Finite Group Databasebeta

← D11×#2821 #14960332

Subgroups — D11×#2821 #14960332

Order 2816.

2370 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×D11×#126C211yesmaximal, characteristic
3#13076681C212yesmaximal, complemented
4#13076680C212yesmaximal, complemented
5#13076679C212yesmaximal, complemented
6#13076678C212yesmaximal, complemented
7#13076677C211yesmaximal, characteristic, complemented
8#13076676C212yesmaximal, complemented
9#13076675C211yesmaximal, characteristic, complemented
10#13076674C211yesmaximal, characteristic, complemented
11#13076673C212yesmaximal, complemented
12D11×#400C212yesmaximal, complemented
13D11×#399C212yesmaximal
14D11×#398C212yesmaximal, complemented
15D11×#397C212yesmaximal
16D11×#395C212yesmaximal, complemented
17D11×#393C212yesmaximal
18D11×#383C211yesmaximal, characteristic, complemented
19C11×#2821C211yesmaximal, characteristic, complemented
20C22×Q8×D11C2212yes—
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C2×C11×#126C2211yescharacteristic
23C2×#66997C2212yescomplemented
24D11×C4⋊Q8—28no—
25D11×#126—28no—
26C2×#66951C2211yescharacteristic
27C2×#66951C2211yescharacteristic
28C2×#66951C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2214yes—
35C2×#66941C2212yescomplemented
36C2×#66941C2212yescomplemented
37C2×C22⋊C4×D11C2211yescharacteristic
38C2×C22⋊C4×D11C2211yescharacteristic
39C2×C22⋊C4×D11C2211yescharacteristic
40C2×C22⋊C4×D11C2214yes—
41C2×#66932C2211yescharacteristic
42C2×#66932C2211yescharacteristic
43C2×#66932C2211yescharacteristic
44C2×#66929C2211yescharacteristic
45C2×C42×D11C2211yescharacteristic
46C2×#66922C2211yescharacteristic, complemented
47C11×#400C2212yescomplemented
48C11×#399C2212yes—
49C11×#398C2212yescomplemented
50C11×#397C2212yes—
51C11×#395C2212yescomplemented
52C11×#393C2212yes—
53C11×#383C2211yescharacteristic, complemented
54#10622844C2212yes—
55#10622842C2212yescomplemented
56#10622606C2212yes—
57#10622605C2212yes—
58#10622605C2214yes—
59#10622599C2212yescomplemented
60#10622597C2214yescomplemented
61#10622596C2212yescomplemented
62#10622595C2212yescomplemented
63#10622593C2212yescomplemented
64#10622592C2212yescomplemented
65#10622592C2214yescomplemented
66#10622566C2212yes—
67#10622565C2214yes—
68#10622562C2214yes—
69#10622562C2212yes—
70#10622560C2214yes—
71#10622560C2212yes—
72#10622550C2211yescharacteristic, complemented
73#10622290C2212yes—
74#10622288C2214yes—
75#10622287C2212yes—
76#10622286C2214yes—
77#10622286C2212yes—
78D11×#95C2212yes—
79D11×#95C2212yes—
80D11×#95C2212yes—
81D11×#95C2214yes—
82D11×#95C2214yes—
83#10622274C2212yescomplemented
84#10622273C2214yescomplemented
85#10622272C2212yescomplemented
86#10622271C2214yescomplemented
87#10622270C2214yescomplemented
88#10622269C2214yescomplemented
89#10622269C2212yescomplemented
90#10622264C2212yescomplemented
91#10622264C2212yescomplemented
92#10622264C2212yescomplemented
93C24×D11C2311yescharacteristic
94C22×Q8×C11C2312yes—
95C2×Q8×D11—28no—
96C2×Q8×D11—48no—
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2314yes—
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2314yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×Dic22C2312yes—
106C22×Dic22C2314yes—
107C11×C4⋊Q8—24no—
