Finite Group Databasebeta

← #14770571

Subgroups — #14770571

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2#13071573C211yesmaximal, characteristic, complemented
3#13069546C212yesmaximal
4#13069538C211yesmaximal, characteristic, complemented
5#13069427C212yesmaximal
6#13069418C211yesmaximal, characteristic, complemented
7#13068632C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic
9C4×#66880C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14#10623115—24no—
15#10623115C418yescomplemented
16C2×#66951—22no—
17C2×#66945—21no—
18C2×#66928C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2212yes—
22C8×Q8×C11—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C2×C4×C8×C11C2212yes—
27#10622843—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35#10622594—22no—
36C4⋊C4×Dic11—21no—
37#10622549C2212yes—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11C2×C414yes—
52C4×Q8×C11D414yes—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D412yes—
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57#66999—28no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73#66951—216no—
74#66945—28no—
75#66928—24no—
76#66928C2×C418yes—
77C4×D44—22no—
78C4×D44C2×C414yes—
79#66922—22no—
80#66922C2×C414yes—
81C4×Dic22—24no—
82C4×Dic22C2×C418yes—
83C11×C4⋊C8—24no—
84C11×C4⋊C8—22no—
85C4×C8×C11—24no—
86C4×C8×C11—22no—
87C11⋊#95—22no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91#66885—22no—
92#66885—22no—
93#66885—42no—
94#66880—24no—
95#66880—24no—
96#66880—42no—
97#66880—42no—
98#22541—111nomaximal, Sylow
99C23×D11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11C22⋊C414yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44C22×C412yes—
119C2×C4×D11—24no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22C22×C414yes—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11#4112yes—
137C11×C4⋊C4C22⋊C414yes—
138C11×C4⋊C4C22⋊C418yes—
139C42×C11C22×C414yes—
140C42×C11C22×C412yes—
141C42×C11C2×D414yes—
142C42×C11C2×D412yes—
143(C2×D11)⋊C4—24no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—28no—
146C4⋊Dic11—24no—
147C4⋊Dic11—24no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—42no—
155C4⋊Dic11—81no—
156C4⋊Dic11C22×C412yes—
157C4⋊Dic11#4112yes—
158Dic11⋊C4—28no—
159C4×Dic11—28no—
160C4×Dic11—42no—
161C4×Dic11—82no—
162C2×#556—111no—
163C2×C8×Q8D1111yescharacteristic, complemented
164#2355—111no—
165#1983—112no—
166#1981—111no—
167#1958—112no—
168#1956—111no—
169#1805—112no—
170#1802—111no—
171C4×#103—112no—
172C4×#102—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181Q8×C11—28no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11C2×C22⋊C414yes—
189C2×C4×C11C2×C22⋊C414yes—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C2×C22⋊C412yes—
192C2×C4×C11#13512yes—
193C2×C4×C11#13512yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—24no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215D44—22no—
216D44—22no—
217D44—41no—
218D44—41no—
219C4×D11—48no—
220Dic22—24no—
221Dic22—24no—
222Dic22—42no—
223Dic22—42no—
224C8×C11—22no—
225C8×C11—42no—
226C8×C11—41no—
227#556—118no—
228#556—224no—
229C2×C4⋊Q8—111no—
230C2×#126—222no—
231C2×#124—112no—
232C2×C22⋊Q8—221no—
233C2×C4×Q8—112no—
234C2×C4×Q8C2×D1111yescharacteristic
235C2×C4×D4—111no—
236C2×#117—221no—
237C8×Q8—24no—
238C2×C4⋊C8C2×D1111yescharacteristic
239C2×C4⋊C8C2×D1112yes—
240C2×#103—112no—
241C2×#103—112no—
242C2×#103—112no—
243C2×#103—112no—
244C2×#102—111no—
245C2×#102—111no—
246C2×#102—112no—
247C2×C4×C8C2×D1111yescharacteristic
248C2×C4×C8C2×D1112yes—
249#391—221no—
250#387—222no—
251#384—111no—
252#382—112no—
253C4×C4⋊C4—111no—
254C4×C4⋊C4—112no—
255C4×C4⋊C4—221no—
256#340—112no—
257#340—111no—
258#340—111no—
259C22×C11C22×C22⋊C411yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11#55011yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×#13511yescharacteristic
264C22×C11#57711yescharacteristic
265C22×C11#57811yescharacteristic
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C4×C11—24no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11#41614yes—
277C4×C11C4×#4111yescharacteristic
278C4×C11#52011yescharacteristic
279C4×C11#54811yescharacteristic
280C4×C11#55011yescharacteristic
281Dic11—42no—
282Dic11—44no—
283Dic11—42no—
284Dic11—81no—
285Dic11—82no—
286C22×Q8—112no—
287C22×Q8D4411yescharacteristic
