Finite Group Databasebeta

← #15638517

Subgroups — #15638517

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082457C211yesmaximal, characteristic, complemented
2C2×#10623348C211yesmaximal, characteristic, complemented
3#13080514C214yesmaximal, complemented
4#13080507C214yesmaximal, complemented
5#13080357C214yesmaximal, complemented
6#13080316C214yesmaximal, complemented
7#13079586C212yesmaximal, complemented
8#13079400C212yesmaximal, complemented
9#13079369C211yesmaximal, characteristic, complemented
10#13079367C211yesmaximal, characteristic, complemented
11#13078697C212yesmaximal, complemented
12#13077839C212yesmaximal, complemented
13C2×#10622840C211yesmaximal, characteristic, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C2×C11×#451C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×#4343C2211yescharacteristic, complemented
18C22×C11×Q16C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic
20#10623348—22no—
21#10623348—22no—
22#10623348C2214yes—
23#10623348C2212yescomplemented
24#10623348C2214yescomplemented
25C2×#67000—21no—
26C2×#67000C2211yescharacteristic, complemented
27C2×#66999—21no—
28C2×#66999C2211yescharacteristic, complemented
29C2×Q8×Dic11C2211yescharacteristic, complemented
30C22×#4325C2212yescomplemented
31C2×#66983—21no—
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66972C2214yescomplemented
37#10623176—21no—
38#10623175—21no—
39#10623173C2212yescomplemented
40#10623168—22no—
41#10623161C2212yescomplemented
42#10623158C2212yes—
43#10623155C2212yes—
44#10623045—22no—
45#10623045C2212yescomplemented
46#10623024—21no—
47#10623017—21no—
48C11×#451C2212yescomplemented
49C11×#451C2212yescomplemented
50C11×#451C2214yescomplemented
51C2×C11×#103C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic
53#10622840C2212yes—
54#10622840C2212yes—
55#10622840C2212yescomplemented
56#10622840C2214yescomplemented
57C2×#66899C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic
59#10622804C2214yescomplemented
60#10622801C2214yescomplemented
61#10622800C2214yescomplemented
62#10622800C2214yescomplemented
63#10622798C2214yescomplemented
64#10622798C2214yescomplemented
65Q16×Dic11C2214yescomplemented
66#10622728C2214yescomplemented
67C8×C22⋊D11C2214yescomplemented
68#10622661C2214yescomplemented
69#10622659C2212yescomplemented
70#10622656C2212yescomplemented
71#10622581C2212yescomplemented
72#10622432C2214yescomplemented
73#10622427C2214yescomplemented
74#10622424C2214yescomplemented
75#10622420C2214yescomplemented
76#10622417C2214yescomplemented
77#10622413C2214yescomplemented
78#10622409C2214yescomplemented
79#10622401C2214yescomplemented
80#10622349C2212yes—
81#10622349C2212yescomplemented
82#10622345C2212yes—
83#10622345C2212yescomplemented
84(C22⋊D11)⋊C8C2214yescomplemented
85D11×C22⋊C8C2212yescomplemented
86#10622331C2212yescomplemented
87C22×Q8×C11—21no—
88C22×Q8×C11—21no—
89C22×Q8×C11—21no—
90C22×Q8×C11—44no—
91C22×Q8×C11C2311yescharacteristic
92C22×Q8×C11C2312yes—
93C22×Q8×C11C2312yes—
94C22×Q8×C11C2311yescharacteristic
95C22×Q8×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11D411yescharacteristic
101C2×#4343—22no—
102C2×#4343—44no—
103C2×#4343C2314yes—
104C2×#4343C2312yes—
105C22×D44—21no—
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C22×C4×D11C2311yescharacteristic
110C2×C11×Q16—44no—
111C2×C11×Q16C2314yes—
112C2×C11×Q16C2314yes—
113C22×C8×C11C2312yes—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8C2312yes—
117C11×C22⋊Q8C2312yes—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11D411yescharacteristic
122#67000—24no—
123#67000—24no—
124#67000—22no—
125#67000—22no—
126#67000C2312yes—
127#67000C2314yes—
128#66999—22no—
129#66999—24no—
130#66999—24no—
131#66999—22no—
132#66999C2312yes—
133#66999C2314yes—
