Finite Group Databasebeta

← #14910742

Subgroups — #14910742

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080961C211yesmaximal, characteristic, complemented
2#13080298C211yesmaximal, characteristic, complemented
3#13070854C211yesmaximal, characteristic, complemented
4#13070803C211yesmaximal, characteristic, complemented
5#13070762C211yesmaximal, characteristic, complemented
6#13070720C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070674C211yesmaximal, characteristic, complemented
9#13070542C211yesmaximal, characteristic, complemented
10#13070530C211yesmaximal, characteristic, complemented
11#13070491C211yesmaximal, characteristic, complemented
12#13070438C211yesmaximal, characteristic, complemented
13#13070327C211yesmaximal, characteristic, complemented
14C2×#10622129C211yesmaximal, characteristic, complemented
15C11×#2235C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623161—21no—
19#10623038—21no—
20C11×#467C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622804C2211yescharacteristic
23C2×#66892C2211yescharacteristic, complemented
24#10622728C2211yescharacteristic
25C8×C22⋊D11C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622659—21no—
28#10622580—21no—
29C2×D176C2211yescharacteristic
30C2×D176C2211yescharacteristic
31C2×#66862C2211yescharacteristic, complemented
32#10622503—21no—
33#10622496C2211yescharacteristic
34#10622496C2211yescharacteristic, complemented
35#10622495—21no—
36D11×#107C2211yescharacteristic, complemented
37#10622487C2211yescharacteristic, complemented
38#10622485C2211yescharacteristic
39#10622485C2211yescharacteristic, complemented
40#10622432—21no—
41#10622424—21no—
42C11×#367C2211yescharacteristic, complemented
43C11×#367C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×C22⋊C16C2211yescharacteristic
47#10622202C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622140C2211yescharacteristic, complemented
52Dic11⋊C16C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622129C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C2×#4343—21no—
60C2×#4339—41no—
61C22×D44—21no—
62C2×C11×Q16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C2×C11×C4⋊C4—21no—
66#67000—21no—
67C2×#4325—21no—
68C2×#4325—21no—
69#66983—21no—
70#66982—41no—
71C4×C22⋊D11D411yescharacteristic
72#66972—22no—
73#66972—41no—
74C2×D88—22no—
75C2×D88—21no—
76C2×D88—41no—
77C2×D88C2311yescharacteristic
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81#66949—41no—
82#66948—21no—
83#66948—21no—
84#66948—41no—
85#66947—41no—
86#66947—41no—
87#66946—21no—
88#66946—21no—
89C4⋊C4×D11—21no—
90#66941—21no—
91#66935—41no—
92C22⋊C4×D11—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C22⋊(C11⋊C8)D411yescharacteristic
101#66892—41no—
102#66885—21no—
103(C2×D11)⋊C8D411yescharacteristic
104#66882C2311yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16—41no—
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66873—21no—
111#66873—21no—
112#66873—21no—
113#66873—21no—
114#66871—21no—
115#66871—21no—
116D176—22no—
117D176—41no—
118#66862—41no—
119#33873—111nomaximal, Sylow
120C23×D11—41no—
121C2×Q8×C11—21no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11D811yescharacteristic
126#4343—42no—
127#4343—81no—
128#4339—84no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—42no—
133C2×D44—41no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—81no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×C4×D11C2×D411yescharacteristic
143C2×Dic22—41no—
144C11×Q16—21no—
145C11×Q16—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2411yescharacteristic
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C22⋊C4—41no—
156C22⋊Dic11D811yescharacteristic
157#4325—42no—
158#4325—81no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4D811yescharacteristic
