Finite Group Databasebeta

← #14909585

Subgroups — #14909585

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#13078198C211yesmaximal, characteristic
2D11×#467C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070820C211yesmaximal, characteristic, complemented
5#13070803C211yesmaximal, characteristic, complemented
6#13070732C211yesmaximal, characteristic, complemented
7#13070730C211yesmaximal, characteristic, complemented
8#13070725C211yesmaximal, characteristic, complemented
9#13070723C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070554C211yesmaximal, characteristic, complemented
12#13070551C211yesmaximal, characteristic, complemented
13#13070534C211yesmaximal, characteristic, complemented
14#13070225C211yesmaximal, characteristic, complemented
15C11×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19D11×C22⋊Q8—21no—
20#10623055—21no—
21C11×#467C2211yescharacteristic
22C11×#427C2211yescharacteristic
23#10622801C2211yescharacteristic
24C2×#66893C2211yescharacteristic, complemented
25C2×#66892C2211yescharacteristic, complemented
26#10622729C2211yescharacteristic
27#10622664—21no—
28#10622615—21no—
29C2×Dic88C2211yescharacteristic, complemented
30C2×#66864C2211yescharacteristic, complemented
31C2×#66862C2211yescharacteristic
32C2×#66862C2211yescharacteristic
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622500C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622496C2211yescharacteristic
38D11×#107C2211yescharacteristic
39#10622477—21no—
40#10622477—21no—
41#10622426—21no—
42D11×#103—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#366C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×#358C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622141C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×Q8×D11—21no—
60C2×#4339—21no—
61C22×C4×D11D411yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×#117—21no—
66#66999—21no—
67C2×#4326—21no—
68#66977—21no—
69C22×C11⋊C8D411yescharacteristic
70Q16×D11—41no—
71Q16×D11—41no—
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74#66957—41no—
75#66957—41no—
76C2×D88C2311yescharacteristic
77C2×#4314—21no—
78C2×C8×D11—41no—
79C2×C8×D11—41no—
80C2×C8×D11D411yescharacteristic
81C2×C8×D11D411yescharacteristic
82C2×C8×D11C2311yescharacteristic
83C2×C8×D11C2311yescharacteristic
84#66950—21no—
85#66950—21no—
86#66950—21no—
87#66949—41no—
88#66948—21no—
89#66948—21no—
90C4⋊C4×D11—21no—
91C4⋊C4×D11—41no—
92#66939—41no—
93#66935—41no—
94C22⋊C4×D11—41no—
95#66931—41no—
96C4×D44—41no—
97C4×D44—41no—
98C2×C11×C16C2311yescharacteristic
99C2×C11×C16C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#106—21no—
104C11×#103—21no—
105#66899—21no—
106#66893—41no—
107#66892—41no—
108#66882C2311yescharacteristic
109#66880—21no—
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66874—21no—
114#66874—21no—
115#66873—21no—
116#66873—21no—
117#66871—21no—
118Dic88—41no—
119#66864—41no—
120#66862—41no—
121#66862—41no—
122#33762—111nomaximal, Sylow
123C23×D11D811yescharacteristic
124C2×Q8×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C22×Dic11D811yescharacteristic
128Q8×D11—42no—
129Q8×D11—42no—
130#4339—42no—
131#4339—42no—
132C2×D44—21no—
133C2×D44—41no—
134C2×D44—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11D811yescharacteristic
141C2×C4×D11D811yescharacteristic
142C2×C4×D11C2×D411yescharacteristic
143C2×C4×D11C2×D411yescharacteristic
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—41no—
147C11×Q16—21no—
148C11×Q16—21no—
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—21no—
156C11×C4⋊C4—41no—
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C42×C11—41no—
160C22⋊Dic11—41no—
161#4326—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168C4⋊Dic11—21no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4—41no—
175C2×C11⋊C8—41no—
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178Dic44—21no—
179Dic44—21no—
180Dic44—21no—
181Dic44—21no—
182D88—21no—
183D88—21no—
184#4314—42no—
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#2237D1111yescharacteristic, complemented
199#2236—111no—
200#2233—111no—
201#2220—111no—
202#2220—111no—
203#2219—111no—
204#2219—111no—
205#2189—111no—
206#2189—111no—
207#2188—111no—
208#2185—111no—
209#2112—111no—
210C23×C11C2×D811yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11C2×D811yescharacteristic
216C22×D11C2×D811yescharacteristic
217Q8×C11—41no—
218Q8×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C22⋊D11—82no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11C2×D811yescharacteristic
233C2×Dic11C2×D811yescharacteristic
234D44—41no—
235D44—41no—
236D44—82no—
237D44—82no—
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—82no—
245C4×D11—82no—
246C4×D11—82no—
247Dic22—41no—
248Dic22—41no—
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×#135—111no—
258C22×Q16—111no—
259C23×C8—111no—
260#525—221no—
261C2×C22⋊Q8—221no—
262C2×Q32—111no—
263C2×Q32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
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#427C2×D1111yescharacteristic
281C2×#107—111no—
