Finite Group Databasebeta

← #14737781

Subgroups — #14737781

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068161C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068117C212yesmaximal, complemented
7#13068083C212yesmaximal, complemented
8#13067374C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067294C211yesmaximal, characteristic, complemented
11C11×#3077C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66985—21no—
15C22×#4318—21no—
16#10623008C2211yescharacteristic
17C11×#478—22no—
18C11×#476C2212yes—
19C11×#474C2212yes—
20C11×#428—21no—
21C11×#423C2211yescharacteristic
22C11×#418—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622701C2211yescharacteristic, complemented
25#10622698C2211yescharacteristic, complemented
26#10622694C2211yescharacteristic, complemented
27#10622692C2211yescharacteristic, complemented
28#10622661—21no—
29#10622661—21no—
30C4×#4325—21no—
31C4×#4325—21no—
32#10622632C2212yes—
33#10622629—22no—
34#10622628C2212yes—
35#10622625—21no—
36#10622625—21no—
37#10622625C2212yes—
38#10622625C2212yes—
39#10622579—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622123C2212yescomplemented
46#10622120C2212yescomplemented
47#10622117C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C2×C11×M16—21no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D412yes—
63C4×D4×C11C2312yes—
64C11×#117—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4325—21no—
69C2×#4325—21no—
70C2×#4324—22no—
71#66985—44no—
72C2×#4323—22no—
73#66983—21no—
74#66983—21no—
75C2×#4318—21no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—44no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8D411yescharacteristic
81C22×C11⋊C8D411yescharacteristic
82#66928—21no—
83#66927C2311yescharacteristic
84C4×D44—21no—
85C4×D44—21no—
86#66922C2311yescharacteristic
87C11×#107—22no—
88C11×#106—22no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×#102—22no—
92C11×#102—22no—
93#66899—21no—
94#66899—21no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)—22no—
97#66874—22no—
98#66873—22no—
99#66873—21no—
100#66873—21no—
101#66872—21no—
102#66872—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111#19279—111nomaximal, Sylow
112C24×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×C22⋊D11—41no—
128#4339—42no—
129#4339—42no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×C4×D11—41no—
134C2×Dic22—21no—
135C11×M16—42no—
136C2×C8×C11—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4C2×D412yes—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—41no—
148C42×C11—41no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153#4325—42no—
154#4325—42no—
155#4324—44no—
156#4323—44no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161#4318—44no—
162#4318—44no—
163#4318—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—41no—
168C2×C11⋊C8—42no—
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173#3167—111no—
174#3077D1111yescharacteristic, complemented
175#3036—111no—
176C2×#436—111no—
177#1699—112no—
178#1697—112no—
179#1691—112no—
180#1685—112no—
181#1567—111no—
182#1550—111no—
183#1547—111no—
184C23×C11—22no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11#12111yescharacteristic
189C22×D11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—81no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—42no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11#13712yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C22⋊D11—82no—
215C2×Dic11—41no—
216D44—41no—
217D44—41no—
218D44—41no—
219D44—41no—
220D44—81no—
221C4×D11—82no—
222Dic22—41no—
223Dic22—41no—
224C8×C11—42no—
225C11⋊C8—21no—
226C11⋊C8—21no—
227C11⋊C8—21no—
228C11⋊C8—42no—
229C11⋊C8—42no—
230C11⋊C8AGL(1,ℤ/8)12yescomplemented
231C2×AGL(1,ℤ/8)—221no—
232C22×M16—221no—
233#533C2×D1111yescharacteristic
234#532—111no—
235C2×C4×D4C2×D1111yescharacteristic
236#498—111no—
237#492—111no—
238#487—111no—
239#486—111no—
240#478—22no—
241#476C2×D1112yes—
242#474C2×D1112yes—
243#465—221no—
244#465—221no—
245#463—222no—
246#461—112no—
247#459—112no—
248C4×SD16—221no—
249C4×SD16—221no—
250#436—112no—
251#436—112no—
252#436—221no—
253#436—221no—
254#428—21no—
255#423—111no—
256#423C2×D1111yescharacteristic
257C2×C4⋊C8—111no—
258#418—21no—
259#417—221no—
260C2×C22⋊C8—221no—
261C2×C4×C8—111no—
262#335—112no—
263#335—112no—
264#333—112no—
265#332—112no—
