Finite Group Databasebeta

← D11×#2580 #14924983

Subgroups — D11×#2580 #14924983

Order 2816.

3222 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic
3#13073976C212yesmaximal, complemented
4#13073975C211yesmaximal, characteristic, complemented
5#13073974C211yesmaximal, characteristic, complemented
6#13073973C214yesmaximal, complemented
7#13073972C212yesmaximal, complemented
8#13073971C212yesmaximal, complemented
9#13073970C211yesmaximal, characteristic, complemented
10#13073969C212yesmaximal, complemented
11D11×#399C212yesmaximal, complemented
12D11×#393C212yesmaximal, complemented
13D11×#390C212yesmaximal
14D11×#389C212yesmaximal, complemented
15D11×#385C214yesmaximal, complemented
16D11×#382C211yesmaximal, characteristic, complemented
17C11×#2580C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C23×C4×D11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic, complemented
24C2×D4×Dic11C2211yescharacteristic
25C2×C4×C22⋊D11C2212yes—
26C4×Q8×D11—28no—
27C4×D4×D11—28no—
28C2×#66946C2211yescharacteristic
29C2×C4⋊C4×D11C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C4⋊C4×D11C2214yes—
34C2×#66940C2211yescharacteristic, complemented
35C2×#66940C2212yescomplemented
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×C22⋊C4×D11C2214yes—
38C2×C22⋊C4×D11C2212yes—
39C2×C22⋊C4×D11C2214yes—
40C2×C4×D44C2211yescharacteristic
41C2×C42×D11C2212yes—
42C2×C42×D11C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic, complemented
44C2×C4×Dic22C2212yescomplemented
45C11×#399C2212yescomplemented
46C11×#393C2212yescomplemented
47C11×#390C2212yes—
48C11×#389C2212yescomplemented
49C11×#385C2214yescomplemented
50C11×#382C2211yescharacteristic, complemented
51#10622844C2212yescomplemented
52#10622834C2212yes—
53#10622823C2214yescomplemented
54#10622605C2212yescomplemented
55#10622605C2214yescomplemented
56#10622602C2214yescomplemented
57#10622602C2214yescomplemented
58#10622601C2212yes—
59#10622598C2212yescomplemented
60#10622590C2212yescomplemented
61#10622586C2212yescomplemented
62#10622585C2214yescomplemented
63#10622570C2214yes—
64#10622570C2214yes—
65#10622563C2214yescomplemented
66#10622562C2212yescomplemented
67#10622562C2214yescomplemented
68#10622560C2212yescomplemented
69#10622560C2214yescomplemented
70#10622559C2214yescomplemented
71#10622552C2212yes—
72#10622549C2211yescharacteristic, complemented
73#10622541C2212yescomplemented
74#10622290C2212yescomplemented
75#10622286C2212yescomplemented
76#10622286C2214yescomplemented
77#10622281C2214yescomplemented
78#10622281C2214yescomplemented
79D11×#95C2212yes—
80D11×#95C2212yes—
81D11×#95C2214yes—
82#10622263C2212yescomplemented
83#10622263C2212yescomplemented
84#10622260C2214yescomplemented
85C24×D11C2312yes—
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C22×C22⋊D11C2312yes—
90C23×Dic11C2312yes—
91C2×Q8×D11—24no—
92C2×Q8×D11—28no—
93C2×D4×D11—24no—
94C2×D4×D11—24no—
95C2×D4×D11Q818yescomplemented
96C22×D44C2311yescharacteristic
97C22×C4×D11—28no—
98C22×C4×D11—48no—
99C22×C4×D11C2312yes—
100C22×C4×D11C2314yes—
101C22×C4×D11C2312yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2312yes—
105C22×C4×D11C2312yes—
106C22×C4×D11C2312yes—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2312yes—
109C22×Dic22C2311yescharacteristic
110C4×Q8×C11—24no—
111C4×D4×C11—24no—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C42×C11C2312yes—
