Finite Group Databasebeta

← #14769243

Subgroups — #14769243

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622726C212yesmaximal, complemented
3#13071565C211yesmaximal, characteristic, complemented
4#13069542C211yesmaximal, characteristic, complemented
5#13069422C211yesmaximal, characteristic, complemented
6#13069044C212yesmaximal, complemented
7#13068936C212yesmaximal, complemented
8#13068622C211yesmaximal, characteristic, complemented
9#13068557C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C23×C8×C11C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66993—21no—
16C2×#66983C2212yes—
17C2×#66979C2212yes—
18#10623084—24no—
19#10623084C418yescomplemented
20C2×#66946—21no—
21C2×#66937—22no—
22C2×#66927C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C8×D4×C11—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28#10622834—21no—
29#10622825C2212yes—
30#10622726—28no—
31C2×#66885C2212yes—
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34C2×#66885C2212yes—
35C2×#66880C2211yescharacteristic
36C2×#66880C2212yes—
37C2×#66880C2211yescharacteristic
38C4⋊C4×Dic11—21no—
39#10622564—22no—
40#10622548C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2211yescharacteristic
44#10622189C2211yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C2×#4339—24no—
50C2×#4339—24no—
51C2×#4339—24no—
52C2×#4339—42no—
53C2×#4339—42no—
54C2×#4339C2×C418yes—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×Dic22C2311yescharacteristic
60C22×C8×C11—24no—
61C22×C8×C11—24no—
62C22×C8×C11—42no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2312yes—
65C22×C8×C11C2311yescharacteristic
66C4×D4×C11C2×C414yes—
67C4×D4×C11D414yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73#66993—28no—
74#66983—24no—
75#66983C2×C418yes—
76C2×(C2×D11)⋊C4—22no—
77#66979—24no—
78#66979—42no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—22no—
89#66946—28no—
90#66937—216no—
91#66927—22no—
92#66927C2×C414yes—
93C4×Dic22—22no—
94C4×Dic22C2×C414yes—
95C11×C4⋊C8—22no—
96C11×C22⋊C8—24no—
97C4×C8×C11—22no—
98C11⋊#95—21no—
99C11⋊#95—22no—
100#66885—24no—
101#66885—24no—
102#66885—42no—
103#66885—42no—
104#66880—24no—
105#66880—22no—
106#66880D414yescomplemented
107#22418—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C23×D11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—28no—
124C2×C22⋊D11—28no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—82no—
128C2×C22⋊D11—82no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134#4339—216no—
135#4339—48no—
136#4339—48no—
137#4339—48no—
138C2×D44—24no—
139C2×D44—24no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—42no—
146C2×D44—42no—
147C2×D44—81no—
148C2×D44—81no—
149C2×D44C22×C414yes—
150C2×C4×D11—28no—
151C2×C4×D11—44no—
152C2×C4×D11—44no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C412yes—
157C2×Dic22C2×D412yes—
158C2×Dic22#4112yes—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11—21no—
162C2×C8×C11—22no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—48no—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4C22⋊C414yes—
170C11×C22⋊C4C22⋊C418yes—
171C42×C11C22×C412yes—
172C42×C11C2×D412yes—
173C22⋊Dic11—44no—
174C22⋊Dic11—82no—
175(C2×D11)⋊C4—28no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—22no—
182C4⋊Dic11—42no—
183C4⋊Dic11—81no—
184C4⋊Dic11C22×C412yes—
185C4⋊Dic11C2×D412yes—
186Dic11⋊C4—24no—
187C4×Dic11—24no—
188C4×Dic11—44no—
189C4×Dic11—42no—
190C2×#550—111no—
191C2×C8×D4D1111yescharacteristic, complemented
192C2×#416—112no—
193#2354—111no—
194#1982—111no—
195#1957—111no—
196#1893—112no—
197#1875—112no—
198#1803—111no—
199#1788—112no—
200C4×#103—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11C2×C22⋊C414yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216D4×C11—28no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11#13512yes—
229C2×C4×C11#13512yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C22⋊D11—416no—
237C22⋊D11—88no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253D44—24no—
254D44—24no—
255D44—42no—
256D44—42no—
257D44—48no—
258D44—84no—
259C4×D11—416no—
260Dic22—22no—
261Dic22—22no—
262Dic22—22no—
263Dic22C4×D414yes—
264C8×C11—22no—
265C8×C11—42no—
266C8×C11—41no—
267C22×#41—112no—
268C23×C8C2×D1112yes—
269#550—118no—
270#550—224no—
271C2×#127—111no—
272C2×#127—221no—
273C2×#121—112no—
274C2×#121—222no—
275C2×C4×Q8—111no—
276C2×C4×D4—221no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117—112no—
279C8×D4—24no—
280C2×C4⋊C8C2×D1111yescharacteristic
281#416—228no—
282C2×#103—111no—
283C2×#103—112no—
284C2×#103—111no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—112no—
289C2×C22⋊C8C2×D1112yes—
290C2×C4×C8C2×D1111yescharacteristic
291#390—221no—
292#388—222no—
293#384—111no—
294#380—112no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4—221no—
297#340—112no—
298#340—111no—
299#340—111no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11D4211yescharacteristic
309C22×C11#54611yescharacteristic
310C22×C11C2×#13511yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11#57611yescharacteristic
313C22×C11#57711yescharacteristic
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11#41614yescomplemented
