Finite Group Databasebeta

← #14725513

Subgroups — #14725513

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077650C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13067528C212yesmaximal, complemented
4#13067445C212yesmaximal, complemented
5#13067443C212yesmaximal, complemented
6#13067438C212yesmaximal, complemented
7#13067377C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic, complemented
9#13067058C211yesmaximal, characteristic, complemented
10#13066906C211yesmaximal, characteristic, complemented
11C11×#2974C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C411yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#436C2212yescomplemented
16C11×#435—22no—
17C8×D4×C11C2212yescomplemented
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#407—21no—
21C2×C11×C22⋊C8—21no—
22C2×#66896C411yescharacteristic
23C4×#4323C411yescharacteristic
24C4×#4323C411yescharacteristic
25C4×#4323C411yescharacteristic
26C4×#4323C411yescharacteristic
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29C4×#4323C2211yescharacteristic
30C4×#4323C2211yescharacteristic
31C2×#66873C411yescharacteristic
32C2×#66871C411yescharacteristic
33#10622539C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622449—22no—
37#10622339—21no—
38D11×C22⋊C8—21no—
39#10622301C2212yescomplemented
40C8×D44C2212yescomplemented
41D4⋊(C11⋊C8)C2212yescomplemented
42D4⋊(C11⋊C8)C2212yescomplemented
43#10622121C2212yescomplemented
44#10622121C2212yescomplemented
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47#10622093C2212yescomplemented
48#10622092C2212yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C22×D44C2×C411yescharacteristic
52C22×C4×D11—21no—
53C2×C11×M16—22no—
54C22×C8×C11—22no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11C2×C411yescharacteristic
58C4×D4×C11C2×C411yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C4×D4×C11C2311yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4323—24no—
65C2×#4323C2×C411yescharacteristic
66C2×#4323C2×C411yescharacteristic
67C2×#4323C2×C411yescharacteristic
68C2×#4323C2×C411yescharacteristic
69C2×(C2×D11)⋊C4—21no—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×#4318—21no—
72C22×C11⋊C8C2×C411yescharacteristic
73C22×C11⋊C8C2×C411yescharacteristic
74C2×#4313—22no—
75C2×C8×D11—22no—
76C4×D44—21no—
77C4×D44—21no—
78C4×D44C2×C411yescharacteristic
79C4×D44C2×C411yescharacteristic
80C4×D44C2311yescharacteristic
81C4×D44C2311yescharacteristic
82C11×C4⋊C8D412yes—
83C11×C4⋊C8C2312yes—
84C11×C22⋊C8—21no—
85C11×C22⋊C8—22no—
86C11×C22⋊C8—22no—
87C11×C22⋊C8D411yescharacteristic
88C11×C22⋊C8D411yescharacteristic
89C11×#97—21no—
90C4×C8×C11C2312yes—
91#66896C2×C411yescharacteristic
92#66896C2×C411yescharacteristic
93#66896C2×C411yescharacteristic
94#66896C2×C411yescharacteristic
95C22⋊(C11⋊C8)—21no—
96(C2×D11)⋊C8—22no—
97(C2×D11)⋊C8—22no—
98#66873C2×C411yescharacteristic
99#66873C2×C411yescharacteristic
100#66873C2×C411yescharacteristic
101#66873C2×C411yescharacteristic
102#66871C2×C411yescharacteristic
103#66871C2×C411yescharacteristic
104#66871C2×C411yescharacteristic
105#66871C2×C411yescharacteristic
106C4⋊(C11⋊C8)C2312yes—
107#66867—21no—
108#66867—21no—
109C4×C11⋊C8C2×C411yescharacteristic
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2312yes—
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114#18064—111nomaximal, Sylow
115C24×C11—21no—
116C23×D11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C2×D4×C11C22×C411yescharacteristic
121C2×D4×C11C22×C411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—82no—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×Dic11—21no—
132C2×D44—22no—
133C2×D44—21no—
134C2×D44—41no—
135C2×D44C22×C411yescharacteristic
136C2×D44C22×C411yescharacteristic
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—82no—
142C11×M16—82no—
143C2×C8×C11—22no—
144C2×C8×C11—82no—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C22×C411yescharacteristic
149C11×C4⋊C4C22×C411yescharacteristic
