Finite Group Databasebeta

← #15626842

Subgroups — #15626842

Order 2816.

1758 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
1#13082006C211yesmaximal, characteristic
2#13080066C214yesmaximal, complemented
3#13080057C214yesmaximal, complemented
4#13080036C218yesmaximal, complemented
5#13078434C212yesmaximal, complemented
6#13078421C212yesmaximal, complemented
7#13078242C214yesmaximal, complemented
8#13078099C212yesmaximal, complemented
9#13078088C212yesmaximal, complemented
10#13077180C211yesmaximal, characteristic, complemented
11C2×C11×#541C211yesmaximal, characteristic, complemented
12C11×#541—24no—
13C11×#541C2214yes—
14C11×#541C2214yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#125—22no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11C2212yes—
21C2×C11×#117C2211yescharacteristic
22C2×#66995C2214yes—
23#10623322C2212yes—
24C22×#4318C2212yes—
25#10623066C2212yes—
26#10623065C2214yes—
27#10623059—24no—
28#10623049C2212yes—
29#10623046—22no—
30#10623025—22no—
31#10623008C2211yescharacteristic
32C4×#4339C2212yes—
33#10623001C2211yescharacteristic
34#10622838C2214yes—
35#10622703C2218yescomplemented
36#10622696C2218yescomplemented
37#10622679C2218yescomplemented
38#10622676C2218yescomplemented
39#10622665C2218yes—
40#10622664C2218yes—
41#10622662C2218yes—
42#10622661C2218yes—
43#10622644C2214yescomplemented
44#10622641C2218yescomplemented
45#10622640C2214yescomplemented
46#10622635C2218yescomplemented
47#10622634C2214yescomplemented
48#10622633C2214yescomplemented
49#10622612C2214yes—
50#10622612C2214yes—
51#10622579C2214yes—
52#10622577C2214yes—
53#10622537C2212yes—
54#10622537C2212yes—
55C22×Q8×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C2×#4339C2312yes—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8C2314yes—
60C11×#126—28no—
61C11×#126—28no—
62C11×#125—28no—
63C11×#125—28no—
64C11×#125—22no—
65C11×#125C2314yes—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8C2318yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11C2314yes—
71C4×Q8×C11C2314yes—
72C11×#117D414yes—
73C11×#117C2312yes—
74C11×#117C2312yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4D412yes—
83C2×C42×C11—22no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86#67006—22no—
87C2×#4326C2318yes—
88#66995—48no—
89C2×#4325C2318yes—
90#66983—22no—
91#66983C2314yes—
92#66982—22no—
93C4×C22⋊D11—24no—
94C4×C22⋊D11—24no—
95#66979C2312yes—
96#66977—22no—
97#66977C2314yes—
98C2×#4318—44no—
99C2×#4318C2314yes—
100C2×#4318C2314yes—
101C22×C11⋊C8C2314yes—
102#66951—24no—
103#66949—24no—
104#66947—24no—
105#66942—24no—
106#66938—24no—
107#66937—24no—
108#66936—24no—
109#66932—24no—
110#66928C2312yes—
111#66927C2311yescharacteristic
112C4×D44—22no—
113C4×D44C2314yes—
114#66925—22no—
115C42×D11—22no—
116#66923C2312yes—
117#66922C2311yescharacteristic
118#66922C2312yes—
119C4×Dic22—22no—
120C4×Dic22C2314yes—
121#66899C2318yes—
122#66899C2318yes—
123#66874C2318yes—
124#66873C2318yes—
125#66872C2318yes—
126#66871C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C4⋊(C11⋊C8)C2314yes—
129C4⋊(C11⋊C8)C2318yes—
130#60921—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—24no—
135C2×Q8×C11C2414yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—22no—
147C2×C22⋊D11—24no—
148#4339—24no—
149#4339—24no—
150C2×D44—22no—
151C2×D44C2412yes—
152C2×C4×D11—22no—
153C2×C4×D11—24no—
154C2×Dic22—22no—
155C2×Dic22C2412yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2414yes—
165C11×C22⋊C4—28no—
166C11×C22⋊C4C2×D414yes—
