Finite Group Databasebeta

← #14769672

Subgroups — #14769672

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623366C211yesmaximal, characteristic
2#13077464C212yesmaximal, complemented
3#13077077C211yesmaximal, characteristic, complemented
4#13077075C211yesmaximal, characteristic, complemented
5#13069513C212yesmaximal, complemented
6#13069101C212yesmaximal, complemented
7#13069100C212yesmaximal, complemented
8#13068660C211yesmaximal, characteristic, complemented
9#13068587C211yesmaximal, characteristic, complemented
10#13068419C211yesmaximal, characteristic, complemented
11C11×#1795C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C2×#67042C2211yescharacteristic
14#10623366—24no—
15#10623366—24no—
16C2×#67003C412yescomplemented
17C2×#67003C2211yescharacteristic
18C2×#67002C412yescomplemented
19C2×#67002C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21#10623329C2212yescomplemented
22C2×#66985C412yescomplemented
23C2×#66985C2211yescharacteristic
24C22×#4323C412yescomplemented
25C22×#4323C2211yescharacteristic
26#10623052C2212yescomplemented
27C11×#421C2212yescomplemented
28C11×#418C2212yescomplemented
29C11×#413C2211yescharacteristic
30C11×#410C2211yescharacteristic
31#10622853C2211yescharacteristic
32#10622853C2211yescharacteristic
33#10622853C2212yescomplemented
34C2×#66898—24no—
35#10622752C2212yescomplemented
36#10622744C2212yescomplemented
37#10622735C2212yescomplemented
38#10622619C2212yescomplemented
39#10622611C2212yescomplemented
40#10622398—24no—
41#10622369—24no—
42D11×#99—24no—
43#10622197C2212yescomplemented
44#10622169C2212yescomplemented
45C11×H(5,𝔽2)—24no—
46C11×H(5,𝔽2)—42no—
47C2×C11×#41—21no—
48C2×C11×#41C2×C412yescomplemented
49C2×C11×#41C2311yescharacteristic
50C2×C11×#41C2311yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11C2×C412yescomplemented
54C22×D4×C11C2311yescharacteristic
55#67042—24no—
56#67042—42no—
57C2×#4343—21no—
58C2×D4×D11—22no—
59C2×D4×D11—21no—
60C2×#4339C2×C412yescomplemented
61C2×#4339C2311yescharacteristic
62C22×D44C2×C412yescomplemented
63C22×D44C2311yescharacteristic
64C2×C11×M16C2312yes—
65C11×#117C2312yes—
66C2×C22⋊Dic11—24no—
67#67003—24no—
68#67003—24no—
69#67003—22no—
70#67003—22no—
71#67002—24no—
72#67002—28no—
73#67001—22no—
74#67001—22no—
75C2×#4326C2×C411yescharacteristic, complemented
76C2×#4325C2×C411yescharacteristic, complemented
77C2×#4325C2×C412yescomplemented
78D4×Dic11—24no—
79D4×Dic11—42no—
80C2×#4324C2×C411yescharacteristic, complemented
81C2×#4324C2×C412yescomplemented
82#66985—24no—
83#66985—28no—
84C2×#4323—24no—
85C2×#4323—24no—
86C2×#4323C2×C412yes—
87C2×#4323C2×C412yes—
88C2×#4323C2×C411yescharacteristic, complemented
89C2×#4323C2×C412yescomplemented
90C2×#4323C2×C412yescomplemented
91C2×#4323D414yes—
92C2×#4323D414yes—
93#66979C2312yes—
94#66979C2312yes—
95C2×#4318C2×C412yescomplemented
96C2×#4318C2311yescharacteristic
97C22×C11⋊C8C2×C412yescomplemented
98C22×C11⋊C8C2311yescharacteristic
99#66946—24no—
100C22⋊C4×D11—24no—
101C4×D44—42no—
102C11×#104—42no—
103C11×#102—24no—
104C11×#101—21no—
105C11×#100—21no—
106C11×#99—22no—
107#66898—22no—
108#66898—24no—
109#66898D414yes—
110#66889—42no—
111#66885—24no—
112#66879—22no—
113C8×Dic11—22no—
114#66872—22no—
115#66871—22no—
116#66870—24no—
117#22455—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11—22no—
120C23×D11—21no—
121C23×D11—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—24no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—42no—
128C11×#41—44no—
129C2×Q8×C11C22×C411yescharacteristic
130C2×Q8×C11#4111yescharacteristic
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—42no—
138C2×D4×C11—44no—
139C2×D4×C11—48no—
140C2×D4×C11C22×C411yescharacteristic
141C2×D4×C11C22×C412yes—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×D414yes—
144C2×D4×C11#4111yescharacteristic
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—22no—
150C2×C22⋊D11—21no—
151C22×Dic11—44no—
152#4343—44no—
153D4×D11—48no—
154D4×D11—44no—
