Finite Group Databasebeta

← #14725482

Subgroups — #14725482

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077705C211yesmaximal, characteristic, complemented
2#13077653C211yesmaximal, characteristic
3C2×C4×#4325C211yesmaximal, characteristic
4#13067521C212yesmaximal, complemented
5#13067456C212yesmaximal, complemented
6#13067455C212yesmaximal, complemented
7#13067431C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067060C211yesmaximal, characteristic
10#13066903C211yesmaximal, characteristic, complemented
11C11×#1491C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C411yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17C2×#66899C411yescharacteristic
18C4×#4325C411yescharacteristic
19C4×#4325C411yescharacteristic
20C4×#4325C411yescharacteristic
21C4×#4325C411yescharacteristic
22C4×#4325C2211yescharacteristic
23C4×#4325C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25C4×#4325C2211yescharacteristic
26#10622637—22no—
27#10622637C2212yescomplemented
28Q8×C11⋊C8C2212yescomplemented
29C2×#66873C411yescharacteristic
30C2×#66872C411yescharacteristic
31#10622539—21no—
32#10622539C2211yescharacteristic
33#10622538—21no—
34#10622538C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622451C2212yes—
37#10622447C2212yes—
38#10622339—21no—
39D11×C22⋊C8—21no—
40#10622319—22no—
41C11×Q8⋊C8C2212yescomplemented
42C11×Q8⋊C8C2212yescomplemented
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45#10622097C2212yes—
46#10622097C2212yes—
47#10622092C2212yescomplemented
48#10622092C2212yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C22×D44C2×C411yescharacteristic
51C22×C4×D11—21no—
52C2×C11×M16—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11C2×C411yescharacteristic
56C4×Q8×C11C2×C411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—24no—
64C2×#4325C2×C411yescharacteristic
65C2×#4325C2×C411yescharacteristic
66C2×#4325C2×C411yescharacteristic
67C2×#4325C2×C411yescharacteristic
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11C2×C411yescharacteristic
70C22×C11⋊C8C2×C411yescharacteristic
71C22×C11⋊C8C2×C411yescharacteristic
72C2×#4313—22no—
73C2×C8×D11—22no—
74C4×D44—21no—
75C4×D44—21no—
76C4×D44C2×C411yescharacteristic
77C4×D44C2×C411yescharacteristic
78C4×D44C2311yescharacteristic
79C4×D44C2311yescharacteristic
80C11×C4⋊C8C2312yes—
81C11×C22⋊C8—21no—
82C11×#97—21no—
83C11×#97—21no—
84C4×C8×C11C2312yes—
85#66899C2×C411yescharacteristic
86#66899C2×C411yescharacteristic
87#66899C2×C411yescharacteristic
88#66899C2×C411yescharacteristic
89C22⋊(C11⋊C8)—21no—
90C22⋊(C11⋊C8)D411yescharacteristic
91C22⋊(C11⋊C8)D411yescharacteristic
92(C2×D11)⋊C8—22no—
93(C2×D11)⋊C8—22no—
94#66873C2×C411yescharacteristic
95#66873C2×C411yescharacteristic
96#66873C2×C411yescharacteristic
97#66873C2×C411yescharacteristic
98#66872C2×C411yescharacteristic
99#66872C2×C411yescharacteristic
100#66872C2×C411yescharacteristic
101#66872C2×C411yescharacteristic
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)D412yes—
105C4⋊(C11⋊C8)C2312yes—
106#66867—21no—
107#66867—22no—
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2×C411yescharacteristic
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2312yes—
114#18060—111nomaximal, Sylow
115C23×D11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11C22×C411yescharacteristic
120C2×Q8×C11C22×C411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×Dic11—21no—
127C2×D44—22no—
128C2×D44—21no—
129C2×D44—41no—
130C2×D44C22×C411yescharacteristic
131C2×D44C22×C411yescharacteristic
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—82no—
