Finite Group Databasebeta

← #14737774

Subgroups — #14737774

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#13078409C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3C2×#10622301C211yesmaximal, characteristic, complemented
4#13068160C212yesmaximal, complemented
5#13068146C212yesmaximal, complemented
6#13068112C212yesmaximal, complemented
7#13068078C212yesmaximal, complemented
8#13067375C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3167C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67002—21no—
15C22×#4313—21no—
16C2×C4×D44C2211yescharacteristic
17C11×#498C2211yescharacteristic, complemented
18C11×#492C2211yescharacteristic, complemented
19C11×#487C2211yescharacteristic, complemented
20C11×#486C2211yescharacteristic, complemented
21C11×#465—21no—
22C11×#465—21no—
23C4×C11×SD16—21no—
24C4×C11×SD16—21no—
25C2×C4×C8×C11C2211yescharacteristic
26#10622845—21no—
27C2×(C2×D11)⋊C8—21no—
28#10622700C2212yes—
29#10622697C2212yes—
30#10622696C2212yes—
31#10622685C2212yes—
32#10622679—22no—
33#10622670—22no—
34#10622614—21no—
35#10622608—21no—
36#10622537C2211yescharacteristic
37#10622537C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622301—21no—
40#10622301—21no—
41#10622301C2212yes—
42#10622301C2212yes—
43#10622185C2212yescomplemented
44#10622185C2212yescomplemented
45#10622184C2212yescomplemented
46#10622182C2212yescomplemented
47#10622096C2212yescomplemented
48#10622096C2212yescomplemented
49C2×C11×#41—21no—
50C22×D44D411yescharacteristic
51C22×C4×D11—21no—
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11D411yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#125—21no—
61C11×#124—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65C11×#121—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C11×#117—21no—
71C2×C42×C11C2311yescharacteristic
72#67002—44no—
73C2×#4325—22no—
74C2×#4323—22no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×#4318—21no—
78C2×#4318—21no—
79C22×C11⋊C8—21no—
80C2×#4313—22no—
81C2×#4313—22no—
82C2×#4313—44no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44D412yes—
86C4×D44C2312yes—
87C11×#106—21no—
88C11×#106—21no—
89C11×#103—21no—
90C11×#103—21no—
91C11×#102—21no—
92C11×#102—21no—
93C4×C8×C11D411yescharacteristic
94C4×C8×C11D411yescharacteristic
95C4×C8×C11C2311yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66899—22no—
98#66896—22no—
99(C2×D11)⋊C8—22no—
100(C2×D11)⋊C8—22no—
101#66873—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110C4⋊(C11⋊C8)C2312yes—
111#19279—111nomaximal, Sylow
112C23×D11—21no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×Dic11—21no—
127C2×D44—21no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44C2×D412yes—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C11×SD16—42no—
136C11×SD16—42no—
137C2×C8×C11—22no—
138C2×C8×C11—41no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C42×C11—41no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11#4111yescharacteristic
158C42×C11C2411yescharacteristic
159#4325—44no—
160#4323—44no—
161(C2×D11)⋊C4—22no—
162(C2×D11)⋊C4—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D412yes—
165#4318—42no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171#4313—44no—
172#4313—44no—
173#3167D1111yescharacteristic, complemented
174#3077—111no—
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—41no—
185C23×C11#12111yescharacteristic
186C22×D11—22no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—81no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—81no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—82no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—42no—
218D44—22no—
219D44—22no—
220D44—42no—
221C4×D11—44no—
222C4×D11—42no—
223C4×D11—42no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11—21no—
227C8×C11AGL(1,ℤ/8)12yescomplemented
228C11⋊C8—42no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C2×AGL(1,ℤ/8)—221no—
232C22×M16—221no—
233#533C2×D1111yescharacteristic
234#532C2×D1111yescharacteristic
235C2×C4×D4—111no—
236#498C2×D1111yescharacteristic, complemented
237#492C2×D1111yescharacteristic, complemented
238#487C2×D1111yescharacteristic, complemented
239#486C2×D1111yescharacteristic, complemented
240#478—222no—
241#476—112no—
242#474—112no—
243#465—21no—
244#465—21no—
245#463—222no—
246#461—112no—
247#459—112no—
248C4×SD16—21no—
249C4×SD16—21no—
250#436—112no—
251#436—112no—
252#436—221no—
253#436—221no—
254#428—221no—
255#423—111no—
256#423—111no—
257C2×C4⋊C8—111no—
258#418—221no—
259#417—221no—
260C2×C22⋊C8—221no—
261C2×C4×C8C2×D1111yescharacteristic
