Finite Group Databasebeta

← #15623431

Subgroups — #15623431

Order 2816.

1890 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2D11×#533C211yesmaximal, characteristic
3#13079167C214yesmaximal, complemented
4#13079166C214yesmaximal, complemented
5#13079163C211yesmaximal, characteristic, complemented
6#13079162C211yesmaximal, characteristic, complemented
7#13079159C212yesmaximal, complemented
8#13079158C211yesmaximal, characteristic, complemented
9#13079157C212yesmaximal, complemented
10#13079137C214yesmaximal, complemented
11#13079127C212yesmaximal, complemented
12#13079125C212yesmaximal, complemented
13#13077203C214yesmaximal
14C4×M16×D11C211yesmaximal, characteristic
15C11×#3165C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66999—21no—
19C2×Q8×Dic11—21no—
20C2×M16×D11C2212yes—
21#10623259—21no—
22#10623259—21no—
23#10623259—21no—
24#10623259—21no—
25#10623259C2211yescharacteristic
26#10623259C2211yescharacteristic
27#10623259C2212yes—
28#10623259C2212yes—
29#10623259C2212yes—
30#10623259C2212yes—
31D11×C4⋊Q8C2211yescharacteristic
32D11×C4⋊Q8C2211yescharacteristic
33#10623219C2212yes—
34D11×#125C2212yes—
35D11×C22⋊Q8—21no—
36D11×C22⋊Q8—21no—
37#10623153—21no—
38#10623153—21no—
39#10623109—21no—
40#10623109—21no—
41C4×Q8×D11—21no—
42C4×Q8×D11—21no—
43D11×#117C2212yes—
44#10623048C2212yes—
45C2×#66950—21no—
46C2×#66945C2212yes—
47C2×#66943C2212yes—
48C2×#66940—21no—
49C2×C42×D11C2211yescharacteristic
50#10623001C2211yescharacteristic
51C2×#66922C2211yescharacteristic
52C11×#501C2214yescomplemented
53C11×#500C2212yescomplemented
54C11×#498C2212yescomplemented
55C11×#428C2214yes—
56C4×C11×M16C2211yescharacteristic
57#10622734C2214yes—
58M16×Dic11C2212yes—
59#10622693C2214yescomplemented
60#10622692C2212yescomplemented
61#10622692C2212yescomplemented
62#10622691C2212yescomplemented
63#10622691C2212yescomplemented
64#10622678C2214yescomplemented
65#10622608C2214yes—
66#10622577C2214yes—
67C4×#4318C2211yescharacteristic
68#10622494C2218yes—
69#10622493C2218yes—
70#10622491C2218yescomplemented
71#10622489C2218yescomplemented
72#10622474C2218yes—
73#10622473C2218yes—
74#10622471C2218yescomplemented
75#10622469C2218yescomplemented
76#10622320C2212yes—
77D11×#97C2212yes—
78#10622315C2214yescomplemented
79C4×#4313C2212yes—
80C4×C8×D11C2212yes—
81#10622295C2212yescomplemented
82#10622293C2212yescomplemented
83C22×Q8×C11—21no—
84C2×Q8×D11—21no—
85C2×Q8×D11—21no—
86C22×C4×D11D411yescharacteristic
87C22×C4×D11D411yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×Dic22—21no—
90C2×C11×M16C2312yes—
91C11×C4⋊Q8—21no—
92C11×C4⋊Q8—21no—
93C11×C4⋊Q8C2311yescharacteristic
94C11×C4⋊Q8C2312yes—
95C11×C4⋊Q8C2311yescharacteristic
96C11×C4⋊Q8C2312yes—
97C11×#125C2312yes—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—21no—
100C4×Q8×C11—21no—
101C4×Q8×C11—21no—
102C11×#117C2312yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2312yes—
105C2×C42×C11C2311yescharacteristic
106#66999—22no—
