Finite Group Databasebeta

← #14770600

Subgroups — #14770600

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069546C212yesmaximal
4#13069538C211yesmaximal, characteristic, complemented
5#13069432C212yesmaximal
6#13069418C211yesmaximal, characteristic, complemented
7#13068622C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic
9#13068447C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14C2×Q8×Dic11—21no—
15#10623115—24no—
16#10623115C418yescomplemented
17C2×#66951—22no—
18C2×#66945—21no—
19C2×#66928C2212yes—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2212yes—
23C11×#446—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#97C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35#10622598—21no—
36#10622598—22no—
37#10622548C2211yescharacteristic
38#10622548C2212yes—
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×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
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—
58Q8×Dic11—44no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—21no—
76#66951—216no—
77#66945—28no—
78#66928—24no—
79#66928C2×C418yes—
80C4×D44—22no—
81C4×D44C2×C414yes—
82#66922—22no—
83#66922C2×C414yes—
84C4×Dic22—24no—
85C4×Dic22C2×C418yes—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—24no—
88C11×#97—24no—
89C4×C8×C11—22no—
90C11⋊#95—22no—
91C11⋊#95—21no—
92#66885—22no—
93#66885—22no—
94#66885—42no—
95#66880—24no—
96#66880—24no—
97#66880—42no—
98#66880—42no—
99#22544—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C22⋊C414yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44C22×C412yes—
120C2×C4×D11—24no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22C22×C414yes—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11#4112yes—
138C11×C4⋊C4C22⋊C414yes—
139C11×C4⋊C4C22⋊C418yes—
140C42×C11C22×C414yes—
141C42×C11C22×C412yes—
142C42×C11C2×D412yes—
143C42×C11C2×D414yes—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—28no—
147C4⋊Dic11—24no—
148C4⋊Dic11—24no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—44no—
156C4⋊Dic11—42no—
157C4⋊Dic11—82no—
158C4⋊Dic11—81no—
159C4⋊Dic11C22×C412yes—
160C4⋊Dic11#4112yes—
161Dic11⋊C4—28no—
162C4×Dic11—28no—
163C4×Dic11—44no—
164C4×Dic11—42no—
165C2×#556—111no—
166C2×#446D1111yescharacteristic, complemented
167Q8×C4⋊C4—111no—
168#1983—112no—
169#1981—111no—
170#1959—112no—
171#1956—111no—
172#1803—112no—
173#1802—111no—
174#1763—112no—
175C4×#102—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184Q8×C11—28no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11C2×C22⋊C414yes—
192C2×C4×C11C2×C22⋊C414yes—
193C2×C4×C11C2×C22⋊C412yes—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218D44—22no—
219D44—22no—
220D44—41no—
221D44—41no—
222C4×D11—48no—
223Dic22—24no—
224Dic22—24no—
225Dic22—42no—
226Dic22—42no—
227C8×C11—22no—
228C8×C11—41no—
229C8×C11—42no—
230#556—118no—
231#556—224no—
232C2×C4⋊Q8—111no—
233C2×#126—222no—
234C2×#124—112no—
235C2×C22⋊Q8—221no—
236C2×C4×Q8—112no—
237C2×C4×Q8—221no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4—111no—
240C2×#117—221no—
241#446—24no—
242C2×C4⋊C8C2×D1111yescharacteristic
243C2×C4⋊C8C2×D1112yes—
244C2×#103—112no—
245C2×#103—112no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#102—111no—
249C2×#102—111no—
250C2×#102—112no—
251C2×#97C2×D1112yes—
252C2×C4×C8C2×D1111yescharacteristic
253#389—221no—
254#389—222no—
255#384—111no—
256#384—112no—
257C4×C4⋊C4—111no—
258C4×C4⋊C4—112no—
259#340—112no—
260#340—111no—
261#340—111no—
262C22×C11C22×C22⋊C411yescharacteristic
263C22×C11#54811yescharacteristic
264C22×C11#55011yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11#57711yescharacteristic
268C22×C11#57811yescharacteristic
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C4×C11—24no—
277C4×C11—24no—
278C4×C11—22no—
279C4×C11#41714yes—
280C4×C11C4×#4111yescharacteristic
281C4×C11#52011yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11#55011yescharacteristic
284Dic11—44no—
285Dic11—42no—
286Dic11—42no—
287Dic11—82no—
288Dic11—81no—
289C22×Q8—112no—
290C22×Q8D4411yescharacteristic
291C22×D4—111no—
292C23×C4—221no—
293C22×C8C22×D1111yescharacteristic
294C22×C8C22×D1112yes—
