Finite Group Databasebeta

← #15620353

Subgroups — #15620353

Order 2816.

4824 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623368C211yesmaximal, characteristic, complemented
2C2×#10623366C211yesmaximal, characteristic, complemented
3#13082285C211yesmaximal, characteristic, complemented
4#13077931C213yesmaximal, complemented
5#13077920C213yesmaximal, complemented
6#13077902C213yesmaximal, complemented
7#13077884C213yesmaximal, complemented
8#13077868C213yesmaximal, complemented
9#13077858C213yesmaximal, complemented
10#13077834C213yesmaximal, complemented
11C2×#10622851C213yesmaximal, complemented
12#13077149C211yesmaximal, characteristic, complemented
13#13077142C211yesmaximal, characteristic, complemented
14#13077065C211yesmaximal, characteristic, complemented
15C2×C11×#585C211yesmaximal, characteristic, complemented
16C11×#585—28no—
17C11×#585—28no—
18C2×C11×2−1+4—21no—
19C2×C11×2−1+4C2211yescharacteristic
20C2×C11×2−1+4C2213yescomplemented
21C2×C11×H(5,𝔽2)—23no—
22C2×C11×H(5,𝔽2)C2211yescharacteristic
23C2×C11×H(5,𝔽2)C2213yescomplemented
24C22×C11×#41—23no—
25C22×C11×#41—21no—
26C22×C11×#41C2211yescharacteristic
27C22×C11×#41C2213yescomplemented
28C22×C11×#41C2213yescomplemented
29C2×#67042C2211yescharacteristic, complemented
30#10623368—28no—
31#10623366—28no—
32#10623365—21no—
33#10623364C2213yescomplemented
34#10623361C2213yescomplemented
35#10623360—23no—
36#10623358C2211yescharacteristic, complemented
37C2×#67003C2213yescomplemented
38C2×#67003C2213yescomplemented
39C2×#67002C2213yescomplemented
40C2×#67002C2213yescomplemented
41C2×#67001C2211yescharacteristic, complemented
42C2×#67001C2211yescharacteristic, complemented
43#10623348—21no—
44C2×#66995C2213yescomplemented
45C22×#4325C2213yescomplemented
46D4×C22⋊D11—23no—
47C2×#66985C2213yescomplemented
48C22×#4323C2213yescomplemented
49#10623322C2213yescomplemented
50C2×#66983C2213yescomplemented
51#10622852C2211yescharacteristic, complemented
52#10622852C2213yescomplemented
53#10622852C2216yescomplemented
54#10622851C2213yescomplemented
55#10622851C2216yescomplemented
56#10622851C2216yescomplemented
57#10622851C2216yescomplemented
58#10622851C2213yescomplemented
59#10622851C2216yescomplemented
60#10622847C2213yescomplemented
61#10622847C2213yescomplemented
62#10622846C2213yescomplemented
63#10622846C2213yescomplemented
64#10622845C2213yescomplemented
65#10622845C2213yescomplemented
66#10622841C2213yescomplemented
67#10622840C2213yescomplemented
68#10622840C2216yescomplemented
69#10622838C2213yescomplemented
70C2×#66899C2213yescomplemented
71#10622831C2213yescomplemented
