Finite Group Databasebeta

← #14908062

Subgroups — #14908062

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C212yesmaximal, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3C4×#66972C211yesmaximal, characteristic, complemented
4#13070656C211yesmaximal, characteristic, complemented
5#13070654C212yesmaximal, complemented
6#13070652C211yesmaximal, characteristic, complemented
7#13070650C212yesmaximal, complemented
8#13070648C211yesmaximal, characteristic, complemented
9#13070370C211yesmaximal, characteristic, complemented
10#13070330C212yesmaximal, complemented
11C11×#2207C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13C2×D8×D11—21no—
14C2×D8×D11C2212yes—
15D11×#127—21no—
16C4×#4343—21no—
17C2×C11×SD32C2212yescomplemented
18C11×#493C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic, complemented
20Q16×Dic11C2211yescharacteristic, complemented
21C2×#66892C2212yescomplemented
22#10622764—21no—
23#10622764C2212yes—
24C2×#66890C2212yescomplemented
25#10622686—21no—
26C4×#4325—21no—
27#10622527—28no—
28C2×D176C2212yescomplemented
29C2×#66862C2212yes—
30#10622493C2211yescharacteristic
31#10622485C2211yescharacteristic, complemented
32#10622417—21no—
33#10622401—21no—
34#10622308C2211yescharacteristic
35C4×D88C2211yescharacteristic, complemented
36C4×C8×D11C2211yescharacteristic
37C11×C4⋊C16C2211yescharacteristic, complemented
38C11×#357C2212yescomplemented
39#10622200C2212yescomplemented
40#10622147C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42#10622129C2212yescomplemented
43C4⋊(C11⋊C16)C2211yescharacteristic, complemented
44C2×#4343—21no—
45C2×D4×D11—22no—
46C2×D4×D11—41no—
47C2×D4×D11—41no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×D8—21no—
50C2×C11×D8C2312yes—
51C11×#127—21no—
52C4×Q8×C11—21no—
53Q8×Dic11—21no—
54C2×#4325—21no—
55#66993—22no—
56#66993—41no—
57#66993—41no—
58C2×#4323—22no—
59C2×#4323—22no—
60#66972—22no—
61#66972D414yescomplemented
62D8×D11—24no—
63D8×D11—24no—
64D8×D11—44no—
65C2×D88—21no—
66C2×D88C2312yes—
67C2×D88C2311yescharacteristic
68C2×C8×D11D411yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66946—21no—
71#66946—41no—
72#66945—21no—
73#66945—41no—
74#66927—21no—
75C4×D44—21no—
76C4×D44—41no—
77C42×D11—41no—
78C42×D11D411yescharacteristic
79C11×SD32—24no—
80C2×C11×C16C2312yes—
81C11×#107C2311yescharacteristic
82C11×#103—21no—
83C4×C8×C11C2311yescharacteristic
84#66899—21no—
85#66892—24no—
86#66890—24no—
87#66885—21no—
88#66882C2311yescharacteristic
89C8×Dic11D411yescharacteristic
90C8×Dic11C2311yescharacteristic
91C2×C11⋊C16C2312yes—
92#66873—21no—
93#66872—21no—
94C4×C11⋊C8D411yescharacteristic
95D176—24no—
96#66862—24no—
97#33582—111nomaximal, Sylow
98C23×D11—42no—
99C2×Q8×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×C22⋊D11—42no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106#4343—24no—
107#4343—42no—
108D4×D11—44no—
109D4×D11—44no—
110D4×D11—84no—
111D4×D11—84no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—41no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11D811yescharacteristic
121C2×C4×D11D811yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C11×Q16—21no—
124C11×Q16C2×D412yescomplemented
125C11×D8—22no—
126C11×D8—22no—
127C11×D8—42no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134#4325—24no—
135#4323—44no—
136#4323—44no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—41no—
142C4×Dic11—41no—
143C4×Dic11—41no—
144C4×Dic11D811yescharacteristic
145C4×Dic11D811yescharacteristic
