Finite Group Databasebeta

← #14730906

Subgroups — #14730906

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic, complemented
2C2×#10622689C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067743C214yesmaximal, complemented
5#13067732C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3498C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)—21no—
11C11×#550—21no—
12C11×#550C2212yes—
13D42×C11—22no—
14D42×C11—22no—
15D42×C11—21no—
16D42×C11C2212yes—
17C11×#535—22no—
18C11×#535—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×#127—21no—
22C2×C11×#127C2211yescharacteristic
23C4×C11×#41C2211yescharacteristic
24C22×#4324—22no—
25C2×#66922C2211yescharacteristic, complemented
26#10622845—21no—
27#10622692—21no—
28#10622689—22no—
29#10622689C2214yescomplemented
30#10622683—21no—
31#10622647—22no—
32#10622634C2212yescomplemented
33#10622633—21no—
34#10622621C2212yescomplemented
35#10622621C2214yescomplemented
36#10622620—21no—
37#10622608—21no—
38#10622538C2211yescharacteristic, complemented
39#10622537C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2211yescharacteristic, complemented
41#10622182C2214yescomplemented
42Q8⋊(C11⋊C8)C2212yescomplemented
43D4⋊(C11⋊C8)C2214yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C11×H(5,𝔽2)—44no—
46C11×H(5,𝔽2)—44no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—24no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11D412yes—
59C22×Dic22—21no—
60C11×C4⋊Q8D411yescharacteristic
61C11×#127—22no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#127—21no—
65C11×#127—21no—
66C11×#127D411yescharacteristic
67C11×#127D412yes—
68C11×#127C2312yes—
69C11×#124—22no—
70C11×#124—21no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—21no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121D412yes—
79C11×#120—24no—
80C11×#120—24no—
81C11×#120—24no—
82C4×Q8×C11D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11D411yescharacteristic
90C4×D4×C11C2311yescharacteristic
91C4×D4×C11C2312yes—
92C11×#117—21no—
93C11×#117D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×#4324—28no—
97C2×#4324—48no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×#4318—21no—
101C22×C11⋊C8—21no—
102#66922—21no—
103#66922—21no—
104#66922—21no—
105#66922C2312yes—
106#66899—22no—
107#66896—22no—
108#66896—24no—
109C22⋊(C11⋊C8)—21no—
110#66872—22no—
111#66872—24no—
112#66871—22no—
113C4⋊(C11⋊C8)—21no—
114C4⋊(C11⋊C8)C2312yes—
115C4⋊(C11⋊C8)C2312yes—
116C4×C11⋊C8—21no—
117C4×C11⋊C8—21no—
118C4×C11⋊C8C2312yes—
119#18621—111nomaximal, Sylow
120C24×C11—24no—
121C24×C11—22no—
122C11×#41—22no—
123C11×#41—48no—
124C11×#41—44no—
125C11×#41—44no—
126C11×#41—42no—
127C11×#41—42no—
128C11×#41SD1614yescomplemented
129C2×Q8×C11—21no—
130C2×Q8×C11C2×D411yescharacteristic
131C2×D4×C11—21no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—48no—
145C2×D4×C11—44no—
146C2×D4×C11—416no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—82no—
152C2×D4×C11—84no—
153C2×D4×C11—84no—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D411yescharacteristic
156C2×D4×C11C2×D414yes—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×Dic11—41no—
166C2×Dic22—22no—
167C2×Dic22—44no—
168C2×Dic22—41no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—22no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189#4324—416no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—41no—
193C4⋊Dic11—41no—
194#4318—42no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199#3498D1111yescharacteristic
200#3227—111no—
201C2×#492—111no—
202#3079—111no—
203#1631—114no—
204#1629—114no—
205#1545—111no—
206#1492—111no—
207#1476—111no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—48no—
212C23×C11—44no—
213C23×C11—82no—
214C23×C11—82no—
215C23×C11—84no—
216C23×C11—84no—
217C23×C11#12011yescharacteristic
218Q8×C11—21no—
219Q8×C11—42no—
220Q8×C11C2×SD1612yescomplemented
221D4×C11—24no—
222D4×C11—21no—
223D4×C11—24no—
224D4×C11—44no—
225D4×C11—48no—
226D4×C11—48no—
227D4×C11—44no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—44no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—42no—
235D4×C11—82no—
236D4×C11—84no—
237D4×C11—84no—
238D4×C11C2×SD1612yescomplemented
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—48no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11AGL(1,ℤ/8)12yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×Dic11—42no—
260C2×Dic11—82no—
261Dic22—44no—
262Dic22—82no—
263C11⋊C8—24no—
264C11⋊C8—42no—
265C11⋊C8—42no—
266C2×H(5,𝔽2)—21no—
267C22×SD16—222no—
268#550—21no—
269#550C2×D1112yes—
270D42—22no—
271D42—22no—
272D42—21no—
273D42C2×D1112yes—
274#535—22no—
275#535—21no—
276#532—21no—
277#532C2×D1111yescharacteristic
278C2×C4⋊Q8—111no—
279C2×#127—21no—
280C2×#127C2×D1111yescharacteristic
281C4×#41C2×D1111yescharacteristic
282#498—221no—
283#492—114no—
284#492—222no—
285#486—221no—
286#481—222no—
287#477—112no—
288#476—112no—
289#476—114no—
290#475—221no—
291#474—221no—
292#431—111no—
293#428—221no—
294#423—111no—
295#417—221no—
296C2×C4×C8—111no—
297#331—114no—
298Q8⋊C8—112no—
299D4⋊C8—112no—
300D4⋊C8—114no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—22no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—44no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—42no—