72#10622830C2213yescomplemented
73#10622830C2216yescomplemented
74#10622828C2213yescomplemented
75C2×#66896C2213yescomplemented
76#10622820C2213yescomplemented
77C2×C22⋊(C11⋊C8)C2213yescomplemented
78C11×2−1+4—216no—
79C11×2−1+4—24no—
80C11×2−1+4—212no—
81C11×2−1+4—212no—
82C11×2−1+4D418yescomplemented
83C11×H(5,𝔽2)—248no—
84C11×H(5,𝔽2)—24no—
85C11×H(5,𝔽2)—212no—
86C11×H(5,𝔽2)—212no—
87C11×H(5,𝔽2)D418yescomplemented
88C2×C11×#41—216no—
89C2×C11×#41—248no—
90C2×C11×#41—24no—
91C2×C11×#41—24no—
92C2×C11×#41—212no—
93C2×C11×#41—212no—
94C2×C11×#41—21no—
95C2×C11×#41—23no—
96C2×C11×#41—212no—
97C2×C11×#41—23no—
98C2×C11×#41—26no—
99C2×C11×#41—23no—
100C2×C11×#41—212no—
101C2×C11×#41—23no—
102C2×C11×#41—23no—
103C2×C11×#41—23no—
104C2×C11×#41—23no—
105C2×C11×#41D413yes—
106C2×C11×#41D411yescharacteristic
107C2×C11×#41C2313yes—
108C2×C11×#41C2311yescharacteristic
109C2×C11×#41C2316yes—
110C2×C11×#41C2313yes—
111C2×C11×#41C2313yes—
112C2×C11×#41C2313yes—
113C2×C11×#41C2311yescharacteristic
114C22×Q8×C11—21no—
115C22×Q8×C11—23no—
116C22×Q8×C11D411yescharacteristic
117C22×Q8×C11C2313yes—
118C22×Q8×C11C2313yes—
119C22×D4×C11—23no—
120C22×D4×C11—23no—
121C22×D4×C11—23no—
122C22×D4×C11—26no—
123C22×D4×C11—23no—
124C22×D4×C11D413yes—
125C22×D4×C11C2313yes—
126C22×D4×C11C2313yes—
127C23×C4×C11—23no—
128C23×C4×C11—23no—
129C23×C4×C11C2313yes—
130C22×C22⋊D11—23no—
131#67042—24no—
132#67042—24no—
133C2×#4343—21no—
134C2×D4×D11—23no—
135C2×#4339C2313yes—
136C22×D44C2313yes—
137#67006—23no—
138#67003—212no—
139#67003—212no—
140#67002—212no—
141#67002—212no—
142#67001—24no—
143#67001—24no—
144#67000—23no—
145#66999—23no—
146Q8×Dic11—21no—
147C2×#4326C2313yes—
148C2×#4326C2311yescharacteristic
149#66995—212no—
150C2×#4325—212no—
151C2×#4325C2313yes—
152C2×#4325C2316yes—
153C2×#4325C2313yes—
154#66993—23no—
155#66992—26no—
156#66991—23no—
157#66990—26no—
158D4×Dic11—23no—
159C2×#4324C2313yes—
160C2×#4324C2311yescharacteristic
161#66985—212no—
162C2×#4323—212no—
163C2×#4323C2313yes—
164C2×#4323C2316yes—
165C2×#4323C2313yes—
166#66983—23no—
167#66983—23no—
168#66983C2313yes—
169#66983C2316yes—
170#66983C2313yes—
171#66982—23no—
172C4×C22⋊D11—23no—
173C4×C22⋊D11—23no—
174C2×(C2×D11)⋊C4—23no—
175#66979C2313yes—
176C2×C4⋊Dic11C2313yes—
177#66977C2311yescharacteristic
178#66977C2313yes—
179C2×#4318C2313yes—
180C2×#4318C2313yes—
181C22×C11⋊C8C2313yes—
182C22×C11⋊C8C2313yes—
183#66899C2313yes—
184#66899C2316yes—
185#66899C2313yes—
186#66899C2311yescharacteristic
187#66899C2313yes—
188#66896C2313yes—
189#66896C2316yes—
190#66896C2313yes—
191#66896C2311yescharacteristic
192#66896C2313yes—
