Finite Group Databasebeta

← #14762788

Subgroups — #14762788

Order 2816.

1518 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13069042C212yesmaximal, complemented
4#13069037C212yesmaximal, complemented
5#13068938C212yesmaximal, complemented
6#13068928C212yesmaximal, complemented
7#13068708C212yesmaximal, complemented
8#13068554C212yesmaximal, complemented
9C11×#2280C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C2×C11×#117C2212yes—
13C2×#67006—21no—
14#10623322—24no—
15#10623322C418yescomplemented
16C2×#66983C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66982—21no—
19C2×C4×C22⋊D11—21no—
20C2×C4×C22⋊D11—21no—
21C2×#66979C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C23×C11⋊C8C2212yes—
25C11×#381—21no—
26C11×#380C2212yes—
27C11×#380C2212yes—
28C11×#379—21no—
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4—21no—
31C2×C22⋊(C11⋊C8)—24no—
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×#66874C2214yescomplemented
35C2×#66873C2214yescomplemented
36#10622167C2214yescomplemented
37#10622167C2214yescomplemented
38C25×C11D411yescharacteristic
39C23×C4×C11—44no—
40C23×C4×C11C2×C414yes—
41C23×C4×C11D414yes—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C2×#4339—22no—
52C2×#4339—44no—
53C2×#4339C2×C414yes—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×Dic22C2311yescharacteristic
57C11×#117—44no—
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—22no—
63#67006—28no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67#66983—22no—
68#66983—22no—
69#66983C2×C414yes—
70#66983C2×C414yes—
71#66982—28no—
72C4×C22⋊D11—28no—
73C4×C22⋊D11—28no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76#66979—22no—
77#66979C2×C414yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—22no—
81#66977—22no—
82#66977C2×C414yes—
83#66977C2×C414yes—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8—24no—
88C22×C11⋊C8—44no—
89C22×C11⋊C8C2314yes—
90C11×#95—22no—
91C11×#95—22no—
92C22⋊(C11⋊C8)—24no—
93C22⋊(C11⋊C8)—24no—
94#66874—44no—
95#66873—44no—
96#21760—111nomaximal, Sylow
97C24×C11—24no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11C22⋊C414yes—
101C24×C11C2×D411yescharacteristic
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C23×D11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—48no—
110C22×C4×C11—48no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C22⋊C414yes—
115C22×C4×C11C22⋊C414yes—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—24no—
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136#4339—48no—
137#4339—48no—
138C2×D44—21no—
139C2×D44—24no—
140C2×D44C22×C412yes—
141C2×C4×D11—24no—
142C2×C4×D11—44no—
143C2×Dic22—21no—
144C2×Dic22—24no—
145C2×Dic22C22×C412yes—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C42×C11—44no—
152C22⋊Dic11—24no—
153C22⋊Dic11—24no—
154C22⋊Dic11—24no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11C22×C412yes—
160C4⋊Dic11C22×C412yes—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163C4×Dic11—24no—
164C2×C11⋊C8—24no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—48no—
168C2×#525—111no—
169C22×C22⋊C8—111no—
170#2280D1111yescharacteristic, complemented
171#1893—112no—
172#1892—112no—
173#1875—112no—
174#1873—112no—
175#1825—112no—
176#1788—112no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—28no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—416no—
189C23×C11C2×C22⋊C412yes—
190C23×C11C2×C22⋊C412yes—
191C23×C11C2×C22⋊C412yes—
192C23×C11#13514yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11H(5,𝔽2)14yes—
219C22⋊D11—48no—
220C22⋊D11—48no—
221C22⋊D11—48no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228D44—24no—
229D44—42no—
230C4×D11—48no—
231Dic22—24no—
232Dic22—42no—
233C11⋊C8—44no—
234C22×#41—111no—
235C24×C4C2×D1111yescharacteristic
236C23×C8—112no—
237#525—118no—
238#525—224no—
239C2×#123—221no—
240C2×C22⋊Q8—111no—
241C2×C22⋊Q8—111no—
242C2×#121—111no—
243C2×#121—111no—
244C2×#120—221no—
245C2×C4×D4—221no—
246C2×C4×D4—221no—
247C2×#117—111no—
248C2×#117C2×D1112yes—
249C2×#103—114no—
250C2×#102—114no—
251C2×C22⋊C8—112no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—224no—
254#381—21no—
255#380C2×D1112yes—
256#380C2×D1112yes—
257#379—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260#340—114no—
261#340—114no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—28no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—416no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11#41614yes—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11#53412yes—
277C22×C11C2×#13512yes—
