Finite Group Databasebeta

← #14752534

Subgroups — #14752534

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13068493C211yesmaximal, characteristic, complemented
5#13068492C211yesmaximal, characteristic, complemented
6#13068491C211yesmaximal, characteristic, complemented
7#13068490C211yesmaximal, characteristic, complemented
8#13068489C211yesmaximal, characteristic, complemented
9#13068488C211yesmaximal, characteristic, complemented
10#13068487C211yesmaximal, characteristic, complemented
11#13068385C211yesmaximal, characteristic
12#13068383C211yesmaximal, characteristic
13#13068381C211yesmaximal, characteristic
14#13068381C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic, complemented
16C2×#66925C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622600C412yes—
37#10622589C412yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622448C418yescomplemented
46#10622318C418yescomplemented
47#10622280C412yes—
48#10622263C412yes—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4C2×C412yes—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×C4⋊Dic11C2×C412yes—
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×Dic11⋊C4C2×C412yes—
74C2×Dic11⋊C4C2×C412yes—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66925—41no—
85#66925—41no—
86#66925—41no—
87#66925—41no—
88C42×D11C2×C414yes—
89C42×D11C2×C414yes—
90C11×C4⋊C8C2×C414yes—
91C11×#97—41no—
92C11×#97C2×C414yes—
93C4×C8×C11—41no—
94C11×#95C2×C412yes—
95C11⋊#95C2×C412yes—
96C11⋊#95C2×C412yes—
97C11⋊#95C2×C412yes—
98(C2×D11)⋊C8C2×C414yes—
99(C2×D11)⋊C8C2×C414yes—
100(C2×D11)⋊C8C2×C414yes—
101(C2×D11)⋊C8C2×C414yes—
102#66879—41no—
103#66879—41no—
104#66879C2×C414yes—
105#66879C2×C414yes—
106Dic11⋊C8C2×C414yes—
107Dic11⋊C8C2×C414yes—
108C8×Dic11—41no—
109C8×Dic11—41no—
110C4⋊(C11⋊C8)C2×C414yes—
111#66867—41no—
112#66867C2×C414yes—
113C4×C11⋊C8—41no—
114#20539—111nomaximal, Sylow
115C23×D11C22×C411yescharacteristic
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11C22×C412yes—
122C22×Dic11C22×C412yes—
123C22×Dic11C22×C411yescharacteristic
124C22×Dic11C22×C411yescharacteristic
125C22×Dic11C22×C411yescharacteristic
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C4×D11C4214yes—
133C2×C4×D11C4214yes—
134C2×C4×D11C22×C412yes—
135C2×C4×D11C22×C412yes—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C22×C412yes—
145C2×C8×C11C22×C412yes—
146C2×C8×C11C22×C412yes—
147C2×C8×C11C22×C412yes—
148C11×C4⋊C4—42no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11C22×C412yes—
154C42×C11C22×C412yes—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157C4⋊Dic11—42no—
158Dic11⋊C4—42no—
159Dic11⋊C4—42no—
160Dic11⋊C4—42no—
161Dic11⋊C4—42no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11C4214yes—
167C4×Dic11C4214yes—
168C4×Dic11C22×C412yes—
169C4×Dic11C22×C412yes—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8C22×C412yes—
179C2×C11⋊C8C22×C412yes—
180C2×C11⋊C8C22×C412yes—
181C2×C11⋊C8C22×C412yes—
182C2×#432—111no—
183C2×#432—111no—
184#2285—111no—
185#1771—111no—
186#1771—111no—
187#1771—111no—
188#1771—111no—
189#1771—111no—
190#1771—111no—
191#1771—111no—
192#1771D1111yescharacteristic, complemented
193#1750—111no—
194#1750—111no—
195#1750—111no—
196#1750—111no—
197C23×C11C23×C411yescharacteristic
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11C2×C4212yes—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11C2×C4212yes—
212C2×C4×C11C2×C4212yes—
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11C2×C4212yes—
230C2×Dic11C2×C4212yes—
231C2×Dic11C2×C4212yes—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—22no—
236C4×D11—44no—
237C4×D11—44no—
238C8×C11—22no—
239C8×C11—22no—
240C8×C11—22no—
241C8×C11—22no—
242C11⋊C8—22no—
243C11⋊C8—22no—
244C11⋊C8—22no—
245C11⋊C8—22no—
246C2×#117—111no—
247C2×#117—111no—
248C22×C42—111no—
249#432—118no—
250#432—118no—
251C2×C4⋊C8—111no—
252C2×C4⋊C8—111no—
253C2×C4⋊C8—111no—
254C2×C4⋊C8C2×D1111yescharacteristic
255C2×C22⋊C8—111no—
256C2×C22⋊C8—111no—
257C2×C22⋊C8—111no—
258C2×C22⋊C8—111no—
259C2×#97—111no—
260C2×#97—111no—
261C2×#97—111no—
262C2×#97—111no—
263C2×#97—111no—
264C2×#97—111no—
265C2×#97C2×D1111yescharacteristic
266C2×#97C2×D1111yescharacteristic
267C2×C4×C8—111no—
268C2×C4×C8—111no—
269C2×C4×C8—111no—
270C2×C4×C8C2×D1111yescharacteristic
271#384—112no—
272#382—112no—
273#380—112no—
274#380—112no—
275C4×C4⋊C4—111no—
276C4×C4⋊C4—111no—
277C4×C4⋊C4—111no—
278C4×C4⋊C4C2×D1111yescharacteristic
279#336—111no—
280#336—111no—
281#336—111no—
282#336—111no—
283#336—111no—
284#336—111no—
285#336C2×D1111yescharacteristic
