Finite Group Databasebeta

← #15618107

Subgroups — #15618107

Order 2816.

2612 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#13083327C211yesmaximal, characteristic, complemented
3#13077531C216yesmaximal, complemented
4#13077523C216yesmaximal, complemented
5#13077517C216yesmaximal, complemented
6C2×#10622757C216yesmaximal, complemented
7#13077225C211yesmaximal, characteristic, complemented
8#13077163C211yesmaximal, characteristic, complemented
9#13077161C211yesmaximal, characteristic, complemented
10#131×Dic11C211yesmaximal, characteristic, complemented
11C11×#3573C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13#10623453C2211yescharacteristic
14C11×#568—24no—
15C11×#568C2211yescharacteristic
16C11×#568C2216yescomplemented
17C2×C11×#131—24no—
18C2×C11×#131C2211yescharacteristic
19C2×C11×#131C2216yescomplemented
20#10623369C414yescomplemented
21#10623368C414yescomplemented
22#10623367C414yescomplemented
23#10623366C414yescomplemented
24#41×Dic11C2211yescharacteristic
25#10623353C2216yes—
26C2×#67003C2216yes—
27#10623350C2211yescharacteristic
28C2×#67001C2211yescharacteristic
29#10623281—24no—
30D11×#131—24no—
31#10623276C2216yescomplemented
32C2×#66954C2216yescomplemented
33#10622849C2216yescomplemented
34C2×#66901C2216yescomplemented
35#10622758C22124yescomplemented
36#10622757C2214yescomplemented
37#10622757C22112yescomplemented
38#10622757C22112yescomplemented
39#10622757C22112yescomplemented
40#10622752C2216yescomplemented
41C2×#66889C2216yescomplemented
42#10622737C2216yescomplemented
43C2×#66886C2216yescomplemented
44#10622735C2213yescomplemented
45M16×Dic11C2213yescomplemented
46#10622714C2213yescomplemented
47C2×C8×Dic11C2213yescomplemented
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—
62C11×#131—212no—
63C11×#131—26no—
64C11×#131—26no—
65C11×#131D414yes—
66C11×#131D414yes—
67C11×#131C2314yes—
68C11×#131C23112yes—
69C2×C11×M16—212no—
70C2×C11×M16—26no—
71C2×C11×M16C2316yes—
72C2×C11×M16C2313yes—
73C22×C8×C11—26no—
74C22×C8×C11C2313yes—
75#67004C2×C4112yescomplemented
76#67003C2×C4112yescomplemented
77#67003C2×C4112yescomplemented
78#67003C2314yes—
79#67003C23112yes—
80#67002C2×C4112yescomplemented
81#67001—24no—
82#67001C2×C414yes—
83#67001C2×C414yes—
84Q8×Dic11—21no—
85C2×#4326C2×C416yescomplemented
86#66995C2×C4112yescomplemented
87C2×#4325C2×C416yescomplemented
88D4×Dic11—23no—
89C2×#4324C2×C416yescomplemented
90#66985C2×C4112yescomplemented
91C2×#4323C2×C416yescomplemented
92#66979C2313yes—
93C2×C4×Dic11C2313yes—
94C2×#4318C2316yes—
95C2×#4318C2313yes—
96C22×C11⋊C8C2313yes—
97#66960—212no—
98M16×D11—212no—
99#66954—26no—
100#66954—26no—
101#66954C2314yes—
102#66954C23112yes—
103C2×#4313—26no—
104C2×C8×D11—26no—
105#66901C2314yes—
106#66901C23112yes—
107#66889C2314yes—
108#66889C23112yes—
109#66886C2314yes—
110#66886C23112yes—
111#66879C2316yes—
112C8×Dic11C2313yes—
113C8×Dic11C2313yes—
114C8×Dic11C2311yescharacteristic
115C8×Dic11C2313yes—
116#60183—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×C11C2413yes—
134C2×C22⋊D11—26no—
135C22×Dic11—23no—
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—212no—
148C11×M16—24no—
149C11×M16—26no—
150C11×M16C2×D4112yes—
151C11×M16C2414yes—
152C2×C8×C11—24no—
153C2×C8×C11—212no—
154C2×C8×C11—26no—
155C2×C8×C11C2×D416yes—
156C2×C8×C11C2×D416yes—
157C2×C8×C11C2411yescharacteristic
158C2×C8×C11C2413yes—
159C22⋊Dic11—23no—
160#4326C22×C4112yes—
161#4326C22×C414yes—
162#4325C22×C414yes—
163#4325C22×C4112yes—
164#4324C22×C4112yes—
165#4324C22×C414yes—
166#4323C22×C414yes—
167#4323C22×C4112yes—
168C4⋊Dic11—23no—
169C4×Dic11—23no—
170C4×Dic11C2411yescharacteristic
171C4×Dic11C2413yes—
172#4318—26no—
173#4318C22×C4112yes—
174#4318C2414yes—
175C2×C11⋊C8—26no—
176C2×C11⋊C8C22×C416yes—
177C2×C11⋊C8C22×C416yes—
178C2×C11⋊C8C2411yescharacteristic
179C2×C11⋊C8C2413yes—
180#4313—24no—
181#4313—212no—
182C8×D11—24no—
183C8×D11—212no—
184#3584—111no—
185#3573—111no—
186#3573D1111yescharacteristic, complemented
187#2957—116no—
188#2956—116no—
189#2955—116no—
190C2×#443—116no—
191#2916—111no—
192#2901—111no—
193#2901—111no—
194C4×#131—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×C11C23×C416yes—
210C2×C4×C11C22×D416yes—
211C2×C4×C11C2×#4113yes—
212C2×C4×C11C2511yescharacteristic
213C22⋊D11—212no—
214C22⋊D11—24no—
