Finite Group Databasebeta

← #14910805

Subgroups — #14910805

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#13080984C211yesmaximal, characteristic, complemented
2D8×C22⋊D11C211yesmaximal, characteristic
3#13070856C211yesmaximal, characteristic, complemented
4#13070807C211yesmaximal, characteristic, complemented
5#13070795C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070711C211yesmaximal, characteristic, complemented
9#13070655C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070545C211yesmaximal, characteristic, complemented
12#13070477C211yesmaximal, characteristic, complemented
13#13070439C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2140C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17D4×C22⋊D11—21no—
18C2×D8×D11C2211yescharacteristic
19#10623060—21no—
20C2×C11×M32C2211yescharacteristic, complemented
21C11×#427C2211yescharacteristic, complemented
22#10622830—21no—
23#10622770C2211yescharacteristic
24#10622769—21no—
25#10622764C2211yescharacteristic
26#10622763—21no—
27D8×Dic11C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C2×#66891C2211yescharacteristic, complemented
30#10622729C2211yescharacteristic, complemented
31#10622728C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622609—21no—
34C2×#66864C2211yescharacteristic, complemented
35C2×C16×D11C2211yescharacteristic, complemented
36#10622500C2211yescharacteristic, complemented
37D11×#107C2211yescharacteristic, complemented
38#10622491C2211yescharacteristic, complemented
39#10622486C2211yescharacteristic, complemented
40#10622475—21no—
41#10622470—21no—
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic, complemented
48C22⋊(C11⋊C16)C2211yescharacteristic, complemented
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622142C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C22×C22⋊D11—41no—
61C2×D4×D11—21no—
62C2×C11×D8—22no—
63C2×C11×D8—21no—
64C2×C11×D8—41no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#117—21no—
69#67006—41no—
70#66993—21no—
71#66992—41no—
72#66991—21no—
73#66990—41no—
74D4×Dic11—21no—
75C2×#4323—21no—
76C2×#4323—21no—
77#66983—21no—
78C4×C22⋊D11D411yescharacteristic
79#66977—21no—
80D8×D11—22no—
81D8×D11—41no—
82C2×Dic44C2311yescharacteristic
83C2×D88C2311yescharacteristic
84C2×C8×D11C2311yescharacteristic
85#66950—21no—
86C4⋊C4×D11—21no—
87#66943—21no—
88#66940—21no—
89#66936—41no—
90#66932—41no—
91#66925—41no—
92#66923—41no—
93C11×M32—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99#66896—21no—
100#66896—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66891—22no—
103#66891—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#66874—21no—
114#66874—21no—
115#66872—21no—
116#66871—21no—
117#66864—41no—
118C16×D11—41no—
119#33877—111nomaximal, Sylow
120C24×C11—41no—
121C23×D11—41no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—42no—
125C2×D4×C11—41no—
126C2×D4×C11—81no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C2×C22⋊D11—41no—
133C2×C22⋊D11—84no—
134C2×C22⋊D11D811yescharacteristic
135C22×Dic11—41no—
136D4×D11—42no—
137D4×D11—81no—
138C2×D44—21no—
139C2×C4×D11—41no—
140C2×C4×D11C2×D411yescharacteristic
141C2×Dic22—21no—
142C11×D8—21no—
143C11×D8—21no—
144C11×D8—21no—
145C11×D8—42no—
146C11×D8#4112yes—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C22⋊C4—41no—
154C42×C11—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11D811yescharacteristic
159#4323—42no—
160#4323—81no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4D811yescharacteristic
173C4×Dic11—41no—
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#3336—111no—
188D4×D8—111no—
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#2140D1111yescharacteristic, complemented
201C2×#357—111no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—82no—
205C23×C11—82no—
206C23×C11—161no—
207C23×C11C2×D811yescharacteristic
208C22×D11—41no—
209C22×D11—82no—
210C22×D11—82no—
211C22×D11—161no—
212C22×D11C2×D811yescharacteristic
213D4×C11—22no—
214D4×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×C11C2×D811yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C22⋊D11—22no—
225C22⋊D11—82no—
226C22⋊D11—82no—
227C22⋊D11—82no—
228C22⋊D11—82no—
229C22⋊D11—161no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—82no—
234C2×Dic11C2×D811yescharacteristic
235C2×Dic11C2×D811yescharacteristic
236C2×Dic11C2×D811yescharacteristic
237D44—41no—
238D44—41no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—82no—
242Dic22—41no—
243Dic22—41no—
244C8×C11—21no—
245C8×C11C2×#4111yescharacteristic
246C8×C11H(5,𝔽2)11yescharacteristic
247C11⋊C8—21no—
248C11⋊C8—21no—
249C22×D8—111no—
250C22×D8C2×D1111yescharacteristic
251#552—221no—
252D42—221no—
253C2×SD32—111no—
254C2×SD32—111no—
255C2×SD32—111no—
256C2×M32C2×D1111yescharacteristic, complemented
257C22×C16—111no—
258#499—111no—
259#493—111no—
260#485—221no—
261#483—221no—
262#479—221no—
263#467—111no—
264#467—111no—
265#466—111no—
266#466—111no—
267#459—221no—
268#447—221no—
269#447—221no—
270C4×Q16—111no—
271C4×D8—111no—
272C8×D4—111no—
273#427C2×D1111yescharacteristic, complemented
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#357C2×D1111yescharacteristic
286#357C2×D1111yescharacteristic
287#357C2×D1111yescharacteristic, complemented
