Finite Group Databasebeta

← #14736552

Subgroups — #14736552

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079075C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic
3C2×#10622620C211yesmaximal, characteristic, complemented
4#13068105C212yesmaximal, complemented
5#13068081C212yesmaximal, complemented
6#13067981C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10#13067289C211yesmaximal, characteristic, complemented
11D4×C11×M16C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66962—21no—
15C2×#66962—21no—
16#10623008C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C11×#436C2212yes—
19C11×#435—22no—
20C8×D4×C11C2212yes—
21C11×#423C2211yescharacteristic
22C11×#407—21no—
23C4×C11×M16C2211yescharacteristic
24#10622830—21no—
25C2×#66896—21no—
26#10622628C2211yescharacteristic
27#10622628C2211yescharacteristic
28C4×#4323—21no—
29C4×#4323—21no—
30#10622620—21no—
31#10622620—21no—
32#10622620C2212yes—
33#10622620C2211yescharacteristic
34#10622620C2211yescharacteristic
35#10622620C2212yes—
36#10622580—21no—
37C2×#66871—21no—
38#10622538C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622328—22no—
41#10622312C2212yescomplemented
42#10622306C2212yescomplemented
43#10622123C2212yescomplemented
44#10622120C2212yescomplemented
45#10622120C2212yescomplemented
46#10622120C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C22×Dic22—21no—
53C2×C11×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—44no—
56C2×C11×M16D411yescharacteristic
57C2×C11×M16D411yescharacteristic
58C22×C8×C11—22no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D411yescharacteristic
62C4×D4×C11D411yescharacteristic
63C4×D4×C11C2311yescharacteristic
64C4×D4×C11C2311yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4323—21no—
69C2×#4323—21no—
70#66983—21no—
71#66983—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C22×C11⋊C8—21no—
75#66962—44no—
76#66962—44no—
77C2×Dic44—22no—
78C2×Dic44—22no—
79C2×#4314—22no—
80C2×#4314—22no—
81#66928—21no—
82#66927C2311yescharacteristic
83C4×D44—21no—
84C4×D44—21no—
85#66922—21no—
86#66922—21no—
87#66922—21no—
88#66922C2312yes—
89#66922C2311yescharacteristic
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×C22⋊C8—22no—
93C11×C22⋊C8—22no—
94C11×#97D412yes—
95C4×C8×C11C2312yes—
96#66896—22no—
97#66896—22no—
98#66896—21no—
99#66896—21no—
100C22⋊(C11⋊C8)—21no—
101#66873—21no—
102#66873—21no—
103#66871—22no—
104#66871—22no—
105#66871—21no—
106#66871—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2311yescharacteristic
111C4×C11⋊C8—21no—
112#19163—111nomaximal, Sylow
113C24×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C2×D4×C11C2×D411yescharacteristic
118C2×D4×C11C2×D411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C2×C22⋊D11—41no—
130C22×Dic11—41no—
131#4339—42no—
132#4339—42no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×C4×D11—41no—
137C2×Dic22—22no—
138C2×Dic22—21no—
139C2×Dic22—41no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C11×M16—22no—
143C11×M16—44no—
144C11×M16—42no—
145C11×M16D814yescomplemented
146C2×C8×C11—22no—
147C2×C8×C11—44no—
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D411yescharacteristic
152C11×C4⋊C4C2×D411yescharacteristic
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161#4323—42no—
162#4323—42no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—21no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—42no—
175Dic44—44no—
176Dic44—44no—
177#4314—44no—
178#4314—44no—
179#3152—111no—
180#3100—111no—
181C2×#474—111no—
182D4×M16D1111yescharacteristic, complemented
183#1689—112no—
184#1685—112no—
185#1669—112no—
186#1665—112no—
187#1565—111no—
188#1547—111no—
189#1546—111no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—81no—
195C23×C11#12111yescharacteristic
196C22×D11—41no—
197D4×C11—21no—
198D4×C11—21no—
199D4×C11—21no—
200D4×C11—42no—
201D4×C11#13712yescomplemented
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11C2×D812yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C22⋊D11—82no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—82no—
226D44—41no—
227D44—41no—
228D44—41no—
229D44—41no—
230D44—81no—
231C4×D11—82no—
232Dic22—42no—
233Dic22—41no—
234Dic22—42no—
235Dic22—41no—
236Dic22—82no—
237C8×C11—22no—
238C8×C11—42no—
239C8×C11C2×D814yes—
240C11⋊C8—41no—
241C11⋊C8—42no—
242C11⋊C8—41no—
243C2×#137—221no—
244C2×#137—221no—
245C22×M16—21no—
246#532—111no—
247C2×C4⋊Q8—111no—
248C2×C4×D4C2×D1111yescharacteristic
249#497—222no—
250#494—112no—
251#492—112no—
252#480—221no—
253#474—111no—
254#474—111no—
255#474—112no—
256#474—112no—
257#474—221no—
258#474—221no—
259#459—111no—
260#459—111no—
261#447—221no—
262C4×D8—221no—
263C4×D8—221no—
264#436C2×D1112yes—
265#435—22no—
266C8×D4C2×D1112yes—
267#431—111no—
268C2×#107—221no—
269#423C2×D1111yescharacteristic
270C2×C4⋊C8—111no—
271C2×#102—221no—
272#407—21no—
273C4×M16C2×D1111yescharacteristic
274#335—112no—
275#334—112no—
276#332—112no—
277#332—112no—
278#332—112no—
279#331—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—84no—
