Finite Group Databasebeta

← #14909820

Subgroups — #14909820

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#13079271C211yesmaximal, characteristic, complemented
2#13079098C211yesmaximal, characteristic
3#13070884C211yesmaximal, characteristic, complemented
4#13070870C211yesmaximal, characteristic, complemented
5#13070856C211yesmaximal, characteristic, complemented
6#13070849C211yesmaximal, characteristic, complemented
7#13070675C211yesmaximal, characteristic, complemented
8#13070657C211yesmaximal, characteristic, complemented
9#13070656C211yesmaximal, characteristic, complemented
10#13070559C211yesmaximal, characteristic, complemented
11#13070555C211yesmaximal, characteristic, complemented
12#13070546C211yesmaximal, characteristic, complemented
13#13070543C211yesmaximal, characteristic, complemented
14#13070422C211yesmaximal, characteristic, complemented
15C11×#2211C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66967—21no—
18C2×D8×D11C2211yescharacteristic
19#10623205—21no—
20#10623114—21no—
21C2×C11×Q32C2211yescharacteristic, complemented
22C2×C11×SD32C2211yescharacteristic
23C11×#495C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic, complemented
25#10622804C2211yescharacteristic
26#10622801C2211yescharacteristic
27#10622794C2211yescharacteristic, complemented
28C2×#66893C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic, complemented
31#10622789—21no—
32#10622764C2211yescharacteristic
33C2×#66891C2211yescharacteristic
34#10622671—21no—
35#10622643—21no—
36C2×#66864C2211yescharacteristic
37C2×#66864C2211yescharacteristic, complemented
38#10622500C2211yescharacteristic
39#10622491C2211yescharacteristic, complemented
40#10622429—21no—
41#10622410—21no—
42C4×Dic44C2211yescharacteristic, complemented
43#10622308C2211yescharacteristic
44#10622302C2211yescharacteristic
45C11×C4⋊C16C2211yescharacteristic, complemented
46C11×#358C2211yescharacteristic, complemented
47C11×#357C2211yescharacteristic
48#10622202C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic
53(C2×D11)⋊C16C2211yescharacteristic
54#10622140C2211yescharacteristic, complemented
55C16×Dic11C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic
57#10622129C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×#4343—21no—
60C2×D4×D11—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×D8C2311yescharacteristic
65C11×#124—21no—
66C4×Q8×C11—21no—
67#67000—21no—
68#66999—21no—
69#66997—21no—
70C2×#4326—21no—
71C2×#4325—21no—
72C2×#4325—21no—
73#66993—21no—
74C2×#4323—21no—
75C2×#4323—21no—
76#66972—41no—
77#66972—41no—
78#66967—44no—
79D8×D11—41no—
80D8×D11—41no—
81C2×Dic44C2311yescharacteristic
82C2×D88—21no—
83C2×D88C2311yescharacteristic
84C2×D88C2311yescharacteristic
85C2×#4313D411yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66951—41no—
88#66950—21no—
89#66943—21no—
90#66942—41no—
91#66937—41no—
92#66937—41no—
93#66935—41no—
94#66935—41no—
95#66929—41no—
96#66927—21no—
97#66925D411yescharacteristic
98#66923—41no—
99C4×Dic22—21no—
100C11×Q32—41no—
101C11×SD32—41no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#103—21no—
106C4×C8×C11C2311yescharacteristic
107#66899—21no—
108#66893—41no—
109#66892—41no—
110#66892—41no—
111#66891—41no—
112#66882C2311yescharacteristic
113#66880—21no—
114#66879D411yescharacteristic
115C8×Dic11C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118#66874—21no—
119#66872—21no—
120#66867D411yescharacteristic
121#66864—41no—
122#66864—41no—
123#33788—111nomaximal, Sylow
124C23×D11—41no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×D4×C11—21no—
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131#4343—42no—
132#4343—42no—
133D4×D11—42no—
134D4×D11—42no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—41no—
140C2×C4×D11—41no—
141C2×C4×D11C2×D411yescharacteristic
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×C11C2×D411yescharacteristic
151C2×C8×C11C2411yescharacteristic
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C42×C11—41no—
157C42×C11C2×D411yescharacteristic
158#4326—42no—
159#4325—42no—
160#4325—42no—
161#4323—42no—
162#4323—42no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4D811yescharacteristic
168(C2×D11)⋊C4D811yescharacteristic
169C4⋊Dic11—21no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4D811yescharacteristic
178Dic11⋊C4D811yescharacteristic
179C4×Dic11—41no—
180C4×Dic11C2×D411yescharacteristic
181C2×C11⋊C8C2×D411yescharacteristic
182C2×C11⋊C8C2×D411yescharacteristic
183Dic44—21no—
184Dic44—21no—
185D88—21no—
186D88—21no—
187D88—21no—
188D88—21no—
189D88—42no—
190#4313—22no—
191C8×D11—21no—
192C8×D11—21no—
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#2211D1111yescharacteristic, complemented
205#2207—111no—
206#2207—111no—
207#2189—111no—
208#2189—111no—
209#2187—111no—
210#2187—111no—
211#2164—111no—
212C23×C11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—82no—
216C22×D11—161no—
217C22×D11—161no—
218C22×D11C2×D811yescharacteristic
219Q8×C11—41no—
220Q8×C11—41no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C22⋊D11—82no—
232C22⋊D11—161no—
233C22⋊D11—161no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11C2×D811yescharacteristic
237C2×Dic11C2×D811yescharacteristic