286#336C2×D1111yescharacteristic
287C22×C11C22×C4211yescharacteristic
288C22×C11#51811yescharacteristic
289C22×C11#51911yescharacteristic
290C22×C11#56812yes—
291C22×C11#56812yes—
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—42no—
296C2×D11—42no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11#52011yescharacteristic
302C4×C11#52011yescharacteristic
303C4×C11#52011yescharacteristic
304C4×C11#52011yescharacteristic
305Dic11—22no—
306Dic11—22no—
307Dic11—22no—
308Dic11—42no—
309Dic11—42no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—111no—
313C22×C8—111no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—111no—
317C22×C8C22×D1111yescharacteristic
318C22×C8C22×D1111yescharacteristic
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321#117—441no—
322#117—441no—
323#117—441no—
324#117—441no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4C4×D1112yes—
331C2×C22⋊C4—112no—
332C2×C22⋊C4—112no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—114no—
337C2×C42—114no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42C22×D1111yescharacteristic
341C2×C42C22×D1111yescharacteristic
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—114no—
344C4⋊C8—114no—
345C4⋊C8—114no—
346C4⋊C8C4×D1114yes—
347C22⋊C8—114no—
348C22⋊C8—114no—
349C22⋊C8—114no—
350C22⋊C8—114no—
351#97—41no—
352#97—114no—
353#97—114no—
354#97—114no—
355#97—441no—
356#97—441no—
357#97—441no—
358#97C4×D1114yes—
359C4×C8—41no—
360C4×C8—441no—
361C4×C8—441no—
362C4×C8—441no—
363#95—112no—
364#95—112no—
365#95—112no—
366#95C4×D1112yes—
367C2×C11#227411yescharacteristic
368C2×C11#287311yescharacteristic
369C2×C11#287311yescharacteristic
370C2×C11#298012yes—
371C2×C11#298712yes—
372D11—42no—
373C24—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—114no—
380C22×C4—114no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4C2×C4×D1112yes—
390C22×C4C2×C4×D1112yes—
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4C23×D1111yescharacteristic
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—112no—
403C2×C8—112no—
404C2×C8—112no—
405C2×C8—112no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8C2×C4×D1112yes—
415C2×C8C2×C4×D1112yes—
416C2×C8C2×C4×D1112yes—
417C2×C8C2×C4×D1112yes—
418C4⋊C4—42no—
419C4⋊C4—442no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4—442no—
423C4⋊C4—442no—
424C22⋊C4—442no—
425C22⋊C4—442no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—114no—
431C42—114no—
432C42—112no—
433C42—112no—
434C42—221no—
435C42—221no—
436C42—221no—
437C42—221no—
438C42C2×C4×D1112yes—
439C42C2×C4×D1112yes—
440C11#2053911yescharacteristic, complemented, Sylow
441C23—112no—
442C23—222no—
443C23—222no—
444C23—221no—
445C23—221no—
446C23C22×C4×D1111yescharacteristic
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—112no—
456C2×C4—112no—
457C2×C4—112no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—444no—
473C2×C4—444no—
474C2×C4C42×D1112yes—
475C2×C4C42×D1112yes—
476C2×C4C22×C4×D1111yescharacteristic
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4#6703711yescharacteristic
479C2×C4#6704011yescharacteristic
480C2×C4#6704211yescharacteristic
481C2×C4#6704311yescharacteristic
482C8—22no—
483C8—22no—
484C8—22no—
485C8—22no—
486C8—222no—
487C8—222no—
488C8—222no—
489C8—222no—
490C22—222no—
491C22—222no—
492C22—222no—
493C22—442no—
494C22—442no—
495C22C2×C42×D1111yescharacteristic
496C22#1062307611yescharacteristic
497C22#1062310311yescharacteristic
498C22#1062327612yes—
499C22#1062328112yes—
500C4—22no—
501C4—22no—
502C4—42no—
503C4—42no—
504C4—222no—
505C4—222no—
506C4—222no—
507C4—442no—
508C4—442no—
509C4#1062303511yescharacteristic
510C4#1062305411yescharacteristic
511C4#1062307711yescharacteristic
512C4#1062310511yescharacteristic
513C2—442no—
514C2#1307097011yescharacteristic
515C2#1307703211yescharacteristic
516C2#1307703311yescharacteristic
517C2#1307768412yes—
518C2#1307771912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1771C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#20539
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #13068493C2semidirect
5. #13068492C2semidirect
6. #13068491C2semidirect
7. #13068490C2semidirect
8. #13068489C2semidirect
9. #13068488C2semidirect
10. #13068487C2semidirect
15. C11×#1771C2semidirect
45. #10622448C4semidirect
46. #10622318C4semidirect
192. #1771D11semidirect
440. C11#20539semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
C2×#106223182
#130710202
#130684932
#130684922
#130684912
#130684902
#130684892
#130684882
#130684872
#130683852
#130683832
#130683812
C11×#17712
#2053911