167C11×C22⋊C4C2×D414yes—
168C42×C11—24no—
169C42×C11—24no—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C42×C11C2412yes—
173C42×C11C2411yescharacteristic
174C42×C11C2411yescharacteristic
175C22⋊Dic11—24no—
176C22⋊Dic11—22no—
177#4326—48no—
178#4325—48no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—24no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11C2414yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188C4×Dic11—22no—
189C4×Dic11—24no—
190#4318—28no—
191#4318—44no—
192C2×C11⋊C8—44no—
193C2×C11⋊C8C2418yes—
194#3455—111no—
195C2×#541D1111yescharacteristic, complemented
196#3261—114no—
197#3260—114no—
198#3258—118no—
199#3080—112no—
200#3078—112no—
201#3056—114no—
202#3039—112no—
203#3037—112no—
204#2905—111no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11C22×D412yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210Q8×C11—24no—
211Q8×C11—24no—
212Q8×C11—44no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11H(5,𝔽2)12yes—
229C2×C4×C112−1+412yes—
230C2×C4×C11C2511yescharacteristic
231C22⋊D11—44no—
232C22⋊D11—84no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235D44—22no—
236D44—22no—
237D44—82no—
238C4×D11—44no—
239C4×D11—84no—
240Dic22—22no—
241Dic22—22no—
242Dic22—82no—
243C11⋊C8—28no—
244C2×#137—114no—
245C22×M16—112no—
246#542—114no—
247#541—24no—
248#541—112no—
249#541C2×D1114yes—
250#541C2×D1114yes—
251#540—112no—
252#539—222no—
253#538—222no—
254#533—111no—
255#532—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257#529—224no—
258C2×#126—22no—
259C2×#125—22no—
260C2×#125C2×D1111yescharacteristic
261#525—112no—
262C2×C22⋊Q8C2×D1112yes—
263C4×#41—112no—
264C2×C4×Q8C2×D1112yes—
265C2×#117C2×D1111yescharacteristic
266#479—118no—
267#479—118no—
268#478—118no—
269#477—114no—
270#475—114no—
271#470—118no—
272#468—118no—
273#467—118no—
274#465—118no—
275#464—118no—
276#462—118no—
277#462—114no—
278#461—118no—
279#460—114no—
280#428—114no—
281#424—114no—
282#424—114no—
283#423—112no—
284#423—112no—
285#419—114no—
286#417—114no—
287C22×C11—22no—
288C22×C11—24no—
289C22×C11—22no—
290C22×C11—82no—
291C22×C11#53712yes—
292C22×C11C23×D411yescharacteristic
293C2×D11—44no—
294C2×D11—42no—
295C4×C11—22no—
296C4×C11—24no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—44no—
300C4×C11—44no—
301C4×C11#53712yes—
302C4×C11C2×H(5,𝔽2)11yescharacteristic
303C4×C11C2×2−1+411yescharacteristic
304Dic11—44no—
305Dic11—42no—
306C2×#41—112no—
307C22×Q8C22×D1112yes—
308C23×C4C22×D1111yescharacteristic
309#137—448no—
310C2×Q16—118no—
311C2×SD16—118no—
312C2×M16—114no—
313C2×M16—114no—
314C2×M16—444no—
315C22×C8—114no—
316C4⋊Q8—22no—
317C4⋊Q8—112no—
318C4⋊Q8—111no—
319C4⋊Q8C22×D1114yes—
320#127—111no—
321#126—28no—
322#126—28no—
323#126—224no—
324#126—224no—
325#125—28no—
326#125—28no—
327#125—22no—
328#125—112no—
329#125—224no—
330#125C22×D1114yes—
331#124—112no—
332#124—224no—
333#123—222no—
334#123—224no—
335#123—224no—
336C22⋊Q8—24no—
337C22⋊Q8—114no—
338C22⋊Q8—222no—
339C22⋊Q8—224no—
340C22⋊Q8C22×D1118yes—
341#121—114no—
342#121—222no—
343#121—224no—
344#120—222no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—114no—
348C4×Q8—222no—
349C4×Q8C22×D1114yes—
350C4×Q8C22×D1114yes—
351C4×D4—114no—
352C4×D4—224no—
353C4×D4—224no—
354C4×D4—222no—
355#117—112no—
356#117—222no—
357#117C22⋊D1114yes—
358#117C22×D1112yes—
359#117C22×D1112yes—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4C22⋊D1112yes—
365C2×C4⋊C4C22×D1112yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4C22⋊D1112yes—