108C11×#126—24no—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C22⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4C2314yes—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11C2311yescharacteristic
121C2×C22⋊Dic11C2311yescharacteristic
122C2×C22⋊Dic11C2311yescharacteristic
123C2×C22⋊Dic11C2314yes—
124#66997—28no—
125C2×(C2×D11)⋊C4C2311yescharacteristic
126C2×(C2×D11)⋊C4C2311yescharacteristic
127C2×(C2×D11)⋊C4C2311yescharacteristic
128C2×(C2×D11)⋊C4C2311yescharacteristic
129C2×(C2×D11)⋊C4C2311yescharacteristic
130C2×(C2×D11)⋊C4C2311yescharacteristic
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4C2311yescharacteristic
140C2×Dic11⋊C4C2311yescharacteristic
141C2×Dic11⋊C4C2311yescharacteristic
142C2×Dic11⋊C4C2311yescharacteristic
143C2×Dic11⋊C4C2311yescharacteristic
144C2×Dic11⋊C4C2311yescharacteristic
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152#66951—24no—
153#66951—24no—
154#66951—24no—
155C4⋊C4×D11—24no—
156C4⋊C4×D11—24no—
157C4⋊C4×D11—24no—
158C4⋊C4×D11—28no—
159C4⋊C4×D11—28no—
160C4⋊C4×D11—48no—
161#66941—28no—
162#66941—28no—
163C22⋊C4×D11—24no—
164C22⋊C4×D11—24no—
165C22⋊C4×D11—24no—
166C22⋊C4×D11—48no—
167#66932—24no—
168#66932—24no—
169#66932—24no—
170#66929—24no—
171C42×D11D418yes—
172#66922—24no—
173C11×#95C2312yes—
174C11×#95C2312yes—
175C11×#95C2312yes—
176C11×#95C2314yes—
177C11×#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C11⋊#95C2312yes—
182C11⋊#95C2312yes—
183C11⋊#95C2312yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C11⋊#95C2314yes—
187C11⋊#95C2314yes—
188C11⋊#95C2314yes—
189C11⋊#95C2314yes—
190C2×#2821—111nomaximal, Sylow
191C24×C11C2411yescharacteristic
192C23×D11—22no—
193C23×D11—24no—
194C23×D11—24no—
195C23×D11—24no—
196C23×D11C2411yescharacteristic
197C23×D11C2411yescharacteristic
198C2×Q8×C11—24no—
199C2×Q8×C11—44no—
200C22×C4×C11C2414yes—
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C22×C4×C11C2414yes—
204C22×C4×C11C2411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×Dic11C2414yes—
209C22×Dic11C2411yescharacteristic
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2414yes—
212C22×Dic11C2411yescharacteristic
213C22×Dic11C2411yescharacteristic
214C22×Dic11C2411yescharacteristic
215C22×Dic11C2411yescharacteristic
216Q8×D11—432no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—28no—
221C2×C4×D11—24no—
222C2×C4×D11—28no—
223C2×C4×D11—28no—
224C2×C4×D11—24no—
225C2×C4×D11—28no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—28no—
231C2×C4×D11—28no—
232C2×C4×D11C2×D414yes—
233C2×C4×D11C2×D414yes—
234C2×C4×D11C2×D414yes—
235C2×Dic22—28no—
236C2×Dic22—24no—
237C2×Dic22—44no—
238C2×Dic22—44no—
239C2×Dic22—44no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—44no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—44no—
250C42×C11C2×D414yes—
251C22⋊Dic11—22no—
252C22⋊Dic11—22no—
253C22⋊Dic11—22no—
254C22⋊Dic11—44no—
255(C2×D11)⋊C4—22no—
256(C2×D11)⋊C4—22no—
257(C2×D11)⋊C4—22no—
258(C2×D11)⋊C4—22no—
259(C2×D11)⋊C4—22no—
260(C2×D11)⋊C4—22no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263C4⋊Dic11—22no—
264C4⋊Dic11—22no—
265C4⋊Dic11—22no—
266C4⋊Dic11—24no—
267C4⋊Dic11—24no—
268C4⋊Dic11—44no—
269Dic11⋊C4—22no—
270Dic11⋊C4—22no—
271Dic11⋊C4—22no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—22no—