146C4×Dic11C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148C2×C11⋊C8C2×D411yescharacteristic
149D88—22no—
150D88—21no—
151D88—22no—
152D88—42no—
153D88C2×D412yescomplemented
154C8×D11—22no—
155C8×D11C2×D412yes—
156C8×D11#4112yes—
157C11×C16—22no—
158C11⋊C16—22no—
159C2×#509—112no—
160C2×#493—111no—
161C4×#135—111no—
162#2207—112no—
163#2207—111no—
164#2207D1111yescharacteristic, complemented
165#2206—111no—
166#2206—111no—
167#2206—112no—
168#2150—111no—
169#2140—112no—
170C23×C11—42no—
171C22×D11—41no—
172C22×D11—42no—
173C22×D11—84no—
174C22×D11—84no—
175C22×D11—84no—
176C22×D11C2×D811yescharacteristic
177Q8×C11—22no—
178Q8×C11—41no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—82no—
182D4×C11—82no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C22⋊D11—84no—
189C22⋊D11—84no—
190C22⋊D11—84no—
191C2×Dic11—41no—
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194C2×Dic11C2×D811yescharacteristic
195D44—22no—
196D44—44no—
197D44—42no—
198D44—41no—
199D44—42no—
200D44—82no—
201D44—82no—
202C4×D11—22no—
203C4×D11—22no—
204C4×D11—44no—
205C4×D11—82no—
206C4×D11—82no—
207C4×D11#12112yes—
208C4×D11AGL(1,ℤ/8)12yes—
209C8×C11—21no—
210C8×C11C22×D411yescharacteristic
211C8×C11C2×#4111yescharacteristic
212C11⋊C8—21no—
213C11⋊C8#12112yes—
214C2×#135—111no—
215C22×D8—112no—
216C22×D8—221no—
217C2×#127—221no—
218C4×#41—221no—
219#509—228no—
220C2×SD32—112no—
221C2×SD32C2×D1112yescomplemented
222C2×D16—112no—
223C2×D16—112no—
224C2×M32—112no—
225#493—112no—
226#493—111no—
227#493—221no—
228#493—221no—
229#493C2×D1111yescharacteristic
230C4×Q16—111no—
231C4×Q16C2×D1111yescharacteristic, complemented
232C4×SD16—221no—
233C4×SD16—221no—
234C4×D8—111no—
235C4×D8—111no—
236#427—111no—
237#416—221no—
238C2×C4×C8—111no—
239C4⋊C16—112no—
240C4⋊C16—111no—
241C4⋊C16C2×D1111yescharacteristic, complemented
242#357—112no—
243#357—112no—
244#357—112no—
245#357C2×D1112yescomplemented
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11C22×D811yescharacteristic
250C2×D11—21no—
251C2×D11—21no—
252C2×D11—42no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—168no—
259C2×D11#45912yes—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—81no—
263C4×C11#50912yescomplemented
264C4×C11C2×#12111yescharacteristic
265C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
266Dic11—21no—
267Dic11—81no—
268Dic11#45912yes—
269Dic11#50912yescomplemented
270C2×#41—221no—
271C22×D4—222no—
272C22×D4—441no—
273C22×D4—441no—
274#135—114no—
275#135—222no—
276C2×Q16C22×D1111yescharacteristic
277C2×SD16—221no—
278C2×D8—21no—
279C2×D8—111no—
280C2×D8—112no—
281C2×D8—224no—
282C2×D8—224no—
283C2×D8—222no—
284C2×D8—222no—
285C2×D8—221no—
286C2×D8—444no—
287C2×D8C22×D1112yes—
288C22×C8—111no—
289C22×C8—111no—
290#127—21no—
291#127—222no—
292#127—221no—
293#127—441no—
294#127—441no—
295C4×Q8—21no—
296C4×Q8—221no—
297C4×D4—221no—
298C4×D4—221no—
299C4×D4—441no—
300C4×D4—441no—
301#117—221no—
302#117—441no—
303C2×C42—111no—
304C2×C42—441no—
305SD32—24no—
306SD32—224no—
307D16—224no—
308D16—224no—
309M32—224no—
310C2×C16—112no—
311C2×C16C22×D1112yes—
312#107—111no—
313#107C22×D1111yescharacteristic
314#106—221no—
315#103—21no—
316#103—221no—
317#102—221no—
318#102—221no—
319C4×C8—111no—
320C4×C8—111no—
321C4×C8—111no—
322C4×C8C22×D1111yescharacteristic
323C2×C11—162no—
324C2×C11C2×#45911yescharacteristic
325C2×C11C2×#50911yescharacteristic
326C2×C11C2×#50911yescharacteristic
327D11—22no—
328D11—82no—
329D11—162no—
330C24—442no—
331#41—224no—
332#41—442no—
