Finite Group Databasebeta

← #14763074

Subgroups — #14763074

Order 2816.

2054 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#127C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3#13071021C211yesmaximal, characteristic, complemented
4#13069541C214yesmaximal, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069422C211yesmaximal, characteristic, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13068545C214yesmaximal, complemented
9C11×#1957C211yesmaximal, characteristic, complemented
10C22×D4×D11—21no—
11C22×D4×D11—21no—
12C22×D4×D11C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×#66993—21no—
15C2×#66993—21no—
16C2×#66993C2212yes—
17D11×#127—24no—
18D11×#127C418yescomplemented
19C2×#66945—21no—
20C2×#66927C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×#102C2214yescomplemented
23C2×C4×C8×C11C2211yescharacteristic, complemented
24C11×#384C2211yescharacteristic, complemented
25C2×#66896C2214yescomplemented
26C2×#66885C2214yescomplemented
27C2×(C2×D11)⋊C8C2212yes—
28C2×Dic11⋊C8C2212yescomplemented
29#10622600—21no—
30#10622600C2212yes—
31#10622590—21no—
32C4⋊C4×Dic11—21no—
33C4⋊C4×Dic11C2212yescomplemented
34C2×#66873C2214yescomplemented
35#10622548C2211yescharacteristic, complemented
36C2×C4×C11⋊C8C2211yescharacteristic, complemented
37#10622298—24no—
38C24×D11—22no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11C2312yes—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—22no—
44C22×C22⋊D11—22no—
45C2×D4×D11—28no—
46C2×D4×D11—28no—
47C2×D4×D11—24no—
48C2×D4×D11—44no—
49C2×D4×D11—44no—
50C2×D4×D11—44no—
51C2×D4×D11—44no—
52C2×D4×D11—44no—
53C2×D4×D11—44no—
54C2×D4×D11C2×C418yes—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C11×#127—22no—
63C11×#127C2×C414yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2311yescharacteristic
68#66993—28no—
69#66993—28no—
70#66993—24no—
71#66993C2×C418yes—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2312yes—
76C2×C4×Dic11—22no—
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81#66945—44no—
82#66927—22no—
83#66927C2×C414yes—
84C42×D11C2×C414yes—
85C42×D11D414yes—
86C11×#102—44no—
87C4×C8×C11—22no—
88#66896—44no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91#66885—44no—
92(C2×D11)⋊C8—24no—
93Dic11⋊C8—24no—
94#66873—44no—
95C4×C11⋊C8—22no—
96#21803—111nomaximal, Sylow
97C24×C11—22no—
98C23×D11—22no—
99C23×D11—28no—
100C23×D11—44no—
101C23×D11—44no—
102C23×D11—44no—
103C23×D11—44no—
104C23×D11—44no—
105C23×D11—44no—
106C23×D11C2×D411yescharacteristic
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11C22×C414yes—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—28no—
122C2×C22⋊D11—28no—
123C2×C22⋊D11—28no—
124C2×C22⋊D11—44no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C2×C22⋊D11—44no—
129C2×C22⋊D11—44no—
130C22×Dic11—22no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134D4×D11—416no—
135D4×D11—416no—
136D4×D11—432no—
137D4×D11—432no—
138C2×D44—24no—
139C2×D44—24no—
140C2×D44—22no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44—42no—
146C2×D44—42no—
147C2×D44C22×C414yes—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11C22⋊C414yes—
153C2×C4×D11C22⋊C414yes—
154C2×C4×D11D814yes—
155C2×C4×D11SD1614yes—
156C2×C4×D11C22×C412yes—
157C2×C4×D11C2×D412yes—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C42×C11C22×C412yes—
165C42×C11C2×D412yes—
166(C2×D11)⋊C4—44no—
167C4⋊Dic11—24no—
168C4⋊Dic11—42no—
169C4⋊Dic11—42no—
170C4×Dic11—44no—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22⋊C414yes—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C22×#127—111no—
179C2×#431—111no—
180#2285—111no—
181#1982—114no—
182#1957—111no—
183#1957—111no—
184#1957—111no—
185#1957D1111yescharacteristic, complemented