288#357C2×D1111yescharacteristic, complemented
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—42no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—164no—
302C22×C11C22×D811yescharacteristic
303C2×D11—21no—
304C2×D11—21no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—164no—
309C2×D11#50912yes—
310C4×C11—21no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11#54611yescharacteristic
314C4×C11#57711yescharacteristic
315Dic11—21no—
316Dic11—21no—
317Dic11—21no—
318Dic11—81no—
319Dic11—81no—
320Dic11—81no—
321C22×D4—21no—
322C22×D4—221no—
323C22×D4—441no—
324C2×Q16—111no—
325C2×D8—22no—
326C2×D8—21no—
327C2×D8—41no—
328C2×D8—111no—
329C2×D8—221no—
330C2×D8—221no—
331C2×D8—222no—
332C2×D8—441no—
333C2×D8C22×D1111yescharacteristic
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—221no—
343C22⋊Q8—221no—
344#121—221no—
345#121—221no—
346#121—441no—
347#120—441no—
348#120—441no—
349C4×Q8—221no—
350C4×D4—111no—
351C4×D4—221no—
352#117—21no—
353#117—441no—
354C2×C4⋊C4—221no—
355SD32—222no—
356SD32—441no—
357SD32—441no—
358M32—41no—
359C2×C16—111no—
360C2×C16—111no—
361C2×C16—441no—
362C2×C16C22×D1111yescharacteristic
363C2×C16C22×D1111yescharacteristic
364#107—111no—
365#107—111no—
366#107—221no—
367#107C22×D1111yescharacteristic
368#107C22×D1111yescharacteristic
369#106—21no—
370#106—221no—
371C4⋊C8—111no—
372#103—221no—
373#103—221no—
374#103—221no—
375#102—221no—
376#102—221no—
377#102—221no—
378C22⋊C8—111no—
379C22⋊C8—111no—
380C4×C8—111no—
381C2×C11—41no—
382C2×C11—82no—
383C2×C11—161no—
384C2×C11#329411yescharacteristic
385C2×C11C2×#50911yescharacteristic
386C2×C11#341611yescharacteristic
387D11—22no—
388D11—161no—
389C24—41no—
390C24—441no—
391C2×Q8—221no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4—41no—
396C2×D4—81no—
397C2×D4—111no—
398C2×D4—221no—
399C2×D4—441no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—442no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—881no—
406C2×D4—884no—
407C22×C4—111no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4D4×D1111yescharacteristic
411Q16—221no—
412Q16—221no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—42no—
417D8—221no—
418D8—221no—
419D8—442no—
420D8—881no—
421D8#433912yes—
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—111no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4—441no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4—441no—
441C22⋊C4—41no—
442C22⋊C4—111no—
443C22⋊C4—111no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4—441no—
449C42—41no—
450C42—111no—
451C42—441no—
452C16—21no—
453C16—21no—
454C16—221no—
455C16—221no—
456C11#3387711yescharacteristic, complemented, Sylow
457C23—41no—
458C23—41no—
459C23—82no—
460C23—82no—
461C23—111no—
462C23—161no—
463C23—441no—
464C23—882no—
465C23—882no—
466C23—1761no—
467C23D8×D1111yescharacteristic
468Q8—441no—
469Q8—441no—
470D4—22no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—82no—
475D4—222no—
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—111no—
488C2×C4—111no—
489C2×C4—111no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—441no—
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—
502C8C2×#433911yescharacteristic
503C8#6703711yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—112no—
514C22—164no—
515C22—221no—
516C22—221no—
517C22—881no—
518C22—881no—
519C22—881no—
520C22—1764no—
521C22C2×D8×D1111yescharacteristic
522C4—21no—
523C4—81no—
524C4—81no—
525C4—221no—
526C4—221no—
527C4—221no—
528C4—881no—
529C4—881no—
530C4—881no—
531C4#1062302111yescharacteristic
532C4#1062329311yescharacteristic
533C2—41no—
534C2—82no—
535C2—161no—
536C2—222no—
537C2—1761no—
538C2#1308042511yescharacteristic
539C2D11×#50911yescharacteristic
540C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2140C2
socleC22×C11C22×D8
prime radicalD8×C22⋊D11C2
hypercenter#2140D11
hypocenterC11#33877
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
1. #13080984C2semidirect
3. #13070856C2semidirect
4. #13070807C2semidirect
5. #13070795C2semidirect
6. #13070771C2semidirect
7. #13070729C2semidirect
8. #13070711C2semidirect
9. #13070655C2semidirect
10. #13070546C2semidirect
11. #13070545C2semidirect
12. #13070477C2semidirect
13. #13070439C2semidirect
14. D11×#357C2semidirect
15. C11×#2140C2semidirect
20. C2×C11×M32C22semidirect
21. C11×#427C22semidirect
29. C2×#66891C22semidirect
30. #10622729C22semidirect
34. C2×#66864C22semidirect
35. C2×C16×D11C22semidirect
36. #10622500C22semidirect
37. D11×#107C22semidirect
38. #10622491C22semidirect
39. #10622486C22semidirect
44. C11×#357C22semidirect
45. C11×#357C22semidirect
47. #10622200C22semidirect
48. C22⋊(C11⋊C16)C22semidirect
49. #10622147C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622142C22semidirect
52. #10622141C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. #10622129C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
200. #2140D11semidirect
256. C2×M32C2×D11semidirect
273. #427C2×D11semidirect
287. #357C2×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
#130809842
D8×C22⋊D112
#130708562
#130708072
#130707952
#130707712
#130707292
#130707112
#130706552
#130705462
#130705452
#130704772
#130704392
D11×#3572
C11×#21402
#3387711