Finite Group Databasebeta

← #14909579

Subgroups — #14909579

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078193C211yesmaximal, characteristic
2D11×#467C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070821C211yesmaximal, characteristic, complemented
5#13070817C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070726C211yesmaximal, characteristic, complemented
9#13070723C211yesmaximal, characteristic, complemented
10#13070721C211yesmaximal, characteristic, complemented
11#13070556C211yesmaximal, characteristic, complemented
12#13070548C211yesmaximal, characteristic, complemented
13#13070531C211yesmaximal, characteristic, complemented
14#13070225C211yesmaximal, characteristic, complemented
15C11×#2189C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17#10623359—21no—
18C2×Q16×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20D11×C22⋊Q8—21no—
21C2×C11×Q32C2211yescharacteristic, complemented
22C2×C11×SD32C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic
24#10622846—21no—
25#10622801C2211yescharacteristic
26#10622801C2211yescharacteristic
27#10622801C2211yescharacteristic
28C2×#66893C2211yescharacteristic, complemented
29#10622784—21no—
30#10622784—21no—
31#10622770C2211yescharacteristic
32#10622770C2211yescharacteristic
33C2×#66891C2211yescharacteristic, complemented
34#10622729C2211yescharacteristic
35#10622719C2211yescharacteristic
36#10622664—21no—
37C2×#66862C2211yescharacteristic
38C2×#66862C2211yescharacteristic
39#10622500C2211yescharacteristic
40D11×#107C2211yescharacteristic
41#10622426—21no—
42D11×#103—21no—
43C11×#358C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45C11×C22⋊C16C2211yescharacteristic
46#10622202C2211yescharacteristic, complemented
47#10622202C2211yescharacteristic, complemented
48#10622202C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50C22⋊(C11⋊C16)C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53#10622143C2211yescharacteristic, complemented
54#10622142C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C2×Q8×D11—21no—
61C22×C4×D11D411yescharacteristic
62C11×#135—41no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—21no—
70#66999—21no—
71#66999—21no—
72#66999—21no—
73C2×#4326—21no—
74#66991—21no—
75#66991—21no—
76#66990—41no—
77#66988—41no—
78C4×C22⋊D11—41no—
79C4×C22⋊D11—41no—
80#66979—21no—
81#66977—21no—
82C22×C11⋊C8D411yescharacteristic
83Q16×D11—41no—
84Q16×D11—41no—
85C2×Dic44C2311yescharacteristic
86C2×C8×D11—41no—
87C2×C8×D11—41no—
88C2×C8×D11D411yescharacteristic
89C2×C8×D11D411yescharacteristic
90C2×C8×D11C2311yescharacteristic
91C2×C8×D11C2311yescharacteristic
92#66950—21no—
93#66949—41no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—41no—
96C22⋊C4×D11—41no—
97#66931—41no—
98C11×Q32—41no—
99C11×SD32—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#103—21no—
104#66899—21no—
105#66899—21no—
106#66899—21no—
107#66896—21no—
108#66896—21no—
109#66893—41no—
110#66891—41no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66881—21no—
115#66880—21no—
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118#66874—21no—
119#66871—21no—
120#66862—41no—
121#66862—41no—
122#33762—111nomaximal, Sylow
123C23×D11D811yescharacteristic
124C11×#41—42no—
125C11×#41—42no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134C22×Dic11D811yescharacteristic
135Q8×D11—42no—
136Q8×D11—42no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11D811yescharacteristic
142C2×C4×D11D811yescharacteristic
143C2×C4×D11C2×D411yescharacteristic
144C2×C4×D11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—41no—
147C11×Q16—21no—
148C11×Q16—21no—
149C11×Q16—21no—
150C11×Q16—21no—
151C11×SD16—42no—
152C11×D8—21no—
153C11×D8—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2411yescharacteristic
158C11×C4⋊C4—21no—
159C11×C4⋊C4—41no—
160C11×C22⋊C4—41no—
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163C22⋊Dic11—41no—
164C22⋊Dic11—41no—
165#4326—42no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180C2×C11⋊C8—41no—
181C2×C11⋊C8C2×D411yescharacteristic
182C2×C11⋊C8C2×D411yescharacteristic
183Dic44—21no—
184Dic44—21no—
185C8×D11—21no—
186C8×D11—21no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—41no—
190C8×D11—41no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3050—111no—
196C2×#467—111no—
197#2237—111no—
198#2237—111no—
199#2236—111no—
200#2233—111no—
201#2220—111no—
202#2220—111no—
203#2219—111no—
204#2219—111no—
205#2189—111no—
206#2189D1111yescharacteristic, complemented
207#2188—111no—
208#2185—111no—
209#2112—111no—
210C23×C11—41no—
211C23×C11C2×D811yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11C2×D811yescharacteristic
216C22×D11C2×D811yescharacteristic
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—82no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—82no—
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—82no—
233C22⋊D11—82no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11C2×D811yescharacteristic
240C2×Dic11C2×D811yescharacteristic
241C4×D11—21no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—21no—
245C4×D11—41no—
246C4×D11—41no—
247C4×D11—82no—
248C4×D11—82no—
249Dic22—41no—
250Dic22—41no—
251Dic22—82no—
252C8×C11—21no—