186#1786—114no—
187C23×C11—24no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C22×D411yescharacteristic
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—24no—
200C22×D11—416no—
201C22×D11—416no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—416no—
209C22×D11—88no—
210C22×D11—88no—
211C22×D11—88no—
212C22×D11—88no—
213C22×D11C2×C22⋊C412yes—
214C22×D11C2×D812yes—
215C22×D11C2×SD1612yes—
216D4×C11—28no—
217D4×C11—44no—
218D4×C11—48no—
219D4×C11—48no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11C2×C22⋊C412yes—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×D812yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11H(5,𝔽2)12yes—
232C2×C4×C11H(5,𝔽2)12yes—
233C22⋊D11—416no—
234C22⋊D11—416no—
235C22⋊D11—416no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11C2×C22⋊C412yes—
244C2×Dic11C2×C22⋊C412yes—
245C2×Dic11C2×C22⋊C412yes—
246C2×Dic11C2×D812yes—
247C2×Dic11C2×SD1612yes—
248D44—28no—
249D44—44no—
250D44—48no—
251D44—48no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—28no—
255C4×D11#102116yescomplemented
256C8×C11—42no—
257C11⋊C8—42no—
258C23×D4—112no—
259C23×D4—221no—
260C23×D4—221no—
261C2×#127—112no—
262C2×#127—118no—
263C2×#127—111no—
264C2×#127—224no—
265C2×#127—221no—
266C2×#127—221no—
267C2×#127C2×D1111yescharacteristic
268C2×#117—221no—
269C22×C42—111no—
270#431—224no—
271C2×C4⋊C8—112no—
272C2×#102—114no—
273C2×#102—114no—
274C2×#102—114no—
275C2×#102C2×D1114yescomplemented
276C2×C22⋊C8—112no—
277C2×C4×C8—111no—
278C2×C4×C8C2×D1111yescharacteristic, complemented
279#384—111no—
280#384C2×D1111yescharacteristic, complemented
281#382—221no—
282#380—112no—
283#380—221no—
284C4×C4⋊C4—112no—
285C4×C4⋊C4—221no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11#53511yescharacteristic
295C22×C11#53511yescharacteristic
296C22×C11C22×D811yescharacteristic
297C22×C11C22×SD1611yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—22no—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—44no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—832no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—82no—
314C2×D11C2×#10214yes—
315C4×C11—82no—
316C4×C11C2×#10214yes—
317C4×C11#41814yes—
318C4×C11#51812yes—
319C4×C11#53512yes—
320Dic11—22no—
321Dic11—22no—
322Dic11—82no—
323Dic11C2×#10214yes—
324C25—222no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—118no—
328C22×D4—112no—
329C22×D4—228no—
330C22×D4—228no—
331C22×D4—224no—
332C22×D4—222no—
333C22×D4—222no—
334C22×D4—222no—
335C22×D4—221no—
336C22×D4—221no—
337C22×D4—444no—
338C22×D4—444no—
339C22×D4—444no—
340C22×D4—444no—
341C22×D4—444no—
342C22×D4—444no—
343C22×D4C22×D1112yes—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C22×C8—112no—
348C22×C8C22×D1112yes—
349#127—22no—
350#127—118no—
351#127—114no—
352#127—228no—
353#127—228no—
354#127—224no—
355#127—222no—
356#127C4×D1114yes—
357#117—444no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—222no—
365C2×C42—111no—
366C2×C42—111no—
367C2×C42—111no—
368C2×C42—114no—
369C2×C42—114no—
370C2×C42—222no—
371C2×C42C22×D1111yescharacteristic
372C4⋊C8—224no—
373#102—44no—
374#102—444no—
375#102—444no—
376#102—444no—
377C22⋊C8—224no—
378C4×C8—22no—
379C4×C8—222no—
380#95—222no—
381#95—222no—
382C2×C11—84no—
383C2×C11#230911yescharacteristic
384C2×C11C22×#10211yescharacteristic
385C2×C11C2×#41811yescharacteristic
386C2×C11#320511yescharacteristic
387C2×C11#320511yescharacteristic
388C2×C11#320811yescharacteristic
389C2×C11#320811yescharacteristic
390D11—24no—
391D11—84no—
392C24—22no—
393C24—111no—
394C24—228no—
395C24—222no—
396C24—444no—
397C24—444no—
398C24—444no—
399C24—444no—
400C24—444no—
401C24—444no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—22no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—114no—