312C22×C11—164no—
313C22×C11—168no—
314C22×C11#45012yes—
315C22×C11C2×#12011yescharacteristic
316C4×C11—22no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11#45012yes—
323C4×C11#45312yes—
324C4×C11C22×SD1611yescharacteristic
325C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C4×C11#57712yes—
327Dic11—82no—
328H(5,𝔽2)—44no—
329H(5,𝔽2)—44no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—21no—
333C2×#41C22⋊D1111yescharacteristic
334C22×Q8—221no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4C22⋊D1112yes—
343C2×SD16—228no—
344C2×SD16—448no—
345C2×M16—221no—
346C22×C8—221no—
347C4⋊Q8—112no—
348C4⋊Q8—221no—
349C4⋊Q8—221no—
350C4⋊Q8—221no—
351C4⋊Q8C22⋊D1111yescharacteristic
352#127—22no—
353#127—22no—
354#127—22no—
355#127—21no—
356#127—21no—
357#127C22⋊D1111yescharacteristic
358#127C22⋊D1112yes—
359#127C22×D1112yes—
360#124—22no—
361#124—21no—
362#121—22no—
363#121—24no—
364#121—24no—
365#121—21no—
366#121—22no—
367#121—22no—
368#121—22no—
369#121C22⋊D1112yes—
370#120—24no—
371#120—24no—
372#120—24no—
373C4×Q8C22⋊D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4C22⋊D1111yescharacteristic
381C4×D4C22×D1111yescharacteristic
382C4×D4C22×D1112yes—
383#117—21no—
384#117C22⋊D1111yescharacteristic
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C42—21no—
388C2×C42C22×D1111yescharacteristic
389#107—222no—
390#106—222no—
391#106—224no—
392C4⋊C8—112no—
393C4⋊C8—112no—
394C4⋊C8—221no—
395#103—222no—
396#102—222no—
397#102—224no—
398C22⋊C8—221no—
399C4×C8—112no—
400C4×C8—221no—
401C4×C8—221no—
402C2×C11—22no—
403C2×C11—42no—
404C2×C11—82no—
405C2×C11—84no—
406C2×C11C2×#45011yescharacteristic
407C2×C11#300911yescharacteristic
408C2×C11C2×#45311yescharacteristic
409C24—24no—
410C24—22no—
411#41—22no—
412#41—48no—
413#41—44no—
414#41—44no—
415#41—42no—
416#41—42no—
417#41#432414yescomplemented
418C2×Q8—21no—
419C2×Q8—222no—
420C2×Q8—444no—
421C2×Q8—441no—
422C2×Q8C2×C22⋊D1111yescharacteristic
423C2×D4—21no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—48no—
437C2×D4—44no—
438C2×D4—416no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—82no—
444C2×D4—84no—
445C2×D4—84no—
446C2×D4C2×C22⋊D1112yes—
447C2×D4C2×C22⋊D1111yescharacteristic
448C2×D4C2×C22⋊D1114yes—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—441no—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458SD16—4416no—
459M16—442no—
460C2×C8—224no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C4⋊C4C2×C22⋊D1112yes—
473C4⋊C4C2×C22⋊D1111yescharacteristic
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42C2×C22⋊D1111yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C2×C22⋊D1111yescharacteristic
487C42C23×D1111yescharacteristic
488C11#1862111yescharacteristic, complemented, Sylow
489C23—21no—
490C23—22no—
491C23—24no—
492C23—48no—
493C23—44no—
494C23—82no—
495C23—82no—
496C23—84no—
497C23—84no—
498C23#6700611yescharacteristic
499Q8—21no—
500Q8—42no—
501Q8—444no—
502Q8—882no—
503Q8C2×#432412yescomplemented
504D4—24no—
505D4—21no—
506D4—24no—
507D4—44no—
508D4—48no—
509D4—48no—
510D4—44no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—44no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—82no—
519D4—84no—
520D4—84no—
521D4C2×#432412yescomplemented
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—48no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—442no—
535C2×C4—882no—
536C2×C4#6698512yes—
537C2×C4C2×#432412yes—
538C2×C4#6700611yescharacteristic
539C2×C4#6700611yescharacteristic
540C2×C4#6700611yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—224no—
545C8—442no—
546C8—442no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—41no—
551C22—41no—
552C22—44no—
553C22—42no—
554C22—42no—
555C22—44no—
556C22—44no—
557C22—42no—
558C22—164no—
559C22—168no—
560C22#1062283112yes—
561C22C2×#6700611yescharacteristic
562C4—22no—
563C4—21no—
564C4—21no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—882no—
569C4#1062283112yes—
570C4#1062285412yes—
571C4C2×#6698511yescharacteristic
572C4C22×#432411yescharacteristic
573C4#1062336712yes—
574C2—22no—
575C2—42no—
576C2—82no—
577C2—84no—
578C2C2×#1062283111yescharacteristic
579C2#1307789311yescharacteristic
580C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3498C2
socleC22×C11C2×#120
hypercenter#3498D11
hypocenterC11#18621
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. C2×#10622689C2semidirect
3. #13078431C2semidirect
4. #13067743C2semidirect
5. #13067732C2semidirect
6. #13067284C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
25. C2×#66922C22semidirect
29. #10622689C22semidirect
32. #10622634C22semidirect
34. #10622621C22semidirect
35. #10622621C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. #10622182C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. D4⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
128. C11×#41SD16semidirect
220. Q8×C11C2×SD16semidirect
238. D4×C11C2×SD16semidirect
417. #41#4324semidirect
488. C11#18621semidirect
503. Q8C2×#4324semidirect
521. D4C2×#4324semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226892
#130784312
#130677432
#130677322
#130672842
#130670672
#130669982
C11×#34982
#1862111