Finite Group Databasebeta

← #14736014

Subgroups — #14736014

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079042C211yesmaximal, characteristic, complemented
2#13078617C211yesmaximal, characteristic, complemented
3#13078612C211yesmaximal, characteristic, complemented
4C2×#10622447C211yesmaximal, characteristic, complemented
5#13067980C212yesmaximal, complemented
6#13067970C212yesmaximal, complemented
7#13067960C212yesmaximal, complemented
8#13067956C212yesmaximal, complemented
9#13067362C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic, complemented
11C11×#1540C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×#67003—21no—
14C2×#67003—21no—
15C22×C8×D11—21no—
16#10623008C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×(C2×D11)⋊C8—21no—
21#10622705C2211yescharacteristic, complemented
22#10622700C2212yes—
23#10622698C2211yescharacteristic, complemented
24#10622689C2211yescharacteristic, complemented
25#10622686C2211yescharacteristic, complemented
26#10622685C2212yes—
27#10622672—21no—
28#10622672—21no—
29#10622649—21no—
30#10622646—21no—
31C4×#4323—22no—
32#10622538C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622459C2212yes—
35#10622456C2212yes—
36#10622447—21no—
37#10622447—21no—
38#10622447C2212yes—
39#10622447C2212yes—
40#10622349—21no—
41#10622345—21no—
42C4×D88—22no—
43C11×#332C2212yescomplemented
44C11×#331C2212yescomplemented
45#10622123C2212yescomplemented
46#10622120C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C2×#4339—21no—
51C22×D44D411yescharacteristic
52C22×C4×D11—21no—
53C22×C8×C11—21no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×#127C2311yescharacteristic
56C11×#124—21no—
57C11×#121—21no—
58C11×#121—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#67003—44no—
63#67003—44no—
64C2×#4326—21no—
65C2×#4326—21no—
66C2×#4325—21no—
67C2×#4325—21no—
68C2×#4324—21no—
69C2×#4324—21no—
70C2×#4323—22no—
71C2×#4323—21no—
72C2×#4323—21no—
73#66983—21no—
74#66983—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79C2×D88—22no—
80C2×C8×D11—22no—
81C2×C8×D11—22no—
82C2×C8×D11—44no—
83#66928—21no—
84#66927C2311yescharacteristic
85C4×D44—21no—
86C4×D44—21no—
87C4×D44—21no—
88C4×D44—21no—
89C4×D44D412yes—
90C4×D44C2312yes—
91#66922C2311yescharacteristic
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2312yes—
94C11×C4⋊C8C2312yes—
95C11×C22⋊C8—21no—
96C4×C8×C11—21no—
97#66896—22no—
98C22⋊(C11⋊C8)—21no—
99#66885—22no—
100#66885—22no—
101(C2×D11)⋊C8—22no—
102(C2×D11)⋊C8—22no—
103#66882—22no—
104#66873—22no—
105#66871—22no—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19101—111nomaximal, Sylow
113C23×D11—21no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—41no—
126C22×Dic11—21no—
127#4339—42no—
128#4339—42no—
129C2×D44—24no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44C2×D412yes—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—41no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×Dic22—21no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—42no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11#4111yescharacteristic
151C42×C11C2411yescharacteristic
152#4326—42no—
153#4326—42no—
154#4325—42no—
155#4325—42no—
156#4324—42no—
157#4324—42no—
158#4323—42no—
159#4323—44no—
160#4323—42no—
161(C2×D11)⋊C4—22no—
162(C2×D11)⋊C4—22no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11C2×D412yes—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8D814yescomplemented
