Finite Group Databasebeta

← #14769520

Subgroups — #14769520

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D11C211yesmaximal, characteristic
2C2×#10622329C211yesmaximal, characteristic, complemented
3C2×#10622466C211yesmaximal, characteristic, complemented
4#13071450C212yesmaximal
5#13069488C211yesmaximal, characteristic, complemented
6#13068960C212yesmaximal, complemented
7#13068954C212yesmaximal, complemented
8#13068638C211yesmaximal, characteristic
9#13068549C212yesmaximal
10#13068393C211yesmaximal, characteristic
11C11×#1971C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C22×#4326C2212yes—
15C2×Q16×D11—24no—
16C2×Q16×D11—24no—
17C2×Q16×D11C418yescomplemented
18C22×Dic44C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66940C2212yes—
21C2×C4×Dic22C2212yes—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#97C2211yescharacteristic
25C11×#391C2212yes—
26#10622843C2212yes—
27C2×#66899C2212yes—
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2212yes—
31C2×#66879C2211yescharacteristic
32#10622600C2212yes—
33C2×#66874C2212yes—
34C4×(C2×D11)⋊C4C2211yescharacteristic
35#10622466—24no—
36#10622329—24no—
37#10622280—22no—
38#10622279—22no—
39#10622259—22no—
40#10622259—22no—
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C2×Q8×D11—24no—
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—42no—
49C2×Q8×D11—42no—
50C2×Q8×D11C2×C418yes—
51C22×C4×D11—22no—
52C22×C4×D11C2311yescharacteristic
53C22×Dic22—22no—
54C22×Dic22C2312yes—
55C2×C11×Q16—22no—
56C2×C11×Q16—22no—
57C2×C11×Q16C2×C414yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—24no—
63C2×#4326—24no—
64C2×#4326C2×C418yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75Q16×D11—232no—
76C2×Dic44C2×C414yes—
77C2×Dic44D414yes—
78C2×Dic44D414yes—
79C2×C8×D11—22no—
80C2×C8×D11—22no—
81C2×C8×D11C2×C414yes—
82#66940—24no—
83#66940—42no—
84C4×Dic22—24no—
85C4×Dic22—42no—
86C11×#106—22no—
87C11×#103—42no—
88C11×#97—22no—
89C11×#95—22no—
90C11×#95—22no—
91#66899—42no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95D412yes—
96(C2×D11)⋊C8—22no—
97#66881—22no—
98#66880—24no—
99#66879—22no—
100#66874—24no—
101#22440—111nomaximal, Sylow
102C23×D11C2×D411yescharacteristic
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C22×C414yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D411yescharacteristic
117Q8×D11—216no—
118Q8×D11—48no—
119Q8×D11—48no—
120Q8×D11—48no—
121C2×C4×D11—28no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11C22×C412yes—
129C2×C4×D11#4112yes—
130C2×Dic22—28no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—44no—
135C2×Dic22—44no—
136C2×Dic22C22×C414yes—
137C2×Dic22C2×D414yes—
138C2×Dic22C2×D414yes—
139C11×Q16—28no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C22×C412yes—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C42×C11—21no—
149C42×C11—21no—
150#4326—216no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—44no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155Dic11⋊C4—44no—
156Dic11⋊C4—44no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159C4×Dic11—44no—
160C4×Dic11—44no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8C22×C412yes—
167Dic44C22⋊C4116yescomplemented
168C8×D11—28no—
169C23×Q16—111no—
170C2×#441—111no—
171C2×#441—111no—
172Q8×C22⋊C4—112no—
173#1971—111no—
174#1971D1111yescharacteristic, complemented
175#1878—112no—
176#1878—112no—
177#1807—111no—
178#1787—112no—
179#1752—111no—
180C23×C11C22×D411yescharacteristic
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—22no—
184C22×D11C4×D412yes—
185C22×D11#13714yes—
186Q8×C11—24no—
187Q8×C11—24no—
188Q8×C11—42no—
189Q8×C11—42no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11C4×D412yes—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—22no—
220C4×D11—22no—
221C4×D11—416no—
222Dic22—24no—
223Dic22—24no—
224Dic22—24no—
225Dic22—416no—
226Dic22C2×C22⋊C418yes—
227C8×C11—41no—
228C8×C11C2×C22⋊C414yes—
229C11⋊C8—22no—
230C11⋊C8—41no—
231C23×Q8—112no—
232C22×Q16—112no—
233C22×Q16—118no—
234C22×Q16—111no—
235C22×Q16—224no—
236C22×Q16—224no—
237C22×Q16C2×D1111yescharacteristic
238C23×C8—111no—
239C2×C4×Q8—112no—
240C2×C4×Q8—112no—
241#441—224no—
242#441—224no—
243C2×#106—111no—
244C2×#106C2×D1111yescharacteristic
245C2×#103—112no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#103C2×D1112yes—
249C2×C22⋊C8—111no—
250C2×#97—111no—
251C2×#97C2×D1111yescharacteristic
252#391—112no—
253#391—222no—
254#391—222no—
255#391C2×D1112yes—
256#380—112no—
257#380—222no—
258C4×C22⋊C4—111no—
259C4×C22⋊C4—222no—
260#340—112no—
261#336—111no—
262#336—111no—
263C22×C11C2×C4×D411yescharacteristic
264C22×C11D4211yescharacteristic
265C22×C11D4211yescharacteristic