368C2×C42—22no—
369C2×C42—222no—
370C2×C42C22×D1111yescharacteristic
371C2×C42C22×D1111yescharacteristic
372#107—118no—
373#106—118no—
374C4⋊C8—114no—
375C4⋊C8—118no—
376C4⋊C8—114no—
377#103—118no—
378#103—118no—
379#103—118no—
380#102—118no—
381C2×C11—22no—
382C2×C11—42no—
383C2×C11C2×#53711yescharacteristic
384C2×C11#358612yes—
385D11—82no—
386C24C2×C22⋊D1111yescharacteristic
387#41—224no—
388#41—224no—
389C2×Q8—22no—
390C2×Q8—24no—
391C2×Q8—24no—
392C2×Q8—112no—
393C2×Q8—222no—
394C2×Q8C23×D1114yes—
395C2×D4—112no—
396C2×D4—222no—
397C2×D4—224no—
398C2×D4—222no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—222no—
404C22×C4—224no—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C23×D1112yes—
410C22×C4C23×D1111yescharacteristic
411Q16—448no—
412SD16—448no—
413M16—228no—
414M16—444no—
415C2×C8—118no—
416C2×C8—444no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—28no—
420C4⋊C4—28no—
421C4⋊C4—28no—
422C4⋊C4—22no—
423C4⋊C4—114no—
424C4⋊C4—224no—
425C4⋊C4—222no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—222no—
429C4⋊C4C2×C22⋊D1114yes—
430C4⋊C4C2×C22⋊D1114yes—
431C4⋊C4C23×D1114yes—
432C22⋊C4—28no—
433C22⋊C4—222no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C22⋊C4C2×C22⋊D1114yes—
439C22⋊C4C2×C22⋊D1114yes—
440C42—24no—
441C42—24no—
442C42—222no—
443C42—224no—
444C42C2×C22⋊D1112yes—
445C42C2×C22⋊D1112yes—
446C42C23×D1112yes—
447C42C23×D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#6092111yescharacteristic, complemented, Sylow
450C23—22no—
451C23—42no—
452C23—222no—
453C23C22×C22⋊D1112yes—
454C23C22×C22⋊D1111yescharacteristic
455Q8—24no—
456Q8—24no—
457Q8—44no—
458Q8—222no—
459Q8—222no—
460Q8—882no—
461D4—222no—
462D4—222no—
463D4—444no—
464D4—882no—
465D4—884no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—224no—
477C2×C4—222no—
478C2×C4—444no—
479C2×C4—884no—
480C2×C4#6704212yes—
481C2×C4#6704312yes—
482C2×C4C22×C22⋊D1112yes—
483C2×C4C22×C22⋊D1112yes—
484C2×C4C22×C22⋊D1114yes—
485C2×C4C22×C22⋊D1112yes—
486C2×C4C22×C22⋊D1111yescharacteristic
487C2×C4C24×D1111yescharacteristic
488C8—228no—
489C22—22no—
490C22—24no—
491C22—22no—
492C22—82no—
493C22—444no—
494C22—442no—
495C22#1062336412yes—
496C22C23×C22⋊D1111yescharacteristic
497C4—24no—
498C4—22no—
499C4—22no—
500C4—22no—
501C4—44no—
502C4—44no—
503C4—444no—
504C4—442no—
505C4#1062336412yes—
506C4C2×#6704211yescharacteristic
507C4C2×#6704311yescharacteristic
508C2—22no—
509C2—42no—
510C2—882no—
511C2C2×#1062336411yescharacteristic
512C2#1308340312yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#541C2
socleC22×C11C23×D4
prime radical#13082006C2
hypercenterC2×#541D11
hypocenterC11#60921
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #13080066C2semidirect
3. #13080057C2semidirect
4. #13080036C2semidirect
5. #13078434C2semidirect
6. #13078421C2semidirect
7. #13078242C2semidirect
8. #13078099C2semidirect
9. #13078088C2semidirect
10. #13077180C2semidirect
11. C2×C11×#541C2semidirect
35. #10622703C22semidirect
36. #10622696C22semidirect
37. #10622679C22semidirect
38. #10622676C22semidirect
43. #10622644C22semidirect
44. #10622641C22semidirect
45. #10622640C22semidirect
46. #10622635C22semidirect
47. #10622634C22semidirect
48. #10622633C22semidirect
195. C2×#541D11semidirect
449. C11#60921semidirect

Maximal subgroups

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

subgroupindex
#130820062
#130800662
#130800572
#130800362
#130784342
#130784212
#130782422
#130780992
#130780882
#130771802
C2×C11×#5412
#6092111