107#66999—22no—
108#66999—22no—
109#66999—22no—
110#66999—21no—
111#66999—21no—
112Q8×Dic11—22no—
113Q8×Dic11—22no—
114Q8×Dic11—22no—
115Q8×Dic11—22no—
116Q8×Dic11—21no—
117Q8×Dic11—21no—
118#66997—21no—
119#66997—21no—
120C2×(C2×D11)⋊C4—22no—
121#66979C2312yes—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11C2312yes—
125#66977—21no—
126#66977—21no—
127C2×Dic11⋊C4—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11D411yescharacteristic
130C2×C4×Dic11D411yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×#4318C2312yes—
133M16×D11Q8116yescomplemented
134C2×#4313C2314yes—
135C2×C8×D11C2314yes—
136#66950—22no—
137#66950—22no—
138#66950—22no—
139#66950—22no—
140#66950—21no—
141#66950—21no—
142#66949—22no—
143#66949—22no—
144#66945—22no—
145#66945—22no—
146#66945C2312yes—
147#66945C2314yes—
148#66945C2314yes—
149#66945C2312yes—
150C4⋊C4×D11—21no—
151C4⋊C4×D11—21no—
152C4⋊C4×D11—22no—
153C4⋊C4×D11—22no—
154C4⋊C4×D11C2312yes—
155C4⋊C4×D11C2312yes—
156#66943—22no—
157#66943—22no—
158#66943C2314yes—
159#66943C2312yes—
160#66943C2314yes—
161#66943C2312yes—
162#66942—22no—
163#66942—22no—
164#66941—21no—
165#66941—21no—
166#66941C2312yes—
167#66941C2312yes—
168#66940—22no—
169#66940—22no—
170#66940—22no—
171#66940—22no—
172#66940—21no—
173#66940—21no—
174#66940—22no—
175#66940—22no—
176C22⋊C4×D11—22no—
177#66931—22no—
178#66931—22no—
179#66930—22no—
180#66925—22no—
181C42×D11—22no—
182C42×D11D411yescharacteristic
183C42×D11D411yescharacteristic
184C42×D11D411yescharacteristic
185C42×D11D411yescharacteristic
186C42×D11C2311yescharacteristic
187C42×D11C2311yescharacteristic
188C42×D11C2311yescharacteristic
189C42×D11C2311yescharacteristic
190#66923C2312yes—
191#66922—21no—
192#66922—21no—
193#66922C2311yescharacteristic
194#66922C2311yescharacteristic
195#66922C2312yes—
196#66922C2312yes—
197C4×Dic22—21no—
198C4×Dic22—21no—
199C4×Dic22—22no—
200C4×Dic22—22no—
201C11×#107C2318yes—
202C11×#106C2318yes—
203C11×#97C2312yes—
204C4×C8×C11C2312yes—
205#66882C2318yes—
206#66881C2318yes—
207#66879C2314yes—
208C8×Dic11C2314yes—
209#66872C2318yes—
210#66872C2318yes—
211#66871C2318yes—
212#66871C2318yes—
213#66867C2312yes—
214C4×C11⋊C8C2312yes—
215#60663—111nomaximal, Sylow
216C23×D11C2×D411yescharacteristic
217C2×Q8×C11—21no—
218C2×Q8×C11—21no—
219C2×Q8×C11—22no—
220C2×Q8×C11—22no—
221C2×Q8×C11—44no—
222C22×C4×C11—22no—
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C22×Dic11—22no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230Q8×D11—44no—
231Q8×D11—44no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11C2×D411yescharacteristic
237C2×C4×D11C2×D411yescharacteristic
238C2×C4×D11C2×D411yescharacteristic
239C2×C4×D11C2×D411yescharacteristic
240C2×C4×D11C2×D411yescharacteristic
241C2×C4×D11C2×D411yescharacteristic
242C2×C4×D11C2×D411yescharacteristic
243C2×C4×D11C2×D411yescharacteristic
244C2×C4×D11C2×D411yescharacteristic
245C2×C4×D11C2×D411yescharacteristic
246C2×C4×D11C2×Q818yes—