275Dic11⋊C4—22no—
276Dic11⋊C4—22no—
277Dic11⋊C4—44no—
278Dic11⋊C4—44no—
279C4×Dic11C2×D414yes—
280C4×Dic11C2×D414yes—
281C4×Dic11C2×D414yes—
282C22×C4⋊Q8—111no—
283C22×#126—111no—
284#2821—112no—
285#2821—112no—
286#2821—112no—
287#2821—112no—
288#2821—112no—
289#2821—112no—
290#2821—111no—
291#2821—111no—
292#2821—111no—
293#2821D1111yescharacteristic, direct product factor
294C2×#400—112no—
295C2×#399—112no—
296C2×#398—112no—
297C2×#397—112no—
298C2×#395—112no—
299C2×#393—112no—
300C2×#383—111no—
301C23×C11—21no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11C2511yescharacteristic
306C22×D11—21no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—44no—
311C22×D11—44no—
312C22×D11—44no—
313C22×D11—416no—
314C22×D11C22×D412yes—
315C22×D11H(5,𝔽2)14yes—
316C22×D112−1+414yes—
317C22×D112−1+414yes—
318Q8×C11—48no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—24no—
333C2×C4×C11—24no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D412yes—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—24no—
344C2×Dic11—22no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11C22×D412yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355C4×D11—28no—
356C4×D11—28no—
357C4×D11—28no—
358C4×D11—44no—
359C4×D11—416no—
360C4×D11—44no—
361C4×D11—44no—
362C4×D11—416no—
363Dic22—416no—
364Dic22—48no—
365C23×Q8—112no—
366C2×C4⋊Q8—112no—
367C2×C4⋊Q8—112no—
368C2×C4⋊Q8—112no—
369C2×C4⋊Q8—111no—
370C2×C4⋊Q8—228no—
371C2×C4⋊Q8C2×D1111yescharacteristic, complemented
372C2×#126—111no—
373C2×#126—111no—
374C2×#126—111no—
375C2×#126—111no—
376C2×#126—111no—
377C2×#126—111no—
378C2×#126—111no—
379C2×#126—228no—
380C2×#126C2×D1111yescharacteristic
381C22×C4⋊C4—111no—
382C22×C4⋊C4—112no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—112no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—114no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—111no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—114no—
391C22×C42—111no—
392#400—112no—
393#400—112no—
394#400—114no—
395#400—112no—
396#400—114no—
397#400C2×D1112yescomplemented
398#399—114no—
399#399—112no—
400#399—114no—
401#399—112no—
402#399—112no—
403#399C2×D1112yes—
404#398—112no—
405#398—112no—
406#398—114no—
407#398—114no—
408#398—112no—
409#398C2×D1112yescomplemented
410#397—112no—
411#397—114no—
412#397—112no—
413#397—112no—
414#397—114no—
415#397C2×D1112yes—
416#395—112no—
417#395—114no—
418#395—112no—
419#395—114no—
420#395—112no—
421#395C2×D1112yescomplemented
422#393—112no—
423#393—114no—
424#393—112no—
425#393—114no—
426#393—112no—
427#393C2×D1112yes—
428#383—111no—
429#383—112no—
430#383—112no—
431#383—112no—
432#383C2×D1111yescharacteristic, complemented
433C2×#95—112no—
434C2×#95—114no—
435C2×#95—114no—
436C2×#95—112no—
437C2×#95—112no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—44no—
442C22×C11C23×D411yescharacteristic
443C22×C11C2×H(5,𝔽2)12yes—
444C22×C11C2×2−1+412yes—
445C22×C11C2×2−1+412yes—
446C2×D11—41no—
447C2×D11—41no—
448C2×D11—41no—
449C2×D11—44no—
450C2×D11—88no—
451C2×D11#53514yes—
452C2×D11#53614yes—
453C2×D11#53614yes—
454C2×D11#563116yes—
455C4×C11—22no—
456C4×C11—22no—
457C4×C11—22no—
458C4×C11—44no—
459C4×C11—41no—
460C4×C11—41no—
461C4×C11—41no—
