Finite Group Databasebeta

← #14770603

Subgroups — #14770603

Order 2816.

1098 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×#10623263C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3#13071528C211yesmaximal, characteristic, complemented
4#13069545C212yesmaximal
5#13069540C211yesmaximal, characteristic, complemented
6#13069429C212yesmaximal
7#13068619C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic
9#13068448C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000C2212yes—
14C2×Q8×Dic11C2212yes—
15#10623263—24no—
16#10623263C418yescomplemented
17C2×#66951—22no—
18C2×#66950—21no—
19C2×#66945—21no—
20C2×#66940—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66879C2212yes—
32C2×Dic11⋊C8C2212yes—
33#10622589C2212yes—
34C4⋊C4×Dic11C2212yes—
35#10622586—21no—
36#10622585—22no—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622292—24no—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2312yes—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#67000—24no—
59#67000C2×C418yes—
60Q8×Dic11—24no—
61Q8×Dic11C2×C418yes—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4D412yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66951—216no—
79#66950—28no—
80#66945—28no—
81#66940—44no—
82C4×D44—22no—
83C4×D44C2×C414yes—
84C4×Dic22C2×C414yes—
85C4×Dic22D414yes—
86C11×#103—24no—
87C11×#103—42no—
88C4×C8×C11—22no—
89#66899—24no—
90#66899—42no—
91C11⋊#95—21no—
92C11⋊#95—22no—
93#66885—22no—
94#66885—22no—
95#66879—24no—
96Dic11⋊C8—24no—
97#66873—42no—
98C4⋊(C11⋊C8)—22no—
99#22544—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11C22×C414yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44C22×C412yes—
123C2×C4×D11—24no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22C22⋊C414yes—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—81no—
141C42×C11C22×C412yes—
142C42×C11C2×D412yes—
143(C2×D11)⋊C4—28no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—24no—
146C4⋊Dic11—28no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11C22⋊C414yes—
152C4⋊Dic11C22×C412yes—
153C4⋊Dic11#4112yes—
154Dic11⋊C4—44no—
155Dic11⋊C4—82no—
156Dic11⋊C4C22⋊C418yes—
157C4×Dic11—28no—
158C4×Dic11—44no—
159C4×Dic11—42no—
160C4×Dic11C22×C414yes—
161C4×Dic11C2×D414yes—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×#556—111no—
166C2×#446—111no—
167Q8×C4⋊C4—111no—
168#1983—112no—
169#1981—111no—
170#1959—112no—
171#1956D1111yescharacteristic, complemented
172#1803—112no—
173#1802—111no—
174#1763—112no—
175C4×#102—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184Q8×C11—24no—
185Q8×C11—24no—
186Q8×C11—42no—
187Q8×C11—42no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11C2×C22⋊C414yes—
220C2×Dic11C2×C22⋊C414yes—
221D44—22no—
222D44—22no—
223D44—41no—
224D44—41no—
225C4×D11—48no—
226Dic22—28no—
227C8×C11—22no—
228C8×C11—41no—
229C11⋊C8—42no—
230#556—118no—
231#556—224no—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#126—222no—
234C2×#124—112no—
235C2×C22⋊Q8—221no—
236C2×C4×Q8—111no—
237C2×C4×Q8—112no—
238C2×C4×Q8—221no—
239C2×C4×D4—111no—
240C2×#117—221no—
241#446—224no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8—111no—
244C2×#103—112no—
245C2×#103—112no—
246C2×#103C2×D1112yes—
247C2×#103C2×D1112yes—
248C2×#102—111no—
249C2×#102—111no—
250C2×#102—112no—
251C2×#97—112no—
252C2×C4×C8C2×D1111yescharacteristic
253#389—222no—
254#389—221no—
255#384—112no—
256#384C2×D1111yescharacteristic
257C4×C4⋊C4—112no—
258C4×C4⋊C4—111no—
259#340—111no—
260#340—111no—
261#340—112no—
262C22×C11C22×C22⋊C411yescharacteristic
263C22×C11#54811yescharacteristic
264C22×C11#55011yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11#57711yescharacteristic
268C22×C11#57811yescharacteristic
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—44no—
278C4×C11—82no—
279C4×C11#41714yes—
280C4×C11C4×#4111yescharacteristic
281C4×C11#52011yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11#55011yescharacteristic