324C4×C11C2×C4×D411yescharacteristic
325C4×C11#51811yescharacteristic
326C4×C11D4211yescharacteristic
327C4×C11#54611yescharacteristic
328Dic11—24no—
329Dic11—42no—
330Dic11—42no—
331Dic11—82no—
332Dic11—81no—
333C2×#41—118no—
334C2×#41—224no—
335C2×#41—224no—
336C2×#41—224no—
337C2×#41—442no—
338C2×#41—442no—
339C22×Q8—111no—
340C22×D4—112no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4—221no—
345C22×D4D4411yescharacteristic
346C23×C4—222no—
347C23×C4C22×D1112yes—
348C22×C8—24no—
349C22×C8—24no—
350C22×C8—42no—
351C22×C8C22×D1112yes—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354#127—114no—
355#127—228no—
356#127—222no—
357#121—118no—
358#121—224no—
359#121—2216no—
360C4×Q8—114no—
361C4×Q8—222no—
362C4×D4—228no—
363C4×D4C4×D1114yes—
364C4×D4C22⋊D1114yes—
365#117—224no—
366#117—442no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4D4411yescharacteristic
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4D4412yes—
379C2×C42—221no—
380C2×C42—222no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—22no—
384#103—114no—
385#103—222no—
386#103—224no—
387#102—224no—
388#102—224no—
389#102—442no—
390#102—442no—
391C22⋊C8—24no—
392C4×C8—22no—
393#95—221no—
394#95—222no—
395C2×C11—44no—
396C2×C11D4×C22⋊C411yescharacteristic
397C2×C11C2×#41611yescharacteristic
398C2×C11#289711yescharacteristic
399C2×C11#328411yescharacteristic
400C2×C11#328711yescharacteristic
401C2×C11#330411yescharacteristic
402C2×C11#330511yescharacteristic
403D11—84no—
404C24—222no—
405C24C2×D4412yes—
406#41—2216no—
407#41—448no—
408#41—448no—
409#41—448no—
410C2×Q8—112no—
411C2×Q8—112no—
412C2×Q8—112no—
413C2×Q8—221no—
414C2×Q8—221no—
415C2×Q8—221no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—114no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—442no—
431C2×D4—442no—
432C2×D4—881no—
433C2×D4—881no—
434C2×D4—882no—
435C2×D4—882no—
436C2×D4(C2×D11)⋊C414yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—228no—
445C22×C4—221no—
446C22×C4—222no—
447C22×C4—444no—
448C22×C4—444no—
449C22×C4C2×C4×D1114yes—
450C22×C4C2×D4412yes—
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×C22⋊D1114yes—
454C22×C4C23×D1111yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—22no—
463C2×C8—48no—
464C2×C8D4×D1112yes—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—224no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—222no—
474C4⋊C4—442no—
475C4⋊C4—881no—
476C4⋊C4(C2×D11)⋊C414yes—
477C22⋊C4—228no—
478C22⋊C4—444no—
479C22⋊C4—882no—
480C22⋊C4(C2×D11)⋊C418yes—
481C42—224no—
482C42—444no—
483C42—442no—
484C42C2×C4×D1112yes—
485C42C2×C22⋊D1112yes—
486C11#2241811yescharacteristic, complemented, Sylow
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—224no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23C2×(C2×D11)⋊C414yes—
501C23C22×D4411yescharacteristic
502Q8—114no—
503Q8—222no—
504Q8—222no—
505Q8—222no—
506D4—28no—
507D4—224no—
508D4—224no—
509D4—4416no—
510D4—448no—
511D4—442no—
512D4—442no—
513D4—884no—
514D4—888no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—4416no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—442no—
535C2×C4—441no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—441no—
539C2×C4#6695712yes—
540C2×C4#6695712yes—
541C2×C4C2×(C2×D11)⋊C412yes—
542C2×C4C2×(C2×D11)⋊C414yes—
543C2×C4C2×(C2×D11)⋊C412yes—
544C2×C4C22×C4×D1111yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4#6703711yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#6704211yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C8—22no—
551C8—42no—
552C8—41no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22—882no—
564C22—882no—
565C22—882no—
566C22—882no—
567C22D4×D4411yescharacteristic
568C22#1062308511yescharacteristic
569C22C2×#6695711yescharacteristic
570C22C2×#6695711yescharacteristic
571C22#1062328211yescharacteristic
572C22#1062328311yescharacteristic
573C22C22×(C2×D11)⋊C411yescharacteristic
574C4—24no—
575C4—22no—
576C4—224no—
577C4—442no—
578C4—442no—
579C4—882no—
580C4—881no—
581C4#1062272614yescomplemented
582C4C4×D4×D1111yescharacteristic
583C4#1062307611yescharacteristic
584C4D4×C22⋊D1111yescharacteristic
585C4#1062336011yescharacteristic
586C2—44no—
587C2—884no—
588C2D4×(C2×D11)⋊C411yescharacteristic
589C2C2×#1062272611yescharacteristic
590C2#1307714311yescharacteristic
591C2#1308034811yescharacteristic
592C2#1308037611yescharacteristic
593C2#1308055611yescharacteristic
594C2#1308056711yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
cosocleC22×C4×C11C24
hypercenterC2×C8×D4D11
hypocenterC11#22418
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622726C2semidirect
3. #13071565C2semidirect
4. #13069542C2semidirect
5. #13069422C2semidirect
6. #13069044C2semidirect
7. #13068936C2semidirect
8. #13068622C2semidirect
9. #13068557C2semidirect
10. C4×#66880C2semidirect
11. C2×C8×D4×C11C2semidirect
19. #10623084C4semidirect
106. #66880D4semidirect
191. C2×C8×D4D11semidirect
323. C4×C11#416semidirect
486. C11#22418semidirect
581. C4#10622726semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106227262
#130715652
#130695422
#130694222
#130690442
#130689362
#130686222
#130685572
C4×#668802
C2×C8×D4×C112
#2241811