Finite Group Databasebeta

← #15630954

Subgroups — #15630954

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2#41×D44C211yesmaximal, characteristic
3#13080901C212yesmaximal, complemented
4#13080849C212yesmaximal, complemented
5#13080687C214yesmaximal, complemented
6#13080657C214yesmaximal, complemented
7#13080557C212yesmaximal, complemented
8#13080535C212yesmaximal, complemented
9#13079010C211yesmaximal, characteristic, complemented
10#13078550C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic, complemented
12#13078244C212yesmaximal, complemented
13#13078088C211yesmaximal, characteristic, complemented
14#13077872C212yesmaximal, complemented
15M16×D44C211yesmaximal, characteristic, complemented
16#13077132C212yesmaximal, complemented
17C4×C11×#137C211yesmaximal, characteristic, complemented
18C2×#41×D11C2212yes—
19C2×C11×#137C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic, complemented
22C2×#66999C2212yescomplemented
23C2×#66995C2212yescomplemented
24C2×M16×D11C2212yescomplemented
25#10623115—21no—
26#10623115—21no—
27#10623115—22no—
28#10623115C2212yes—
29#10623115C2214yescomplemented
30#10623115C2212yescomplemented
31#10623108C2211yescharacteristic
32#10623107C2212yes—
33Q8×D44C2211yescharacteristic
34#10623086—21no—
35#10623086C2211yescharacteristic
36#10623085—22no—
37#10623085C2212yes—
38D4×D44—21no—
39D4×D44C2211yescharacteristic
40#10623055—22no—
41#10623055C2212yes—
42C2×#66951—22no—
43C2×#66945C2212yescomplemented
44#10623008—21no—
45#10623008C2211yescharacteristic
46C2×#66928—21no—
47C2×C4×D44—21no—
48C2×C4×D44C2211yescharacteristic
49C2×#66922C2211yescharacteristic, complemented
50C2×C4×Dic22—21no—
51C11×#441C2212yescomplemented
52C11×#440C2212yescomplemented
53C4×C11×Q16C2212yescomplemented
54C4×C11×SD16C2212yescomplemented
55C11×#428C2211yescharacteristic, complemented
56C11×#419C2211yescharacteristic, complemented
57C11×#417C2211yescharacteristic
58C4×C11×M16C2211yescharacteristic, complemented
59#10622845C2212yes—
60#10622800C2214yescomplemented
61#10622799C2214yescomplemented
62#10622786C2214yescomplemented
63#10622782C2214yescomplemented
64#10622746C2212yescomplemented
65#10622746C2212yescomplemented
66#10622739C2212yescomplemented
67#10622644C2212yescomplemented
68#10622641C2214yescomplemented
69#10622640C2212yescomplemented
70#10622634C2212yescomplemented
71#10622633C2212yescomplemented
72#10622621C2212yescomplemented
73#10622620C2212yescomplemented
74#10622608C2212yescomplemented
75#10622579C2212yescomplemented
76#10622537C2211yescharacteristic, complemented
77#10622501C2214yescomplemented
78#10622498C2214yescomplemented
79#10622480C2214yescomplemented
80#10622479C2214yescomplemented
81#10622429C2214yescomplemented
82#10622426C2214yescomplemented
83#10622425C2214yescomplemented
84#10622420C2214yescomplemented
85#10622417C2214yescomplemented
86#10622415C2214yescomplemented
87#10622385C2214yescomplemented
88#10622383C2214yescomplemented