134Q8×Dic11—22no—
135Q8×Dic11C2312yes—
136Q8×Dic11C2314yes—
137C2×#4325—44no—
138C2×#4325C2314yes—
139C2×#4325C2314yes—
140C2×#4325C2314yes—
141#66983—21no—
142#66983—21no—
143#66983—21no—
144#66983—21no—
145#66983—22no—
146#66983—22no—
147#66983—24no—
148#66983—24no—
149#66983C2312yes—
150#66983C2312yes—
151#66983C2312yes—
152#66983C2312yes—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—24no—
156C4×C22⋊D11—24no—
157C4×C22⋊D11D412yes—
158C4×C22⋊D11D412yes—
159C4×C22⋊D11C2312yes—
160C4×C22⋊D11C2312yes—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4D411yescharacteristic
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4D411yescharacteristic
172C2×C4×Dic11—21no—
173C2×C4×Dic11C2311yescharacteristic
174C22×C11⋊C8C2312yes—
175#66972—48no—
176C2×D88C2314yes—
177C2×C8×D11C2314yes—
178#66951—22no—
179#66951—22no—
180#66951—22no—
181#66948—22no—
182#66948C2312yes—
183#66947—22no—
184#66947—22no—
185#66947—22no—
186#66946—22no—
187#66946C2312yes—
188#66945—22no—
189#66945C2312yes—
190#66943—22no—
191#66943C2312yes—
192#66939—22no—
193#66939—22no—
194#66935—22no—
195#66935—22no—
196(C22⋊D11)⋊C4—22no—
197(C22⋊D11)⋊C4—22no—
198C22⋊C4×D11—22no—
199#66930—22no—
200C11×#103C2314yes—
201C11×#103C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yes—
204#66899C2314yes—
205#66899C2314yes—
206#66899C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209#66885C2314yes—
210#66885C2314yes—
211(C2×D11)⋊C8C2314yes—
212#66882C2314yes—
213Dic11⋊C8C2314yes—
214C8×Dic11C2314yes—
215#66873C2314yes—
216#66872C2314yes—
217#61564—111nomaximal, Sylow
218C24×C11C2×D411yescharacteristic
219C23×D11—21no—
220C23×D11—21no—
221C23×D11C2×D411yescharacteristic
222C2×Q8×C11—24no—
223C2×Q8×C11—21no—
224C2×Q8×C11—22no—
225C2×Q8×C11—22no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—24no—
229C2×Q8×C11—24no—
230C2×Q8×C11—42no—
231C2×Q8×C11—42no—
232C2×Q8×C11—42no—
233C2×Q8×C11—44no—
234C2×Q8×C11—42no—
235C2×Q8×C11—44no—
236C2×Q8×C11—44no—
237C2×Q8×C11C2412yes—
238C2×Q8×C11C2412yes—
239C2×Q8×C11C2412yes—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—42no—
247C22×C4×C11—44no—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—24no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11C2×D412yes—
262C2×C22⋊D11C2×D412yes—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11C2×D411yescharacteristic
266C22×Dic11C2×D411yescharacteristic
267C22×Dic11C2×D411yescharacteristic
268#4343—28no—
269#4343—44no—
270#4343—44no—
271#4343—48no—
272C2×D44—24no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—21no—
276C2×D44—21no—
277C2×D44—42no—
278C2×D44—44no—
279C2×D44—42no—
280C2×D44C2412yes—
281C2×D44C2412yes—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—42no—
286C2×C4×D11—44no—
287C2×C4×D11C2×D412yes—
288C2×C4×D11C2412yes—
289C11×Q16—28no—
290C11×Q16—44no—
291C2×C8×C11—42no—
292C2×C8×C11C2414yes—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C2412yes—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C22⋊Dic11C2×D412yes—
300C22⋊Dic11C2×D412yes—
301#4325—28no—
302#4325—44no—
303#4325—44no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4C2×D412yes—
318(C2×D11)⋊C4C2×D412yes—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—24no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11C2412yes—
325C4⋊Dic11C2412yes—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—24no—
329Dic11⋊C4C2×D412yes—
330Dic11⋊C4C2×D412yes—
331C4×Dic11—22no—
332C4×Dic11—22no—
333C4×Dic11—24no—
334C4×Dic11C2×D412yes—
335C4×Dic11C2412yes—
336C2×C11⋊C8—42no—
337C2×C11⋊C8C2414yes—
338D88—44no—
339C8×D11—44no—
340#3505—111no—
341C2×#548—111no—
342#3301—114no—
343#3300—114no—
344#3285—114no—
345#3282—114no—
346#3211—112no—
347#3190—112no—
348#3187—111no—
349#3186—111no—
350#3108—112no—
351#3002—112no—
