Finite Group Databasebeta

← #15624416

Subgroups — #15624416

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C212yesmaximal, complemented
2#13079458C214yesmaximal, complemented
3#13079448C214yesmaximal, complemented
4#13079440C211yesmaximal, characteristic, complemented
5#13079432C214yesmaximal, complemented
6#13079423C212yesmaximal, complemented
7#13079416C211yesmaximal, characteristic, complemented
8#13078531C214yesmaximal, complemented
9#13078225C214yesmaximal, complemented
10#13077838C214yesmaximal, complemented
11C2×C11×#407C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2212yescomplemented
14C22×C11×M16C2212yescomplemented
15C2×#67006—22no—
16#10623322—22no—
17#10623322—22no—
18#10623322—22no—
19#10623322—22no—
20#10623322C2214yes—
21#10623322C2214yes—
22#10623322C2214yescomplemented
23#10623322C2214yescomplemented
24C2×#66983C2212yes—
25C2×#66983C2212yescomplemented
26C2×#66982—22no—
27C2×C4×C22⋊D11—22no—
28C2×C4×C22⋊D11—22no—
29C2×#66979C2212yescomplemented
30C2×#66977C2212yes—
31C2×#66977C2212yescomplemented
32C2×#66957C2214yescomplemented
33C11×#407C2211yescharacteristic
34C11×#407C2211yescharacteristic
35C11×#407C2214yescomplemented
36C11×#407C2212yescomplemented
37C2×C11×C22⋊C8C2214yescomplemented
38#10622750C2214yescomplemented
39#10622750C2214yescomplemented
40#10622748C2214yescomplemented
41#10622748C2214yescomplemented
42#10622747C2218yescomplemented
43#10622747C2218yescomplemented
44#10622726C2218yescomplemented
45#10622719C2214yescomplemented
46#10622352C2214yescomplemented
47#10622351C2214yescomplemented
48#10622350C2218yescomplemented
49#10622349C2214yescomplemented
50#10622348C2214yescomplemented
51#10622347C2218yescomplemented
52#10622346C2218yescomplemented
53#10622345C2214yescomplemented
54#10622344C2214yescomplemented
55#10622336C2218yescomplemented
56#10622335C2214yescomplemented
57#10622334C2214yescomplemented
58C25×C11D411yescharacteristic
59C23×C4×C11—44no—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D412yes—
62C23×C4×C11D412yes—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2312yes—
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—48no—
76C2×#4339C2314yes—
77C2×#4339C2314yes—
78C22×D44C2312yes—
79C22×C4×D11—22no—
80C22×Dic22C2312yes—
81C2×C11×M16—44no—
82C2×C11×M16C2312yes—
83C2×C11×M16C2314yes—
84C2×C11×M16C2312yes—
85C22×C8×C11C2314yes—
86#67006—24no—
87#67006—24no—
88#67006—24no—
89#67006—24no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93#66983—22no—
94#66983—22no—
95#66983—22no—
96#66983—22no—
97#66983C2314yes—
98#66983C2314yes—
99#66983C2314yes—
100#66983C2314yes—
101#66982—24no—
102#66982—24no—
103#66982—24no—
104#66982—24no—
105C4×C22⋊D11—24no—
106C4×C22⋊D11—24no—
107C4×C22⋊D11—24no—
108C4×C22⋊D11—24no—
109C4×C22⋊D11—24no—
110C4×C22⋊D11—24no—
111C4×C22⋊D11—24no—
112C4×C22⋊D11—24no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115#66979—22no—
116#66979—22no—
117#66979C2314yes—
118#66979C2314yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121#66977—22no—
122#66977—22no—
123#66977—22no—
124#66977—22no—
125#66977C2314yes—
126#66977C2314yes—
127#66977C2314yes—
128#66977C2314yes—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×C4×Dic11—22no—
132C2×Dic44C2314yescomplemented
133#66957—48no—
134C2×D88C2314yescomplemented
135C2×#4314C2318yescomplemented
136C11×C22⋊C8C2314yes—
137C11×C22⋊C8C2314yes—
138C11×C22⋊C8C2318yes—
139#66885C2318yescomplemented
140#66885C2318yescomplemented
141#66882C2318yescomplemented
142#66881C2314yescomplemented
143#66881C2314yescomplemented