193C22⋊(C11⋊C8)C2311yescharacteristic
194C22⋊(C11⋊C8)C2313yes—
195C22⋊(C11⋊C8)C2313yes—
196C22⋊(C11⋊C8)C2313yes—
197C22⋊(C11⋊C8)C2316yes—
198#60376—111nomaximal, Sylow
199C24×C11—23no—
200C24×C11—23no—
201C24×C11C2×D413yes—
202C23×D11—23no—
203C11×#41—224no—
204C11×#41—224no—
205C11×#41—248no—
206C11×#41—224no—
207C11×#41—224no—
208C11×#41—224no—
209C11×#41—224no—
210C11×#41—24no—
211C11×#41—28no—
212C11×#41—22no—
213C11×#41—26no—
214C11×#41—212no—
215C11×#41—212no—
216C11×#41—224no—
217C11×#41—22no—
218C11×#41—26no—
219C11×#41—212no—
220C11×#41—26no—
221C11×#41—26no—
222C11×#41—26no—
223C11×#41—26no—
224C11×#41C2×D414yes—
225C11×#41C2×D414yes—
226C11×#41C2×D4112yescomplemented
227C11×#41C2×D4112yescomplemented
228C2×Q8×C11—224no—
229C2×Q8×C11—28no—
230C2×Q8×C11—24no—
231C2×Q8×C11—26no—
232C2×Q8×C11—26no—
233C2×Q8×C11—23no—
234C2×Q8×C11—23no—
235C2×Q8×C11—26no—
236C2×Q8×C11C2×D413yes—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D4112yescomplemented
239C2×Q8×C11C2411yescharacteristic
240C2×Q8×C11C2413yes—
241C2×D4×C11—224no—
242C2×D4×C11—248no—
243C2×D4×C11—224no—
244C2×D4×C11—224no—
245C2×D4×C11—26no—
246C2×D4×C11—23no—
247C2×D4×C11—21no—
248C2×D4×C11—23no—
249C2×D4×C11—23no—
250C2×D4×C11—224no—
251C2×D4×C11—212no—
252C2×D4×C11—26no—
253C2×D4×C11—26no—
254C2×D4×C11—23no—
255C2×D4×C11—23no—
256C2×D4×C11—26no—
257C2×D4×C11C2×D416yes—
258C2×D4×C11C2×D413yes—
259C2×D4×C11C2×D413yes—
260C2×D4×C11C2×D4112yescomplemented
261C2×D4×C11C2411yescharacteristic
262C2×D4×C11C2413yes—
263C22×C4×C11—224no—
264C22×C4×C11—224no—
265C22×C4×C11—23no—
266C22×C4×C11—23no—
267C22×C4×C11—23no—
268C22×C4×C11—21no—
269C22×C4×C11—26no—
270C22×C4×C11—23no—
271C22×C4×C11—23no—
272C22×C4×C11—26no—
273C22×C4×C11—26no—
274C22×C4×C11C2×D413yes—
275C22×C4×C11C2×D413yes—
276C22×C4×C11C2×D413yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2413yes—
279C22×C4×C11C2413yes—
280C2×C22⋊D11—23no—
281C2×C22⋊D11—23no—
282C2×C22⋊D11—23no—
283C2×C22⋊D11—26no—
284C2×C22⋊D11—86no—
285C22×Dic11—23no—
286#4343—44no—
287D4×D11—412no—
288#4339—26no—
289#4339—26no—
290C2×D44—23no—
291C2×D44—26no—
292C2×D44—26no—
293C2×D44C2413yes—
294C2×C4×D11—23no—
295C2×Dic22C2411yescharacteristic
296C22⋊Dic11—21no—
297C22⋊Dic11—23no—
298C22⋊Dic11—23no—
299#4326—26no—
300#4326—22no—
301#4325—26no—
302#4325—212no—
303#4325—26no—
304#4324—26no—
305#4324—22no—
306#4323—26no—
307#4323—212no—
308#4323—26no—
309(C2×D11)⋊C4—23no—
310(C2×D11)⋊C4—26no—
311(C2×D11)⋊C4—23no—
312C4⋊Dic11—23no—
313C4⋊Dic11C2413yes—
314C4⋊Dic11C2411yescharacteristic
315Dic11⋊C4—21no—
316Dic11⋊C4—23no—
317C4×Dic11—23no—
318#4318—26no—
