Finite Group Databasebeta

← #14725253

Subgroups — #14725253

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×Dic22C211yesmaximal, characteristic, complemented
2C2×C4×#4314C211yesmaximal, characteristic
3M16×D44C211yesmaximal, characteristic
4#13067520C212yesmaximal, complemented
5#13067496C212yesmaximal, complemented
6#13067475C212yesmaximal, complemented
7#13067430C212yesmaximal, complemented
8#13067375C211yesmaximal, characteristic, complemented
9#13067046C211yesmaximal, characteristic, complemented
10#13067042C211yesmaximal, characteristic
11C11×#1451C211yesmaximal, characteristic, complemented
12C2×M16×D11—21no—
13C22×#4314C411yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C4×C11×M16C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19#10622739—21no—
20#10622731—21no—
21M16×Dic11—21no—
22C2×#66885C411yescharacteristic
23C2×#66881C411yescharacteristic
24C2×#66880C411yescharacteristic
25#10622537C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622319—22no—
28#10622314—22no—
29C4×#4314C411yescharacteristic
30C4×#4314C411yescharacteristic
31C4×#4314C411yescharacteristic
32C4×#4314C411yescharacteristic
33C4×#4314C2211yescharacteristic
34C4×#4314C2211yescharacteristic
35C4×#4314C2211yescharacteristic
36C4×#4314C2211yescharacteristic
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622292C2212yescomplemented
40C8×Dic22C2212yescomplemented
41C11×#322C2212yescomplemented
42C11×#322C2212yescomplemented
43#10622097C2212yes—
44#10622097C2212yes—
45#10622096C2212yescomplemented
46#10622096C2212yescomplemented
47#10622094C2212yescomplemented
48#10622094C2212yescomplemented
49C22×D44C2×C411yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22C2×C411yescharacteristic
52C2×C11×M16D411yescharacteristic
53C2×C11×M16D411yescharacteristic
54C22×C8×C11C2×C411yescharacteristic
55C22×C8×C11C2×C411yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×Dic11⋊C4—21no—
61C2×C4×Dic11—21no—
62C2×#4318—21no—
63C2×#4318—21no—
64M16×D11—44no—
65C2×#4314—24no—
66C2×#4314C2×C411yescharacteristic
67C2×#4314C2×C411yescharacteristic
68C2×#4314C2×C411yescharacteristic
69C2×#4314C2×C411yescharacteristic
70C2×#4313—22no—
71C2×C8×D11—22no—
72C4×D44—21no—
73C4×D44—21no—
74C4×D44C2×C411yescharacteristic
75C4×D44C2×C411yescharacteristic
76C4×D44C2311yescharacteristic
77C4×D44C2311yescharacteristic
78C4×Dic22—21no—
79C4×Dic22—21no—
80C4×Dic22C2×C411yescharacteristic
81C4×Dic22C2×C411yescharacteristic
82C4×Dic22C2311yescharacteristic
83C4×Dic22C2311yescharacteristic
84C11×C4⋊C8—21no—
85C11×C22⋊C8—21no—
86C11×#97D412yes—
87C4×C8×C11C2×C411yescharacteristic
88C4×C8×C11C2×C411yescharacteristic
89C4×C8×C11C2312yes—
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92C4×C8×C11C2312yes—
93#66885C2×C411yescharacteristic
94#66885C2×C411yescharacteristic
95#66885C2×C411yescharacteristic
96#66885C2×C411yescharacteristic
97(C2×D11)⋊C8—22no—
98(C2×D11)⋊C8—22no—
99#66881C2×C411yescharacteristic
100#66881C2×C411yescharacteristic
101#66881C2×C411yescharacteristic
102#66881C2×C411yescharacteristic
103#66880C2×C411yescharacteristic
104#66880C2×C411yescharacteristic
105#66880C2×C411yescharacteristic
106#66880C2×C411yescharacteristic
107#66879—22no—
108Dic11⋊C8—22no—
109Dic11⋊C8—22no—
110C8×Dic11—22no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)—21no—
113C4⋊(C11⋊C8)C2312yes—
114C4⋊(C11⋊C8)C2312yes—
115#18040—111nomaximal, Sylow
116C23×D11—21no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C2×D44—22no—
124C2×D44—21no—
125C2×D44—41no—
126C2×D44C22×C411yescharacteristic
127C2×D44C22×C411yescharacteristic
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×Dic22—22no—
135C2×Dic22—21no—
136C2×Dic22—41no—
137C2×Dic22C22×C411yescharacteristic
138C2×Dic22C22×C411yescharacteristic
139C11×M16—22no—
140C11×M16—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—41no—
144C2×C8×C11C22×C411yescharacteristic
145C2×C8×C11C22×C411yescharacteristic
