Finite Group Databasebeta

← #14770583

Subgroups — #14770583

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069548C212yesmaximal, complemented
4#13069543C211yesmaximal, characteristic
5#13069425C212yesmaximal, complemented
6#13069421C211yesmaximal, characteristic
7#13068623C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9C4×#66874C211yesmaximal, characteristic, complemented
10C4×#66873C212yesmaximal, complemented
11C11×#2355C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000—21no—
14#10623116—24no—
15#10623116C418yescomplemented
16C2×#66947—22no—
17C2×#66946—21no—
18C2×#66928C2212yes—
19C2×#66927C2211yescharacteristic
20C2×C4×D44C2212yes—
21C2×C4×Dic22C2211yescharacteristic
22C11×#391—21no—
23C11×#387—22no—
24C11×#384C2211yescharacteristic
25C11×#382C2212yes—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C4⋊C4C2211yescharacteristic
29Q8×C11⋊C8—24no—
30C2×#66874C2211yescharacteristic
31C2×#66874C2211yescharacteristic
32C2×#66874C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40C2×C4×C11⋊C8C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×Dic22C2311yescharacteristic
50C4×Q8×C11C2×C414yes—
51C4×Q8×C11D414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11—22no—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2312yes—
63#67000—28no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8C2312yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73#66947—216no—
74#66946—28no—
75#66928—24no—
76#66928C2×C418yes—
77#66927—22no—
78#66927C2×C414yes—
79C4×D44—24no—
80C4×D44C2×C418yes—
81C4×Dic22—22no—
82C4×Dic22C2×C414yes—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—22no—
87#66874—22no—
88#66874—22no—
89#66874—42no—
90#66873—24no—
91#66873—24no—
92#66873—42no—
93#66873—42no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)—24no—
96C4×C11⋊C8—22no—
97C4×C11⋊C8—24no—
98#22543—111nomaximal, Sylow
99C23×D11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11C22⋊C414yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C2×D44—24no—
114C2×D44—24no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—42no—
121C2×D44—42no—
122C2×D44—81no—
123C2×D44—81no—
124C2×D44C22×C414yes—
125C2×C4×D11—28no—
126C2×C4×D11—82no—
127C2×C4×D11—82no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22C22×C412yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—81no—
141C11×C4⋊C4C22⋊C414yes—
142C11×C4⋊C4C22⋊C418yes—
143C11×C4⋊C4#4112yes—
144C42×C11—42no—
145C42×C11—82no—
146C42×C11C22×C412yes—
147C42×C11C22×C414yes—
148C42×C11C2×D412yes—
149C42×C11C2×D414yes—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153C4⋊Dic11—21no—
154C4⋊Dic11C22×C412yes—
155Dic11⋊C4—24no—
156C4×Dic11—24no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8#4112yes—
166C2×#559—111no—
167C2×C8×Q8—111no—
168#2355D1111yescharacteristic, complemented
169#1983—112no—
170#1982—111no—
171#1958—112no—
172#1957—111no—
173#1804—112no—
174#1803—111no—
175C4×#103—111no—
176C4×#102—112no—
177C23×C11C22×D411yescharacteristic
178C22×D11—24no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185Q8×C11—28no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C414yes—
203C2×C4×C11C2×C22⋊C414yes—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11#13512yes—
206C2×C4×C11#13512yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×C4×C112−1+411yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219D44—24no—
220D44—24no—
221D44—42no—
222D44—42no—
223D44—48no—
224D44—84no—
225C4×D11—88no—
226Dic22—22no—
227Dic22—22no—
228Dic22—41no—
229Dic22—41no—
230C11⋊C8—22no—
231C11⋊C8—42no—
232C11⋊C8—41no—
233#559—118no—
234#559—224no—
235C2×#127—111no—
236C2×#124—112no—
237C2×#124—221no—
238C2×#123—222no—
239C2×C4×Q8—111no—
240C2×C4×Q8C2×D1111yescharacteristic
241C2×C4×D4—112no—
242C2×C4×D4—221no—
243C8×Q8—224no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—112no—
246C2×#103—111no—
247C2×#103—111no—
248C2×#103—112no—
249C2×#102—112no—
250C2×#102—112no—
251C2×#102—112no—
252C2×#102—112no—
253C2×C4×C8—111no—
254C2×C4×C8—112no—
255#391—21no—
256#387—22no—
257#384C2×D1111yescharacteristic
258#382C2×D1112yes—
259C4×C4⋊C4—21no—
260C4×C4⋊C4C2×D1111yescharacteristic
261C4×C4⋊C4C2×D1112yes—
262#340—112no—
263#340—111no—
264#340—111no—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11#54811yescharacteristic
267C22×C11#55011yescharacteristic
268C22×C11C2×#13511yescharacteristic
269C22×C11C2×#13511yescharacteristic
270C22×C11#57611yescharacteristic
271C22×C11#57711yescharacteristic
272C2×D11—44no—
273C2×D11—44no—
274C2×D11—44no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—82no—
279C4×C11—24no—
280C4×C11—24no—
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11—82no—
285C4×C11#41614yes—