289C22×C11#45912yes—
290C22×C11C2×#12111yescharacteristic
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11#45912yes—
300C4×C11C22×D811yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11C2×#13711yescharacteristic
303C4×C11#57511yescharacteristic
304Dic11—82no—
305Dic11—81no—
306C2×#41—221no—
307C22×Q8—221no—
308C22×D4D4411yescharacteristic
309C23×C4—21no—
310#137—444no—
311#137—444no—
312C2×Q16—222no—
313C2×Q16—222no—
314C2×SD16—222no—
315C2×SD16—222no—
316C2×D8—221no—
317C2×D8—221no—
318C2×M16—21no—
319C2×M16—22no—
320C2×M16—44no—
321C2×M16C22⋊D1111yescharacteristic
322C2×M16C22⋊D1111yescharacteristic
323C22×C8—22no—
324C22×C8—221no—
325C4⋊Q8—112no—
326C4⋊Q8—111no—
327C4⋊Q8—221no—
328C4⋊Q8—221no—
329C4⋊Q8—221no—
330#127—111no—
331#124—221no—
332#121—221no—
333#121—221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—221no—
337C4×D4—221no—
338C4×D4D4411yescharacteristic
339C4×D4D4411yescharacteristic
340C4×D4C22×D1111yescharacteristic
341C4×D4C22×D1111yescharacteristic
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4D4411yescharacteristic
345C2×C22⋊C4—21no—
346C2×C42C22×D1111yescharacteristic
347#107—222no—
348#107—222no—
349#107—221no—
350#107—221no—
351C4⋊C8—21no—
352C4⋊C8—112no—
353C4⋊C8—111no—
354C4⋊C8—111no—
355C4⋊C8—221no—
356C4⋊C8C22×D1112yes—
357#102—222no—
358#102—222no—
359#102—221no—
360#102—221no—
361#102—221no—
362#102—221no—
363C22⋊C8—22no—
364C22⋊C8—22no—
365C22⋊C8—221no—
366#97C22⋊D1112yes—
367C4×C8—221no—
368C4×C8C22×D1112yes—
369C2×C11—22no—
370C2×C11—42no—
371C2×C11—81no—
372C2×C11C2×#45911yescharacteristic
373C2×C11#305611yescharacteristic
374C2×C11#306911yescharacteristic
375D11—161no—
376C24—21no—
377#41—442no—
378#41—442no—
379C2×Q8—221no—
380C2×Q8—222no—
381C2×Q8—441no—
382C2×Q8—442no—
383C2×Q8—442no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—441no—
391C2×D4C2×D4411yescharacteristic
392C2×D4C2×D4411yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4C2×D4411yescharacteristic
403C22×C4#433911yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405Q16—444no—
406Q16—444no—
407SD16—444no—
408SD16—444no—
409D8—442no—
410D8—442no—
411M16—22no—
412M16—42no—
413M16—44no—
414M16#432314yescomplemented
415C2×C8—22no—
416C2×C8—44no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—222no—
420C2×C8—442no—
421C2×C8C2×C22⋊D1112yes—
422C2×C8C2×C22⋊D1112yes—
423C4⋊C4—21no—
424C4⋊C4—222no—
425C4⋊C4—221no—
426C4⋊C4—222no—
427C4⋊C4—221no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4C2×D4411yescharacteristic
431C4⋊C4C2×D4411yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42C2×D4411yescharacteristic
439C42#433911yescharacteristic
440C42C2×C22⋊D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11#1916311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—42no—
446C23—42no—
447C23—81no—
448C23—441no—
449C23#6698311yescharacteristic
450Q8—442no—
451Q8—441no—
452Q8—442no—
453Q8—441no—
454Q8—882no—
455D4—21no—
456D4—21no—
457D4—21no—
458D4—42no—
459D4—441no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—881no—
464D4—882no—
465D4#6696212yescomplemented
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4#6698311yescharacteristic
483C2×C4#6698311yescharacteristic
484C2×C4#6698311yescharacteristic
485C2×C4C2×#432312yes—
486C2×C4#6700212yes—
487C2×C4C22×D4411yescharacteristic
488C2×C4C2×#433911yescharacteristic
489C2×C4C22×C22⋊D1111yescharacteristic
490C8—22no—
491C8—42no—
492C8—441no—
493C8—442no—
494C8—441no—
495C8C2×#432314yes—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—84no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22#1062262812yes—
509C22C2×#6698311yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—881no—
516C4—882no—
517C4#1062262812yes—
518C4C2×#6696211yescharacteristic
519C4#1062327911yescharacteristic
520C4C22×#432311yescharacteristic
521C4C2×#6700211yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—1761no—
526C2C2×#1062262811yescharacteristic
527C2#1307824611yescharacteristic
528C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×#121
prime radical#13078616C2
hypercenterD4×M16D11
hypocenterC11#19163
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
1. #13079075C2semidirect
3. C2×#10622620C2semidirect
4. #13068105C2semidirect
5. #13068081C2semidirect
6. #13067981C2semidirect
7. #13067957C2semidirect
8. #13067368C2semidirect
9. #13067294C2semidirect
10. #13067289C2semidirect
11. D4×C11×M16C2semidirect
41. #10622312C22semidirect
42. #10622306C22semidirect
43. #10622123C22semidirect
44. #10622120C22semidirect
45. #10622120C22semidirect
46. #10622120C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
145. C11×M16D8semidirect
182. D4×M16D11semidirect
201. D4×C11#137semidirect
414. M16#4323semidirect
442. C11#19163semidirect
465. D4#66962semidirect

Maximal subgroups

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

subgroupindex
#130790752
#130786162
C2×#106226202
#130681052
#130680812
#130679812
#130679572
#130673682
#130672942
#130672892
D4×C11×M162
#1916311