Finite Group Databasebeta

← #14769239

Subgroups — #14769239

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×#10623108C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic, complemented
3C2×#10622417C212yesmaximal, complemented
4#13071567C211yesmaximal, characteristic, complemented
5#13069542C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13069043C212yesmaximal, complemented
8#13068937C212yesmaximal, complemented
9#13068555C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×C8×D11C2212yes—
15#10623108—24no—
16#10623108C418yescomplemented
17C2×#66948—22no—
18C2×#66948C2212yes—
19C2×#66945C2212yes—
20C2×#66927—21no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2212yes—
26C11×#384C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32#10622603—22no—
33#10622601—21no—
34#10622600C2212yes—
35C4⋊C4×Dic11—21no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622447—24no—
41#10622417—28no—
42C11×#340C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—24no—
49C2×#4343—42no—
50C2×#4343—42no—
51C2×#4343C2×C418yes—
52C22×D44—22no—
53C22×D44—21no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44D411yescharacteristic
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×C4×D11C2312yes—
60C22×C8×C11C2312yes—
61C4×Q8×C11—22no—
62C4×Q8×C11C2×C414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D412yes—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4×Dic11—21no—
78C2×C4×Dic11—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—42no—
84#66948—24no—
85#66948—216no—
86#66948C2×C418yes—
87#66945—24no—
88#66945—42no—
89#66927—28no—
90#66927—22no—
91#66927C2×C414yes—
92C4×D44—28no—
93C4×D44C2×C414yes—
94C4×D44D414yes—
95C11×C4⋊C8—22no—
96C11×#103—24no—
97#66899—22no—
98#66899D414yescomplemented
99C11⋊#95—21no—
100C11⋊#95—22no—
101#66885—24no—
102#66885—42no—
103(C2×D11)⋊C8—24no—
104#66873—24no—
105#66873—42no—
106C4×C11⋊C8—22no—
107#22418—111nomaximal, Sylow
108C23×D11—22no—
109C23×D11C2×D412yes—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C22×C412yes—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11C2×D412yes—
125#4343—216no—
126#4343—48no—
127#4343—48no—
128#4343—48no—
129C2×D44—28no—
130C2×D44—28no—
131C2×D44—24no—
132C2×D44—24no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—44no—
141C2×D44—44no—
142C2×D44—42no—
143C2×D44—42no—
144C2×D44—81no—
145C2×D44—81no—
146C2×D44—82no—
147C2×D44—82no—
148C2×D44C22⋊C414yes—
149C2×D44C22×C414yes—
150C2×C4×D11—28no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11C22×C414yes—
158C2×C4×D11C2×D414yes—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4C22×C412yes—
169C42×C11—24no—
170C42×C11C22×C412yes—
171C42×C11C2×D412yes—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—82no—
175(C2×D11)⋊C4C22⋊C418yes—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22⋊C414yes—
180C4⋊Dic11C2×D412yes—
181C4×Dic11—44no—
182C4×Dic11—42no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8C2×D412yes—
189C8×D11—48no—
190C2×#550—111no—
191C2×C8×D4—111no—
192C2×#416—112no—
193#2354—111no—
194#1982—111no—
195#1957—111no—
196#1893—112no—
197#1875—112no—
198#1803D1111yescharacteristic, complemented
199#1788—112no—
200C4×#103—111no—
201C23×C11C22×D411yescharacteristic
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—24no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11C2×C22⋊C414yes—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11C4×D414yes—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11#13512yes—
234C2×C4×C11#13512yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11C2×C22⋊C414yes—
250D44—24no—
251D44—24no—
252D44—28no—
253D44—416no—
254D44—42no—
255D44—42no—
256D44—48no—
257D44—84no—
258D44—88no—
259C4×D11—24no—
260C4×D11—24no—
261C4×D11—24no—
262C4×D11—24no—
263C4×D11—416no—
264C8×C11—42no—
265C11⋊C8—22no—
266C11⋊C8—41no—
267C22×#41—112no—
268C23×C8—112no—
269#550—118no—
270#550—224no—
271C2×#127—111no—
272C2×#127—221no—
273C2×#121—112no—
274C2×#121—222no—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—112no—
279C8×D4—224no—
280C2×C4⋊C8C2×D1111yescharacteristic
281#416—228no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103C2×D1112yes—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—112no—
289C2×C22⋊C8—112no—
290C2×C4×C8—111no—
291#390—221no—
292#388—222no—
293#384C2×D1111yescharacteristic
294#380—112no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4—221no—
297#340—111no—
298#340—111no—
299#340C2×D1112yes—
300C22×C11C22×C22⋊C411yescharacteristic
301C22×C11D4211yescharacteristic
302C22×C11#54611yescharacteristic
303C22×C11C2×#13511yescharacteristic
304C22×C11C2×#13511yescharacteristic
305C22×C11#57611yescharacteristic
306C22×C11#57711yescharacteristic
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
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—42no—
324C4×C11—82no—
325C4×C11#41614yescomplemented
326C4×C11C2×C4×D411yescharacteristic