319#4318—26no—
320C2×C11⋊C8—26no—
321C2×C11⋊C8—26no—
322C2×C11⋊C8C2411yescharacteristic
323C2×C11⋊C8C2413yes—
324C2×C11⋊C8C2411yescharacteristic
325C2×C11⋊C8C2413yes—
326C2×#585D1111yescharacteristic, complemented
327C2×#577—111no—
328C2×#576—111no—
329#3488—111no—
330#3013—113no—
331#3012—113no—
332#3010—113no—
333#3008—113no—
334#3006—113no—
335#3005—113no—
336#3002—113no—
337C2×#449—113no—
338#2898—111no—
339#2897—111no—
340#2880—111no—
341C23×C11—212no—
342C23×C11—23no—
343C23×C11—21no—
344C23×C11—26no—
345C23×C11—212no—
346C23×C11—43no—
347C23×C11—43no—
348C23×C11—83no—
349C23×C11—83no—
350C23×C11—83no—
351C23×C11—83no—
352C23×C11C22×D413yes—
353C23×C11C22×D411yescharacteristic
354C23×C11C22×D413yes—
355C22×D11—23no—
356C22×D11—46no—
357C22×D11—83no—
358C22×D11—83no—
359Q8×C11—212no—
360Q8×C11—26no—
361Q8×C11—212no—
362Q8×C11—21no—
363Q8×C11—23no—
364Q8×C11#12014yes—
365Q8×C11C22×D412yes—
366Q8×C11C22×D416yes—
367D4×C11—224no—
368D4×C11—212no—
369D4×C11—24no—
370D4×C11—212no—
371D4×C11—212no—
372D4×C11—212no—
373D4×C11—212no—
374D4×C11—26no—
375D4×C11—212no—
376D4×C11—23no—
377D4×C11—21no—
378D4×C11#120112yes—
379D4×C11C22×D412yes—
380D4×C11C22×D416yes—
381C2×C4×C11—212no—
382C2×C4×C11—24no—
383C2×C4×C11—212no—
384C2×C4×C11—224no—
385C2×C4×C11—26no—
386C2×C4×C11—212no—
387C2×C4×C11—23no—
388C2×C4×C11—21no—
389C2×C4×C11—26no—
390C2×C4×C11—212no—
391C2×C4×C11—212no—
392C2×C4×C11—26no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—23no—
396C2×C4×C11—23no—
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D413yes—
399C2×C4×C11C22×D413yes—
400C2×C4×C11C22×D416yes—
401C2×C4×C11C22×D416yes—
402C2×C4×C11C2511yescharacteristic
403C22⋊D11—46no—
404C22⋊D11—46no—
405C22⋊D11—83no—
406C22⋊D11—86no—
407C2×Dic11—21no—
408C2×Dic11—23no—
409C2×Dic11—21no—
410C2×Dic11—83no—
411D44—23no—
412D44—23no—
413D44—46no—
414C4×D11—46no—
415Dic22—21no—
416Dic22—21no—
417C11⋊C8—21no—
418C11⋊C8—21no—
419C11⋊C8—23no—
420C11⋊C8—23no—
421#585—28no—
422#585—28no—
423C2×2−1+4—21no—
424C2×2−1+4C2×D1111yescharacteristic
425C2×2−1+4C2×D1113yescomplemented
426C2×H(5,𝔽2)—23no—
427C2×H(5,𝔽2)—111no—
428C2×H(5,𝔽2)C2×D1111yescharacteristic
429C2×H(5,𝔽2)C2×D1113yescomplemented
430C22×#41—23no—
431C22×#41—21no—
432C22×#41C2×D1111yescharacteristic
433C22×#41C2×D1113yescomplemented
434C22×#41C2×D1113yescomplemented
435#577—228no—
436#576—228no—
437C2×#137—113no—
438C2×AGL(1,ℤ/8)—113no—
439C2×AGL(1,ℤ/8)—113no—
440C2×AGL(1,ℤ/8)—113no—
441C2×#135—113no—
442C2×#135—113no—
443C22×SD16—113no—
444C22×D8—113no—
445C2×#131—111no—
446C2×#131—111no—
447#550—221no—
448#548—221no—