352C2×#451D1111yescharacteristic, complemented
353C2×#448—111no—
354#2972—111no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11#13514yescomplemented
358C23×C11C22×D411yescharacteristic
359C23×C11C22×D411yescharacteristic
360C23×C11C22×D411yescharacteristic
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—81no—
371C22×D11—81no—
372C22×D11C22×D412yes—
373Q8×C11—24no—
374Q8×C11—22no—
375Q8×C11—22no—
376Q8×C11—24no—
377Q8×C11—22no—
378Q8×C11—44no—
379Q8×C11—44no—
380Q8×C11—42no—
381Q8×C11—81no—
382Q8×C11H(5,𝔽2)14yes—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—42no—
397C2×C4×C11—81no—
398C2×C4×C11—81no—
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C2511yescharacteristic
403C22⋊D11—24no—
404C22⋊D11—24no—
405C22⋊D11—44no—
406C22⋊D11—44no—
407C22⋊D11—44no—
408C22⋊D11—44no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11C22×D412yes—
417C2×Dic11C22×D412yes—
418C2×Dic11C22×D412yes—
419D44—24no—
420D44—24no—
421D44—48no—
422D44—42no—
423D44—81no—
424D44—82no—
425D44—82no—
426C4×D11—24no—
427C4×D11—42no—
428C4×D11—48no—
429C4×D11—82no—
430C4×D11—82no—
431C8×C11—24no—
432C11⋊C8—24no—
433C22×#41—111no—
434C23×Q8C2×D1111yescharacteristic
435C2×#135—114no—
436C22×Q16C2×D1112yescomplemented
437C22×SD16—112no—
438#553—112no—
439#553—222no—
440#552—112no—
441#551—222no—
442#548—114no—
443#548—114no—
444#548—112no—
445#548—222no—
446#548—222no—
447#546—112no—
448#539—221no—
449#538—221no—
450#534—221no—
451#529—112no—
452C2×#124—111no—
453C2×#124—221no—
454#525—112no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—221no—
457C2×C22⋊Q8C2×D1111yescharacteristic
458C2×#121—111no—
459C2×#121—111no—
460C2×#121—221no—
461#518—221no—
462C2×C4×Q8—111no—
463C2×C4×D4—111no—
464C2×C4×D4—221no—
465#495—114no—
466#488—114no—
467#485—114no—
468#483—112no—
469#481—112no—
470#480—112no—
471#480—112no—
472#479—114no—
473#467—114no—
474#466—114no—
475#465—114no—
476#465—114no—
477#464—114no—
478#464—114no—
479#463—114no—
480#452—114no—
481#452—114no—
482#451C2×D1112yescomplemented
483#451C2×D1112yescomplemented
484#451C2×D1114yescomplemented
485#450—112no—
486#449—114no—
487#448—112no—
488#448—112no—
489#448—112no—
490#448—114no—
491#447—112no—
492#447—112no—
493C4×Q16—114no—
494C4×SD16—114no—
495C8×D4—114no—
496C8×D4—114no—
497#431—112no—
498#416—114no—
499C2×#103—112no—
500C2×#103C2×D1112yescomplemented
501C2×C22⋊C8—111no—
502C2×C22⋊C8—112no—
503C2×C22⋊C8C2×D1111yescharacteristic
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—44no—
511C22×C11C2×#13512yes—
512C22×C11C2×#13512yes—
513C22×C11C2×#13512yes—
514C22×C11C23×D411yescharacteristic
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—22no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—82no—
525C2×D11—84no—
526C2×D11—162no—
527C4×C11—24no—
528C4×C11—21no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11C2×H(5,𝔽2)12yes—
535Dic11—22no—
536Dic11—22no—
537Dic11—22no—
538Dic11—42no—
539Dic11—42no—
540C2×#41—114no—
541C2×#41—112no—
542C2×#41—222no—
543C2×#41—444no—
544C22×Q8—21no—
545C22×Q8—21no—
546C22×Q8—21no—
547C22×Q8—44no—
548C22×Q8C22×D1111yescharacteristic
549C22×Q8C22×D1112yes—
550C22×Q8C22×D1112yes—
551C22×Q8C22×D1111yescharacteristic
552C22×Q8C22×D1111yescharacteristic
553C22×D4—111no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—221no—
557C22×D4—221no—
558C22×D4—221no—
559C23×C4—21no—
560C23×C4—111no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#135—448no—
564C2×Q16—44no—
565C2×Q16C22×D1114yes—
566C2×Q16C22×D1114yes—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—114no—
570C2×SD16—444no—
571C2×D8—114no—
572C22×C8—112no—
573C22×C8—114no—
574C22×C8C22×D1112yes—
575#126—222no—
576#126—222no—
577#126—222no—
578#125—112no—
579#125—222no—
580#124—114no—
581#124—112no—
582#124—222no—
