Finite Group Databasebeta

← #14770371

Subgroups — #14770371

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2#13071573C211yesmaximal, characteristic, complemented
3#13069581C212yesmaximal, complemented
4#13069577C211yesmaximal, characteristic, complemented
5#13069571C212yesmaximal, complemented
6#13069563C211yesmaximal, characteristic, complemented
7#13068627C212yesmaximal
8#13068617C211yesmaximal, characteristic
9C4×#66885C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14#10623110—24no—
15#10623110C418yescomplemented
16C2×#66949—22no—
17C2×C4⋊C4×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2212yes—
20C2×#66923C2212yes—
21C2×#66922C2211yescharacteristic
22C8×Q8×C11—24no—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×C4×C8×C11C2212yes—
27#10622843—21no—
28C2×#66885C2212yes—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31#10622594—22no—
32C4⋊C4×Dic11—21no—
33#10622549C2212yes—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622189C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2212yes—
44C22×Q8×C11D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11C2×C414yes—
53C4×Q8×C11D414yes—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2312yes—
58#66999—28no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73#66949—216no—
74C4⋊C4×D11—28no—
75C4×D44—24no—
76C4×D44—22no—
77C4×D44C2×C418yes—
78C4×D44C2×C414yes—
79#66923—24no—
80#66923C2×C418yes—
81#66922—22no—
82#66922C2×C414yes—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—24no—
85C4×C8×C11—22no—
86C4×C8×C11—24no—
87C11⋊#95—22no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91#66885—24no—
92#66885—22no—
93#66885Q814yescomplemented
94#22519—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22⋊C414yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—22no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44C22×C412yes—
113C2×D44C2×Q812yes—
114C2×D44#4112yes—
115C2×C4×D11—24no—
116C2×C4×D11—28no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—82no—
120C2×C4×D11—82no—
121C2×Dic22—24no—
122C2×Dic22—81no—
123C2×Dic22—81no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11C2×Q812yes—
133C11×C4⋊C4C22⋊C414yes—
134C11×C4⋊C4C22⋊C418yes—
135C42×C11C22×C412yes—
136C42×C11C22×C414yes—
137C42×C11C2×D412yes—
138C42×C11C2×D414yes—
139(C2×D11)⋊C4—24no—
140(C2×D11)⋊C4—28no—
141C4⋊Dic11—24no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11—81no—
151C4⋊Dic11C22×C414yes—
152C4⋊Dic11C22×C412yes—
153C4⋊Dic11C2×Q812yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156C4×Dic11—42no—
157C4×Dic11—82no—
158C2×#554—111no—
159C2×C8×Q8D1111yescharacteristic, complemented
160#2355—111no—
161#1991—112no—
162#1990—111no—
163#1989—112no—
164#1987—111no—
165#1804—112no—
166#1802—111no—
167C4×#102—111no—
168C4×#102—112no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177Q8×C11—28no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11C2×C22⋊C414yes—
185C2×C4×C11C2×C22⋊C414yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11#13512yes—
189C2×C4×C11#13512yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×Q811yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211D44—22no—
212D44—22no—
213D44—22no—
214D44C4×Q814yes—
215C4×D11—48no—
216C4×D11—88no—
217Dic22—84no—
218C8×C11—22no—
219C8×C11—41no—
220C8×C11—42no—
221#554—118no—
222#554—224no—
223C2×C4⋊Q8—111no—
224C2×#125—112no—
225C2×C22⋊Q8—221no—
226C2×C22⋊Q8—222no—
227C2×C4×Q8C2×D1111yescharacteristic
228C2×C4×D4—111no—
229C2×C4×D4—112no—
230C22×C4⋊C4—221no—
231C8×Q8—24no—
232C2×C4⋊C8C2×D1111yescharacteristic
233C2×C4⋊C8C2×D1112yes—
234C2×#102—111no—
235C2×#102—112no—
236C2×#102—111no—
237C2×C4×C8C2×D1111yescharacteristic
238C2×C4×C8C2×D1112yes—
239#391—221no—
240#387—222no—
241#384—111no—
242#382—112no—
243C4×C4⋊C4—111no—
244C4×C4⋊C4—112no—
245C4×C4⋊C4—221no—
246#340—112no—
247#340—112no—
248#340—112no—
249#340—112no—
250#340—111no—
251#340—112no—
252#340—111no—
253C22×C11C22×C22⋊C411yescharacteristic
254C22×C11#54811yescharacteristic
255C22×C11D4×Q811yescharacteristic
256C22×C11C2×#13511yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57711yescharacteristic
260C2×D11—24no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C4×C11—24no—
268C4×C11—22no—
269C4×C11—24no—
270C4×C11#41614yes—
271C4×C11C2×C4×Q811yescharacteristic
272C4×C11#51911yescharacteristic
273C4×C11#54811yescharacteristic
274C4×C11D4×Q811yescharacteristic
