Finite Group Databasebeta

← #14910810

Subgroups — #14910810

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080987C211yesmaximal, characteristic, complemented
2#13080290C211yesmaximal, characteristic
3#13070856C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070794C211yesmaximal, characteristic, complemented
6#13070772C211yesmaximal, characteristic, complemented
7#13070732C211yesmaximal, characteristic, complemented
8#13070654C211yesmaximal, characteristic, complemented
9#13070544C211yesmaximal, characteristic, complemented
10#13070543C211yesmaximal, characteristic, complemented
11#13070483C211yesmaximal, characteristic, complemented
12#13070441C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14C2×#10622147C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623173—21no—
19#10623140—21no—
20C2×C11×SD32C2211yescharacteristic, complemented
21C22×C11×C16C2211yescharacteristic, complemented
22C11×#467C2211yescharacteristic, complemented
23C11×#466C2211yescharacteristic
24#10622801C2211yescharacteristic, complemented
25Q16×Dic11C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic
27C2×#66892C2211yescharacteristic, complemented
28#10622764C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic, complemented
31#10622656—21no—
32#10622649—21no—
33C2×#66862C2211yescharacteristic, complemented
34#10622496C2211yescharacteristic
35#10622493C2211yescharacteristic, complemented
36#10622491C2211yescharacteristic, complemented
37#10622485C2211yescharacteristic
38#10622427—21no—
39#10622409—21no—
40#10622399—21no—
41#10622386—21no—
42C11×#367C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47C22⋊(C11⋊C16)C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×D4×D11—41no—
61C22×D44—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C22⋊Q8—21no—
66C11×#121—21no—
67#66999—21no—
68Q8×Dic11—21no—
69#66993—21no—
70#66990—41no—
71C2×#4323—21no—
72C2×#4323—21no—
73C4×C22⋊D11D411yescharacteristic
74C2×C4⋊Dic11—21no—
75D8×D11—22no—
76D8×D11—41no—
77C2×D88—22no—
78C2×D88—21no—
79C2×D88—41no—
80C2×D88C2311yescharacteristic
81C2×D88C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66951—41no—
84#66948—21no—
85#66946—21no—
86#66945—21no—
87#66943—21no—
88#66943—41no—
89#66939—41no—
90#66937—41no—
91#66935—41no—
92#66930—41no—
93C11×SD32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C11×#102—21no—
101#66899—21no—
102#66899—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66892—22no—
105#66892—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66873—21no—
116#66872—21no—
117#66872—21no—
118#66862—41no—
119#33877—111nomaximal, Sylow
120C23×D11—41no—
121C23×D11—41no—
122C2×Q8×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C2×C22⋊D11D811yescharacteristic
130C22×Dic11—41no—
131D4×D11—42no—
132D4×D11—81no—
133D4×D11—84no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—42no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—81no—
140C2×C4×D11—41no—
141C2×C4×D11C2×D411yescharacteristic
142C11×Q16—21no—
143C11×Q16—21no—
144C11×D8—21no—
145C11×D8—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—41no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C22⋊Dic11D811yescharacteristic
156#4323—42no—
157#4323—81no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4D811yescharacteristic
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4D811yescharacteristic
171C4×Dic11—41no—
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176D88—21no—
177D88—21no—
178D88—21no—
179D88—42no—
180D88#4112yes—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3336—111no—
188D4×D8—111no—
189#2244—111no—
190#2234—111no—
191#2232—111no—
192#2228—111no—
193#2220—111no—
194#2217D1111yescharacteristic, complemented