238C2×Dic11C2×D811yescharacteristic
239D44—41no—
240D44—41no—
241D44—41no—
242D44—41no—
243D44—82no—
244D44—161no—
245D44—161no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—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×#135—111no—
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
269#499—111no—
270#496—221no—
271#496—221no—
272#495—111no—
273#495C2×D1111yescharacteristic
274#494—111no—
275#493—111no—
276#493—111no—
277#491—221no—
278#470—221no—
279#467—111no—
280#467—111no—
281#441—221no—
282C4×Q16—111no—
283C4×Q16C2×D1111yescharacteristic, complemented
284#405—111no—
285C4⋊C16—111no—
286C4⋊C16C2×D1111yescharacteristic, complemented
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
295C22⋊C16—111no—
296C22⋊C16—111no—
297#346—111no—
298C4×C16—111no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C22×D811yescharacteristic
303C2×D11—21no—
304C2×D11—21no—
305C2×D11—21no—
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—21no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11#53511yescharacteristic
319C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
320Dic11—21no—
321Dic11—21no—
322Dic11—21no—
323Dic11—81no—
324Dic11—81no—
325C2×#41—221no—
326C22×D4—221no—
327AGL(1,ℤ/8)—444no—
328#135—441no—
329#135—441no—
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×C8—111no—
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—21no—
356#124—221no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359#121—441no—
360#121—441no—
361#120—441no—
362#120—441no—
363C4×Q8—21no—
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×C8C22×D1111yescharacteristic
389C2×C11—161no—
390C2×C11#320511yescharacteristic
391C2×C11#341611yescharacteristic
392C2×C11#341611yescharacteristic
393D11—41no—
394D11—161no—
395D11—161no—
396C24—441no—
397#41—442no—
398#41—442no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—221no—
402C2×D4—21no—
403C2×D4—221no—
404C2×D4—221no—
405C2×D4—441no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—441no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4—441no—
412C2×D4—441no—
413C22×C4—111no—
414C22×C4—441no—
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—111no—
436C2×C8—111no—
437C2×C8—221no—
438C2×C8—221no—
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—41no—
455C22⋊C4—111no—
456C22⋊C4—111no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C42—41no—
462C42—111no—
463C42—441no—
464C42D4×D1111yescharacteristic
465C16—21no—
466C16—21no—
467C16—221no—
468C16—221no—
469C11#3378811yescharacteristic, complemented, Sylow
470C23—41no—
471C23—111no—
472C23—441no—
473C23—441no—
474C23—882no—
475C23—1761no—
476C23—1761no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—41no—
481Q8—441no—
482Q8—441no—
483D4—41no—
484D4—41no—
485D4—441no—
486D4—441no—
487D4—441no—
488D4—441no—
489D4—882no—
490D4—882no—
491D4—1761no—
492D4—1761no—
493D4—1761no—
494D4—1761no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—111no—
499C2×C4—111no—
500C2×C4—111no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—882no—
506C2×C4D8×D1111yescharacteristic
507C2×C4D8×D1111yescharacteristic
508C2×C4C2×D4×D1111yescharacteristic
509C8—21no—
510C8—112no—
511C8—221no—
512C8#6703711yescharacteristic
513C8#6704211yescharacteristic
514C22—81no—
515C22—81no—
516C22—81no—
517C22—221no—
518C22—221no—
519C22—221no—
520C22—881no—
521C22—881no—
522C22—881no—
523C22—881no—
524C22—881no—
525C22—881no—
526C22—1764no—
527C22C2×D8×D1111yescharacteristic
528C4—21no—
529C4—21no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—221no—
534C4—221no—
535C4—221no—
536C4—881no—
537C4—881no—
538C4#1062313811yescharacteristic
539C4D11×AGL(1,ℤ/8)11yescharacteristic
540C2—161no—
541C2—441no—
542C2—1761no—
543C2—1761no—
544C2#1307953311yescharacteristic
545C2#1308175911yescharacteristic
546C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radical#13079098C2
hypercenter#2211D11
hypocenterC11#33788
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
1. #13079271C2semidirect
3. #13070884C2semidirect
4. #13070870C2semidirect
5. #13070856C2semidirect
6. #13070849C2semidirect
7. #13070675C2semidirect
8. #13070657C2semidirect
9. #13070656C2semidirect
10. #13070559C2semidirect
11. #13070555C2semidirect
12. #13070546C2semidirect
13. #13070543C2semidirect
14. #13070422C2semidirect
15. C11×#2211C2semidirect
21. C2×C11×Q32C22semidirect
24. C4×C11×Q16C22semidirect
27. #10622794C22semidirect
28. C2×#66893C22semidirect
30. C2×#66892C22semidirect
37. C2×#66864C22semidirect
39. #10622491C22semidirect
42. C4×Dic44C22semidirect
45. C11×C4⋊C16C22semidirect
46. C11×#358C22semidirect
48. #10622202C22semidirect
51. #10622147C22semidirect
54. #10622140C22semidirect
55. C16×Dic11C22semidirect
57. #10622129C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
204. #2211D11semidirect
262. C2×Q32C2×D11semidirect
283. C4×Q16C2×D11semidirect
286. C4⋊C16C2×D11semidirect
288. #358C2×D11semidirect
469. C11#33788semidirect

Maximal subgroups

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

subgroupindex
#130792712
#130790982
#130708842
#130708702
#130708562
#130708492
#130706752
#130706572
#130706562
#130705592
#130705552
#130705462
#130705432
#130704222
C11×#22112
#3378811