167C4⋊Dic11—21no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4D811yescharacteristic
171C4×Dic11C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174D88—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—21no—
179D88—42no—
180D88#4112yescomplemented
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188#3280—111no—
189#2243—111no—
190#2235D1111yescharacteristic, complemented
191#2233—111no—
192#2226—111no—
193#2218—111no—
194#2217—111no—
195#2210—111no—
196#2186—111no—
197#2184—111no—
198#2177—111no—
199#2168—111no—
200#2139—111no—
201C2×#357—111no—
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—161no—
209C22×D11C2×D811yescharacteristic
210Q8×C11—41no—
211Q8×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—82no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—22no—
222C22⋊D11—82no—
223C2×Dic11—41no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227D44—22no—
228D44—41no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—82no—
234D44—82no—
235D44—82no—
236D44—161no—
237C4×D11—21no—
238C4×D11—21no—
239C4×D11—82no—
240C4×D11—82no—
241C4×D11—82no—
242C4×D11—161no—
243Dic22—82no—
244C8×C11—21no—
245C8×C11C2×#4111yescharacteristic
246C8×C11H(5,𝔽2)11yescharacteristic
247C11⋊C8—21no—
248C11⋊C8—21no—
249C2×#135—111no—
250C22×D8—111no—
251#547—221no—
252#546—221no—
253C2×SD32—111no—
254C2×D16—111no—
255C2×D16—111no—
256C2×M32—111no—
257C22×C16—111no—
258#500—111no—
259#495—111no—
260#480—221no—
261#480—221no—
262#474—221no—
263#467C2×D1111yescharacteristic
264#466—111no—
265#466—111no—
266#466—111no—
267#463—221no—
268#450—221no—
269#449—221no—
270C4×D8—111no—
271C4×D8—111no—
272C8×D4—111no—
273C2×#107—111no—
274C2×#107C2×D1111yescharacteristic
275#367—111no—
276#367C2×D1111yescharacteristic, complemented
277#367C2×D1111yescharacteristic, complemented
278C4⋊C16—111no—
279#358—111no—
280#358C2×D1111yescharacteristic, complemented
281#358C2×D1111yescharacteristic, complemented
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286#357—111no—
287#357—111no—
288#357—111no—
289C22⋊C16—111no—
290C22⋊C16C2×D1111yescharacteristic
291#346—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11#50912yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—42no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—164no—
309C4×C11—21no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11#54611yescharacteristic
315C4×C11#57711yescharacteristic
316Dic11—21no—
317Dic11—21no—
318Dic11—21no—
319Dic11—81no—
320C2×#41—221no—
321C2×#41—441no—
322C22×D4—221no—
323#135—222no—
324#135—441no—
325C2×Q16C22×D1111yescharacteristic
326C2×SD16—221no—
327C2×SD16—221no—
328C2×D8—111no—
329C2×D8—111no—
330C2×D8—111no—
331C2×D8—222no—
332C2×D8—221no—
333C2×D8—441no—
334C22×C8—111no—
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—221no—
337#124—221no—
338#123—441no—
339#123—441no—
340#123—441no—
341C22⋊Q8—21no—
342C22⋊Q8—441no—
343#121—221no—
344#121—221no—
345#121—221no—
346#121—441no—
347#120—441no—
348C4×D4—111no—
349C4×D4—221no—
350C4×D4—221no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—221no—
353C2×C22⋊C4—441no—
354SD32—441no—
355D16—222no—
356D16—441no—
357M32—441no—
358C2×C16—111no—
359C2×C16—111no—
360C2×C16—441no—
361C2×C16C22×D1111yescharacteristic
362C2×C16C22×D1111yescharacteristic
363#107—21no—
364#107—111no—
365#107—221no—
366#107—221no—
367#107C22×D1111yescharacteristic
368#107C22×D1111yescharacteristic
369#107C22×D1111yescharacteristic
370C4⋊C8—111no—
371#103—21no—
372#102—221no—
373#102—221no—
374#102—221no—
375#102—221no—
376#102—221no—
377C22⋊C8—111no—
378C22⋊C8—111no—
379C4×C8—111no—
380C2×C11—22no—
381C2×C11#329411yescharacteristic
382C2×C11C2×#50911yescharacteristic
383C2×C11#341611yescharacteristic
384D11—41no—
385D11—82no—