146C2×C8×C11C22×C411yescharacteristic
147C2×C8×C11C22×C411yescharacteristic
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
150C42×C11C22×C411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154(C2×D11)⋊C4—21no—
155(C2×D11)⋊C4—21no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11C22×C411yescharacteristic
161C4⋊Dic11C22×C411yescharacteristic
162C4⋊Dic11C22×C411yescharacteristic
163C4⋊Dic11C22×C411yescharacteristic
164Dic11⋊C4—21no—
165Dic11⋊C4—21no—
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C4×Dic11—21no—
172#4318—42no—
173#4318—42no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176#4314—22no—
177#4314—22no—
178#4314—22no—
179#4314M1614yescomplemented
180#4313—44no—
181C8×D11—44no—
182Q8×M16—111no—
183C2×C4×SD16—111no—
184D4×M16—111no—
185#1592—112no—
186#1588—112no—
187#1585—112no—
188SD16⋊C8—112no—
189#1567—111no—
190#1487—111no—
191#1486—111no—
192#1451D1111yescharacteristic, complemented
193C23×C11C4×D411yescharacteristic
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—81no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11C4×D411yescharacteristic
203C2×C4×C11C4×D411yescharacteristic
204C2×C4×C11C4×D411yescharacteristic
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11#13712yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—81no—
219D44—21no—
220D44—21no—
221D44—21no—
222D44—42no—
223D44C2×M1612yes—
224C4×D11—41no—
225C4×D11—41no—
226C4×D11—41no—
227C4×D11—41no—
228C4×D11—42no—
229C4×D11—42no—
230Dic22—21no—
231Dic22—21no—
232Dic22—21no—
233Dic22—42no—
234Dic22C2×M1612yescomplemented
235C8×C11—21no—
236C8×C11—21no—
237C8×C11—21no—
238C8×C11—22no—
239C8×C11—22no—
240C8×C11—42no—
241C8×C11C2×M1612yescomplemented
242C11⋊C8—42no—
243C11⋊C8—42no—
244C22×SD16—111no—
245C22×M16—221no—
246C2×C4×Q8—111no—
247C2×C4×D4—111no—
248#446—112no—
249#446—222no—
250C8×Q8—112no—
251C4×SD16—111no—
252C4×SD16—111no—
253C4×SD16—111no—
254C4×SD16—111no—
255C4×SD16—111no—
256C4×SD16—111no—
257C4×SD16—111no—
258C4×SD16—111no—
259#436—112no—
260#435—222no—
261C8×D4—112no—
262#431C2×D1111yescharacteristic
263C2×#106—111no—
264#423—111no—
265#423—111no—
266#423—221no—
267C2×#103—111no—
268C2×#102—111no—
269#407—221no—
270C4×M16—221no—
271C4×M16C2×D1111yescharacteristic
272C2×C4×C8C2×D1111yescharacteristic
273#335—112no—
274#335—112no—
275Q8⋊C8—112no—
276Q8⋊C8—112no—
277D4⋊C8—112no—
278D4⋊C8—112no—
279#322C2×D1112yescomplemented
280#322C2×D1112yescomplemented
281C22×C11—21no—
282C22×C11—21no—
283C22×C11#44012yes—
284C22×C11C2×C4×D411yescharacteristic
285C2×D11—22no—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C2×D11—41no—
290C2×D11—41no—
291C2×D11—84no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11#44012yes—
296C4×C11C22×M1611yescharacteristic
297C4×C11#56811yescharacteristic
298C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C11C2×#13711yescharacteristic
300Dic11—22no—
301Dic11—41no—
302Dic11—41no—
303Dic11—41no—
304Dic11—41no—
305Dic11—41no—
306C22×Q8—111no—
307C22×D4—111no—
308C23×C4—221no—
309C2×SD16—111no—
310C2×SD16—111no—
311C2×SD16—111no—
312C2×SD16—111no—
313C2×SD16—224no—
314C2×M16—221no—
315C2×M16—221no—
316C2×M16—222no—
317C2×M16—444no—
318C2×M16D4411yescharacteristic
319C2×M16D4411yescharacteristic
320C22×C8—222no—
321C22×C8C4×D1111yescharacteristic
322C22×C8C4×D1111yescharacteristic
323C4×Q8—111no—
324C4×Q8—111no—
325C4×Q8—111no—
326C4×Q8—111no—
327C4×Q8—221no—
328C4×Q8—221no—
329C4×D4—111no—
330C4×D4—111no—
331C4×D4—111no—
332C4×D4—111no—
333C4×D4—221no—
334C4×D4—221no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C42—221no—
340C2×C42C22×D1111yescharacteristic
341#106—111no—
342#106—111no—
343#106—111no—
344#106—111no—
345C4⋊C8—21no—
346C4⋊C8—112no—
347C4⋊C8—112no—
348C4⋊C8—222no—
349C4⋊C8—222no—
350C4⋊C8—221no—
351C4⋊C8—221no—
352#103—111no—
353#103—111no—
354#103—111no—
355#103—111no—
356#102—111no—
357#102—111no—
358#102—111no—
359#102—111no—
360C22⋊C8—21no—
361C22⋊C8—222no—
362C22⋊C8—222no—
