Finite Group Databasebeta

← #14725477

Subgroups — #14725477

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#13077706C211yesmaximal, characteristic, complemented
2#13077653C211yesmaximal, characteristic
3C2×C4×#4314C211yesmaximal, characteristic
4#13067517C212yesmaximal, complemented
5#13067458C212yesmaximal, complemented
6#13067451C212yesmaximal, complemented
7#13067427C212yesmaximal, complemented
8#13067062C211yesmaximal, characteristic, complemented
9#13067058C211yesmaximal, characteristic
10#13066905C211yesmaximal, characteristic, complemented
11C11×#1568C211yesmaximal, characteristic, complemented
12C22×#4314C411yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#432C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C2×#66885C411yescharacteristic
19C2×#66881C411yescharacteristic
20C2×#66880C411yescharacteristic
21#10622538C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622451C2212yes—
24#10622447C2212yes—
25#10622444C2212yescomplemented
26#10622443C2212yescomplemented
27#10622339—21no—
28D11×C22⋊C8—21no—
29#10622332—21no—
30#10622331—21no—
31#10622319—22no—
32#10622314—22no—
33C4×#4314C411yescharacteristic
34C4×#4314C411yescharacteristic
35C4×#4314C411yescharacteristic
36C4×#4314C411yescharacteristic
37C4×#4314C2211yescharacteristic
38C4×#4314C2211yescharacteristic
39C4×#4314C2211yescharacteristic
40C4×#4314C2211yescharacteristic
41C11×#335C2212yescomplemented
42C11×#334C2212yescomplemented
43#10622122C2212yescomplemented
44#10622122C2212yescomplemented
45#10622121C2212yes—
46#10622121C2212yes—
47#10622093C2212yescomplemented
48#10622092C2212yescomplemented
49C22×D44C2×C411yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22C2×C411yescharacteristic
52C22×C8×C11C2×C411yescharacteristic
53C22×C8×C11C2×C411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×C4⋊Dic11C2×C411yescharacteristic
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×Dic11⋊C4—21no—
59C2×C4×Dic11—21no—
60C2×#4318—21no—
61C2×#4314—24no—
62C2×#4314C2×C411yescharacteristic
63C2×#4314C2×C411yescharacteristic
64C2×#4314C2×C411yescharacteristic
65C2×#4314C2×C411yescharacteristic
66C2×#4313—22no—
67C2×C8×D11—22no—
68C4×D44—21no—
69C4×D44—21no—
70C4×D44C2×C411yescharacteristic
71C4×D44C2×C411yescharacteristic
72C4×D44C2311yescharacteristic
73C4×D44C2311yescharacteristic
74C4×Dic22—21no—
75C4×Dic22—21no—
76C4×Dic22C2×C411yescharacteristic
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C4×Dic22C2311yescharacteristic
80C11×C4⋊C8C2312yes—
81C11×C4⋊C8C2312yes—
82C11×C22⋊C8—21no—
83C11×C22⋊C8—21no—
84C11×#97—21no—
85C11×#97—21no—
86C4×C8×C11C2×C411yescharacteristic
87C4×C8×C11C2×C411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C22⋊(C11⋊C8)D411yescharacteristic
91C22⋊(C11⋊C8)D411yescharacteristic
92#66885C2×C411yescharacteristic
93#66885C2×C411yescharacteristic
94#66885C2×C411yescharacteristic
95#66885C2×C411yescharacteristic
96(C2×D11)⋊C8—22no—
97(C2×D11)⋊C8—22no—
98#66881C2×C411yescharacteristic
99#66881C2×C411yescharacteristic
100#66881C2×C411yescharacteristic
101#66881C2×C411yescharacteristic
102#66880C2×C411yescharacteristic
103#66880C2×C411yescharacteristic
104#66880C2×C411yescharacteristic
105#66880C2×C411yescharacteristic
106#66879—22no—
107Dic11⋊C8—22no—
108Dic11⋊C8—22no—
109C8×Dic11—22no—
110C4⋊(C11⋊C8)D412yes—
111#66867—21no—
112C4×C11⋊C8C2312yes—
113C4×C11⋊C8C2312yes—
114#18060—111nomaximal, Sylow
