Finite Group Databasebeta

← #14732546

Subgroups — #14732546

Order 2816.

1192 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
1C2×Q8×D44C211yesmaximal, characteristic, complemented
2#13079734C211yesmaximal, characteristic, complemented
3#13078612C211yesmaximal, characteristic
4#13067863C214yesmaximal, complemented
5#13067717C214yesmaximal, complemented
6#13067289C211yesmaximal, characteristic, complemented
7#13067040C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C11×#3037C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×#137—21no—
12C11×#532C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14Q8×D44—22no—
15Q8×D44—22no—
16Q8×D44—22no—
17Q8×D44C2214yes—
18C2×#66950—21no—
19C2×#66950—22no—
20C2×C4×D44—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922—21no—
23C2×#66922C2211yescharacteristic
24C11×#464—22no—
25C11×#462C2212yescomplemented
26C11×#460C2212yescomplemented
27C11×#423C2211yescharacteristic
28C11×#417—21no—
29#10622700C2212yes—
30#10622691C2212yescomplemented
31#10622685C2212yes—
32#10622683C2212yescomplemented
33#10622649—21no—
34#10622646—21no—
35#10622646—22no—
36C4×#4323—22no—
37#10622620—22no—
38#10622538C2211yescharacteristic
39#10622538C2211yescharacteristic
40Q8⋊(C11⋊C8)C2214yescomplemented
41#10622121C2214yes—
42#10622120C2214yescomplemented
43C2×C11×#41—21no—
44C22×Q8×C11D411yescharacteristic
45C2×Q8×D11—24no—
46C2×Q8×D11—24no—
47C2×Q8×D11—44no—
48C2×Q8×D11—44no—
49C22×D44D411yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11—21no—
52C22×Dic22—22no—
53C22×Dic22—21no—
54C11×#137—44no—
55C2×C11×Q16—22no—
56C2×C11×SD16—22no—
57C2×C11×M16—21no—
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#124—21no—
61C11×#121—21no—
62C11×#121—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×#4323—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11D412yes—
80#66950—24no—
81#66950—28no—
82#66950—24no—
83#66950—28no—
84C4×D44—24no—
85C4×D44—24no—
86C4×D44—21no—
87C4×D44—21no—
88C4×D44D412yes—
89C4×D44C2312yes—
90#66922—24no—
91#66922—21no—
92#66922—21no—
93#66922—24no—
94#66922D412yes—
95#66922C2312yes—
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2312yes—
98C11×#103—22no—
99C11×#102—22no—
100#66896—24no—
101#66896—22no—
102C22⋊(C11⋊C8)—21no—
103C22⋊(C11⋊C8)—21no—
104#66873—22no—
105#66871—24no—
106#66871—22no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yes—
111#18776—111nomaximal, Sylow
112C23×D11—21no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—21no—
118C2×Q8×C11D814yescomplemented
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—22no—
132Q8×D11—48no—
133Q8×D11—416no—
134Q8×D11—48no—
135C2×D44—24no—
136C2×D44—21no—
137C2×D44C2×D412yes—
138C2×C4×D11—28no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—48no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×Dic22—28no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—48no—
148C2×Dic22—42no—
149C2×Dic22—42no—
150C11×Q16—44no—
151C11×SD16—44no—
152C11×M16—42no—
153C2×C8×C11—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2411yescharacteristic
168#4323—44no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—22no—
171(C2×D11)⋊C4—22no—
172C4⋊Dic11—28no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11C2×D412yes—
178C4⋊Dic11C2×D414yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×D4×Q8—111no—
182#3226—111no—
183#3100—111no—
184#3037D1111yescharacteristic, complemented
185#1649—114no—
186#1627—114no—
187#1546—111no—
188#1486—111no—
189#1479—111no—
190C23×C11—41no—
191C23×C11#12011yescharacteristic
192C22×D11—24no—
193C22×D11—22no—
194C22×D11—42no—
195C22×D11—42no—
196Q8×C11—22no—
197Q8×C11—24no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11C2×D814yes—
201D4×C11—42no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—42no—
205D4×C11—82no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—82no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C2×D812yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226D44—24no—
227D44—22no—
228D44#13714yescomplemented
229C4×D11—416no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—44no—
233Dic22—416no—
234Dic22—42no—
235Dic22—42no—
236Dic22—44no—
237C8×C11—42no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C23×Q8—221no—
241C2×#137—21no—
242D4×Q8—114no—
243D4×Q8—222no—
244D4×Q8—222no—
245D4×Q8—222no—
246#532C2×D1111yescharacteristic
247C2×C4⋊Q8—111no—
248C2×C4⋊Q8—221no—
249C2×C22⋊Q8—222no—
250C2×C22⋊Q8—221no—
251C2×C4×Q8C2×D1111yescharacteristic
252C2×C4×D4—111no—
253C2×C4×D4—221no—
254#500—112no—
255#486—112no—
256#480—221no—
257#480—222no—
258#474—112no—
259#474—222no—
260#464—22no—
261#462C2×D1112yescomplemented
262#460C2×D1112yescomplemented
263#459—112no—
264#447—221no—
265C4×D8—222no—
266#431—111no—
267#431—111no—
268#423C2×D1111yescharacteristic
269#417—21no—
270#332—114no—
271Q8⋊C8—114no—
272D4⋊C8—114no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11#44712yes—
279C22×C11C2×#12011yescharacteristic