215C2×Dic11—26no—
216C2×Dic11—21no—
217C2×Dic11—23no—
218C2×Dic11—46no—
219D44—26no—
220D44C23×C414yes—
221C4×D11—212no—
222C4×D11—24no—
223Dic22—26no—
224Dic22C23×C414yes—
225C8×C11—24no—
226C8×C11C22×D416yes—
227C8×C11C22×D411yescharacteristic
228C8×C11C22×D411yescharacteristic
229C11⋊C8—24no—
230C11⋊C8C23×C411yescharacteristic
231C11⋊C8C23×C411yescharacteristic
232C11⋊C8C23×C416yes—
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—24no—
242#568—111no—
243#568—116no—
244#568—224no—
245#568C2×D1111yescharacteristic
246#568C2×D1116yescomplemented
247C2×#131—24no—
248C2×#131—111no—
249C2×#131—116no—
250C2×#131—224no—
251C2×#131C2×D1111yescharacteristic
252C2×#131C2×D1116yescomplemented
253C4×#41—111no—
254#444—1124no—
255#443—114no—
256#443—1112no—
257#443—1112no—
258#443—1112no—
259#430—116no—
260C2×#108—116no—
261#421—116no—
262#421—116no—
263C2×#104—116no—
264C2×#104—116no—
265#405—113no—
266#405—113no—
267C4×M16—113no—
268C2×C4×C8—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×C11C2×C4×D416yes—
278C4×C11C24×C411yescharacteristic
279C4×C11C23×D411yescharacteristic
280Dic11—22no—
281Dic11—24no—
282Dic11—43no—
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—212no—
310#131—26no—
311#131—26no—
312#131—114no—
313#131—114no—
314#131—114no—
315#131—1112no—
316#131—224no—
317#131—2212no—
318#131—226no—
319#131—226no—
320#131C22⋊D1114yes—
321#131C22⋊D1114yes—
322#131C22×D1114yes—
323#131C22×D11112yes—
324C2×M16—212no—
325C2×M16—26no—
326C2×M16—113no—
327C2×M16—116no—
328C2×M16—2212no—
329C2×M16—226no—
330C2×M16C22×D1116yes—
331C2×M16C22×D1113yes—
332C22×C8—26no—
333C22×C8—113no—
334C22×C8—226no—
335C22×C8C22×D1113yes—
336C4×Q8—221no—
337C4×D4—223no—
338#117—113no—
339C2×C42—113no—
340#108—114no—
341#108—1112no—
342#104—114no—
343#104—1112no—
344#104—114no—
345#104—1112no—
346#97—116no—
347C4×C8—111no—
348C4×C8—113no—
349C4×C8—113no—
350C4×C8—113no—
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#41C2×C22⋊D1114yes—
369#41C23×D1114yes—
370C2×Q8—24no—
371C2×Q8—116no—
372C2×Q8—224no—
373C2×Q8C2×C4×D1116yes—
374C2×Q8#433911yescharacteristic
375C2×D4—26no—
376C2×D4—212no—
377C2×D4—116no—
378C2×D4—226no—
379C2×D4—2212no—
380C2×D4C2×C4×D1116yes—
381C2×D4#433913yes—
382C22×C4—26no—
383C22×C4—226no—
384C22×C4—223no—
385C22×C4C23×D1113yes—
386Q16—114no—
387Q16—1112no—
388SD16—114no—
389SD16—1112no—
390SD16—114no—
391SD16—1112no—
392D8—114no—
393D8—1112no—
394M16—26no—
395M16—212no—
396M16—24no—
397M16—1112no—
398M16—114no—
399M16—226no—
400M16—2212no—
401M16—224no—
402M16C2×C22⋊D11112yes—
403M16C23×D1114yes—
404C2×C8—26no—
405C2×C8—212no—
406C2×C8—24no—
407C2×C8—116no—
408C2×C8—116no—
409C2×C8—111no—
410C2×C8—113no—
411C2×C8—226no—
412C2×C8—2212no—
413C2×C8—224no—
414C2×C8C2×C22⋊D1116yes—
415C2×C8C2×C22⋊D1116yes—
416C2×C8C23×D1113yes—
417C2×C8C23×D1111yescharacteristic
418C4⋊C4—223no—
419C22⋊C4—223no—
420C42—111no—
421C42—113no—
422C42—223no—
423C11#6018311yescharacteristic, complemented, Sylow
424C23—26no—
425C23—226no—
426C23C2×#433913yes—
427Q8—26no—
428Q8—114no—
429Q8—226no—
430Q8C4×C22⋊D1114yes—
431Q8C22×C4×D1114yes—
432D4—212no—
433D4—24no—
434D4—26no—
435D4—114no—
436D4—2212no—
437D4—224no—
438D4—226no—
439D4C4×C22⋊D11112yes—
440D4C22×C4×D1114yes—
441C2×C4—26no—
442C2×C4—212no—
443C2×C4—24no—
444C2×C4—226no—
445C2×C4—221no—
446C2×C4—2212no—
447C2×C4—224no—
448C2×C4—223no—
449C2×C4—446no—
450C2×C4C22×C4×D1116yes—
451C2×C4C2×#433913yes—
452C2×C4C22×C22⋊D1116yes—
453C2×C4C24×D1111yescharacteristic
454C8—24no—
455C8—111no—
456C8—111no—
457C8—116no—
458C8—224no—
459C8C22×C22⋊D1116yes—
460C8C22×C22⋊D1111yescharacteristic
461C8C22×C22⋊D1111yescharacteristic
462C22—24no—
463C22—43no—
464C22—86no—
465C22—224no—
466C22—886no—
467C22C2×C4×C22⋊D1116yes—
468C22C22×#433911yescharacteristic
469C4—24no—
470C4—222no—
471C4—224no—
472C4—443no—
473C4C2×C4×C22⋊D1116yes—
474C4C23×C4×D1111yescharacteristic
475C4C23×C22⋊D1111yescharacteristic
476C2—21no—
477C2—26no—
478C2—44no—
479C2—444no—
480C2C22×C4×C22⋊D1111yescharacteristic
subgroupG/H
centerC8C22×C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#3573C2
socleC2×C11C22×C4×D4
prime radical#13083387C2
cosocleC2×C4×C11C25
hypercenter#3573D11
hypocenterC11#60183
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C2×#131 ◁ #3573

