Finite Group Databasebeta

← #14910866

Subgroups — #14910866

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081009C211yesmaximal, characteristic, complemented
2#13080303C211yesmaximal, characteristic
3#13070853C211yesmaximal, characteristic, complemented
4#13070819C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070707C211yesmaximal, characteristic, complemented
9#13070679C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070547C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13#13070329C211yesmaximal, characteristic, complemented
14C2×#10622147C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623081—21no—
19#10623074—21no—
20C2×C11×M32C2211yescharacteristic, complemented
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622729C2211yescharacteristic, complemented
26#10622728C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic, complemented
29C2×Dic88C2211yescharacteristic, complemented
30C2×#66864C2211yescharacteristic
31C2×#66864C2211yescharacteristic
32#10622463—21no—
33#10622457—21no—
34#10622347—21no—
35#10622344—21no—
36#10622335—21no—
37#10622335—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#10622142C2211yescharacteristic, complemented
53#10622142C2211yescharacteristic, 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—
65D4×Dic11—41no—
66#66983—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—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#66943—41no—
85#66937—41no—
86C22⋊C4×D11—41no—
87#66931—41no—
88#66931—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#66882—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66880—21no—
113#66880—21no—
114#66880—21no—
115#66880—21no—
116Dic88—41no—
117#66864—22no—
118#66864—41no—
119#33881—111nomaximal, Sylow
120C23×D11—41no—
121C2×D4×C11D811yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128#4339—42no—
129#4339—81no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—42no—
133C2×D44—41no—
134C2×D44—81no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—41no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4D811yescharacteristic
149C11×C22⋊C4D811yescharacteristic
150C11×C22⋊C4D811yescharacteristic
151C42×C11C2×D411yescharacteristic
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—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—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#3338—111no—
187#3280—111no—
188#2243—111no—
189#2236—111no—
190#2232—111no—
191#2224—111no—
192#2220—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197#2175—111no—
198#2168D1111yescharacteristic, complemented
199#2139—111no—
200C2×#357—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—161no—
208D4×C11—22no—
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—
226C2×Dic11—161no—
227C2×Dic11—161no—
228D44—22no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—82no—
233C4×D11—82no—
234C4×D11—161no—
235Dic22—41no—
236Dic22—41no—
237Dic22—41no—
238Dic22—41no—
239Dic22—161no—
240C8×C11—21no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11C2×#4111yescharacteristic
244C8×C11H(5,𝔽2)11yescharacteristic
245C2×#135—111no—
246C22×D8—111no—
247#554—221no—
248#546—221no—
249C2×Q32—111no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×M32C2×D1111yescharacteristic, complemented
253C22×C16C2×D1111yescharacteristic
254#500—111no—
255#495—111no—
256#484—221no—
257#484—221no—
258#477—221no—
259#467—111no—
260#467—111no—
261#467—111no—
262#466—111no—
263#463—221no—
264#450—221no—
265#449—221no—
266C4×Q16—111no—
267C4×D8—111no—
268C8×D4C2×D1111yescharacteristic
269C2×#107—111no—
270C2×#107—111no—
271#366—111no—
272#366—111no—
273#366—111no—
274C4⋊C16C2×D1111yescharacteristic, complemented
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285C22⋊C16C2×D1111yescharacteristic
286C22⋊C16C2×D1111yescharacteristic, complemented
287#346C2×D1111yescharacteristic, complemented
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11#51012yes—
294C22×C11C22×D811yescharacteristic
295C2×D11—42no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—164no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C22×D4—221no—
316#135—222no—
317#135—441no—
318C2×Q16—111no—
319C2×Q16—111no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C2×D8—222no—
325C2×D8—221no—
326C2×D8—441no—
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329C4⋊Q8—221no—
330#125—441no—