449#546—223no—
450D42—223no—
451#537—113no—
452#535—113no—
453#525—113no—
454C2×#121—113no—
455#520—111no—
456#452—111no—
457#452—113no—
458#452—116no—
459#451—113no—
460#450—113no—
461#449—113no—
462#449—116no—
463#449—116no—
464#449—116no—
465#449—113no—
466#449—116no—
467#448—113no—
468#448—116no—
469#447—113no—
470#447—116no—
471#419—113no—
472#418—113no—
473#417—113no—
474#417—113no—
475#416—113no—
476#416—113no—
477C2×#103—113no—
478C2×#102—113no—
479#408—113no—
480#408—113no—
481#407—113no—
482C2×C22⋊C8—113no—
483C22×C11—23no—
484C22×C11—23no—
485C22×C11—21no—
486C22×C11—23no—
487C22×C11—21no—
488C22×C11—23no—
489C22×C11—23no—
490C22×C11—21no—
491C22×C11—26no—
492C22×C11—22no—
493C22×C11—43no—
494C22×C11—41no—
495C22×C11—43no—
496C22×C11—41no—
497C22×C11—86no—
498C22×C11—812no—
499C22×C11—812no—
500C22×C11C2×#12016yes—
501C22×C11C23×D411yescharacteristic
502C2×D11—43no—
503C2×D11—43no—
504C2×D11—43no—
505C2×D11—166no—
506C4×C11—21no—
507C4×C11—26no—
508C4×C11—22no—
509C4×C11—23no—
510C4×C11C2×#12016yes—
511C4×C11C23×D411yescharacteristic
512C4×C11C23×D411yescharacteristic
513Dic11—41no—
514Dic11—43no—
515Dic11—41no—
5162−1+4—216no—
5172−1+4—24no—
5182−1+4—212no—
5192−1+4—212no—
5202−1+4C22⋊D1118yescomplemented
521H(5,𝔽2)—248no—
522H(5,𝔽2)—24no—
523H(5,𝔽2)—212no—
524H(5,𝔽2)—212no—
525H(5,𝔽2)—224no—
526H(5,𝔽2)—224no—
527H(5,𝔽2)C22⋊D1118yescomplemented
528C2×#41—216no—
529C2×#41—248no—
530C2×#41—24no—
531C2×#41—24no—
532C2×#41—212no—
533C2×#41—212no—
534C2×#41—21no—
535C2×#41—23no—
536C2×#41—212no—
537C2×#41—23no—
538C2×#41—26no—
539C2×#41—23no—
540C2×#41—212no—
541C2×#41—23no—
542C2×#41—23no—
543C2×#41—23no—
544C2×#41—23no—
545C2×#41—113no—
546C2×#41—221no—
547C2×#41C22⋊D1113yes—
548C2×#41C22⋊D1111yescharacteristic
549C2×#41C22×D1113yes—
550C2×#41C22×D1111yescharacteristic
551C2×#41C22×D1116yes—
552C2×#41C22×D1113yes—
553C2×#41C22×D1113yes—
554C2×#41C22×D1113yes—
555C2×#41C22×D1111yescharacteristic
556C22×Q8—21no—
557C22×Q8—23no—
558C22×Q8C22⋊D1111yescharacteristic
559C22×Q8C22×D1113yes—
560C22×Q8C22×D1113yes—
561C22×D4—23no—
562C22×D4—23no—
563C22×D4—23no—
564C22×D4—26no—
565C22×D4—23no—
566C22×D4—113no—
567C22×D4—223no—
568C22×D4—223no—
569C22×D4C22⋊D1113yes—
570C22×D4C22×D1113yes—
571C22×D4C22×D1113yes—
572C23×C4—23no—
573C23×C4—23no—
574C23×C4C22×D1113yes—
575#137—2212no—
576AGL(1,ℤ/8)—2212no—
577AGL(1,ℤ/8)—2212no—
578AGL(1,ℤ/8)—2212no—
579#135—2212no—
580#135—2212no—
581C2×Q16—111no—
582C2×Q16—113no—
583C2×SD16—113no—
584C2×SD16—116no—
585C2×SD16—113no—
586C2×SD16—111no—
587C2×SD16—113no—
588C2×SD16—2212no—
589C2×D8—113no—
590C2×D8—116no—
