Finite Group Databasebeta

← #14908244

Subgroups — #14908244

Order 2816.

738 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×M32C211yesmaximal, characteristic, complemented
2#13078193C211yesmaximal, characteristic, complemented
3C2×#10622770C211yesmaximal, characteristic, complemented
4#13070726C212yesmaximal, complemented
5#13070716C212yesmaximal, complemented
6#13070709C212yesmaximal, complemented
7#13070699C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070332C211yesmaximal, characteristic, complemented
10#13070328C211yesmaximal, characteristic, complemented
11C2×C11×#509C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#10623359—21no—
15C2×#66991—21no—
16C22×C8×D11C2211yescharacteristic
17C11×#509—24no—
18C2×C11×SD32C2212yescomplemented
19C2×C11×D16C2212yescomplemented
20C2×C11×M32C2211yescharacteristic
21#10622846—21no—
22C2×#66896—21no—
23#10622801C2211yescharacteristic, complemented
24#10622801C2211yescharacteristic, complemented
25#10622784—21no—
26#10622784—21no—
27#10622770—21no—
28#10622770—21no—
29#10622770C2212yes—
30#10622770C2212yes—
31#10622770C2211yescharacteristic, complemented
32#10622770C2211yescharacteristic, complemented
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36D11×M32—24no—
37C2×#66862C2212yescomplemented
38C2×C16×D11C2212yescomplemented
39#10622202C2212yescomplemented
40#10622200C2212yescomplemented
41#10622200C2212yescomplemented
42#10622200C2212yescomplemented
43#10622143C2212yescomplemented
44#10622142C2212yescomplemented
45C2×C11×#41—21no—
46C22×D4×C11—21no—
47C22×C22⋊D11—41no—
48C22×C4×D11D411yescharacteristic
49C11×#135—22no—
50C11×#135—22no—
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×D8—22no—
54C2×C11×D8—21no—
55C2×C11×D8—22no—
56C2×C11×D8C2311yescharacteristic
57C2×C11×D8C2312yes—
58C22×C8×C11C2311yescharacteristic
59C2×C22⋊Dic11—41no—
60#66999—21no—
61#66999—21no—
62#66991—22no—
63#66991—22no—
64#66991—21no—
65#66991—21no—
66#66991—41no—
67#66991—41no—
68#66990—41no—
69#66988—41no—
70C4×C22⋊D11—41no—
71C4×C22⋊D11—41no—
72#66979—21no—
73C2×C4⋊Dic11—21no—
74C22×C11⋊C8D411yescharacteristic
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77C2×C8×D11D411yescharacteristic
78C2×C8×D11D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81C11×SD32—24no—
82C11×D16—24no—
83C11×M32D414yescomplemented
84C2×C11×C16C2312yes—
85#66899—21no—
86#66899—21no—
87#66896—22no—
88#66896—22no—
89#66896—21no—
90#66896—21no—
91#66882—21no—
92#66882C2312yes—
93#66882C2311yescharacteristic
94#66882C2311yescharacteristic
95#66881—21no—
96#66876—22no—
97C2×C11⋊C16C2312yes—
98#66862—24no—
99C16×D11—24no—
100#33605—111nomaximal, Sylow
101C24×C11—41no—
102C23×D11D811yescharacteristic
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C2×D4×C11—42no—
110C2×D4×C11—41no—
111C2×D4×C11—42no—
112C22×C4×C11—41no—
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—84no—
119C22×Dic11—41no—
120C22×Dic11D811yescharacteristic
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11D811yescharacteristic
124C2×C4×D11D811yescharacteristic
125C2×C4×D11C2×D411yescharacteristic
126C2×C4×D11C2×D411yescharacteristic
127C11×Q16—21no—
128C11×Q16—21no—
129C11×SD16—42no—
130C11×D8—21no—
131C11×D8—22no—
132C11×D8—22no—
133C11×D8—21no—
134C11×D8—42no—
135C2×C8×C11C2×D412yes—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11#4112yes—
138C2×C8×C11C2411yescharacteristic
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—42no—
142C22⋊Dic11—42no—
