Finite Group Databasebeta

← #14725285

Subgroups — #14725285

Order 2816.

786 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
2M16×D44C211yesmaximal, characteristic, complemented
3#13067528C212yesmaximal, complemented
4#13067480C212yesmaximal, complemented
5#13067478C212yesmaximal, complemented
6#13067438C212yesmaximal, complemented
7#13067371C211yesmaximal, characteristic, complemented
8#13067041C211yesmaximal, characteristic, complemented
9#13067040C211yesmaximal, characteristic, complemented
10#13066903C211yesmaximal, characteristic, complemented
11D4×C11×M16C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4323C411yescharacteristic
15C2×M16×D11—21no—
16C2×C4×D44C2211yescharacteristic
17C11×#436C2212yescomplemented
18C11×#435—22no—
19C8×D4×C11C2212yescomplemented
20C11×#423C2211yescharacteristic
21C11×#407—21no—
22C4×C11×M16C2211yescharacteristic
23C2×#66896C411yescharacteristic
24#10622739—21no—
25C4×#4323C411yescharacteristic
26C4×#4323C411yescharacteristic
27C4×#4323C411yescharacteristic
28C4×#4323C411yescharacteristic
29C4×#4323C2211yescharacteristic
30C4×#4323C2211yescharacteristic
31C4×#4323C2211yescharacteristic
32C4×#4323C2211yescharacteristic
33C2×#66873C411yescharacteristic
34C2×#66871C411yescharacteristic
35#10622538C2211yescharacteristic
36#10622537C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622319—22no—
39#10622301C2212yescomplemented
40C8×D44C2212yescomplemented
41D4⋊(C11⋊C8)C2212yescomplemented
42D4⋊(C11⋊C8)C2212yescomplemented
43#10622121C2212yescomplemented
44#10622121C2212yescomplemented
45#10622118C2212yescomplemented
46#10622118C2212yescomplemented
47#10622092C2212yescomplemented
48#10622092C2212yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C22×D44C2×C411yescharacteristic
52C22×C4×D11—21no—
53C2×C11×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—44no—
56C2×C11×M16D411yescharacteristic
57C2×C11×M16D411yescharacteristic
58C22×C8×C11—22no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11C2311yescharacteristic
64C4×D4×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4323—24no—
69C2×#4323C2×C411yescharacteristic
70C2×#4323C2×C411yescharacteristic
71C2×#4323C2×C411yescharacteristic
72C2×#4323C2×C411yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×#4318—21no—
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⋊C8C2312yes—
89C11×C22⋊C8—22no—
90C11×C22⋊C8—22no—
91C11×#97D412yes—
92C4×C8×C11C2312yes—
93#66896C2×C411yescharacteristic
94#66896C2×C411yescharacteristic
95#66896C2×C411yescharacteristic
96#66896C2×C411yescharacteristic
97C22⋊(C11⋊C8)—21no—
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)—21no—
110C4⋊(C11⋊C8)C2312yes—
111C4×C11⋊C8C2×C411yescharacteristic
112C4×C11⋊C8C2×C411yescharacteristic
113C4×C11⋊C8C2312yes—
114C4×C11⋊C8C2311yescharacteristic
115C4×C11⋊C8C2311yescharacteristic
116#18044—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—22no—
147C11×M16—22no—
148C11×M16—44no—
149C11×M16—42no—
150C2×C8×C11—22no—
151C2×C8×C11—44no—
152C2×C8×C11C2×D412yes—
153C2×C8×C11C2×D412yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C22×C411yescharacteristic
156C11×C4⋊C4C22×C411yescharacteristic
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—21no—
160C11×C22⋊C4—21no—
161C42×C11C22×C411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11#4111yescharacteristic
164C42×C11C2411yescharacteristic
165#4323—22no—
166#4323—22no—
167#4323—22no—
168#4323M1614yescomplemented
169(C2×D11)⋊C4—21no—
170(C2×D11)⋊C4—21no—
171(C2×D11)⋊C4—21no—
172(C2×D11)⋊C4—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11C22×C411yescharacteristic
175C4⋊Dic11C22×C411yescharacteristic
176#4318—42no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—41no—
181C2×C11⋊C8C22×C411yescharacteristic
182C2×C11⋊C8C22×C411yescharacteristic
183C2×C11⋊C8C22×C411yescharacteristic
184C2×C11⋊C8C22×C411yescharacteristic
185#4313—44no—
186C8×D11—44no—
187C2×C4×D8—111no—
188D4×M16—111no—
189D4×M16D1111yescharacteristic, complemented
190#1594—112no—
191#1586—112no—
192#1586—112no—
193#1580—112no—
194#1566—111no—
195#1486—111no—
196#1486—111no—
197#1451—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×C11AGL(1,ℤ/8)12yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
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—22no—