583#124—224no—
584#124—224no—
585#124—222no—
586#123—222no—
587#123—222no—
588#123—222no—
589#123—222no—
590#123—222no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—114no—
594C22⋊Q8—112no—
595C22⋊Q8—224no—
596C22⋊Q8—224no—
597C22⋊Q8—222no—
598C22⋊Q8—222no—
599C22⋊Q8C22×D1112yes—
600C22⋊Q8C22×D1112yes—
601#121—112no—
602#121—112no—
603#121—112no—
604#121—112no—
605#121—112no—
606#121—222no—
607#121—224no—
608#121—224no—
609#121—222no—
610#121—222no—
611#121—221no—
612#121—221no—
613#121—221no—
614#121—221no—
615#120—222no—
616#120—222no—
617C4×Q8—114no—
618C4×Q8—112no—
619C4×Q8—222no—
620C4×D4—112no—
621C4×D4—112no—
622C4×D4—112no—
623C4×D4—112no—
624C4×D4—112no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—224no—
628C4×D4—224no—
629C4×D4—222no—
630C4×D4—222no—
631C4×D4—222no—
632#117—112no—
633#117—222no—
634#117—222no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—221no—
640C2×C4⋊C4—221no—
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—111no—
644C2×C22⋊C4—111no—
645C2×C22⋊C4—222no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C42—111no—
652C2×C42—221no—
653#107—114no—
654#106—114no—
655C4⋊C8—114no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103C22×D1114yes—
660#103C22×D1114yes—
661#102—114no—
662#102—114no—
663#102—114no—
664C22⋊C8—112no—
665C22⋊C8—112no—
666C22⋊C8—114no—
667C22⋊C8C22×D1112yes—
668C22⋊C8C22×D1112yes—
669C4×C8—114no—
670C2×C11—22no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11#348411yescharacteristic
674C2×C11C22×#13511yescharacteristic
675C2×C11#358611yescharacteristic
676D11—42no—
677D11—82no—
678D11—82no—
679C24—111no—
680C24—221no—
681C24—221no—
682C24D4×D1111yescharacteristic
683#41—228no—
684#41—444no—
685#41—444no—
686#41—448no—
687C2×Q8—24no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—42no—
698C2×Q8—44no—
699C2×Q8—42no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8C23×D1112yes—
703C2×Q8C23×D1112yes—
704C2×Q8C23×D1112yes—
705C2×D4—112no—
706C2×D4—112no—
707C2×D4—112no—
708C2×D4—112no—
709C2×D4—224no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—224no—
713C2×D4—222no—
714C2×D4—222no—
715C2×D4—222no—
716C2×D4—222no—
717C2×D4—221no—
718C2×D4—221no—
719C2×D4—442no—
720C2×D4—442no—
721C2×D4—444no—
722C2×D4—444no—
723C2×D4—444no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—224no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—442no—
743C22×C4—444no—
744C22×C4D4×D1111yescharacteristic
745C22×C4D4×D1111yescharacteristic
746C22×C4D4×D1111yescharacteristic
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1111yescharacteristic
750Q16—28no—
751Q16—44no—
752SD16—228no—
753SD16—444no—
754SD16—444no—
755D8—444no—
756C2×C8—42no—
757C2×C8—114no—
758C2×C8—444no—
759C2×C8—442no—
760C2×C8C23×D1114yes—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—21no—
764C4⋊C4—112no—
765C4⋊C4—112no—
766C4⋊C4—112no—
767C4⋊C4—112no—
768C4⋊C4—224no—
769C4⋊C4—224no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4—222no—
774C4⋊C4—221no—
775C4⋊C4—221no—
776C4⋊C4C23×D1112yes—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—112no—
780C22⋊C4—112no—
781C22⋊C4—112no—
782C22⋊C4—112no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—224no—
786C22⋊C4—224no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—224no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4—222no—
793C22⋊C4—222no—
794C22⋊C4—222no—
795C22⋊C4—222no—
796C42—112no—
797C42—112no—
798C42—224no—
799C42—222no—
800C42—222no—
801C11#6156411yescharacteristic, complemented, Sylow
802C23—41no—
803C23—41no—
804C23—112no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—441no—
809C23—441no—
810C23—442no—
811C23—442no—
812C23—442no—
813C23—442no—
814C23—881no—
815C23—881no—
816C23#6697214yescomplemented
817C23C2×D4×D1111yescharacteristic