280C2×D11—24no—
281C2×D11—48no—
282C2×D11—42no—
283C2×D11—42no—
284C4×C11—24no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—42no—
289C4×C11—81no—
290C4×C11#44712yes—
291C4×C11C22×D811yescharacteristic
292C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C11C2×#13712yes—
294Dic11—42no—
295Dic11—44no—
296C2×#41—21no—
297C22×Q8—222no—
298C22×Q8—224no—
299C22×Q8—224no—
300C22×Q8—221no—
301C22×Q8—444no—
302C22×Q8—444no—
303C22×Q8C22⋊D1111yescharacteristic
304C22×D4—111no—
305C23×C4—222no—
306C23×C4—221no—
307#137—44no—
308C2×Q16—22no—
309C2×SD16—22no—
310C2×D8—222no—
311C2×M16—21no—
312C4⋊Q8—112no—
313C4⋊Q8—112no—
314C4⋊Q8—224no—
315C4⋊Q8—224no—
316C4⋊Q8—221no—
317C4⋊Q8—221no—
318C4⋊Q8C22×D1111yescharacteristic
319#127C22×D1111yescharacteristic
320#124—21no—
321C22⋊Q8—228no—
322C22⋊Q8—224no—
323C22⋊Q8—228no—
324C22⋊Q8—224no—
325#121—21no—
326#121—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8C22⋊D1112yes—
330C4×Q8C22×D1112yes—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—112no—
334C4×D4—112no—
335C4×D4—224no—
336C4×D4—224no—
337C4×D4—221no—
338C4×D4—221no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C22⋊C4—222no—
346C2×C22⋊C4—221no—
347C2×C42—21no—
348C2×C42C22×D1111yescharacteristic
349#107—222no—
350#107—224no—
351C4⋊C8—21no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354C4⋊C8C22×D1112yes—
355#103—22no—
356#102—22no—
357#102—222no—
358#102—222no—
359#102—224no—
360C22⋊C8—221no—
361C22⋊C8—221no—
362C4×C8—112no—
363C4×C8—221no—
364C2×C11—22no—
365C2×C11—161no—
366C2×C11C2×#44711yescharacteristic
367C2×C11#300411yescharacteristic
368C2×C11#302011yescharacteristic
369D11—44no—
370C24—221no—
371#41—42no—
372#41—42no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—228no—
377C2×Q8—222no—
378C2×Q8—222no—
379C2×Q8—448no—
380C2×Q8—448no—
381C2×Q8—4416no—
382C2×Q8—448no—
383C2×Q8—442no—
384C2×Q8—442no—
385C2×Q8#432314yescomplemented
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—112no—
392C2×D4—224no—
393C2×D4—221no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—228no—
398C22×C4—222no—
399C22×C4—221no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—448no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4D4×D1111yescharacteristic
406C22×C4D4×D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408Q16—44no—
409SD16—44no—
410D8—444no—
411M16—42no—
412C2×C8—22no—
413C2×C8—222no—
414C2×C8—222no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—112no—
421C4⋊C4—114no—
422C4⋊C4—228no—
423C4⋊C4—221no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4C2×C22⋊D1112yes—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—228no—
431C22⋊C4—222no—
432C22⋊C4—222no—
433C42—22no—
434C42—22no—
435C42D4×D1111yescharacteristic
436C42D4×D1111yescharacteristic
437C42C2×C22⋊D1111yescharacteristic
438C42C23×D1111yescharacteristic
439C11#1877611yescharacteristic, complemented, Sylow
440C23—41no—
441C23—224no—
442C23—222no—
443C23—442no—
444C23—442no—
445C23#6699011yescharacteristic
446Q8—22no—
447Q8—24no—
448Q8—41no—
449Q8—41no—
450Q8—4416no—
451Q8—442no—
452Q8—442no—
453Q8—444no—
454Q8C2×#432314yes—
455D4—42no—
456D4—42no—
457D4—41no—
458D4—41no—
459D4—82no—
460D4—114no—
461D4—224no—
462D4—222no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—4416no—
474C2×C4—444no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—444no—
479C2×C4C2×#432312yes—
480C2×C4#6699011yescharacteristic
481C2×C4#6699011yescharacteristic
482C2×C4#6699011yescharacteristic
483C2×C4#6700212yes—
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—42no—
488C8—442no—
489C8—442no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—224no—
496C22—448no—
497C22—442no—
498C22—442no—
499C22#1062264912yes—
500C22C2×#6699011yescharacteristic
501C4—24no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—81no—
507C4—444no—
508C4—442no—
509C4#1062264912yes—
510C4D11×#13712yes—
511C4C22×#432311yescharacteristic
512C4C2×#6700211yescharacteristic
513C2—22no—
514C2—161no—
515C2—444no—
516C2C2×#1062264911yescharacteristic
517C2#1307784811yescharacteristic
518C2#1307797811yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3037C2
socleC22×C11C2×#120
prime radical#13078612C2
hypercenter#3037D11
hypocenterC11#18776
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D44C2semidirect
2. #13079734C2semidirect
4. #13067863C2semidirect
5. #13067717C2semidirect
6. #13067289C2semidirect
7. #13067040C2semidirect
8. #13067011C2semidirect
9. C11×#3037C2semidirect
25. C11×#462C22semidirect
26. C11×#460C22semidirect
30. #10622691C22semidirect
32. #10622683C22semidirect
40. Q8⋊(C11⋊C8)C22semidirect
42. #10622120C22semidirect
118. C2×Q8×C11D8semidirect
184. #3037D11semidirect
228. D44#137semidirect
261. #462C2×D11semidirect
262. #460C2×D11semidirect
385. C2×Q8#4323semidirect
439. C11#18776semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130797342
#130786122
#130678632
#130677172
#130672892
#130670402
#130670112
C11×#30372
#1877611