Finite Group Databasebeta

← #14909049

Subgroups — #14909049

Order 2816.

512 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079273C211yesmaximal, characteristic, complemented
2#13077516C211yesmaximal, characteristic
3#13070837C211yesmaximal, characteristic, complemented
4#13070834C211yesmaximal, characteristic, complemented
5#13070791C211yesmaximal, characteristic, complemented
6#13070790C211yesmaximal, characteristic, complemented
7#13070696C211yesmaximal, characteristic, complemented
8#13070695C211yesmaximal, characteristic, complemented
9#13070568C211yesmaximal, characteristic
10#13070565C211yesmaximal, characteristic
11#13070509C211yesmaximal, characteristic, complemented
12#13070507C211yesmaximal, characteristic, complemented
13#13070505C211yesmaximal, characteristic, complemented
14#13070430C211yesmaximal, characteristic, complemented
15C11×#2180C211yesmaximal, characteristic, complemented
16#10623299C2211yescharacteristic
17D11×#131—21no—
18#10623114—21no—
19C11×#510C2211yescharacteristic
20C11×#444C2211yescharacteristic
21C11×#441C2211yescharacteristic, complemented
22#10622809C2211yescharacteristic
23#10622808C2211yescharacteristic
24#10622802C2211yescharacteristic
25#10622794C2211yescharacteristic, complemented
26#10622792C2211yescharacteristic
27#10622758—21no—
28C4×#4326—21no—
29#10622522C2211yescharacteristic
30#10622508C2211yescharacteristic
31#10622506C2211yescharacteristic
32#10622481C2211yescharacteristic
33#10622471C2211yescharacteristic, complemented
34#10622437—21no—
35#10622434—21no—
36#10622426—21no—
37#10622410—21no—
38#10622330C2211yescharacteristic
39#10622329C2211yescharacteristic, complemented
40#10622321C2211yescharacteristic
41C11×#365C2211yescharacteristic, complemented
42C11×#362C2211yescharacteristic, complemented
43C11×#360C2211yescharacteristic
44C11×#347C2211yescharacteristic, complemented
45#10622204C2211yescharacteristic
46#10622203C2211yescharacteristic, complemented
47#10622156C2211yescharacteristic
48#10622155C2211yescharacteristic, complemented
49#10622152C2211yescharacteristic
50#10622152C2211yescharacteristic
51#10622151C2211yescharacteristic, complemented
52#10622149C2211yescharacteristic, complemented
53#10622149C2211yescharacteristic, complemented
54#10622134C2211yescharacteristic, complemented
55#10622132C2211yescharacteristic, complemented
56#10622126C2211yescharacteristic
57#10622125C2211yescharacteristic, complemented
58#10622104C2211yescharacteristic, complemented
59#41×D11—21no—
60C11×#135C2311yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C11×#131—21no—
63C4×Q8×C11—21no—
64#67003—21no—
65#67001—21no—
66#66999—21no—
67#66997—21no—
68C2×#4326—21no—
69#66971—21no—
70#66968—21no—
71#66967—21no—
72#66964—21no—
73#66960—21no—
74#66960—41no—
75M16×D11—21no—
76M16×D11—41no—
77C2×Dic44C2311yescharacteristic
78#66957C2311yescharacteristic
79#66954—21no—
80#66954—41no—
81C2×#4313C2311yescharacteristic
82C2×C8×D11—41no—
83C2×C8×D11D411yescharacteristic
84#66951—41no—
85#66950—21no—
86#66943—21no—
87#66942—41no—
88#66929—41no—
89#66925D411yescharacteristic
90#66923—41no—
91C4×Dic22—21no—
92C11×Q32—21no—
93C11×SD32—21no—
94C11×M32C2311yescharacteristic
95C11×M32C2311yescharacteristic
96C11×#108C2311yescharacteristic
97C11×#106C2311yescharacteristic
98C11×#104—21no—
99C11×#103—21no—
100C11×#97C2311yescharacteristic
101#66901—21no—
102#66899—21no—
103#66893—21no—
104#66893—21no—
105#66892—21no—
106#66891—21no—
107#66889—21no—
108#66886—21no—
109#66883C2311yescharacteristic
110#66881C2311yescharacteristic
111#66880—21no—
112#66879D411yescharacteristic
113C8×Dic11C2311yescharacteristic
114#66876C2311yescharacteristic
115#66876C2311yescharacteristic
116#66874—21no—
117#66871—21no—
118#66869—21no—
119C4×C11⋊C8D411yescharacteristic
120Dic88—21no—
121#66864—21no—
122#33693—111nomaximal, Sylow
123C11×#41—21no—
124C2×Q8×C11—21no—
125#4343—21no—
126Q8×D11—21no—
127#4341—21no—
128#4341—41no—
129D4×D11—21no—
130D4×D11—41no—
131#4339—21no—
132#4339—41no—
133C2×C4×D11—41no—
134C2×C4×D11C2×D411yescharacteristic
135C2×Dic22—21no—
136C11×Q16—21no—
137C11×Q16—21no—
138C11×Q16#4111yescharacteristic
139C11×SD16—21no—
140C11×D8#4111yescharacteristic
141C11×M16—21no—
142C11×M16—41no—
143C2×C8×C11—41no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C42×C11—41no—
149C42×C11C2×D411yescharacteristic
150#4326—21no—
151#4326—41no—
152#4326—41no—
153#4325—21no—
154#4324—21no—
155#4323—21no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162Dic11⋊C4—21no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11C2×D411yescharacteristic
170#4318—21no—
171#4318—41no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44—21no—
177Dic44#4111yescharacteristic
178D88#4111yescharacteristic
179#4314—21no—
180#4313—21no—
181#4313—21no—
182#4313—41no—
183#4313—41no—
184#4313—41no—
185C8×D11—21no—
186C8×D11—21no—
187C8×D11—41no—
188C8×D11—41no—
189C8×D11—41no—
190C11×C16—21no—
191C11×C16—21no—
192C11⋊C16—21no—
193C11⋊C16—21no—
194#3177—111no—
195#2955—111no—
196#2239—111no—
197#2239—111no—
198#2231—111no—
199#2231—111no—
200#2214—111no—
201#2214—111no—
202#2191—111no—
203#2191—111no—
204#2180—111no—
205#2180—111no—
206#2180—111no—
207#2180D1111yescharacteristic, complemented
208#2166—111no—
209C22×D11—41no—
210C22×D11AGL(1,ℤ/8)11yescharacteristic