818C23C2×D4×D1111yescharacteristic
819C23C2×D4×D1111yescharacteristic
820Q8—24no—
821Q8—22no—
822Q8—22no—
823Q8—24no—
824Q8—22no—
825Q8—44no—
826Q8—44no—
827Q8—42no—
828Q8—81no—
829Q8#6703714yes—
830D4—224no—
831D4—224no—
832D4—224no—
833D4—224no—
834D4—448no—
835D4—442no—
836D4—444no—
837D4—444no—
838D4—444no—
839D4—444no—
840D4—881no—
841D4—882no—
842D4—882no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—112no—
860C2×C4—112no—
861C2×C4—112no—
862C2×C4—222no—
863C2×C4—224no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—442no—
867C2×C4—448no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—442no—
871C2×C4—442no—
872C2×C4—882no—
873C2×C4—882no—
874C2×C4C2×D4×D1111yescharacteristic
875C2×C4C2×D4×D1111yescharacteristic
876C2×C4C2×D4×D1111yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—24no—
879C8—224no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—44no—
887C22—222no—
888C22—222no—
889C22—222no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22—442no—
895C22—442no—
896C22—882no—
897C22—884no—
898C22—1762no—
899C22C2×#6697212yes—
900C22C2×#6697212yes—
901C22C2×#6697212yes—
902C22C22×D4×D1111yescharacteristic
903C4—24no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—222no—
911C4—222no—
912C4—222no—
913C4—442no—
914C4—442no—
915C4C2×#6703712yes—
916C2—22no—
917C2—22no—
918C2—22no—
919C2—442no—
920C2—882no—
921C2—882no—
922C2#1308224511yescharacteristic
923C2C22×#6697211yescharacteristic
924C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC22×C11C23×D4
hypercenterC2×#451D11
hypocenterC11#61564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. #13082457C2semidirect
2. C2×#10623348C2semidirect
3. #13080514C2semidirect
4. #13080507C2semidirect
5. #13080357C2semidirect
6. #13080316C2semidirect
7. #13079586C2semidirect
8. #13079400C2semidirect
9. #13079369C2semidirect
10. #13079367C2semidirect
11. #13078697C2semidirect
12. #13077839C2semidirect
13. C2×#10622840C2semidirect
14. #13077638C2semidirect
15. C2×C11×#451C2semidirect
17. C22×#4343C22semidirect
18. C22×C11×Q16C22semidirect
23. #10623348C22semidirect
24. #10623348C22semidirect
26. C2×#67000C22semidirect
28. C2×#66999C22semidirect
29. C2×Q8×Dic11C22semidirect
30. C22×#4325C22semidirect
36. C2×#66972C22semidirect
39. #10623173C22semidirect
41. #10623161C22semidirect
45. #10623045C22semidirect
48. C11×#451C22semidirect
49. C11×#451C22semidirect
50. C11×#451C22semidirect
51. C2×C11×#103C22semidirect
55. #10622840C22semidirect
56. #10622840C22semidirect
57. C2×#66899C22semidirect
59. #10622804C22semidirect
60. #10622801C22semidirect
61. #10622800C22semidirect
62. #10622800C22semidirect
63. #10622798C22semidirect
64. #10622798C22semidirect
65. Q16×Dic11C22semidirect
66. #10622728C22semidirect
67. C8×C22⋊D11C22semidirect
68. #10622661C22semidirect
69. #10622659C22semidirect
70. #10622656C22semidirect
71. #10622581C22semidirect
72. #10622432C22semidirect
73. #10622427C22semidirect
74. #10622424C22semidirect
75. #10622420C22semidirect
76. #10622417C22semidirect
77. #10622413C22semidirect
78. #10622409C22semidirect
79. #10622401C22semidirect
81. #10622349C22semidirect
83. #10622345C22semidirect
84. (C22⋊D11)⋊C8C22semidirect
85. D11×C22⋊C8C22semidirect
86. #10622331C22semidirect
352. C2×#451D11semidirect
357. C23×C11#135semidirect
436. C22×Q16C2×D11semidirect
482. #451C2×D11semidirect
483. #451C2×D11semidirect
484. #451C2×D11semidirect
500. C2×#103C2×D11semidirect
801. C11#61564semidirect
816. C23#66972semidirect

Maximal subgroups

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

subgroupindex
#130824572
C2×#106233482
#130805142
#130805072
#130803572
#130803162
#130795862
#130794002
#130793692
#130793672
#130786972
#130778392
C2×#106228402
#130776382
C2×C11×#4512
#6156411