266C22×C11C2×#13712yes—
267C22×C11#57812yes—
268C2×D11—22no—
269C2×D11—22no—
270C2×D11—24no—
271C2×D11—24no—
272C2×D11#44114yescomplemented
273C4×C11—44no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11C22×C22⋊C411yescharacteristic
277C4×C11#51811yescharacteristic
278C4×C11#54611yescharacteristic
279C4×C11#54611yescharacteristic
280Dic11—28no—
281Dic11—22no—
282Dic11—42no—
283Dic11—82no—
284C22×Q8—118no—
285C22×Q8—112no—
286C22×Q8—222no—
287C22×Q8—224no—
288C22×Q8—224no—
289C22×Q8—224no—
290C22×Q8—442no—
291C22×Q8—442no—
292C22×Q8C22×D1112yes—
293C23×C4—111no—
294C23×C4—222no—
295C2×Q16—22no—
296C2×Q16—22no—
297C2×Q16—118no—
298C2×Q16—114no—
299C2×Q16—114no—
300C2×Q16—114no—
301C2×Q16—2232no—
302C2×Q16—224no—
303C2×Q16—224no—
304C2×Q16C4×D1114yes—
305C22×C8—111no—
306C22×C8—114no—
307C22×C8—111no—
308C22×C8—222no—
309C22×C8—222no—
310C22×C8C22×D1111yescharacteristic
311C22×C8C22×D1111yescharacteristic
312C4×Q8—224no—
313C4×Q8—224no—
314C4×Q8—442no—
315C4×Q8—442no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4C22×D1112yes—
320C2×C22⋊C4—112no—
321C2×C22⋊C4—222no—
322C2×C42—111no—
323C2×C42—222no—
324C2×C42—222no—
325C2×C42C22×D1111yescharacteristic
326#106—22no—
327#106—222no—
328#103—42no—
329#103—224no—
330#103—224no—
331#103—442no—
332C22⋊C8—222no—
333#97—22no—
334#97—222no—
335#95—22no—
336#95—22no—
337#95—112no—
338#95—222no—
339#95—222no—
340#95—222no—
341C2×C11D4×C22⋊C411yescharacteristic
342C2×C11C2×#44111yescharacteristic
343C2×C11#295011yescharacteristic
344C2×C11#327012yes—
345C2×C11#327012yes—
346D11—24no—
347C24—111no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—114no—
354C2×Q8—114no—
355C2×Q8—114no—
356C2×Q8—228no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—2216no—
361C2×Q8—444no—
362C2×Q8—444no—
363C2×Q8—448no—
364C2×Q8—448no—
365C2×Q8—448no—
366C2×Q8C2×C4×D1114yes—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—111no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—228no—
374C22×C4—222no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—222no—
380C22×C4—444no—
381C22×C4—444no—
382C22×C4D4×D1112yes—
383C22×C4C23×D1111yescharacteristic
384Q16—28no—
385Q16—1116no—
386Q16—2216no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—112no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—228no—
394C2×C8—221no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8C2×C4×D1112yes—
398C2×C8D4×D1112yes—
399C2×C8D4×D1112yes—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—444no—
405C4⋊C4—444no—
406C22⋊C4—224no—
407C22⋊C4—444no—
408C42—21no—
409C42—21no—
410C42—221no—
411C42—221no—
412C42—444no—
413C42—444no—
414C11#2244011yescharacteristic, complemented, Sylow
415C23—114no—
416C23—112no—
417C23—221no—
418C23—222no—
419C23—221no—
420C23C2×D4×D1111yescharacteristic
421Q8—24no—
422Q8—24no—
423Q8—42no—
424Q8—42no—
425Q8—118no—
426Q8—224no—
427Q8—224no—
428Q8—224no—
429Q8—4416no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—112no—
440C2×C4—224no—
441C2×C4—221no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—221no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—4416no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4C22×C4×D1111yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4#6703711yescharacteristic
460C2×C4#41×D1111yescharacteristic
461C2×C4#6704211yescharacteristic
462C8—41no—
463C8—222no—
464C8—441no—
465C8C22⋊C4×D1114yes—
466C22—114no—
467C22—222no—
468C22—224no—
469C22—224no—
470C22—222no—
471C22C4×D4×D1111yescharacteristic
472C22#1062314011yescharacteristic
473C22#1062324811yescharacteristic
474C22D11×#13712yes—
475C22#1062331012yes—
476C4—44no—
477C4—42no—
478C4—82no—
479C4—222no—
480C4—228no—
481C4—442no—
482C4—882no—
483C4C2×C22⋊C4×D1111yescharacteristic
484C4#1062307611yescharacteristic
485C4#1062314311yescharacteristic
486C4#1062320711yescharacteristic
487C2—224no—
488C2#1307143711yescharacteristic
489C2D11×#44111yescharacteristic
490C2#1307748111yescharacteristic
491C2#1308018512yes—
492C2#1308019312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1971C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1971D11
hypocenterC11#22440
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
2. C2×#10622329C2semidirect
3. C2×#10622466C2semidirect
5. #13069488C2semidirect
6. #13068960C2semidirect
7. #13068954C2semidirect
11. C11×#1971C2semidirect
17. C2×Q16×D11C4semidirect
167. Dic44C22⋊C4semidirect
174. #1971D11semidirect
272. C2×D11#441semidirect
414. C11#22440semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D112
C2×#106223292
C2×#106224662
#130714502
#130694882
#130689602
#130689542
#130686382
#130685492
#130683932
C11×#19712
#2244011