Finite Group Databasebeta

← #15618114

Subgroups — #15618114

Order 2816.

2604 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083387C211yesmaximal, characteristic
2#13083329C211yesmaximal, characteristic, complemented
3#13083328C211yesmaximal, characteristic, complemented
4#13077529C216yesmaximal, complemented
5#13077522C216yesmaximal, complemented
6#13077515C216yesmaximal, complemented
7C2×#10622436C216yesmaximal, complemented
8#13077225C211yesmaximal, characteristic, complemented
9#13077164C211yesmaximal, characteristic, complemented
10#13077044C211yesmaximal, characteristic, complemented
11C11×#2901C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13#10623453C2211yescharacteristic
14C11×#568C2211yescharacteristic
15C4×C11×#41C2211yescharacteristic
16#10623369C414yescomplemented
17#10623368C414yescomplemented
18#10623367C414yescomplemented
19#10623366C414yescomplemented
20#10623353C2216yes—
21C2×#67003C2216yes—
22#10623350—24no—
23#10623350C2211yescharacteristic
24#10623350C2216yescomplemented
25C2×#67001—24no—
26C2×#67001C2211yescharacteristic
27C2×#67001C2211yescharacteristic
28C2×#67001C2216yescomplemented
29#10623281—24no—
30D11×#131—24no—
31#10623276C2216yescomplemented
32C2×#66960C2216yescomplemented
33C11×#421C2216yescomplemented
34C2×C11×#104C2216yescomplemented
35#10622737C2216yescomplemented
36C2×#66886C2216yescomplemented
37#10622618C2216yescomplemented
38#10622610C2213yescomplemented
39#10622610C2213yescomplemented
40C2×#66869C2216yescomplemented
41C4×#4318C2213yescomplemented
42C2×#66867C2213yescomplemented
43#10622437C22124yescomplemented
44#10622436C2214yescomplemented
45#10622436C22112yescomplemented
46#10622436C22112yescomplemented
47#10622436C22112yescomplemented
48C11×2−1+4—21no—
49C11×2−1+4C2×C414yes—
50C11×H(5,𝔽2)—23no—
51C11×H(5,𝔽2)C2×C414yes—
52C2×C11×#41—24no—
53C2×C11×#41C2316yes—
54C2×C11×#41C2311yescharacteristic
55#67043C2×C414yes—
56#67042C2×C414yes—
57#41×D11—24no—
58#67040—21no—
59#67037—23no—
60C2×#4339C2316yes—
61C11×#131—24no—
62C2×C11×M16C2316yes—
63C4×Q8×C11—21no—
64C4×D4×C11—23no—
65C11×#117C2313yes—
66C2×C42×C11C2313yes—
67#67004C2×C4112yescomplemented
68#67003C2×C4112yescomplemented
69#67003C2×C4112yescomplemented
70#67003C2314yes—
71#67003C23112yes—
72#67002C2×C4112yescomplemented
73#67001—24no—
74#67001—212no—
75#67001—26no—
76#67001—26no—
77#67001C2×C414yes—
78#67001C2×C414yes—
79#67001D414yes—
80#67001D414yes—
81#67001C2314yes—
82#67001C23112yes—
83C2×#4326C2×C416yescomplemented
84#66995C2×C4112yescomplemented
85C2×#4325C2×C416yescomplemented
86C2×#4324C2×C416yescomplemented
87#66985C2×C4112yescomplemented
88C2×#4323C2×C416yescomplemented
89C2×#4318—212no—
90C2×#4318—26no—
91C2×#4318C2316yes—
92C2×#4318C2313yes—
93C2×#4318C2313yes—
94C22×C11⋊C8—26no—
95C22×C11⋊C8C2313yes—
96C22×C11⋊C8C2313yes—
97#66960—26no—
98#66960—26no—
99#66960C2314yes—
100#66960C23112yes—
101M16×D11—212no—
102#66954—212no—
103C2×#4313—26no—
104C2×C8×D11—26no—
105C11×#104C2314yes—
106C11×#104C23112yes—
107#66886C2314yes—
108#66886C23112yes—
109#66869C2314yes—
110#66869C23112yes—
111#66867C2311yescharacteristic
112#66867C2313yes—
113#66867C2313yes—
114#66867C2313yes—
115C4×C11⋊C8C2316yes—
116#60184—111nomaximal, Sylow
117C11×#41—24no—
118C11×#41—212no—
119C11×#41—26no—
120C11×#41—26no—
121C11×#41C22×C4112yes—
122C11×#41C22×C414yes—
123C11×#41C2×D414yes—
124C11×#41C2414yes—
125C2×Q8×C11—24no—
126C2×Q8×C11C22×C416yes—