282#416—221no—
283C2×#103—221no—
284#367—111no—
285#367C2×D1111yescharacteristic, complemented
286#366—111no—
287#366C2×D1111yescharacteristic, complemented
288#358—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#358C2×D1111yescharacteristic, complemented
293#358C2×D1111yescharacteristic, complemented
294#357—111no—
295#357—111no—
296C22⋊C16—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16C2×D1111yescharacteristic
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11C22×D811yescharacteristic
304C2×D11—21no—
305C2×D11—21no—
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—44no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11#51012yes—
314C4×C11—21no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11#53411yescharacteristic
320C4×C11#57511yescharacteristic
321Dic11—21no—
322Dic11—21no—
323Dic11—81no—
324Dic11—81no—
325Dic11—81no—
326C2×#41—221no—
327C22×Q8—221no—
328C23×C4—111no—
329#135—441no—
330#135—441no—
331C2×Q16—111no—
332C2×Q16—111no—
333C2×Q16—221no—
334C2×Q16—441no—
335C2×Q16—441no—
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—221no—
338C2×D8—111no—
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—21no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—441no—
364C2×C22⋊C4—441no—
365Q32—441no—
366Q32—441no—
367SD32—441no—
368SD32—441no—
369M32—441no—
370M32—441no—
371C2×C16—111no—
372C2×C16—111no—
373C2×C16C22×D1111yescharacteristic
374C2×C16C22×D1111yescharacteristic
375#107—111no—
376#107—221no—
377#107C22×D1111yescharacteristic
378#107C22×D1111yescharacteristic
379#107C22×D1111yescharacteristic
380#106—21no—
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#318611yescharacteristic
391C2×C11C2×#51011yescharacteristic
392C2×C11#341411yescharacteristic
393D11—22no—
394D11—41no—
395D11—161no—
396C24—111no—
397#41—442no—
398#41—442no—
399C2×Q8—21no—
400C2×Q8—221no—
401C2×Q8—221no—
402C2×Q8—441no—
403C2×Q8—442no—
404C2×Q8—442no—
405C2×D4—221no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—441no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—441no—
415C22×C4—441no—
416C22×C4—441no—
417C22×C4—441no—
418C22×C4—441no—
419C22×C4D4×D1111yescharacteristic
420Q16—21no—
421Q16—21no—
422Q16—221no—
423Q16—221no—
424Q16—221no—
425Q16—221no—
426Q16—442no—
427SD16—442no—
428D8—221no—
429D8—221no—
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—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
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—41no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C42—41no—
464C16—21no—
465C16—21no—
466C16—221no—
467C16—221no—
468C11#3376211yescharacteristic, complemented, Sylow
469C23—111no—
470C23—111no—
471C23—222no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23D8×D1111yescharacteristic
476Q8—41no—
477Q8—41no—
478Q8—441no—
479Q8—441no—
480Q8—441no—
481Q8—441no—
482Q8—882no—
483D4—441no—
484D4—441no—
485D4—882no—
486D4—882no—
487D4—882no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
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—882no—
507C2×C4—882no—
508C2×C4—882no—
509C2×C4D8×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C8—21no—
512C8—221no—
513C8—221no—
514C8#6704211yescharacteristic
515C8#6704211yescharacteristic
516C22—21no—
517C22—21no—
518C22—21no—
519C22—112no—
520C22—221no—
521C22—221no—
522C22—221no—
523C22—221no—
524C22—221no—
525C22—444no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22C2×D8×D1111yescharacteristic
530C4—21no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4—221no—
536C4—221no—
537C4—881no—
538C4—881no—
539C4—881no—
540C4#1062318411yescharacteristic
541C4#1062330811yescharacteristic
542C2—41no—
543C2—222no—
544C2—441no—
545C2—1761no—
546C2#1307936611yescharacteristic
547C2D11×#51011yescharacteristic
548C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
prime radical#13078198C2
hypercenter#2237D11
hypocenterC11#33762
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
2. D11×#467C2semidirect
3. #13070824C2semidirect
4. #13070820C2semidirect
5. #13070803C2semidirect
6. #13070732C2semidirect
7. #13070730C2semidirect
8. #13070725C2semidirect
9. #13070723C2semidirect
10. #13070558C2semidirect
11. #13070554C2semidirect
12. #13070551C2semidirect
13. #13070534C2semidirect
14. #13070225C2semidirect
15. C11×#2237C2semidirect
24. C2×#66893C22semidirect
25. C2×#66892C22semidirect
29. C2×Dic88C22semidirect
30. C2×#66864C22semidirect
43. C11×#367C22semidirect
44. C11×#366C22semidirect
45. C11×#358C22semidirect
46. C11×#358C22semidirect
49. #10622147C22semidirect
52. #10622141C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
55. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
198. #2237D11semidirect
285. #367C2×D11semidirect
287. #366C2×D11semidirect
292. #358C2×D11semidirect
293. #358C2×D11semidirect
468. C11#33762semidirect

Maximal subgroups

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

subgroupindex
#130781982
D11×#4672
#130708242
#130708202
#130708032
#130707322
#130707302
#130707252
#130707232
#130705582
#130705542
#130705512
#130705342
#130702252
C11×#22372
#3376211