266#332—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—84no—
274C22×C11#46812yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#46812yes—
286C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11C2×#13711yescharacteristic
289C4×C11#57511yescharacteristic
290Dic11—81no—
291C2×#41—221no—
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—21no—
294AGL(1,ℤ/8)—444no—
295C2×SD16—221no—
296C2×SD16—221no—
297C2×SD16—222no—
298C2×D8—222no—
299C2×M16—21no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16—221no—
303C2×M16—444no—
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—221no—
307C4⋊Q8—111no—
308C4⋊Q8C22×D1111yescharacteristic
309C4⋊Q8C22×D1111yescharacteristic
310#127—111no—
311#125—21no—
312#124—221no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315#121—221no—
316#121—221no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4C22⋊D1112yes—
324C4×D4C22×D1112yes—
325#117—21no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C42C22×D1111yescharacteristic
329#107—22no—
330#106—22no—
331#106—221no—
332#106—221no—
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22×D1112yes—
339#103—221no—
340#103—221no—
341#103—222no—
342#102—22no—
343#102—22no—
344#102—221no—
345#102—221no—
346#102—222no—
347C22⋊C8—222no—
348C22⋊C8—222no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8—111no—
352C4×C8—111no—
353C2×C11—22no—
354C2×C11—82no—
355C2×C11#303611yescharacteristic
356C2×C11C2×#46811yescharacteristic
357C2×C11#306711yescharacteristic
358D11—161no—
359C24—21no—
360#41—442no—
361#41—442no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—221no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—441no—
372C2×D4C2×C22⋊D1112yes—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—441no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382SD16—442no—
383SD16—442no—
384SD16—444no—
385D8—444no—
386M16—42no—
387M16—444no—
388M16—444no—
389M16—442no—
390C2×C8—22no—
391C2×C8—111no—
392C2×C8—111no—
393C2×C8—111no—
394C2×C8—111no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—441no—
399C2×C8—442no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4C2×C22⋊D1112yes—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—41no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—41no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1927911yescharacteristic, complemented, Sylow
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—441no—
426C23#6699211yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—81no—
430Q8—441no—
431Q8—441no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—441no—
436D4—441no—
437D4—441no—
438D4—441no—
439D4—881no—
440D4—882no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—441no—
452C2×C4—882no—
453C2×C4#6699211yescharacteristic
454C2×C4#6699211yescharacteristic
455C2×C4#6699211yescharacteristic
456C2×C4#6699512yes—
457C2×C4#6700212yes—
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—42no—
462C8—112no—
463C8—221no—
464C8—221no—
465C8—221no—
466C8—442no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—881no—
475C22—881no—
476C22—881no—
477C22#1062266212yes—
478C22C2×#6699211yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—881no—
486C4#1062266212yes—
487C4D11×AGL(1,ℤ/8)11yescharacteristic
488C4#1062330411yescharacteristic
489C4C2×#6699511yescharacteristic
490C4C2×#6700211yescharacteristic
491C2—22no—
492C2—82no—
493C2—1761no—
494C2#1307807711yescharacteristic
495C2C2×#1062266211yescharacteristic
496C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3077C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenter#3077D11
hypocenterC11#19279
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
3. C2×#10622625C2semidirect
4. #13068161C2semidirect
5. #13068151C2semidirect
6. #13068117C2semidirect
7. #13068083C2semidirect
8. #13067374C2semidirect
9. #13067306C2semidirect
10. #13067294C2semidirect
11. C11×#3077C2semidirect
24. #10622701C22semidirect
25. #10622698C22semidirect
26. #10622694C22semidirect
27. #10622692C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
45. #10622123C22semidirect
46. #10622120C22semidirect
47. #10622117C22semidirect
48. #10622117C22semidirect
174. #3077D11semidirect
230. C11⋊C8AGL(1,ℤ/8)semidirect
420. C11#19279semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130780802
C2×#106226252
#130681612
#130681512
#130681172
#130680832
#130673742
#130673062
#130672942
C11×#30772
#1927911