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176D88—44no—
177C8×D11—44no—
178C8×D11—44no—
179#3147—111no—
180#3100—111no—
181#3100—111no—
182C2×C8×D4—111no—
183#1669—112no—
184#1667—112no—
185#1665—112no—
186#1665—112no—
187#1564—111no—
188#1540—111no—
189#1540D1111yescharacteristic, complemented
190C23×C11—41no—
191C23×C11#12111yescharacteristic
192C22×D11—24no—
193C22×D11—22no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199D4×C11—41no—
200D4×C11—42no—
201D4×C11—41no—
202D4×C11—81no—
203D4×C11—82no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—82no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11C2×D812yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C22⋊D11—82no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220D44—24no—
221D44—22no—
222D44—41no—
223D44—42no—
224D44—41no—
225D44—81no—
226D44#13514yescomplemented
227C4×D11—42no—
228C4×D11—42no—
229C4×D11—44no—
230C4×D11—82no—
231Dic22—41no—
232Dic22—41no—
233C8×C11—42no—
234C8×C11—42no—
235C11⋊C8—21no—
236C11⋊C8—21no—
237C11⋊C8—42no—
238C11⋊C8C2×D812yes—
239C11⋊C8C2×D812yes—
240C2×#135—221no—
241C2×#135—221no—
242C23×C8—221no—
243#532—111no—
244#532C2×D1111yescharacteristic
245C2×C4×D4—111no—
246#495—221no—
247#495—221no—
248#494—111no—
249#493—111no—
250#492—111no—
251#492—111no—
252#480—221no—
253#480—221no—
254#474—112no—
255#474—112no—
256#459—112no—
257#459—112no—
258#447—221no—
259#447—221no—
260C4×D8—222no—
261C4×D8—222no—
262C8×D4—112no—
263C8×D4—112no—
264C8×D4—221no—
265C8×D4—221no—
266#431—111no—
267#431C2×D1111yescharacteristic
268C2×C4⋊C8C2×D1111yescharacteristic
269C2×C22⋊C8—221no—
270C2×C4×C8—111no—
271#335—112no—
272#334—112no—
273#332—112no—
274#332C2×D1112yescomplemented
275#331—112no—
276#331C2×D1112yescomplemented
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11#45912yes—
283C22×C11C2×#12111yescharacteristic
284C2×D11—24no—
285C2×D11—48no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—81no—
295C4×C11#45912yes—
296C4×C11C22×D811yescharacteristic
297C4×C11C2×#13512yes—
298C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
299Dic11—42no—
300Dic11—81no—
301C2×#41—21no—
302C2×#41—221no—
303C22×D4—111no—
304C23×C4—221no—
305#135—444no—
306#135—444no—
307C2×Q16—221no—
308C2×Q16—221no—
309C2×SD16—221no—
310C2×SD16—221no—
311C2×SD16—221no—
312C2×SD16—221no—
313C2×D8—222no—
314C2×D8—221no—
315C2×D8—221no—
316C2×D8—222no—
317C22×C8—21no—
318C22×C8—111no—
319C22×C8—111no—
320C22×C8—222no—
321C22×C8—222no—
322C22×C8—444no—
323C4⋊Q8—111no—
324C4⋊Q8C22×D1111yescharacteristic
325#127—111no—
326#127C22×D1111yescharacteristic
327#124—21no—
328#124—221no—
329#121—21no—
330#121—21no—
331#121—221no—
332#121—221no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—112no—
336C4×D4—112no—
337C4×D4—221no—
338C4×D4—221no—
339C4×D4—221no—
340C4×D4—221no—
341C2×C4⋊C4—111no—
342C2×C22⋊C4—221no—
343C2×C42C22×D1111yescharacteristic
344#107—222no—
345#107—222no—
346C4⋊C8—21no—
347C4⋊C8—112no—
348C4⋊C8C22×D1112yes—
349C4⋊C8C22×D1112yes—
350#102—222no—
351#102—222no—
352#102—222no—
353#102—222no—
354C22⋊C8—21no—
355C22⋊C8—222no—
356C22⋊C8—222no—
357C22⋊C8—221no—
358C4×C8—21no—
359C4×C8—111no—
360C4×C8—111no—
361C4×C8—111no—
362C4×C8—111no—
363C4×C8—221no—
364C2×C11—22no—
365C2×C11—161no—
366C2×C11C2×#45911yescharacteristic
367C2×C11#305011yescharacteristic
368C2×C11#306711yescharacteristic
369D11—44no—
370D11—161no—
371C24—221no—
372#41—42no—
373#41—42no—
374#41—442no—
375#41—442no—
376C2×Q8—21no—