363#97—222no—
364#97D4412yes—
365C4×C8—222no—
366C4×C8C4×D1111yescharacteristic
367C4×C8C4×D1111yescharacteristic
368C4×C8C22×D1112yes—
369C4×C8C22×D1111yescharacteristic
370C4×C8C22×D1111yescharacteristic
371C4×C8C22×D1112yes—
372C2×C11—22no—
373C2×C11D4×M1611yescharacteristic
374C2×C11C2×#44011yescharacteristic
375C2×C11#295711yescharacteristic
376D11—42no—
377D11—81no—
378C24—221no—
379C2×Q8—111no—
380C2×Q8—111no—
381C2×Q8—222no—
382C2×Q8—221no—
383C2×Q8—441no—
384C2×D4—111no—
385C2×D4—111no—
386C2×D4—222no—
387C2×D4—221no—
388C2×D4—441no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4C2×C4×D1111yescharacteristic
399C22×C4C2×D4411yescharacteristic
400C22×C4#433911yescharacteristic
401SD16—114no—
402SD16—222no—
403SD16—222no—
404SD16—222no—
405M16—22no—
406M16—22no—
407M16—444no—
408M16—442no—
409M16—442no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—41no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—444no—
416C2×C8C2×C4×D1111yescharacteristic
417C2×C8C2×C4×D1111yescharacteristic
418C2×C8C2×C4×D1111yescharacteristic
419C2×C8C2×C4×D1111yescharacteristic
420C2×C8C2×D4412yes—
421C2×C8C2×D4412yes—
422C4⋊C4—111no—
423C4⋊C4—111no—
424C4⋊C4—111no—
425C4⋊C4—111no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C22⋊C4—221no—
433C22⋊C4—221no—
434C22⋊C4—221no—
435C22⋊C4—221no—
436C42—221no—
437C42—221no—
438C42—221no—
439C42—221no—
440C42C2×C4×D1111yescharacteristic
441C42C2×D4411yescharacteristic
442C42#433911yescharacteristic
443C42C23×D1111yescharacteristic
444C11#1804011yescharacteristic, complemented, Sylow
445C23—221no—
446C23—221no—
447C23—442no—
448C23—442no—
449C23—881no—
450C23C4×D4411yescharacteristic
451Q8—112no—
452Q8—221no—
453Q8—221no—
454Q8—221no—
455Q8—442no—
456D4—112no—
457D4—221no—
458D4—221no—
459D4—221no—
460D4—442no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—881no—
479C2×C4C4×D4411yescharacteristic
480C2×C4C4×D4411yescharacteristic
481C2×C4C4×D4411yescharacteristic
482C2×C4#6696112yes—
483C2×C4#6696212yes—
484C2×C4C22×C4×D1111yescharacteristic
485C2×C4C22×D4411yescharacteristic
486C2×C4C2×#433911yescharacteristic
487C8—21no—
488C8—21no—
489C8—21no—
490C8—22no—
491C8—22no—
492C8—42no—
493C8—442no—
494C8—442no—
495C8M16×D1112yescomplemented
496C22—21no—
497C22—21no—
498C22—222no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22—441no—
503C22—441no—
504C22—884no—
505C22#1062232312yes—
506C22C2×C4×D4411yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—222no—
511C4—441no—
512C4—441no—
513C4—441no—
514C4—441no—
515C4—441no—
516C4#1062232312yes—
517C4C2×M16×D1111yescharacteristic
518C4#1062327611yescharacteristic
519C4C2×#6696111yescharacteristic
520C4C2×#6696211yescharacteristic
521C2—22no—
522C2—442no—
523C2—881no—
524C2M16×D4411yescharacteristic
525C2C2×#1062232311yescharacteristic
526C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1451C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1451D11
hypocenterC11#18040
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1451

Complements

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

NH ≅ G/Ntype
1. M16×Dic22C2semidirect
4. #13067520C2semidirect
5. #13067496C2semidirect
6. #13067475C2semidirect
7. #13067430C2semidirect
8. #13067375C2semidirect
9. #13067046C2semidirect
11. C11×#1451C2semidirect
39. #10622292C22semidirect
40. C8×Dic22C22semidirect
41. C11×#322C22semidirect
42. C11×#322C22semidirect
45. #10622096C22semidirect
46. #10622096C22semidirect
47. #10622094C22semidirect
48. #10622094C22semidirect
179. #4314M16semidirect
192. #1451D11semidirect
234. Dic22C2×M16semidirect
241. C8×C11C2×M16semidirect
279. #322C2×D11semidirect
280. #322C2×D11semidirect
444. C11#18040semidirect
495. C8M16×D11semidirect

Maximal subgroups

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

subgroupindex
M16×Dic222
C2×C4×#43142
M16×D442
#130675202
#130674962
#130674752
#130674302
#130673752
#130670462
#130670422
C11×#14512
#1804011