284Dic11—24no—
285Dic11—24no—
286Dic11—42no—
287Dic11—42no—
288Dic11—81no—
289C22×Q8—111no—
290C22×Q8C22×D1112yes—
291C22×D4—111no—
292C23×C4—221no—
293C22×C8—112no—
294C22×C8C22×D1111yescharacteristic
295C22×C8C22×D1111yescharacteristic
296C4⋊Q8—22no—
297C4⋊Q8C4×D1114yes—
298#126—2216no—
299#124—118no—
300#124—224no—
301C22⋊Q8—228no—
302C4×Q8—114no—
303C4×Q8—114no—
304C4×Q8—118no—
305C4×Q8—224no—
306C4×Q8—444no—
307C4×D4—114no—
308C4×D4—222no—
309#117—228no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4C22×D1112yes—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—221no—
326C2×C42—112no—
327C2×C42—222no—
328C2×C42—222no—
329C2×C42—221no—
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—224no—
332C4⋊C8—222no—
333#103—24no—
334#103—42no—
335#103—224no—
336#103—442no—
337#102—222no—
338#102—222no—
339#102—442no—
340#97—224no—
341C4×C8—22no—
342#95—222no—
343#95—221no—
344C2×C11#234111yescharacteristic
345C2×C11C2×#41711yescharacteristic
346C2×C11#289811yescharacteristic
347C2×C11#336711yescharacteristic
348C2×C11#336911yescharacteristic
349C2×C11#339711yescharacteristic
350C2×C11#339811yescharacteristic
351D11—82no—
352C24—221no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—114no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8C2×C4×D1114yes—
362C2×D4—112no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—224no—
375C22×C4—221no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8#434112yes—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—81no—
396C4⋊C4—114no—
397C4⋊C4—118no—
398C4⋊C4—112no—
399C4⋊C4—112no—
400C4⋊C4—228no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—444no—
406C4⋊C4—882no—
407C22⋊C4—228no—
408C22⋊C4—228no—
409C22⋊C4—224no—
410C42—114no—
411C42—114no—
412C42—228no—
413C42—444no—
414C42—442no—
415C42C2×C4×D1112yes—
416C42D4×D1112yes—
417C11#2254411yescharacteristic, complemented, Sylow
418C23—222no—
419C23—441no—
420C23—441no—
421C23—441no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23C2×D4×D1111yescharacteristic
426Q8—24no—
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—228no—
431D4—222no—
432D4—222no—
433D4—441no—
434D4—441no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—114no—
444C2×C4—114no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—448no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4#6696712yes—
462C2×C4#6697112yes—
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4C2×#434111yescharacteristic
466C2×C4#6703711yescharacteristic
467C2×C4#41×D1111yescharacteristic
468C2×C4#6704311yescharacteristic
469C8—22no—
470C8—41no—
471C8—442no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22C2×C22⋊C4×D1111yescharacteristic
480C22#1062320811yescharacteristic
481C22#1062324911yescharacteristic
482C22C2×#6696711yescharacteristic
483C22#1062329311yescharacteristic
484C22C2×#6697111yescharacteristic
485C22#1062329711yescharacteristic
486C4—22no—
487C4—44no—
488C4—82no—
489C4—224no—
490C4—224no—
491C4—442no—
492C4—442no—
493C4—881no—
494C4#1062241614yes—
495C4C4×#434111yescharacteristic
496C4#1062307711yescharacteristic
497C4#1062312911yescharacteristic
498C4#1062313011yescharacteristic
499C2—882no—
500C2#1307145511yescharacteristic
501C2C2×#1062241611yescharacteristic
502C2#1307714411yescharacteristic
503C2#1308133911yescharacteristic
504C2#1308136111yescharacteristic
505C2#1308164111yescharacteristic
506C2#1308165211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1956D11
hypocenterC11#22544
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. #13071528C2semidirect
5. #13069540C2semidirect
7. #13068619C2semidirect
9. #13068448C2semidirect
11. C11×#1956C2semidirect
16. #10623263C4semidirect
171. #1956D11semidirect
417. C11#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106222922
#130715282
#130695452
#130695402
#130694292
#130686192
#130686132
#130684482
C4×#668852
C11×#19562
#2254411