Finite Group Databasebeta

← #14910600

Subgroups — #14910600

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081005C211yesmaximal, characteristic, complemented
2D8×C22⋊D11C211yesmaximal, characteristic
3#13070838C211yesmaximal, characteristic, complemented
4#13070802C211yesmaximal, characteristic, complemented
5#13070800C211yesmaximal, characteristic, complemented
6#13070761C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070709C211yesmaximal, characteristic, complemented
9#13070654C211yesmaximal, characteristic, complemented
10#13070543C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13C2×#10622200C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2187C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17D4×C22⋊D11—21no—
18C2×D8×D11C2211yescharacteristic
19#10623166—21no—
20C2×C11×SD32C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic, complemented
22C11×#467C2211yescharacteristic, complemented
23#10622830—21no—
24#10622801C2211yescharacteristic, complemented
25Q16×Dic11C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic, complemented
27#10622770C2211yescharacteristic
28#10622769—21no—
29#10622764C2211yescharacteristic
30#10622763—21no—
31D8×Dic11C2211yescharacteristic
32#10622728C2211yescharacteristic
33C8×C22⋊D11C2211yescharacteristic
34C2×#66882C2211yescharacteristic, complemented
35C22×C11⋊C16C2211yescharacteristic, complemented
36#10622657—21no—
37C2×C16×D11C2211yescharacteristic, complemented
38D11×#107C2211yescharacteristic, complemented
39#10622487C2211yescharacteristic, complemented
40#10622422—21no—
41#10622407—21no—
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic, complemented
44C11×C22⋊C16C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50#10622147C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622143C2211yescharacteristic, complemented
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C22×C22⋊D11—41no—
61C2×D4×D11—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8—22no—
64C2×C11×D8—21no—
65C2×C11×D8—41no—
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—21no—
70#67006—41no—
71#66999—21no—
72Q8×Dic11—21no—
73#66993—21no—
74#66992—41no—
75#66991—21no—
76#66990—41no—
77D4×Dic11—21no—
78C2×#4323—21no—
79C2×#4323—21no—
80#66983—21no—
81C4×C22⋊D11D411yescharacteristic
82C2×C4⋊Dic11—21no—
83D8×D11—22no—
84D8×D11—41no—
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66950—41no—
88C4⋊C4×D11—21no—
89#66942—41no—
90#66941—21no—
91(C22⋊D11)⋊C4—41no—
92#66931—41no—
93C11×SD32—22no—
94C11×SD32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99#66899—21no—
100#66899—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66892—41no—
105#66885—21no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111Dic11⋊C8D411yescharacteristic
112C8×Dic11C2311yescharacteristic
113C2×C11⋊C16—41no—
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#66871—21no—
117#66871—21no—
118C16×D11—41no—
119#33862—111nomaximal, Sylow
120C24×C11—41no—
121C23×D11—41no—
122C2×Q8×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—42no—
126C2×D4×C11—41no—
127C2×D4×C11—81no—
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134C2×C22⋊D11—84no—
135C2×C22⋊D11D811yescharacteristic
136C22×Dic11—41no—
137C22×Dic11—41no—
138D4×D11—42no—
139D4×D11—81no—
140C2×D44—21no—
141C2×C4×D11—41no—
142C2×C4×D11C2×D411yescharacteristic
143C2×Dic22—41no—
144C11×Q16—21no—
145C11×Q16—21no—
146C11×D8—21no—
147C11×D8—21no—
148C11×D8—21no—
149C11×D8—42no—
150C11×D8#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2411yescharacteristic
155C11×C4⋊C4—21no—
156C11×C4⋊C4—41no—
157C11×C22⋊C4—41no—
158C22⋊Dic11—41no—
159C22⋊Dic11—41no—
160C22⋊Dic11D811yescharacteristic
161#4323—42no—
162#4323—81no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4D811yescharacteristic
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4D811yescharacteristic
175C4×Dic11—41no—