121C2×C42×C11C2311yescharacteristic
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125Q8×Dic11—24no—
126D4×Dic11—24no—
127C4×C22⋊D11—28no—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152#66946—24no—
153C4⋊C4×D11—24no—
154C4⋊C4×D11—24no—
155C4⋊C4×D11—28no—
156C4⋊C4×D11—28no—
157C4⋊C4×D11—48no—
158#66940—24no—
159#66940—28no—
160(C22⋊D11)⋊C4—28no—
161C22⋊C4×D11—28no—
162C22⋊C4×D11—216no—
163C22⋊C4×D11—48no—
164C4×D44—24no—
165C42×D11—28no—
166C42×D11D418yes—
167C4×Dic22—24no—
168C4×Dic22—28no—
169C11×#95C2314yes—
170C11×#95C2312yes—
171C11×#95C2312yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2312yes—
176C11⋊#95C2312yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C2×#2580—111nomaximal, Sylow
180C24×C11C2412yes—
181C23×D11—24no—
182C23×D11—28no—
183C23×D11—24no—
184C23×D11—28no—
185C23×D11C2×Q818yes—
186C23×D11C2412yes—
187C23×D11C2411yescharacteristic
188C2×Q8×C11—22no—
189C2×Q8×C11—24no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11C2×Q814yescomplemented
193C22×C4×C11—24no—
194C22×C4×C11—44no—
195C22×C4×C11C2414yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11C2×Q818yescomplemented
205C22×Dic11—24no—
206C22×Dic11—44no—
207C22×Dic11C2414yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2411yescharacteristic
212C22×Dic11C2412yes—
213C22×Dic11C2411yescharacteristic
214Q8×D11—232no—
215D4×D11—232no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44C2×Q814yescomplemented
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—28no—
226C2×C4×D11—28no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—28no—
230C2×C4×D11—24no—
231C2×C4×D11—28no—
232C2×C4×D11—24no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—432no—
236C2×C4×D11C2×D414yes—
237C2×C4×D11C2×D414yes—
238C2×C4×D11C2×D414yes—
239C2×C4×D11C2×Q814yes—
240C2×C4×D11#4118yes—
241C2×C4×D11#4114yes—
242C2×Dic22—24no—
243C2×Dic22—24no—
244C2×Dic22—24no—
245C2×Dic22—22no—
246C2×Dic22—24no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—44no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—44no—
255C42×C11—24no—
256C42×C11C2×D414yes—
257C22⋊Dic11—24no—
258C22⋊Dic11—28no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266C4⋊Dic11—24no—
267C4⋊Dic11—22no—
268C4⋊Dic11—22no—
269C4⋊Dic11—24no—
270C4⋊Dic11—44no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—28no—
275Dic11⋊C4—24no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11C2×D414yes—
282C4×Dic11C2×D414yes—
283C4×Dic11C2×D414yes—
284C22×C4×Q8—111no—
285C22×C4×D4—111no—
286#2580—112no—
287#2580—112no—
288#2580—112no—
289#2580—112no—
290#2580—114no—
291#2580—111no—
292#2580—111no—
293#2580—111no—
294#2580D1111yescharacteristic, direct product factor
295C2×#399—112no—
296C2×#393—112no—
297C2×#390—112no—
298C2×#389—112no—
299C2×#385—114no—
300C2×#382—111no—
301C23×C11—22no—
302C23×C11—24no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11C22×Q814yes—
306C23×C11C2511yescharacteristic
307C22×D11—22no—
308C22×D11—24no—
309C22×D11—22no—
310C22×D11—24no—
311C22×D11—216no—
312C22×D11—232no—
313C22×D11—48no—
314C22×D11—48no—
315C22×D11—416no—
316C22×D11C22×D412yes—
317C22×D11C22×Q814yes—
318C22×D11C22×Q812yes—
319C22×D11C2×#4112yes—
320C22×D11C2×#4114yes—
321C22×D11H(5,𝔽2)14yes—
322Q8×C11—28no—
323D4×C11—28no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—22no—
333C2×C4×C11—24no—
334C2×C4×C11—24no—
335C2×C4×C11—22no—
