Finite Group Databasebeta

← #14737775

Subgroups — #14737775

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#13079171C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068165C212yesmaximal, complemented
5#13068147C212yesmaximal, complemented
6#13068113C212yesmaximal, complemented
7#13068079C212yesmaximal, complemented
8#13067374C211yesmaximal, characteristic, complemented
9#13067307C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3036C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)—21no—
13C11×#532C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4318—21no—
16#10623001C2211yescharacteristic
17C11×#463—22no—
18C11×#461C2212yes—
19C11×#459C2212yes—
20C11×#423C2211yescharacteristic
21C11×#417—21no—
22#10622828—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622706C2211yescharacteristic, complemented
25#10622692C2211yescharacteristic, complemented
26#10622689C2211yescharacteristic, complemented
27#10622683C2211yescharacteristic, complemented
28#10622654—21no—
29#10622654—21no—
30C4×#4324—21no—
31C4×#4324—21no—
32#10622625—21no—
33#10622625—21no—
34#10622625C2212yes—
35#10622625C2212yes—
36#10622622—22no—
37#10622621C2212yes—
38#10622620C2212yes—
39#10622577—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622124C2212yescomplemented
46#10622119C2212yescomplemented
47#10622117C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C11×AGL(1,ℤ/8)—44no—
53C2×C11×SD16—22no—
54C2×C11×D8—22no—
55C2×C11×M16—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D412yes—
66C4×D4×C11C2312yes—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C42×C11C2311yescharacteristic
70C2×#4324—21no—
71C2×#4324—21no—
72#66979—21no—
73#66977—21no—
74#66977—21no—
75C2×#4318—21no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—44no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8D411yescharacteristic
81C22×C11⋊C8D411yescharacteristic
82#66923—21no—
83#66922C2311yescharacteristic
84#66922C2311yescharacteristic
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×#103—22no—
90C11×#102—22no—
91#66896—22no—
92#66896—22no—
93#66896—21no—
94#66896—21no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)—22no—
97#66874—21no—
98#66874—21no—
99#66872—22no—
100#66872—21no—
101#66872—21no—
102#66871—22no—
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—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C2×D4×C11C2×D412yes—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—41no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C2×Dic22—21no—
134C2×Dic22—21no—
135C11×SD16—44no—
136C11×D8—44no—
137C11×M16—42no—
138C2×C8×C11—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151C22⋊Dic11—41no—
152#4324—42no—
153#4324—42no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
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#3077—111no—
175#3036D1111yescharacteristic
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—41no—
189C23×C11#12111yescharacteristic
190Q8×C11—41no—
191Q8×C11—41no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—42no—
199D4×C11—81no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—44no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—82no—
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×Dic11—41no—
220C2×Dic11—41no—
221Dic22—41no—
222Dic22—41no—
223Dic22—81no—
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)—21no—
232C22×M16—221no—
233#533—111no—
234#532C2×D1111yescharacteristic
235C2×C4×D4C2×D1111yescharacteristic
236#498—111no—
237#492—111no—
238#487—111no—
239#486—111no—
240#478—222no—
241#476—112no—
242#474—112no—
243#465—221no—
244#465—221no—
245#463—22no—
246#461C2×D1112yes—
247#459C2×D1112yes—
248C4×SD16—221no—
249C4×SD16—221no—
250#436—112no—
251#436—112no—
252#436—221no—
253#436—221no—
254#428—221no—
255#423—111no—
256#423C2×D1111yescharacteristic
257C2×C4⋊C8—111no—
258#418—221no—
259#417—21no—
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—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11#46812yes—
278C22×C11C2×#12111yescharacteristic
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11#46812yes—
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C11C2×#13711yescharacteristic
288C4×C11#57511yescharacteristic
289Dic11—81no—
290Dic11—81no—
291C2×#41—21no—
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—21no—
294AGL(1,ℤ/8)—44no—
295C2×SD16—22no—
296C2×SD16—221no—
297C2×SD16—221no—
298C2×D8—22no—
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⋊Q8—111no—
309C4⋊Q8C22×D1111yescharacteristic
310#127C22×D1111yescharacteristic
311#125—221no—
312#124—21no—
313C22⋊Q8—221no—
314C22⋊Q8—221no—
315#121—21no—
316#121—21no—
317C4×Q8—221no—
318C4×Q8—221no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4C22⋊D1112yes—
324C4×D4C22×D1112yes—
325#117—221no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C42C22×D1111yescharacteristic
329#107—222no—
330#106—221no—
331#106—221no—
332#106—222no—
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22×D1112yes—
339#103—22no—
340#103—221no—
341#103—221no—
342#102—22no—
343#102—221no—
344#102—221no—
345#102—222no—
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—161no—
356C2×C11#303611yescharacteristic
357C2×C11C2×#46811yescharacteristic
358C2×C11#306711yescharacteristic
359C24—21no—
360#41—42no—
361#41—42no—
362C2×Q8—21no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C2×D4C2×C22⋊D1112yes—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382SD16—44no—
383SD16—442no—
384SD16—442no—
385D8—44no—
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—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4C2×C22⋊D1112yes—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—441no—
415C42—441no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1927911yescharacteristic, complemented, Sylow
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—41no—
426C23#6699211yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—441no—
430Q8—441no—
431Q8—881no—
432D4—22no—
433D4—22no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—42no—
439D4—81no—
440D4—82no—
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—82no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4#6698512yes—
454C2×C4#6699211yescharacteristic
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4#6700412yes—
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—81no—
475C22—81no—
476C22—81no—
477C22#1062265512yes—
478C22C2×#6699211yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—881no—
485C4—881no—
486C4#1062265512yes—
487C4D11×AGL(1,ℤ/8)11yescharacteristic
488C4#1062330411yescharacteristic
489C4C2×#6698511yescharacteristic
490C4C2×#6700411yescharacteristic
491C2—22no—
492C2—82no—
493C2—161no—
494C2#1307807711yescharacteristic
495C2C2×#1062265511yescharacteristic
496C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11C2×#121
hypercenter#3036D11
hypocenterC11#19279
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079171C2semidirect
2. #13078413C2semidirect
3. C2×#10622625C2semidirect
4. #13068165C2semidirect
5. #13068147C2semidirect
6. #13068113C2semidirect
7. #13068079C2semidirect
8. #13067374C2semidirect
9. #13067307C2semidirect
10. #13067293C2semidirect
24. #10622706C22semidirect
25. #10622692C22semidirect
26. #10622689C22semidirect
27. #10622683C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622119C22semidirect
47. #10622117C22semidirect
48. #10622117C22semidirect
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
#130791712
#130784132
C2×#106226252
#130681652
#130681472
#130681132
#130680792
#130673742
#130673072
#130672932
C11×#30362
#1927911