247C2×C4×D11C2411yescharacteristic
248C2×C4×D11C2411yescharacteristic
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—21no—
252C2×Dic22—21no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—44no—
256C11×M16C2×Q818yescomplemented
257C2×C8×C11C2414yes—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—22no—
264C11×C4⋊C4—22no—
265C11×C4⋊C4C2412yes—
266C11×C4⋊C4C2414yes—
267C11×C4⋊C4C2412yes—
268C11×C22⋊C4—22no—
269C42×C11—22no—
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2411yescharacteristic
273C42×C11C2411yescharacteristic
274C22⋊Dic11—22no—
275(C2×D11)⋊C4—22no—
276(C2×D11)⋊C4—22no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279C4⋊Dic11—22no—
280C4⋊Dic11—22no—
281C4⋊Dic11—24no—
282C4⋊Dic11—24no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11—22no—
286C4⋊Dic11—22no—
287C4⋊Dic11—22no—
288C4⋊Dic11C2412yes—
289C4⋊Dic11C2414yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—22no—
292Dic11⋊C4—22no—
293Dic11⋊C4—22no—
294Dic11⋊C4—22no—
295Dic11⋊C4—22no—
296Dic11⋊C4—22no—
297Dic11⋊C4—24no—
298Dic11⋊C4—24no—
299Dic11⋊C4—22no—
300Dic11⋊C4—22no—
301C4×Dic11—22no—
302C4×Dic11—22no—
303C4×Dic11—24no—
304C4×Dic11—24no—
305C4×Dic11—22no—
306C4×Dic11C2×D411yescharacteristic
307C4×Dic11C2×D411yescharacteristic
308C4×Dic11C2×D411yescharacteristic
309C4×Dic11C2×D411yescharacteristic
310C4×Dic11C2×D411yescharacteristic
311C4×Dic11C2×D411yescharacteristic
312C4×Dic11C2×D411yescharacteristic
313C4×Dic11C2×D411yescharacteristic
314C4×Dic11C2×D411yescharacteristic
315C4×Dic11C2×D411yescharacteristic
316C4×Dic11C2411yescharacteristic
317C4×Dic11C2411yescharacteristic
318#4318C2×Q818yescomplemented
319C2×C11⋊C8C2414yes—
320#4313C2×Q8116yescomplemented
321C8×D11C2×Q8116yescomplemented
322C2×#533—111no—
323C2×#533—111no—
324#3166—114no—
325#3166—114no—
326#3165—112no—
327#3165—112no—
328#3165—111no—
329#3165—111no—
330#3165—111no—
331#3165D1111yescharacteristic, complemented
332#3162—114no—
333#3160—112no—
334#3160—112no—
335#2911—114no—
336C2×C4×M16—111no—
337C23×C11C22×D411yescharacteristic
338C22×D11—41no—
339C22×D11—41no—
340C22×D11C4⋊Q814yes—
341C22×D11C22×D411yescharacteristic
342C22×D11C22×D411yescharacteristic
343Q8×C11—44no—
344Q8×C11—42no—
345Q8×C11—42no—
346Q8×C11—44no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—44no—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×Q814yes—
359C2×C4×C11C2511yescharacteristic
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—44no—
366C2×Dic11C4⋊Q814yes—
367C2×Dic11C22×D411yescharacteristic
368C2×Dic11C22×D411yescharacteristic
369C2×Dic11C22×D411yescharacteristic
370C2×Dic11C22×D411yescharacteristic
371C2×Dic11C22×D411yescharacteristic
372C2×Dic11C22×D411yescharacteristic
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—41no—
378C4×D11—41no—
379C4×D11—41no—
380C4×D11—41no—
381C4×D11—44no—
382C4×D11—44no—
383C4×D11C4⋊Q814yes—
384C4×D11C4⋊Q814yes—
385C4×D11C22×Q814yes—
386C4×D11C22×Q814yes—
387Dic22—44no—
388Dic22—44no—
