Finite Group Databasebeta

← #14770591

Subgroups — #14770591

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×#10622443C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069545C212yesmaximal, complemented
5#13069542C211yesmaximal, characteristic
6#13069424C212yesmaximal, complemented
7#13069421C211yesmaximal, characteristic
8#13068625C212yesmaximal, complemented
9C4×#66899C211yesmaximal, characteristic, complemented
10#13068430C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2212yes—
14#10623116—24no—
15#10623116C418yescomplemented
16C2×#66947—22no—
17C2×#66946C2212yes—
18C2×#66928—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44—21no—
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2212yes—
24C11×#384C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×Dic11⋊C8C2212yes—
30C2×C8×Dic11C2212yes—
31#10622591—22no—
32#10622590C2212yes—
33C4⋊C4×Dic11—21no—
34C4⋊C4×Dic11C2212yes—
35#10622587—21no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622443—24no—
41C11×#340C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×Dic22D411yescharacteristic
50C22×C8×C11C2312yes—
51C4×Q8×C11—22no—
52C4×Q8×C11C2×C414yes—
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#67000—24no—
61#67000C2×C418yes—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4D412yes—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74#66947—216no—
75#66946—24no—
76#66946C2×C418yes—
77#66928—28no—
78#66927—22no—
79#66927C2×C414yes—
80C4×D44—28no—
81C4×Dic22C2×C414yes—
82C4×Dic22D414yes—
83C11×C4⋊C8—22no—
84C11×#103—42no—
85#66899—22no—
86#66899—22no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91#66885—24no—
92#66885—42no—
93Dic11⋊C8—24no—
94C8×Dic11—24no—
95#66873—24no—
96#66873—42no—
97C4×C11⋊C8—22no—
98#22543—111nomaximal, Sylow
99C23×D11—22no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11C22×C412yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×D44—24no—
117C2×D44—24no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—81no—
126C2×D44—81no—
127C2×D44C22×C414yes—
128C2×C4×D11—28no—
129C2×C4×D11—82no—
130C2×C4×D11—82no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C22⋊C414yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C11×C4⋊C4C22×C412yes—
144C42×C11—24no—
145C42×C11C22×C412yes—
146C42×C11C2×D412yes—
147(C2×D11)⋊C4—28no—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—28no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11C22⋊C414yes—
154C4⋊Dic11#4112yes—
155Dic11⋊C4C22⋊C418yes—
156C4×Dic11—42no—
157C4×Dic11—82no—
158C4×Dic11C22×C414yes—
159C4×Dic11C2×D414yes—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8#4112yes—
166C2×#559—111no—
167C2×C8×Q8—111no—
168#2355—111no—
169#1983—112no—
170#1982—111no—
171#1958—112no—
172#1957—111no—
173#1804—112no—
174#1803D1111yescharacteristic, complemented
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—22no—
186Q8×C11—22no—
187Q8×C11—41no—
188Q8×C11—41no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11#13512yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C2×C22⋊C414yes—
222D44—24no—
223D44—24no—
224D44—42no—
225D44—42no—
226D44—48no—
227D44—84no—
228C4×D11—88no—
229Dic22—28no—
230C8×C11—42no—
231C11⋊C8—22no—
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—112no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#103—111no—
247C2×#103—111no—
248C2×#103C2×D1112yes—
249C2×#102—112no—
250C2×#102—112no—
251C2×#102—112no—
252C2×#102—112no—
253C2×C4×C8—112no—
254C2×C4×C8—111no—
255#391—221no—
256#387—222no—
257#384C2×D1111yescharacteristic
258#382—112no—
259C4×C4⋊C4—112no—
260C4×C4⋊C4—111no—
261C4×C4⋊C4—221no—
262#340—111no—
263#340—111no—
264#340C2×D1112yes—
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—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—82no—
283C4×C11#41614yes—
284C4×C11C4×#4111yescharacteristic
285C4×C11#52011yescharacteristic
286C4×C11#54811yescharacteristic
287C4×C11#55011yescharacteristic