295C22×C8C22×D1111yescharacteristic
296C4⋊Q8—114no—
297C4⋊Q8—222no—
298#126—2216no—
299#124—118no—
300#124—224no—
301C22⋊Q8—228no—
302C4×Q8—118no—
303C4×Q8—224no—
304C4×Q8—444no—
305C4×Q8C4×D1114yes—
306C4×Q8C22⋊D1114yes—
307C4×D4—114no—
308C4×D4—222no—
309#117—228no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4D4411yescharacteristic
322C2×C4⋊C4D4412yes—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—222no—
326C2×C42—222no—
327C2×C42—222no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330C2×C42C22×D1112yes—
331C4⋊C8—22no—
332C4⋊C8—24no—
333#103—224no—
334#103—224no—
335#103—442no—
336#103—442no—
337#102—222no—
338#102—222no—
339#102—442no—
340#97—24no—
341C4×C8—22no—
342#95—222no—
343#95—221no—
344C2×C11#234111yescharacteristic
345C2×C11C2×#41711yescharacteristic
346C2×C11#289811yescharacteristic
347C2×C11#336711yescharacteristic
348C2×C11#336911yescharacteristic
349C2×C11#339711yescharacteristic
350C2×C11#339811yescharacteristic
351D11—82no—
352C24—221no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—114no—
356C2×Q8—222no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8(C2×D11)⋊C414yes—
362C2×D4—112no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—222no—
371C22×C4—224no—
372C22×C4—222no—
373C22×C4—221no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4C2×D4412yes—
377C22×C4C2×D4411yescharacteristic
378C22×C4C2×D4412yes—
379C22×C4C2×D4411yescharacteristic
380C22×C4C23×D1111yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8#434312yes—
390C4⋊C4—112no—
391C4⋊C4—112no—
392C4⋊C4—224no—
393C4⋊C4—228no—
394C4⋊C4—224no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—221no—
401C4⋊C4—444no—
402C4⋊C4—442no—
403C4⋊C4—882no—
404C4⋊C4—881no—
405C4⋊C4(C2×D11)⋊C414yes—
406C4⋊C4(C2×D11)⋊C418yes—
407C22⋊C4—228no—
408C22⋊C4—224no—
409C22⋊C4—228no—
410C42—228no—
411C42—444no—
412C42—442no—
413C42C2×C4×D1112yes—
414C42C2×C4×D1114yes—
415C42C2×C22⋊D1112yes—
416C42C2×C22⋊D1114yes—
417C11#2254411yescharacteristic, complemented, Sylow
418C23—222no—
419C23—441no—
420C23—441no—
421C23—441no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23C22×D4411yescharacteristic
426Q8—28no—
427Q8—224no—
428Q8—224no—
429Q8—442no—
430Q8—442no—
431D4—222no—
432D4—222no—
433D4—441no—
434D4—441no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—222no—
442C2×C4—224no—
443C2×C4—222no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—448no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4#6696112yes—
458C2×C4#6696212yes—
459C2×C4C2×(C2×D11)⋊C414yes—
460C2×C4C2×(C2×D11)⋊C412yes—
461C2×C4C2×(C2×D11)⋊C414yes—
462C2×C4C2×(C2×D11)⋊C412yes—
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×#434311yescharacteristic
465C2×C4#6704011yescharacteristic
466C2×C4#41×D1111yescharacteristic
467C2×C4#6704211yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C8—22no—
470C8—41no—
471C8—42no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22#1062310711yescharacteristic
480C22#1062310811yescharacteristic
481C22C2×#6696111yescharacteristic
482C22C2×#6696211yescharacteristic
483C22#1062328211yescharacteristic
484C22#1062328411yescharacteristic
485C22C22×(C2×D11)⋊C411yescharacteristic
486C4—24no—
487C4—24no—
488C4—22no—
489C4—444no—
490C4—442no—
491C4—442no—
492C4—882no—
493C4—881no—
494C4#1062274614yes—
495C4C4×#434311yescharacteristic
496C4#1062310511yescharacteristic
497C4#1062334811yescharacteristic
498C4#1062336511yescharacteristic
499C2—882no—
500C2#1307145411yescharacteristic
501C2C2×#1062274611yescharacteristic
502C2#1307715011yescharacteristic
503C2#1308133611yescharacteristic
504C2#1308135811yescharacteristic
505C2#1308163811yescharacteristic
506C2#1308164911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22544
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. Q8×C4⋊Dic11C2semidirect
4. #13069538C2semidirect
6. #13069418C2semidirect
7. #13068622C2semidirect
9. #13068447C2semidirect
11. C2×C11×#446C2semidirect
16. #10623115C4semidirect
166. C2×#446D11semidirect
417. C11#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
Q8×C4⋊Dic112
#130695462
#130695382
#130694322
#130694182
#130686222
#130686172
#130684472
C4×#668852
C2×C11×#4462
#2254411