412C2×D4—228no—
413C2×D4—228no—
414C2×D4—228no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—4432no—
421C2×D4—444no—
422C2×D4—444no—
423C2×D4—4416no—
424C2×D4—4416no—
425C2×D4—4432no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—442no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—442no—
434C2×D4C2×C4×D1114yes—
435C22×C4—22no—
436C22×C4—111no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—114no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
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—24no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—224no—
463C4⋊C4—442no—
464C4⋊C4—442no—
465C22⋊C4—444no—
466C42—114no—
467C42—114no—
468C42—112no—
469C42—112no—
470C42—444no—
471C42C2×C4×D1112yes—
472C42D4×D1112yes—
473C11#2180311yescharacteristic, complemented, Sylow
474C23—24no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—112no—
482C23—112no—
483C23—112no—
484C23—221no—
485C23—221no—
486C23—221no—
487C23—221no—
488C23—224no—
489C23—4416no—
490C23—4416no—
491C23—4416no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—888no—
499C23—888no—
500C23—888no—
501C23—888no—
502C23C2×D4×D1111yescharacteristic
503D4—28no—
504D4—44no—
505D4—48no—
506D4—48no—
507D4—228no—
508D4—4416no—
509D4—4416no—
510D4—4416no—
511D4—444no—
512D4—448no—
513D4—448no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—1116no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—228no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4C22⋊C4×D1112yes—
534C2×C4C22⋊C4×D1112yes—
535C2×C4D8×D1112yes—
536C2×C4#6696412yes—
537C2×C4SD16×D1112yes—
538C2×C4#6696712yes—
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4#6703712yes—
542C2×C4#6704212yes—
543C8—42no—
544C8—442no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—114no—
553C22—222no—
554C22—222no—
555C22—222no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—444no—
560C22—444no—
561C22—444no—
562C22—8832no—
563C22—882no—
564C22—882no—
565C22—882no—
566C22—882no—
567C22C2×C22⋊C4×D1111yescharacteristic
568C22#1062320511yescharacteristic
569C22#1062324611yescharacteristic
570C22C2×D8×D1111yescharacteristic
571C22C2×#6696411yescharacteristic
572C22C2×SD16×D1111yescharacteristic
573C22C2×#6696711yescharacteristic
574C4—82no—
575C4—114no—
576C4—222no—
577C4—222no—
578C4—882no—
579C4D11×#10214yes—
580C4#1062238314yes—
581C4#1062307612yes—
582C4#1062313812yes—
583C2—84no—
584C2—224no—
585C2—884no—
586C2#1307119511yescharacteristic
587C2C2×D11×#10211yescharacteristic
588C2C2×#1062238311yescharacteristic
589C2#1307953011yescharacteristic
590C2#1307953511yescharacteristic
591C2#1307955311yescharacteristic
592C2#1307955811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1957C2
socleC23×C11C22×D4
prime radicalC2×D11×#127C2
cosocleC22×C4×C11C24
hypercenter#1957D11
hypocenterC11#21803
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. #13071021C2semidirect
4. #13069541C2semidirect
5. #13069423C2semidirect
6. #13069422C2semidirect
7. #13069421C2semidirect
8. #13068545C2semidirect
9. C11×#1957C2semidirect
18. D11×#127C4semidirect
22. C2×C11×#102C22semidirect
23. C2×C4×C8×C11C22semidirect
24. C11×#384C22semidirect
25. C2×#66896C22semidirect
26. C2×#66885C22semidirect
28. C2×Dic11⋊C8C22semidirect
33. C4⋊C4×Dic11C22semidirect
34. C2×#66873C22semidirect
35. #10622548C22semidirect
36. C2×C4×C11⋊C8C22semidirect
185. #1957D11semidirect
255. C4×D11#102semidirect
275. C2×#102C2×D11semidirect
278. C2×C4×C8C2×D11semidirect
280. #384C2×D11semidirect
473. C11#21803semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1272
C2×#106222982
#130710212
#130695412
#130694232
#130694222
#130694212
#130685452
C11×#19572
#2180311