591C2×D8—113no—
592C2×D8—2212no—
593#131—224no—
594#131—224no—
595C2×M16—113no—
596C2×M16—113no—
597C22×C8—113no—
598C22×C8—113no—
599#127—223no—
600#124—223no—
601#123—223no—
602C22⋊Q8—111no—
603C22⋊Q8—113no—
604C22⋊Q8—223no—
605#121—113no—
606#121—116no—
607#121—113no—
608#121—226no—
609#121—223no—
610#121—223no—
611#121—223no—
612#120—223no—
613#120—226no—
614C4×Q8—221no—
615C4×D4—223no—
616C4×D4—223no—
617C4×D4—223no—
618#117—113no—
619C2×C4⋊C4—113no—
620C2×C22⋊C4—223no—
621#103—113no—
622#103—116no—
623#103—111no—
624#103—113no—
625#103—113no—
626#102—113no—
627#102—116no—
628#102—111no—
629#102—113no—
630#102—113no—
631C22⋊C8—111no—
632C22⋊C8—113no—
633C22⋊C8—113no—
634C22⋊C8—113no—
635C22⋊C8—116no—
636C2×C11—26no—
637C2×C11—41no—
638C2×C11—43no—
639C2×C11—46no—
640C2×C11—42no—
641C2×C11C22×#12011yescharacteristic
642C2×C11#358411yescharacteristic
643C2×C11#358511yescharacteristic
644D11—83no—
645C24—23no—
646C24—23no—
647C24—223no—
648C24C2×C22⋊D1113yes—
649#41—224no—
650#41—224no—
651#41—248no—
652#41—224no—
653#41—224no—
654#41—224no—
655#41—224no—
656#41—24no—
657#41—28no—
658#41—22no—
659#41—26no—
660#41—212no—
661#41—212no—
662#41—224no—
663#41—22no—
664#41—26no—
665#41—212no—
666#41—26no—
667#41—26no—
668#41—26no—
669#41—26no—
670#41—226no—
671#41—226no—
672#41—444no—
673#41C2×C22⋊D1114yes—
674#41C2×C22⋊D1114yes—
675#41C2×C22⋊D11112yescomplemented
676#41C2×C22⋊D11112yescomplemented
677C2×Q8—224no—
678C2×Q8—28no—
679C2×Q8—24no—
680C2×Q8—26no—
681C2×Q8—26no—
682C2×Q8—23no—
683C2×Q8—23no—
684C2×Q8—26no—
685C2×Q8—111no—
686C2×Q8C2×C22⋊D1113yes—
687C2×Q8C2×C22⋊D1111yescharacteristic
688C2×Q8C2×C22⋊D11112yescomplemented
689C2×Q8C23×D1111yescharacteristic
690C2×Q8C23×D1113yes—
691C2×D4—224no—
692C2×D4—248no—
693C2×D4—224no—
694C2×D4—224no—
695C2×D4—26no—
696C2×D4—23no—
697C2×D4—21no—
698C2×D4—23no—
699C2×D4—23no—
700C2×D4—224no—
701C2×D4—212no—
702C2×D4—26no—
703C2×D4—26no—
704C2×D4—23no—
705C2×D4—23no—
706C2×D4—26no—
707C2×D4—113no—
708C2×D4—223no—
709C2×D4—223no—
710C2×D4—223no—
711C2×D4—226no—
712C2×D4—226no—
713C2×D4—226no—
714C2×D4—223no—
715C2×D4—4412no—
716C2×D4—886no—
717C2×D4C2×C22⋊D1116yes—
718C2×D4C2×C22⋊D1113yes—
719C2×D4C2×C22⋊D1113yes—
720C2×D4C2×C22⋊D11112yescomplemented
721C2×D4C23×D1111yescharacteristic
722C2×D4C23×D1113yes—
723C22×C4—224no—
724C22×C4—224no—
725C22×C4—23no—
726C22×C4—23no—
727C22×C4—23no—
728C22×C4—21no—
729C22×C4—26no—
730C22×C4—23no—
731C22×C4—23no—
732C22×C4—26no—
733C22×C4—26no—
734C22×C4—223no—
735C22×C4—223no—
736C22×C4C2×C22⋊D1113yes—
737C22×C4C2×C22⋊D1113yes—
738C22×C4C2×C22⋊D1113yes—