278C22×C11#57512yes—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—84no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—84no—
287C4×C11#51812yes—
288C4×C11#53412yes—
289Dic11—42no—
290Dic11—42no—
291Dic11—42no—
292C25C22⋊D1111yescharacteristic
293C2×#41—114no—
294C2×#41—222no—
295C2×#41—444no—
296C22×Q8—111no—
297C22×D4—111no—
298C22×D4—221no—
299C22×D4—221no—
300C22×D4—221no—
301C23×C4—44no—
302C23×C4—221no—
303C23×C4C4×D1114yes—
304C23×C4D4414yes—
305C23×C4C22⋊D1111yescharacteristic
306C23×C4C22⋊D1111yescharacteristic
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C23×C4C22×D1111yescharacteristic
311C22×C8—114no—
312C22×C8—224no—
313C22×C8—444no—
314#123—228no—
315C22⋊Q8—114no—
316C22⋊Q8—114no—
317C22⋊Q8—222no—
318C22⋊Q8—222no—
319#121—114no—
320#121—114no—
321#121—222no—
322#121—222no—
323#120—228no—
324C4×D4—228no—
325C4×D4—228no—
326#117—44no—
327#117—114no—
328#117—222no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22×D1114yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—221no—
342C2×C42—22no—
343C2×C42—221no—
344#103—444no—
345#102—444no—
346C22⋊C8—224no—
347C22⋊C8—224no—
348#95—22no—
349#95—22no—
350C2×C11—24no—
351C2×C11—42no—
352C2×C11—42no—
353C2×C11#230811yescharacteristic
354C2×C11C2×#41611yescharacteristic
355C2×C11#289611yescharacteristic
356C2×C11#319114yes—
357D11—82no—
358C24—24no—
359C24—42no—
360C24—42no—
361C24—221no—
362C24(C2×D11)⋊C414yes—
363C24C2×C22⋊D1111yescharacteristic
364C24C2×C22⋊D1111yescharacteristic
365C24C2×C22⋊D1111yescharacteristic
366#41—448no—
367#41—448no—
368C2×Q8—112no—
369C2×Q8—221no—
370C2×Q8—224no—
371C2×D4—112no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—224no—
375C2×D4—221no—
376C2×D4—224no—
377C2×D4—444no—
378C2×D4—444no—
379C2×D4—444no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—48no—
385C22×C4—48no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—224no—
393C22×C4—444no—
394C22×C4(C2×D11)⋊C414yes—
395C22×C4(C2×D11)⋊C414yes—
396C22×C4(C2×D11)⋊C414yes—
397C22×C4C2×C4×D1112yes—
398C22×C4C2×C4×D1112yes—
399C22×C4C2×C4×D1112yes—
400C22×C4C2×D4412yes—
401C22×C4C2×D4412yes—
402C22×C4C2×D4412yes—
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C23×D1111yescharacteristic
407C2×C8—224no—
408C2×C8—224no—
409C2×C8—224no—
410C2×C8—448no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—112no—
414C4⋊C4—112no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C22⋊C4—44no—
420C22⋊C4—44no—
421C22⋊C4—44no—
422C22⋊C4—224no—
423C22⋊C4—224no—
424C22⋊C4—224no—
425C22⋊C4—224no—
426C22⋊C4—224no—
427C42—44no—
428C42—224no—
429C11#2176011yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—28no—
439C23—44no—
440C23—44no—
441C23—416no—
442C23—222no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23C2×(C2×D11)⋊C412yes—
447C23C2×(C2×D11)⋊C412yes—
448C23C2×(C2×D11)⋊C412yes—
449C23#6700314yes—
450C23C22×C22⋊D1111yescharacteristic
451Q8—224no—
452Q8—442no—
453D4—224no—
454D4—448no—
455D4—448no—
456D4—448no—
457D4—442no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—448no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4C2×(C2×D11)⋊C412yes—
481C2×C4C2×(C2×D11)⋊C412yes—
482C2×C4C2×(C2×D11)⋊C412yes—
483C2×C4C22×C4×D1111yescharacteristic
484C2×C4C22×D4411yescharacteristic
485C2×C4#6703714yes—
486C8—444no—
487C22—22no—
488C22—28no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—416no—
497C22—44no—
498C22—44no—
499C22—442no—
500C22—442no—
501C22—442no—
502C22—884no—
503C22#1062261514yes—
504C22C22×(C2×D11)⋊C411yescharacteristic
505C22#1062333512yes—
506C22C2×#6700312yes—
507C22#1062335312yes—
508C4—22no—
509C4—22no—
510C4—22no—
511C4—84no—
512C4—442no—
513C4—442no—
514C4—442no—
515C4#1062301712yes—
516C4#1062302412yes—
517C2—24no—
518C2—42no—
519C2—42no—
520C2—882no—
521C2#1307119111yescharacteristic
522C2C2×#1062261511yescharacteristic
523C2#1307713311yescharacteristic
524C2#1307940414yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2280C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenter#2280D11
hypocenterC11#21760
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13069042C2semidirect
4. #13069037C2semidirect
5. #13068938C2semidirect
6. #13068928C2semidirect
7. #13068708C2semidirect
8. #13068554C2semidirect
9. C11×#2280C2semidirect
15. #10623322C4semidirect
34. C2×#66874C22semidirect
35. C2×#66873C22semidirect
36. #10622167C22semidirect
37. #10622167C22semidirect
170. #2280D11semidirect
429. C11#21760semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×C22⋊(C11⋊C8)2
#130690422
#130690372
#130689382
#130689282
#130687082
#130685542
C11×#22802
#2176011