288Dic11—24no—
289Dic11—24no—
290Dic11—42no—
291Dic11—81no—
292C22×Q8—111no—
293C22×Q8C22×D1111yescharacteristic
294C22×D4—112no—
295C22×D4—221no—
296C22×D4—221no—
297C23×C4—222no—
298C22×C8—111no—
299C22×C8—111no—
300C22×C8C22×D1112yes—
301#127—114no—
302#127—222no—
303#124—118no—
304#124—228no—
305#124—224no—
306#123—2216no—
307C4×Q8—22no—
308C4×Q8—114no—
309C4×Q8—114no—
310C4×Q8C4×D1114yes—
311C4×D4—118no—
312C4×D4—228no—
313C4×D4—224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
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—112no—
328C2×C42—221no—
329C2×C42—222no—
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—22no—
332C4⋊C8—224no—
333#103—42no—
334#103—222no—
335#103—222no—
336#102—224no—
337#102—224no—
338#102—442no—
339#102—442no—
340C4×C8—224no—
341C4×C8—222no—
342#95—222no—
343#95—222no—
344#95—222no—
345#95—221no—
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—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—114no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8C2×C4×D1112yes—
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—112no—
380C22×C4—112no—
381C22×C4—228no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—882no—
385C22×C4—882no—
386C22×C4D4×D1111yescharacteristic
387C22×C4D4×D1111yescharacteristic
388C22×C4C23×D1111yescharacteristic
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—112no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—221no—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—81no—
404C4⋊C4—114no—
405C4⋊C4—118no—
406C4⋊C4—112no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4C2×C4×D1112yes—
411C22⋊C4—228no—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C42—24no—
415C42—114no—
416C42—114no—
417C42—442no—
418C42—882no—
419C42C2×C4×D1112yes—
420C42D4×D1112yes—
421C11#2254311yescharacteristic, complemented, Sylow
422C23—224no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23C2×D4×D1111yescharacteristic
430Q8—22no—
431Q8—22no—
432Q8—41no—
433Q8—41no—
434Q8—228no—
435D4—224no—
436D4—224no—
437D4—442no—
438D4—442no—
439D4—448no—
440D4—884no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—114no—
453C2×C4—114no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—888no—
465C2×C4C22⋊C4×D1112yes—
466C2×C4C22⋊C4×D1112yes—
467C2×C4#6696912yes—
468C2×C4#6697212yes—
469C2×C4C22×C4×D1111yescharacteristic
470C2×C4C2×D4×D1111yescharacteristic
471C2×C4#6703711yescharacteristic
472C2×C4#6704011yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C8—42no—
476C8—222no—
477C8—441no—
478C22—444no—
479C22—444no—
480C22—444no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22—882no—
485C22C2×C22⋊C4×D1111yescharacteristic
486C22#1062313011yescharacteristic
487C22#1062316411yescharacteristic
488C22C2×#6696911yescharacteristic
489C22C2×#6697211yescharacteristic
490C22#1062330511yescharacteristic
491C22#1062330911yescharacteristic
492C4—22no—
493C4—42no—
494C4—42no—
495C4—82no—
496C4—224no—
497C4—224no—
498C4—442no—
499C4—881no—
500C4#1062241714yes—
501C4#1062303511yescharacteristic
502C4#1062305311yescharacteristic
503C4#1062313011yescharacteristic
504C4#1062316411yescharacteristic
505C2—884no—
506C2#1307145311yescharacteristic
507C2C2×#1062241711yescharacteristic
508C2#1307714011yescharacteristic
509C2#1308127511yescharacteristic
510C2#1308131111yescharacteristic
511C2#1308161111yescharacteristic
512C2#1308162711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22543
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
2. C2×#10622443C2semidirect
3. #13071575C2semidirect
4. #13069545C2semidirect
6. #13069424C2semidirect
8. #13068625C2semidirect
9. C4×#66899C2semidirect
10. #13068430C2semidirect
11. C11×#1803C2semidirect
15. #10623116C4semidirect
174. #1803D11semidirect
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×#106224432
#130715752
#130695452
#130695422
#130694242
#130694212
#130686252
C4×#668992
#130684302
C11×#18032
#2254311