739C22×C4C23×D1111yescharacteristic
740C22×C4C23×D1113yes—
741C22×C4C23×D1113yes—
742Q16—222no—
743Q16—226no—
744SD16—226no—
745SD16—2212no—
746SD16—226no—
747SD16—222no—
748SD16—226no—
749D8—226no—
750D8—2212no—
751D8—226no—
752M16—226no—
753M16—226no—
754C2×C8—111no—
755C2×C8—113no—
756C2×C8—111no—
757C2×C8—113no—
758C2×C8—226no—
759C2×C8—226no—
760C4⋊C4—113no—
761C4⋊C4—111no—
762C4⋊C4—223no—
763C4⋊C4—221no—
764C4⋊C4—223no—
765C22⋊C4—223no—
766C22⋊C4—221no—
767C22⋊C4—223no—
768C22⋊C4—223no—
769C22⋊C4—226no—
770C22⋊C4—223no—
771C42—223no—
772C11#6037611yescharacteristic, complemented, Sylow
773C23—212no—
774C23—23no—
775C23—21no—
776C23—26no—
777C23—212no—
778C23—43no—
779C23—43no—
780C23—83no—
781C23—83no—
782C23—83no—
783C23—83no—
784C23—223no—
785C23—446no—
786C23—883no—
787C23—883no—
788C23C22×C22⋊D1113yes—
789C23C22×C22⋊D1111yescharacteristic
790C23C22×C22⋊D1113yes—
791Q8—212no—
792Q8—26no—
793Q8—212no—
794Q8—21no—
795Q8—23no—
796Q8—221no—
797Q8—221no—
798Q8#6700614yes—
799Q8C22×C22⋊D1112yes—
800Q8C22×C22⋊D1116yes—
801D4—224no—
802D4—212no—
803D4—24no—
804D4—212no—
805D4—212no—
806D4—212no—
807D4—212no—
808D4—26no—
809D4—212no—
810D4—23no—
811D4—21no—
812D4—223no—
813D4—223no—
814D4—446no—
815D4—446no—
816D4—446no—
817D4—886no—
818D4—883no—
819D4#67006112yes—
820D4C22×C22⋊D1112yes—
821D4C22×C22⋊D1116yes—
822C2×C4—212no—
823C2×C4—24no—
824C2×C4—212no—
825C2×C4—224no—
826C2×C4—26no—
827C2×C4—212no—
828C2×C4—23no—
829C2×C4—21no—
830C2×C4—26no—
831C2×C4—212no—
832C2×C4—212no—
833C2×C4—26no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—23no—
837C2×C4—23no—
838C2×C4—221no—
839C2×C4—223no—
840C2×C4—221no—
841C2×C4—446no—
842C2×C4—883no—
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1113yes—
845C2×C4C22×C22⋊D1113yes—
846C2×C4C22×C22⋊D1116yes—
847C2×C4C22×C22⋊D1116yes—
848C2×C4C24×D1111yescharacteristic
849C8—221no—
850C8—221no—
851C8—223no—
852C8—223no—
853C22—23no—
854C22—23no—
855C22—21no—
856C22—23no—
857C22—23no—
858C22—21no—
859C22—26no—
860C22—22no—
861C22—23no—
862C22—21no—
863C22—43no—
864C22—41no—
865C22—43no—
866C22—41no—
867C22—86no—
868C22—812no—
869C22—812no—
870C22—443no—
871C22—443no—
872C22—443no—
873C22—1766no—
874C22C2×#6700616yes—
875C22C23×C22⋊D1111yescharacteristic
876C4—21no—
877C4—26no—
878C4—22no—
879C4—23no—
880C4—443no—
881C4—441no—
882C4—441no—
883C4C2×#6700616yes—
884C4C23×C22⋊D1111yescharacteristic
885C4C23×C22⋊D1111yescharacteristic
886C2—26no—
887C2—41no—
888C2—43no—
889C2—46no—
890C2—42no—
891C2—883no—
892C2C22×#6700611yescharacteristic
893C2#1308338711yescharacteristic
894C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#585C2
