Finite Group Databasebeta

← #14910821

Subgroups — #14910821

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13080303C211yesmaximal, characteristic
3#13070853C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070808C211yesmaximal, characteristic, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070724C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070679C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070547C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13#13070333C211yesmaximal, characteristic, complemented
14#13070324C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623081—21no—
19#10623073—21no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic, complemented
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622729C2211yescharacteristic, complemented
26#10622728C2211yescharacteristic
27#10622719C2211yescharacteristic
28#10622719C2211yescharacteristic, complemented
29C2×Dic88C2211yescharacteristic, complemented
30C2×#66864C2211yescharacteristic
31C2×#66864C2211yescharacteristic
32#10622464—21no—
33#10622457—21no—
34#10622347—21no—
35#10622344—21no—
36#10622336—21no—
37#10622336—21no—
38C4×Dic44C2211yescharacteristic, complemented
39#10622309C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622295C2211yescharacteristic, complemented
42C11×C4⋊C16C2211yescharacteristic, complemented
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic, complemented
45C11×#346C2211yescharacteristic, complemented
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622143C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622142C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59C2×#4339—21no—
60C22×D44—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66990—41no—
65#66989—41no—
66#66983—21no—
67#66979—21no—
68#66979—21no—
69#66977—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74#66957—22no—
75#66957—41no—
76C2×D88—22no—
77C2×D88—21no—
78C2×D88—41no—
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66947—41no—
84#66940—41no—
85#66937—41no—
86C22⋊C4×D11—41no—
87#66932—41no—
88#66932—41no—
89#66928—21no—
90C4×D44—21no—
91#66922—21no—
92C4×Dic22—21no—
93C11×M32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66885—21no—
104#66885—21no—
105#66882—21no—
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66881—21no—
111#66881—21no—
112#66880—21no—
113#66880—21no—
114#66880—21no—
115#66880—21no—
116Dic88—41no—
117#66864—22no—
118#66864—41no—
119#33878—111nomaximal, Sylow
120C23×D11—41no—
121C2×D4×C11D811yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126#4339—42no—
127#4339—81no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—42no—
131C2×D44—41no—
132C2×D44—81no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—41no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4D811yescharacteristic
147C11×C22⋊C4D811yescharacteristic
148C11×C22⋊C4D811yescharacteristic
149C42×C11C2×D411yescharacteristic
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—42no—
179D88#4112yes—
180#4314—42no—
181#4314—81no—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3342—111no—
187#3280—111no—
188#2243—111no—
189#2237—111no—
190#2234—111no—
191#2226—111no—
192#2219—111no—
193#2217—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197#2175—111no—
198#2168D1111yescharacteristic, complemented
199#2140—111no—
200#2138—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—161no—
208D4×C11—41no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—82no—
219C22⋊D11—161no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226D44—22no—
227D44—41no—
228D44—41no—
229D44—41no—
230D44—82no—
231C4×D11—82no—
232C4×D11—161no—
233Dic22—41no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135—111no—
244C22×D8—111no—
245#556—221no—
246#546—221no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C2×M32C2×D1111yescharacteristic
251C22×C16C2×D1111yescharacteristic, complemented
252#500—111no—
253#495—111no—
254#485—221no—
255#485—221no—
256#475—221no—
257#467—111no—
258#467—111no—
259#467—111no—
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4C2×D1111yescharacteristic
267#427—111no—
268#427—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16C2×D1111yescharacteristic, complemented
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16C2×D1111yescharacteristic
284C22⋊C16C2×D1111yescharacteristic, complemented
285#346C2×D1111yescharacteristic, complemented
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11C22×D811yescharacteristic
293C2×D11—42no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—164no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11#54611yescharacteristic
