Finite Group Databasebeta

← #14909821

Subgroups — #14909821

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079268C211yesmaximal, characteristic, complemented
2#13079103C211yesmaximal, characteristic
3#13070884C211yesmaximal, characteristic, complemented
4#13070870C211yesmaximal, characteristic, complemented
5#13070856C211yesmaximal, characteristic, complemented
6#13070849C211yesmaximal, characteristic, complemented
7#13070681C211yesmaximal, characteristic, complemented
8#13070680C211yesmaximal, characteristic, complemented
9#13070655C211yesmaximal, characteristic, complemented
10#13070654C211yesmaximal, characteristic, complemented
11#13070556C211yesmaximal, characteristic, complemented
12#13070547C211yesmaximal, characteristic, complemented
13#13070544C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2189C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17#10623361—21no—
18C2×#67002—21no—
19C22×D88C2211yescharacteristic
20#10623156—21no—
21C2×C11×Q32C2211yescharacteristic, complemented
22C2×C11×SD32C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic
24#10622804C2211yescharacteristic
25#10622804C2211yescharacteristic
26Q16×Dic11C2211yescharacteristic, complemented
27#10622794C2211yescharacteristic, complemented
28C2×#66893C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31#10622789—21no—
32#10622789—21no—
33#10622764C2211yescharacteristic
34#10622764C2211yescharacteristic
35C2×#66891C2211yescharacteristic, complemented
36#10622729C2211yescharacteristic
37#10622714C2211yescharacteristic
38#10622665—21no—
39C2×#66864C2211yescharacteristic
40C2×#66864C2211yescharacteristic
41#10622491C2211yescharacteristic, complemented
42#10622486C2211yescharacteristic, complemented
43#10622410—21no—
44#10622402—21no—
45C11×#358C2211yescharacteristic, complemented
46C11×#357C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic
48#10622202C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50C22⋊(C11⋊C16)C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic
58#10622129C2211yescharacteristic
59C2×C11×#41—21no—
60C22×D44—21no—
61C11×#135—41no—
62C11×#135—41no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69#67002—44no—
70#67000—21no—
71#67000—21no—
72Q8×Dic11—21no—
73#66997—21no—
74C2×#4326—21no—
75C2×#4325—21no—
76C2×#4325—21no—
77#66993—21no—
78#66993—21no—
79#66990—41no—
80#66990—41no—
81C2×#4323—21no—
82C2×#4323—21no—
83#66983—41no—
84#66983—41no—
85#66979D411yescharacteristic
86#66977—21no—
87C2×#4318D411yescharacteristic
88C2×Dic44C2311yescharacteristic
89C2×D88—21no—
90C2×D88—41no—
91C2×D88—41no—
92C2×D88C2311yescharacteristic
93C2×D88C2311yescharacteristic
94#66943—21no—
95#66943—41no—
96#66942—41no—
97#66940—21no—
98#66932—41no—
99#66932—41no—
100C11×Q32—41no—
101C11×SD32—41no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#103—21no—
106#66899—21no—
107#66893—41no—
108#66892—41no—
109#66892—41no—
110#66891—41no—
111#66882C2311yescharacteristic
112#66880—21no—
113#66879D411yescharacteristic
114#66879D411yescharacteristic
115C8×Dic11C2311yescharacteristic
116C8×Dic11C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#66874—21no—
120#66872—21no—
121#66864—41no—
122#66864—41no—
123#33788—111nomaximal, Sylow
124C23×D11—41no—
125C11×#41—42no—
126C11×#41—42no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C2×C22⋊D11—41no—
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—42no—
140C2×D44—42no—
141C2×D44—41no—
142C2×Dic22—21no—
143C11×Q16—21no—
144C11×Q16—21no—
145C11×Q16—21no—
146C11×Q16—21no—
147C11×SD16—42no—
148C11×D8—21no—
149C11×D8—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2411yescharacteristic
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C11×C22⋊C4—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11D811yescharacteristic
159C22⋊Dic11D811yescharacteristic
160#4326—42no—
161#4325—42no—
162#4325—42no—
163#4323—42no—
164#4323—42no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169C4⋊Dic11—21no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172C4⋊Dic11D811yescharacteristic
173C4⋊Dic11D811yescharacteristic
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180C4×Dic11—41no—
181C4×Dic11C2×D411yescharacteristic
182C4×Dic11C2×D411yescharacteristic
183#4318—22no—
184C2×C11⋊C8C2×D411yescharacteristic
185C2×C11⋊C8C2×D411yescharacteristic
186Dic44—21no—
187Dic44—21no—
188D88—21no—
189D88—21no—
190D88—21no—
191D88—21no—
192D88—42no—
193C11×C16—21no—
194C11×C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3177—111no—
198#3155—111no—
199#2251—111no—
200#2248—111no—
201#2244—111no—
202#2242—111no—
203#2211—111no—
204#2211—111no—
205#2207—111no—
206#2207—111no—
207#2189—111no—
208#2189D1111yescharacteristic, complemented
209#2187—111no—
210#2187—111no—
211#2164—111no—
212C23×C11—41no—
213C23×C11C2×D811yescharacteristic
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—82no—
217C22×D11—161no—
218C22×D11—161no—
219Q8×C11—41no—
220Q8×C11—41no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—82no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—82no—
232C2×C4×C11C2×D811yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C22⋊D11—161no—
235C22⋊D11—161no—
236C22⋊D11—161no—
237C22⋊D11—161no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11C2×D811yescharacteristic
241C2×Dic11C2×D811yescharacteristic
242C2×Dic11C2×D811yescharacteristic
243C2×Dic11C2×D811yescharacteristic
