Finite Group Databasebeta

← #14770010

Subgroups — #14770010

Order 2816.

1258 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic
3#13071516C211yesmaximal, characteristic
4#13069576C211yesmaximal, characteristic, complemented
5#13069563C211yesmaximal, characteristic, complemented
6#13069036C212yesmaximal, complemented
7#13068920C212yesmaximal, complemented
8#13068705C212yesmaximal, complemented
9C4×#66899C211yesmaximal, characteristic, complemented
10D11×#340C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×C8×D11C2212yes—
15#10623110—24no—
16#10623110C418yescomplemented
17C2×#66949—22no—
18C2×#66946—21no—
19C2×C4⋊C4×D11C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×C4×D44—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66923—21no—
24C2×#66922C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2212yes—
31#10622602—22no—
32#10622600C2212yes—
33#10622586—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622447—24no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D44D411yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11—22no—
48C22×C4×D11C2312yes—
49C22×Dic22—21no—
50C22×C8×C11C2312yes—
51C4×Q8×C11—22no—
52C4×Q8×C11C2×C414yescomplemented
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60#66999—24no—
61#66999C2×C418yescomplemented
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×C8×D11—24no—
77C2×C8×D11—24no—
78C2×C8×D11—42no—
79#66949—216no—
80#66946—44no—
81C4⋊C4×D11—24no—
82C4⋊C4×D11—24no—
83C4⋊C4×D11—42no—
84C4⋊C4×D11C2×C418yescomplemented
85C4×D44—28no—
86C4×D44C2×C414yes—
87C4×D44D414yes—
88#66923—28no—
89#66922—22no—
90#66922C2×C414yescomplemented
91C11×C4⋊C8—22no—
92C11×#103—42no—
93#66899—22no—
94#66899—22no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97(C2×D11)⋊C8—24no—
98C4×C11⋊C8—22no—
99#22487—111nomaximal, Sylow
100C23×D11C2×D412yes—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11C2×D412yes—
117C2×D44C22⋊C414yes—
118C2×D44SD1614yes—
119C2×D44Q1614yes—
120C2×C4×D11—28no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—82no—
128C2×C4×D11—82no—
129C2×C4×D11—82no—
130C2×C4×D11C22×C414yes—
131C2×C4×D11C2×D414yes—
132C2×Dic22—24no—
133C2×Dic22—81no—
134C2×Dic22—81no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4C22×C412yes—
145C42×C11—24no—
146C42×C11C22×C412yes—
147C42×C11C2×D412yes—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4C22⋊C418yes—
151C4⋊Dic11—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C22⋊C414yes—
157C4⋊Dic11C22×C414yes—
158C4⋊Dic11#4112yes—
159Dic11⋊C4—28no—
160Dic11⋊C4—28no—
161Dic11⋊C4—44no—
162C4×Dic11—42no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8#4112yes—
169C8×D11—48no—
170C2×#554—111no—
171C2×C8×D4—111no—
172D4×C4⋊C4—111no—
173#1990—111no—
174#1987—111no—
175#1892—112no—
176#1872—112no—
177#1824—112no—
178#1803D1111yescharacteristic, complemented
179C4×#103—111no—
180C2×#340—112no—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11C2×C22⋊C414yes—
187C22×D11C2×SD1614yes—
188C22×D11C2×Q1614yes—
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—41no—
192Q8×C11—41no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11C2×SD1612yes—
207C2×C4×C11C2×Q1612yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—22no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11C2×C22⋊C414yes—
226D44#103116yescomplemented
227C4×D11—24no—
228C4×D11—24no—
229C4×D11—24no—
230C4×D11—24no—
231C4×D11—88no—
232C4×D11—88no—
233Dic22—84no—
234C8×C11—42no—
235C11⋊C8—22no—
236C11⋊C8—41no—
237C23×C8—112no—
238#554—118no—
239#554—224no—
240C2×C4⋊Q8—111no—
241C2×#125—221no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—222no—
244C2×C4×Q8C2×D1111yescharacteristic
245C2×C4×D4—111no—
246C2×C4×D4—221no—
247C2×C4×D4—221no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4—112no—
250C8×D4—224no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×#103—111no—
253C2×#103—111no—
254C2×#103C2×D1112yes—
255C2×C22⋊C8—112no—
256C2×C4×C8—111no—
257#389—221no—
258#385—222no—
259#384C2×D1111yescharacteristic
260#380—112no—
261C4×C4⋊C4—111no—
262#340—112no—
263#340—112no—
264#340—111no—
265#340—112no—
266#340—112no—
267#340—111no—
268#340C2×D1112yes—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54611yescharacteristic
271C22×C11#54711yescharacteristic
272C22×C11C22×SD1611yescharacteristic
273C22×C11C22×Q1611yescharacteristic
274C22×C11#57611yescharacteristic
275C22×C11#57711yescharacteristic
276C2×D11—24no—
277C2×D11—24no—
278C2×D11—24no—
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—24no—
282C2×D11C2×#10318yes—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11C2×#10314yes—
288C4×C11C4×#4111yescharacteristic
