Finite Group Databasebeta

← #14910633

Subgroups — #14910633

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13070847C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070773C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070668C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070528C211yesmaximal, characteristic, complemented
11C4×#66890C211yesmaximal, characteristic, complemented
12D4×C11⋊C16C211yesmaximal, characteristic, complemented
13#13070323C211yesmaximal, characteristic, complemented
14C2×#10622200C211yesmaximal, characteristic, complemented
15C11×#3280C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#546—21no—
19#10623096—21no—
20C11×#495C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#463—21no—
24C11×#450—21no—
25C11×#449—21no—
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66892C2211yescharacteristic, complemented
29C2×#66890C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic, complemented
33#10622719C2211yescharacteristic, complemented
34C2×#66882C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic, complemented
37#10622460—21no—
38#10622350—21no—
39#10622348—21no—
40C4×D88C2211yescharacteristic, complemented
41#10622296C2211yescharacteristic, complemented
42#10622202C2211yescharacteristic, complemented
43#10622202C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic, complemented
54#10622128C2211yescharacteristic, complemented
55#10622127C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57C4⋊(C11⋊C16)C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C22×D4×C11—21no—
61C11×#135—22no—
62C11×#135—41no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×SD16—21no—
65C2×C11×SD16—21no—
66C2×C11×D8—22no—
67C2×C11×D8—21no—
68C2×C11×D8—41no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#124—21no—
74C11×#123—41no—
75C11×C22⋊Q8—21no—
76C11×#121—21no—
77C11×#121—41no—
78C11×#120—41no—
79C4×D4×C11—21no—
80C4×D4×C11D411yescharacteristic
81C2×C11×C22⋊C4—41no—
82#66992—41no—
83#66983—21no—
84#66983—21no—
85#66979—21no—
86C2×C4⋊Dic11—21no—
87C2×D88C2311yescharacteristic
88#66951—41no—
89#66936—41no—
90(C22⋊D11)⋊C4—41no—
91C4×D44—21no—
92#66923—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—41no—
102#66890—22no—
103#66890—41no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112#66881—21no—
113C2×C11⋊C16—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33864—111nomaximal, Sylow
120C24×C11—41no—
121C11×#41—42no—
122C11×#41—81no—
123C2×Q8×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—42no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—81no—
131C2×D4×C11D811yescharacteristic
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11—41no—
139C2×D44—21no—
140C2×C4×D11—41no—
141C11×Q16—21no—
142C11×Q16—21no—
143C11×SD16—42no—
144C11×SD16—81no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8—21no—
148C11×D8—42no—
149C11×D8#4112yes—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2411yescharacteristic
158C11×C4⋊C4—21no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4D811yescharacteristic
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4D811yescharacteristic
167C11×C22⋊C4D811yescharacteristic
168C42×C11C2×D411yescharacteristic
169C22⋊Dic11—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180D88—21no—
181D88—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3280D1111yescharacteristic, complemented
188#2242—111no—
189#2236—111no—
190#2234—111no—
191#2228—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2184—111no—
197C4×D16—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#357—111no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—161no—
206C23×C11C2×D811yescharacteristic
207C23×C11C2×D811yescharacteristic
208C22×D11—41no—
209Q8×C11—41no—
210Q8×C11—41no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—41no—
216D4×C11—82no—
217D4×C11—82no—
218D4×C11—161no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—82no—
226C2×C4×C11—161no—
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—82no—
233C22⋊D11—161no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—161no—
238D44—41no—
239D44—41no—
240C4×D11—161no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135C2×D1111yescharacteristic
247C22×D8C2×D1111yescharacteristic
248#553—221no—
249#546—21no—
250C2×SD32—111no—
251C2×D16—111no—
252C2×D16—111no—
253C22×C16—111no—
254C22×C16—111no—
255#499—111no—
256#495C2×D1111yescharacteristic
257#482—221no—
258#481—221no—
259#478—221no—
260#467C2×D1111yescharacteristic
261#466—111no—
262#466—111no—
263#466C2×D1111yescharacteristic
264#463—21no—
265#450—21no—
266#449—21no—
267C4×D8—111no—
268C4×D8C2×D1111yescharacteristic
269C8×D4C2×D1111yescharacteristic
270#427—111no—
271C2×#107—111no—
272#367—111no—
273#366—111no—
274#366—111no—
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286C22⋊C16—111no—
287C22⋊C16—111no—