389Dic22—44no—
390Dic22—44no—
391Dic22—42no—
392Dic22—42no—
393C8×C11C22×Q818yes—
394C11⋊C8C22×Q818yes—
395C22×M16—112no—
396#533—111no—
397#533—111no—
398#533—112no—
399#533—112no—
400#533—112no—
401#533—112no—
402#533—112no—
403#533—112no—
404#533—111no—
405#533—221no—
406#533—221no—
407#533—221no—
408#533—221no—
409#533—221no—
410#533—221no—
411#533—221no—
412#533—221no—
413#533C2×D1111yescharacteristic
414C2×C4⋊Q8—111no—
415C2×C4⋊Q8—111no—
416C2×C4⋊Q8—111no—
417C2×C4⋊Q8C2×D1111yescharacteristic
418C2×#125—112no—
419C2×#125—112no—
420C2×C22⋊Q8—221no—
421C2×C22⋊Q8—221no—
422C2×C22⋊Q8—221no—
423C2×C22⋊Q8—221no—
424C2×C4×Q8—221no—
425C2×C4×Q8—221no—
426C2×C4×Q8—221no—
427C2×C4×Q8—221no—
428C2×#117—112no—
429C2×#117—112no—
430C22×C42—111no—
431#501—114no—
432#501—114no—
433#501—118no—
434#501—118no—
435#501—114no—
436#501C2×D1114yescomplemented
437#500—112no—
438#500—112no—
439#500—112no—
440#500C2×D1112yescomplemented
441#499—118no—
442#499—118no—
443#498—112no—
444#498—112no—
445#498—112no—
446#498C2×D1112yescomplemented
447#428—114no—
448#428—114no—
449#428—114no—
450#428—118no—
451#428—118no—
452#428C2×D1114yes—
453#427—118no—
454#427—118no—
455C4×M16—112no—
456C4×M16—111no—
457C4×M16—112no—
458C4×M16—112no—
459C4×M16C2×D1111yescharacteristic
460C2×#97—112no—
461C2×C4×C8—112no—
462C22×C11—21no—
463C22×C11—21no—
464C22×C11C2×C4⋊Q812yes—
465C22×C11C23×D411yescharacteristic
466C2×D11—21no—
467C2×D11—21no—
468C2×D11—21no—
469C2×D11—21no—
470C2×D11—44no—
471C2×D11C2×C4⋊Q812yes—
472C2×D11C2×C4⋊Q812yes—
473C4×C11—21no—
474C4×C11—21no—
475C4×C11—44no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11C2×C4⋊Q812yes—
479C4×C11#57512yes—
480C4×C11#57512yes—
481C4×C11C23×Q812yes—
482Dic11—21no—
483Dic11—21no—
484Dic11—21no—
485Dic11—21no—
486Dic11—42no—
487Dic11—42no—
488Dic11—44no—
489Dic11C2×C4⋊Q812yes—
490Dic11C2×C4⋊Q812yes—
491C22×Q8—21no—
492C22×Q8—221no—
493C22×Q8—221no—
494C22×Q8—221no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C2×M16—112no—
499C2×M16—1116no—
500C2×M16—114no—
501C2×M16C22×D1112yes—
502C22×C8—114no—
503C4⋊Q8—21no—
504C4⋊Q8—21no—
505C4⋊Q8—112no—
506C4⋊Q8—112no—
507C4⋊Q8—111no—
508C4⋊Q8—111no—
509C4⋊Q8—112no—
510C4⋊Q8—112no—
511C4⋊Q8—221no—
512C4⋊Q8—221no—
513C4⋊Q8—221no—
514C4⋊Q8—221no—
515C4⋊Q8—221no—
516C4⋊Q8—221no—
517C4⋊Q8C22×D1111yescharacteristic
518C4⋊Q8C22×D1111yescharacteristic
519C4⋊Q8C22×D1112yes—
520C4⋊Q8C22×D1112yes—
521#125—112no—
522#125—114no—
523#125—112no—
524#125—114no—
525#125—112no—
526#125—222no—
527#125—222no—
528#125—222no—
529#125—222no—
530#125C22×D1112yes—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—222no—
534C22⋊Q8—222no—
535C22⋊Q8—222no—
536C22⋊Q8—222no—
537C22⋊Q8—222no—
538C22⋊Q8—222no—
539C22⋊Q8—222no—
540C22⋊Q8—222no—
541C22⋊Q8—221no—
542C22⋊Q8—221no—
543C22⋊Q8—222no—
544C22⋊Q8—221no—
545C22⋊Q8—221no—
546C22⋊Q8—222no—
547C22⋊Q8—222no—
548C22⋊Q8—222no—
549C22⋊Q8—221no—
550C22⋊Q8—221no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—222no—