333C2×Q8—21no—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—221no—
338C2×D4—222no—
339C2×D4—441no—
340C2×D4—444no—
341C2×D4—444no—
342C2×D4—442no—
343C2×D4—442no—
344C2×D4—442no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—884no—
348C2×D4—884no—
349C22×C4—111no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—441no—
353C22×C4—441no—
354C22×C4—441no—
355Q16—21no—
356Q16D4×D1112yescomplemented
357SD16—224no—
358D8—22no—
359D8—22no—
360D8—42no—
361D8—112no—
362D8—222no—
363D8—221no—
364D8—222no—
365D8—442no—
366D8—444no—
367D8—444no—
368C2×C8—111no—
369C2×C8—112no—
370C2×C8—112no—
371C2×C8—111no—
372C2×C8—222no—
373C2×C8D4×D1111yescharacteristic
374C2×C8C23×D1111yescharacteristic
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C42—41no—
383C42—111no—
384C42—111no—
385C42—111no—
386C42—441no—
387C42—441no—
388C42D4×D1111yescharacteristic
389C16—22no—
390C16—222no—
391C11#3358211yescharacteristic, complemented, Sylow
392C23—42no—
393C23—111no—
394C23—441no—
395C23—442no—
396C23—884no—
397C23—884no—
398C23—884no—
399Q8—22no—
400Q8—41no—
401D4—42no—
402D4—42no—
403D4—82no—
404D4—82no—
405D4—222no—
406D4—444no—
407D4—441no—
408D4—442no—
409D4—442no—
410D4—882no—
411D4—884no—
412D4—884no—
413D4—884no—
414D4—882no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—112no—
420C2×C4—112no—
421C2×C4—111no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—444no—
425C2×C4—441no—
426C2×C4—882no—
427C2×C4—882no—
428C2×C4D8×D1111yescharacteristic
429C2×C4D8×D1111yescharacteristic
430C2×C4C2×D4×D1111yescharacteristic
431C8—21no—
432C8—112no—
433C8—221no—
434C8C2×D4×D1111yescharacteristic
435C8#41×D1111yescharacteristic
436C22—82no—
437C22—82no—
438C22—82no—
439C22—112no—
440C22—221no—
441C22—221no—
442C22—442no—
443C22—881no—
444C22—881no—
445C22—882no—
446C22—882no—
447C22—882no—
448C22—1768no—
449C22C2×D8×D1111yescharacteristic
450C4—21no—
451C4—42no—
452C4—81no—
453C4—112no—
454C4—112no—
455C4—221no—
456C4—881no—
457C4#1062252712yescomplemented
458C4D11×#12111yescharacteristic
459C4D11×AGL(1,ℤ/8)11yescharacteristic
460C2—162no—
461C2—222no—
462C2—882no—
463C2—1762no—
464C2D11×#45911yescharacteristic
465C2D11×#50911yescharacteristic
466C2C2×#1062252711yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
hypercenter#2207D11
hypocenterC11#33582
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. D11×#493C2semidirect
3. C4×#66972C2semidirect
4. #13070656C2semidirect
5. #13070654C2semidirect
6. #13070652C2semidirect
7. #13070650C2semidirect
8. #13070648C2semidirect
9. #13070370C2semidirect
10. #13070330C2semidirect
11. C11×#2207C2semidirect
17. C2×C11×SD32C22semidirect
19. C4×C11×Q16C22semidirect
20. Q16×Dic11C22semidirect
21. C2×#66892C22semidirect
24. C2×#66890C22semidirect
28. C2×D176C22semidirect
31. #10622485C22semidirect
35. C4×D88C22semidirect
37. C11×C4⋊C16C22semidirect
38. C11×#357C22semidirect
39. #10622200C22semidirect
40. #10622147C22semidirect
41. Dic11⋊C16C22semidirect
42. #10622129C22semidirect
43. C4⋊(C11⋊C16)C22semidirect
61. #66972D4semidirect
124. C11×Q16C2×D4semidirect
153. D88C2×D4semidirect
164. #2207D11semidirect
221. C2×SD32C2×D11semidirect
231. C4×Q16C2×D11semidirect
241. C4⋊C16C2×D11semidirect
245. #357C2×D11semidirect
263. C4×C11#509semidirect
269. Dic11#509semidirect
356. Q16D4×D11semidirect
391. C11#33582semidirect
457. C4#10622527semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
D11×#4932
C4×#669722
#130706562
#130706542
#130706522
#130706502
#130706482
#130703702
#130703302
C11×#22072
#3358211