288C4×C16—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—42no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—164no—
301C22×C11#50812yes—
302C22×C11C22×D811yescharacteristic
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#54611yescharacteristic
313C4×C11#57711yescharacteristic
314Dic11—81no—
315Dic11—81no—
316Dic11—81no—
317C2×#41—21no—
318C22×D4—21no—
319#135—22no—
320#135—41no—
321C2×Q16C22×D1111yescharacteristic
322C2×SD16—21no—
323C2×SD16—21no—
324C2×D8—22no—
325C2×D8—21no—
326C2×D8—41no—
327C2×D8—111no—
328C2×D8C22×D1111yescharacteristic
329C2×D8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1111yescharacteristic
332#126—441no—
333#125—221no—
334#124—21no—
335#123—41no—
336#123—441no—
337C22⋊Q8—21no—
338#121—21no—
339#121—41no—
340#121—221no—
341#121—221no—
342#121—441no—
343#120—41no—
344C4×D4—21no—
345C4×D4—221no—
346C4×D4—441no—
347C4×D4C22⋊D1111yescharacteristic
348#117—221no—
349C2×C4⋊C4—221no—
350C2×C22⋊C4—41no—
351SD32—441no—
352D16—222no—
353D16—441no—
354C2×C16—111no—
355C2×C16—111no—
356C2×C16—111no—
357C2×C16—111no—
358C2×C16—441no—
359C2×C16—441no—
360#107—111no—
361#107—111no—
362#107—111no—
363#107—221no—
364#107C22×D1111yescharacteristic
365#106—221no—
366#106—221no—
367C4⋊C8C22⋊D1111yescharacteristic
368#103—21no—
369#102—21no—
370#102—21no—
371#102—221no—
372#102—221no—
373#102—221no—
374C22⋊C8C22⋊D1111yescharacteristic
375C22⋊C8C22⋊D1111yescharacteristic
376C4×C8C22×D1111yescharacteristic
377C2×C11—22no—
378C2×C11—41no—
379C2×C11—82no—
380C2×C11—161no—
381C2×C11#329411yescharacteristic
382C2×C11C2×#50811yescharacteristic
383C2×C11#341511yescharacteristic
384D11—161no—
385C24—41no—
386#41—42no—
387#41—81no—
388C2×Q8—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—81no—
396C2×D4—221no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4#432311yescharacteristic
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406Q16—21no—
407Q16—21no—
408SD16—42no—
409SD16—81no—
410D8—21no—
411D8—21no—
412D8—21no—
413D8—42no—
414D8—221no—
415D8—221no—
416D8#434112yes—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C2×C22⋊D1111yescharacteristic
422C2×C8C2×C22⋊D1111yescharacteristic
423C2×C8C2×C22⋊D1111yescharacteristic
424C2×C8C23×D1111yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4#432311yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C22⋊C4—441no—
443C22⋊C4#432311yescharacteristic
444C22⋊C4#432311yescharacteristic
445C42—441no—
446C42C2×C22⋊D1111yescharacteristic
447C16—221no—
448C16—221no—
449C16—221no—
450C16—221no—
451C11#3386411yescharacteristic, complemented, Sylow
452C23—41no—
453C23—41no—
454C23—82no—
455C23—82no—
456C23—161no—
457C23—441no—
458C23C2×#432311yescharacteristic
459C23C2×#432311yescharacteristic
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—82no—
468D4—82no—
469D4—161no—
470D4—441no—
471D4—441no—
472D4—882no—
473D4—1761no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—82no—
481C2×C4—161no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—1761no—
486C2×C4—1761no—
487C2×C4C2×#432311yescharacteristic
488C2×C4C2×#432311yescharacteristic
489C2×C4C2×#432311yescharacteristic
490C2×C4C2×#432311yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×#434111yescharacteristic
496C8#6703711yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—164no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22#1062280712yes—
513C22C22×#432311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—881no—
521C4—881no—
522C4—881no—
523C4#1062333711yescharacteristic
524C4#1062336711yescharacteristic
525C2—22no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—1761no—
530C2#1308042911yescharacteristic
531C2C2×#1062280711yescharacteristic
532C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3280C2
socleC22×C11C22×D8
hypercenter#3280D11
hypocenterC11#33864
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13070847C2semidirect
3. #13070816C2semidirect
4. #13070804C2semidirect
5. #13070773C2semidirect
6. #13070714C2semidirect
7. #13070700C2semidirect
8. #13070668C2semidirect
9. #13070539C2semidirect
10. #13070528C2semidirect
11. C4×#66890C2semidirect
12. D4×C11⋊C16C2semidirect
13. #13070323C2semidirect
14. C2×#10622200C2semidirect
15. C11×#3280C2semidirect
28. C2×#66892C22semidirect
32. #10622728C22semidirect
33. #10622719C22semidirect
36. C22×C11⋊C16C22semidirect
40. C4×D88C22semidirect
41. #10622296C22semidirect
42. #10622202C22semidirect
43. #10622202C22semidirect
44. #10622202C22semidirect
52. C22⋊(C11⋊C16)C22semidirect
53. #10622129C22semidirect
54. #10622128C22semidirect
55. #10622127C22semidirect
56. #10622127C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. C4×C11⋊C16C22semidirect
187. #3280D11semidirect
451. C11#33864semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708472
#130708162
#130708042
#130707732
#130707142
#130707002
#130706682
#130705392
#130705282
C4×#668902
D4×C11⋊C162
#130703232
C2×#106222002
C11×#32802
#3386411