336C2×C4×C11—48no—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×Q812yes—
341C2×C4×C11C2×#4114yes—
342C2×C4×C11C2×#4112yes—
343C22⋊D11—216no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—22no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—22no—
356C2×Dic11—48no—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×Q812yes—
361C2×Dic11C2×#4114yes—
362C2×Dic11C2×#4112yes—
363D44—28no—
364C4×D11—28no—
365C4×D11—216no—
366C4×D11—28no—
367C4×D11—48no—
368C4×D11—48no—
369C4×D11—48no—
370C4×D11—48no—
371C4×D11—416no—
372C4×D11C22⋊Q8116yes—
373Dic22—216no—
374Dic22—28no—
375C23×Q8—111no—
376C23×D4—111no—
377C24×C4—112no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—112no—
381C2×C4×Q8—112no—
382C2×C4×Q8—111no—
383C2×C4×Q8—228no—
384C2×C4×Q8C2×D1111yescharacteristic, complemented
385C2×C4×D4—111no—
386C2×C4×D4—112no—
387C2×C4×D4—111no—
388C2×C4×D4—112no—
389C2×C4×D4—111no—
390C2×C4×D4—228no—
391C2×C4×D4C2×D1111yescharacteristic
392C22×C4⋊C4—111no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4—112no—
395C22×C4⋊C4—112no—
396C22×C4⋊C4—114no—
397C22×C22⋊C4—112no—
398C22×C22⋊C4—114no—
399C22×C22⋊C4—114no—
400C22×C42—111no—
401C22×C42—112no—
402#399—114no—
403#399—112no—
404#399—114no—
405#399—112no—
406#399—112no—
407#399C2×D1112yescomplemented
408#393—112no—
409#393—114no—
410#393—112no—
411#393—114no—
412#393—112no—
413#393C2×D1112yescomplemented
414#390—112no—
415#390—112no—
416#390—114no—
417#390—114no—
418#390—112no—
419#390C2×D1112yes—
420#389—114no—
421#389—112no—
422#389—112no—
423#389—112no—
424#389—114no—
425#389C2×D1112yescomplemented
426#385—114no—
427#385—114no—
428#385—114no—
429#385—114no—
430#385—114no—
431#385—114no—
432#385—114no—
433#385C2×D1114yescomplemented
434#382—112no—
435#382—111no—
436#382—112no—
437#382—112no—
438#382C2×D1111yescharacteristic, complemented
439C2×#95—112no—
440C2×#95—114no—
441C2×#95—112no—
442C22×C11—24no—
443C22×C11—28no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—44no—
447C22×C11C23×D411yescharacteristic
448C22×C11C23×Q811yescharacteristic
449C22×C11C22×#4111yescharacteristic
450C22×C11C22×#4112yes—
451C22×C11C2×H(5,𝔽2)12yes—
452C2×D11—24no—
453C2×D11—28no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—44no—
457C2×D11—432no—
458C2×D11C2×C22⋊Q814yes—
459C2×D11#52514yes—
460C2×D11#53514yes—
461C2×D11#55418yes—
462C2×D11#55918yes—
463C4×C11—22no—
464C4×C11—24no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—44no—
469C4×C11C2×C22⋊Q814yes—
470Dic11—22no—
471Dic11—24no—
472Dic11—22no—
473Dic11—42no—
474Dic11—42no—
475Dic11—44no—
476Dic11C2×C22⋊Q814yes—
477C25—112no—
478C22×Q8—111no—
479C22×Q8—112no—
480C22×Q8—224no—
481C22×Q8—228no—
482C22×Q8C22×D1111yescharacteristic
483C22×D4—112no—
484C22×D4—118no—
485C22×D4—111no—
486C22×D4—224no—
487C22×D4—224no—
488C22×D4C22×D1111yescharacteristic
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—112no—
492C23×C4—111no—
493C23×C4—112no—
494C23×C4—112no—
495C23×C4—114no—
496C23×C4—112no—
497C23×C4—112no—
498C23×C4—112no—
499C23×C4—228no—
500C23×C4—448no—
501C23×C4C22×D1112yes—
502C4×Q8—24no—
503C4×Q8—228no—
504C4×Q8—224no—
505C4×Q8—228no—
506C4×Q8—224no—
507C4×Q8—224no—
508C4×D4—24no—
509C4×D4—228no—
510C4×D4—224no—
511C4×D4—228no—
512C4×D4—224no—
513C4×D4—224no—
514C2×C4⋊C4—112no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—112no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—112no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4—228no—