144#66880C2318yescomplemented
145#66880C2318yescomplemented
146#60741—111nomaximal, Sylow
147C24×C11—42no—
148C24×C11—44no—
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D412yes—
151C24×C11C2×D412yes—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C23×D11—22no—
155C22×C4×C11—24no—
156C22×C4×C11—28no—
157C22×C4×C11—42no—
158C22×C4×C11—44no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—44no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—24no—
184C2×C22⋊D11—24no—
185C2×C22⋊D11—24no—
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—24no—
189C2×C22⋊D11—48no—
190C2×C22⋊D11—48no—
191C2×C22⋊D11—48no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195#4339—216no—
196#4339—48no—
197#4339—48no—
198#4339—48no—
199C2×D44—22no—
200C2×D44—44no—
201C2×D44C2414yes—
202C2×C4×D11—24no—
203C2×C4×D11—24no—
204C2×C4×D11—48no—
205C2×Dic22—22no—
206C2×Dic22—44no—
207C2×Dic22C2414yes—
208C11×M16—42no—
209C11×M16—44no—
210C11×M16—42no—
211C2×C8×C11—28no—
212C2×C8×C11C2414yes—
213C2×C8×C11C2414yes—
214C22⋊Dic11—24no—
215C22⋊Dic11—24no—
216C22⋊Dic11—24no—
217C22⋊Dic11—24no—
218C22⋊Dic11—24no—
219C22⋊Dic11—24no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11C2414yes—
227C4⋊Dic11C2414yes—
228Dic11⋊C4—24no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231Dic11⋊C4—24no—
232C4×Dic11—24no—
233C4×Dic11—24no—
234Dic44—44no—
235D88—44no—
236#4314—48no—
237C2×#525—112no—
238#3197—114no—
239#3196—114no—
240#3195—111no—
241#3194—114no—
242#3193—112no—
243#3192—111no—
244#3091—114no—
245#3054—114no—
246#3002—114no—
247C2×#407D1111yescharacteristic, complemented
248C23×C11—24no—
249C23×C11—22no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—41no—
254C23×C11—42no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—416no—
261C23×C11C22×D411yescharacteristic
262C23×C11C22×D411yescharacteristic
263C23×C11C22×D412yes—
264C23×C11C22×D411yescharacteristic
265C23×C11C22×D412yes—
266C22×D11—24no—
267C22×D11—44no—
268C22×D11—44no—
269C22×D11—44no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—41no—
287C2×C4×C11C22×D412yes—
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D412yes—
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11H(5,𝔽2)14yes—
293C2×C4×C11C2511yescharacteristic
294C22⋊D11—48no—
295C22⋊D11—48no—
296C22⋊D11—48no—
297C22⋊D11—48no—
298C22⋊D11—48no—
299C22⋊D11—48no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—44no—
304C2×Dic11—44no—
305C2×Dic11—44no—
306D44—28no—
307D44—44no—
308C4×D11—48no—
309C4×D11—48no—
310Dic22—28no—
311Dic22—44no—
312C8×C11—24no—
313C8×C11—24no—
314C22×#41—112no—
315C24×C4C2×D1111yescharacteristic
316C2×#135—114no—
317C22×M16C2×D1112yescomplemented
318#525—114no—
319#525—114no—
320#525—114no—
321#525—114no—
322#525—222no—
323#525—222no—
324#525—222no—
325#525—222no—
326C2×#123—222no—
327C2×C22⋊Q8—112no—
328C2×C22⋊Q8—112no—
329C2×#121—112no—
330C2×#121—112no—
331C2×#120—222no—
332C2×C4×D4—222no—
333C2×C4×D4—222no—
334C2×#117—112no—
335#485—118no—
336#484—114no—
337#483—114no—
338#482—118no—
339#481—114no—
340#480—114no—
341#470—114no—
342#470—114no—
343#469—114no—
344#469—114no—
345#468—118no—
346#468—118no—
347#452—118no—
348#451—114no—
349#450—114no—
350#449—118no—
351#448—114no—
352#447—114no—
353#427—114no—
354#416—118no—
355#407C2×D1111yescharacteristic
356#407C2×D1111yescharacteristic
357#407C2×D1114yescomplemented
358#407C2×D1112yescomplemented
359C2×C22⋊C8C2×D1114yescomplemented
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—21no—
364C22×C11—21no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—44no—