143C22⋊Dic11—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152C4×Dic11—41no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8C2×D411yescharacteristic
155C2×C11⋊C8C2×D411yescharacteristic
156C8×D11—22no—
157C8×D11—22no—
158C8×D11—21no—
159C8×D11—21no—
160C8×D11—21no—
161C8×D11—21no—
162C11×C16C2×D414yescomplemented
163C11⋊C16—22no—
164C2×#509D1111yescharacteristic, complemented
165C22×M32—111no—
166#3050—111no—
167C2×#466—111no—
168#2220—112no—
169#2218—112no—
170#2217—112no—
171#2215—112no—
172#2159—111no—
173#2140—111no—
174#2139—111no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—82no—
178C23×C11—82no—
179C23×C11—82no—
180C23×C11C2×D811yescharacteristic
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—41no—
184C22×D11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188D4×C11—42no—
189D4×C11—41no—
190D4×C11—42no—
191D4×C11—41no—
192D4×C11—82no—
193D4×C11—82no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11#12112yes—
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11#13512yes—
199C2×C4×C11C22×D411yescharacteristic
200C22⋊D11—82no—
201C22⋊D11—84no—
202C22⋊D11—82no—
203C22⋊D11—84no—
204C2×Dic11—22no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—82no—
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—21no—
214C4×D11—21no—
215C4×D11—22no—
216C4×D11—22no—
217C8×C11#12112yes—
218C8×C11C22×D411yescharacteristic
219C8×C11C2×#4111yescharacteristic
220C11⋊C8—21no—
221C11⋊C8—21no—
222C2×#135C2×D1111yescharacteristic
223C22×D8C2×D1111yescharacteristic
224C23×C8—111no—
225#525—221no—
226C2×#121—221no—
227#509—24no—
228C2×SD32C2×D1112yescomplemented
229C2×D16C2×D1112yescomplemented
230C2×M32—111no—
231C2×M32—112no—
232C2×M32—224no—
233C2×M32C2×D1111yescharacteristic
234C22×C16—112no—
235#467—111no—
236#467—111no—
237#466—112no—
238#466—112no—
239#466—111no—
240#466—111no—
241#466—221no—
242#466—221no—
243#465—221no—
244#465—221no—
245#427—111no—
246C2×#107—111no—
247#416—221no—
248C2×#102—221no—
249#367—112no—
250#366—112no—
251#358—112no—
252#357—112no—
253#357—112no—
254#357—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—82no—
258C22×C11—81no—
259C22×C11—82no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—82no—
263C22×C11—164no—
264C22×C11#46612yes—
265C22×C11C22×D811yescharacteristic
266C2×D11—21no—
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C2×D11—44no—
272C2×D11#50912yescomplemented
273C4×C11—81no—
274C4×C11#46612yes—
275C4×C11C2×#12111yescharacteristic
276C4×C11C2×#13511yescharacteristic
277Dic11—21no—
278Dic11—21no—
279Dic11—82no—
280Dic11—81no—
281Dic11—81no—
282C2×#41—21no—
283C22×D4—21no—
284C22×D4—441no—
285C23×C4—111no—
286#135—22no—
287#135—22no—
288C2×Q16C22×D1111yescharacteristic
289C2×SD16—21no—
290C2×D8—21no—
291C2×D8—22no—
292C2×D8—22no—
293C2×D8C22×D1112yes—
294C2×D8C22×D1111yescharacteristic
295C22×C8—111no—
296C22×C8—111no—
297C22×C8—111no—
298C22×C8—111no—
299C22×C8—111no—
300C22×C8—222no—
301C22×C8—222no—
302C22×C8C22×D1111yescharacteristic
303#123—441no—
304C22⋊Q8—221no—
305C22⋊Q8—221no—
306#121—222no—
307#121—222no—
308#121—221no—
309#121—221no—
310#121—441no—
311#121—441no—
312#120—441no—
313C4×D4—441no—
314C4×D4—441no—
315#117—221no—
316C2×C4⋊C4—221no—
317C2×C22⋊C4—441no—
318SD32—24no—
319D16—24no—
320M32—222no—
321M32—224no—
322M32C22⋊D1114yescomplemented
323C2×C16—112no—
324C2×C16—224no—
325C2×C16C22×D1112yes—
326#107—111no—
327#107—111no—
328#107—112no—
329#107—221no—
330#106—221no—
331#103—221no—
332#103—221no—
333#102—222no—
334#102—222no—
335#102—221no—
