Finite Group Databasebeta

← #14737348

Subgroups — #14737348

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic, complemented
3#13079069C211yesmaximal, characteristic
4#13077559C211yesmaximal, characteristic, complemented
5#13068099C212yesmaximal, complemented
6#13068091C212yesmaximal, complemented
7#13067975C212yesmaximal, complemented
8#13067967C212yesmaximal, complemented
9#13067369C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#1540C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×#67002—21no—
14C2×#67002—21no—
15C2×#66927C2211yescharacteristic
16#10623001C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19#10622715—21no—
20#10622714—21no—
21#10622707C2212yescomplemented
22#10622698C2212yes—
23#10622688C2212yescomplemented
24#10622686C2212yes—
25#10622671—22no—
26#10622654—22no—
27#10622632—21no—
28#10622621—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622461C2212yes—
32#10622461C2212yes—
33#10622444C2212yescomplemented
34#10622443C2212yescomplemented
35#10622441—22no—
36#10622344—22no—
37#10622307—21no—
38#10622306—21no—
39C11×#332C2211yescharacteristic, complemented
40C11×#332C2211yescharacteristic, complemented
41C11×#331C2211yescharacteristic, complemented
42C11×#331C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×C8×C11—21no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×#127C2311yescharacteristic
54C11×#124—21no—
55C11×#121—21no—
56C11×#121—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C2×C42×C11C2311yescharacteristic
60#67002—44no—
61#67002—44no—
62C2×#4325—22no—
63C2×#4325—22no—
64C2×#4324—22no—
65C2×#4323—22no—
66C2×#4323—22no—
67#66979—21no—
68#66977—21no—
69#66977D412yes—
70C2×#4318D411yescharacteristic
71C2×#4318D411yescharacteristic
72C22×C11⋊C8—21no—
73C2×#4314—22no—
74C2×#4314—22no—
75#66927—21no—
76#66927—21no—
77#66927—21no—
78#66927C2312yes—
79#66923—21no—
80#66922D411yescharacteristic
81#66922D411yescharacteristic
82C4×Dic22—21no—
83C4×Dic22C2312yes—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2311yescharacteristic
86C11×C4⋊C8C2311yescharacteristic
87C11×C4⋊C8C2311yescharacteristic
88C11×C4⋊C8C2311yescharacteristic
89C11×C22⋊C8—21no—
90C4×C8×C11—21no—
91#66896—22no—
92#66885—22no—
93#66885—22no—
94#66879—22no—
95Dic11⋊C8—22no—
96Dic11⋊C8—22no—
97C8×Dic11—22no—
98#66874—22no—
99#66872—22no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2312yes—
102#66867D412yes—
103C4×C11⋊C8C2312yes—
104#19238—111nomaximal, Sylow
105C23×D11—41no—
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—41no—
121C2×D44—41no—
122C2×D44—41no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—81no—
126C2×D44—81no—
127C2×D44—82no—
128C2×Dic22—21no—
129C2×Dic22C2×D412yes—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—42no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142C42×C11C2411yescharacteristic
143C22⋊Dic11—22no—
144#4325—44no—
145#4325—44no—
146#4324—82no—
147#4323—44no—
148#4323—44no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11C2×D412yes—
153Dic11⋊C4—22no—
154Dic11⋊C4—22no—
155C4×Dic11—22no—
156#4318—22no—
157#4318SD1614yescomplemented
158C2×C11⋊C8—22no—
159C2×C11⋊C8—81no—
160C2×C11⋊C8C2×D412yes—
161C2×C11⋊C8C2×D412yes—
162#4314—82no—
163#4314—82no—
164#3246—111no—
165#3208—111no—
166#3151—111no—
167#2962—111no—
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565—111no—
173#1540D1111yescharacteristic, complemented
174C2×#331—111no—
175C23×C11—41no—
176C23×C11#12111yescharacteristic
177C22×D11—42no—
178C22×D11—82no—
179C22×D11—82no—
180C22×D11—82no—
181Q8×C11—41no—
182Q8×C11—41no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—81no—
188D4×C11—82no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—82no—
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204D44—42no—
205D44—42no—
206D44—42no—
207D44—42no—
208D44—82no—
209D44—82no—
210D44—82no—
211D44—82no—
212Dic22—22no—
213Dic22—22no—
214Dic22—81no—
215C8×C11—41no—
216C8×C11—41no—
217C8×C11—41no—
218C8×C11—41no—
219C11⋊C8—22no—
220C11⋊C8—42no—
221C11⋊C8C2×SD1614yes—
222C2×AGL(1,ℤ/8)—221no—
223C2×AGL(1,ℤ/8)—221no—
224#533—111no—
225#532C2×D1111yescharacteristic
226C2×#127—111no—
227#496—222no—
228#493—112no—
229#492—112no—
230#492—221no—
231#486—221no—
232#476—221no—
233#475—112no—
234#465—222no—
235#461—221no—
236#460—112no—
237#460—112no—
238#460—112no—
239#450—222no—
240#446—112no—
241#446—222no—
242C8×Q8—112no—
243#431C2×D1111yescharacteristic
244#424—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8C2×D1111yescharacteristic
247#405—221no—
248C4×M16—111no—
249#335—112no—
250#334—112no—
251#332C2×D1111yescharacteristic, complemented
252#332C2×D1111yescharacteristic, complemented
253#331—112no—