371C22×C11—48no—
372C22×C11—48no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11#53412yes—
376C22×C11#57514yes—
377C22×C11C23×D411yescharacteristic
378C2×D11—44no—
379C2×D11—44no—
380C2×D11—44no—
381C2×D11—88no—
382C4×C11—21no—
383C4×C11—21no—
384C4×C11—22no—
385C4×C11—22no—
386C4×C11#53412yes—
387C4×C11C2×H(5,𝔽2)12yes—
388Dic11—44no—
389Dic11—44no—
390Dic11—44no—
391C25D4411yescharacteristic
392C2×#41—114no—
393C2×#41—114no—
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—448no—
397C22×Q8—112no—
398C22×D4—112no—
399C22×D4—222no—
400C22×D4—222no—
401C22×D4—222no—
402C23×C4—44no—
403C23×C4—222no—
404C23×C4D4411yescharacteristic
405C23×C4D4412yes—
406C23×C4D4412yes—
407C23×C4D4411yescharacteristic
408C23×C4D4411yescharacteristic
409C23×C4C22×D1112yes—
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414#135—448no—
415C2×Q16—114no—
416C2×SD16—118no—
417C2×D8—114no—
418C2×M16—44no—
419C2×M16C22×D1112yes—
420C2×M16C22×D1112yes—
421C2×M16C22×D1114yes—
422C22×C8C22×D1114yes—
423#123—224no—
424#123—224no—
425#123—224no—
426#123—224no—
427C22⋊Q8—114no—
428C22⋊Q8—114no—
429C22⋊Q8—114no—
430C22⋊Q8—114no—
431C22⋊Q8—222no—
432C22⋊Q8—222no—
433C22⋊Q8—222no—
434C22⋊Q8—222no—
435#121—114no—
436#121—114no—
437#121—114no—
438#121—114no—
439#121—222no—
440#121—222no—
441#121—222no—
442#121—222no—
443#120—224no—
444#120—224no—
445#120—224no—
446#120—224no—
447C4×D4—224no—
448C4×D4—224no—
449C4×D4—224no—
450C4×D4—224no—
451C4×D4—224no—
452C4×D4—224no—
453C4×D4—224no—
454C4×D4—224no—
455#117—114no—
456#117—114no—
457#117—222no—
458#117—222no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—222no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C42—222no—
469#107—118no—
470#106—114no—
471#106—114no—
472#103—118no—
473#103—118no—
474#102—118no—
475#102—118no—
476C22⋊C8C22×D1114yes—
477C22⋊C8C22×D1114yes—
478C22⋊C8C22×D1118yes—
479C2×C11—24no—
480C2×C11—22no—
481C2×C11—41no—
482C2×C11—41no—
483C2×C11—42no—
484C2×C11C2×#53411yescharacteristic
485C2×C11C2×#57512yes—
486D11—84no—
487C24—42no—
488C24—44no—
489C24—222no—
490C24C2×D4411yescharacteristic
491C24C2×D4412yes—
492C24C2×D4412yes—
493C24C2×D4411yescharacteristic
494C24C2×D4411yescharacteristic
495#41—2216no—
496#41—448no—
497#41—448no—
498#41—448no—
499C2×Q8—114no—
500C2×Q8—222no—
501C2×Q8—444no—
502C2×D4—114no—
503C2×D4—224no—
504C2×D4—224no—
505C2×D4—224no—
506C2×D4—224no—
507C2×D4—224no—
508C2×D4—224no—
509C2×D4—222no—
510C2×D4—444no—
511C2×D4—448no—
512C2×D4—448no—
513C2×D4—448no—
514C22×C4—24no—
515C22×C4—28no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—44no—
521C22×C4—42no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—224no—
528C22×C4—224no—
529C22×C4—448no—
530C22×C4C2×D4412yes—
531C22×C4C2×D4411yescharacteristic
532C22×C4C2×D4412yes—
533C22×C4C2×D4412yes—
534C22×C4C2×D4411yescharacteristic
535C22×C4C2×D4411yescharacteristic
536C22×C4C2×D4412yes—
537C22×C4C2×D4412yes—
538C22×C4C2×D4411yescharacteristic
539C22×C4C2×D4412yes—
540C22×C4C2×D4412yes—
541C22×C4C2×D4411yescharacteristic
542C22×C4C2×D4412yes—
543C22×C4C23×D1112yes—
544C22×C4C23×D1112yes—
545C22×C4C23×D1111yescharacteristic
546C22×C4C23×D1111yescharacteristic
547C22×C4C23×D1111yescharacteristic
548Q16—444no—
549SD16—448no—
550D8—444no—
551M16—42no—
552M16—44no—
553M16—42no—
554C2×C8—28no—
555C2×C8C23×D1114yes—
556C2×C8C23×D1114yes—
557C4⋊C4—114no—
558C4⋊C4—114no—
559C4⋊C4—222no—
560C4⋊C4—222no—
561C4⋊C4—224no—
562C4⋊C4—224no—
563C4⋊C4—224no—
564C4⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—224no—