331#124—221no—
332#123—441no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—221no—
339#121—441no—
340#120—441no—
341C4×Q8—221no—
342C4×D4—221no—
343C4×D4—441no—
344C4×D4D4411yescharacteristic
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C22⋊C4—441no—
348Q32—441no—
349SD32—222no—
350SD32—441no—
351M32—41no—
352C2×C16—41no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—111no—
360#107—111no—
361#107—221no—
362#107—221no—
363#107—221no—
364C4⋊C8D4411yescharacteristic
365#103—221no—
366#103—221no—
367#103—221no—
368#103—221no—
369#102—221no—
370#102—221no—
371C22⋊C8D4411yescharacteristic
372C22⋊C8D4411yescharacteristic
373C4×C8C22×D1111yescharacteristic
374C2×C11—22no—
375C2×C11—41no—
376C2×C11#329411yescharacteristic
377C2×C11C2×#51011yescharacteristic
378C2×C11#341511yescharacteristic
379D11—82no—
380D11—161no—
381C24—441no—
382#41—442no—
383#41—881no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—441no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—442no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—881no—
394C2×D4D8811yescharacteristic
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4C2×D4411yescharacteristic
400C22×C4C2×D4411yescharacteristic
401Q16—221no—
402Q16—221no—
403Q16—221no—
404Q16—221no—
405SD16—442no—
406SD16—881no—
407D8—112no—
408D8—221no—
409D8—221no—
410D8—221no—
411D8—442no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8C2×D4411yescharacteristic
417C2×C8C2×D4411yescharacteristic
418C2×C8C2×D4411yescharacteristic
419C2×C8C23×D1111yescharacteristic
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4D8811yescharacteristic
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4D8811yescharacteristic
440C22⋊C4D8811yescharacteristic
441C42—441no—
442C42C2×D4411yescharacteristic
443C16—21no—
444C16—21no—
445C16—21no—
446C16—21no—
447C11#3388111yescharacteristic, complemented, Sylow
448C23—441no—
449C23—441no—
450C23—882no—
451C23—882no—
452C23—1761no—
453C23C2×D8811yescharacteristic
454C23C2×D8811yescharacteristic
455Q8—441no—
456Q8—441no—
457Q8—441no—
458Q8—441no—
459Q8—1761no—
460D4—22no—
461D4—222no—
462D4—441no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—1761no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—882no—
479C2×C4—1761no—
480C2×C4—1761no—
481C2×C4—1761no—
482C2×C4C2×D8811yescharacteristic
483C2×C4C2×D8811yescharacteristic
484C2×C4C2×D8811yescharacteristic
485C2×C4C2×D8811yescharacteristic
486C2×C4C22×D4411yescharacteristic
487C8—21no—
488C8—21no—
489C8—21no—
490C8#6703711yescharacteristic
491C8#41×D1111yescharacteristic
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—442no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—1764no—
504C22#1062252212yes—
505C22C22×D8811yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—881no—
511C4—881no—
512C4—881no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062308511yescharacteristic
517C4#1062328211yescharacteristic
518C2—22no—
519C2—41no—
520C2—882no—
521C2—1761no—
522C2#1308043011yescharacteristic
523C2C2×#1062252211yescharacteristic
524C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radical#13080303C2
hypercenter#2168D11
hypocenterC11#33881
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. #13081009C2semidirect
3. #13070853C2semidirect
4. #13070819C2semidirect
5. #13070797C2semidirect
6. #13070754C2semidirect
7. #13070729C2semidirect
8. #13070707C2semidirect
9. #13070679C2semidirect
10. #13070558C2semidirect
11. #13070547C2semidirect
12. #13070482C2semidirect
13. #13070329C2semidirect
14. C2×#10622147C2semidirect
15. C11×#2168C2semidirect
20. C2×C11×M32C22semidirect
25. #10622729C22semidirect
28. C2×#66882C22semidirect
29. C2×Dic88C22semidirect
38. C4×Dic44C22semidirect
41. #10622295C22semidirect
42. C11×C4⋊C16C22semidirect
44. C11×C22⋊C16C22semidirect
45. C11×#346C22semidirect
52. #10622142C22semidirect
53. #10622142C22semidirect
54. #10622142C22semidirect
55. #10622141C22semidirect
56. #10622141C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
198. #2168D11semidirect
252. C2×M32C2×D11semidirect
274. C4⋊C16C2×D11semidirect
286. C22⋊C16C2×D11semidirect
287. #346C2×D11semidirect
447. C11#33881semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130803032
#130708532
#130708192
#130707972
#130707542
#130707292
#130707072
#130706792
#130705582
#130705472
#130704822
#130703292
C2×#106221472
C11×#21682
#3388111