195#2207—111no—
196#2187—111no—
197#2187—111no—
198#2175—111no—
199#2168—111no—
200#2140—111no—
201C2×#357—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—82no—
209C22×D11—82no—
210C22×D11—161no—
211C22×D11—161no—
212C22×D11C2×D811yescharacteristic
213Q8×C11—41no—
214Q8×C11—41no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—82no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C22⋊D11—22no—
226C22⋊D11—82no—
227C22⋊D11—82no—
228C22⋊D11—161no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—82no—
232C2×Dic11C2×D811yescharacteristic
233C2×Dic11C2×D811yescharacteristic
234C2×Dic11C2×D811yescharacteristic
235D44—22no—
236D44—41no—
237D44—41no—
238D44—41no—
239D44—82no—
240D44—82no—
241C4×D11—21no—
242C4×D11—21no—
243C4×D11—82no—
244C8×C11—21no—
245C8×C11C2×#4111yescharacteristic
246C8×C11H(5,𝔽2)11yescharacteristic
247C11⋊C8—21no—
248C11⋊C8—21no—
249C22×D8—111no—
250C22×D8—111no—
251#552—221no—
252D42—221no—
253C2×SD32—111no—
254C2×SD32—111no—
255C2×SD32C2×D1111yescharacteristic, complemented
256C2×M32—111no—
257C22×C16C2×D1111yescharacteristic, complemented
258#499—111no—
259#493—111no—
260#485—221no—
261#483—221no—
262#479—221no—
263#467—111no—
264#467C2×D1111yescharacteristic, complemented
265#466—111no—
266#466C2×D1111yescharacteristic
267#459—221no—
268#447—221no—
269#447—221no—
270C4×Q16—111no—
271C4×D8—111no—
272C8×D4—111no—
273#427—111no—
274C2×#107—111no—
275#367C2×D1111yescharacteristic, complemented
276#366—111no—
277#366—111no—
278C4⋊C16—111no—
279#358C2×D1111yescharacteristic, complemented
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286#357—111no—
287#357—111no—
288#357C2×D1111yescharacteristic, complemented
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11#50912yes—
298C22×C11C22×D811yescharacteristic
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—42no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—164no—
309C2×D11—164no—
310C4×C11—21no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11#54611yescharacteristic
315C4×C11#57711yescharacteristic
316Dic11—21no—
317Dic11—21no—
318Dic11—21no—
319Dic11—81no—
320Dic11—81no—
321C22×D4—221no—
322C22×D4—221no—
323C22×D4—441no—
324C2×Q16C22×D1111yescharacteristic
325C2×D8—111no—
326C2×D8—111no—
327C2×D8—222no—
328C2×D8—221no—
329C2×D8—221no—
330C2×D8—222no—
331C2×D8—221no—
332C2×D8—441no—
333C2×D8—441no—
334C2×D8C22×D1111yescharacteristic
335C22×C8—111no—
336C22×C8C22×D1111yescharacteristic
337#127—221no—
338#126—441no—
339#125—221no—
340#125—441no—
341#123—441no—
342C22⋊Q8—21no—
343C22⋊Q8—221no—
344#121—21no—
345#121—221no—
346#121—441no—
347#120—441no—
348#120—441no—
349C4×Q8—221no—
350C4×D4—111no—
351C4×D4—221no—
352#117—221no—
353#117—441no—
354C2×C4⋊C4—221no—
355SD32—41no—
356SD32—222no—
357SD32—441no—
358M32—441no—
359C2×C16—41no—
360C2×C16—111no—
361C2×C16—111no—
362C2×C16C22×D1111yescharacteristic
363C2×C16C22×D1111yescharacteristic
364#107—111no—
365#107—111no—
366#107—221no—
367#107C22×D1111yescharacteristic
368#107C22×D1111yescharacteristic
369#106—221no—
370#106—221no—
371C4⋊C8—111no—
372#103—21no—
373#103—221no—
374#103—221no—
375#102—21no—
376#102—221no—
377#102—221no—
378C22⋊C8—111no—
379C22⋊C8—111no—
380C4×C8—111no—
381C2×C11—22no—
382C2×C11—161no—
383C2×C11#329411yescharacteristic
384C2×C11C2×#50911yescharacteristic
385C2×C11#341611yescharacteristic
386D11—41no—
387D11—82no—
388D11—161no—
389C24—441no—
390C24—441no—
391C2×Q8—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—111no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—442no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—442no—
403C2×D4—441no—
404C2×D4—881no—
405C2×D4—881no—
406C2×D4—884no—
