Finite Group Databasebeta

← #14910740

Subgroups — #14910740

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#13080301C211yesmaximal, characteristic, complemented
3#13070851C211yesmaximal, characteristic, complemented
4#13070813C211yesmaximal, characteristic, complemented
5#13070800C211yesmaximal, characteristic, complemented
6#13070761C211yesmaximal, characteristic, complemented
7#13070718C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070670C211yesmaximal, characteristic, complemented
10#13070540C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070489C211yesmaximal, characteristic, complemented
13#13070441C211yesmaximal, characteristic, complemented
14#13070325C211yesmaximal, characteristic, complemented
15C2×C11×#357C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623337—21no—
18C2×#66965C2211yescharacteristic
19#10623038—21no—
20C22×C11×C16C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622831—21no—
23#10622771—21no—
24#10622770C2211yescharacteristic
25#10622768C2211yescharacteristic
26#10622766—21no—
27D8×Dic11C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29C2×#66890C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622728C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622580—21no—
34C2×#66864C2211yescharacteristic, complemented
35C2×#66862C2211yescharacteristic, complemented
36#10622503—21no—
37#10622496C2211yescharacteristic, complemented
38#10622495—21no—
39D11×#107C2211yescharacteristic, complemented
40#10622487C2211yescharacteristic, complemented
41#10622485C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622143C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×#4341—21no—
61C2×#4339—41no—
62C2×C11×D8—22no—
63C2×C11×D8—21no—
64C2×C11×D8—41no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69#67006—41no—
70C2×C22⋊Dic11—41no—
71#66992—41no—
72#66991—21no—
73#66989—21no—
74#66988—41no—
75D4×Dic11—21no—
76C2×#4324—21no—
77C2×#4324—21no—
78#66983—21no—
79#66982—41no—
80C4×C22⋊D11D411yescharacteristic
81#66977—21no—
82#66965—22no—
83#66965—41no—
84C2×Dic44C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66949—41no—
88#66948—21no—
89#66947—41no—
90#66946—21no—
91C4⋊C4×D11—21no—
92#66941—21no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107—21no—
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99#66896—21no—
100#66896—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66890—22no—
103#66890—41no—
104#66885—21no—
105(C2×D11)⋊C8D411yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66873—21no—
115#66871—21no—
116#66871—21no—
117#66864—41no—
118#66862—41no—
119#33873—111nomaximal, Sylow
120C24×C11—41no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—81no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C22×Dic11—41no—
133C22×Dic11—41no—
134#4341—42no—
135#4341—81no—
136#4339—84no—
137C2×D44—21no—
138C2×D44—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11C2×D411yescharacteristic
142C2×Dic22—21no—
143C2×Dic22—41no—
144C11×D8—21no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8—42no—
148C11×D8#4112yescomplemented
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11—41no—
159C22⋊Dic11—41no—
160C22⋊Dic11—41no—
161C22⋊Dic11D811yescharacteristic
162#4324—42no—
163#4324—81no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4D811yescharacteristic
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4D811yescharacteristic
174C4×Dic11C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177Dic44—21no—
178Dic44—21no—
179D88—21no—
180D88—21no—
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#2235—111no—
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×#357D1111yescharacteristic, complemented
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—82no—
205C23×C11—82no—
206C23×C11—161no—
207C23×C11C2×D811yescharacteristic
208C22×D11—41no—
209C22×D11C2×D811yescharacteristic
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—82no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—82no—
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C22⋊D11—22no—
223C22⋊D11—82no—
224C22⋊D11—82no—
225C22⋊D11—161no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—82no—
230C2×Dic11—161no—
231C2×Dic11C2×D811yescharacteristic
232C2×Dic11C2×D811yescharacteristic
233C2×Dic11C2×D811yescharacteristic
234D44—41no—
235D44—41no—
236D44—82no—
237C4×D11—21no—
238C4×D11—21no—
239C4×D11—82no—
240C4×D11—82no—
241Dic22—41no—
242Dic22—41no—
243Dic22—82no—
244C8×C11—21no—
245C8×C11C2×#4111yescharacteristic
246C8×C11H(5,𝔽2)11yescharacteristic
247C11⋊C8—21no—
248C11⋊C8—21no—
249C2×#135—111no—
250C22×D8C2×D1111yescharacteristic
251#547—221no—
252#546—221no—
253C2×SD32—111no—
254C2×D16—111no—
255C2×D16—111no—
256C2×M32—111no—
257C22×C16C2×D1111yescharacteristic
258#500—111no—
259#495—111no—
260#480—221no—
261#480—221no—
262#474—221no—
263#467—111no—
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#367—111no—
277#367—111no—
278C4⋊C16—111no—
279#358—111no—