288C22×D4—111no—
289C23×C4—221no—
290C22×C8C22×D1111yescharacteristic
291C22×C8C22×D1112yes—
292C22×C8C22×D1111yescharacteristic
293C4⋊Q8—114no—
294C4⋊Q8—222no—
295#126—2216no—
296#124—118no—
297#124—224no—
298C22⋊Q8—228no—
299C4×Q8—118no—
300C4×Q8—224no—
301C4×Q8C4×D1114yes—
302C4×Q8C22⋊D1114yes—
303C4×D4—114no—
304C4×D4—222no—
305#117—228no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4D4411yescharacteristic
316C2×C4⋊C4D4412yes—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—222no—
320C2×C42—222no—
321C2×C42—221no—
322C2×C42—222no—
323C2×C42C22×D1111yescharacteristic
324C2×C42C22×D1112yes—
325C4⋊C8—22no—
326C4⋊C8—24no—
327#103—224no—
328#103—224no—
329#103—442no—
330#103—442no—
331#102—222no—
332#102—222no—
333#102—442no—
334C4×C8—22no—
335C4×C8—24no—
336#95—221no—
337#95—222no—
338#95—222no—
339#95—222no—
340C2×C11#234111yescharacteristic
341C2×C11C2×#41611yescharacteristic
342C2×C11#289811yescharacteristic
343C2×C11#336011yescharacteristic
344C2×C11#336411yescharacteristic
345C2×C11#339311yescharacteristic
346C2×C11#339411yescharacteristic
347D11—82no—
348C24—221no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—114no—
352C2×Q8—222no—
353C2×Q8—222no—
354C2×Q8—222no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8(C2×D11)⋊C414yes—
358C2×D4—112no—
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—221no—
363C2×D4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—222no—
367C22×C4—224no—
368C22×C4—221no—
369C22×C4—222no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4C2×D4412yes—
373C22×C4C2×D4412yes—
374C22×C4C2×D4411yescharacteristic
375C22×C4C2×D4411yescharacteristic
376C22×C4C23×D1111yescharacteristic
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8#434312yes—
386C4⋊C4—112no—
387C4⋊C4—112no—
388C4⋊C4—224no—
389C4⋊C4—228no—
390C4⋊C4—224no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—442no—
398C4⋊C4—881no—
399C4⋊C4(C2×D11)⋊C414yes—
400C4⋊C4(C2×D11)⋊C418yes—
401C22⋊C4—228no—
402C22⋊C4—224no—
403C22⋊C4—228no—
404C42—228no—
405C42—442no—
406C42—882no—
407C42C2×C4×D1112yes—
408C42C2×C4×D1114yes—
409C42C2×C22⋊D1112yes—
410C42C2×C22⋊D1114yes—
411C11#2254111yescharacteristic, complemented, Sylow
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23—441no—
419C23C22×D4411yescharacteristic
420Q8—28no—
421Q8—224no—
422Q8—224no—
423Q8—442no—
424Q8—442no—
425D4—222no—
426D4—222no—
427D4—441no—
428D4—441no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—222no—
436C2×C4—224no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—448no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—442no—
451C2×C4#6695712yes—
452C2×C4#6695712yes—
453C2×C4C2×(C2×D11)⋊C414yes—
454C2×C4C2×(C2×D11)⋊C412yes—
455C2×C4C2×(C2×D11)⋊C414yes—
456C2×C4C2×(C2×D11)⋊C412yes—
457C2×C4C22×C4×D1111yescharacteristic
458C2×C4C2×#434311yescharacteristic
459C2×C4#6704011yescharacteristic
460C2×C4#41×D1111yescharacteristic
461C2×C4#6704211yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—22no—
464C8—41no—
465C8—42no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22#1062310711yescharacteristic
474C22#1062310811yescharacteristic
475C22C2×#6695711yescharacteristic
476C22C2×#6695711yescharacteristic
477C22#1062328211yescharacteristic
478C22#1062328411yescharacteristic
479C22C22×(C2×D11)⋊C411yescharacteristic
480C4—24no—
481C4—24no—
482C4—22no—
483C4—444no—
484C4—442no—
485C4—442no—
486C4—881no—
487C4—882no—
488C4#1062272614yes—
489C4C4×#434311yescharacteristic
490C4#1062310511yescharacteristic
491C4#1062334811yescharacteristic
492C4#1062336511yescharacteristic
493C2—882no—
494C2#1307145411yescharacteristic
495C2C2×#1062272611yescharacteristic
496C2#1307715011yescharacteristic
497C2#1308126711yescharacteristic
498C2#1308130311yescharacteristic
499C2#1308160511yescharacteristic
500C2#1308161411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11#22541
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13071573C2semidirect
4. #13069538C2semidirect
6. #13069418C2semidirect
7. #13068632C2semidirect
9. C4×#66880C2semidirect
11. C2×C8×Q8×C11C2semidirect
15. #10623115C4semidirect
163. C2×C8×Q8D11semidirect
411. C11#22541semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
#130715732
#130695462
#130695382
#130694272
#130694182
#130686322
#130686172
C4×#668802
C4×#668852
C2×C8×Q8×C112
#2254111