Finite Group Databasebeta

← #14763471

Subgroups — #14763471

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3#13071021C211yesmaximal, characteristic, complemented
4#13069579C212yesmaximal, complemented
5#13069426C212yesmaximal, complemented
6#13068935C212yesmaximal
7#13068927C212yesmaximal, complemented
8#13068622C211yesmaximal, characteristic, complemented
9#13068618C211yesmaximal, characteristic, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991C2211yescharacteristic
14C2×#66989C2211yescharacteristic
15C2×C4×C22⋊D11—21no—
16C2×#66979—21no—
17#10623088—24no—
18#10623088C418yescomplemented
19C2×#66950C2211yescharacteristic
20C2×#66945C2212yes—
21C2×#66943C2211yescharacteristic
22C2×#66936—21no—
23C2×#66932—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102C2212yes—
28C11×#384C2211yescharacteristic
29C2×#66896C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32C2×C8×Dic11C2212yes—
33#10622600—21no—
34#10622600—21no—
35#10622590C2212yes—
36C4⋊C4×Dic11—21no—
37C4⋊C4×Dic11—21no—
38C2×#66874C2212yes—
39#10622548C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622446—24no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—21no—
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C4×D4×C11—22no—
55C4×D4×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65#66991—22no—
66#66991C2×C414yes—
67#66989—22no—
68#66989C2×C414yes—
69C4×C22⋊D11—28no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72#66979—28no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87#66950—22no—
88#66950C2×C414yes—
89#66945—42no—
90#66945—42no—
91#66943—22no—
92#66943C2×C414yes—
93#66936—28no—
94#66932—28no—
95C42×D11C2×C414yes—
96C42×D11D414yes—
97C4×Dic22—22no—
98C4×Dic22C2×C414yes—
99C11×C4⋊C8—22no—
100C11×#102—42no—
101#66896—42no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105#66880—42no—
106C8×Dic11—24no—
107#66874—42no—
108C4⋊(C11⋊C8)—22no—
109#21862—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C2×D411yescharacteristic
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—42no—
128C2×C22⋊D11—42no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—41no—
142C2×C4×D11—41no—
143C2×C4×D11C22⋊C414yes—
144C2×C4×D11C22⋊C414yes—
145C2×C4×D11C22×C412yes—
146C2×C4×D11C2×D412yes—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C412yes—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4C22×C412yes—
162C11×C22⋊C4—24no—
163C42×C11C22×C412yes—
164C42×C11C2×D412yes—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—24no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—44no—
170C4⋊Dic11—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4⋊Dic11—42no—
177C4⋊Dic11C22×C412yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—24no—
180C4×Dic11—24no—
181C4×Dic11—44no—
182C4×Dic11C22⋊C414yes—
183C4×Dic11C22⋊C414yes—
184C4×Dic11C22×C412yes—
185C4×Dic11C2×D412yes—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×#529—111no—
190C2×#431—111no—
191#2285—111no—
192#1991—112no—
193#1958—112no—
194#1875—112no—
195#1873—112no—
196#1803—111no—
197#1803—111no—
198#1802—111no—
199#1802D1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C22×D411yescharacteristic
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11C2×C22⋊C412yes—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—48no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11#13512yes—
231C2×C4×C11#13512yes—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C22⋊D11—48no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11C2×C22⋊C412yes—
255C2×Dic11C2×C22⋊C412yes—
256C2×Dic11C2×C22⋊C412yes—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—22no—
260C4×D11—22no—
261C4×D11—28no—
262C4×D11—44no—
263Dic22—22no—
264Dic22—22no—
265Dic22—41no—
266Dic22—41no—
267C8×C11—42no—
268C11⋊C8—42no—
269#529—118no—
270#529—224no—
271C2×#126—221no—
272C2×#125—111no—
273C2×#124—111no—
274C2×#123—221no—
275C2×C22⋊Q8—111no—
276C2×#121—111no—
277C2×C4×Q8—111no—
278C2×C4×D4—221no—
279C2×C4×D4C2×D1111yescharacteristic
280C2×#117—112no—
281C2×#117—221no—
282C22×C42—111no—
283#431—224no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×#103—112no—
287C2×#103—112no—
288C2×#102—112no—
289C2×#102C2×D1112yes—
290C2×C22⋊C8—112no—
291C2×C4×C8—112no—
292#384—111no—
293#384C2×D1111yescharacteristic
294#382—112no—
295#380—221no—
296#380—221no—
297C4×C4⋊C4—221no—
298C4×C4⋊C4—221no—
299#340—112no—
300#340—112no—
301#340—112no—
302#340C2×D1112yes—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11C22×C22⋊C411yescharacteristic
311C22×C11#53511yescharacteristic
312C22×C11#53611yescharacteristic