462C4×C11—44no—
463Dic11—22no—
464Dic11—22no—
465Dic11—22no—
466Dic11—44no—
467Dic11—41no—
468Dic11—41no—
469Dic11—41no—
470Dic11—44no—
471C25—111no—
472C22×Q8—114no—
473C22×Q8—112no—
474C22×Q8—228no—
475C22×Q8—448no—
476C22×Q8C22×D1112yes—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—114no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—114no—
485C4⋊Q8—24no—
486C4⋊Q8—228no—
487C4⋊Q8—228no—
488C4⋊Q8—228no—
489C4⋊Q8—224no—
490#126—24no—
491#126—224no—
492#126—224no—
493#126—224no—
494#126—224no—
495#126—224no—
496#126—224no—
497#126—224no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—224no—
515C2×C4⋊C4—224no—
516C2×C4⋊C4—224no—
517C2×C4⋊C4—228no—
518C2×C4⋊C4—228no—
519C2×C4⋊C4—448no—
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1112yes—
524C2×C4⋊C4C22×D1112yes—
525C2×C4⋊C4C22×D1114yes—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—111no—
531C2×C22⋊C4—111no—
532C2×C22⋊C4—111no—
533C2×C22⋊C4—111no—
534C2×C22⋊C4—111no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—224no—
539C2×C22⋊C4—224no—
540C2×C22⋊C4—224no—
541C2×C22⋊C4—448no—
542C2×C22⋊C4C22×D1111yescharacteristic
543C2×C22⋊C4C22×D1111yescharacteristic
544C2×C22⋊C4C22×D1111yescharacteristic
545C2×C22⋊C4C22×D1114yes—
546C2×C42—111no—
547C2×C42—111no—
548C2×C42—111no—
549C2×C42—118no—
550C2×C42C22×D1111yescharacteristic
551#95—114no—
552#95—112no—
553#95—114no—
554#95—112no—
555#95—114no—
556#95—112no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—114no—
563#95C22×D1112yes—
564#95C22×D1112yes—
565#95C22×D1112yes—
566#95C22×D1114yes—
567#95C22×D1114yes—
568C2×C11—81no—
569C2×C11C2×#53511yescharacteristic
570C2×C11C2×#53611yescharacteristic
571C2×C11C2×#53611yescharacteristic
572C2×C11C2×#56314yes—
573D11—81no—
574D11#282118yesdirect product factor
575C24—111no—
576C24—111no—
577C24—222no—
578C24—224no—
579C24—224no—
580C24—224no—
581C24C23×D1111yescharacteristic
582C2×Q8—24no—
583C2×Q8—44no—
584C2×Q8—228no—
585C2×Q8—224no—
586C2×Q8—444no—
587C2×Q8—444no—
588C2×Q8—444no—
589C2×Q8—4432no—
590C22×C4—111no—
591C22×C4—111no—
592C22×C4—111no—
593C22×C4—114no—
594C22×C4—114no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—114no—
600C22×C4—111no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—228no—
608C22×C4—228no—
609C22×C4—228no—
610C22×C4—224no—
611C22×C4—228no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—228no—
615C22×C4—228no—
616C22×C4C23×D1114yes—
617C22×C4C23×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619C22×C4C23×D1114yes—
620C22×C4C23×D1111yescharacteristic
621C22×C4C23×D1111yescharacteristic
622C22×C4C23×D1111yescharacteristic
623C22×C4C23×D1111yescharacteristic
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—44no—
630C4⋊C4—222no—
631C4⋊C4—222no—
632C4⋊C4—222no—
633C4⋊C4—222no—
634C4⋊C4—222no—
635C4⋊C4—222no—
636C4⋊C4—228no—
637C4⋊C4—228no—
638C4⋊C4—222no—
639C4⋊C4—222no—
640C4⋊C4—222no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—444no—
644C4⋊C4—444no—
645C4⋊C4—444no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—44no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—222no—
655C22⋊C4—222no—
656C22⋊C4—222no—
657C22⋊C4—222no—
658C22⋊C4—222no—
659C22⋊C4—444no—
660C22⋊C4—444no—
661C22⋊C4—444no—
662C42—114no—
663C42—114no—