554C4×Q8—222no—
555C4×Q8—222no—
556C4×Q8—222no—
557C4×Q8—222no—
558C4×Q8—222no—
559C4×Q8—221no—
560C4×Q8—221no—
561C4×Q8—222no—
562C4×Q8—222no—
563C4×Q8—221no—
564C4×Q8—221no—
565C4×Q8—222no—
566C4×Q8—222no—
567C4×Q8—222no—
568C4×Q8—222no—
569C4×Q8—221no—
570C4×Q8—221no—
571#117—112no—
572#117—112no—
573#117—114no—
574#117—112no—
575#117—114no—
576#117—222no—
577#117—222no—
578#117—222no—
579#117—222no—
580#117C22×D1112yes—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—112no—
583C2×C4⋊C4—112no—
584C2×C4⋊C4—112no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—222no—
587C2×C4⋊C4—221no—
588C2×C4⋊C4—221no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4C22×D1112yes—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C42—111no—
596C2×C42—111no—
597C2×C42—111no—
598C2×C42—111no—
599C2×C42—111no—
600C2×C42—111no—
601C2×C42—111no—
602C2×C42—111no—
603C2×C42—111no—
604C2×C42—111no—
605C2×C42—111no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42C22×D1111yescharacteristic
609#107—118no—
610#107—118no—
611#107—118no—
612#107C22×D1118yes—
613#106—118no—
614#106—118no—
615#106—118no—
616#106C22×D1118yes—
617#97—114no—
618#97—112no—
619#97C22×D1112yes—
620C4×C8—114no—
621C4×C8—112no—
622C4×C8C22×D1112yes—
623C2×C11—22no—
624C2×C11C22×C4⋊Q811yescharacteristic
625C2×C11C2×#57511yescharacteristic
626C2×C11C2×#57511yescharacteristic
627D11—22no—
628D11—22no—
629C24—111no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—44no—
635C2×Q8—222no—
636C2×Q8—222no—
637C2×Q8—222no—
638C2×Q8—221no—
639C2×Q8—222no—
640C2×Q8—221no—
641C2×Q8—444no—
642C2×Q8—444no—
643C2×Q8—444no—
644C22×C4—22no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—118no—
649C22×C4—111no—
650C22×C4—111no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4D4×D1111yescharacteristic
667C22×C4D4×D1111yescharacteristic
668C22×C4C23×D1111yescharacteristic
669M16—118no—
670M16—1116no—
671M16Q8×D1118yescomplemented
672C2×C8—114no—
673C2×C8—1116no—
674C2×C8C23×D1114yes—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—112no—
683C4⋊C4—114no—
684C4⋊C4—112no—
685C4⋊C4—222no—
686C4⋊C4—222no—
687C4⋊C4—222no—
688C4⋊C4—222no—
689C4⋊C4—224no—
690C4⋊C4—224no—
691C4⋊C4—222no—
692C4⋊C4—222no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—222no—
696C4⋊C4—222no—
697C4⋊C4—222no—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C4⋊C4—221no—
702C4⋊C4—222no—
703C4⋊C4—221no—
704C4⋊C4C23×D1112yes—
705C4⋊C4C23×D1114yes—
706C4⋊C4C23×D1112yes—
707C22⋊C4—22no—
708C22⋊C4—222no—
709C22⋊C4—222no—
710C22⋊C4—224no—
711C22⋊C4—224no—
712C22⋊C4—222no—
713C42—22no—
714C42—111no—
715C42—111no—
716C42—111no—
717C42—111no—
718C42—111no—
719C42—111no—
720C42—111no—
721C42—111no—
722C42—111no—
723C42—111no—
724C42—111no—
725C42—111no—
726C42—222no—
727C42—222no—
728C42—224no—
729C42—224no—
730C42—222no—
731C42D4×D1111yescharacteristic
732C42D4×D1111yescharacteristic
733C42C23×D1111yescharacteristic
734C42C23×D1111yescharacteristic