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C42×C11C22×C411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11#4111yescharacteristic
157C42×C11C2411yescharacteristic
158#4323—22no—
159#4323—22no—
160#4323—22no—
161#4323M1614yescomplemented
162(C2×D11)⋊C4—21no—
163(C2×D11)⋊C4—21no—
164(C2×D11)⋊C4—21no—
165(C2×D11)⋊C4—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11C22×C411yescharacteristic
168C4⋊Dic11C22×C411yescharacteristic
169#4318—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8C22×C411yescharacteristic
175C2×C11⋊C8C22×C411yescharacteristic
176C2×C11⋊C8C22×C411yescharacteristic
177C2×C11⋊C8C22×C411yescharacteristic
178#4313—82no—
179C8×D11—82no—
180#2974—111no—
181#2974D1111yescharacteristic, complemented
182C2×C4×D8—111no—
183#1594—112no—
184#1581—112no—
185#1581—112no—
186#1580—112no—
187#1568—111no—
188#1490—111no—
189#1490—111no—
190#1451—111no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—81no—
196C23×C11C4×D411yescharacteristic
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—81no—
202D4×C11—21no—
203D4×C11—21no—
204D4×C11—21no—
205D4×C11—42no—
206D4×C11C2×M1612yes—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—81no—
216C2×C4×C11—81no—
217C2×C4×C11—81no—
218C2×C4×C11C4×D411yescharacteristic
219C2×C4×C11C4×D411yescharacteristic
220C2×C4×C11C4×D411yescharacteristic
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—81no—
227D44—21no—
228D44—21no—
229D44—21no—
230D44—42no—
231D44C2×M1612yes—
232C4×D11—42no—
233C4×D11—42no—
234C4×D11—81no—
235C4×D11—81no—
236C8×C11—22no—
237C8×C11—22no—
238C8×C11—42no—
239C11⋊C8—21no—
240C11⋊C8—21no—
241C11⋊C8—21no—
242C11⋊C8—42no—
243C11⋊C8—42no—
244C11⋊C8C2×M1612yes—
245C22×D8—111no—
246C2×C4×D4—111no—
247C2×C4×D4C2×D1111yescharacteristic
248C4×D8—111no—
249C4×D8—111no—
250C4×D8—111no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256#436—112no—
257#436C2×D1112yescomplemented
258#435—22no—
259#435—222no—
260C8×D4—112no—
261C8×D4C2×D1112yescomplemented
262#432—111no—
263#432C2×D1111yescharacteristic
264#431C2×D1111yescharacteristic
265C2×#107—111no—
266C2×#102—111no—
267C2×#102—111no—
268#407—21no—
269#407—221no—
270C2×C22⋊C8—21no—
271C2×C22⋊C8—221no—
272C4×M16—111no—
273C2×C4×C8—111no—
274#335—112no—
275#334—112no—
276D4⋊C8—112no—
277D4⋊C8—112no—
278D4⋊C8—112no—
279D4⋊C8—112no—
280#322—112no—
281#322—112no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—84no—
291C22×C11#44412yes—
292C22×C11C2×C4×D411yescharacteristic
293C2×D11—22no—
294C2×D11—41no—
295C2×D11—41no—
296C2×D11—41no—
297C2×D11—41no—
298C2×D11—41no—
299C2×D11—84no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—41no—
305C4×C11—41no—
306C4×C11C22×M1611yescharacteristic
307C4×C11#56811yescharacteristic
308C4×C11#57612yes—
309Dic11—41no—
310Dic11—41no—
311C22×D4—111no—
312C22×D4C4×D1111yescharacteristic
313C23×C4—21no—
314C23×C4—221no—
315C2×D8—111no—
316C2×D8—111no—
317C2×D8—111no—
318C2×D8—111no—
319C2×D8—224no—
320C2×M16—22no—
321C2×M16—221no—
322C2×M16—222no—
323C22×C8—22no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—222no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—111no—
330C4×D4—111no—
331C4×D4—111no—
332C4×D4—111no—
333C4×D4—221no—
334C4×D4—221no—
335C4×D4C4×D1111yescharacteristic
336C4×D4C4×D1111yescharacteristic
337C4×D4C22×D1111yescharacteristic
338C4×D4C22×D1111yescharacteristic
339C2×C4⋊C4—111no—
340C2×C4⋊C4C4×D1111yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—221no—
343C2×C42C22×D1111yescharacteristic
344#107—111no—
345#107—111no—
346#107—111no—
347#107—111no—
348C4⋊C8—112no—
349C4⋊C8C22⋊D1112yes—
350C4⋊C8C22×D1112yes—
351#102—111no—
352#102—111no—
353#102—111no—
354#102—111no—
355#102—111no—
356#102—111no—
357#102—111no—
358#102—111no—
359C22⋊C8—21no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362C22⋊C8—221no—
363C22⋊C8—222no—
364C22⋊C8—222no—
365C22⋊C8C22⋊D1111yescharacteristic
366C22⋊C8C22⋊D1111yescharacteristic
367#97—21no—
