Finite Group Databasebeta

← #14730915

Subgroups — #14730915

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic, complemented
2C2×#10622698C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic
4#13067694C214yesmaximal, complemented
5#13067688C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3503C211yesmaximal, characteristic, complemented
10Q82×C11C2212yescomplemented
11C11×#557—21no—
12C11×#554—22no—
13C11×#554C2212yescomplemented
14D4×Q8×C11—22no—
15D4×Q8×C11—21no—
16C11×#544—22no—
17C11×#544—21no—
18C11×#533—21no—
19C11×#533C2211yescharacteristic
20C2×C11×C4⋊Q8—21no—
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#67002—21no—
25C22×#4325—22no—
26C2×#66927C2211yescharacteristic
27#10622701—21no—
28#10622698—21no—
29#10622698—22no—
30#10622698C2214yes—
31#10622659—22no—
32#10622640—21no—
33#10622640C2214yes—
34#10622640C2212yes—
35#10622628—21no—
36#10622628C2212yes—
37#10622614—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yescomplemented
42Q8⋊(C11⋊C8)C2214yescomplemented
43Q8⋊(C11⋊C8)C2212yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C2×C11×#41D411yescharacteristic
46C22×Q8×C11—22no—
47C22×Q8×C11D412yes—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8D412yes—
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8C2312yes—
62C11×#125—22no—
63C11×#125—24no—
64C11×#125—22no—
65C11×#125—21no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8D412yes—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×Q8×C11C2312yes—
80C4×D4×C11—24no—
81C4×D4×C11—22no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C11×#117—22no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117D411yescharacteristic
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96#67002—44no—
97C2×#4325—28no—
98C2×#4325—22no—
99C2×#4325—24no—
100C2×#4325—48no—
101C2×#4323—22no—
102C2×#4318—21no—
103C22×C11⋊C8—21no—
104#66927—21no—
105#66927—21no—
106#66927—21no—
107#66927C2312yes—
108C22⋊(C11⋊C8)—21no—
109#66873—22no—
110#66873—22no—
111#66873—24no—
112C4⋊(C11⋊C8)—21no—
113C4⋊(C11⋊C8)C2312yes—
114C4⋊(C11⋊C8)C2312yes—
115C4×C11⋊C8—21no—
116C4×C11⋊C8—21no—
117C4×C11⋊C8C2312yes—
118#18622—111nomaximal, Sylow
119C23×D11—41no—
120C11×#41—22no—
121C11×#41SD1614yescomplemented
122C2×Q8×C11—24no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—44no—
126C2×Q8×C11—84no—
127C2×Q8×C11C2×D412yes—
128C2×Q8×C11C2×D411yescharacteristic
129C2×Q8×C11C2×D414yes—
130C2×D4×C11—21no—
131C2×D4×C11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—44no—
144C2×D44—41no—
145C2×D44—41no—
146C2×D44—41no—
147C2×D44—42no—
148C2×D44—42no—
149C2×D44—82no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D411yescharacteristic
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C42×C11—24no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—22no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2411yescharacteristic
182#4325—416no—
183#4325—44no—
184#4325—84no—
185#4323—44no—
186#4318—42no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191#3503D1111yescharacteristic, complemented
192#3208—111no—
193C2×#492—111no—
194#3038—111no—
195#1623—114no—
196#1622—114no—
197#1548—111no—
198#1493—111no—
199#1476—111no—
200C23×C11—21no—
201C23×C11#12011yescharacteristic
202C22×D11—42no—
203C22×D11—82no—
204C22×D11—82no—
205C22×D11—82no—
206Q8×C11—21no—
207Q8×C11—24no—
208Q8×C11—44no—
209Q8×C11—44no—
210Q8×C11—42no—
211Q8×C11—84no—
212Q8×C11C2×SD1612yescomplemented
213D4×C11—24no—
214D4×C11—21no—
215D4×C11C2×SD1612yescomplemented
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—82no—
228C2×C4×C11—84no—
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11C2×SD1612yes—
233C2×C4×C11#13712yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237D44—44no—
238D44—42no—
239D44—42no—
240D44—44no—
241D44—82no—
242D44—82no—
243D44—82no—
244C11⋊C8—24no—
245C11⋊C8—42no—
246C11⋊C8—42no—
247C2×AGL(1,ℤ/8)—221no—
248C22×SD16—222no—
249Q82C2×D1112yescomplemented
250#557—21no—
251#554—22no—
252#554C2×D1112yescomplemented
253D4×Q8—22no—
254D4×Q8—21no—
255#544—22no—
256#544—21no—
257#533—21no—
258#533C2×D1111yescharacteristic
259C2×C4⋊Q8—21no—
260C2×C4⋊Q8C2×D1111yescharacteristic
261C2×#127—111no—
262#520—21no—
263C4×#41C2×D1111yescharacteristic
264#492—114no—
265#492—222no—
266#492—221no—
267#486—221no—
268#460—114no—
269#460—112no—
270#460—221no—
271#459—112no—
272#459—221no—
273#450—222no—
274#431—111no—
275#423—111no—
276#418—221no—
277C2×C4×C8—111no—
278#333—114no—
279Q8⋊C8—114no—
280Q8⋊C8—112no—
281D4⋊C8—112no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11#44812yes—
288C22×C11C2×#12011yescharacteristic
289C2×D11—82no—
290C2×D11—82no—
291C2×D11—82no—
292C2×D11—164no—
293C4×C11—22no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—41no—
297C4×C11—42no—
298C4×C11—41no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11#44812yes—