89#10622327C2214yescomplemented
90#10622319C2214yescomplemented
91#10622307C2212yescomplemented
92#10622301C2212yes—
93C8×D44C2212yescomplemented
94#10622294C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97#41×D11—28no—
98#41×D11—44no—
99C2×#4343C2312yes—
100C2×Q8×D11C2312yes—
101C2×#4341—22no—
102C2×#4341C2312yes—
103C2×D4×D11—22no—
104C2×D4×D11C2312yes—
105C2×#4339—22no—
106C2×#4339C2312yes—
107C22×D44—21no—
108C22×D44D411yescharacteristic
109C22×C4×D11—22no—
110C22×C4×D11C2312yes—
111C22×Dic22—21no—
112C11×#137—24no—
113C2×C11×Q16C2312yes—
114C2×C11×SD16C2312yes—
115C2×C11×M16C2311yescharacteristic
116C2×C11×M16C2311yescharacteristic
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11C2311yescharacteristic
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11C2311yescharacteristic
126C4×D4×C11C2311yescharacteristic
127C11×#117—21no—
128C11×#117C2311yescharacteristic
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C42×C11—21no—
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134#66999—22no—
135#66999—22no—
136#66999C2314yes—
137#66999C2314yes—
138C2×#4326C2314yes—
139#66995—44no—
140C2×#4325C2314yes—
141#66983—21no—
142#66983—21no—
143#66983—21no—
144#66983—22no—
145#66983—21no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4D412yes—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11—21no—
152C2×C4⋊Dic11D411yescharacteristic
153C2×C4⋊Dic11C2312yes—
154C2×Dic11⋊C4—22no—
155C2×C4×Dic11—22no—
156C2×#4318C2312yes—
157M16×D11—44no—
158C2×#4313C2314yes—
159C2×C8×D11C2314yes—
160#66951—24no—
161#66951—24no—
162#66951—24no—
163#66951—24no—
164#66950—22no—
165#66950—22no—
166#66950C2312yes—
167#66950C2312yes—
168#66948—22no—
169#66948—22no—
170#66948C2312yes—
171#66948C2312yes—
172#66945—22no—
173#66945—22no—
174#66945C2314yes—
175#66945C2314yes—
176#66939—22no—
177#66939—22no—
178#66939—22no—
179#66935—22no—
180#66935—22no—
181#66935—22no—
182#66928—22no—
183#66928—22no—
184#66928—24no—
185#66928—22no—
186#66928C2312yes—
187#66927—21no—
188#66927C2311yescharacteristic
189C4×D44—21no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44—21no—
193C4×D44—21no—
194C4×D44—22no—
195C4×D44—21no—
196C4×D44D411yescharacteristic
197C4×D44D411yescharacteristic
198C4×D44D412yes—
199C4×D44C2311yescharacteristic
200C4×D44C2311yescharacteristic
201C4×D44C2312yes—
202#66922—21no—
203#66922—21no—
204#66922—21no—
205#66922C2311yescharacteristic
206#66922C2312yes—
207#66922C2312yes—
208C4×Dic22—22no—
209C4×Dic22—22no—
210C4×Dic22—24no—
211C11×#107C2312yes—
212C11×#106C2312yes—
213C11×#103C2312yes—
214C11×#103C2312yes—
215C11×#103C2312yes—
216C11×#102C2312yes—
217C11×#97C2312yes—
218C4×C8×C11C2312yes—
219#66899C2314yes—
220#66896C2314yes—
221#66885C2314yes—
222#66885C2314yes—
223(C2×D11)⋊C8C2314yes—
224(C2×D11)⋊C8C2314yes—
225#66880C2314yes—
226#66880C2314yes—
227#66874C2314yes—
228#66873C2314yes—
229#66872C2314yes—
230#66871C2314yes—
231C4⋊(C11⋊C8)C2312yes—
232C4⋊(C11⋊C8)C2312yes—