253C8×C11H(5,𝔽2)11yescharacteristic
254C8×C11H(5,𝔽2)11yescharacteristic
255C11⋊C8—21no—
256C11⋊C8—21no—
257C2×#135C2×D1111yescharacteristic
258C22×Q16—111no—
259C23×C8—111no—
260#525—221no—
261C2×C22⋊Q8—221no—
262C2×Q32—111no—
263C2×Q32C2×D1111yescharacteristic, complemented
264C2×SD32—111no—
265C2×SD32C2×D1111yescharacteristic, complemented
266C2×M32—111no—
267C2×M32—111no—
268#467—111no—
269#467—111no—
270#467—111no—
271#467—111no—
272#467—111no—
273#467—221no—
274#467—221no—
275#467C2×D1111yescharacteristic
276#466—111no—
277#466—111no—
278#465—221no—
279#465—221no—
280#427—111no—
281C2×#107—111no—
282#416—221no—
283C2×#103—221no—
284#367—111no—
285#367—111no—
286#366—111no—
287#366—111no—
288#358—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#358—111no—
293#358C2×D1111yescharacteristic, complemented
294#357—111no—
295#357C2×D1111yescharacteristic, complemented
296C22⋊C16—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16C2×D1111yescharacteristic
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11C22×D811yescharacteristic
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—21no—
311C2×D11—21no—
312C2×D11—44no—
313C2×D11#51012yes—
314C4×C11—21no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11#53411yescharacteristic
319C4×C11#57511yescharacteristic
320Dic11—21no—
321Dic11—21no—
322Dic11—81no—
323Dic11—81no—
324Dic11—81no—
325Dic11—81no—
326C2×#41—21no—
327C22×Q8—221no—
328C23×C4—111no—
329#135—41no—
330#135—41no—
331C2×Q16—111no—
332C2×Q16—221no—
333C2×Q16—441no—
334C2×Q16—441no—
335C2×Q16C22×D1111yescharacteristic
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—21no—
338C2×D8C22×D1111yescharacteristic
339C22×C8—111no—
340C22×C8—111no—
341C22×C8—111no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—441no—
345C22×C8—441no—
346C22×C8C22×D1111yescharacteristic
347#123—441no—
348C22⋊Q8—21no—
349C22⋊Q8—221no—
350C22⋊Q8—221no—
351C22⋊Q8—221no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—441no—
355C22⋊Q8—441no—
356#121—221no—
357#121—221no—
358#120—441no—
359C4×D4—441no—
360C4×D4—441no—
361#117—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—441no—
364C2×C22⋊C4—441no—
365Q32—41no—
366Q32—441no—
367SD32—41no—
368SD32—441no—
369M32—441no—
370M32—441no—
371C2×C16—111no—
372C2×C16—111no—
373C2×C16C22×D1111yescharacteristic
374C2×C16C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#107—111no—
378#107—221no—
379#107C22×D1111yescharacteristic
380#106—221no—
381#103—21no—
382#103—221no—
383#103—221no—
384#103—221no—
385#103—221no—
386#103—221no—
387#102—221no—
388#102—221no—
389C2×C11—41no—
390C2×C11—161no—
391C2×C11#318611yescharacteristic
392C2×C11C2×#51011yescharacteristic
393C2×C11#341411yescharacteristic
394D11—22no—
395D11—41no—
396C24—111no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—221no—
402C2×Q8—441no—
403C2×Q8—442no—
404C2×Q8—442no—
405C2×D4—21no—
406C2×D4—41no—
407C2×D4—441no—
408C2×D4—441no—
409C22×C4—41no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—441no—
416C22×C4—441no—
417C22×C4—441no—
418C22×C4—441no—
419C22×C4D4×D1111yescharacteristic
420Q16—21no—
421Q16—21no—
422Q16—21no—
423Q16—21no—
424Q16—221no—
425Q16—221no—
426Q16—442no—
427SD16—42no—
428D8—21no—
429D8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—111no—
433C2×C8—111no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—441no—
439C2×C8—441no—
440C2×C8—441no—
441C2×C8D4×D1111yescharacteristic
442C2×C8C23×D1111yescharacteristic
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—221no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—441no—
449C4⋊C4—441no—
450C4⋊C4—441no—
451C4⋊C4—441no—
452C4⋊C4—441no—
453C4⋊C4—441no—
454C22⋊C4—41no—
455C22⋊C4—441no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C42—441no—
464C16—21no—
465C16—21no—
466C16—221no—
467C16—221no—
468C11#3376211yescharacteristic, complemented, Sylow
469C23—41no—
470C23—111no—
471C23—111no—
472C23—222no—
473C23—441no—
474C23—441no—
475C23D8×D1111yescharacteristic
476Q8—41no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—441no—
481Q8—441no—
482Q8—882no—
483D4—41no—
484D4—41no—
485D4—82no—
486D4—882no—
487D4—882no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—82no—
494C2×C4—111no—
495C2×C4—111no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—882no—
508C2×C4—882no—
509C2×C4D8×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C8—21no—
512C8—221no—
513C8—221no—
514C8#6703711yescharacteristic
515C8#6703711yescharacteristic
516C22—21no—
517C22—21no—
518C22—21no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—112no—
523C22—221no—
524C22—221no—
525C22—221no—
526C22—221no—
527C22—221no—
528C22—444no—
529C22C2×D8×D1111yescharacteristic
530C4—21no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—221no—
535C4—221no—
536C4—881no—
537C4—881no—
538C4—881no—
539C4—881no—
540C4#1062312011yescharacteristic
541C4#1062330411yescharacteristic
542C2—41no—
543C2—161no—
544C2—222no—
545C2—441no—
546C2#1307936511yescharacteristic
547C2D11×#51011yescharacteristic
548C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2189C2
socleC22×C11C22×D8
prime radical#13078193C2
hypercenter#2189D11
hypocenterC11#33762
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2189