302C4×C11#45312yes—
303C4×C11C22×SD1611yescharacteristic
304C4×C11C2×#13711yescharacteristic
305C4×C11#57712yes—
306C2×#41C22⋊D1111yescharacteristic
307C22×Q8—22no—
308C22×Q8C22⋊D1112yes—
309C22×D4—221no—
310C22×D4—221no—
311C22×D4—221no—
312AGL(1,ℤ/8)—444no—
313C2×SD16—228no—
314C2×SD16—222no—
315C2×SD16—224no—
316C2×SD16—448no—
317C2×D8—222no—
318C2×M16—221no—
319C22×C8—221no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—24no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8C22⋊D1112yes—
328C4⋊Q8C22⋊D1111yescharacteristic
329C4⋊Q8C22⋊D1111yescharacteristic
330C4⋊Q8C22×D1112yes—
331#127—112no—
332#127—221no—
333#127—221no—
334#127—221no—
335#125—22no—
336#125—24no—
337#125—22no—
338#125—21no—
339C22⋊Q8—22no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—22no—
343C22⋊Q8—24no—
344C22⋊Q8—21no—
345C22⋊Q8C22⋊D1112yes—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—21no—
350C4×Q8C22⋊D1111yescharacteristic
351C4×Q8C22×D1111yescharacteristic
352C4×Q8C22×D1112yes—
353C4×D4—24no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4C22⋊D1111yescharacteristic
358C4×D4C22×D1111yescharacteristic
359#117—22no—
360#117—21no—
361#117—21no—
362#117C22⋊D1111yescharacteristic
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C42—21no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—112no—
370C4⋊C8—112no—
371C4⋊C8—221no—
372#102—222no—
373#102—222no—
374#102—224no—
375C22⋊C8—221no—
376C4×C8—112no—
377C4×C8—221no—
378C4×C8—221no—
379C2×C11—22no—
380C2×C11—42no—
381C2×C11C2×#44811yescharacteristic
382C2×C11#301011yescharacteristic
383C2×C11C2×#45311yescharacteristic
384D11—162no—
385C24—441no—
386#41—22no—
387#41#432514yescomplemented
388C2×Q8—24no—
389C2×Q8—22no—
390C2×Q8—21no—
391C2×Q8—44no—
392C2×Q8—84no—
393C2×Q8C2×C22⋊D1112yes—
394C2×Q8C2×C22⋊D1111yescharacteristic
395C2×Q8C2×C22⋊D1114yes—
396C2×D4—21no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—444no—
401C2×D4—442no—
402C2×D4—442no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—441no—
406C2×D4—882no—
407C2×D4C2×C22⋊D1111yescharacteristic
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416SD16—4416no—
417SD16—444no—
418SD16—884no—
419D8—444no—
420M16—442no—
421C2×C8—224no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4C2×C22⋊D1112yes—
441C4⋊C4C2×C22⋊D1111yescharacteristic
442C4⋊C4C2×C22⋊D1111yescharacteristic
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C42—24no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—22no—
453C42C2×C22⋊D1111yescharacteristic
454C42C2×C22⋊D1111yescharacteristic
455C42C2×C22⋊D1111yescharacteristic
456C42C23×D1111yescharacteristic
457C11#1862211yescharacteristic, complemented, Sylow
458C23—21no—
459C23—442no—
460C23—882no—
461C23—882no—
462C23—882no—
463C23#6700611yescharacteristic
464Q8—21no—
465Q8—24no—
466Q8—44no—
467Q8—44no—
468Q8—42no—
469Q8—84no—
470Q8C2×#432512yescomplemented
471D4—24no—
472D4—21no—
473D4—444no—
474D4—442no—
475D4—442no—
476D4—444no—
477D4—882no—
478D4—882no—
479D4—882no—
480D4C2×#432512yescomplemented
481C2×C4—21no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—82no—
493C2×C4—84no—
494C2×C4C2×#432512yes—
495C2×C4#6699512yes—
496C2×C4#6700611yescharacteristic
497C2×C4#6700611yescharacteristic
498C2×C4#6700611yescharacteristic
499C2×C4C22×C22⋊D1111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C2×C4C22×C22⋊D1111yescharacteristic
502C8—224no—
503C8—442no—
504C8—442no—
505C22—21no—
506C22—21no—
507C22—22no—
508C22—41no—
509C22—41no—
510C22—882no—
511C22—882no—
512C22—882no—
513C22—1764no—
514C22#1062284012yes—
515C22C2×#6700611yescharacteristic
516C4—22no—
517C4—21no—
518C4—21no—
519C4—41no—
520C4—42no—
521C4—41no—
522C4—44no—
523C4—42no—
524C4#1062284012yes—
525C4#1062285412yes—
526C4C22×#432511yescharacteristic
527C4C2×#6699511yescharacteristic
528C4#1062336812yes—
529C2—22no—
530C2—42no—
531C2—1762no—
532C2C2×#1062284011yescharacteristic
533C2#1307790211yescharacteristic
534C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radical#13078096C2
hypercenter#3503D11
hypocenterC11#18622
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
2. C2×#10622698C2semidirect
4. #13067694C2semidirect
5. #13067688C2semidirect
6. #13067297C2semidirect
7. #13067071C2semidirect
8. #13066998C2semidirect
9. C11×#3503C2semidirect
10. Q82×C11C22semidirect
13. C11×#554C22semidirect
41. #10622184C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
121. C11×#41SD16semidirect
191. #3503D11semidirect
212. Q8×C11C2×SD16semidirect
215. D4×C11C2×SD16semidirect
249. Q82C2×D11semidirect
252. #554C2×D11semidirect
387. #41#4325semidirect
457. C11#18622semidirect
470. Q8C2×#4325semidirect
480. D4C2×#4325semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226982
#130780962
#130676942
#130676882
#130672972
#130670712
#130669982
C11×#35032
#1862211