233#61165—111nomaximal, Sylow
234C23×D11—22no—
235C23×D11C2×D412yes—
236C11×#41—22no—
237C11×#41#4114yes—
238C2×Q8×C11—21no—
239C2×Q8×C11—22no—
240C2×Q8×C11—22no—
241C2×Q8×C11C2412yes—
242C2×Q8×C11C2411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11C2411yescharacteristic
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—22no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11C2×D412yes—
259#4343—24no—
260#4343—42no—
261Q8×D11—24no—
262Q8×D11—42no—
263#4341—24no—
264#4341—42no—
265#4341—48no—
266D4×D11—24no—
267D4×D11—48no—
268D4×D11—42no—
269#4339—24no—
270#4339—24no—
271#4339—48no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—21no—
276C2×D44—21no—
277C2×D44—42no—
278C2×D44—44no—
279C2×D44C2×D411yescharacteristic
280C2×D44C2×D411yescharacteristic
281C2×D44C2×D412yes—
282C2×D44C2412yes—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—24no—
287C2×C4×D11—24no—
288C2×C4×D11—48no—
289C2×C4×D11C2×D412yes—
290C2×C4×D11C2×D412yes—
291C2×C4×D11C2412yes—
292C2×C4×D11C2412yes—
293C2×Dic22—22no—
294C2×Dic22—22no—
295C2×Dic22—22no—
296C2×Dic22—44no—
297C2×Dic22C2412yes—
298C11×Q16—24no—
299C11×SD16—24no—
300C11×M16—22no—
301C11×M16—22no—
302C2×C8×C11C2412yes—
303C2×C8×C11C2412yes—
304C11×C4⋊C4—21no—
305C11×C4⋊C4—21no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4C2411yescharacteristic
310C11×C4⋊C4C2411yescharacteristic
311C11×C4⋊C4C2412yes—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C42×C11—22no—
316C42×C11—22no—
317C42×C11—21no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11C2×D411yescharacteristic
321C42×C11C2×D411yescharacteristic
322C42×C11C2411yescharacteristic
323C42×C11C2411yescharacteristic
324#4326—44no—
325#4325—44no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4C2×D412yes—
337(C2×D11)⋊C4C2×D412yes—
338(C2×D11)⋊C4C2×D412yes—
339(C2×D11)⋊C4C2×D412yes—
340C4⋊Dic11—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—21no—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—21no—
347C4⋊Dic11C2×D411yescharacteristic
348C4⋊Dic11C2×D411yescharacteristic
349C4⋊Dic11C2×D412yes—
350C4⋊Dic11C2414yes—
351Dic11⋊C4—24no—
352Dic11⋊C4—24no—
353C4×Dic11—24no—
354C4×Dic11—24no—
355#4318—24no—
356C2×C11⋊C8C2414yes—
357#4313—44no—
358C8×D11—44no—
359C2×#556—111no—
360D4×#41—111no—
361#3328—112no—
362#3324—112no—
363#3313—114no—
364#3311—114no—
365#3304—112no—
366#3302—112no—
367#3141—111no—
368#3093—112no—
369#3079—111no—
370#3056—112no—
371#3037—111no—
372#3007—112no—
373C4×#137D1111yescharacteristic, complemented
374D4×M16—111no—
375#2896—112no—
376C23×C11—21no—
377C23×C11C22×D411yescharacteristic
378C22×D11—24no—
379C22×D11—22no—
380C22×D11—42no—
381C22×D11—42no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—82no—
385C22×D11C22×D412yes—
386C22×D11C22×D412yes—
387Q8×C11—21no—
388Q8×C11—22no—
389Q8×C11—22no—
390Q8×C11—42no—
391Q8×C11C2×#4112yes—
392D4×C11—24no—
393D4×C11—21no—
394D4×C11C2×#4112yes—
395C2×C4×C11—21no—