155#4339—24no—
156#4339—22no—
157#4339—22no—
158#4339—42no—
159C2×D44—24no—
160C2×D44—22no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44—42no—
164C2×D44C22×C411yescharacteristic
165C2×D44C22×C412yes—
166C2×D44C2×D414yes—
167C2×C4×D11—22no—
168C2×C4×D11—21no—
169C2×C4×D11—44no—
170C2×Dic22C22×C411yescharacteristic
171C11×M16—22no—
172C11×M16—22no—
173C2×C8×C11—22no—
174C11×C4⋊C4—22no—
175C11×C22⋊C4—22no—
176C42×C11—22no—
177C22⋊Dic11—22no—
178C22⋊Dic11—44no—
179C22⋊Dic11C2×D414yes—
180#4326—21no—
181#4326—21no—
182#4325—24no—
183#4325—22no—
184#4324—22no—
185#4324—24no—
186#4323—24no—
187#4323—21no—
188#4323—21no—
189#4323—24no—
190#4323C22⋊C414yes—
191#4323C22⋊C414yes—
192#4323C22⋊C418yes—
193(C2×D11)⋊C4—44no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4×Dic11—22no—
197C4×Dic11—22no—
198#4318—24no—
199#4318—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D412yes—
206C2×C11⋊C8C2×D412yes—
207C2×#576—111no—
208#2948—112no—
209#2883—111no—
210#2883—111no—
211#1976—112no—
212#1904—112no—
213#1904—112no—
214#1812—111no—
215#1795—111no—
216#1795D1111yescharacteristic, complemented
217#1757—111no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—21no—
221C23×C11—44no—
222C23×C11—161no—
223C23×C11—162no—
224C23×C11C4×D412yes—
225C23×C11C22×D411yescharacteristic
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—21no—
229C22×D11—44no—
230C22×D11—161no—
231C22×D11—162no—
232Q8×C11—22no—
233Q8×C11—21no—
234Q8×C11—21no—
235D4×C11—24no—
236D4×C11—21no—
237D4×C11—22no—
238D4×C11—21no—
239D4×C11—22no—
240D4×C11—24no—
241D4×C11—44no—
242D4×C11—44no—
243D4×C11—42no—
244D4×C11C2×C22⋊C414yes—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—44no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)12yes—
256C22⋊D11—44no—
257C22⋊D11—42no—
258C2×Dic11—21no—
259C2×Dic11—24no—
260C2×Dic11—42no—
261C2×Dic11—164no—
262D44—21no—
263D44—22no—
264D44—21no—
265D44—24no—
266D44—44no—
267D44C2×C22⋊C414yes—
268C4×D11—44no—
269C4×D11—42no—
270C4×D11—164no—
271Dic22—21no—
272Dic22—21no—
273C8×C11—42no—
274C11⋊C8—22no—
275C11⋊C8C2×C22⋊C411yescharacteristic
276C11⋊C8C2×C22⋊C411yescharacteristic
277C11⋊C8C2×C22⋊C412yes—
278C2×H(5,𝔽2)—111no—
279C2×H(5,𝔽2)C2×D1111yescharacteristic
280#576—224no—
281#576—224no—
282C2×AGL(1,ℤ/8)—111no—
283C2×AGL(1,ℤ/8)—112no—
284C2×AGL(1,ℤ/8)—111no—
285C2×AGL(1,ℤ/8)—112no—
286C2×#135—111no—
287C2×#135—112no—
288C22×D8—111no—
289C22×D8—112no—
290C2×#131—111no—
291#518—112no—
292#518—112no—
293#442—224no—
294C4×D8—224no—
295#427—112no—
296#421—112no—
297#421C2×D1112yescomplemented
298#418—112no—
299#418C2×D1112yescomplemented
300#413C2×D1111yescharacteristic
301#410—111no—
302#410—111no—
303#410—112no—
304#410—112no—
305#410C2×D1111yescharacteristic
306C2×#99—224no—
307C2×#99—224no—
308#405—112no—
309#344—112no—
310H(3,ℤ/4)—112no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—41no—
314C22×C11—42no—
315C22×C11—41no—
316C22×C11—82no—
317C22×C11—84no—
318C22×C11—81no—
319C22×C11—164no—
320C22×C11C2×C4×D411yescharacteristic
321C22×C11D4212yes—
322C2×D11—24no—
323C2×D11—41no—
324C2×D11—82no—
325C2×D11—84no—
326C2×D11—81no—
327C2×D11—164no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—82no—
331C4×C11C22×C22⋊C411yescharacteristic
332C4×C11#51811yescharacteristic
333C4×C11#54612yes—
334Dic11—44no—
335Dic11—41no—
336Dic11—82no—
337H(5,𝔽2)—24no—
338H(5,𝔽2)—42no—
339H(5,𝔽2)—224no—
340H(5,𝔽2)—442no—
341C2×#41—21no—
342C2×#41—112no—
343C2×#41—111no—
344C2×#41—221no—
345C2×#41C4×D1112yescomplemented
346C2×#41C22×D1111yescharacteristic
347C2×#41C22×D1111yescharacteristic
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—112no—
351C22×D4—111no—
352C22×D4—222no—
353C22×D4—221no—
354C22×D4C4×D1112yescomplemented
355C22×D4C22×D1111yescharacteristic
356AGL(1,ℤ/8)—228no—
357AGL(1,ℤ/8)—228no—
358AGL(1,ℤ/8)—224no—
359AGL(1,ℤ/8)—224no—
360#135—222no—
361#135—222no—
362#135—224no—
363#135—224no—
364C2×Q16—111no—
365C2×SD16—111no—
366C2×SD16—112no—
367C2×SD16—111no—