115C23×D11—21no—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C2×D44—22no—
123C2×D44—21no—
124C2×D44—41no—
125C2×D44C22×C411yescharacteristic
126C2×D44C22×C411yescharacteristic
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—82no—
132C2×Dic22—22no—
133C2×Dic22—21no—
134C2×Dic22—41no—
135C2×Dic22C22×C411yescharacteristic
136C2×Dic22C22×C411yescharacteristic
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—41no—
141C2×C8×C11C22×C411yescharacteristic
142C2×C8×C11C22×C411yescharacteristic
143C2×C8×C11C22×C411yescharacteristic
144C2×C8×C11C22×C411yescharacteristic
145C42×C11C22×C411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11#4111yescharacteristic
148C42×C11C2411yescharacteristic
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152(C2×D11)⋊C4—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11C22×C411yescharacteristic
156C4⋊Dic11C22×C411yescharacteristic
157C4⋊Dic11C22×C411yescharacteristic
158C4⋊Dic11C22×C411yescharacteristic
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162Dic11⋊C4—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167#4318—42no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8C2×D412yes—
170C2×C11⋊C8C2×D412yes—
171#4314—22no—
172#4314—22no—
173#4314—22no—
174#4314M1614yescomplemented
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#1568D1111yescharacteristic, complemented
185#1491—111no—
186#1490—111no—
187#1451—111no—
188C23×C11C4×D411yescharacteristic
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—81no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—81no—
213D44—21no—
214D44—21no—
215D44—21no—
216D44—42no—
217D44C2×M1612yes—
218C4×D11—42no—
219C4×D11—42no—
220C4×D11—81no—
221C4×D11—81no—
222Dic22—21no—
223Dic22—21no—
224Dic22—21no—
225Dic22—42no—
226Dic22C2×M1612yes—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11—42no—
231C8×C11—42no—
232C8×C11C2×M1612yes—
233C11⋊C8—22no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C22×SD16—111no—
237C2×C4×Q8—111no—
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—221no—
254#432C2×D1111yescharacteristic
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×M16—111no—
264C2×C4×C8C2×D1111yescharacteristic
265#335C2×D1112yescomplemented
266#334C2×D1112yescomplemented
267Q8⋊C8—112no—
268Q8⋊C8—112no—
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—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11C22×M1611yescharacteristic
289C4×C11#56811yescharacteristic
290C4×C11#57712yes—
291Dic11—22no—
292Dic11—41no—
293Dic11—41no—
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297C22×Q8—111no—
298C22×D4—111no—
299C23×C4—221no—
300C2×SD16—111no—
301C2×SD16—111no—
302C2×SD16—111no—
303C2×SD16—111no—
304C2×SD16—224no—
305C2×M16—222no—
306C2×M16—221no—
307C22×C8—222no—
308C22×C8C4×D1111yescharacteristic
309C22×C8C4×D1111yescharacteristic
310C4×Q8—111no—
311C4×Q8—111no—
312C4×Q8—111no—
313C4×Q8—111no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—111no—
317C4×D4—111no—
318C4×D4—111no—
319C4×D4—111no—
320C4×D4—221no—
321C4×D4—221no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C42—221no—
327C2×C42C22×D1111yescharacteristic
328#106—111no—
329#106—111no—
330#106—111no—
331#106—111no—
332C4⋊C8—112no—
333C4⋊C8—222no—
334C4⋊C8—222no—
335C4⋊C8C22×D1112yes—
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—21no—
347C22⋊C8—111no—
348C22⋊C8—111no—
349C22⋊C8—222no—
350C22⋊C8—222no—
351#97—21no—
352#97—21no—
353#97—222no—