396C2×C4×C11—24no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—41no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11—42no—
406C2×C4×C11—81no—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C2×#4112yes—
413C2×C4×C11H(5,𝔽2)12yes—
414C2×C4×C11C2511yescharacteristic
415C22⋊D11—44no—
416C22⋊D11—44no—
417C22⋊D11—44no—
418C2×Dic11—24no—
419C2×Dic11—24no—
420C2×Dic11—22no—
421C2×Dic11—44no—
422C2×Dic11—44no—
423C2×Dic11C22×D412yes—
424C2×Dic11C22×D412yes—
425D44—22no—
426D44—22no—
427D44—22no—
428D44—22no—
429D44—42no—
430D44—44no—
431D44—44no—
432D44—42no—
433D44—81no—
434D44—82no—
435C4×D11—24no—
436C4×D11—24no—
437C4×D11—22no—
438C4×D11—22no—
439C4×D11—22no—
440C4×D11—22no—
441C4×D11—44no—
442C4×D11—44no—
443C4×D11—44no—
444Dic22—22no—
445Dic22—22no—
446Dic22—44no—
447Dic22—44no—
448Dic22—44no—
449C8×C11—22no—
450C8×C11—22no—
451C11⋊C8—24no—
452C22×#41—112no—
453C2×#137—112no—
454C2×#137C2×D1111yescharacteristic
455C22×M16—112no—
456#556—112no—
457#556—112no—
458#556—114no—
459#556—221no—
460#556—222no—
461#556—221no—
462#550—111no—
463D4×Q8—111no—
464#548—112no—
465#547—111no—
466#547—221no—
467#546—112no—
468#546—222no—
469D42—111no—
470D42—221no—
471#532—111no—
472#532—221no—
473C2×C4⋊Q8—111no—
474C2×#126—222no—
475C2×#124—221no—
476#525—112no—
477#525—222no—
478C2×C22⋊Q8—112no—
479C4×#41C2×D1111yescharacteristic
480C2×C4×Q8—221no—
481C2×C4×Q8C2×D1111yescharacteristic, complemented
482C2×C4×D4—111no—
483C2×C4×D4—221no—
484C2×#117—112no—
485#489—114no—
486#487—112no—
487#486—112no—
488#485—114no—
489#485—114no—
490#482—114no—
491#482—114no—
492#477—112no—
493#476—112no—
494#475—112no—
495#474—112no—
496#470—114no—
497#468—114no—
498#467—114no—
499#465—114no—
500#464—114no—
501#462—112no—
502#460—112no—
503#452—114no—
504#452—114no—
505#451—114no—
506#450—114no—
507#441C2×D1112yescomplemented
508#440C2×D1112yescomplemented
509C4×Q16C2×D1112yescomplemented
510C4×SD16C2×D1112yescomplemented
511#436—112no—
512#435—114no—
513C8×D4—112no—
514#428—112no—
515#428C2×D1111yescharacteristic, complemented
516#423—111no—
517#419—114no—
518#419C2×D1111yescharacteristic, complemented
519#418—114no—
520#417—112no—
521#417—112no—
522#417—112no—
523#417—112no—
524#417C2×D1111yescharacteristic
525#416—114no—
526#416—114no—
527#407—112no—
528C4×M16C2×D1111yescharacteristic, complemented
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—22no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11#54612yes—
535C22×C11C23×D411yescharacteristic
536C2×D11—22no—
537C2×D11—22no—
538C2×D11—22no—
539C2×D11—22no—
540C2×D11—22no—
541C2×D11—22no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—84no—
546C2×D11—88no—
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—22no—
550C4×C11—21no—
551C4×C11—42no—
552C4×C11—41no—
553C4×C11—42no—
554C4×C11—41no—
555C4×C11#54612yes—
556C4×C11#57512yes—
557C4×C11C22×#4111yescharacteristic
558C4×C11C2×H(5,𝔽2)11yescharacteristic
559Dic11—22no—
560Dic11—22no—
561Dic11—42no—
562Dic11—44no—
563C2×#41—112no—