249C8×C11—22no—
250C8×C11—42no—
251C11⋊C8—21no—
252C11⋊C8—21no—
253C11⋊C8—21no—
254C11⋊C8—42no—
255C11⋊C8—42no—
256C11⋊C8C2×M1612yescomplemented
257C22×D8—111no—
258C22×M16—21no—
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#436C2×D1112yescomplemented
272#435—22no—
273#435—222no—
274C8×D4—112no—
275C8×D4C2×D1112yescomplemented
276#431—111no—
277C2×#107—111no—
278#423—111no—
279#423C2×D1111yescharacteristic
280C2×#102—111no—
281C2×#102—111no—
282#407—21no—
283#407—221no—
284C4×M16C2×D1111yescharacteristic
285C2×C4×C8—111no—
286#334—112no—
287#334—112no—
288D4⋊C8—112no—
289D4⋊C8—112no—
290D4⋊C8—112no—
291D4⋊C8—112no—
292#322—112no—
293#322—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×C11#44212yes—
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×C11#44212yes—
318C4×C11C22×M1611yescharacteristic
319C4×C11#56811yescharacteristic
320C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
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—22no—
335C2×M16—44no—
336C2×M16—221no—
337C2×M16—222no—
338C2×M16—444no—
339C2×M16C22⋊D1111yescharacteristic
340C2×M16C22⋊D1111yescharacteristic
341C22×C8—22no—
342C22×C8—111no—
343C22×C8—111no—
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—112no—
368C4⋊C8—221no—
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—22no—
380C22⋊C8—22no—
381C22⋊C8—221no—
382C22⋊C8—222no—
383C22⋊C8—222no—
384#97C22⋊D1112yes—
385C4×C8—111no—
386C4×C8—111no—
387C4×C8—111no—
388C4×C8—111no—
389C4×C8—112no—
390C4×C8C22×D1112yes—
391C2×C11—22no—
392C2×C11—42no—
393C2×C11—81no—
394C2×C11D4×M1611yescharacteristic
395C2×C11C2×#44211yescharacteristic
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×C4#433911yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428D8—114no—
429D8—222no—
430D8—222no—
431D8—222no—
432M16—22no—
433M16—22no—
434M16—44no—
435M16—42no—
436M16—444no—
437M16—442no—
438C2×C8—22no—
439C2×C8—44no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8—222no—
447C2×C8—444no—
448C2×C8—441no—
449C2×C8C2×C22⋊D1112yes—
450C2×C8C2×C22⋊D1112yes—
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
466C42#433911yescharacteristic
467C42C2×C22⋊D1111yescharacteristic
468C42C23×D1111yescharacteristic
469C11#1804411yescharacteristic, complemented, Sylow
470C23—21no—
471C23—21no—
472C23—42no—
473C23—42no—
474C23—81no—
475C23—221no—
476C23—221no—
477C23—442no—
478C23—442no—
479C23—881no—
480C23C4×C22⋊D1111yescharacteristic
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×C4C4×C22⋊D1111yescharacteristic
513C2×C4C4×C22⋊D1111yescharacteristic
514C2×C4C4×C22⋊D1111yescharacteristic
515C2×C4#6698512yes—
516C2×C4#6700212yes—
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×#433911yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—22no—
521C8—22no—
522C8—42no—
523C8—112no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—442no—
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#1062262712yes—
546C22C2×C4×C22⋊D1111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—441no—
553C4—441no—
554C4#1062262712yes—
555C4C2×M16×D1111yescharacteristic
556C4#1062327611yescharacteristic
557C4C2×#6698511yescharacteristic
558C4C2×#6700211yescharacteristic
559C2—22no—
560C2—42no—
561C2—81no—
562C2—442no—
563C2—881no—
564C2M16×C22⋊D1111yescharacteristic
565C2C2×#1062262711yescharacteristic
566C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC22×#4323C4
cosocleC42×C11C24
hypercenterD4×M16D11
hypocenterC11#18044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. M16×D44C2semidirect
3. #13067528C2semidirect
4. #13067480C2semidirect
5. #13067478C2semidirect
6. #13067438C2semidirect
7. #13067371C2semidirect
8. #13067041C2semidirect
9. #13067040C2semidirect
10. #13066903C2semidirect
11. D4×C11×M16C2semidirect
17. C11×#436C22semidirect
19. 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. #10622118C22semidirect
47. #10622092C22semidirect
48. #10622092C22semidirect
168. #4323M16semidirect
189. D4×M16D11semidirect
213. D4×C11C2×M16semidirect
241. D44C2×M16semidirect
256. C11⋊C8C2×M16semidirect
271. #436C2×D11semidirect
275. C8×D4C2×D11semidirect
469. C11#18044semidirect
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
M16×D442
#130675282
#130674802
#130674782
#130674382
#130673712
#130670412
#130670402
#130669032
D4×C11×M162
#1804411