Finite Group Databasebeta

← #14910746

Subgroups — #14910746

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#13080964C211yesmaximal, characteristic, complemented
2#13080303C211yesmaximal, characteristic, complemented
3#13070853C211yesmaximal, characteristic, complemented
4#13070814C211yesmaximal, characteristic, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070719C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070672C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070530C211yesmaximal, characteristic, complemented
12#13070493C211yesmaximal, characteristic, complemented
13#13070329C211yesmaximal, characteristic, complemented
14C2×#10622147C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623086—21no—
19#10623081—21no—
20C2×C11×M32C2211yescharacteristic, complemented
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic, complemented
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic, complemented
29C2×#66864C2211yescharacteristic, complemented
30C2×D176C2211yescharacteristic
31C2×D176C2211yescharacteristic
32#10622459—21no—
33#10622457—21no—
34#10622349—21no—
35#10622349—21no—
36#10622347—21no—
37#10622344—21no—
38#10622309C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic, complemented
41#10622295C2211yescharacteristic, complemented
42C11×C4⋊C16C2211yescharacteristic, complemented
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic, complemented
45C11×#346C2211yescharacteristic, complemented
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622143C2211yescharacteristic, complemented
55#10622143C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59C2×#4341—41no—
60C2×#4339—21no—
61C22×D44—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11D411yescharacteristic
65#66990—41no—
66#66983—21no—
67#66983—21no—
68#66983—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73#66957—22no—
74#66957—41no—
75C2×D88—22no—
76C2×D88—21no—
77C2×D88—41no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66950—41no—
84#66947—41no—
85#66939—41no—
86#66939—41no—
87#66937—41no—
88C22⋊C4×D11—41no—
89#66928—21no—
90C4×D44—21no—
91C4×D44—21no—
92#66922—21no—
93C11×M32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66885—21no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66885—21no—
108#66882—21no—
109#66882—21no—
110#66882—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66880—21no—
116#66864—41no—
117D176—22no—
118D176—41no—
119#33873—111nomaximal, Sylow
120C23×D11—41no—
121C2×D4×C11D811yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130#4341—84no—
131#4339—42no—
132#4339—81no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—42no—
137C2×D44—41no—
138C2×D44—81no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C2×Dic22—41no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2411yescharacteristic
152C11×C4⋊C4D811yescharacteristic
153C11×C22⋊C4D811yescharacteristic
154C11×C22⋊C4D811yescharacteristic
155C42×C11C2×D411yescharacteristic
156C22⋊Dic11—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
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—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—41no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171Dic11⋊C4—41no—
172Dic44—21no—
173Dic44—21no—
174D88—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—21no—
179D88—42no—
180D88#4112yescomplemented
181#4314—42no—
182#4314—81no—
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#2168D1111yescharacteristic, complemented
200#2139—111no—
201C2×#357—111no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—82no—
208C22×D11—82no—
209C22×D11—161no—
210D4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—82no—
221C22⋊D11—82no—
222C22⋊D11—82no—
223C22⋊D11—161no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—82no—
230C2×Dic11—82no—
231D44—22no—
232D44—41no—
233D44—41no—
234D44—41no—
235D44—41no—
236D44—41no—
237D44—82no—
238C4×D11—82no—
239C4×D11—82no—
240C4×D11—161no—
241Dic22—41no—
242Dic22—41no—
243Dic22—82no—
244C8×C11—21no—
245C8×C11—21no—
246C8×C11—21no—
247C8×C11C2×#4111yescharacteristic
248C8×C11H(5,𝔽2)11yescharacteristic
249C2×#135—111no—
250C22×D8—111no—
251#547—221no—
252#546—221no—
253C2×SD32—111no—
254C2×D16—111no—
255C2×D16—111no—
256C2×M32C2×D1111yescharacteristic, complemented
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×D4C2×D1111yescharacteristic
273C2×#107—111no—
274C2×#107—111no—
275#367—111no—
276#367—111no—
277#367—111no—
278C4⋊C16C2×D1111yescharacteristic, complemented
279#358—111no—
280#358—111no—
281#358—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286#357—111no—
287#357—111no—
288#357—111no—
289C22⋊C16C2×D1111yescharacteristic
290C22⋊C16C2×D1111yescharacteristic, complemented
291#346C2×D1111yescharacteristic, complemented
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11#50912yes—