735C11#6066311yescharacteristic, complemented, Sylow
736C23—111no—
737C23—111no—
738C23—114no—
739C23—441no—
740C23—441no—
741C23C2×D4×D1111yescharacteristic
742Q8—44no—
743Q8—44no—
744Q8—42no—
745Q8—42no—
746Q8—444no—
747Q8—444no—
748Q8—444no—
749Q8—442no—
750Q8—444no—
751Q8—442no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—44no—
758C2×C4—114no—
759C2×C4—111no—
760C2×C4—111no—
761C2×C4—114no—
762C2×C4—114no—
763C2×C4—114no—
764C2×C4—114no—
765C2×C4—111no—
766C2×C4—111no—
767C2×C4—111no—
768C2×C4—111no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—224no—
775C2×C4—222no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—444no—
781C2×C4—444no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—444no—
785C2×C4C2×D4×D1111yescharacteristic
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4C2×D4×D1111yescharacteristic
789C2×C4C2×D4×D1111yescharacteristic
790C2×C4C2×Q8×D1114yes—
791C2×C4C24×D1111yescharacteristic
792C8—118no—
793C8C2×Q8×D1118yes—
794C22—21no—
795C22—21no—
796C22—112no—
797C22—112no—
798C22—221no—
799C22—221no—
800C22—221no—
801C22—221no—
802C22—444no—
803C22D11×C4⋊Q812yes—
804C22C22×D4×D1111yescharacteristic
805C4—21no—
806C4—21no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—112no—
811C4—112no—
812C4—221no—
813C4—221no—
814C4—221no—
815C4—221no—
816C4—442no—
817C4—442no—
818C4—444no—
819C4D11×C4⋊Q812yes—
820C4#1062330412yes—
821C4#1062330812yes—
822C4C22×Q8×D1112yes—
823C2—22no—
824C2—222no—
825C2—222no—
826C2C2×D11×C4⋊Q811yescharacteristic
827C2C2×#1062330411yescharacteristic
828C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3165C2
socleC22×C11C23×D4
prime radicalC23×D11C2×D4
hypercenter#3165D11
hypocenterC11#60663
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #13079167C2semidirect
4. #13079166C2semidirect
5. #13079163C2semidirect
6. #13079162C2semidirect
7. #13079159C2semidirect
8. #13079158C2semidirect
9. #13079157C2semidirect
10. #13079137C2semidirect
11. #13079127C2semidirect
12. #13079125C2semidirect
15. C11×#3165C2semidirect
52. C11×#501C22semidirect
53. C11×#500C22semidirect
54. C11×#498C22semidirect
59. #10622693C22semidirect
60. #10622692C22semidirect
61. #10622692C22semidirect
62. #10622691C22semidirect
63. #10622691C22semidirect
64. #10622678C22semidirect
70. #10622491C22semidirect
71. #10622489C22semidirect
74. #10622471C22semidirect
75. #10622469C22semidirect
78. #10622315C22semidirect
81. #10622295C22semidirect
82. #10622293C22semidirect
133. M16×D11Q8semidirect
256. C11×M16C2×Q8semidirect
318. #4318C2×Q8semidirect
320. #4313C2×Q8semidirect
321. C8×D11C2×Q8semidirect
331. #3165D11semidirect
436. #501C2×D11semidirect
440. #500C2×D11semidirect
446. #498C2×D11semidirect
671. M16Q8×D11semidirect
735. C11#60663semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
D11×#5332
#130791672
#130791662
#130791632
#130791622
#130791592
#130791582
#130791572
#130791372
#130791272
#130791252
#130772032
C4×M16×D112
C11×#31652
#6066311