127C2×Q8×C11#4111yescharacteristic
128C2×D4×C11—26no—
129C2×D4×C11—212no—
130C2×D4×C11C22×C416yes—
131C2×D4×C11#4113yes—
132C22×C4×C11—26no—
133C22×C4×C11—23no—
134C22×C4×C11C2413yes—
135C2×C22⋊D11—26no—
136#4343—24no—
137Q8×D11—24no—
138#4341—212no—
139D4×D11—212no—
140#4339—26no—
141#4339—26no—
142#4339C22×C4112yes—
143#4339C2414yes—
144C2×D44C22×C416yes—
145C2×C4×D11—26no—
146C2×Dic22C22×C416yes—
147C11×M16—26no—
148C11×M16C2414yes—
149C2×C8×C11—26no—
150C11×C4⋊C4—23no—
151C11×C22⋊C4—23no—
152C42×C11—23no—
153C42×C11C2413yes—
154C42×C11C2411yescharacteristic
155#4326C22×C4112yes—
156#4326C22×C414yes—
157#4325C22×C414yes—
158#4325C22×C4112yes—
159#4324C22×C4112yes—
160#4324C22×C414yes—
161#4323C22×C414yes—
162#4323C22×C4112yes—
163#4318—24no—
164#4318—212no—
165#4318—26no—
166#4318C22×C4112yes—
167#4318C2×D4112yes—
168#4318C2414yes—
169C2×C11⋊C8—24no—
170C2×C11⋊C8—212no—
171C2×C11⋊C8—26no—
172C2×C11⋊C8C22×C416yes—
173C2×C11⋊C8C22×C416yes—
174C2×C11⋊C8C2×D416yes—
175C2×C11⋊C8C2×D416yes—
176C2×C11⋊C8C2413yes—
177C2×C11⋊C8C2411yescharacteristic
178C2×C11⋊C8C2413yes—
179C2×C11⋊C8C2411yescharacteristic
180#4313—24no—
181#4313—212no—
182C8×D11—24no—
183C8×D11—212no—
184#3584—111no—
185#3573—111no—
186#3573—111no—
187#2957—116no—
188#2956—116no—
189#2955—116no—
190C2×#444—116no—
191#2916—111no—
192#2901—111no—
193#2901D1111yescharacteristic, complemented
194#2875—111no—
195C23×C11—26no—
196C23×C11C2×#4113yes—
197C22×D11—26no—
198Q8×C11—26no—
199Q8×C11C4×D414yes—
200Q8×C11C23×C414yes—
201D4×C11—212no—
202D4×C11—24no—
203D4×C11—26no—
204D4×C11C4×D4112yes—
205D4×C11C23×C414yes—
206C2×C4×C11—26no—
207C2×C4×C11—212no—
208C2×C4×C11—24no—
209C2×C4×C11—21no—
210C2×C4×C11—23no—
211C2×C4×C11—83no—
212C2×C4×C11C23×C416yes—
213C2×C4×C11C22×D416yes—
214C2×C4×C11C2×#4113yes—
215C2×C4×C11C2511yescharacteristic
216C22⋊D11—212no—
217C22⋊D11—24no—
218C2×Dic11—26no—
219D44—26no—
220D44C23×C414yes—
221C4×D11—212no—
222C4×D11—24no—
223Dic22—26no—
224Dic22C23×C414yes—
225C8×C11—24no—
226C11⋊C8—24no—
227C11⋊C8C23×C411yescharacteristic
228C11⋊C8C23×C411yescharacteristic
229C11⋊C8C23×C416yes—
230C11⋊C8C22×D411yescharacteristic
231C11⋊C8C22×D416yes—
232C11⋊C8C22×D411yescharacteristic
233#585—111no—
234#585C2×D1111yescharacteristic
235#578—114no—
236#577—114no—
237#577—114no—
238#576—114no—
239#575—116no—
240C2×#135—116no—
241#568—111no—
242#568—116no—
243#568—116no—
244#568—224no—
245#568—224no—
246#568C2×D1111yescharacteristic
247C2×#131—111no—
248C2×#131—111no—
249C2×#131—116no—
250C2×#131—116no—
251C2×#131—224no—
252C2×#131—224no—
253C4×#41C2×D1111yescharacteristic
254#444—114no—
255#444—1112no—
256#444—1112no—
257#444—1112no—
258#443—1124no—
259#430—116no—
260C2×#108—116no—
261#421—116no—
262#421C2×D1116yescomplemented
263C2×#104—116no—
264C2×#104C2×D1116yescomplemented
265#405—113no—
266#405—113no—
267C4×M16—113no—
268C2×#97—113no—
269C22×C11—24no—
270C22×C11—43no—
271C22×C11—86no—
272C22×C11C2×C4×D416yes—
273C22×C11C22×#4111yescharacteristic
274C2×D11—24no—
275C2×D11—86no—
276C4×C11—24no—
277C4×C11—43no—
278C4×C11—41no—
279C4×C11C2×C4×D416yes—
280C4×C11C24×C411yescharacteristic
281C4×C11C23×D411yescharacteristic
282Dic11—24no—
2832−1+4—21no—
2842−1+4—114no—
2852−1+4—221no—
2862−1+4C4×D1114yes—
287H(5,𝔽2)—23no—
288H(5,𝔽2)—114no—
289H(5,𝔽2)—223no—
290H(5,𝔽2)C4×D1114yes—
291C2×#41—24no—
292C2×#41—116no—
293C2×#41—224no—
294C2×#41C22×D1116yes—
295C2×#41C22×D1111yescharacteristic
296#137—1112no—