289C4×C11#52011yescharacteristic
290C4×C11#54611yescharacteristic
291C4×C11#54711yescharacteristic
292Dic11—24no—
293Dic11—44no—
294Dic11—42no—
295Dic11—81no—
296C22×Q8—221no—
297C22×Q8C22×D1111yescharacteristic
298C22×D4—111no—
299C23×C4—112no—
300C23×C4—222no—
301C23×C4—222no—
302C22×C8—111no—
303C22×C8—111no—
304C22×C8—224no—
305C22×C8—224no—
306C22×C8—442no—
307C22×C8C22×D1112yes—
308C4⋊Q8—114no—
309C4⋊Q8—222no—
310#125—228no—
311C22⋊Q8—118no—
312C22⋊Q8—2216no—
313C22⋊Q8—224no—
314C4×Q8—22no—
315C4×Q8C4×D1114yescomplemented
316C4×D4—114no—
317C4×D4—114no—
318C4×D4—228no—
319C4×D4—444no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4—224no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—442no—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—112no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C42—21no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—22no—
344#103—42no—
345#103—222no—
346#103—222no—
347C22⋊C8—224no—
348C4×C8—222no—
349#95—222no—
350#95—221no—
351C2×C11#233911yescharacteristic
352C2×C11C22×#10311yescharacteristic
353C2×C11#289711yescharacteristic
354C2×C11#329511yescharacteristic
355C2×C11#329911yescharacteristic
356C2×C11#333511yescharacteristic
357C2×C11#333811yescharacteristic
358D11—28no—
359C24—112no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—224no—
366C2×Q8—881no—
367C2×Q8—881no—
368C2×Q8C2×C4×D1112yes—
369C2×D4—114no—
370C2×D4—114no—
371C2×D4—114no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—112no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—228no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—444no—
387C22×C4—444no—
388C22×C4—882no—
389C22×C4—882no—
390C22×C4—882no—
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1111yescharacteristic
393C22×C4C23×D1111yescharacteristic
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—112no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—448no—
404C4⋊C4—24no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—81no—
410C4⋊C4—114no—
411C4⋊C4—114no—
412C4⋊C4—112no—
413C4⋊C4—228no—
414C4⋊C4—228no—
415C4⋊C4—224no—
416C4⋊C4—222no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—444no—
421C4⋊C4C2×C4×D1112yes—
422C22⋊C4—118no—
423C22⋊C4—228no—
424C22⋊C4—444no—
425C42—24no—
426C42—442no—
427C42C2×C4×D1112yes—
428C42D4×D1112yes—
429C11#2248711yescharacteristic, complemented, Sylow
430C23—114no—
431C23—114no—
432C23—114no—
433C23—222no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23C2×D4×D1111yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—41no—
441Q8—41no—
442Q8—884no—
443D4—1116no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—114no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—222no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—888no—
472C2×C4—888no—
473C2×C4C22⋊C4×D1112yes—
474C2×C4C22⋊C4×D1112yes—
475C2×C4SD16×D1112yes—
476C2×C4Q16×D1112yes—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4#6703711yescharacteristic
480C2×C4#6704011yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C8—42no—
484C8—222no—
485C8—441no—
486C22—118no—
487C22—224no—
488C22—224no—
489C22—224no—
490C22—224no—
491C22—224no—
492C22—224no—
493C22C2×C22⋊C4×D1111yescharacteristic
494C22#1062314311yescharacteristic
495C22#1062316211yescharacteristic
496C22C2×SD16×D1111yescharacteristic
497C22C2×Q16×D1111yescharacteristic
498C22#1062330511yescharacteristic
499C22#1062330911yescharacteristic
500C4—22no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—224no—
505C4—442no—
506C4—444no—
507C4—881no—
508C4D11×#10314yes—
509C4#1062303511yescharacteristic
510C4#1062305311yescharacteristic
511C4#1062314311yescharacteristic
512C4#1062316211yescharacteristic
513C2—228no—
514C2#1307144411yescharacteristic
515C2C2×D11×#10311yescharacteristic
516C2#1307714011yescharacteristic
517C2#1308044311yescharacteristic
518C2#1308049511yescharacteristic
519C2#1308097611yescharacteristic
520C2#1308100711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22487
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13069576C2semidirect
5. #13069563C2semidirect
6. #13069036C2semidirect
7. #13068920C2semidirect
8. #13068705C2semidirect
9. C4×#66899C2semidirect
10. D11×#340C2semidirect
11. C11×#1803C2semidirect
16. #10623110C4semidirect
52. C4×Q8×C11C2×C4semidirect
61. #66999C2×C4semidirect
84. C4⋊C4×D11C2×C4semidirect
90. #66922C2×C4semidirect
178. #1803D11semidirect
226. D44#103semidirect
315. C4×Q8C4×D11semidirect
429. C11#22487semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106224472
#130715162
#130695762
#130695632
#130690362
#130689202
#130687052
C4×#668992
D11×#3402
C11×#18032
#2248711