Finite Group Databasebeta

← #14763287

Subgroups — #14763287

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069583C212yesmaximal, complemented
5#13069583C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069573C211yesmaximal, characteristic, complemented
8#13069571C211yesmaximal, characteristic, complemented
9#13068705C212yesmaximal
10#13068701C212yesmaximal
11C11×#1989C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13D11×#125—24no—
14D11×#125C418yescomplemented
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66942—21no—
22C2×#66942—21no—
23C2×#66925—21no—
24C2×C42×D11C2211yescharacteristic
25C2×#66923C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66879C2212yes—
30#10622600C2212yes—
31#10622589C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33C4×Dic11⋊C4—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622448—24no—
36#10622280—21no—
37#10622263—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×#125—22no—
53C11×#125C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C4⋊C4×D11—28no—
81C4⋊C4×D11—28no—
82C4⋊C4×D11—22no—
83C4⋊C4×D11—22no—
84C4⋊C4×D11C2×C414yes—
85C4⋊C4×D11C2×C414yes—
86#66943—22no—
87#66943—22no—
88#66943C2×C414yes—
89#66943C2×C414yes—
90#66942—28no—
91#66942—28no—
92#66925—44no—
93C42×D11C2×C414yes—
94C42×D11D414yes—
95#66923—22no—
96#66923C2×C414yes—
97C11×C4⋊C8—22no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101(C2×D11)⋊C8—24no—
102#66879—24no—
103C4⋊(C11⋊C8)—22no—
104#21838—111nomaximal, Sylow
105C23×D11C2×D411yescharacteristic
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×Dic11—22no—
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C2×C4×D11—24no—
119C2×C4×D11—24no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11C22⋊C414yes—
129C2×C4×D11C22⋊C414yes—
130C2×C4×D11C22×C412yes—
131C2×C4×D11C2×D412yes—
132C2×C8×C11—22no—
133C2×C8×C11—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C22×C412yes—
141C11×C4⋊C4C22×C412yes—
142C42×C11—42no—
143C42×C11C22×C412yes—
144C42×C11C2×D412yes—
145(C2×D11)⋊C4—44no—
146C4⋊Dic11—24no—
147C4⋊Dic11—24no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11C22×C412yes—
153C4⋊Dic11C22×C412yes—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159Dic11⋊C4—24no—
160Dic11⋊C4—44no—
161Dic11⋊C4—44no—
162C4×Dic11—42no—
163C4×Dic11C22⋊C414yes—
164C4×Dic11C22⋊C414yes—
165C4×Dic11C22×C412yes—
166C4×Dic11C2×D412yes—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—24no—
169C22×#125—111no—
170C2×#432—111no—
171#2285—111no—
172#1992—112no—
173#1992—112no—
174#1989—111no—
175#1989—111no—
176#1989—111no—
177#1989D1111yescharacteristic, complemented
178#1824—112no—
179#1823—112no—
180C23×C11C22×D411yescharacteristic
181C22×D11—22no—
182C22×D11—22no—
183C22×D11C2×C22⋊C412yes—
184C22×D11AGL(1,ℤ/8)12yes—
185C22×D11#13712yes—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11C2×C22⋊C412yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C112−1+412yes—
202C2×C4×C112−1+412yes—
203C2×Dic11—22no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C2×C22⋊C412yes—
216C2×Dic11C2×C22⋊C412yes—
217C2×Dic11C2×C22⋊C412yes—
218C4×D11—28no—
219C4×D11—24no—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—44no—
223C4×D11—48no—
224C4×D11—48no—
225C8×C11—42no—
226C11⋊C8—42no—
227C2×#125—118no—
228C2×#125—111no—
229C2×#125—111no—
230C2×#125—111no—
231C2×#125—221no—
232C2×#125—221no—
233C2×#125—224no—
234C2×#125C2×D1111yescharacteristic
235C2×#117—221no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4—221no—
239C22×C4⋊C4—221no—
240C22×C42—111no—
241#432—224no—
242C2×C4⋊C8—111no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×C22⋊C8—112no—
245C2×#97—112no—
246#384—112no—
247#382—221no—
248#380—112no—
249#380—221no—
250C4×C4⋊C4—111no—
251C4×C4⋊C4—221no—
252C4×C4⋊C4C2×D1111yescharacteristic
253#340—112no—
254#340—112no—
255#340—112no—
256#340—112no—
257#340—112no—
258#340—112no—
259#340C2×D1112yes—
260#340C2×D1112yes—
261C22×C11C22×C22⋊C411yescharacteristic
262C22×C11#53612yes—
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C22×C11#57512yes—
