Finite Group Databasebeta

← #14910804

Subgroups — #14910804

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#13080985C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic, complemented
3#13070804C211yesmaximal, characteristic, complemented
4#13070794C211yesmaximal, characteristic, complemented
5#13070773C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070653C211yesmaximal, characteristic, complemented
9#13070545C211yesmaximal, characteristic, complemented
10#13070545C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070332C211yesmaximal, characteristic, complemented
14C2×#10622200C211yesmaximal, characteristic, complemented
15D4×C11×D8C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18D42×C11—21no—
19#10623072—21no—
20C11×#493C2211yescharacteristic
21C11×#466C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#459—21no—
24C11×#447—21no—
25C11×#447—21no—
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C2×#66891C2211yescharacteristic, complemented
30C2×#66891C2211yescharacteristic, complemented
31#10622729C2211yescharacteristic, complemented
32#10622729C2211yescharacteristic, complemented
33#10622719C2211yescharacteristic, complemented
34C2×#66882C2211yescharacteristic, complemented
35C2×#66876C2211yescharacteristic, complemented
36C22×C11⋊C16C2211yescharacteristic, complemented
37#10622442—21no—
38#10622336—21no—
39#10622334—21no—
40C4×Dic44C2211yescharacteristic, complemented
41#10622296C2211yescharacteristic, complemented
42#10622200C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50#10622200C2211yescharacteristic, complemented
51C22⋊(C11⋊C16)C2211yescharacteristic, complemented
52C22⋊(C11⋊C16)C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622128C2211yescharacteristic, complemented
55#10622127C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57C4⋊(C11⋊C16)C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—41no—
62C2×C11×D8—22no—
63C2×C11×D8—22no—
64C2×C11×D8—21no—
65C2×C11×D8—21no—
66C2×C11×D8—21no—
67C2×C11×D8—41no—
68C2×C11×D8—41no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#127—21no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121—41no—
78C11×#120—41no—
79C11×#120—41no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82#66988—41no—
83#66979—21no—
84C2×C4⋊Dic11—21no—
85#66977—21no—
86#66977—21no—
87C2×Dic44C2311yescharacteristic
88#66942—41no—
89#66932—41no—
90#66930—41no—
91#66923—21no—
92C4×Dic22—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#102—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66891—22no—
102#66891—41no—
103#66891—41no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109#66881—21no—
110#66880—21no—
111#66880—21no—
112#66880—21no—
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33877—111nomaximal, Sylow
120C24×C11—41no—
121C24×C11—41no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—81no—
134C2×D4×C11—81no—
135C2×D4×C11—84no—
136C2×D4×C11D811yescharacteristic
137C22×C4×C11—41no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×Dic11—41no—
141C2×Dic22—21no—
142C11×D8—21no—
143C11×D8—21no—
144C11×D8—21no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8—42no—
148C11×D8—42no—
149C11×D8—81no—
150C11×D8#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2411yescharacteristic
159C11×C4⋊C4—21no—
160C11×C4⋊C4D811yescharacteristic
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4D811yescharacteristic
165C11×C22⋊C4D811yescharacteristic
166C42×C11C2×D411yescharacteristic
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180C4×Dic11—41no—
181Dic44—21no—
182Dic44—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3336—111no—
188D4×D8D1111yescharacteristic
189#2244—111no—
190#2234—111no—
191#2232—111no—
192#2228—111no—
193#2220—111no—
194#2217—111no—
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×C11—41no—
204C23×C11—41no—
205C23×C11—82no—
206C23×C11—82no—
207C23×C11—82no—
208C23×C11—82no—
209C23×C11—161no—
210C23×C11—161no—
211C23×C11C2×D811yescharacteristic
212C23×C11C2×D811yescharacteristic
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—82no—
221D4×C11—82no—
222D4×C11—82no—
223D4×C11—82no—
224D4×C11—82no—
225D4×C11—161no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—82no—
232C2×C4×C11C2×D811yescharacteristic
233C2×C4×C11C2×D811yescharacteristic
234C2×C4×C11C2×D811yescharacteristic
235C2×C4×C11C2×D811yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—82no—
242Dic22—41no—
243Dic22—41no—
244C8×C11—21no—
245C8×C11—21no—
246C8×C11—21no—
247C8×C11C2×#4111yescharacteristic
248C8×C11H(5,𝔽2)11yescharacteristic
249C22×D8C2×D1111yescharacteristic
250C22×D8C2×D1111yescharacteristic
251#552—221no—
252D42—21no—
253C2×SD32—111no—
254C2×SD32—111no—
255C2×SD32—111no—
256C2×M32—111no—
257C22×C16—111no—
258#499—111no—
259#493C2×D1111yescharacteristic
260#485—221no—
261#483—221no—
262#479—221no—
263#467—111no—
264#467—111no—
265#466C2×D1111yescharacteristic
266#466C2×D1111yescharacteristic
267#459—21no—
268#447—21no—
269#447—21no—
270C4×Q16—111no—
271C4×D8C2×D1111yescharacteristic
272C8×D4C2×D1111yescharacteristic
273#427—111no—
274C2×#107—111no—
275#367—111no—
276#366—111no—
277#366—111no—
278C4⋊C16—111no—
279#358—111no—
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#357—111no—