137C11×M16—42no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C22×C411yescharacteristic
146C11×C4⋊C4C22×C411yescharacteristic
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C22×C411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4325—22no—
156#4325—22no—
157#4325—22no—
158#4325M1614yescomplemented
159(C2×D11)⋊C4—21no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C22×C411yescharacteristic
165C4⋊Dic11C22×C411yescharacteristic
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8C22×C411yescharacteristic
170C2×C11⋊C8C22×C411yescharacteristic
171C2×C11⋊C8C22×C411yescharacteristic
172C2×C11⋊C8C22×C411yescharacteristic
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8C2×D412yes—
175#4313—82no—
176C8×D11—82no—
177#2984—111no—
178#2974—111no—
179C2×C4×SD16—111no—
180#1592—112no—
181#1583—112no—
182#1582—112no—
183SD16⋊C8—112no—
184#1568—111no—
185#1491D1111yescharacteristic, complemented
186#1490—111no—
187#1451—111no—
188C23×C11C4×D411yescharacteristic
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—81no—
194Q8×C11—21no—
195Q8×C11—21no—
196Q8×C11—21no—
197Q8×C11—42no—
198Q8×C11C2×M1612yes—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—81no—
218D44—21no—
219D44—21no—
220D44—21no—
221D44—42no—
222D44C2×M1612yes—
223C4×D11—42no—
224C4×D11—42no—
225C4×D11—81no—
226C4×D11—81no—
227C8×C11—42no—
228C8×C11—42no—
229C11⋊C8—21no—
230C11⋊C8—21no—
231C11⋊C8—21no—
232C11⋊C8—22no—
233C11⋊C8—22no—
234C11⋊C8—42no—
235C11⋊C8C2×M1612yes—
236C22×SD16—111no—
237C2×C4×Q8C2×D1111yescharacteristic
238C2×C4×D4—111no—
239#446—112no—
240#446—222no—
241C8×Q8—112no—
242C4×SD16—111no—
243C4×SD16—111no—
244C4×SD16—111no—
245C4×SD16—111no—
246C4×SD16—111no—
247C4×SD16—111no—
248C4×SD16—111no—
249C4×SD16—111no—
250#436—112no—
251#435—222no—
252C8×D4—112no—
253#432—111no—
254#432—221no—
255#432C2×D1111yescharacteristic
256#431—111no—
257#431—221no—
258C2×#106—111no—
259C2×#103—111no—
260C2×#102—111no—
261#407—221no—
262C2×C22⋊C8—221no—
263C4×M16C2×D1111yescharacteristic
264C2×C4×C8—111no—
265#335—112no—
266#334—112no—
267Q8⋊C8C2×D1112yescomplemented
268Q8⋊C8C2×D1112yescomplemented
269D4⋊C8—112no—
270D4⋊C8—112no—
271#322—112no—
272#322—112no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11#44412yes—
276C22×C11C2×C4×D411yescharacteristic
277C2×D11—22no—
278C2×D11—41no—
279C2×D11—41no—
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C2×D11—84no—
284C4×C11—21no—
285C4×C11—22no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—41no—
292C4×C11C22×M1611yescharacteristic
293C4×C11#56811yescharacteristic
294C4×C11#57712yes—
295Dic11—41no—
296Dic11—41no—
297C22×Q8C4×D1111yescharacteristic
298C22×D4—111no—
299C23×C4—221no—
300C2×SD16—111no—
301C2×SD16—111no—
302C2×SD16—111no—
303C2×SD16—111no—
304C2×SD16—224no—
305C2×M16—21no—
306C2×M16—222no—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8—222no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8C4×D1111yescharacteristic
313C4×Q8C4×D1111yescharacteristic
314C4×Q8C22×D1111yescharacteristic
315C4×Q8C22×D1111yescharacteristic
316C4×D4—111no—
317C4×D4—111no—
318C4×D4—111no—
319C4×D4—111no—
320C4×D4—221no—
321C4×D4—221no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4C4×D1111yescharacteristic
325C2×C22⋊C4—221no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328#106—111no—
329#106—111no—
330#106—111no—
331#106—111no—
332C4⋊C8—112no—
333C4⋊C8—112no—
334C4⋊C8—222no—
335C4⋊C8—222no—
336C4⋊C8C22×D1112yes—
337#103—111no—
338#103—111no—
339#103—111no—
340#103—111no—
341#102—111no—
342#102—111no—
343#102—111no—
344#102—111no—
345C22⋊C8—21no—
346C22⋊C8—111no—
347C22⋊C8—111no—
348C22⋊C8—222no—