368#97—221no—
369#97—221no—
370C4×C8—111no—
371C4×C8—111no—
372C4×C8—111no—
373C4×C8—111no—
374C4×C8—112no—
375C4×C8C22×D1112yes—
376C2×C11—22no—
377C2×C11—42no—
378C2×C11—81no—
379C2×C11D4×M1611yescharacteristic
380C2×C11#294811yescharacteristic
381C2×C11C2×#44411yescharacteristic
382D11—42no—
383D11—81no—
384C24—21no—
385C24—221no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—111no—
390C2×D4—111no—
391C2×D4—222no—
392C2×D4—221no—
393C2×D4—441no—
394C2×D4C2×C4×D1111yescharacteristic
395C2×D4C2×C4×D1111yescharacteristic
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—82no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—882no—
408C22×C4C2×C4×D1111yescharacteristic
409C22×C4#433911yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411D8—114no—
412D8—222no—
413D8—222no—
414D8—222no—
415M16—82no—
416M16—442no—
417M16—882no—
418C2×C8—22no—
419C2×C8—82no—
420C2×C8—111no—
421C2×C8—111no—
422C2×C8—111no—
423C2×C8—111no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—441no—
428C2×C8—882no—
429C2×C8C2×C22⋊D1112yes—
430C2×C8C2×C22⋊D1112yes—
431C4⋊C4—21no—
432C4⋊C4—111no—
433C4⋊C4—111no—
434C4⋊C4—221no—
435C4⋊C4C2×C4×D1111yescharacteristic
436C4⋊C4C2×C4×D1111yescharacteristic
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—221no—
442C22⋊C4—221no—
443C22⋊C4—221no—
444C22⋊C4—221no—
445C42C2×C4×D1111yescharacteristic
446C42#433911yescharacteristic
447C42C2×C22⋊D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#1806411yescharacteristic, complemented, Sylow
450C23—21no—
451C23—21no—
452C23—42no—
453C23—42no—
454C23—81no—
455C23—221no—
456C23—221no—
457C23—442no—
458C23—442no—
459C23—881no—
460C23C4×C22⋊D1111yescharacteristic
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—112no—
466D4—221no—
467D4—221no—
468D4—221no—
469D4—442no—
470D4M16×D1112yes—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—881no—
487C2×C4—881no—
488C2×C4—881no—
489C2×C4C4×C22⋊D1111yescharacteristic
490C2×C4C4×C22⋊D1111yescharacteristic
491C2×C4C4×C22⋊D1111yescharacteristic
492C2×C4C22×C4×D1111yescharacteristic
493C2×C4C2×#433911yescharacteristic
494C2×C4C22×C22⋊D1111yescharacteristic
495C8—22no—
496C8—22no—
497C8—42no—
498C8—112no—
499C8—221no—
500C8—221no—
501C8—221no—
502C8—442no—
503C8—442no—
504C22—21no—
505C22—21no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—84no—
513C22—222no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—441no—
518C22—441no—
519C22—884no—
520C22#1062275812yes—
521C22C2×C4×C22⋊D1111yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—41no—
528C4—441no—
529C4—441no—
530C4C2×M16×D1111yescharacteristic
531C4#1062327611yescharacteristic
532C4#1062336612yes—
533C2—22no—
534C2—42no—
535C2—81no—
536C2—442no—
537C2—881no—
538C2M16×C22⋊D1111yescharacteristic
539C2#1307746611yescharacteristic
540C2C2×#1062275811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2974C2
socleC22×C11C2×C4×D4
prime radicalC22×#4323C4
cosocleC42×C11C24
hypercenter#2974D11
hypocenterC11#18064
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
1. #13077650C2semidirect
3. #13067528C2semidirect
4. #13067445C2semidirect
5. #13067443C2semidirect
6. #13067438C2semidirect
7. #13067377C2semidirect
8. #13067059C2semidirect
9. #13067058C2semidirect
10. #13066906C2semidirect
11. C11×#2974C2semidirect
15. C11×#436C22semidirect
17. C8×D4×C11C22semidirect
39. #10622301C22semidirect
40. C8×D44C22semidirect
41. D4⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
43. #10622121C22semidirect
44. #10622121C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
47. #10622093C22semidirect
48. #10622092C22semidirect
161. #4323M16semidirect
181. #2974D11semidirect
257. #436C2×D11semidirect
261. C8×D4C2×D11semidirect
449. C11#18064semidirect

Maximal subgroups

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

subgroupindex
#130776502
C2×C4×#43232
#130675282
#130674452
#130674432
#130674382
#130673772
#130670592
#130670582
#130669062
C11×#29742
#1806411