368C2×SD16—112no—
369C2×D8—112no—
370C2×D8—112no—
371C2×D8—114no—
372C2×D8—114no—
373C2×D8—111no—
374C2×D8—112no—
375C2×D8—112no—
376C2×D8—224no—
377C2×D8—224no—
378#131—222no—
379#131—222no—
380C2×M16—112no—
381C2×M16—111no—
382C2×M16C22×D1112yes—
383C22×C8—111no—
384C22×C8—112no—
385C4×D4—224no—
386C4×D4—224no—
387C4×D4—442no—
388C4×D4—442no—
389#117—112no—
390#117—112no—
391#117C22×D1112yes—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394#107—222no—
395#106—222no—
396#104—42no—
397#104—442no—
398#102—24no—
399#102—224no—
400#101—21no—
401#100—21no—
402#99—22no—
403#99—114no—
404#99—224no—
405#99—224no—
406#99—222no—
407#97—222no—
408C4×C8—222no—
409C2×C11—22no—
410C2×C11—21no—
411C2×C11—42no—
412C2×C11—44no—
413C2×C11—81no—
414C2×C11D4×C22⋊C411yescharacteristic
415D11—44no—
416D11—81no—
417C24—21no—
418C24—22no—
419C24—221no—
420C24—222no—
421#41—22no—
422#41—22no—
423#41—24no—
424#41—22no—
425#41—22no—
426#41—42no—
427#41—44no—
428#41—224no—
429#41—222no—
430#41—222no—
431#41—442no—
432#41—444no—
433C2×Q8—111no—
434C2×Q8C2×C4×D1111yescharacteristic
435C2×Q8#434111yescharacteristic
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—42no—
443C2×D4—44no—
444C2×D4—48no—
445C2×D4—112no—
446C2×D4—111no—
447C2×D4—114no—
448C2×D4—224no—
449C2×D4—222no—
450C2×D4—221no—
451C2×D4—222no—
452C2×D4—221no—
453C2×D4—222no—
454C2×D4—442no—
455C2×D4—444no—
456C2×D4—448no—
457C2×D4C2×C4×D1111yescharacteristic
458C2×D4C2×C4×D1112yes—
459C2×D4D4×D1112yes—
460C2×D4D4×D1114yes—
461C2×D4#434111yescharacteristic
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4C2×C4×D1112yes—
469C22×C4C23×D1111yescharacteristic
470Q16—221no—
471Q16—221no—
472SD16—222no—
473SD16—222no—
474SD16—224no—
475SD16—224no—
476D8—114no—
477D8—114no—
478D8—118no—
479D8—221no—
480D8—221no—
481D8—224no—
482D8—224no—
483M16—22no—
484M16—22no—
485M16—224no—
486M16—222no—
487C2×C8—22no—
488C2×C8—111no—
489C2×C8—111no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—112no—
493C2×C8—222no—
494C2×C8—222no—
495C4⋊C4—22no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C22⋊C4—22no—
499C22⋊C4—114no—
500C22⋊C4—222no—
501C22⋊C4—444no—
502C22⋊C4—444no—
503C42—22no—
504C42—222no—
505C42—222no—
506C11#2245511yescharacteristic, complemented, Sylow
507C23—22no—
508C23—24no—
509C23—21no—
510C23—44no—
511C23—161no—
512C23—162no—
513C23—222no—
514C23—224no—
515C23—221no—
516C23—444no—
517C23—1761no—
518C23—1762no—
519C23(C22⋊D11)⋊C412yes—
520C23C2×D4×D1111yescharacteristic
521Q8—22no—
522Q8—21no—
523Q8—21no—
524Q8—221no—
525Q8—221no—
526D4—24no—
527D4—21no—
528D4—22no—
529D4—21no—
530D4—24no—
531D4—22no—
532D4—44no—
533D4—44no—
534D4—42no—
535D4—114no—
536D4—221no—
537D4—222no—
538D4—221no—
539D4—224no—
540D4—444no—
541D4—444no—
542D4—442no—
543D4C22⋊C4×D1114yes—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—221no—
551C2×C4—224no—
552C2×C4—444no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—1764no—
556C2×C4—1764no—
557C2×C4(C22⋊D11)⋊C412yes—
558C2×C4C22×C4×D1111yescharacteristic
559C2×C4C2×D4×D1112yes—
560C2×C4C2×#434111yescharacteristic
561C2×C4#6703712yes—
562C8—42no—
563C8—111no—
564C8—111no—
565C8—112no—
566C8—222no—
567C22—22no—
568C22—24no—
569C22—41no—
570C22—42no—
571C22—41no—
572C22—84no—
573C22—82no—
574C22—81no—
575C22—164no—
576C22—224no—
577C22—441no—
578C22—884no—
579C22—882no—
580C22—881no—
581C22—1764no—
582C22C2×(C22⋊D11)⋊C411yescharacteristic
583C22#1062312112yes—
584C4—22no—
585C4—41no—
586C4—82no—
587C4—444no—
588C4—441no—
589C4—882no—
590C4C2×C22⋊C4×D1111yescharacteristic
591C4#1062301711yescharacteristic
592C4#1062312212yes—
593C2—22no—
594C2—21no—
595C2—42no—
596C2—44no—
597C2—81no—
598C2—444no—
599C2—881no—
600C2#1307143211yescharacteristic
subgroupG/H
centerC2#13071432
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1795C2
socleC2×C11D4×C22⋊C4
prime radicalC2×#10623366C2
cosocleC22×C4×C11C24
hypercenter#1795D11
hypocenterC11#22455
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1795