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—42no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—164no—
307C22×C11—164no—
308C22×C11#50912yes—
309C22×C11C22×D811yescharacteristic
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—81no—
315C4×C11#54611yescharacteristic
316C4×C11#57711yescharacteristic
317Dic11—81no—
318Dic11—81no—
319Dic11—81no—
320Dic11—81no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—41no—
324C2×Q16—111no—
325C2×D8—22no—
326C2×D8—22no—
327C2×D8—21no—
328C2×D8—21no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8—41no—
332C2×D8C22×D1111yescharacteristic
333C2×D8C22×D1111yescharacteristic
334C2×D8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337#127—21no—
338#126—441no—
339#125—221no—
340#125—441no—
341#123—441no—
342C22⋊Q8—221no—
343C22⋊Q8—221no—
344#121—21no—
345#121—21no—
346#121—41no—
347#120—41no—
348#120—41no—
349C4×Q8—221no—
350C4×D4—21no—
351C4×D4C22⋊D1111yescharacteristic
352#117—221no—
353#117—441no—
354C2×C4⋊C4—221no—
355SD32—222no—
356SD32—441no—
357SD32—441no—
358M32—441no—
359C2×C16—111no—
360C2×C16—111no—
361C2×C16—111no—
362C2×C16—111no—
363C2×C16—441no—
364#107—111no—
365#107—111no—
366#107—111no—
367#107—221no—
368#107C22×D1111yescharacteristic
369#106—221no—
370#106—221no—
371C4⋊C8C22⋊D1111yescharacteristic
372#103—221no—
373#103—221no—
374#103—221no—
375#102—21no—
376#102—21no—
377#102—21no—
378C22⋊C8C22⋊D1111yescharacteristic
379C22⋊C8C22⋊D1111yescharacteristic
380C4×C8C22×D1111yescharacteristic
381C2×C11—22no—
382C2×C11—41no—
383C2×C11—82no—
384C2×C11—161no—
385C2×C11—161no—
386C2×C11#329411yescharacteristic
387C2×C11C2×#50911yescharacteristic
388C2×C11#341611yescharacteristic
389C24—41no—
390C24—41no—
391C2×Q8—221no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—81no—
404C2×D4—81no—
405C2×D4—84no—
406C2×D4#432311yescharacteristic
407C22×C4—41no—
408C22×C4—441no—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411Q16—221no—
412Q16—221no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—42no—
419D8—42no—
420D8—81no—
421D8#434112yes—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8C2×C22⋊D1111yescharacteristic
427C2×C8C2×C22⋊D1111yescharacteristic
428C2×C8C2×C22⋊D1111yescharacteristic
429C2×C8C23×D1111yescharacteristic
430C4⋊C4—21no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—441no—
435C4⋊C4—441no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4#432311yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4#432311yescharacteristic
448C22⋊C4#432311yescharacteristic
449C42—441no—
450C42—441no—
451C42C2×C22⋊D1111yescharacteristic
452C16—221no—
453C16—221no—
454C16—221no—
455C16—221no—
456C11#3387711yescharacteristic, complemented, Sylow
457C23—41no—
458C23—41no—
459C23—41no—
460C23—82no—
461C23—82no—
462C23—82no—
463C23—82no—
464C23—161no—
465C23—161no—
466C23C2×#432311yescharacteristic
467C23C2×#432311yescharacteristic
468Q8—441no—
469Q8—441no—
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—82no—
478D4—82no—
479D4—82no—
480D4—82no—
481D4—82no—
482D4—161no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—82no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—882no—
494C2×C4C2×#432311yescharacteristic
495C2×C4C2×#432311yescharacteristic
496C2×C4C2×#432311yescharacteristic
497C2×C4C2×#432311yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—21no—
500C8—21no—
501C8—21no—
502C8C2×#434111yescharacteristic
503C8#6703711yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—164no—
519C22—164no—
520C22#1062276012yes—
521C22C22×#432311yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—81no—
527C4—881no—
528C4—881no—
529C4—881no—
530C4—881no—
531C4#1062333711yescharacteristic
532C4#1062336711yescharacteristic
533C2—22no—
534C2—41no—
535C2—82no—
536C2—161no—
537C2—161no—
538C2#1308042911yescharacteristic
539C2C2×#1062276011yescharacteristic
540C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalD4×C11×D8C2
socleC22×C11C22×D8
hypercenterD4×D8D11
hypocenterC11#33877
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #13080985C2semidirect
2. #13070857C2semidirect
3. #13070804C2semidirect
4. #13070794C2semidirect
5. #13070773C2semidirect
6. #13070727C2semidirect
7. #13070710C2semidirect
8. #13070653C2semidirect
9. #13070545C2semidirect
10. #13070545C2semidirect
11. #13070480C2semidirect
12. #13070442C2semidirect
13. #13070332C2semidirect
14. C2×#10622200C2semidirect
29. C2×#66891C22semidirect
30. C2×#66891C22semidirect
31. #10622729C22semidirect
32. #10622729C22semidirect
33. #10622719C22semidirect
34. C2×#66882C22semidirect
35. C2×#66876C22semidirect
36. C22×C11⋊C16C22semidirect
40. C4×Dic44C22semidirect
41. #10622296C22semidirect
45. #10622200C22semidirect
46. #10622200C22semidirect
47. #10622200C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
50. #10622200C22semidirect
51. C22⋊(C11⋊C16)C22semidirect
52. C22⋊(C11⋊C16)C22semidirect
53. #10622130C22semidirect
54. #10622128C22semidirect
55. #10622127C22semidirect
56. #10622127C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
456. C11#33877semidirect

Maximal subgroups

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

subgroupindex
#130809852
#130708572
#130708042
#130707942
#130707732
#130707272
#130707102
#130706532
#130705452
#130704802
#130704422
#130703322
C2×#106222002
D4×C11×D82
#3387711