564C2×#41—112no—
565C2×#41—112no—
566C2×#41—222no—
567C2×#41—222no—
568C2×#41—228no—
569C2×#41—444no—
570C2×#41C22×D1111yescharacteristic
571C22×Q8—112no—
572C22×Q8—221no—
573C22×Q8C22×D1111yescharacteristic
574C22×D4—112no—
575C22×D4—111no—
576C22×D4—221no—
577C22×D4—222no—
578C23×C4—112no—
579C23×C4—222no—
580#137—24no—
581#137—444no—
582C2×Q16—114no—
583C2×Q16C22×D1112yes—
584C2×SD16—114no—
585C2×SD16C22×D1112yes—
586C2×M16—112no—
587C2×M16—114no—
588C2×M16—444no—
589C2×M16C22×D1111yescharacteristic
590C2×M16C22×D1111yescharacteristic
591C22×C8—114no—
592C4⋊Q8—112no—
593C4⋊Q8—112no—
594C4⋊Q8—111no—
595C4⋊Q8—221no—
596C4⋊Q8—221no—
597C4⋊Q8—221no—
598#127—111no—
599#127—221no—
600#126—224no—
601#126—224no—
602#126—224no—
603#126—224no—
604#124—112no—
605#124—222no—
606#124—222no—
607#124—222no—
608#124—224no—
609#123—222no—
610#123—222no—
611#123—222no—
612C22⋊Q8—114no—
613C22⋊Q8—114no—
614C22⋊Q8—112no—
615C22⋊Q8—112no—
616C22⋊Q8—222no—
617C22⋊Q8—222no—
618C22⋊Q8—222no—
619C22⋊Q8—222no—
620#121—112no—
621#121—112no—
622#121—222no—
623#121—222no—
624#121—222no—
625#121—221no—
626#121—221no—
627#121—221no—
628#121—221no—
629#120—222no—
630#120—222no—
631#120—222no—
632C4×Q8—21no—
633C4×Q8—21no—
634C4×Q8—222no—
635C4×Q8—222no—
636C4×Q8—224no—
637C4×Q8C22×D1112yes—
638C4×Q8C22×D1112yes—
639C4×Q8C22×D1111yescharacteristic
640C4×Q8C22×D1111yescharacteristic
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—111no—
644C4×D4—112no—
645C4×D4—111no—
646C4×D4—111no—
647C4×D4—112no—
648C4×D4—111no—
649C4×D4—222no—
650C4×D4—221no—
651C4×D4—222no—
652C4×D4—222no—
653C4×D4—221no—
654C4×D4—221no—
655C4×D4—221no—
656C4×D4C22×D1111yescharacteristic
657C4×D4C22×D1111yescharacteristic
658#117—21no—
659#117—114no—
660#117—114no—
661#117—222no—
662#117—222no—
663#117C22×D1111yescharacteristic
664C2×C4⋊C4—21no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—221no—
668C2×C4⋊C4—222no—
669C2×C4⋊C4—221no—
670C2×C4⋊C4C22×D1111yescharacteristic
671C2×C22⋊C4—112no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—222no—
678C2×C42C22×D1111yescharacteristic
679#107—114no—
680#107C22×D1112yes—
681#106—114no—
682#106C22×D1112yes—
683C4⋊C8—112no—
684C4⋊C8—112no—
685#103—114no—
686#103—114no—
687#103—114no—
688#103—114no—
689#103C22×D1112yes—
690#103C22×D1112yes—
691#103C22×D1112yes—
692#102—114no—
693#102—114no—
694#102—114no—
695#102—114no—
696#102C22×D1112yes—
697C22⋊C8—114no—
698C22⋊C8—114no—
699#97C22×D1112yes—
700C4×C8C22×D1112yes—
701C2×C11—22no—
702C2×C11—42no—
703C2×C11C2×#54611yescharacteristic
704C2×C11C2×#57511yescharacteristic
705C2×C11#358611yescharacteristic
706D11—42no—
707D11—42no—
708D11—82no—
709C24—112no—
710C24—222no—
711#41—22no—
712#41—224no—
713#41—224no—
714#41—224no—
715#41—224no—
716#41—448no—
717#41—442no—
718#41—448no—
719#41—442no—
720#41#433914yes—
721C2×Q8—21no—
722C2×Q8—22no—
723C2×Q8—22no—
724C2×Q8—112no—
725C2×Q8—222no—
726C2×Q8—222no—
727C2×Q8—222no—
728C2×Q8—224no—
729C2×Q8—444no—