336#102—221no—
337C2×C11—22no—
338C2×C11—161no—
339C2×C11—162no—
340C2×C11C2×#46611yescharacteristic
341C2×C11C2×#50911yescharacteristic
342C2×C11#341411yescharacteristic
343D11—22no—
344D11—41no—
345C24—41no—
346C24—111no—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—884no—
361C22×C4—41no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—441no—
370C22×C4D4×D1111yescharacteristic
371Q16—21no—
372Q16—21no—
373SD16—42no—
374D8—22no—
375D8—21no—
376D8—21no—
377D8—22no—
378D8—42no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—221no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8D4×D1111yescharacteristic
389C2×C8#434112yes—
390C2×C8C2×C22⋊D1112yes—
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—222no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—442no—
401C22⋊C4—442no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C42—441no—
406C16—222no—
407C16C2×C22⋊D1114yescomplemented
408C11#3360511yescharacteristic, complemented, Sylow
409C23—41no—
410C23—42no—
411C23—82no—
412C23—82no—
413C23—82no—
414C23—111no—
415C23—111no—
416C23—222no—
417C23—222no—
418C23—441no—
419C23D8×D1111yescharacteristic
420Q8—41no—
421Q8—41no—
422D4—42no—
423D4—41no—
424D4—42no—
425D4—41no—
426D4—82no—
427D4—82no—
428D4—884no—
429D4—882no—
430D4—884no—
431D4—882no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4—111no—
435C2×C4—111no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—442no—
446C2×C4—882no—
447C2×C4D8×D1111yescharacteristic
448C2×C4#6696512yes—
449C2×C4#6699112yes—
450C2×C4C2×D4×D1111yescharacteristic
451C8—221no—
452C8—221no—
453C8#6699112yes—
454C8C2×#434111yescharacteristic
455C8C22×C22⋊D1111yescharacteristic
456C22—21no—
457C22—21no—
458C22—82no—
459C22—81no—
460C22—81no—
461C22—82no—
462C22—81no—
463C22—82no—
464C22—112no—
465C22—164no—
466C22—221no—
467C22—221no—
468C22—221no—
469C22—221no—
470C22—221no—
471C22—444no—
472C22#1062277012yes—
473C22C2×D8×D1111yescharacteristic
474C4—81no—
475C4—221no—
476C4—221no—
477C4—882no—
478C4—881no—
479C4—881no—
480C4#1062277012yes—
481C4C2×#6696511yescharacteristic
482C4C2×#6699111yescharacteristic
483C2—22no—
484C2—162no—
485C2—161no—
486C2—222no—
487C2—441no—
488C2C2×#1062277011yescharacteristic
489C2D11×#50911yescharacteristic
490C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33605
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×D11×M32C2semidirect
2. #13078193C2semidirect
3. C2×#10622770C2semidirect
4. #13070726C2semidirect
5. #13070716C2semidirect
6. #13070709C2semidirect
7. #13070699C2semidirect
8. #13070404C2semidirect
9. #13070332C2semidirect
10. #13070328C2semidirect
11. C2×C11×#509C2semidirect
18. C2×C11×SD32C22semidirect
19. C2×C11×D16C22semidirect
23. #10622801C22semidirect
24. #10622801C22semidirect
31. #10622770C22semidirect
32. #10622770C22semidirect
37. C2×#66862C22semidirect
38. C2×C16×D11C22semidirect
39. #10622202C22semidirect
40. #10622200C22semidirect
41. #10622200C22semidirect
42. #10622200C22semidirect
43. #10622143C22semidirect
44. #10622142C22semidirect
83. C11×M32D4semidirect
162. C11×C16C2×D4semidirect
164. C2×#509D11semidirect
228. C2×SD32C2×D11semidirect
229. C2×D16C2×D11semidirect
272. C2×D11#509semidirect
322. M32C22⋊D11semidirect
407. C16C2×C22⋊D11semidirect
408. C11#33605semidirect

Maximal subgroups

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

subgroupindex
C2×D11×M322
#130781932
C2×#106227702
#130707262
#130707162
#130707092
#130706992
#130704042
#130703322
#130703282
C2×C11×#5092
#3360511