176C4×Dic11C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179D88—21no—
180D88—21no—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3338—111no—
188D4×D8—111no—
189#2240—111no—
190#2233—111no—
191#2233—111no—
192#2226—111no—
193#2217—111no—
194#2217—111no—
195#2207—111no—
196#2187—111no—
197#2187D1111yescharacteristic, complemented
198C4×SD32—111no—
199D4×C16—111no—
200C2×#357—111no—
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
213Q8×C11—41no—
214Q8×C11—41no—
215D4×C11—22no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—82no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C22⋊D11—82no—
227C22⋊D11—82no—
228C22⋊D11—82no—
229C22⋊D11—82no—
230C22⋊D11—161no—
231C22⋊D11SD3214yescomplemented
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—82no—
236C2×Dic11—161no—
237C2×Dic11C2×D811yescharacteristic
238C2×Dic11C2×D811yescharacteristic
239C2×Dic11C2×D811yescharacteristic
240D44—41no—
241D44—41no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—161no—
245Dic22—161no—
246C8×C11—21no—
247C8×C11C2×#4111yescharacteristic
248C8×C11H(5,𝔽2)11yescharacteristic
249C11⋊C8—21no—
250C11⋊C8—21no—
251C22×D8—111no—
252C22×D8C2×D1111yescharacteristic
253#554—221no—
254D42—221no—
255C2×SD32—111no—
256C2×SD32C2×D1111yescharacteristic
257C2×SD32C2×D1111yescharacteristic, complemented
258C22×C16—111no—
259C22×C16—111no—
260#500—111no—
261#493—111no—
262#484—221no—
263#484—221no—
264#477—221no—
265#467—111no—
266#467C2×D1111yescharacteristic, complemented
267#466—111no—
268#466—111no—
269#459—221no—
270#447—221no—
271#447—221no—
272C4×Q16—111no—
273C4×D8—111no—
274C8×D4—111no—
275C2×#107—111no—
276C2×#107—111no—
277#367—111no—
278#367—111no—
279#367—111no—
280C4⋊C16—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—
289#357C2×D1111yescharacteristic
290#357C2×D1111yescharacteristic, complemented
291C22⋊C16—111no—
292C22⋊C16C2×D1111yescharacteristic, complemented
293C4×C16—111no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—164no—
303C22×C11C2×SD3212yes—
304C22×C11C22×D811yescharacteristic
305C2×D11—21no—
306C2×D11—21no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—164no—
311C2×D11C2×SD3212yes—
312C4×C11—21no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11#54611yescharacteristic
316C4×C11#57711yescharacteristic
317Dic11—21no—
318Dic11—21no—
319Dic11—81no—
320Dic11—81no—
321Dic11—81no—
322Dic11C2×SD3212yes—
323C22×D4—21no—
324C22×D4—221no—
325C22×D4—441no—
326C2×Q16C22×D1111yescharacteristic
327C2×D8—22no—
328C2×D8—21no—
329C2×D8—41no—
330C2×D8—111no—
331C2×D8—221no—
332C2×D8—221no—
333C2×D8—222no—
334C2×D8—441no—
335C2×D8C22×D1111yescharacteristic
336C2×D8C22×D1111yescharacteristic
337C22×C8—111no—
338C22×C8C22×D1111yescharacteristic
339C4⋊Q8—221no—
340#127—221no—
341#125—441no—
342C22⋊Q8—21no—
343C22⋊Q8—221no—
344C22⋊Q8—441no—
345C22⋊Q8—441no—
346#121—221no—
347#121—221no—
348#121—441no—
349#120—441no—
350#120—441no—
351C4×Q8—221no—
352C4×D4—111no—
353C4×D4—221no—
354C4×D4—441no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357SD32—22no—
358SD32—41no—
359SD32—441no—
360C2×C16—111no—
361C2×C16—111no—
362C2×C16—441no—
363C2×C16—441no—
364C2×C16C22×D1111yescharacteristic
365C2×C16C22×D1111yescharacteristic
366#107—111no—
367#107—111no—
368#107—111no—
369#107—221no—
370#107—221no—
371#107—221no—
372#107C22×D1111yescharacteristic
373C4⋊C8—111no—
374#103—21no—
375#103—221no—
376#103—221no—
377#102—221no—
378#102—221no—
379#102—221no—
380C22⋊C8—111no—
381C22⋊C8—111no—
382C4×C8—111no—
383C2×C11—22no—
384C2×C11—82no—
385C2×C11—161no—
386C2×C11#329411yescharacteristic
387C2×C11C22×SD3211yescharacteristic
388C2×C11#341511yescharacteristic
389D11—22no—
390D11—161no—
391C24—41no—
392C24—441no—
393C2×Q8—21no—
394C2×Q8—441no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—81no—
400C2×D4—111no—
401C2×D4—221no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—442no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—881no—
