Finite Group Databasebeta

← #14909539

Subgroups — #14909539

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078197C211yesmaximal, characteristic, complemented
2#13070824C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070807C211yesmaximal, characteristic, complemented
5#13070804C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070705C211yesmaximal, characteristic, complemented
9#13070700C211yesmaximal, characteristic, complemented
10#13070556C211yesmaximal, characteristic, complemented
11#13070554C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070537C211yesmaximal, characteristic, complemented
14C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
15C11×#3050C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#525—21no—
19#10623322—21no—
20C2×#66957C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C11×#466C2211yescharacteristic
25C11×#465—21no—
26C11×#465—21no—
27C11×#427C2211yescharacteristic
28C11×#416—21no—
29C2×#66893C2211yescharacteristic, complemented
30C2×#66892C2211yescharacteristic, complemented
31C2×#66891C2211yescharacteristic, complemented
32C2×#66890C2211yescharacteristic, complemented
33#10622729C2211yescharacteristic
34#10622729C2211yescharacteristic
35#10622728C2211yescharacteristic
36#10622728C2211yescharacteristic
37#10622727—21no—
38#10622727—21no—
39#10622726—21no—
40#10622719C2211yescharacteristic
41C22×C11⋊C16C2211yescharacteristic
42C22×C11⋊C16C2211yescharacteristic
43#10622202C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47C22⋊(C11⋊C16)C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49C22⋊(C11⋊C16)C2211yescharacteristic
50C22⋊(C11⋊C16)C2211yescharacteristic
51#10622130C2211yescharacteristic, complemented
52#10622130C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C23×C4×C11D411yescharacteristic
61C2×#4339—21no—
62C11×#135—41no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11—41no—
68C22×C8×C11—41no—
69C22×C8×C11D411yescharacteristic
70C22×C8×C11D411yescharacteristic
71C22×C8×C11D411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#123—41no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#120—41no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C11×#117—21no—
84#67006—41no—
85#66983—21no—
86#66983—21no—
87#66982—41no—
88C4×C22⋊D11—41no—
89C4×C22⋊D11—41no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C2×Dic44C2311yescharacteristic
94#66957—41no—
95#66957—41no—
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C11×#107C2311yescharacteristic
99C11×#107C2311yescharacteristic
100C11×#106—21no—
101C11×#103—21no—
102C11×#103—21no—
103C11×#102—21no—
104C11×#102—21no—
105#66893—41no—
106#66892—41no—
107#66891—41no—
108#66890—41no—
109#66885—21no—
110#66885—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66881—21no—
114#66880—21no—
115#66880—21no—
116C2×C11⋊C16—41no—
117C2×C11⋊C16—41no—
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#33757—111nomaximal, Sylow
123C24×C11D811yescharacteristic
124C11×#41—42no—
125C11×#41—42no—
126C2×Q8×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11D811yescharacteristic
135C22×C4×C11D811yescharacteristic
136C22×C4×C11D811yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143#4339—42no—
144#4339—42no—
145C2×D44—21no—
146C2×C4×D11—41no—
147C2×Dic22—21no—
148C11×Q16—21no—
149C11×Q16—21no—
150C11×SD16—42no—
151C11×D8—21no—
152C11×D8—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—41no—
160C2×C8×C11—41no—
161C2×C8×C11—41no—
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—41no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C42×C11—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185C4×Dic11—41no—
186Dic44—21no—
187Dic44—21no—
188D88—21no—
189D88—21no—
190#4314—42no—
191C11⋊C16—21no—
192C11⋊C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3050—111no—
196#3050D1111yescharacteristic, complemented
197#2237—111no—
198#2237—111no—
199#2234—111no—
200#2234—111no—
201#2217—111no—
202#2217—111no—
203#2216—111no—
204#2215—111no—
205#2189—111no—
206#2189—111no—
207#2186—111no—
208#2186—111no—
209C2×C22⋊C16—111no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C2×D811yescharacteristic
215C23×C11C2×D811yescharacteristic
216C23×C11C2×D811yescharacteristic
217C22×D11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—82no—
223D4×C11—82no—
224D4×C11—82no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—82no—
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C2×D811yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C22⋊D11—82no—
243C22⋊D11—82no—
244C22⋊D11—82no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248D44—41no—
249D44—41no—
250C4×D11—82no—
251Dic22—41no—
252Dic22—41no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11H(5,𝔽2)11yescharacteristic
257C8×C11H(5,𝔽2)11yescharacteristic
258C2×#135—111no—
259C2×#135C2×D1111yescharacteristic
260C23×C8C2×D1111yescharacteristic
261#525—21no—
262#525—221no—
263C2×Q32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×D16—111no—
267C22×C16—111no—
268C22×C16—111no—
269#467—111no—
270#467—111no—
271#467C2×D1111yescharacteristic
272#467C2×D1111yescharacteristic
273#466—111no—
274#466—111no—
275#466C2×D1111yescharacteristic
276#466C2×D1111yescharacteristic
277#465—21no—
278#465—21no—
279#465—221no—
280#465—221no—
281#427—111no—