211Q8×C11—21no—
212Q8×C11—41no—
213Q8×C11—41no—
214D4×C11—21no—
215D4×C11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—41no—
222C22⋊D11—41no—
223C22⋊D11—41no—
224C2×Dic11—21no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11AGL(1,ℤ/8)11yescharacteristic
229D44—21no—
230D44—41no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—41no—
234C4×D11—41no—
235C4×D11—41no—
236Dic22—21no—
237Dic22—41no—
238Dic22—41no—
239Dic22—41no—
240C8×C11—21no—
241C8×C11—41no—
242C8×C11C2×#4111yescharacteristic
243C8×C11C2×#4111yescharacteristic
244C11⋊C8—21no—
245C11⋊C8—41no—
246C11⋊C8AGL(1,ℤ/8)11yescharacteristic
247C11⋊C8AGL(1,ℤ/8)11yescharacteristic
248#575—111no—
249C2×#131—221no—
250#541—221no—
251#510—111no—
252#510—111no—
253#510—111no—
254#510C2×D1111yescharacteristic
255#499—111no—
256#494—111no—
257#491—221no—
258#470—111no—
259#470—111no—
260#467—221no—
261#444—111no—
262#444—221no—
263#444C2×D1111yescharacteristic
264#443—111no—
265#443—111no—
266#443—221no—
267#441—111no—
268#441C2×D1111yescharacteristic, complemented
269C4×Q16—221no—
270#430—111no—
271#421—221no—
272#405—111no—
273#365—111no—
274#365—111no—
275#365—111no—
276#365C2×D1111yescharacteristic, complemented
277#364—111no—
278#364—111no—
279#362—111no—
280#362—111no—
281#362—111no—
282#362C2×D1111yescharacteristic, complemented
283#360—111no—
284#360—111no—
285#360—111no—
286#360C2×D1111yescharacteristic
287#349—111no—
288#349—111no—
289#347—111no—
290#347C2×D1111yescharacteristic, complemented
291C22×C11—41no—
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C2×D11—21no—
294C2×D11—41no—
295C2×D11—41no—
296C2×D11—82no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11#52511yescharacteristic
302C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
303Dic11—21no—
304Dic11—41no—
305Dic11—41no—
306Dic11—81no—
307Dic11—81no—
308C2×#41—221no—
309#137—221no—
310#137—221no—
311AGL(1,ℤ/8)—221no—
312AGL(1,ℤ/8)—221no—
313#135—111no—
314#135—221no—
315#135C22×D1111yescharacteristic
316C2×Q16—111no—
317C2×Q16—221no—
318C2×Q16C22×D1111yescharacteristic
319#131—21no—
320#131—221no—
321#131—221no—
322#131—221no—
323#131—441no—
324#131—441no—
325C2×M16—111no—
326C2×M16—221no—
327C2×M16—441no—
328C22×C8—111no—
329C22×C8—441no—
330C4⋊Q8—221no—
331#126—441no—
332#126—441no—
333#125—221no—
334#125—441no—
335#125—441no—
336C22⋊Q8—221no—
337C22⋊Q8—221no—
338C4×Q8—21no—
339C4×Q8—221no—
340#117—111no—
341Q32—21no—
342Q32—221no—
343Q32—221no—
344Q32—221no—
345SD32—21no—
346SD32—221no—
347SD32—221no—
348SD32—221no—
349M32—111no—
350M32—111no—
351M32C22×D1111yescharacteristic
352M32C22×D1111yescharacteristic
353#108—111no—
354#108—221no—
355#108C22×D1111yescharacteristic
356#107—221no—
357#106—111no—
358#106C22×D1111yescharacteristic
359#104—21no—
360#104—221no—
361#104—221no—
362#104—221no—
363#103—21no—
364#103—221no—
365#103—221no—
366#103—221no—
367#97—111no—
368#97C22×D1111yescharacteristic
369C4×C8—111no—
370C4×C8—111no—
371C2×C11—21no—
372C2×C11—81no—
373C2×C11#310911yescharacteristic
374D11—41no—
375D11—81no—
376#41—21no—
377#41—221no—
378#41—221no—
379#41—221no—
380#41—441no—
381#41—441no—
382C2×Q8—21no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×D4—221no—
386C2×D4—441no—
387C22×C4—111no—
388C22×C4—441no—
389Q16—21no—
390Q16—21no—
391Q16—111no—
392Q16—221no—
393Q16—221no—
394Q16—221no—
395Q16—441no—
396Q16—441no—
397Q16#433911yescharacteristic
398SD16—21no—
399SD16—221no—
400SD16—221no—
401SD16—221no—
402D8—111no—
403D8—221no—
404D8#433911yescharacteristic
405M16—21no—
406M16—41no—
407M16—221no—
408M16—221no—
409M16—221no—
410M16—441no—
411M16—441no—
412M16—441no—
413M16—441no—
414C2×C8—41no—
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—441no—
420C2×C8—441no—
421C2×C8—441no—
422C2×C8—441no—
423C2×C8D4×D1111yescharacteristic
424C2×C8C23×D1111yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C4⋊C4—441no—
435C4⋊C4—441no—
436C22⋊C4—221no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C42—41no—
440C42—111no—
441C42—441no—
442C42D4×D1111yescharacteristic
443C16—21no—
444C16—21no—
445C16—221no—
446C16—221no—
447C11#3369311yescharacteristic, complemented, Sylow
448C23—111no—
449C23—441no—
450Q8—21no—
451Q8—41no—
452Q8—41no—
453Q8—221no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457D4—21no—
458D4—41no—
459D4—221no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—441no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—111no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4C2×D4×D1111yescharacteristic
479C8—21no—
480C8—41no—
481C8—111no—
482C8—111no—
483C8—221no—
484C8—441no—
485C8C2×#433911yescharacteristic
486C8#41×D1111yescharacteristic
487C22—41no—
488C22—221no—
489C22—441no—
490C22—441no—
491C22—882no—
492C22D11×AGL(1,ℤ/8)11yescharacteristic
493C4—41no—
494C4—41no—
495C4—81no—
496C4—81no—
497C4—221no—
498C4—441no—
499C4—441no—
500C4—881no—
501C4—881no—
502C4#1062307811yescharacteristic
503C4D11×AGL(1,ℤ/8)11yescharacteristic
504C2—21no—
505C2—81no—
506C2—441no—
507C2—881no—
508C2#1307870511yescharacteristic
subgroupG/H
centerC2#13078705
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2180C2
socleC2×C11#3109
prime radical#10623299C22
hypercenter#2180D11
hypocenterC11#33693
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