305C4×C11#57711yescharacteristic
306Dic11—81no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—221no—
313C22×D4—221no—
314#135—222no—
315#135—441no—
316C2×Q16—111no—
317C2×Q16—111no—
318C2×SD16—221no—
319C2×SD16—221no—
320C2×D8—111no—
321C2×D8—111no—
322C2×D8—222no—
323C2×D8—221no—
324C2×D8—441no—
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—221no—
328#126—441no—
329#126—441no—
330#124—221no—
331#124—441no—
332#123—441no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—221no—
340C4×Q8—441no—
341C4×D4—221no—
342C4×D4D4411yescharacteristic
343#117—221no—
344#117—221no—
345C2×C22⋊C4—441no—
346Q32—441no—
347SD32—222no—
348SD32—441no—
349M32—41no—
350C2×C16—41no—
351C2×C16C22×D1111yescharacteristic
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355#107—111no—
356#107—111no—
357#107—111no—
358#107—111no—
359#107—221no—
360#106—221no—
361#106—221no—
362C4⋊C8D4411yescharacteristic
363#103—221no—
364#103—221no—
365#103—221no—
366#103—221no—
367#102—221no—
368#102—221no—
369C22⋊C8D4411yescharacteristic
370C22⋊C8D4411yescharacteristic
371C4×C8C22×D1111yescharacteristic
372C2×C11—41no—
373C2×C11—41no—
374C2×C11#329411yescharacteristic
375C2×C11#341411yescharacteristic
376C2×C11#341611yescharacteristic
377D11—82no—
378D11—161no—
379C24—441no—
380#41—442no—
381#41—881no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—441no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—442no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—881no—
392C2×D4D8811yescharacteristic
393C22×C4—441no—
394C22×C4—441no—
395C22×C4C2×D4411yescharacteristic
396C22×C4C2×D4411yescharacteristic
397Q16—221no—
398Q16—221no—
399Q16—221no—
400Q16—221no—
401SD16—442no—
402SD16—881no—
403D8—112no—
404D8—221no—
405D8—221no—
406D8—221no—
407D8—442no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8C2×D4411yescharacteristic
413C2×C8C2×D4411yescharacteristic
414C2×C8C2×D4411yescharacteristic
415C2×C8C23×D1111yescharacteristic
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4D8811yescharacteristic
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4D8811yescharacteristic
436C22⋊C4D8811yescharacteristic
437C42—441no—
438C42—441no—
439C42—441no—
440C42C2×D4411yescharacteristic
441C16—21no—
442C16—21no—
443C16—21no—
444C16—21no—
445C11#3387811yescharacteristic, complemented, Sylow
446C23—441no—
447C23—441no—
448C23—882no—
449C23—882no—
450C23—1761no—
451C23C2×D8811yescharacteristic
452C23C2×D8811yescharacteristic
453Q8—441no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457Q8—882no—
458D4—41no—
459D4—222no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—882no—
464D4—882no—
465D4—1761no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4—1761no—
478C2×C4C2×D8811yescharacteristic
479C2×C4C2×D8811yescharacteristic
480C2×C4C2×D8811yescharacteristic
481C2×C4C2×D8811yescharacteristic
482C2×C4C22×D4411yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8#6703711yescharacteristic
487C8#41×D1111yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—442no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—1764no—
501C22C22×D8811yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4—881no—
511C4—881no—
512C4#1062308511yescharacteristic
513C4#1062328211yescharacteristic
514C2—41no—
515C2—41no—
516C2—882no—
517C2—1761no—
518C2#1308043011yescharacteristic
519C2#1308175211yescharacteristic
520C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radical#13080303C2
hypercenter#2168D11
hypocenterC11#33878
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
3. #13070853C2semidirect
4. #13070825C2semidirect
5. #13070808C2semidirect
6. #13070764C2semidirect
7. #13070724C2semidirect
8. #13070712C2semidirect
9. #13070679C2semidirect
10. #13070558C2semidirect
11. #13070547C2semidirect
12. #13070482C2semidirect
13. #13070333C2semidirect
14. #13070324C2semidirect
15. C11×#2168C2semidirect
21. C22×C11×C16C22semidirect
25. #10622729C22semidirect
28. #10622719C22semidirect
29. C2×Dic88C22semidirect
38. C4×Dic44C22semidirect
41. #10622295C22semidirect
42. C11×C4⋊C16C22semidirect
44. C11×C22⋊C16C22semidirect
45. C11×#346C22semidirect
52. #10622143C22semidirect
53. #10622143C22semidirect
54. #10622142C22semidirect
55. #10622141C22semidirect
56. #10622141C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
198. #2168D11semidirect
251. C22×C16C2×D11semidirect
272. C4⋊C16C2×D11semidirect
284. C22⋊C16C2×D11semidirect
285. #346C2×D11semidirect
445. C11#33878semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130803032
#130708532
#130708252
#130708082
#130707642
#130707242
#130707122
#130706792
#130705582
#130705472
#130704822
#130703332
#130703242
C11×#21682
#3387811