Complements

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

NH ≅ G/Ntype
2. D11×#467C2semidirect
3. #13070825C2semidirect
4. #13070821C2semidirect
5. #13070817C2semidirect
6. #13070800C2semidirect
7. #13070728C2semidirect
8. #13070726C2semidirect
9. #13070723C2semidirect
10. #13070721C2semidirect
11. #13070556C2semidirect
12. #13070548C2semidirect
13. #13070531C2semidirect
14. #13070225C2semidirect
15. C11×#2189C2semidirect
21. C2×C11×Q32C22semidirect
22. C2×C11×SD32C22semidirect
28. C2×#66893C22semidirect
33. C2×#66891C22semidirect
43. C11×#358C22semidirect
44. C11×#357C22semidirect
46. #10622202C22semidirect
47. #10622202C22semidirect
48. #10622202C22semidirect
49. #10622200C22semidirect
53. #10622143C22semidirect
54. #10622142C22semidirect
55. #10622141C22semidirect
56. #10622141C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
206. #2189D11semidirect
263. C2×Q32C2×D11semidirect
265. C2×SD32C2×D11semidirect
293. #358C2×D11semidirect
295. #357C2×D11semidirect
468. C11#33762semidirect

Maximal subgroups

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

subgroupindex
#130781932
D11×#4672
#130708252
#130708212
#130708172
#130708002
#130707282
#130707262
#130707232
#130707212
#130705562
#130705482
#130705312
#130702252
C11×#21892
#3376211