244D44—41no—
245D44—41no—
246D44—41no—
247D44—41no—
248D44—82no—
249Dic22—41no—
250Dic22—41no—
251C8×C11—21no—
252C8×C11H(5,𝔽2)11yescharacteristic
253C8×C11H(5,𝔽2)11yescharacteristic
254C11⋊C8—21no—
255C11⋊C8AGL(1,ℤ/8)12yes—
256C2×AGL(1,ℤ/8)—221no—
257C2×#135C2×D1111yescharacteristic
258C22×D8—111no—
259#541—221no—
260#535—221no—
261C2×Q32—111no—
262C2×Q32C2×D1111yescharacteristic, complemented
263C2×SD32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×SD32C2×D1111yescharacteristic, complemented
269#499—111no—
270#496—221no—
271#496—221no—
272#495—111no—
273#495—111no—
274#494—111no—
275#493—111no—
276#493—111no—
277#491—221no—
278#470—221no—
279#467—111no—
280#467C2×D1111yescharacteristic
281#441—221no—
282C4×Q16—111no—
283C4×Q16—111no—
284#405—111no—
285C4⋊C16—111no—
286C4⋊C16—111no—
287#358—111no—
288#358C2×D1111yescharacteristic, complemented
289#357—111no—
290#357—111no—
291#357—111no—
292#357—111no—
293#357—111no—
294#357C2×D1111yescharacteristic, complemented
295C22⋊C16—111no—
296C22⋊C16C2×D1111yescharacteristic
297#346—111no—
298C4×C16—111no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11C22×D811yescharacteristic
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—164no—
313C4×C11—21no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11#53511yescharacteristic
318C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
319Dic11—21no—
320Dic11—21no—
321Dic11—21no—
322Dic11—21no—
323Dic11—81no—
324Dic11—81no—
325C2×#41—21no—
326C22×D4—221no—
327AGL(1,ℤ/8)—444no—
328#135—41no—
329#135—41no—
330C2×Q16—111no—
331C2×Q16—221no—
332C2×Q16C22×D1111yescharacteristic
333C2×Q16C22×D1111yescharacteristic
334C2×SD16—21no—
335C2×SD16—221no—
336C2×SD16—221no—
337C2×D8—111no—
338C2×D8—111no—
339C2×D8—221no—
340C2×D8—221no—
341C2×D8—221no—
342C2×D8—441no—
343C2×D8—441no—
344C2×D8C22×D1111yescharacteristic
345C2×M16—111no—
346C22×C8C22×D1111yescharacteristic
347C4⋊Q8—221no—
348#127—221no—
349#127—221no—
350#126—441no—
351#126—441no—
352#125—221no—
353#125—441no—
354#125—441no—
355#124—221no—
356#124—221no—
357C22⋊Q8—21no—
358C22⋊Q8—221no—
359#121—441no—
360#121—441no—
361#120—441no—
362#120—441no—
363C4×Q8—221no—
364C4×Q8—221no—
365#117—111no—
366Q32—41no—
367Q32—441no—
368SD32—41no—
369SD32—441no—
370SD32—441no—
371SD32—441no—
372SD32—441no—
373SD32—441no—
374C2×C16—111no—
375C2×C16—111no—
376C2×C16C22×D1111yescharacteristic
377C2×C16C22×D1111yescharacteristic
378#107—111no—
379#107C22×D1111yescharacteristic
380#106—221no—
381#103—21no—
382#103—221no—
383#103—221no—
384#103—221no—
385#97—111no—
386#97—111no—
387C4×C8—111no—
388C4×C8—111no—
389C2×C11—41no—
390C2×C11—161no—
391C2×C11#320511yescharacteristic
392C2×C11#341611yescharacteristic
393C2×C11#341611yescharacteristic
394D11—161no—
395D11—161no—
396C24—441no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—221no—
402C2×D4—21no—
403C2×D4—41no—
404C2×D4—221no—
405C2×D4—221no—
406C2×D4—442no—
407C2×D4—442no—
408C2×D4—441no—
409C2×D4—441no—
410C2×D4—441no—
411C2×D4—441no—
412C2×D4—441no—
413C22×C4—41no—
414C22×C4D4×D1111yescharacteristic
415Q16—21no—
416Q16—21no—
417Q16—21no—
418Q16—21no—
419Q16—221no—
420Q16—221no—
421Q16—442no—
422SD16—42no—
423SD16—442no—
424SD16—442no—
425D8—21no—
426D8—21no—
427D8—221no—
428D8—221no—
429D8—221no—
430D8—221no—
431D8—442no—
432D8—442no—
433D8—442no—
434M16—222no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8D4×D1111yescharacteristic
440C2×C8C23×D1111yescharacteristic
441C4⋊C4—21no—
442C4⋊C4—41no—
443C4⋊C4—111no—
444C4⋊C4—111no—
445C4⋊C4—221no—
446C4⋊C4—441no—
447C4⋊C4—441no—
448C4⋊C4—441no—
449C4⋊C4—441no—
450C4⋊C4—441no—
451C4⋊C4—441no—
452C4⋊C4—441no—
453C22⋊C4—41no—
454C22⋊C4—111no—
455C22⋊C4—111no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C42—111no—
462C42—111no—
463C42—441no—
464C42—441no—
465C16—21no—
466C16—21no—
467C16—221no—
468C16—221no—
469C11#3378811yescharacteristic, complemented, Sylow
470C23—41no—
471C23—441no—
472C23—441no—
473C23—882no—
474C23—1761no—
475C23—1761no—
476C23D8×D1111yescharacteristic
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—41no—
481Q8—441no—
482Q8—441no—
483D4—41no—
484D4—41no—
485D4—82no—
486D4—441no—
487D4—441no—
488D4—441no—
489D4—441no—
490D4—882no—
491D4—1761no—
492D4—1761no—
493D4—1761no—
494D4—1761no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—82no—
501C2×C4—111no—
502C2×C4—111no—
503C2×C4—111no—
504C2×C4—111no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4D8×D1111yescharacteristic
508C2×C4C2×D4×D1111yescharacteristic
509C8—21no—
510C8—112no—
511C8—221no—
512C8#6703711yescharacteristic
513C8#6703711yescharacteristic
514C22—21no—
515C22—21no—
516C22—21no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—881no—
521C22—881no—
522C22—881no—
523C22—881no—
524C22—881no—
525C22—881no—
526C22—1764no—
527C22C2×D8×D1111yescharacteristic
528C4—21no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—221no—
533C4—221no—
534C4—221no—
535C4—221no—
536C4—881no—
537C4—881no—
538C4#1062312311yescharacteristic
539C4D11×AGL(1,ℤ/8)11yescharacteristic
540C2—41no—
541C2—161no—
542C2—1761no—
543C2—1761no—
544C2#1307953211yescharacteristic
545C2#1308175911yescharacteristic
546C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2189C2
socleC22×C11C22×D8
prime radical#13079103C2
hypercenter#2189D11
hypocenterC11#33788
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2189