313C22×C11C2×#13511yescharacteristic
314C22×C11C2×#13511yescharacteristic
315C22×C11#57511yescharacteristic
316C22×C11#57511yescharacteristic
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—41no—
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—82no—
327C4×C11#41614yes—
328C4×C11#52011yescharacteristic
329C4×C11#52011yescharacteristic
330C4×C11#53711yescharacteristic
331C4×C11#53711yescharacteristic
332Dic11—22no—
333Dic11—22no—
334Dic11—22no—
335Dic11—42no—
336Dic11—42no—
337Dic11—82no—
338C22×Q8—111no—
339C22×D4—221no—
340C22×D4C22×D1111yescharacteristic
341C23×C4—21no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C22×C8—112no—
346C22×C8C22×D1112yes—
347#126—228no—
348#125—114no—
349#125—222no—
350#124—114no—
351#124—222no—
352#123—228no—
353C22⋊Q8—114no—
354C22⋊Q8—222no—
355#121—114no—
356#121—222no—
357C4×Q8—114no—
358C4×Q8—222no—
359C4×D4—22no—
360C4×D4—228no—
361C4×D4C4×D1114yes—
362#117—228no—
363#117—442no—
364#117—442no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1112yes—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—222no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—114no—
387C2×C42—114no—
388C2×C42—221no—
389C2×C42—222no—
390C2×C42C22×D1111yescharacteristic
391C4⋊C8—22no—
392C4⋊C8—222no—
393#103—442no—
394#103—442no—
395#102—42no—
396#102—442no—
397C22⋊C8—224no—
398C4×C8—224no—
399#95—222no—
400#95—222no—
401C2×C11—82no—
402C2×C11#231111yescharacteristic
403C2×C11C2×#41611yescharacteristic
404C2×C11#289611yescharacteristic
405C2×C11#321211yescharacteristic
406C2×C11#321211yescharacteristic
407C2×C11#323311yescharacteristic
408C2×C11#323311yescharacteristic
409D11—42no—
410C24—21no—
411C24—111no—
412C2×Q8—112no—
413C2×Q8—221no—
414C2×Q8—221no—
415C2×Q8—221no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—224no—
424C2×D4—442no—
425C2×D4—442no—
426C2×D4C2×C4×D1112yes—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—222no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—112no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4C2×C4×D1112yes—
475C22⋊C4—24no—
476C22⋊C4—224no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—444no—
481C42—114no—
482C42—114no—
483C42—112no—
484C42—112no—
485C42—224no—
486C42—444no—
487C42C2×C4×D1112yes—
488C42D4×D1112yes—
489C11#2186211yescharacteristic, complemented, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—112no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23C2×D4×D1111yescharacteristic
505Q8—222no—
506Q8—222no—
507Q8—441no—
508Q8—441no—
509D4—22no—
510D4—22no—
511D4—41no—
512D4—41no—
513D4—448no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—48no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—228no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—444no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4C22⋊C4×D1112yes—
548C2×C4C22⋊C4×D1112yes—
549C2×C4#6696512yes—
550C2×C4#6696912yes—
551C2×C4C22×C4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#6704011yescharacteristic
555C2×C4#6704211yescharacteristic
556C2×C4#6704311yescharacteristic
557C8—42no—
558C8—442no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—441no—
570C22—441no—
571C22—441no—
572C22—441no—
573C22C2×C22⋊C4×D1111yescharacteristic
574C22#1062313811yescharacteristic
575C22#1062315911yescharacteristic
576C22C2×#6696511yescharacteristic
577C22C2×#6696911yescharacteristic
578C22#1062330411yescharacteristic
579C22#1062330811yescharacteristic
580C4—22no—
581C4—42no—
582C4—82no—
583C4—222no—
584C4—222no—
585C4—222no—
586C4—442no—
587C4—442no—
588C4—882no—
589C4#1062238514yes—
590C4#1062303511yescharacteristic
591C4#1062305411yescharacteristic
592C4#1062313911yescharacteristic
593C4#1062316011yescharacteristic
594C2—82no—
595C2—442no—
596C2#1307120511yescharacteristic
597C2C2×#1062238511yescharacteristic
598C2#1307713211yescharacteristic
599C2#1307959011yescharacteristic
600C2#1307959111yescharacteristic
601C2#1307979311yescharacteristic
602C2#1307979411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11#21862
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622446C2semidirect
3. #13071021C2semidirect
4. #13069579C2semidirect
5. #13069426C2semidirect
7. #13068927C2semidirect
8. #13068622C2semidirect
9. #13068618C2semidirect
10. #13068616C2semidirect
11. C11×#1802C2semidirect
18. #10623088C4semidirect
199. #1802D11semidirect
489. C11#21862semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×#106224462
#130710212
#130695792
#130694262
#130689352
#130689272
#130686222
#130686182
#130686162
C11×#18022
#2186211