409C2×D4—884no—
410C22×C4—111no—
411C22×C4—441no—
412C22×C4—441no—
413C22×C4—441no—
414C22×C4D4×D1111yescharacteristic
415Q16—21no—
416Q16—21no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—42no—
421D8—221no—
422D8—221no—
423D8—442no—
424D8—881no—
425D8#434112yes—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—111no—
429C2×C8—111no—
430C2×C8—221no—
431C2×C8—221no—
432C2×C8D4×D1111yescharacteristic
433C2×C8C23×D1111yescharacteristic
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—111no—
437C4⋊C4—221no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—441no—
441C4⋊C4—441no—
442C4⋊C4—441no—
443C4⋊C4—441no—
444C4⋊C4—441no—
445C22⋊C4—41no—
446C22⋊C4—111no—
447C22⋊C4—111no—
448C22⋊C4—441no—
449C22⋊C4—441no—
450C22⋊C4—441no—
451C22⋊C4—441no—
452C42—111no—
453C42—441no—
454C16—21no—
455C16—21no—
456C16—221no—
457C16—221no—
458C11#3386211yescharacteristic, complemented, Sylow
459C23—41no—
460C23—41no—
461C23—82no—
462C23—82no—
463C23—111no—
464C23—161no—
465C23—441no—
466C23—882no—
467C23—882no—
468C23—1761no—
469C23D8×D1111yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—1761no—
473D4—22no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—82no—
478D4—114no—
479D4—441no—
480D4—441no—
481D4—882no—
482D4—882no—
483D4—882no—
484D4—882no—
485D4—1761no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—111no—
491C2×C4—111no—
492C2×C4—111no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—882no—
499C2×C4—1761no—
500C2×C4—1761no—
501C2×C4D8×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C8—21no—
504C8—221no—
505C8—221no—
506C8C2×#434111yescharacteristic
507C8#6703711yescharacteristic
508C22—21no—
509C22—21no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—112no—
517C22—164no—
518C22—221no—
519C22—221no—
520C22—881no—
521C22—881no—
522C22—881no—
523C22—1764no—
524C22D11×SD3212yes—
525C22C2×D8×D1111yescharacteristic
526C4—21no—
527C4—81no—
528C4—81no—
529C4—112no—
530C4—221no—
531C4—221no—
532C4—881no—
533C4—881no—
534C4—881no—
535C4#1062312211yescharacteristic
536C4#1062330611yescharacteristic
537C2—22no—
538C2—82no—
539C2—161no—
540C2—222no—
541C2—1761no—
542C2#1308042211yescharacteristic
543C2C2×D11×SD3211yescharacteristic
544C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radicalD8×C22⋊D11C2
hypercenter#2187D11
hypocenterC11#33862
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13081005C2semidirect
3. #13070838C2semidirect
4. #13070802C2semidirect
5. #13070800C2semidirect
6. #13070761C2semidirect
7. #13070714C2semidirect
8. #13070709C2semidirect
9. #13070654C2semidirect
10. #13070543C2semidirect
11. SD32×Dic11C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. C2×#10622200C2semidirect
14. D11×#357C2semidirect
15. C11×#2187C2semidirect
21. C2×C11×SD32C22semidirect
22. C11×#467C22semidirect
24. #10622801C22semidirect
25. Q16×Dic11C22semidirect
26. C2×#66892C22semidirect
34. C2×#66882C22semidirect
35. C22×C11⋊C16C22semidirect
37. C2×C16×D11C22semidirect
38. D11×#107C22semidirect
39. #10622487C22semidirect
43. C11×#357C22semidirect
44. C11×C22⋊C16C22semidirect
45. #10622202C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
50. #10622147C22semidirect
51. #10622147C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622143C22semidirect
54. #10622143C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622129C22semidirect
58. #10622128C22semidirect
197. #2187D11semidirect
231. C22⋊D11SD32semidirect
257. C2×SD32C2×D11semidirect
266. #467C2×D11semidirect
290. #357C2×D11semidirect
292. C22⋊C16C2×D11semidirect
458. C11#33862semidirect

Maximal subgroups

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

subgroupindex
#130810052
D8×C22⋊D112
#130708382
#130708022
#130708002
#130707612
#130707142
#130707092
#130706542
#130705432
SD32×Dic112
(C22⋊D11)⋊C162
C2×#106222002
D11×#3572
C11×#21872
#3386211