298C22×C11C22×D811yescharacteristic
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—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11#54611yescharacteristic
314C4×C11#57711yescharacteristic
315Dic11—81no—
316Dic11—81no—
317Dic11—81no—
318Dic11—81no—
319Dic11—81no—
320C2×#41—221no—
321C2×#41—441no—
322C22×D4—221no—
323#135—222no—
324#135—441no—
325C2×Q16—111no—
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×C8C22×D1111yescharacteristic
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—221no—
349C4×D4—221no—
350C4×D4D4411yescharacteristic
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C22⋊C4—441no—
354SD32—441no—
355D16—222no—
356D16—441no—
357M32—41no—
358C2×C16—41no—
359C2×C16C22×D1111yescharacteristic
360C2×C16C22×D1111yescharacteristic
361C2×C16C22×D1111yescharacteristic
362C2×C16C22×D1111yescharacteristic
363#107—111no—
364#107—111no—
365#107—111no—
366#107—111no—
367#107—221no—
368#107—221no—
369#107—221no—
370C4⋊C8D4411yescharacteristic
371#103—221no—
372#102—221no—
373#102—221no—
374#102—221no—
375#102—221no—
376#102—221no—
377C22⋊C8D4411yescharacteristic
378C22⋊C8D4411yescharacteristic
379C4×C8C22×D1111yescharacteristic
380C2×C11—22no—
381C2×C11—41no—
382C2×C11#329411yescharacteristic
383C2×C11C2×#50911yescharacteristic
384C2×C11#341611yescharacteristic
385D11—82no—
386D11—161no—
387D11—161no—
388C24—441no—
389#41—442no—
390#41—881no—
391#41—884no—
392C2×Q8—221no—
393C2×Q8—441no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—442no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—441no—
403C2×D4—881no—
404C2×D4D8811yescharacteristic
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4C2×D4411yescharacteristic
411C22×C4C2×D4411yescharacteristic
412Q16—221no—
413Q16—221no—
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—21no—
426C2×C8—21no—
427C2×C8C2×D4411yescharacteristic
428C2×C8C2×D4411yescharacteristic
429C2×C8C2×D4411yescharacteristic
430C2×C8C23×D1111yescharacteristic
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4—441no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4D8811yescharacteristic
440C22⋊C4—441no—
441C22⋊C4—441no—
442C22⋊C4—441no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4D8811yescharacteristic
449C22⋊C4D8811yescharacteristic
450C42C2×D4411yescharacteristic
451C16—21no—
452C16—21no—
453C16—21no—
454C16—21no—
455C11#3387311yescharacteristic, complemented, Sylow
456C23—441no—
457C23—441no—
458C23—441no—
459C23—882no—
460C23—882no—
461C23—1761no—
462C23C2×D8811yescharacteristic
463C23C2×D8811yescharacteristic
464Q8—441no—
465Q8—441no—
466Q8—882no—
467D4—22no—
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—21no—
482C2×C4—21no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—882no—
489C2×C4—882no—
490C2×C4—882no—
491C2×C4—882no—
492C2×C4—1761no—
493C2×C4C2×D8811yescharacteristic
494C2×C4C2×D8811yescharacteristic
495C2×C4C2×D8811yescharacteristic
496C2×C4C2×D8811yescharacteristic
497C2×C4C22×D4411yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#6703711yescharacteristic
502C8#41×D1111yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—442no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22—1764no—
518C22#1062252112yes—
519C22C22×D8811yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—881no—
525C4—881no—
526C4—881no—
527C4—881no—
528C4—881no—
529C4#1062308511yescharacteristic
530C4#1062328211yescharacteristic
531C2—22no—
532C2—41no—
533C2—882no—
534C2—1761no—
535C2—1761no—
536C2#1308043011yescharacteristic
537C2C2×#1062252111yescharacteristic
538C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33873
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13080303C2semidirect
3. #13070853C2semidirect
4. #13070814C2semidirect
5. #13070802C2semidirect
6. #13070764C2semidirect
7. #13070719C2semidirect
8. #13070712C2semidirect
9. #13070672C2semidirect
10. #13070541C2semidirect
11. #13070530C2semidirect
12. #13070493C2semidirect
13. #13070329C2semidirect
14. C2×#10622147C2semidirect
15. C11×#2168C2semidirect
20. C2×C11×M32C22semidirect
26. #10622728C22semidirect
28. C2×#66882C22semidirect
29. C2×#66864C22semidirect
40. C4×D88C22semidirect
41. #10622295C22semidirect
42. C11×C4⋊C16C22semidirect
44. C11×C22⋊C16C22semidirect
45. C11×#346C22semidirect
52. #10622147C22semidirect
53. #10622143C22semidirect
54. #10622143C22semidirect
55. #10622143C22semidirect
56. #10622141C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
180. D88#41semidirect
199. #2168D11semidirect
256. C2×M32C2×D11semidirect
278. C4⋊C16C2×D11semidirect
290. C22⋊C16C2×D11semidirect
291. #346C2×D11semidirect
455. C11#33873semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130803032
#130708532
#130708142
#130708022
#130707642
#130707192
#130707122
#130706722
#130705412
#130705302
#130704932
#130703292
C2×#106221472
C11×#21682
#3387311