Finite Group Databasebeta

← #14725191

Subgroups — #14725191

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3#13077351C211yesmaximal, characteristic, complemented
4#13067498C212yesmaximal, complemented
5#13067448C212yesmaximal, complemented
6#13067442C212yesmaximal, complemented
7#13067408C212yesmaximal, complemented
8#13067374C211yesmaximal, characteristic, complemented
9#13067042C211yesmaximal, characteristic, complemented
10#13066897C211yesmaximal, characteristic, complemented
11C11×#1486C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C411yescharacteristic
14C22×#4318—21no—
15C2×M16×D11—21no—
16C2×C4×D44C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C11×#423C2211yescharacteristic
19C2×#66896C411yescharacteristic
20#10622820—21no—
21#10622739—21no—
22C4×#4323C411yescharacteristic
23C4×#4323C411yescharacteristic
24C4×#4323C411yescharacteristic
25C4×#4323C411yescharacteristic
26C4×#4323C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29C4×#4323C2211yescharacteristic
30#10622625C2212yescomplemented
31#10622624—22no—
32D4×C11⋊C8C2212yescomplemented
33C2×#66873C411yescharacteristic
34C2×#66871C411yescharacteristic
35#10622537C2211yescharacteristic
36C4×#4318C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622451C2212yescomplemented
39#10622449—22no—
40#10622447C2212yescomplemented
41C11×D4⋊C8C2212yescomplemented
42C11×D4⋊C8C2212yescomplemented
43#10622117C2212yescomplemented
44#10622117C2212yescomplemented
45#10622097C2212yescomplemented
46#10622097C2212yescomplemented
47#10622092C2212yescomplemented
48C8×C11⋊C8C2212yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C22×D44C2×C411yescharacteristic
52C22×C4×D11—21no—
53C2×C11×M16—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11C2×C411yescharacteristic
57C4×D4×C11C2×C411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4323—24no—
64C2×#4323C2×C411yescharacteristic
65C2×#4323C2×C411yescharacteristic
66C2×#4323C2×C411yescharacteristic
67C2×#4323C2×C411yescharacteristic
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×#4318—21no—
71C2×#4318—22no—
72C2×#4318—44no—
73C2×#4318D411yescharacteristic
74C2×#4318D411yescharacteristic
75C22×C11⋊C8—22no—
76C22×C11⋊C8C2×C411yescharacteristic
77C22×C11⋊C8C2×C411yescharacteristic
78M16×D11—44no—
79C2×#4313—22no—
80C2×C8×D11—22no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44C2×C411yescharacteristic
84C4×D44C2×C411yescharacteristic
85C4×D44C2311yescharacteristic
86C4×D44C2311yescharacteristic
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×C22⋊C8—21no—
91C4×C8×C11C2312yes—
92#66896C2×C411yescharacteristic
93#66896C2×C411yescharacteristic
94#66896C2×C411yescharacteristic
95#66896C2×C411yescharacteristic
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)—22no—
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—22no—
100#66873C2×C411yescharacteristic
101#66873C2×C411yescharacteristic
102#66873C2×C411yescharacteristic
103#66873C2×C411yescharacteristic
104#66871C2×C411yescharacteristic
105#66871C2×C411yescharacteristic
106#66871C2×C411yescharacteristic
107#66871C2×C411yescharacteristic
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)C2312yes—
110#66867D412yes—
111C4×C11⋊C8C2×C411yescharacteristic
112C4×C11⋊C8C2×C411yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114C4×C11⋊C8C2311yescharacteristic
115C4×C11⋊C8C2312yes—
116M16×D8—111nomaximal, Sylow
117C24×C11—21no—
118C23×D11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11C22×C411yescharacteristic
123C2×D4×C11C22×C411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C22×Dic11—21no—
135C2×D44—22no—
136C2×D44—21no—
137C2×D44—41no—
138C2×D44C22×C411yescharacteristic
139C2×D44C22×C411yescharacteristic
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C11×M16—42no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C22×C411yescharacteristic
151C11×C4⋊C4C22×C411yescharacteristic
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C42×C11C22×C411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11#4111yescharacteristic