297#137—1112no—
298AGL(1,ℤ/8)—1112no—
299AGL(1,ℤ/8)—1112no—
300#135—1112no—
301#135—1112no—
302#135—114no—
303#135—1112no—
304C2×Q16—116no—
305C2×SD16—116no—
306C2×SD16—116no—
307C2×D8—116no—
308#131—24no—
309#131—114no—
310#131—114no—
311#131—114no—
312#131—114no—
313#131—114no—
314#131—1112no—
315#131—114no—
316#131—1112no—
317#131—2212no—
318#131—226no—
319#131—226no—
320#131—226no—
321#131—226no—
322#131—2212no—
323#131—224no—
324C2×M16—113no—
325C2×M16—113no—
326C2×M16—116no—
327C2×M16—226no—
328C2×M16—226no—
329C2×M16—2212no—
330C2×M16—2212no—
331C2×M16C22×D1116yes—
332C22×C8—113no—
333C22×C8—113no—
334C22×C8—226no—
335C22×C8—226no—
336C4×Q8—21no—
337C4×D4—23no—
338#117C22×D1113yes—
339C2×C42C22×D1113yes—
340#108—114no—
341#108—1112no—
342#104—114no—
343#104—1112no—
344#104C22×D1114yes—
345#104C22×D11112yes—
346#97—111no—
347#97—113no—
348#97—113no—
349#97—113no—
350C4×C8—116no—
351C2×C11—21no—
352C2×C11—26no—
353C2×C11—44no—
354C2×C11C22×C4×D411yescharacteristic
355D11—44no—
356#41—24no—
357#41—212no—
358#41—26no—
359#41—26no—
360#41—1112no—
361#41—114no—
362#41—224no—
363#41—2212no—
364#41—226no—
365#41—226no—
366#41C2×C4×D11112yes—
367#41C2×C4×D1114yes—
368#41D4×D1114yes—
369#41C23×D1114yes—
370C2×Q8—24no—
371C2×Q8—116no—
372C2×Q8—224no—
373C2×Q8C2×C4×D1116yes—
374C2×Q8#434111yescharacteristic
375C2×D4—26no—
376C2×D4—212no—
377C2×D4—116no—
378C2×D4—226no—
379C2×D4—2212no—
380C2×D4C2×C4×D1116yes—
381C2×D4#434113yes—
382C22×C4—26no—
383C22×C4—23no—
384C22×C4—226no—
385C22×C4C23×D1113yes—
386Q16—114no—
387Q16—1112no—
388SD16—114no—
389SD16—1112no—
390SD16—114no—
391SD16—1112no—
392D8—114no—
393D8—1112no—
394M16—26no—
395M16—1112no—
396M16—1112no—
397M16—114no—
398M16—224no—
399M16—2212no—
400M16—224no—
401M16—2212no—
402M16—226no—
403M16C23×D1114yes—
404C2×C8—26no—
405C2×C8—116no—
406C2×C8—116no—
407C2×C8—116no—
408C2×C8—116no—
409C2×C8—113no—
410C2×C8—113no—
411C2×C8—111no—
412C2×C8—111no—
413C2×C8—224no—
414C2×C8—2212no—
415C2×C8—224no—
416C2×C8—2212no—
417C2×C8—226no—
418C4⋊C4—23no—
419C22⋊C4—23no—
420C42—23no—
421C42C23×D1113yes—
422C42C23×D1111yescharacteristic
423C11#6018411yescharacteristic, complemented, Sylow
424C23—26no—
425C23—226no—
426C23C2×#434113yes—
427Q8—26no—
428Q8—114no—
429Q8—226no—
430Q8(C22⋊D11)⋊C414yes—
431Q8C22×C4×D1114yes—
432D4—212no—
433D4—24no—
434D4—26no—
435D4—114no—
436D4—2212no—
437D4—224no—
438D4—226no—
439D4(C22⋊D11)⋊C4112yes—
440D4C22×C4×D1114yes—
441C2×C4—26no—
442C2×C4—212no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—23no—
446C2×C4—83no—
447C2×C4—226no—
448C2×C4—2212no—
449C2×C4—224no—
450C2×C4C22×C4×D1116yes—
451C2×C4C2×D4×D1116yes—
452C2×C4C2×#434113yes—
453C2×C4C24×D1111yescharacteristic
454C8—24no—
455C8—111no—
456C8—111no—
457C8—116no—
458C8—111no—
459C8—111no—
460C8—116no—
461C8—224no—
462C22—24no—
463C22—43no—
464C22—86no—
465C22—224no—
466C22—886no—
467C22C2×(C22⋊D11)⋊C416yes—
468C22C22×#434111yescharacteristic
469C4—24no—
470C4—41no—
471C4—43no—
472C4—224no—
473C4C2×(C22⋊D11)⋊C416yes—
474C4C23×C4×D1111yescharacteristic
475C4C22×D4×D1111yescharacteristic
476C2—21no—
477C2—26no—
478C2—44no—
479C2—444no—
480C2C22×(C22⋊D11)⋊C411yescharacteristic
subgroupG/H
centerC4C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2901C2
socleC2×C11C22×C4×D4
prime radical#13083387C2
cosocleC2×C4×C11C25
hypercenter#2901D11
hypocenterC11#60184
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2901

