Finite Group Databasebeta

← SD16×C4⋊Dic11 #14772176

Subgroups — SD16×C4⋊Dic11 #14772176

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C212yesmaximal
2Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic11C211yesmaximal, characteristic
4#13069345C212yesmaximal, complemented
5#13068886C212yesmaximal, complemented
6#13068879C212yesmaximal
7#13068773C211yesmaximal, characteristic, complemented
8#13068621C211yesmaximal, characteristic, complemented
9#13068616C211yesmaximal, characteristic
10C8×C4⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C4×C11×SD16C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×D4×Dic11C2212yes—
17C22×C4⋊Dic11—21no—
18C4×C11×SD16C418yescomplemented
19C2×C11×#106C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66896C2212yes—
25#10622825—21no—
26SD16×Dic11—28no—
27C2×#66881C2212yes—
28C2×#66881C2212yes—
29C2×C8×Dic11C2212yes—
30#10622598—22no—
31#10622598C2212yes—
32#10622598C2212yes—
33#10622563—22no—
34#10622548—21no—
35#10622548C2211yescharacteristic
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C2×C11×SD16C2×C414yes—
48C2×C11×SD16D414yes—
49C2×C11×SD16Q814yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11C2×C414yescomplemented
54C4×D4×C11—22no—
55C4×D4×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63Q8×Dic11—24no—
64Q8×Dic11—42no—
65D4×Dic11—24no—
66D4×Dic11—42no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—44no—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2312yes—
79C2×C4×Dic11—22no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2312yes—
82C11×#106C2×C414yescomplemented
83C11×#103C2×C414yescomplemented
84C11×#102C2×C414yes—
85C4×C8×C11C2×C414yescomplemented
86#66899—24no—
87#66896—24no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95D412yes—
91#66881—24no—
92#66881—42no—
93C8×Dic11—24no—
94C4⋊(C11⋊C8)—22no—
95C4⋊C4×SD16—111nomaximal, Sylow
96C24×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11C22×C412yes—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C22×C412yes—
107C2×D4×C11C2×D412yes—
108C2×D4×C11C2×Q812yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—44no—
121C22×Dic11—44no—
122C22×Dic11—82no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C11×SD16C4⋊C4116yescomplemented
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C2×D412yes—
131C2×C8×C11C2×Q812yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C22×C412yes—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C42×C11—24no—
139C42×C11C22×C412yes—
140C42×C11#4112yes—
141C22⋊Dic11—44no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—44no—
148C4⋊Dic11—44no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4⋊Dic11—81no—
152C4⋊Dic11—81no—
153C4⋊Dic11—82no—
154C4⋊Dic11SD1614yesdirect product factor
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—44no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C4×SD16—112no—
162C2×C4×SD16D1111yescharacteristic
163Q8×C4⋊C4—111no—
164D4×C4⋊C4—111no—
165#1941—112no—
166#1865—112no—
167#1864—112no—
168#1844—111no—
169#1803—111no—
170#1802—111no—
171C8×C4⋊C4—111no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11C22×D411yescharacteristic
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11C2×C4⋊C414yescomplemented
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11C2×C4⋊C414yes—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—48no—
200C2×C4×C11C4×D412yes—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×Q811yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—88no—
222C2×Dic11C2×SD1614yes—
223C8×C11—22no—
224C8×C11C2×C4⋊C414yescomplemented
225C11⋊C8—42no—
226C22×SD16C2×D1111yescharacteristic
227C2×C4×Q8—112no—
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—112no—
230C2×C4×D4C2×D1111yescharacteristic
231C22×C4⋊C4—221no—
232C4×SD16—228no—
233C4×SD16Dic1118yescomplemented
234C2×#106—112no—
235C2×#106—112no—
236C2×#106C2×D1111yescharacteristic
237C2×C4⋊C8—111no—
238C2×#103—112no—
239C2×#103C2×D1111yescharacteristic
240C2×#102—112no—
241C2×#102C2×D1111yescharacteristic
242C2×C4×C8—112no—
243C2×C4×C8C2×D1111yescharacteristic
244#389—112no—
245#389—112no—
246#389—222no—
247#385—222no—
248#384—111no—
249#384—111no—
250#384—221no—
251#380—221no—
252C4×C4⋊C4—111no—
253C4×C4⋊C4—221no—
254#340—112no—
255#340—112no—
256#336—112no—
257C22×C11—24no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11C2×C4×D411yescharacteristic
265C22×C11D4211yescharacteristic
266C22×C11D4×Q811yescharacteristic
267C22×C11C22×SD1611yescharacteristic
268C22×C11C2×#13511yescharacteristic
269C22×C11#57711yescharacteristic
270C22×C11#57711yescharacteristic
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11C4×SD1614yescomplemented
276C4×C11C22×C4⋊C411yescharacteristic
277C4×C11#52011yescharacteristic
278C4×C11#54711yescharacteristic
279C4×C11#55411yescharacteristic
280Dic11—24no—
281Dic11—42no—