socleC22×C11C23×D4
hypercenterC2×#585D11
hypocenterC11#60376
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#10623368C2semidirect
2. C2×#10623366C2semidirect
3. #13082285C2semidirect
4. #13077931C2semidirect
5. #13077920C2semidirect
6. #13077902C2semidirect
7. #13077884C2semidirect
8. #13077868C2semidirect
9. #13077858C2semidirect
10. #13077834C2semidirect
11. C2×#10622851C2semidirect
12. #13077149C2semidirect
13. #13077142C2semidirect
14. #13077065C2semidirect
15. C2×C11×#585C2semidirect
20. C2×C11×2−1+4C22semidirect
23. C2×C11×H(5,𝔽2)C22semidirect
27. C22×C11×#41C22semidirect
28. C22×C11×#41C22semidirect
29. C2×#67042C22semidirect
33. #10623364C22semidirect
34. #10623361C22semidirect
36. #10623358C22semidirect
37. C2×#67003C22semidirect
38. C2×#67003C22semidirect
39. C2×#67002C22semidirect
40. C2×#67002C22semidirect
41. C2×#67001C22semidirect
42. C2×#67001C22semidirect
44. C2×#66995C22semidirect
45. C22×#4325C22semidirect
47. C2×#66985C22semidirect
48. C22×#4323C22semidirect
49. #10623322C22semidirect
50. C2×#66983C22semidirect
51. #10622852C22semidirect
52. #10622852C22semidirect
53. #10622852C22semidirect
54. #10622851C22semidirect
55. #10622851C22semidirect
56. #10622851C22semidirect
57. #10622851C22semidirect
58. #10622851C22semidirect
59. #10622851C22semidirect
60. #10622847C22semidirect
61. #10622847C22semidirect
62. #10622846C22semidirect
63. #10622846C22semidirect
64. #10622845C22semidirect
65. #10622845C22semidirect
66. #10622841C22semidirect
67. #10622840C22semidirect
68. #10622840C22semidirect
69. #10622838C22semidirect
70. C2×#66899C22semidirect
71. #10622831C22semidirect
72. #10622830C22semidirect
73. #10622830C22semidirect
74. #10622828C22semidirect
75. C2×#66896C22semidirect
76. #10622820C22semidirect
77. C2×C22⋊(C11⋊C8)C22semidirect
82. C11×2−1+4D4semidirect
87. C11×H(5,𝔽2)D4semidirect
226. C11×#41C2×D4semidirect
227. C11×#41C2×D4semidirect
238. C2×Q8×C11C2×D4semidirect
260. C2×D4×C11C2×D4semidirect
326. C2×#585D11semidirect
425. C2×2−1+4C2×D11semidirect
429. C2×H(5,𝔽2)C2×D11semidirect
433. C22×#41C2×D11semidirect
434. C22×#41C2×D11semidirect
520. 2−1+4C22⋊D11semidirect
527. H(5,𝔽2)C22⋊D11semidirect
675. #41C2×C22⋊D11semidirect
676. #41C2×C22⋊D11semidirect
688. C2×Q8C2×C22⋊D11semidirect
720. C2×D4C2×C22⋊D11semidirect
772. C11#60376semidirect

Maximal subgroups

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

subgroupindex
C2×#106233682
C2×#106233662
#130822852
#130779312
#130779202
#130779022
#130778842
#130778682
#130778582
#130778342
C2×#106228512
#130771492
#130771422
#130770652
C2×C11×#5852
#6037611