567C22⋊C4—224no—
568C22⋊C4—224no—
569C22⋊C4—224no—
570C22⋊C4—224no—
571C22⋊C4—224no—
572C22⋊C4—224no—
573C22⋊C4—224no—
574C22⋊C4—224no—
575C42—224no—
576C42—224no—
577C11#6074111yescharacteristic, complemented, Sylow
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—41no—
584C23—42no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—416no—
591C23—224no—
592C23—444no—
593C23—444no—
594C23—444no—
595C23C22×D4412yes—
596C23C22×D4411yescharacteristic
597C23C22×D4411yescharacteristic
598C23C22×D4412yes—
599C23C22×D4411yescharacteristic
600Q8—228no—
601Q8—444no—
602D4—228no—
603D4—444no—
604D4—448no—
605D4—448no—
606D4—448no—
607D4—448no—
608D4—448no—
609D4—448no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—224no—
628C2×C4—224no—
629C2×C4—224no—
630C2×C4—448no—
631C2×C4—444no—
632C2×C4—444no—
633C2×C4—444no—
634C2×C4—448no—
635C2×C4C22×D4412yes—
636C2×C4C22×D4411yescharacteristic
637C2×C4C22×D4411yescharacteristic
638C2×C4C22×D4412yes—
639C2×C4C22×D4411yescharacteristic
640C2×C4#6703714yes—
641C2×C4C24×D1111yescharacteristic
642C8—24no—
643C8—24no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—21no—
649C22—21no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—44no—
655C22—48no—
656C22—48no—
657C22—44no—
658C22—44no—
659C22—444no—
660C22—444no—
661C22—444no—
662C22—888no—
663C22#1062302412yes—
664C22#1062327914yes—
665C22C23×D4411yescharacteristic
666C4—22no—
667C4—22no—
668C4—21no—
669C4—21no—
670C4—444no—
671C4—444no—
672C4—444no—
673C4#1062302412yes—
674C4C2×#6703712yes—
675C2—24no—
676C2—22no—
677C2—42no—
678C2—41no—
679C2—41no—
680C2—884no—
681C2C2×#1062302411yescharacteristic
682C2C2×#1062327912yes—
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC22×C11C23×D4
hypercenterC2×#407D11
hypocenterC11#60741
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13079458C2semidirect
3. #13079448C2semidirect
4. #13079440C2semidirect
5. #13079432C2semidirect
6. #13079423C2semidirect
7. #13079416C2semidirect
8. #13078531C2semidirect
9. #13078225C2semidirect
10. #13077838C2semidirect
11. C2×C11×#407C2semidirect
13. C22×#4339C22semidirect
14. C22×C11×M16C22semidirect
22. #10623322C22semidirect
23. #10623322C22semidirect
25. C2×#66983C22semidirect
29. C2×#66979C22semidirect
31. C2×#66977C22semidirect
32. C2×#66957C22semidirect
35. C11×#407C22semidirect
36. C11×#407C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. #10622750C22semidirect
39. #10622750C22semidirect
40. #10622748C22semidirect
41. #10622748C22semidirect
42. #10622747C22semidirect
43. #10622747C22semidirect
44. #10622726C22semidirect
45. #10622719C22semidirect
46. #10622352C22semidirect
47. #10622351C22semidirect
48. #10622350C22semidirect
49. #10622349C22semidirect
50. #10622348C22semidirect
51. #10622347C22semidirect
52. #10622346C22semidirect
53. #10622345C22semidirect
54. #10622344C22semidirect
55. #10622336C22semidirect
56. #10622335C22semidirect
57. #10622334C22semidirect
132. C2×Dic44C23semidirect
134. C2×D88C23semidirect
135. C2×#4314C23semidirect
139. #66885C23semidirect
140. #66885C23semidirect
141. #66882C23semidirect
142. #66881C23semidirect
143. #66881C23semidirect
144. #66880C23semidirect
145. #66880C23semidirect
247. C2×#407D11semidirect
317. C22×M16C2×D11semidirect
357. #407C2×D11semidirect
358. #407C2×D11semidirect
359. C2×C22⋊C8C2×D11semidirect
577. C11#60741semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130794582
#130794482
#130794402
#130794322
#130794232
#130794162
#130785312
#130782252
#130778382
C2×C11×#4072
#6074111