730C2×Q8—442no—
731C2×Q8C23×D1112yes—
732C2×Q8C23×D1111yescharacteristic
733C2×D4—21no—
734C2×D4—111no—
735C2×D4—111no—
736C2×D4—112no—
737C2×D4—112no—
738C2×D4—222no—
739C2×D4—222no—
740C2×D4—222no—
741C2×D4—222no—
742C2×D4—224no—
743C2×D4—222no—
744C2×D4—222no—
745C2×D4—221no—
746C2×D4—221no—
747C2×D4—442no—
748C2×D4—444no—
749C2×D4—442no—
750C2×D4—448no—
751C2×D4C23×D1111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—224no—
766C22×C4—224no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—448no—
770C22×C4D4×D1111yescharacteristic
771C22×C4D4×D1111yescharacteristic
772C22×C4C23×D1111yescharacteristic
773Q16—24no—
774Q16—444no—
775SD16—24no—
776SD16—444no—
777M16—22no—
778M16—22no—
779M16—224no—
780M16—444no—
781C2×C8—114no—
782C2×C8—444no—
783C2×C8C23×D1112yes—
784C2×C8C23×D1112yes—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—111no—
791C4⋊C4—111no—
792C4⋊C4—112no—
793C4⋊C4—114no—
794C4⋊C4—222no—
795C4⋊C4—224no—
796C4⋊C4—224no—
797C4⋊C4—222no—
798C4⋊C4—222no—
799C4⋊C4—221no—
800C4⋊C4—222no—
801C4⋊C4—222no—
802C4⋊C4—221no—
803C4⋊C4C23×D1112yes—
804C4⋊C4C23×D1111yescharacteristic
805C4⋊C4C23×D1111yescharacteristic
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—112no—
810C22⋊C4—112no—
811C22⋊C4—112no—
812C22⋊C4—112no—
813C22⋊C4—222no—
814C22⋊C4—222no—
815C22⋊C4—224no—
816C22⋊C4—224no—
817C22⋊C4—222no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—222no—
821C22⋊C4—222no—
822C22⋊C4—222no—
823C42—21no—
824C42—21no—
825C42—21no—
826C42—22no—
827C42—22no—
828C42—224no—
829C42—224no—
830C42D4×D1111yescharacteristic
831C42D4×D1111yescharacteristic
832C42C23×D1111yescharacteristic
833C42C23×D1111yescharacteristic
834C11#6116511yescharacteristic, complemented, Sylow
835C23—21no—
836C23—112no—
837C23—112no—
838C23—224no—
839C23—222no—
840C23—442no—
841C23—442no—
842C23—444no—
843C23—444no—
844C23—882no—
845C23C2×D4×D1111yescharacteristic
846Q8—21no—
847Q8—22no—
848Q8—22no—
849Q8—42no—
850Q8—222no—
851Q8—222no—
852Q8—444no—
853Q8—444no—
854Q8—444no—
855Q8C2×#433912yes—
856D4—24no—
857D4—21no—
858D4—222no—
859D4—222no—
860D4—222no—
861D4—222no—
862D4—442no—
863D4—444no—
864D4—444no—
865D4—444no—
866D4—444no—
867D4—444no—
868D4—442no—
869D4—881no—
870D4—882no—
871D4C2×#433912yes—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—81no—
884C2×C4—112no—
885C2×C4—112no—
886C2×C4—224no—
887C2×C4—224no—
888C2×C4—224no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—224no—
894C2×C4—222no—
895C2×C4—444no—
896C2×C4—444no—
897C2×C4—444no—
898C2×C4—444no—
899C2×C4—444no—
900C2×C4C2×#433912yes—
901C2×C4C2×D4×D1111yescharacteristic
902C2×C4C2×D4×D1111yescharacteristic
903C2×C4C2×D4×D1111yescharacteristic
904C2×C4C2×D4×D1111yescharacteristic
905C2×C4C2×D4×D1111yescharacteristic
906C2×C4#6704212yes—
907C2×C4C24×D1111yescharacteristic
908C8—22no—
909C8—22no—
910C8—224no—
911C22—21no—
912C22—21no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—222no—
920C22—222no—