159C42×C11C2411yescharacteristic
160#4323—22no—
161#4323—22no—
162#4323—22no—
163#4323M1614yescomplemented
164(C2×D11)⋊C4—21no—
165(C2×D11)⋊C4—21no—
166(C2×D11)⋊C4—21no—
167(C2×D11)⋊C4—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11C22×C411yescharacteristic
170C4⋊Dic11C22×C411yescharacteristic
171#4318—22no—
172#4318—44no—
173#4318—42no—
174#4318D814yescomplemented
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—41no—
178C2×C11⋊C8—44no—
179C2×C11⋊C8C22×C411yescharacteristic
180C2×C11⋊C8C22×C411yescharacteristic
181C2×C11⋊C8C22×C411yescharacteristic
182C2×C11⋊C8C22×C411yescharacteristic
183C2×C11⋊C8C2×D412yes—
184C2×C11⋊C8C2×D412yes—
185#4313—44no—
186C8×D11—44no—
187C2×C4×D8—111no—
188D4×M16—111no—
189D4×M16—111no—
190#1589—112no—
191#1581—112no—
192#1581—112no—
193C8×D8—112no—
194#1567—111no—
195#1486—111no—
196#1486D1111yescharacteristic, complemented
197C8×M16—111no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—81no—
203C23×C11C4×D411yescharacteristic
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—81no—
209D4×C11—21no—
210D4×C11—21no—
211D4×C11—21no—
212D4×C11—42no—
213D4×C11C2×M1612yescomplemented
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C2×D812yes—
230C2×C4×C11#13512yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—42no—
237D44—21no—
238D44—21no—
239D44—21no—
240D44—42no—
241D44C2×M1612yescomplemented
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—41no—
246C4×D11—42no—
247C4×D11—42no—
248C8×C11—42no—
249C8×C11—42no—
250C11⋊C8—21no—
251C11⋊C8—21no—
252C11⋊C8—21no—
253C11⋊C8—22no—
254C11⋊C8—42no—
255C11⋊C8C2×M1612yescomplemented
256C11⋊C8C2×D814yescomplemented
257C22×D8—111no—
258C22×M16—221no—
259C22×M16—221no—
260C2×C4×D4—111no—
261C2×C4×D4C2×D1111yescharacteristic
262C4×D8—111no—
263C4×D8—111no—
264C4×D8—111no—
265C4×D8—111no—
266C4×D8—111no—
267C4×D8—111no—
268C4×D8—111no—
269C4×D8—111no—
270#436—112no—
271#436—112no—
272#435—222no—
273#435—222no—
274C8×D4—112no—
275C8×D4—112no—
276#431C2×D1111yescharacteristic
277C2×#107—111no—
278#423—111no—
279#423C2×D1111yescharacteristic
280C2×#102—111no—
281C2×#102—111no—
282#407—221no—
283#407—221no—
284C4×M16—111no—
285C2×C4×C8—111no—
286#335—112no—
287#335—112no—
288D4⋊C8—112no—
289D4⋊C8—112no—
290D4⋊C8C2×D1112yescomplemented
291D4⋊C8C2×D1112yescomplemented
292#322—112no—
293C82—112no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—22no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—84no—
303C22×C11C4×D812yes—
304C22×C11C2×C4×D411yescharacteristic
305C2×D11—22no—
306C2×D11—41no—
307C2×D11—41no—
308C2×D11—41no—
309C2×D11—41no—
310C2×D11—41no—
311C2×D11—84no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11C4×D812yes—
318C4×C11C22×M1611yescharacteristic
319C4×C11#56811yescharacteristic
320C4×C11C22×D811yescharacteristic
321C4×C11C2×#13511yescharacteristic
322Dic11—41no—
323Dic11—41no—
324C22×D4—111no—
325C22×D4C4×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—221no—
328C2×D8—111no—
329C2×D8—111no—
330C2×D8—111no—
331C2×D8—111no—
332C2×D8—224no—
333C2×M16—21no—
334C2×M16—111no—
335C2×M16—111no—
336C2×M16—222no—
337C2×M16—222no—
338C2×M16—221no—
339C2×M16—444no—
340C2×M16—444no—
341C22×C8—111no—
342C22×C8—111no—
343C22×C8—222no—
344C22×C8—222no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—111no—
348C4×D4—111no—
349C4×D4—111no—
350C4×D4—111no—
351C4×D4—221no—
352C4×D4—221no—
353C4×D4C4×D1111yescharacteristic
354C4×D4C4×D1111yescharacteristic
355C4×D4C22×D1111yescharacteristic
356C4×D4C22×D1111yescharacteristic
357C2×C4⋊C4—111no—
358C2×C4⋊C4C4×D1111yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—221no—
361C2×C42C22×D1111yescharacteristic
362#107—111no—
363#107—111no—
364#107—111no—
365#107—111no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—112no—
369C4⋊C8—221no—
370C4⋊C8C22×D1112yes—
371#102—111no—
372#102—111no—
373#102—111no—
374#102—111no—
375#102—111no—
376#102—111no—
377#102—111no—
378#102—111no—
379C22⋊C8—21no—
380C22⋊C8—222no—
381C22⋊C8—222no—
382C22⋊C8—222no—
383C22⋊C8—222no—
384#97—112no—