377C2×Q8—221no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—41no—
382C2×D4—112no—
383C2×D4—224no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—441no—
389C22×C4—41no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—441no—
396C22×C4#433911yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4D4×D1111yescharacteristic
399Q16—442no—
400Q16—442no—
401SD16—442no—
402SD16—442no—
403SD16—442no—
404SD16—442no—
405D8—444no—
406D8—442no—
407D8—442no—
408D8—444no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—42no—
412C2×C8—114no—
413C2×C8—111no—
414C2×C8—111no—
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—444no—
420C2×C8—444no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—112no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—222no—
430C22⋊C4—222no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C42#433911yescharacteristic
434C42D4×D1111yescharacteristic
435C42D4×D1111yescharacteristic
436C42C23×D1111yescharacteristic
437C11#1910111yescharacteristic, complemented, Sylow
438C23—41no—
439C23—224no—
440C23—222no—
441C23—442no—
442C23—442no—
443C23—441no—
444C23#6693711yescharacteristic
445Q8—41no—
446Q8—41no—
447Q8—441no—
448Q8—441no—
449D4—41no—
450D4—41no—
451D4—42no—
452D4—81no—
453D4—82no—
454D4—114no—
455D4—224no—
456D4—222no—
457D4—441no—
458D4—441no—
459D4—442no—
460D4—881no—
461D4—882no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—82no—
466C2×C4—222no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—444no—
471C2×C4—441no—
472C2×C4—882no—
473C2×C4#6693711yescharacteristic
474C2×C4#6693711yescharacteristic
475C2×C4#6693711yescharacteristic
476C2×C4D8×D1112yes—
477C2×C4#6696712yes—
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×D4×D1111yescharacteristic
481C8—42no—
482C8—42no—
483C8—112no—
484C8—112no—
485C8—221no—
486C8—221no—
487C8—442no—
488C22—21no—
489C22—21no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—224no—
494C22—448no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22#1062239912yes—
501C22C2×#6693711yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—81no—
506C4—442no—
507C4—881no—
508C4#1062239912yes—
509C4C2×D8×D1111yescharacteristic
510C4C2×#6696711yescharacteristic
511C4D11×#13512yes—
512C2—22no—
513C2—161no—
514C2—444no—
515C2—1761no—
516C2C2×#1062239911yescharacteristic
517C2#1307819611yescharacteristic
518C2#1307833511yescharacteristic
subgroupG/H
centerC2×C4#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
hypercenter#1540D11
hypocenterC11#19101
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079042C2semidirect
2. #13078617C2semidirect
3. #13078612C2semidirect
4. C2×#10622447C2semidirect
5. #13067980C2semidirect
6. #13067970C2semidirect
7. #13067960C2semidirect
8. #13067956C2semidirect
9. #13067362C2semidirect
10. #13067266C2semidirect
11. C11×#1540C2semidirect
21. #10622705C22semidirect
23. #10622698C22semidirect
24. #10622689C22semidirect
25. #10622686C22semidirect
43. C11×#332C22semidirect
44. C11×#331C22semidirect
45. #10622123C22semidirect
46. #10622120C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
171. C2×C11⋊C8D8semidirect
189. #1540D11semidirect
226. D44#135semidirect
274. #332C2×D11semidirect
276. #331C2×D11semidirect
437. C11#19101semidirect

Maximal subgroups

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

subgroupindex
#130790422
#130786172
#130786122
C2×#106224472
#130679802
#130679702
#130679602
#130679562
#130673622
#130672662
C11×#15402
#1910111