921C22—222no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—884no—
926C22—888no—
927C22#1062308112yes—
928C22C22×D4×D1111yescharacteristic
929C4—21no—
930C4—21no—
931C4—22no—
932C4—21no—
933C4—42no—
934C4—41no—
935C4—42no—
936C4—41no—
937C4—222no—
938C4—222no—
939C4—442no—
940C4—444no—
941C4#1062308112yes—
942C4#1062330812yes—
943C4C22×#433911yescharacteristic
944C4C2×#6704211yescharacteristic
945C2—22no—
946C2—42no—
947C2—442no—
948C2—442no—
949C2—882no—
950C2C2×#1062308111yescharacteristic
951C2C2×#1062330811yescharacteristic
952C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#137C2
socleC22×C11C23×D4
prime radical#41×D44C2
hypercenterC4×#137D11
hypocenterC11#61165
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
3. #13080901C2semidirect
4. #13080849C2semidirect
5. #13080687C2semidirect
6. #13080657C2semidirect
7. #13080557C2semidirect
8. #13080535C2semidirect
9. #13079010C2semidirect
10. #13078550C2semidirect
11. #13078431C2semidirect
12. #13078244C2semidirect
13. #13078088C2semidirect
14. #13077872C2semidirect
15. M16×D44C2semidirect
16. #13077132C2semidirect
17. C4×C11×#137C2semidirect
21. C2×C4×Q8×C11C22semidirect
22. C2×#66999C22semidirect
23. C2×#66995C22semidirect
24. C2×M16×D11C22semidirect
29. #10623115C22semidirect
30. #10623115C22semidirect
43. C2×#66945C22semidirect
49. C2×#66922C22semidirect
51. C11×#441C22semidirect
52. C11×#440C22semidirect
53. C4×C11×Q16C22semidirect
54. C4×C11×SD16C22semidirect
55. C11×#428C22semidirect
56. C11×#419C22semidirect
58. C4×C11×M16C22semidirect
60. #10622800C22semidirect
61. #10622799C22semidirect
62. #10622786C22semidirect
63. #10622782C22semidirect
64. #10622746C22semidirect
65. #10622746C22semidirect
66. #10622739C22semidirect
67. #10622644C22semidirect
68. #10622641C22semidirect
69. #10622640C22semidirect
70. #10622634C22semidirect
71. #10622633C22semidirect
72. #10622621C22semidirect
73. #10622620C22semidirect
74. #10622608C22semidirect
75. #10622579C22semidirect
76. #10622537C22semidirect
77. #10622501C22semidirect
78. #10622498C22semidirect
79. #10622480C22semidirect
80. #10622479C22semidirect
81. #10622429C22semidirect
82. #10622426C22semidirect
83. #10622425C22semidirect
84. #10622420C22semidirect
85. #10622417C22semidirect
86. #10622415C22semidirect
87. #10622385C22semidirect
88. #10622383C22semidirect
89. #10622327C22semidirect
90. #10622319C22semidirect
91. #10622307C22semidirect
93. C8×D44C22semidirect
94. #10622294C22semidirect
373. C4×#137D11semidirect
481. C2×C4×Q8C2×D11semidirect
507. #441C2×D11semidirect
508. #440C2×D11semidirect
509. C4×Q16C2×D11semidirect
510. C4×SD16C2×D11semidirect
515. #428C2×D11semidirect
518. #419C2×D11semidirect
528. C4×M16C2×D11semidirect
834. C11#61165semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
#41×D442
#130809012
#130808492
#130806872
#130806572
#130805572
#130805352
#130790102
#130785502
#130784312
#130782442
#130780882
#130778722
M16×D442
#130771322
C4×C11×#1372
#6116511