Finite Group Databasebeta

← #14767591

Subgroups — #14767591

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622328C211yesmaximal, characteristic
2C4×#66922C211yesmaximal, characteristic, complemented
3C4×#66928C211yesmaximal, characteristic
4#13069436C211yesmaximal, characteristic, complemented
5#13069432C211yesmaximal, characteristic
6#13068970C212yesmaximal
7#13068956C212yesmaximal, complemented
8#13068956C212yesmaximal, complemented
9#13068949C212yesmaximal
10#13068750C211yesmaximal, characteristic, complemented
11C11×#1745C211yesmaximal, characteristic, complemented
12C22×Dic44C2212yes—
13C22×#4314C2212yes—
14C2×#66928C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C2×C4×Dic22C2212yes—
19C2×C11×#97C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C43×C11C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66880C2212yes—
24C2×#66880C2212yes—
25C2×#66880C2212yes—
26#10622553—21no—
27#10622553—21no—
28#10622552C2211yescharacteristic
29C4×(C2×D11)⋊C4—21no—
30C4×(C2×D11)⋊C4—21no—
31#10622549C2211yescharacteristic
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11—21no—
34C4×C4⋊Dic11—21no—
35#10622542C2211yescharacteristic
36#10622542C2212yes—
37#10622541—21no—
38#10622541—21no—
39#10622328C418yescomplemented
40C11×#336C2212yes—
41C11×#336C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22C2312yes—
47C22×Dic22C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11D411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—21no—
73C2×Dic44—42no—
74C2×Dic44—42no—
75C2×Dic44C2×C418yescomplemented
76C2×#4314—42no—
77C2×#4314—42no—
78C2×#4314C2×C418yes—
79#66928—22no—
80#66928C2×C414yes—
81C4×D44—42no—
82#66922—22no—
83#66922C2×C414yescomplemented
84C4×Dic22—42no—
85C4×Dic22—42no—
86C4×Dic22—42no—
87C11×#97—22no—
88C11×#97C2×C414yescomplemented
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95#66885—42no—
96#66880—42no—
97#66880—42no—
98#66880—42no—
99#22273—111nomaximal, Sylow
100C23×D11—21no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C2×D44—21no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44C22×C412yes—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×Dic22—22no—
121C2×Dic22—21no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22C22×C414yes—
129C2×Dic22C22×C412yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11C22×C414yes—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—41no—
141C42×C11—41no—
142C42×C11C22×C412yes—
143C42×C11#4112yes—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—24no—
150C4⋊Dic11—24no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—42no—
156C4⋊Dic11—42no—
157Dic11⋊C4—44no—
158Dic11⋊C4—42no—
159C4×Dic11—44no—
160C4×Dic11—42no—
161Dic44—48no—
162#4314—48no—
163C2×#497—111no—
164C4×C4⋊Q8—111no—
165C4×#124—111no—
166#1960—111no—
167#1959—111no—
168#1880—112no—
169#1878—112no—
170#1878—112no—
171#1877—112no—
172#1836—111no—
173#1745D1111yescharacteristic, complemented
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11C4×D412yes—
197C2×C4×C11C4×D412yes—
198C2×C4×C11#13712yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)12yes—
203C2×C4×C11H(5,𝔽2)12yes—
204C2×Dic11—24no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219D44—24no—
220D44—42no—
221C4×D11—84no—
222Dic22—24no—
223Dic22—24no—
224Dic22—24no—
225Dic22—42no—
226Dic22—42no—
227Dic22—42no—
228C8×C11—24no—
229C8×C11—42no—
230C22×Q16—112no—
231C22×SD16—112no—
232C2×C4⋊Q8—111no—
233C2×#124—111no—
234C2×C4×Q8—112no—
235C2×C4×Q8—111no—
236C2×C4×D4—111no—
237#497—118no—
238C2×#103—112no—
239C2×#103—112no—
240C2×#103—112no—
241C2×#102—112no—
242C2×#97C2×D1111yescharacteristic
243C2×#97C2×D1111yescharacteristic
244#391—112no—
245#391—111no—
246#390—111no—
247#389—221no—
248#389—221no—
249#388—221no—
250#388—221no—
251#384—111no—
252#382—111no—
253C4×C4⋊C4—221no—
254C4×C4⋊C4—221no—
255C4×C22⋊C4—221no—
256C4×C22⋊C4—221no—
257C43C2×D1111yescharacteristic
258#340—112no—
259#340—112no—
260#336C2×D1112yes—
261#336C2×D1112yes—
262C22×C11C2×C4×D411yescharacteristic
263C22×C11#53511yescharacteristic
264C22×C11#53511yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11#57511yescharacteristic
268C22×C11#57511yescharacteristic
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C4×C11—22no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—41no—
281C4×C11—41no—
282C4×C11#51812yes—
283C4×C11#54012yes—
284Dic11—44no—