266C2×D11—22no—
267C2×D11—22no—
268C2×D11—24no—
269C2×D11—24no—
270C2×D11#41714yes—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11#51912yes—
277C4×C11#53611yescharacteristic
278C4×C11#53611yescharacteristic
279Dic11—22no—
280Dic11—22no—
281Dic11—22no—
282Dic11—42no—
283Dic11—42no—
284Dic11—82no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—111no—
288C23×C4—221no—
289C23×C4—221no—
290C22×C8—112no—
291C22×C8C22×D1112yes—
292#125—22no—
293#125—114no—
294#125—114no—
295#125—114no—
296#125—228no—
297#125—228no—
298#125—222no—
299#125—222no—
300#125—222no—
301#125C4×D1114yes—
302#117—444no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—114no—
308C2×C4⋊C4—114no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—228no—
313C2×C4⋊C4—228no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4C22×D1112yes—
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C22⋊C4—222no—
328C2×C42—21no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—114no—
333C2×C42—114no—
334C2×C42—221no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—22no—
337C4⋊C8—222no—
338C22⋊C8—224no—
339#97—224no—
340#95—21no—
341#95—222no—
342#95—221no—
343C2×C11#231011yescharacteristic
344C2×C11C2×#41711yescharacteristic
345C2×C11#289611yescharacteristic
346C2×C11#323412yes—
347C2×C11#323612yes—
348D11—24no—
349C24—111no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—114no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—114no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—224no—
363C22×C4—224no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—222no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4—444no—
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376C2×C8—22no—
377C2×C8—24no—
378C2×C8—222no—
379C2×C8—224no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—112no—
387C4⋊C4—112no—
388C4⋊C4—224no—
389C4⋊C4—224no—
390C4⋊C4—224no—
391C4⋊C4—224no—
392C4⋊C4—224no—
393C4⋊C4—224no—
394C4⋊C4—224no—
395C4⋊C4—224no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—444no—
401C4⋊C4—444no—
402C4⋊C4C2×C4×D1112yes—
403C4⋊C4C2×C4×D1112yes—
404C22⋊C4—444no—
405C42—42no—
406C42—114no—
407C42—114no—
408C42—112no—
409C42—112no—
410C42—442no—
411C42C2×C4×D1112yes—
412C42D4×D1112yes—
413C11#2183811yescharacteristic, complemented, Sylow
414C23—112no—
415C23—112no—
416C23—112no—
417C23—222no—
418C23—222no—
419C23C2×D4×D1111yescharacteristic
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—112no—
432C2×C4—112no—
433C2×C4—112no—
434C2×C4—228no—
435C2×C4—222no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—224no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—444no—
445C2×C4—448no—
446C2×C4—448no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4C22⋊C4×D1112yes—
454C2×C4C22⋊C4×D1112yes—
455C2×C4C22×C4×D1111yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C2×C4#6704012yes—
458C2×C4#6704312yes—
459C8—42no—
460C8—442no—
461C22—114no—
462C22—224no—
463C22—222no—
464C22—222no—
465C22—224no—
466C22C2×C22⋊C4×D1111yescharacteristic
467C22#1062315912yes—
468C22#1062329912yes—
469C22D11×AGL(1,ℤ/8)11yescharacteristic
470C22D11×#13711yescharacteristic
471C4—22no—
472C4—22no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4—222no—
477C4—222no—
478C4—222no—
479C4—442no—
480C4—442no—
481C4—882no—
482C4#1062310312yes—
483C4#1062320611yescharacteristic
484C4#1062325511yescharacteristic
485C2—224no—
486C2#1307119911yescharacteristic
487C2D11×#41711yescharacteristic
488C2#1307713111yescharacteristic
489C2#1307980412yes—
490C2#1307982012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11#21838
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #13069583C2semidirect
5. #13069583C2semidirect
6. #13069574C2semidirect
7. #13069573C2semidirect
8. #13069571C2semidirect
11. C11×#1989C2semidirect
14. D11×#125C4semidirect
177. #1989D11semidirect
413. C11#21838semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106224482
#130710202
#130695832
#130695742
#130695732
#130695712
#130687052
#130687012
C11×#19892
#2183811