529C2×C4⋊C4—228no—
530C2×C4⋊C4—448no—
531C2×C4⋊C4C22×D1111yescharacteristic
532C2×C4⋊C4C22×D1112yes—
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1112yes—
535C2×C4⋊C4C22×D1114yes—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—228no—
546C2×C22⋊C4—2216no—
547C2×C22⋊C4—448no—
548C2×C22⋊C4C22×D1112yes—
549C2×C22⋊C4C22×D1114yes—
550C2×C22⋊C4C22×D1114yes—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—111no—
554C2×C42—118no—
555C2×C42—112no—
556C2×C42—112no—
557C2×C42—112no—
558C2×C42—228no—
559C2×C42C22×D1112yes—
560C2×C42C22×D1111yescharacteristic
561#95—114no—
562#95—112no—
563#95—114no—
564#95—112no—
565#95—114no—
566#95—114no—
567#95—114no—
568#95C22×D1112yes—
569#95C22×D1112yes—
570#95C22×D1114yes—
571C2×C11—44no—
572C2×C11C22×C22⋊Q811yescharacteristic
573C2×C11C2×#52511yescharacteristic
574C2×C11C2×#53511yescharacteristic
575C2×C11C2×#55412yes—
576C2×C11C2×#55912yes—
577D11—44no—
578D11#258018yesdirect product factor
579C24—111no—
580C24—118no—
581C24—112no—
582C24—224no—
583C24—228no—
584C24—228no—
585C24—224no—
586C24C23×D1112yes—
587C2×Q8—22no—
588C2×Q8—24no—
589C2×Q8—224no—
590C2×Q8—224no—
591C2×Q8—224no—
592C2×Q8—2232no—
593C2×Q8—222no—
594C2×Q8—224no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—118no—
598C2×D4—114no—
599C2×D4—2232no—
600C2×D4—224no—
601C2×D4—224no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4Q8×D1114yescomplemented
605C22×C4—24no—
606C22×C4—44no—
607C22×C4—111no—
608C22×C4—114no—
609C22×C4—114no—
610C22×C4—114no—
611C22×C4—111no—
612C22×C4—112no—
613C22×C4—111no—
614C22×C4—114no—
615C22×C4—114no—
616C22×C4—118no—
617C22×C4—114no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—224no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—224no—
627C22×C4—228no—
628C22×C4—224no—
629C22×C4—228no—
630C22×C4—228no—
631C22×C4—224no—
632C22×C4—228no—
633C22×C4—224no—
634C22×C4—224no—
635C22×C4—444no—
636C22×C4—444no—
637C22×C4—4432no—
638C22×C4—444no—
639C22×C4C23×D1114yes—
640C22×C4C23×D1112yes—
641C22×C4C23×D1112yes—
642C22×C4C23×D1111yescharacteristic
643C22×C4C23×D1111yescharacteristic
644C22×C4C23×D1112yes—
645C22×C4C23×D1111yescharacteristic
646C4⋊C4—22no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—44no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C4⋊C4—224no—
655C4⋊C4—228no—
656C4⋊C4—222no—
657C4⋊C4—224no—
658C4⋊C4—222no—
659C4⋊C4—224no—
660C4⋊C4—444no—
661C4⋊C4—444no—
662C4⋊C4—444no—
663C22⋊C4—24no—
664C22⋊C4—28no—
665C22⋊C4—44no—
666C22⋊C4—224no—
667C22⋊C4—228no—
668C22⋊C4—224no—
669C22⋊C4—228no—
670C22⋊C4—224no—
671C22⋊C4—228no—
672C22⋊C4—444no—
673C22⋊C4—444no—
674C22⋊C4—444no—
675C42—24no—
676C42—114no—
677C42—114no—
678C42—114no—
679C42—224no—
680C42—224no—
681C42—224no—
682C42D4×D1114yes—
683C11C2×#258011yescharacteristic, complemented, Sylow
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—112no—
689C23—112no—
690C23—114no—
691C23—112no—
692C23—114no—
693C23—114no—
694C23—2216no—
695C23—2232no—
696C23—222no—
697C23—224no—
698C23—222no—
699C23—224no—
700C23—448no—
701C23—4416no—
702C23—448no—
703C23C2×Q8×D1114yes—
704C23C24×D1111yescharacteristic
705Q8—28no—
706Q8—228no—
707Q8—2216no—
708D4—28no—
709D4—2216no—
710D4—228no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—48no—