Complements

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

NH ≅ G/Ntype
1. #13079268C2semidirect
3. #13070884C2semidirect
4. #13070870C2semidirect
5. #13070856C2semidirect
6. #13070849C2semidirect
7. #13070681C2semidirect
8. #13070680C2semidirect
9. #13070655C2semidirect
10. #13070654C2semidirect
11. #13070556C2semidirect
12. #13070547C2semidirect
13. #13070544C2semidirect
14. #13070420C2semidirect
15. C11×#2189C2semidirect
21. C2×C11×Q32C22semidirect
22. C2×C11×SD32C22semidirect
26. Q16×Dic11C22semidirect
27. #10622794C22semidirect
28. C2×#66893C22semidirect
35. C2×#66891C22semidirect
41. #10622491C22semidirect
42. #10622486C22semidirect
45. C11×#358C22semidirect
46. C11×#357C22semidirect
48. #10622202C22semidirect
49. #10622200C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
208. #2189D11semidirect
262. C2×Q32C2×D11semidirect
268. C2×SD32C2×D11semidirect
288. #358C2×D11semidirect
294. #357C2×D11semidirect
469. C11#33788semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130791032
#130708842
#130708702
#130708562
#130708492
#130706812
#130706802
#130706552
#130706542
#130705562
#130705472
#130705442
#130704202
C11×#21892
#3378811