354#97—221no—
355C4×C8—112no—
356C4×C8—112no—
357C4×C8—222no—
358C4×C8C4×D1111yescharacteristic
359C4×C8C4×D1111yescharacteristic
360C4×C8C22×D1111yescharacteristic
361C4×C8C22×D1111yescharacteristic
362C2×C11—22no—
363C2×C11D4×M1611yescharacteristic
364C2×C11#294911yescharacteristic
365C2×C11C2×#44411yescharacteristic
366D11—42no—
367D11—81no—
368C24—221no—
369C2×Q8—111no—
370C2×Q8—111no—
371C2×Q8—222no—
372C2×Q8—221no—
373C2×Q8—441no—
374C2×D4—111no—
375C2×D4—111no—
376C2×D4—222no—
377C2×D4—221no—
378C2×D4—441no—
379C22×C4—221no—
380C22×C4—221no—
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#434311yescharacteristic
390SD16—114no—
391SD16—222no—
392SD16—222no—
393SD16—222no—
394M16—442no—
395M16—882no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—112no—
401C2×C8—112no—
402C2×C8—222no—
403C2×C8—882no—
404C2×C8C2×C4×D1111yescharacteristic
405C2×C8C2×C4×D1111yescharacteristic
406C2×C8C2×C4×D1111yescharacteristic
407C2×C8C2×C4×D1111yescharacteristic
408C4⋊C4—111no—
409C4⋊C4—111no—
410C4⋊C4—111no—
411C4⋊C4—111no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C22⋊C4—221no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C22⋊C4—221no—
422C42—221no—
423C42—221no—
424C42—221no—
425C42—221no—
426C42C2×C4×D1111yescharacteristic
427C42D4×D1111yescharacteristic
428C42#434311yescharacteristic
429C42C23×D1111yescharacteristic
430C11#1806011yescharacteristic, complemented, Sylow
431C23—221no—
432C23—221no—
433C23—442no—
434C23—442no—
435C23—881no—
436C23#6694611yescharacteristic
437Q8—112no—
438Q8—221no—
439Q8—221no—
440Q8—221no—
441Q8—442no—
442D4—112no—
443D4—221no—
444D4—221no—
445D4—221no—
446D4—442no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—881no—
462C2×C4—881no—
463C2×C4—881no—
464C2×C4#6694611yescharacteristic
465C2×C4#6694611yescharacteristic
466C2×C4#6694611yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C2×#434311yescharacteristic
470C8—21no—
471C8—21no—
472C8—21no—
473C8—42no—
474C8—42no—
475C8—222no—
476C8—222no—
477C8—442no—
478C8M16×D1112yes—
479C22—21no—
480C22—21no—
481C22—222no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—884no—
488C22#1062250712yes—
489C22C2×#6694611yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—222no—
495C4—441no—
496C4—441no—
497C4—441no—
498C4—441no—
499C4—441no—
500C4C2×M16×D1111yescharacteristic
501C4#1062327611yescharacteristic
502C4#1062330112yes—
503C2—22no—
504C2—442no—
505C2—881no—
506C2#1307735111yescharacteristic
507C2#1307747411yescharacteristic
508C2C2×#1062250711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1568D11
hypocenterC11#18060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #13077706C2semidirect
4. #13067517C2semidirect
5. #13067458C2semidirect
6. #13067451C2semidirect
7. #13067427C2semidirect
8. #13067062C2semidirect
10. #13066905C2semidirect
11. C11×#1568C2semidirect
25. #10622444C22semidirect
26. #10622443C22semidirect
41. C11×#335C22semidirect
42. C11×#334C22semidirect
43. #10622122C22semidirect
44. #10622122C22semidirect
47. #10622093C22semidirect
48. #10622092C22semidirect
174. #4314M16semidirect
184. #1568D11semidirect
265. #335C2×D11semidirect
266. #334C2×D11semidirect
430. C11#18060semidirect

Maximal subgroups

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

subgroupindex
#130777062
#130776532
C2×C4×#43142
#130675172
#130674582
#130674512
#130674272
#130670622
#130670582
#130669052
C11×#15682
#1806011