Complements

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

NH ≅ G/Ntype
2. #13077464C2semidirect
3. #13077077C2semidirect
4. #13077075C2semidirect
5. #13069513C2semidirect
6. #13069101C2semidirect
7. #13069100C2semidirect
8. #13068660C2semidirect
9. #13068587C2semidirect
10. #13068419C2semidirect
11. C11×#1795C2semidirect
16. C2×#67003C4semidirect
18. C2×#67002C4semidirect
21. #10623329C22semidirect
22. C2×#66985C4semidirect
24. C22×#4323C4semidirect
26. #10623052C22semidirect
27. C11×#421C22semidirect
28. C11×#418C22semidirect
33. #10622853C22semidirect
35. #10622752C22semidirect
36. #10622744C22semidirect
37. #10622735C22semidirect
38. #10622619C22semidirect
39. #10622611C22semidirect
43. #10622197C22semidirect
44. #10622169C22semidirect
48. C2×C11×#41C2×C4semidirect
53. C22×D4×C11C2×C4semidirect
60. C2×#4339C2×C4semidirect
62. C22×D44C2×C4semidirect
75. C2×#4326C2×C4semidirect
76. C2×#4325C2×C4semidirect
77. C2×#4325C2×C4semidirect
80. C2×#4324C2×C4semidirect
81. C2×#4324C2×C4semidirect
88. C2×#4323C2×C4semidirect
89. C2×#4323C2×C4semidirect
90. C2×#4323C2×C4semidirect
95. C2×#4318C2×C4semidirect
97. C22×C11⋊C8C2×C4semidirect
216. #1795D11semidirect
297. #421C2×D11semidirect
299. #418C2×D11semidirect
345. C2×#41C4×D11semidirect
354. C22×D4C4×D11semidirect
506. C11#22455semidirect

Maximal subgroups

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

subgroupindex
C2×#106233662
#130774642
#130770772
#130770752
#130695132
#130691012
#130691002
#130686602
#130685872
#130684192
C11×#17952
#2245511