Complements

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

NH ≅ G/Ntype
2. #13083329C2semidirect
3. #13083328C2semidirect
4. #13077529C2semidirect
5. #13077522C2semidirect
6. #13077515C2semidirect
7. C2×#10622436C2semidirect
8. #13077225C2semidirect
9. #13077164C2semidirect
10. #13077044C2semidirect
11. C11×#2901C2semidirect
16. #10623369C4semidirect
17. #10623368C4semidirect
18. #10623367C4semidirect
19. #10623366C4semidirect
24. #10623350C22semidirect
28. C2×#67001C22semidirect
31. #10623276C22semidirect
32. C2×#66960C22semidirect
33. C11×#421C22semidirect
34. C2×C11×#104C22semidirect
35. #10622737C22semidirect
36. C2×#66886C22semidirect
37. #10622618C22semidirect
38. #10622610C22semidirect
39. #10622610C22semidirect
40. C2×#66869C22semidirect
41. C4×#4318C22semidirect
42. C2×#66867C22semidirect
43. #10622437C22semidirect
44. #10622436C22semidirect
45. #10622436C22semidirect
46. #10622436C22semidirect
47. #10622436C22semidirect
67. #67004C2×C4semidirect
68. #67003C2×C4semidirect
69. #67003C2×C4semidirect
72. #67002C2×C4semidirect
83. C2×#4326C2×C4semidirect
84. #66995C2×C4semidirect
85. C2×#4325C2×C4semidirect
86. C2×#4324C2×C4semidirect
87. #66985C2×C4semidirect
88. C2×#4323C2×C4semidirect
193. #2901D11semidirect
262. #421C2×D11semidirect
264. C2×#104C2×D11semidirect
423. C11#60184semidirect

Maximal subgroups

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

subgroupindex
#130833872
#130833292
#130833282
#130775292
#130775222
#130775152
C2×#106224362
#130772252
#130771642
#130770442
C11×#29012
#6018411