275Dic11—42no—
276Dic11—42no—
277Dic11—44no—
278Dic11—81no—
279Dic11—82no—
280C22×Q8—221no—
281C22×Q8D4411yescharacteristic
282C22×D4—111no—
283C23×C4—221no—
284C23×C4—222no—
285C22×C8C22×D1112yes—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—114no—
289C4⋊Q8—222no—
290#125—118no—
291#125—224no—
292C22⋊Q8—228no—
293C22⋊Q8—2216no—
294C4×Q8C4×D1114yes—
295C4×Q8C22⋊D1114yes—
296C4×D4—118no—
297C4×D4—114no—
298C4×D4—224no—
299C4×D4—222no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—228no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4D4411yescharacteristic
312C2×C4⋊C4D4412yes—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—222no—
315C2×C42—221no—
316C2×C42—222no—
317C2×C42C22×D1112yes—
318C2×C42C22×D1111yescharacteristic
319C4⋊C8—24no—
320C4⋊C8—22no—
321#102—114no—
322#102—224no—
323#102—222no—
324C4×C8—24no—
325C4×C8—22no—
326#95—221no—
327#95—222no—
328#95—222no—
329#95—222no—
330C2×C11Q8×C22⋊C411yescharacteristic
331C2×C11C2×#41611yescharacteristic
332C2×C11#289711yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#336111yescharacteristic
335C2×C11#338011yescharacteristic
336C2×C11#338111yescharacteristic
337D11—44no—
338C24—221no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—224no—
342C2×Q8—881no—
343C2×Q8—881no—
344C2×Q8(C2×D11)⋊C414yes—
345C2×D4—112no—
346C2×D4—112no—
347C2×D4—112no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—224no—
355C22×C4—228no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—882no—
361C22×C4—882no—
362C22×C4C2×D4412yes—
363C22×C4C2×D4412yes—
364C22×C4C2×D4411yescharacteristic
365C22×C4C2×D4411yescharacteristic
366C22×C4C23×D1111yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8Q8×D1112yes—
376C4⋊C4—112no—
377C4⋊C4—114no—
378C4⋊C4—112no—
379C4⋊C4—228no—
380C4⋊C4—224no—
381C4⋊C4—228no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—222no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—442no—
390C4⋊C4—881no—
391C4⋊C4(C2×D11)⋊C414yes—
392C4⋊C4(C2×D11)⋊C418yes—
393C22⋊C4—224no—
394C22⋊C4—228no—
395C42—442no—
396C42—882no—
397C42C2×C4×D1114yes—
398C42C2×C4×D1112yes—
399C42C2×C22⋊D1114yes—
400C42C2×C22⋊D1112yes—
401C11#2251911yescharacteristic, complemented, Sylow
402C23—222no—
403C23—222no—
404C23—222no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23C22×D4411yescharacteristic
410Q8—28no—
411Q8—884no—
412D4—114no—
413D4—222no—
414D4—222no—
415D4—222no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—222no—
423C2×C4—224no—
424C2×C4—222no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—442no—
429C2×C4—441no—
430C2×C4—442no—
431C2×C4—448no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—888no—
439C2×C4#6695712yes—
440C2×C4#6695712yes—
441C2×C4C2×(C2×D11)⋊C414yes—
442C2×C4C2×(C2×D11)⋊C412yes—
443C2×C4C2×(C2×D11)⋊C414yes—
444C2×C4C2×(C2×D11)⋊C412yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×Q8×D1111yescharacteristic
447C2×C4#6704011yescharacteristic
448C2×C4#41×D1111yescharacteristic
449C2×C4#6704311yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—22no—
452C8—42no—
453C8—41no—
454C22—224no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22Q8×D4411yescharacteristic
462C22#1062310711yescharacteristic
463C22C2×#6695711yescharacteristic
464C22C2×#6695711yescharacteristic
465C22#1062328211yescharacteristic
466C22#1062328311yescharacteristic
467C22C22×(C2×D11)⋊C411yescharacteristic
468C4—24no—
469C4—24no—
470C4—22no—
471C4—442no—
472C4—442no—
473C4—444no—
474C4—881no—
475C4—882no—
476C4#1062272614yes—
477C4C4×Q8×D1111yescharacteristic
478C4#1062310311yescharacteristic
479C4Q8×C22⋊D1111yescharacteristic
480C4#1062336211yescharacteristic
481C2—444no—
482C2Q8×(C2×D11)⋊C411yescharacteristic
483C2C2×#1062272611yescharacteristic
484C2#1307714311yescharacteristic
485C2#1308126711yescharacteristic
486C2#1308127811yescharacteristic
487C2#1308148411yescharacteristic
488C2#1308149311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11#22519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13071573C2semidirect
3. #13069581C2semidirect
4. #13069577C2semidirect
5. #13069571C2semidirect
6. #13069563C2semidirect
11. C2×C8×Q8×C11C2semidirect
15. #10623110C4semidirect
93. #66885Q8semidirect
159. C2×C8×Q8D11semidirect
401. C11#22519semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
#130715732
#130695812
#130695772
#130695712
#130695632
#130686272
#130686172
C4×#668852
C2×C8×Q8×C112
#2251911