285Dic11—42no—
286Dic11—81no—
287Dic11—81no—
288Dic11—82no—
289C22×Q8—111no—
290C22×Q8—112no—
291C22×D4—111no—
292C23×C4—221no—
293C2×Q16—118no—
294C2×Q16—442no—
295C2×Q16—442no—
296C2×SD16—118no—
297C2×SD16—442no—
298C2×SD16—442no—
299C22×C8C22×D1112yes—
300C22×C8C22×D1112yes—
301C4⋊Q8—114no—
302C4⋊Q8—222no—
303#124—114no—
304#124—222no—
305C4×Q8—442no—
306C4×Q8—442no—
307C4×Q8—442no—
308C4×D4—442no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C42—221no—
324C2×C42—222no—
325C2×C42D4411yescharacteristic
326C2×C42D4411yescharacteristic
327C2×C42D4411yescharacteristic
328C2×C42D4411yescharacteristic
329C2×C42C22×D1111yescharacteristic
330C2×C42C22×D1111yescharacteristic
331C2×C42C22×D1111yescharacteristic
332#103—442no—
333#103—442no—
334#103—442no—
335#102—442no—
336#97—22no—
337#97C4×D1114yescomplemented
338#95—221no—
339#95—221no—
340#95—221no—
341#95—221no—
342#95—222no—
343#95—222no—
344C2×C11#232811yescharacteristic
345C2×C11C4×#13711yescharacteristic
346C2×C11C4×#13711yescharacteristic
347C2×C11#321511yescharacteristic
348C2×C11#321611yescharacteristic
349C2×C11#321811yescharacteristic
350C2×C11#321911yescharacteristic
351D11—82no—
352C24—221no—
353C2×Q8—112no—
354C2×Q8—114no—
355C2×Q8—221no—
356C2×Q8—222no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×D4—112no—
364C2×D4—221no—
365C2×D4—222no—
366C2×D4—222no—
367C22×C4—221no—
368C22×C4—222no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—222no—
372C22×C4—442no—
373C22×C4—442no—
374C22×C4—442no—
375C22×C4C2×D4411yescharacteristic
376C22×C4C2×D4411yescharacteristic
377C22×C4C2×D4411yescharacteristic
378C22×C4C2×D4411yescharacteristic
379C22×C4C2×D4411yescharacteristic
380C22×C4C2×D4411yescharacteristic
381C22×C4C23×D1111yescharacteristic
382Q16—448no—
383SD16—448no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8C2×C4×D1114yes—
390C4⋊C4—224no—
391C4⋊C4—224no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—442no—
397C4⋊C4—444no—
398C4⋊C4—442no—
399C4⋊C4—442no—
400C22⋊C4—224no—
401C22⋊C4—224no—
402C22⋊C4—442no—
403C22⋊C4—442no—
404C22⋊C4—442no—
405C42—22no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42—41no—
410C42—41no—
411C42—444no—
412C42—442no—
413C42C2×C4×D1112yes—
414C42#433912yes—
415C11#2227311yescharacteristic, complemented, Sylow
416C23—222no—
417C23—441no—
418C23—441no—
419C23—441no—
420C23—441no—
421C23—441no—
422C23—441no—
423C23C22×D4411yescharacteristic
424Q8—224no—
425Q8—224no—
426Q8—224no—
427Q8—442no—
428Q8—442no—
429Q8—442no—
430D4—224no—
431D4—442no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—222no—
447C2×C4—224no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—442no—
460C2×C4—441no—
461C2×C4—884no—
462C2×C4C4×D4412yes—
463C2×C4C4×D4412yes—
464C2×C4#6696212yes—
465C2×C4#6696212yes—
466C2×C4C22×C4×D1111yescharacteristic
467C2×C4C2×#433911yescharacteristic
468C2×C4#6704212yes—
469C2×C4#6704212yes—
470C8—24no—
471C8—42no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22C2×C4×D4411yescharacteristic
480C22#1062305611yescharacteristic
481C22#1062305611yescharacteristic
482C22C2×#6696211yescharacteristic
483C22C2×#6696211yescharacteristic
484C22#1062327911yescharacteristic
485C22#1062327911yescharacteristic
486C4—22no—
487C4—22no—
488C4—22no—
489C4—22no—
490C4—41no—
491C4—41no—
492C4—442no—
493C4—444no—
494C4—881no—
495C4—881no—
496C4—882no—
497C4#1062305212yes—
498C4#1062306612yes—
499C2—882no—
500C2#1307134111yescharacteristic
501C2C4×#6696211yescharacteristic
502C2C4×#6696211yescharacteristic
503C2#1307962111yescharacteristic
504C2#1307962911yescharacteristic
505C2#1307964511yescharacteristic
506C2#1307965511yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1745C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1745D11
hypocenterC11#22273
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. C4×#66922C2semidirect
4. #13069436C2semidirect
7. #13068956C2semidirect
8. #13068956C2semidirect
10. #13068750C2semidirect
11. C11×#1745C2semidirect
39. #10622328C4semidirect
75. C2×Dic44C2×C4semidirect
83. #66922C2×C4semidirect
88. C11×#97C2×C4semidirect
173. #1745D11semidirect
337. #97C4×D11semidirect
415. C11#22273semidirect

Maximal subgroups

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

subgroupindex
C2×#106223282
C4×#669222
C4×#669282
#130694362
#130694322
#130689702
#130689562
#130689492
#130687502
C11×#17452
#2227311