286C4×C11C4×#4111yescharacteristic
287C4×C11#52011yescharacteristic
288C4×C11#54811yescharacteristic
289C4×C11#55011yescharacteristic
290Dic11—42no—
291Dic11—42no—
292C22×Q8—111no—
293C22×Q8C22⋊D1111yescharacteristic
294C22×D4—112no—
295C22×D4—221no—
296C22×D4—221no—
297C23×C4—222no—
298C22×C8—111no—
299C22×C8—112no—
300C22×C8—111no—
301#127—114no—
302#127—222no—
303#124—118no—
304#124—228no—
305#124—224no—
306#123—2216no—
307C4×Q8—114no—
308C4×Q8—222no—
309C4×Q8C4×D1114yes—
310C4×Q8D4414yes—
311C4×D4—118no—
312C4×D4—228no—
313C4×D4—224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22⋊D1111yescharacteristic
319C2×C4⋊C4C22⋊D1112yes—
320C2×C4⋊C4C22×D1111yescharacteristic
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—222no—
326C2×C42—21no—
327C2×C42—22no—
328C2×C42—221no—
329C2×C42C22×D1112yes—
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—224no—
332C4⋊C8—222no—
333#103—222no—
334#103—222no—
335#103—442no—
336#102—224no—
337#102—224no—
338#102—442no—
339#102—442no—
340C4×C8—224no—
341C4×C8—222no—
342#95—22no—
343#95—21no—
344#95—22no—
345#95—22no—
346C2×C11#234111yescharacteristic
347C2×C11C2×#41611yescharacteristic
348C2×C11#289711yescharacteristic
349C2×C11#336111yescharacteristic
350C2×C11#336511yescharacteristic
351C2×C11#339411yescharacteristic
352C2×C11#339611yescharacteristic
353D11—84no—
354C24—222no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—112no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×Q8—221no—
363C2×Q8(C2×D11)⋊C414yes—
364C2×D4—114no—
365C2×D4—224no—
366C2×D4—224no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—442no—
373C2×D4—442no—
374C2×D4—881no—
375C2×D4—881no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—228no—
382C22×C4—882no—
383C22×C4—882no—
384C22×C4C2×C22⋊D1112yes—
385C22×C4C2×C22⋊D1112yes—
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C23×D1111yescharacteristic
389C2×C8—112no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—222no—
393C2×C8—221no—
394C2×C8—222no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—222no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—81no—
405C4⋊C4—112no—
406C4⋊C4—224no—
407C4⋊C4—221no—
408C4⋊C4(C2×D11)⋊C414yes—
409C4⋊C4(C2×D11)⋊C418yes—
410C4⋊C4#434312yes—
411C22⋊C4—228no—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C42—42no—
415C42—82no—
416C42—224no—
417C42C2×C4×D1114yes—
418C42C2×C4×D1112yes—
419C42C2×D4414yes—
420C42C2×D4412yes—
421C11#2254311yescharacteristic, complemented, Sylow
422C23—224no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23C22×C22⋊D1111yescharacteristic
430Q8—28no—
431Q8—222no—
432Q8—222no—
433Q8—441no—
434Q8—441no—
435D4—224no—
436D4—224no—
437D4—442no—
438D4—442no—
439D4—448no—
440D4—884no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—888no—
463C2×C4C2×(C2×D11)⋊C414yes—
464C2×C4C2×(C2×D11)⋊C414yes—
465C2×C4C2×(C2×D11)⋊C412yes—
466C2×C4C2×(C2×D11)⋊C412yes—
467C2×C4#6700312yes—
468C2×C4#6700312yes—
469C2×C4C22×C4×D1111yescharacteristic
470C2×C4C22×D4411yescharacteristic
471C2×C4C2×#434311yescharacteristic
472C2×C4#6704011yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4#6704211yescharacteristic
475C8—222no—
476C8—442no—
477C8—441no—
478C22—444no—
479C22—444no—
480C22—444no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22—882no—
485C22C22×(C2×D11)⋊C411yescharacteristic
486C22#1062334811yescharacteristic
487C22C2×#6700311yescharacteristic
488C22C2×#6700311yescharacteristic
489C22#1062336511yescharacteristic
490C22#1062336611yescharacteristic
491C22#1062336811yescharacteristic
492C4—24no—
493C4—24no—
494C4—22no—
495C4—42no—
496C4—81no—
497C4—82no—
498C4—442no—
499C4—442no—
500C4#1062261514yes—
501C4C4×#434311yescharacteristic
502C4#1062310511yescharacteristic
503C4#1062310711yescharacteristic
504C4#1062310811yescharacteristic
505C2—884no—
506C2#1307145411yescharacteristic
507C2C2×#1062261511yescharacteristic
508C2#1307713911yescharacteristic
509C2#1308127611yescharacteristic
510C2#1308131211yescharacteristic
511C2#1308161211yescharacteristic
512C2#1308162411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2355C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
cosocleC22×C4×C11C24
hypercenter#2355D11
hypocenterC11#22543
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13069548C2semidirect
5. #13069425C2semidirect
7. #13068623C2semidirect
8. #13068618C2semidirect
9. C4×#66874C2semidirect
10. C4×#66873C2semidirect
11. C11×#2355C2semidirect
15. #10623116C4semidirect
168. #2355D11semidirect
421. C11#22543semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×Q8×C11⋊C82
#130695482
#130695432
#130694252
#130694212
#130686232
#130686182
C4×#668742
C4×#668732
C11×#23552
#2254311