282#427C2×D1111yescharacteristic
283#416—21no—
284#416—221no—
285#367—111no—
286#367—111no—
287#366—111no—
288#366—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#358—111no—
293#357—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300C22⋊C16—111no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—44no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11#50812yes—
314C22×C11C22×D811yescharacteristic
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11—81no—
324C4×C11#53411yescharacteristic
325C4×C11#57511yescharacteristic
326Dic11—81no—
327Dic11—81no—
328Dic11—81no—
329C2×#41—21no—
330C2×#41—221no—
331C23×C4C22⋊D1111yescharacteristic
332#135—41no—
333#135—41no—
334#135—441no—
335#135—441no—
336C2×Q16—111no—
337C2×Q16C22×D1111yescharacteristic
338C2×SD16—21no—
339C2×SD16—221no—
340C2×D8—111no—
341C2×D8C22×D1111yescharacteristic
342C22×C8—41no—
343C22×C8—41no—
344C22×C8C22⋊D1111yescharacteristic
345C22×C8C22⋊D1111yescharacteristic
346C22×C8C22⋊D1111yescharacteristic
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350#123—41no—
351#123—441no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—221no—
355C22⋊Q8—221no—
356#121—21no—
357#121—21no—
358#121—221no—
359#121—221no—
360#120—41no—
361#120—441no—
362C4×D4—41no—
363C4×D4—41no—
364C4×D4—441no—
365C4×D4—441no—
366#117—21no—
367#117—221no—
368Q32—441no—
369SD32—441no—
370SD32—441no—
371D16—441no—
372C2×C16—111no—
373C2×C16—111no—
374C2×C16—111no—
375C2×C16—111no—
376C2×C16—441no—
377C2×C16—441no—
378#107—111no—
379#107—111no—
380#107C22×D1111yescharacteristic
381#107C22×D1111yescharacteristic
382#106—21no—
383#106—221no—
384#103—21no—
385#103—21no—
386#103—221no—
387#103—221no—
388#102—21no—
389#102—21no—
390#102—221no—
391#102—221no—
392C2×C11—22no—
393C2×C11—41no—
394C2×C11—41no—
395C2×C11—161no—
396C2×C11#318611yescharacteristic
397C2×C11C2×#50811yescharacteristic
398C2×C11#341411yescharacteristic
399D11—161no—
400C24#432311yescharacteristic
401#41—42no—
402#41—42no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—221no—
407C2×D4—21no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—221no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—441no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—441no—
419C22×C4#432311yescharacteristic
420C22×C4#432311yescharacteristic
421C22×C4#432311yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425Q16—21no—
426Q16—21no—
427Q16—221no—
428Q16—221no—
429SD16—42no—
430SD16—442no—
431D8—21no—
432D8—21no—
433D8—221no—
434D8—221no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8C2×C22⋊D1111yescharacteristic
445C2×C8C2×C22⋊D1111yescharacteristic
446C2×C8C2×C22⋊D1111yescharacteristic
447C2×C8C23×D1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—441no—
455C4⋊C4—441no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C42—41no—
467C42—441no—
468C16—221no—
469C16—221no—
470C16—221no—
471C16—221no—
472C11#3375711yescharacteristic, complemented, Sylow
473C23—22no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—441no—
478C23C2×#432311yescharacteristic
479C23C2×#432311yescharacteristic
480C23C2×#432311yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—441no—
484Q8—441no—
485D4—41no—
486D4—41no—
487D4—82no—
488D4—82no—
489D4—82no—
490D4—441no—
491D4—441no—
492D4—882no—
493D4—882no—
494D4—882no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—882no—
512C2×C4C2×#432311yescharacteristic
513C2×C4C2×#432311yescharacteristic
514C2×C4C2×#432311yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8#6703711yescharacteristic
520C8#6703711yescharacteristic
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—44no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22#1062280712yes—
537C22C22×#432311yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—881no—
545C4—881no—
546C4—881no—
547C4#1062333511yescharacteristic
548C4#1062335311yescharacteristic
549C2—22no—
550C2—41no—
551C2—41no—
552C2—161no—
553C2—1761no—
554C2#1307936411yescharacteristic
555C2C2×#1062280711yescharacteristic
556C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3050C2
socleC22×C11C22×D8
hypercenter#3050D11
hypocenterC11#33757
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #13078197C2semidirect
2. #13070824C2semidirect
3. #13070821C2semidirect
4. #13070807C2semidirect
5. #13070804C2semidirect
6. #13070714C2semidirect
7. #13070710C2semidirect
8. #13070705C2semidirect
9. #13070700C2semidirect
10. #13070556C2semidirect
11. #13070554C2semidirect
12. #13070539C2semidirect
13. #13070537C2semidirect
14. C2×C22⋊(C11⋊C16)C2semidirect
15. C11×#3050C2semidirect
29. C2×#66893C22semidirect
30. C2×#66892C22semidirect
31. C2×#66891C22semidirect
32. C2×#66890C22semidirect
43. #10622202C22semidirect
44. #10622202C22semidirect
45. #10622200C22semidirect
46. #10622200C22semidirect
51. #10622130C22semidirect
52. #10622130C22semidirect
53. #10622129C22semidirect
54. #10622129C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
196. #3050D11semidirect
472. C11#33757semidirect

Maximal subgroups

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

subgroupindex
#130781972
#130708242
#130708212
#130708072
#130708042
#130707142
#130707102
#130707052
#130707002
#130705562
#130705542
#130705392
#130705372
C2×C22⋊(C11⋊C16)2
C11×#30502
#3375711