349C22⋊C8—222no—
350C22⋊C8—221no—
351#97—21no—
352#97—21no—
353#97—222no—
354#97—221no—
355C4×C8—111no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8—111no—
359C4×C8—112no—
360C4×C8—222no—
361C4×C8C22×D1112yes—
362C2×C11—22no—
363C2×C11D4×M1611yescharacteristic
364C2×C11#294911yescharacteristic
365C2×C11C2×#44411yescharacteristic
366D11—42no—
367D11—81no—
368C24—221no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8C2×C4×D1111yescharacteristic
373C2×Q8C2×C4×D1111yescharacteristic
374C2×D4—111no—
375C2×D4—111no—
376C2×D4—222no—
377C2×D4—221no—
378C2×D4—441no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—882no—
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4#434111yescharacteristic
390SD16—114no—
391SD16—222no—
392SD16—222no—
393SD16—222no—
394M16—42no—
395M16—882no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—111no—
399C2×C8—111no—
400C2×C8—111no—
401C2×C8—111no—
402C2×C8—112no—
403C2×C8—112no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—441no—
407C2×C8—882no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—111no—
414C4⋊C4—111no—
415C4⋊C4—221no—
416C4⋊C4C2×C4×D1111yescharacteristic
417C4⋊C4C2×C4×D1111yescharacteristic
418C22⋊C4—221no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C22⋊C4—221no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42C2×C4×D1111yescharacteristic
427C42D4×D1111yescharacteristic
428C42#434111yescharacteristic
429C42C23×D1111yescharacteristic
430C11#1806011yescharacteristic, complemented, Sylow
431C23—221no—
432C23—221no—
433C23—442no—
434C23—442no—
435C23—881no—
436C23(C22⋊D11)⋊C411yescharacteristic
437Q8—21no—
438Q8—21no—
439Q8—21no—
440Q8—42no—
441Q8M16×D1112yes—
442D4—112no—
443D4—221no—
444D4—221no—
445D4—221no—
446D4—442no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—881no—
462C2×C4—881no—
463C2×C4—881no—
464C2×C4(C22⋊D11)⋊C411yescharacteristic
465C2×C4(C22⋊D11)⋊C411yescharacteristic
466C2×C4(C22⋊D11)⋊C411yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C2×#434111yescharacteristic
470C8—42no—
471C8—42no—
472C8—112no—
473C8—221no—
474C8—221no—
475C8—221no—
476C8—222no—
477C8—222no—
478C8—442no—
479C22—21no—
480C22—21no—
481C22—222no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—884no—
488C22#1062243612yes—
489C22C2×(C22⋊D11)⋊C411yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—22no—
494C4—21no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—441no—
499C4—441no—
500C4C2×M16×D1111yescharacteristic
501C4#1062327611yescharacteristic
502C4#1062330912yes—
503C2—22no—
504C2—442no—
505C2—881no—
506C2#1307734811yescharacteristic
507C2#1307747111yescharacteristic
508C2C2×#1062243611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1491C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1491D11
hypocenterC11#18060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
1. #13077705C2semidirect
4. #13067521C2semidirect
5. #13067456C2semidirect
6. #13067455C2semidirect
7. #13067431C2semidirect
8. #13067377C2semidirect
10. #13066903C2semidirect
11. C11×#1491C2semidirect
27. #10622637C22semidirect
28. Q8×C11⋊C8C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×Q8⋊C8C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
47. #10622092C22semidirect
48. #10622092C22semidirect
158. #4325M16semidirect
185. #1491D11semidirect
267. Q8⋊C8C2×D11semidirect
268. Q8⋊C8C2×D11semidirect
430. C11#18060semidirect

Maximal subgroups

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

subgroupindex
#130777052
#130776532
C2×C4×#43252
#130675212
#130674562
#130674552
#130674312
#130673772
#130670602
#130669032
C11×#14912
#1806011