280#358—111no—
281#358—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357C2×D1111yescharacteristic
286#357C2×D1111yescharacteristic
287#357C2×D1111yescharacteristic
288#357C2×D1111yescharacteristic
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
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#50912yes—
302C22×C11C22×D811yescharacteristic
303C2×D11—21no—
304C2×D11—21no—
305C2×D11—21no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C4×C11—21no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#54611yescharacteristic
313C4×C11#57711yescharacteristic
314Dic11—21no—
315Dic11—21no—
316Dic11—21no—
317Dic11—81no—
318Dic11—81no—
319Dic11—81no—
320C2×#41—221no—
321C2×#41—441no—
322C22×D4—21no—
323#135—222no—
324#135—441no—
325C2×Q16—111no—
326C2×SD16—221no—
327C2×SD16—221no—
328C2×D8—22no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8—111no—
332C2×D8C22×D1111yescharacteristic
333C2×D8C22×D1111yescharacteristic
334C22×C8—111no—
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—221no—
337#124—221no—
338#123—441no—
339#123—441no—
340#123—441no—
341C22⋊Q8—221no—
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—41no—
359C2×C16—111no—
360C2×C16—111no—
361C2×C16C22×D1111yescharacteristic
362C2×C16C22×D1111yescharacteristic
363#107—21no—
364#107—111no—
365#107—111no—
366#107—221no—
367#107—221no—
368#107C22×D1111yescharacteristic
369#107C22×D1111yescharacteristic
370C4⋊C8—111no—
371#103—221no—
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—82no—
382C2×C11—161no—
383C2×C11#329411yescharacteristic
384C2×C11C2×#50911yescharacteristic
385C2×C11#341611yescharacteristic
386D11—41no—
387D11—161no—
388C24—41no—
389#41—442no—
390#41—884no—
391#41—881no—
392C2×Q8—221no—
393C2×Q8—441no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—81no—
399C2×D4—111no—
400C2×D4—221no—
401C2×D4—441no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4—441no—
405C22×C4—41no—
406C22×C4—111no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4—441no—
411C22×C4D4×D1111yescharacteristic
412Q16—221no—
413Q16—221no—
414SD16—442no—
415SD16—881no—
416D8—21no—
417D8—21no—
418D8—21no—
419D8—42no—
420D8—221no—
421D8—221no—
422D8#433912yescomplemented
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—41no—
434C4⋊C4—111no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C22⋊C4—111no—
441C22⋊C4—111no—
442C22⋊C4—441no—
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—41no—
457C23—41no—
458C23—82no—
459C23—82no—
460C23—111no—
461C23—161no—
462C23—441no—
463C23D8×D1111yescharacteristic
464Q8—441no—
465Q8—441no—
466Q8—882no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—82no—
472D4—222no—
473D4—441no—
474D4—441no—
475D4—882no—
476D4—882no—
477D4—882no—
478D4—1761no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—111no—
485C2×C4—111no—
486C2×C4—111no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—441no—
490C2×C4—441no—
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—
501C8C2×#433911yescharacteristic
502C8#6703711yescharacteristic
503C22—21no—
504C22—21no—
505C22—42no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—164no—
512C22—221no—
513C22—221no—
514C22—221no—
515C22—881no—
516C22—881no—
517C22—881no—
518C22#1062252412yes—
519C22C2×D8×D1111yescharacteristic
520C4—21no—
521C4—81no—
522C4—81no—
523C4—221no—
524C4—221no—
525C4—221no—
526C4—881no—
527C4—881no—
528C4—881no—
529C4#1062302111yescharacteristic
530C4#1062329311yescharacteristic
531C2—22no—
532C2—82no—
533C2—161no—
534C2—441no—
535C2—1761no—
536C2#1308042511yescharacteristic
537C2C2×#1062252411yescharacteristic
538C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#357C2
socleC22×C11C22×D8
hypercenterC2×#357D11
hypocenterC11#33873
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. #13080961C2semidirect
2. #13080301C2semidirect
3. #13070851C2semidirect
4. #13070813C2semidirect
5. #13070800C2semidirect
6. #13070761C2semidirect
7. #13070718C2semidirect
8. #13070712C2semidirect
9. #13070670C2semidirect
10. #13070540C2semidirect
11. #13070528C2semidirect
12. #13070489C2semidirect
13. #13070441C2semidirect
14. #13070325C2semidirect
15. C2×C11×#357C2semidirect
34. C2×#66864C22semidirect
35. C2×#66862C22semidirect
37. #10622496C22semidirect
39. D11×#107C22semidirect
40. #10622487C22semidirect
41. #10622485C22semidirect
49. #10622147C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622143C22semidirect
52. #10622141C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. #10622130C22semidirect
56. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622128C22semidirect
148. C11×D8#41semidirect
201. C2×#357D11semidirect
422. D8#4339semidirect
455. C11#33873semidirect

Maximal subgroups

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

subgroupindex
#130809612
#130803012
#130708512
#130708132
#130708002
#130707612
#130707182
#130707122
#130706702
#130705402
#130705282
#130704892
#130704412
#130703252
C2×C11×#3572
#3387311