407C22×C4—111no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4D4×D1111yescharacteristic
411Q16—21no—
412Q16—21no—
413D8—21no—
414D8—21no—
415D8—112no—
416D8—221no—
417D8—221no—
418D8—221no—
419D8—442no—
420D8—442no—
421D8—881no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—111no—
425C2×C8—111no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8D4×D1111yescharacteristic
429C2×C8C23×D1111yescharacteristic
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—41no—
433C4⋊C4—111no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4—441no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—111no—
444C22⋊C4—111no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4—441no—
449C42—111no—
450C42—441no—
451C42—441no—
452C16—21no—
453C16—21no—
454C16—221no—
455C16—221no—
456C11#3387711yescharacteristic, complemented, Sylow
457C23—41no—
458C23—111no—
459C23—441no—
460C23—441no—
461C23—882no—
462C23—882no—
463C23—882no—
464C23—882no—
465C23—1761no—
466C23—1761no—
467C23D8×D1111yescharacteristic
468Q8—41no—
469Q8—41no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—222no—
474D4—222no—
475D4—441no—
476D4—441no—
477D4—441no—
478D4—882no—
479D4—882no—
480D4—882no—
481D4—882no—
482D4—1761no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—111no—
489C2×C4—111no—
490C2×C4—111no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—882no—
496C2×C4—882no—
497C2×C4D8×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C8—21no—
500C8—221no—
501C8—221no—
502C8#6703711yescharacteristic
503C8#41×D1111yescharacteristic
504C22—21no—
505C22—21no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—221no—
510C22—221no—
511C22—221no—
512C22—442no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22—881no—
518C22—1764no—
519C22—1764no—
520C22#1062252712yes—
521C22C2×D8×D1111yescharacteristic
522C4—21no—
523C4—81no—
524C4—81no—
525C4—81no—
526C4—221no—
527C4—221no—
528C4—221no—
529C4—881no—
530C4—881no—
531C4#1062314111yescharacteristic
532C4#1062330111yescharacteristic
533C2—22no—
534C2—161no—
535C2—441no—
536C2—882no—
537C2—1761no—
538C2#1308042411yescharacteristic
539C2C2×#1062252711yescharacteristic
540C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13080290C2
hypercenter#2217D11
hypocenterC11#33877
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13080987C2semidirect
3. #13070856C2semidirect
4. #13070809C2semidirect
5. #13070794C2semidirect
6. #13070772C2semidirect
7. #13070732C2semidirect
8. #13070654C2semidirect
9. #13070544C2semidirect
10. #13070543C2semidirect
11. #13070483C2semidirect
12. #13070441C2semidirect
13. #13070330C2semidirect
14. C2×#10622147C2semidirect
15. C11×#2217C2semidirect
20. C2×C11×SD32C22semidirect
21. C22×C11×C16C22semidirect
22. C11×#467C22semidirect
24. #10622801C22semidirect
25. Q16×Dic11C22semidirect
27. C2×#66892C22semidirect
30. C2×#66882C22semidirect
33. C2×#66862C22semidirect
35. #10622493C22semidirect
36. #10622491C22semidirect
42. C11×#367C22semidirect
43. C11×#358C22semidirect
44. C11×#357C22semidirect
45. #10622200C22semidirect
46. #10622200C22semidirect
47. C22⋊(C11⋊C16)C22semidirect
50. #10622147C22semidirect
51. #10622147C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
56. #10622129C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
194. #2217D11semidirect
255. C2×SD32C2×D11semidirect
257. C22×C16C2×D11semidirect
264. #467C2×D11semidirect
275. #367C2×D11semidirect
279. #358C2×D11semidirect
288. #357C2×D11semidirect
456. C11#33877semidirect

Maximal subgroups

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

subgroupindex
#130809872
#130802902
#130708562
#130708092
#130707942
#130707722
#130707322
#130706542
#130705442
#130705432
#130704832
#130704412
#130703302
C2×#106221472
C11×#22172
#3387711