254#331—112no—
255#331C2×D1111yescharacteristic, complemented
256#331C2×D1111yescharacteristic, complemented
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11#46012yes—
263C22×C11C2×#12111yescharacteristic
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—164no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—81no—
272C4×C11#46012yes—
273C4×C11C22×SD1611yescharacteristic
274C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C4×C11#57611yescharacteristic
276C4×C11#57711yescharacteristic
277Dic11—42no—
278Dic11—42no—
279C2×#41—21no—
280C22×D4—221no—
281C22×D4—221no—
282C22×D4—221no—
283AGL(1,ℤ/8)—444no—
284AGL(1,ℤ/8)—444no—
285C2×SD16—222no—
286C2×SD16—222no—
287C2×SD16—222no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×D8—222no—
292C2×M16—111no—
293C2×M16—111no—
294C22×C8—21no—
295C22×C8—221no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298C4⋊Q8C22×D1111yescharacteristic
299#127—112no—
300#127—221no—
301#127—221no—
302#127—221no—
303#127C22×D1111yescharacteristic
304#125—221no—
305#124—21no—
306C22⋊Q8—112no—
307C22⋊Q8—221no—
308#121—21no—
309#121—21no—
310C4×Q8—112no—
311C4×Q8—221no—
312C4×D4—21no—
313C4×D4—21no—
314#117—221no—
315C2×C42C22×D1111yescharacteristic
316#106—222no—
317C4⋊C8—21no—
318C4⋊C8—112no—
319C4⋊C8—222no—
320C4⋊C8—222no—
321C4⋊C8—221no—
322C4⋊C8C22×D1111yescharacteristic
323C4⋊C8C22×D1111yescharacteristic
324C4⋊C8C22×D1111yescharacteristic
325C4⋊C8C22×D1111yescharacteristic
326#103—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330C22⋊C8—21no—
331#97—112no—
332#97—222no—
333C4×C8—21no—
334C4×C8—112no—
335C4×C8—222no—
336C2×C11—22no—
337C2×C11—161no—
338C2×C11C2×#46011yescharacteristic
339C2×C11#306211yescharacteristic
340C2×C11#306811yescharacteristic
341D11—162no—
342C24—441no—
343#41—42no—
344#41—42no—
345C2×Q8—21no—
346C2×Q8—112no—
347C2×Q8—221no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—881no—
361C2×D4—881no—
362C2×D4—882no—
363C22×C4—41no—
364C22×C4#433911yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367SD16—444no—
368SD16—444no—
369SD16—882no—
370SD16—882no—
371SD16—882no—
372D8—444no—
373D8—444no—
374M16—114no—
375M16—222no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—42no—
381C2×C8—112no—
382C2×C8—112no—
383C2×C8—222no—
384C2×C8—881no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—112no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—222no—
396C42—222no—
397C42#433911yescharacteristic
398C42D4×D1111yescharacteristic
399C42D4×D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—41no—
403C23—442no—
404C23—882no—
405C23—882no—
406C23—882no—
407C23#6693711yescharacteristic
408Q8—41no—
409Q8—41no—
410Q8—222no—
411Q8—222no—
412Q8—881no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—81no—
418D4—82no—
419D4—442no—
420D4—442no—
421D4—442no—
422D4—442no—
423D4—882no—
424D4—882no—
425D4—882no—
426D4—882no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4#6693711yescharacteristic
435C2×C4#6693711yescharacteristic
436C2×C4#6693711yescharacteristic
437C2×C4#6696412yes—
438C2×C4SD16×D1112yes—
439C2×C4C2×#433911yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C8—41no—
443C8—41no—
444C8—41no—
445C8—41no—
446C8—114no—
447C8—222no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—882no—
455C22—882no—
456C22—882no—
457C22—1764no—
458C22#1062237512yes—
459C22C2×#6693711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—81no—
464C4—442no—
465C4—442no—
466C4#1062237512yes—
467C4C2×#6696411yescharacteristic
468C4C2×SD16×D1111yescharacteristic
469C4#1062330011yescharacteristic
470C4#1062330111yescharacteristic
471C2—22no—
472C2—161no—
473C2—1762no—
474C2C2×#1062237511yescharacteristic
475C2#1307829911yescharacteristic
476C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
prime radical#13079069C2
hypercenter#1540D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13079559C2semidirect
4. #13077559C2semidirect
5. #13068099C2semidirect
6. #13068091C2semidirect
7. #13067975C2semidirect
8. #13067967C2semidirect
9. #13067369C2semidirect
10. C2×#10622123C2semidirect
11. C11×#1540C2semidirect
21. #10622707C22semidirect
23. #10622688C22semidirect
33. #10622444C22semidirect
34. #10622443C22semidirect
39. C11×#332C22semidirect
40. C11×#332C22semidirect
41. C11×#331C22semidirect
42. C11×#331C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
157. #4318SD16semidirect
173. #1540D11semidirect
251. #332C2×D11semidirect
252. #332C2×D11semidirect
255. #331C2×D11semidirect
256. #331C2×D11semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130795592
#130790692
#130775592
#130680992
#130680912
#130679752
#130679672
#130673692
C2×#106221232
C11×#15402
#1923811