Complements

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

NH ≅ G/Ntype
2. #13083327C2semidirect
3. #13077531C2semidirect
4. #13077523C2semidirect
5. #13077517C2semidirect
6. C2×#10622757C2semidirect
7. #13077225C2semidirect
8. #13077163C2semidirect
9. #13077161C2semidirect
10. #131×Dic11C2semidirect
11. C11×#3573C2semidirect
16. C11×#568C22semidirect
19. C2×C11×#131C22semidirect
20. #10623369C4semidirect
21. #10623368C4semidirect
22. #10623367C4semidirect
23. #10623366C4semidirect
31. #10623276C22semidirect
32. C2×#66954C22semidirect
33. #10622849C22semidirect
34. C2×#66901C22semidirect
35. #10622758C22semidirect
36. #10622757C22semidirect
37. #10622757C22semidirect
38. #10622757C22semidirect
39. #10622757C22semidirect
40. #10622752C22semidirect
41. C2×#66889C22semidirect
42. #10622737C22semidirect
43. C2×#66886C22semidirect
44. #10622735C22semidirect
45. M16×Dic11C22semidirect
46. #10622714C22semidirect
47. C2×C8×Dic11C22semidirect
75. #67004C2×C4semidirect
76. #67003C2×C4semidirect
77. #67003C2×C4semidirect
80. #67002C2×C4semidirect
85. C2×#4326C2×C4semidirect
86. #66995C2×C4semidirect
87. C2×#4325C2×C4semidirect
89. C2×#4324C2×C4semidirect
90. #66985C2×C4semidirect
91. C2×#4323C2×C4semidirect
186. #3573D11semidirect
246. #568C2×D11semidirect
252. C2×#131C2×D11semidirect
423. C11#60183semidirect

Maximal subgroups

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

subgroupindex
#130833872
#130833272
#130775312
#130775232
#130775172
C2×#106227572
#130772252
#130771632
#130771612
#131×Dic112
C11×#35732
#6018311