386D11—161no—
387D11—161no—
388C24—441no—
389#41—442no—
390#41—884no—
391#41—881no—
392C2×Q8—21no—
393C2×Q8—441no—
394C2×D4—111no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—442no—
399C2×D4—441no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4—881no—
405C22×C4—41no—
406C22×C4—111no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4—441no—
411C22×C4D4×D1111yescharacteristic
412Q16—21no—
413Q16—21no—
414SD16—442no—
415SD16—881no—
416D8—112no—
417D8—221no—
418D8—221no—
419D8—221no—
420D8—221no—
421D8—221no—
422D8—442no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—111no—
426C2×C8—111no—
427C2×C8—221no—
428C2×C8—221no—
429C2×C8D4×D1111yescharacteristic
430C2×C8C23×D1111yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—111no—
437C4⋊C4—221no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C22⋊C4—41no—
441C22⋊C4—111no—
442C22⋊C4—111no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4—441no—
449C22⋊C4—441no—
450C42—111no—
451C16—21no—
452C16—21no—
453C16—221no—
454C16—221no—
455C11#3387311yescharacteristic, complemented, Sylow
456C23—111no—
457C23—441no—
458C23—441no—
459C23—441no—
460C23—882no—
461C23—882no—
462C23—1761no—
463C23D8×D1111yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—882no—
467D4—222no—
468D4—222no—
469D4—441no—
470D4—441no—
471D4—441no—
472D4—441no—
473D4—441no—
474D4—882no—
475D4—882no—
476D4—882no—
477D4—882no—
478D4—1761no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—111no—
487C2×C4—111no—
488C2×C4—111no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—441no—
492C2×C4—882no—
493C2×C4—882no—
494C2×C4—882no—
495C2×C4—1761no—
496C2×C4D8×D1111yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C8—21no—
499C8—221no—
500C8—221no—
501C8#41×D1111yescharacteristic
502C8#6704211yescharacteristic
503C22—21no—
504C22—21no—
505C22—221no—
506C22—221no—
507C22—221no—
508C22—442no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22—1764no—
518C22#1062252712yes—
519C22C2×D8×D1111yescharacteristic
520C4—21no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4—221no—
526C4—221no—
527C4—221no—
528C4—881no—
529C4#1062318511yescharacteristic
530C4#1062330911yescharacteristic
531C2—22no—
532C2—441no—
533C2—882no—
534C2—1761no—
535C2—1761no—
536C2#1308042711yescharacteristic
537C2C2×#1062252711yescharacteristic
538C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2235C2
socleC22×C11C22×D8
hypercenter#2235D11
hypocenterC11#33873
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
1. #13080961C2semidirect
2. #13080298C2semidirect
3. #13070854C2semidirect
4. #13070803C2semidirect
5. #13070762C2semidirect
6. #13070720C2semidirect
7. #13070714C2semidirect
8. #13070674C2semidirect
9. #13070542C2semidirect
10. #13070530C2semidirect
11. #13070491C2semidirect
12. #13070438C2semidirect
13. #13070327C2semidirect
14. C2×#10622129C2semidirect
15. C11×#2235C2semidirect
23. C2×#66892C22semidirect
31. C2×#66862C22semidirect
34. #10622496C22semidirect
36. D11×#107C22semidirect
37. #10622487C22semidirect
39. #10622485C22semidirect
42. C11×#367C22semidirect
43. C11×#367C22semidirect
44. C11×#358C22semidirect
45. C11×#358C22semidirect
47. #10622202C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622140C22semidirect
52. Dic11⋊C16C22semidirect
57. #10622129C22semidirect
58. #10622128C22semidirect
180. D88#41semidirect
190. #2235D11semidirect
276. #367C2×D11semidirect
277. #367C2×D11semidirect
280. #358C2×D11semidirect
281. #358C2×D11semidirect
455. C11#33873semidirect

Maximal subgroups

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

subgroupindex
#130809612
#130802982
#130708542
#130708032
#130707622
#130707202
#130707142
#130706742
#130705422
#130705302
#130704912
#130704382
#130703272
C2×#106221292
C11×#22352
#3387311