664C42—114no—
665C42D4×D1114yes—
666C11C2×#282111yescharacteristic, complemented, Sylow
667C23—21no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—112no—
672C23—114no—
673C23—114no—
674C23—114no—
675C23—221no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23—444no—
680C23—444no—
681C23—444no—
682C23—4416no—
683C23C24×D1111yescharacteristic
684Q8—48no—
685Q8—448no—
686Q8—4416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—112no—
705C2×C4—228no—
706C2×C4—228no—
707C2×C4—228no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—224no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—4416no—
724C2×C4—444no—
725C2×C4—444no—
726C2×C4—444no—
727C2×C4—4416no—
728C2×C4C2×D4×D1112yes—
729C2×C4C2×D4×D1112yes—
730C2×C4C2×D4×D1112yes—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—114no—
736C22—114no—
737C22—114no—
738C22—1116no—
739C22—441no—
740C22—441no—
741C22—441no—
742C22—444no—
743C22—888no—
744C22C22×D4×D1111yescharacteristic
745C22D11×H(5,𝔽2)12yes—
746C22D11×2−1+412yes—
747C22D11×2−1+412yes—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—44no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—44no—
756C4—222no—
757C4—222no—
758C4—222no—
759C4—444no—
760C4—441no—
761C4—441no—
762C4—441no—
763C4—444no—
764C2—81no—
765C2—118no—
766C2—881no—
767C2D11×#53511yescharacteristic
768C2D11×#53611yescharacteristic
769C2D11×#53611yescharacteristic
770C2D11×#56314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2821C2
prime radicalC24×D11C23
hypercenter#2821D11
hypocenterC11C2×#2821
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2821

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
3. #13076681C2semidirect
4. #13076680C2semidirect
5. #13076679C2semidirect
6. #13076678C2semidirect
7. #13076677C2semidirect
8. #13076676C2semidirect
9. #13076675C2semidirect
10. #13076674C2semidirect
11. #13076673C2semidirect
12. D11×#400C2semidirect
14. D11×#398C2semidirect
16. D11×#395C2semidirect
18. D11×#383C2semidirect
19. C11×#2821C2semidirect
21. C2×C11×C4⋊Q8C22semidirect
23. C2×#66997C22semidirect
35. C2×#66941C22semidirect
36. C2×#66941C22semidirect
46. C2×#66922C22semidirect
47. C11×#400C22semidirect
49. C11×#398C22semidirect
51. C11×#395C22semidirect
53. C11×#383C22semidirect
55. #10622842C22semidirect
59. #10622599C22semidirect
60. #10622597C22semidirect
61. #10622596C22semidirect
62. #10622595C22semidirect
63. #10622593C22semidirect
64. #10622592C22semidirect
65. #10622592C22semidirect
72. #10622550C22semidirect
83. #10622274C22semidirect
84. #10622273C22semidirect
85. #10622272C22semidirect
86. #10622271C22semidirect
87. #10622270C22semidirect
88. #10622269C22semidirect
89. #10622269C22semidirect
90. #10622264C22semidirect
91. #10622264C22semidirect
92. #10622264C22semidirect
293. #2821D11direct (N × H)
371. C2×C4⋊Q8C2×D11semidirect
397. #400C2×D11semidirect
409. #398C2×D11semidirect
421. #395C2×D11semidirect
432. #383C2×D11semidirect
574. D11#2821direct (N × H)
666. C11C2×#2821semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×D11×#1262
#130766812
#130766802
#130766792
#130766782
#130766772
#130766762
#130766752
#130766742
#130766732
D11×#4002
D11×#3992
D11×#3982
D11×#3972
D11×#3952
D11×#3932
D11×#3832
C11×#28212
C2×#282111