724C2×C4—112no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—1116no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—114no—
731C2×C4—228no—
732C2×C4—228no—
733C2×C4—2216no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—222no—
743C2×C4—224no—
744C2×C4—222no—
745C2×C4—224no—
746C2×C4—448no—
747C2×C4—448no—
748C2×C4—448no—
749C2×C4—448no—
750C2×C4—4416no—
751C2×C4—448no—
752C2×C4C2×D4×D1112yes—
753C2×C4C2×D4×D1112yes—
754C2×C4C2×D4×D1112yes—
755C2×C4C2×Q8×D1112yes—
756C2×C4#41×D1114yes—
757C2×C4#41×D1112yes—
758C22—28no—
759C22—24no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—118no—
764C22—114no—
765C22—118no—
766C22—114no—
767C22—114no—
768C22—228no—
769C22—224no—
770C22—4432no—
771C22—442no—
772C22—444no—
773C22—442no—
774C22C22×D4×D1111yescharacteristic
775C22C22×Q8×D1111yescharacteristic
776C22C2×#41×D1112yes—
777C22C2×#41×D1111yescharacteristic
778C22D11×H(5,𝔽2)12yes—
779C4—22no—
780C4—22no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—114no—
786C4—222no—
787C4—222no—
788C4—224no—
789C4—442no—
790C4—442no—
791C4—444no—
792C4D11×C22⋊Q814yes—
793C2—44no—
794C2—118no—
795C2—444no—
796C2C2×D11×C22⋊Q811yescharacteristic
797C2D11×#52511yescharacteristic
798C2D11×#53511yescharacteristic
799C2D11×#55412yes—
800C2D11×#55912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2580C2
prime radicalC22×D4×D11C22
hypercenter#2580D11
hypocenterC11C2×#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D11C2semidirect
3. #13073976C2semidirect
4. #13073975C2semidirect
5. #13073974C2semidirect
6. #13073973C2semidirect
7. #13073972C2semidirect
8. #13073971C2semidirect
9. #13073970C2semidirect
10. #13073969C2semidirect
11. D11×#399C2semidirect
12. D11×#393C2semidirect
14. D11×#389C2semidirect
15. D11×#385C2semidirect
16. D11×#382C2semidirect
17. C11×#2580C2semidirect
21. C2×C4×Q8×C11C22semidirect
23. C2×Q8×Dic11C22semidirect
34. C2×#66940C22semidirect
35. C2×#66940C22semidirect
43. C2×C4×Dic22C22semidirect
44. C2×C4×Dic22C22semidirect
45. C11×#399C22semidirect
46. C11×#393C22semidirect
48. C11×#389C22semidirect
49. C11×#385C22semidirect
50. C11×#382C22semidirect
51. #10622844C22semidirect
53. #10622823C22semidirect
54. #10622605C22semidirect
55. #10622605C22semidirect
56. #10622602C22semidirect
57. #10622602C22semidirect
59. #10622598C22semidirect
60. #10622590C22semidirect
61. #10622586C22semidirect
62. #10622585C22semidirect
65. #10622563C22semidirect
66. #10622562C22semidirect
67. #10622562C22semidirect
68. #10622560C22semidirect
69. #10622560C22semidirect
70. #10622559C22semidirect
72. #10622549C22semidirect
73. #10622541C22semidirect
74. #10622290C22semidirect
75. #10622286C22semidirect
76. #10622286C22semidirect
77. #10622281C22semidirect
78. #10622281C22semidirect
82. #10622263C22semidirect
83. #10622263C22semidirect
84. #10622260C22semidirect
95. C2×D4×D11Q8semidirect
192. C2×D4×C11C2×Q8semidirect
204. C2×C22⋊D11C2×Q8semidirect
218. C2×D44C2×Q8semidirect
294. #2580D11direct (N × H)
384. C2×C4×Q8C2×D11semidirect
407. #399C2×D11semidirect
413. #393C2×D11semidirect
425. #389C2×D11semidirect
433. #385C2×D11semidirect
438. #382C2×D11semidirect
578. D11#2580direct (N × H)
604. C2×D4Q8×D11semidirect
683. C11C2×#2580semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×C4×D4×D112
#130739762
#130739752
#130739742
#130739732
#130739722
#130739712
#130739702
#130739692
D11×#3992
D11×#3932
D11×#3902
D11×#3892
D11×#3852
D11×#3822
C11×#25802
C2×#258011