114no—
642C22×C4—111no—
643C22×C4—114no—
644C22×C4—114no—
645C22×C4—114no—
646C22×C4—114no—
647C22×C4—114no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—228no—
656C22×C4—228no—
657C22×C4—228no—
658C22×C4—224no—
659C22×C4—222no—
660C22×C4—224no—
661C22×C4—228no—
662C22×C4—444no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—444no—
666C22×C4—4416no—
667C22×C4—4416no—
668C22×C4D4×D1114yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1114yes—
675C22×C4C23×D1112yes—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—22no—
679C4⋊C4—24no—
680C4⋊C4—28no—
681C4⋊C4—44no—
682C4⋊C4—224no—
683C4⋊C4—222no—
684C4⋊C4—228no—
685C22⋊C4—24no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—228no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4#434318yescomplemented
703C42—42no—
704C42—224no—
705C42—224no—
706C42—228no—
707C42—224no—
708C42—442no—
709C11#3495711yescharacteristic, complemented, Sylow
710C23—22no—
711C23—22no—
712C23—112no—
713C23—114no—
714C23—112no—
715C23—114no—
716C23—228no—
717C23—228no—
718C23—222no—
719C23—222no—
720C23—228no—
721C23—222no—
722C23—222no—
723C23—224no—
724C23—222no—
725C23—222no—
726C23—224no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—224no—
732C23—224no—
733C23—444no—
734C23—4416no—
735C23—4416no—
736C23—444no—
737C23—444no—
738C23C2×D4×D1112yes—
739C23C2×#434314yes—
740C23C24×D1111yescharacteristic
741Q8—44no—
742D4—2216no—
743D4—2216no—
744D4—4416no—
745D4—444no—
746D4—448no—
747D4—448no—
748D4—448no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—112no—
765C2×C4—114no—
766C2×C4—112no—
767C2×C4—228no—
768C2×C4—228no—
769C2×C4—228no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—224no—
774C2×C4—222no—
775C2×C4—224no—
776C2×C4—222no—
777C2×C4—224no—
778C2×C4—224no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4—4416no—
782C2×C4—448no—
783C2×C4—448no—
784C2×C4—448no—
785C2×C4—444no—
786C2×C4C2×D4×D1112yes—
787C2×C4C2×D4×D1112yes—
788C2×C4C2×#434318yes—
789C2×C4#41×D1114yes—
790C22—22no—
791C22—28no—
792C22—22no—
793C22—114no—
794C22—222no—
795C22—222no—
796C22—228no—
797C22—222no—
798C22—222no—
799C22—228no—
800C22—224no—
801C22—222no—
802C22—4416no—
803C22—4416no—
804C22—442no—
805C22—442no—
806C22—444no—
807C22—444no—
808C22—442no—
809C22—442no—
810C22—444no—
811C22—444no—
812C22—442no—
813C22#1062325614yes—
814C22C22×D4×D1111yescharacteristic
815C22C22×#434312yes—
816C22C2×#41×D1112yes—
817C22D11×H(5,𝔽2)12yes—
818C4—22no—
819C4—22no—
820C4—28no—
821C4—24no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—114no—
826C4—222no—
827C4—442no—
828C4—442no—
829C4—444no—
830C2—24no—
831C2—224no—
832C2—442no—
833C2—444no—
834C2—882no—
835C2D11×#52511yescharacteristic
836C2C2×#1062325611yescharacteristic
837C2D11×#53411yescharacteristic
838C2#1308222714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2583C2
hypercenter#2583D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2583

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C22×#66946C2semidirect
3. #13074227C2semidirect
4. #13074096C2semidirect
5. #13073797C2semidirect
6. #13073775C2semidirect
7. #13073577C2semidirect
8. #13073542C2semidirect
9. #13072010C2semidirect
10. #13071988C2semidirect
11. #13071880C2semidirect
12. #13071834C2semidirect
13. #13071135C2semidirect
14. #13071124C2semidirect
15. #13071117C2semidirect
16. C4×C22⋊C4×D11C2semidirect
17. C11×#2583C2semidirect
18. C22×#4343C22semidirect
24. C2×#66999C22semidirect
31. C2×#66948C22semidirect
32. C2×#66947C22semidirect
38. C2×#66946C22semidirect
39. C2×#66946C22semidirect
40. C2×#66945C22semidirect
46. C2×C42×D11C22semidirect
47. C11×#398C22semidirect
48. C11×#395C22semidirect
49. C11×#389C22semidirect
53. #10622844C22semidirect
57. #10622606C22semidirect
59. #10622604C22semidirect
60. #10622604C22semidirect
61. #10622603C22semidirect
62. #10622603C22semidirect
63. #10622603C22semidirect
64. #10622602C22semidirect
65. #10622600C22semidirect
66. #10622599C22semidirect
67. C4⋊C4×Dic11C22semidirect
71. #10622552C22semidirect
72. C4×(C2×D11)⋊C4C22semidirect
73. #10622290C22semidirect
74. #10622287C22semidirect
76. #10622284C22semidirect
77. #10622279C22semidirect
78. #10622279C22semidirect
79. #10622279C22semidirect
81. #10622278C22semidirect
82. #10622278C22semidirect
83. D11×#95C22semidirect
84. #10622267C22semidirect
107. C22×C4×D11D4semidirect
238. C2×D44#41semidirect
265. C11×C22⋊C4#41semidirect
295. #2583D11semidirect
419. #398C2×D11semidirect
422. #395C2×D11semidirect
430. #389C2×D11semidirect
702. C22⋊C4#4343semidirect
709. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C22×#669462
#130742272
#130740962
#130737972
#130737752
#130735772
#130735422
#130720102
#130719882
#130718802
#130718342
#130711352
#130711242
#130711172
C4×C22⋊C4×D112
C11×#25832
#3495711