327C4×C11#51811yescharacteristic
328C4×C11D4211yescharacteristic
329C4×C11#54611yescharacteristic
330Dic11—24no—
331Dic11—42no—
332Dic11—81no—
333C2×#41—118no—
334C2×#41—224no—
335C2×#41—224no—
336C2×#41—224no—
337C2×#41—442no—
338C2×#41—442no—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—111no—
341C22×D4—112no—
342C22×D4—222no—
343C22×D4—222no—
344C22×D4—221no—
345C22×D4—221no—
346C23×C4—112no—
347C23×C4—222no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—224no—
351C22×C8—224no—
352C22×C8—442no—
353C22×C8C22×D1112yes—
354#127—114no—
355#127—228no—
356#127—222no—
357#121—118no—
358#121—2216no—
359#121—224no—
360C4×Q8—22no—
361C4×Q8C4×D1114yes—
362C4×D4—114no—
363C4×D4—114no—
364C4×D4—228no—
365#117—224no—
366#117—442no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4C22×D1112yes—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—112no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C42—21no—
380C2×C42—222no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—22no—
384#103—24no—
385#103—114no—
386#103—222no—
387#102—224no—
388#102—224no—
389#102—442no—
390#102—442no—
391C22⋊C8—224no—
392C4×C8—222no—
393#95—222no—
394#95—221no—
395C2×C11D4×C22⋊C411yescharacteristic
396C2×C11C2×#41611yescharacteristic
397C2×C11#289711yescharacteristic
398C2×C11#328411yescharacteristic
399C2×C11#328711yescharacteristic
400C2×C11#330411yescharacteristic
401C2×C11#330511yescharacteristic
402D11—44no—
403D11—84no—
404C24—112no—
405C24—222no—
406#41—2216no—
407#41—448no—
408#41—448no—
409#41—448no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8C2×C4×D1112yes—
414C2×Q8D4×D1112yes—
415C2×Q8#434312yes—
416C2×D4—114no—
417C2×D4—114no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—444no—
430C2×D4—444no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—881no—
434C2×D4—881no—
435C2×D4—882no—
436C2×D4—882no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—228no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—112no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—448no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C4⋊C4—81no—
471C4⋊C4—114no—
472C4⋊C4—112no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4C2×C4×D1112yes—
477C22⋊C4—118no—
478C22⋊C4—228no—
479C22⋊C4—444no—
480C22⋊C4—882no—
481C42—24no—
482C42—444no—
483C42—442no—
484C42C2×C4×D1112yes—
485C42D4×D1112yes—
486C11#2241811yescharacteristic, complemented, Sylow
487C23—114no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23—222no—
492C23—222no—
493C23—222no—
494C23—224no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23C2×D4×D1111yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—22no—
505Q8#6694614yes—
506D4—224no—
507D4—224no—
508D4—228no—
509D4—4416no—
510D4—442no—
511D4—442no—
512D4—448no—
513D4—884no—
514D4—888no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—114no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—4416no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4C22⋊C4×D1112yes—
541C2×C4C22⋊C4×D1112yes—
542C2×C4#6696912yes—
543C2×C4#6697212yes—
544C2×C4C22×C4×D1111yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434311yescharacteristic
548C2×C4#6704211yescharacteristic
549C2×C4#6704211yescharacteristic
550C8—42no—
551C8—222no—
552C8—441no—
553C22—224no—
554C22—224no—
555C22—224no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—442no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22—882no—
564C22—882no—
565C22—882no—
566C22—882no—
567C22C2×C22⋊C4×D1111yescharacteristic
568C22#1062314011yescharacteristic
569C22#1062316111yescharacteristic
570C22C2×#6696911yescharacteristic
571C22C2×#6697211yescharacteristic
572C22#1062330511yescharacteristic
573C22#1062330911yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—82no—
578C4—224no—
579C4—442no—
580C4—881no—
581C4#1062241714yescomplemented
582C4C2×#6694611yescharacteristic
583C4#1062305211yescharacteristic
584C4#1062314011yescharacteristic
585C4#1062316111yescharacteristic
586C2—444no—
587C2—884no—
588C2#1307143611yescharacteristic
589C2C2×#1062241711yescharacteristic
590C2#1307714011yescharacteristic
591C2#1308034111yescharacteristic
592C2#1308037111yescharacteristic
593C2#1308055211yescharacteristic
594C2#1308056311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22418
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#10622447C2semidirect
3. C2×#10622417C2semidirect
4. #13071567C2semidirect
5. #13069542C2semidirect
6. #13069421C2semidirect
7. #13069043C2semidirect
8. #13068937C2semidirect
9. #13068555C2semidirect
10. C4×#66899C2semidirect
11. C11×#1803C2semidirect
16. #10623108C4semidirect
98. #66899D4semidirect
198. #1803D11semidirect
325. C4×C11#416semidirect
486. C11#22418semidirect
581. C4#10622417semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106224472
C2×#106224172
#130715672
#130695422
#130694212
#130690432
#130689372
#130685552
C4×#668992
C11×#18032
#2241811