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—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11#46812yes—
274C22×C11C2×#12111yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—84no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—81no—
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—42no—
291C2×#41—21no—
292C22×D4—111no—
293C23×C4—221no—
294AGL(1,ℤ/8)—444no—
295C2×SD16—21no—
296C2×SD16—21no—
297C2×SD16—222no—
298C2×D8—222no—
299C2×M16—221no—
300C2×M16—221no—
301C2×M16—222no—
302C2×M16—222no—
303C2×M16—444no—
304C22×C8—221no—
305C22×C8C22⋊D1111yescharacteristic
306C22×C8C22⋊D1111yescharacteristic
307C4⋊Q8C22×D1111yescharacteristic
308C4⋊Q8C22×D1111yescharacteristic
309C4⋊Q8C22×D1111yescharacteristic
310#127C22×D1111yescharacteristic
311#125—21no—
312#124—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315#121—21no—
316#121—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—112no—
322C4×D4—112no—
323C4×D4—221no—
324C4×D4—221no—
325#117—21no—
326C2×C4⋊C4—111no—
327C2×C22⋊C4—221no—
328C2×C42C22×D1111yescharacteristic
329#107—222no—
330#106—21no—
331#106—21no—
332#106—222no—
333C4⋊C8—112no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339#103—21no—
340#103—21no—
341#103—222no—
342#102—21no—
343#102—21no—
344#102—222no—
345#102—222no—
346#102—222no—
347C22⋊C8—222no—
348C22⋊C8—222no—
349C4×C8C22⋊D1111yescharacteristic
350C4×C8C22⋊D1111yescharacteristic
351C4×C8C22×D1111yescharacteristic
352C4×C8C22×D1111yescharacteristic
353C2×C11—22no—
354C2×C11—161no—
355C2×C11#303611yescharacteristic
356C2×C11C2×#46811yescharacteristic
357C2×C11#306711yescharacteristic
358D11—82no—
359C24—221no—
360#41—42no—
361#41—42no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—112no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—221no—
373C22×C4—41no—
374C22×C4—221no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382SD16—42no—
383SD16—42no—
384SD16—444no—
385D8—444no—
386M16—444no—
387M16—442no—
388M16—442no—
389M16—444no—
390C2×C8—22no—
391C2×C8—41no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—442no—
396C2×C8C2×C22⋊D1111yescharacteristic
397C2×C8C2×C22⋊D1111yescharacteristic
398C2×C8C2×C22⋊D1111yescharacteristic
399C2×C8C2×C22⋊D1111yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—112no—
409C4⋊C4—221no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—222no—
414C22⋊C4—222no—
415C42—41no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1927911yescharacteristic, complemented, Sylow
421C23—41no—
422C23—222no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23#6699111yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431Q8—81no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—81no—
437D4—82no—
438D4—222no—
439D4—222no—
440D4—442no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—82no—
448C2×C4—222no—
449C2×C4—444no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4#6696712yes—
454C2×C4#6696812yes—
455C2×C4#6699111yescharacteristic
456C2×C4#6699111yescharacteristic
457C2×C4#6699111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—21no—
462C8—21no—
463C8—21no—
464C8—442no—
465C8—442no—
466C8—442no—
467C8#6700212yescomplemented
468C22—21no—
469C22—21no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—884no—
477C22#1062278712yes—
478C22C2×#6699111yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—442no—
486C4#1062278712yes—
487C4C2×#6696711yescharacteristic
488C4C2×#6696811yescharacteristic
489C4C2×#6700211yescharacteristic
490C4#1062335311yescharacteristic
491C2—22no—
492C2—161no—
493C2—882no—
494C2#1307807611yescharacteristic
495C2C2×#1062278711yescharacteristic
496C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#3167D11
hypocenterC11#19279
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. C2×#10622301C2semidirect
4. #13068160C2semidirect
5. #13068146C2semidirect
6. #13068112C2semidirect
7. #13068078C2semidirect
8. #13067375C2semidirect
9. #13067306C2semidirect
10. #13067293C2semidirect
11. C11×#3167C2semidirect
17. C11×#498C22semidirect
18. C11×#492C22semidirect
19. C11×#487C22semidirect
20. C11×#486C22semidirect
43. #10622185C22semidirect
44. #10622185C22semidirect
45. #10622184C22semidirect
46. #10622182C22semidirect
47. #10622096C22semidirect
48. #10622096C22semidirect
173. #3167D11semidirect
227. C8×C11AGL(1,ℤ/8)semidirect
236. #498C2×D11semidirect
237. #492C2×D11semidirect
238. #487C2×D11semidirect
239. #486C2×D11semidirect
420. C11#19279semidirect
467. C8#67002semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130780762
C2×#106223012
#130681602
#130681462
#130681122
#130680782
#130673752
#130673062
#130672932
C11×#31672
#1927911