282Dic11—82no—
283Dic11—82no—
284C22×Q8C22×D1111yescharacteristic
285C22×D4C22×D1111yescharacteristic
286C23×C4—21no—
287C23×C4—222no—
288C2×SD16Dic2214yes—
289C2×SD16D4414yes—
290C2×SD16C2×Dic1114yes—
291C22×C8—112no—
292C22×C8C22×D1111yescharacteristic
293C22×C8C22×D1111yescharacteristic
294C4×Q8—22no—
295C4×Q8—224no—
296C4×Q8—442no—
297C4×Q8C2×Dic1114yescomplemented
298C4×D4—22no—
299C4×D4—224no—
300C4×D4—442no—
301C4×D4C2×Dic1114yes—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—444no—
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—222no—
319C2×C42—21no—
320C2×C42—112no—
321C2×C42—222no—
322C2×C42C22×D1111yescharacteristic
323#106—224no—
324#106—442no—
325#106C2×Dic1114yescomplemented
326C4⋊C8—222no—
327#103—224no—
328#103C2×Dic1114yescomplemented
329#102—224no—
330#102C2×Dic1114yes—
331C4×C8—224no—
332C4×C8C2×Dic1114yescomplemented
333#95—112no—
334#95—222no—
335#95—222no—
336C2×C11—44no—
337C2×C11D4×C4⋊C411yescharacteristic
338C2×C11C2×C4×SD1611yescharacteristic
339C2×C11#295211yescharacteristic
340C2×C11D4×SD1611yescharacteristic
341C2×C11#328411yescharacteristic
342C2×C11Q8×SD1611yescharacteristic
343C2×C11#338111yescharacteristic
344C24—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8C2×Dic2212yes—
349C2×Q8C2×D4412yes—
350C2×Q8C22×Dic1112yes—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C2×Dic2212yes—
355C2×D4C2×D4412yes—
356C2×D4C22×Dic1112yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—24no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—444no—
368C22×C4—444no—
369C22×C4—882no—
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4C23×D1111yescharacteristic
373SD16C4⋊Dic11116yesdirect product factor
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8C2×Dic2212yes—
380C2×C8C2×D4412yes—
381C2×C8C22×Dic1112yes—
382C2×C8C22×Dic1112yes—
383C4⋊C4—24no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—114no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—444no—
393C4⋊C4—444no—
394C4⋊C4—442no—
395C4⋊C4—442no—
396C4⋊C4—881no—
397C4⋊C4—881no—
398C4⋊C4—882no—
399C4⋊C4C22×Dic1112yes—
400C4⋊C4C22×Dic1112yes—
401C22⋊C4—24no—
402C22⋊C4—444no—
403C42—24no—
404C42—222no—
405C42—222no—
406C42—444no—
407C42#434112yes—
408C42C22×Dic1112yes—
409C11C4⋊C4×SD1611yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23C2×D4×D1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—22no—
421Q8C2×C4⋊Dic1114yescomplemented
422D4—22no—
423D4—22no—
424D4—22no—
425D4C2×C4⋊Dic1114yes—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—48no—
438C2×C4—114no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—888no—
451C2×C4SD16×D1112yes—
452C2×C4#6696912yes—
453C2×C4D4×Dic1112yes—
454C2×C4D4×Dic1112yes—
455C2×C4C22×Dic2211yescharacteristic
456C2×C4C22×D4411yescharacteristic
457C2×C4C2×#434111yescharacteristic
458C2×C4#6704211yescharacteristic
459C2×C4#6704311yescharacteristic
460C2×C4C23×Dic1111yescharacteristic
461C8—22no—
462C8—442no—
463C8C2×C4⋊Dic1114yescomplemented
464C22—24no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22D4×Dic2211yescharacteristic
472C22D4×D4411yescharacteristic
473C22C2×SD16×D1111yescharacteristic
474C22C2×#6696911yescharacteristic
475C22#1062330111yescharacteristic
476C22#1062330111yescharacteristic
477C22C2×D4×Dic1111yescharacteristic
478C4—24no—
479C4—22no—
480C4—42no—
481C4—42no—
482C4—224no—
483C4—442no—
484C4—882no—
485C4—882no—
486C4SD16×Dic1114yescomplemented
487C4#1062307411yescharacteristic
488C4#1062308611yescharacteristic
489C4C22×C4⋊Dic1111yescharacteristic
490C4#1062335811yescharacteristic
491C2—44no—
492C2D4×C4⋊Dic1111yescharacteristic
493C2C2×SD16×Dic1111yescharacteristic
494C2#1307750011yescharacteristic
495C2SD16×D4411yescharacteristic
496C2#1308034711yescharacteristic
497C2SD16×Dic2211yescharacteristic
498C2#1308148911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×C4×SD16D11
hypocenterC11C4⋊C4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. Q8×C4⋊Dic11C2semidirect
4. #13069345C2semidirect
5. #13068886C2semidirect
7. #13068773C2semidirect
8. #13068621C2semidirect
10. C8×C4⋊Dic11C2semidirect
18. C4×C11×SD16C4semidirect
53. C4×Q8×C11C2×C4semidirect
82. C11×#106C2×C4semidirect
83. C11×#103C2×C4semidirect
85. C4×C8×C11C2×C4semidirect
125. C11×SD16C4⋊C4semidirect
154. C4⋊Dic11SD16direct (N × H)
183. Q8×C11C2×C4⋊C4semidirect
224. C8×C11C2×C4⋊C4semidirect
233. C4×SD16Dic11semidirect
275. C4×C11C4×SD16semidirect
297. C4×Q8C2×Dic11semidirect
325. #106C2×Dic11semidirect
328. #103C2×Dic11semidirect
332. C4×C8C2×Dic11semidirect
373. SD16C4⋊Dic11direct (N × H)
409. C11C4⋊C4×SD16semidirect
421. Q8C2×C4⋊Dic11semidirect
463. C8C2×C4⋊Dic11semidirect
486. C4SD16×Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
Q8×C4⋊Dic112
D4×C4⋊Dic112
#130693452
#130688862
#130688792
#130687732
#130686212
#130686162
C8×C4⋊Dic112
C2×C4×C11×SD162
C4⋊C4×SD1611