Complements

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

NH ≅ G/Ntype
1. #13079273C2semidirect
3. #13070837C2semidirect
4. #13070834C2semidirect
5. #13070791C2semidirect
6. #13070790C2semidirect
7. #13070696C2semidirect
8. #13070695C2semidirect
11. #13070509C2semidirect
12. #13070507C2semidirect
13. #13070505C2semidirect
14. #13070430C2semidirect
15. C11×#2180C2semidirect
21. C11×#441C22semidirect
25. #10622794C22semidirect
33. #10622471C22semidirect
39. #10622329C22semidirect
41. C11×#365C22semidirect
42. C11×#362C22semidirect
44. C11×#347C22semidirect
46. #10622203C22semidirect
48. #10622155C22semidirect
51. #10622151C22semidirect
52. #10622149C22semidirect
53. #10622149C22semidirect
54. #10622134C22semidirect
55. #10622132C22semidirect
57. #10622125C22semidirect
58. #10622104C22semidirect
207. #2180D11semidirect
268. #441C2×D11semidirect
276. #365C2×D11semidirect
282. #362C2×D11semidirect
290. #347C2×D11semidirect
447. C11#33693semidirect

Maximal subgroups

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

subgroupindex
#130792732
#130775162
#130708372
#130708342
#130707912
#130707902
#130706962
#130706952
#130705682
#130705652
#130705092
#130705072
#130705052
#130704302
C11×#21802
#3369311