385C4×C8—111no—
386C4×C8—111no—
387C4×C8—111no—
388C4×C8—112no—
389C4×C8—111no—
390C4×C8C22×D1112yes—
391C2×C11—22no—
392C2×C11—42no—
393C2×C11—81no—
394C2×C11D4×M1611yescharacteristic
395C2×C11C2×C4×D811yescharacteristic
396C2×C11#295711yescharacteristic
397D11—42no—
398D11—81no—
399C24—21no—
400C24—221no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—41no—
404C2×D4—111no—
405C2×D4—111no—
406C2×D4—222no—
407C2×D4—221no—
408C2×D4—441no—
409C2×D4C2×C4×D1111yescharacteristic
410C2×D4C2×C4×D1111yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4C2×C4×D1111yescharacteristic
426C22×C4D4×D1111yescharacteristic
427C22×C4#434111yescharacteristic
428D8—114no—
429D8—222no—
430D8—222no—
431D8—222no—
432M16—42no—
433M16—114no—
434M16—222no—
435M16—444no—
436M16—444no—
437M16—442no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—111no—
441C2×C8—112no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—112no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—444no—
449C2×C8—444no—
450C2×C8—441no—
451C4⋊C4—21no—
452C4⋊C4—111no—
453C4⋊C4—111no—
454C4⋊C4—221no—
455C4⋊C4C2×C4×D1111yescharacteristic
456C4⋊C4C2×C4×D1111yescharacteristic
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—221no—
462C22⋊C4—221no—
463C22⋊C4—221no—
464C22⋊C4—221no—
465C42C2×C4×D1111yescharacteristic
466C42D4×D1111yescharacteristic
467C42#434111yescharacteristic
468C42C23×D1111yescharacteristic
469C11M16×D811yescharacteristic, complemented, Sylow
470C23—21no—
471C23—21no—
472C23—42no—
473C23—42no—
474C23—81no—
475C23—221no—
476C23—221no—
477C23—442no—
478C23—442no—
479C23—881no—
480C23(C22⋊D11)⋊C411yescharacteristic
481D4—21no—
482D4—21no—
483D4—21no—
484D4—42no—
485D4—112no—
486D4—221no—
487D4—221no—
488D4—221no—
489D4—442no—
490D4M16×D1112yescomplemented
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—442no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4(C22⋊D11)⋊C411yescharacteristic
513C2×C4(C22⋊D11)⋊C411yescharacteristic
514C2×C4(C22⋊D11)⋊C411yescharacteristic
515C2×C4D8×D1112yes—
516C2×C4#6696912yes—
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×#434111yescharacteristic
520C8—42no—
521C8—42no—
522C8—112no—
523C8—114no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—222no—
528C8—442no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—84no—
538C22—222no—
539C22—441no—
540C22—441no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22—884no—
545C22#1062236912yes—
546C22C2×(C22⋊D11)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—441no—
553C4—441no—
554C4#1062236912yes—
555C4C2×M16×D1111yescharacteristic
556C4#1062327611yescharacteristic
557C4C2×D8×D1111yescharacteristic
558C4C2×#6696911yescharacteristic
559C2—22no—
560C2—42no—
561C2—81no—
562C2—442no—
563C2—881no—
564C2#1307734811yescharacteristic
565C2C2×#1062236911yescharacteristic
566C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C2×C4×D4
prime radicalC22×#4323C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11M16×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. #13077351C2semidirect
4. #13067498C2semidirect
5. #13067448C2semidirect
6. #13067442C2semidirect
7. #13067408C2semidirect
8. #13067374C2semidirect
9. #13067042C2semidirect
10. #13066897C2semidirect
11. C11×#1486C2semidirect
30. #10622625C22semidirect
32. D4×C11⋊C8C22semidirect
38. #10622451C22semidirect
40. #10622447C22semidirect
41. C11×D4⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
43. #10622117C22semidirect
44. #10622117C22semidirect
45. #10622097C22semidirect
46. #10622097C22semidirect
47. #10622092C22semidirect
48. C8×C11⋊C8C22semidirect
163. #4323M16semidirect
174. #4318D8semidirect
196. #1486D11semidirect
213. D4×C11C2×M16semidirect
241. D44C2×M16semidirect
255. C11⋊C8C2×M16semidirect
256. C11⋊C8C2×D8semidirect
290. D4⋊C8C2×D11semidirect
291. D4⋊C8C2×D11semidirect
469. C11M16×D8semidirect
490. D4M16×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
D4×#43182
#130773512
#130674982
#130674482
#130674422
#130674082
#130673742
#130670422
#130668972
C11×#14862
M16×D811