Finite Group Databasebeta

← SD16×C22⋊D11 #13080306

Subgroups — SD16×C22⋊D11 #13080306

Order 1408.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×SD16C211yesmaximal, characteristic, complemented
2Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3D4×C22⋊D11C211yesmaximal, characteristic
4C2×SD16×D11C211yesmaximal, characteristic, complemented
5#10622840C211yesmaximal, characteristic, complemented
6#10622831C211yesmaximal, characteristic, complemented
7#10622788C211yesmaximal, characteristic, complemented
8#10622784C211yesmaximal, characteristic, complemented
9#10622783C211yesmaximal, characteristic, complemented
10#10622782C211yesmaximal, characteristic, complemented
11#10622776C211yesmaximal, characteristic, complemented
12#10622775C211yesmaximal, characteristic, complemented
13SD16×Dic11C211yesmaximal, characteristic, complemented
14#10622727C211yesmaximal, characteristic, complemented
15C8×C22⋊D11C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic, complemented
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11—21no—
19C2×Q8×D11C2211yescharacteristic, complemented
20C2×D4×D11C2211yescharacteristic
21C2×C11×SD16—24no—
22C2×C11×SD16C2211yescharacteristic
23C2×C11×SD16C2211yescharacteristic
24C2×C11×SD16C2211yescharacteristic, complemented
25C2×C11×SD16C2211yescharacteristic, complemented
26C22×C8×C11C2211yescharacteristic, complemented
27#67006—21no—
28#66999—21no—
29#66999C2211yescharacteristic, complemented
30Q8×Dic11C2211yescharacteristic, complemented
31#66997—21no—
32#66997C2211yescharacteristic, complemented
33C2×#4325C2211yescharacteristic, complemented
34C2×#4325C2211yescharacteristic, complemented
35#66993C2211yescharacteristic
36#66992—21no—
37#66991C2211yescharacteristic
38#66990—21no—
39D4×Dic11C2211yescharacteristic
40C2×#4324C2211yescharacteristic
41C2×#4324C2211yescharacteristic, complemented
42#66983C2211yescharacteristic
43C4×C22⋊D11—21no—
44C4×C22⋊D11C2211yescharacteristic
45#66977—21no—
46#66977C2211yescharacteristic, complemented
47SD16×D11—24no—
48C2×#4314C2211yescharacteristic, complemented
49C2×C8×D11C2211yescharacteristic, complemented
50#66899C2211yescharacteristic, complemented
51#66899C2211yescharacteristic, complemented
52#66896C2211yescharacteristic
53#66896C2211yescharacteristic, complemented
54C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55#66885C2211yescharacteristic, complemented
56(C2×D11)⋊C8C2211yescharacteristic, complemented
57#66881C2211yescharacteristic, complemented
58#66880C2211yescharacteristic, complemented
59Dic11⋊C8C2211yescharacteristic, complemented
60C8×Dic11C2211yescharacteristic, complemented
61C24×C11—21no—
62C23×D11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11C2311yescharacteristic
67C2×Q8×C11C2311yescharacteristic
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11—21no—
80C2×C22⋊D11—44no—
81C2×C22⋊D11D411yescharacteristic
82C22×Dic11—21no—
83Q8×D11—22no—
84Q8×D11—41no—
85D4×D11—22no—
86D4×D11—41no—
87C2×D44C2311yescharacteristic
88C2×C4×D11—21no—
89C2×C4×D11C2311yescharacteristic
90C2×Dic22—21no—
91C2×Dic22C2311yescharacteristic
92C11×SD16—22no—
93C11×SD16—22no—
94C11×SD16—22no—
95C11×SD16D414yescomplemented
96C2×C8×C11—22no—
97C2×C8×C11C2311yescharacteristic
98C2×C8×C11C2311yescharacteristic
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11—21no—
102C22⋊Dic11D411yescharacteristic
103#4325—22no—
104#4325—41no—
105#4324—22no—
106#4324—41no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11C2311yescharacteristic
112C4⋊Dic11C2311yescharacteristic
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4D411yescharacteristic
118C4×Dic11—21no—
119C4×Dic11C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121C2×C11⋊C8C2311yescharacteristic
122#4314—22no—
123C8×D11—22no—
124D4×SD16—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11C2×D411yescharacteristic
131C22×D11—21no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—81no—
135C22×D11C2×D411yescharacteristic
136Q8×C11—21no—
137Q8×C11—21no—
138Q8×C11—21no—
139Q8×C11—42no—
140Q8×C11C2×D412yescomplemented
141D4×C11—21no—
142D4×C11—21no—
143D4×C11—21no—
144D4×C11—42no—
145D4×C11C2×D412yes—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—42no—
151C2×C4×C11C2×D411yescharacteristic
152C2×C4×C11C2411yescharacteristic
153C22⋊D11—42no—
154C22⋊D11—42no—
155C22⋊D11—42no—
156C22⋊D11—42no—
157C22⋊D11—81no—
158C22⋊D11SD1614yesdirect product factor
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—42no—
163C2×Dic11C2×D411yescharacteristic
164C2×Dic11C2×D411yescharacteristic
165C2×Dic11C2×D411yescharacteristic
166D44—21no—
167D44—21no—
168C4×D11—21no—
169C4×D11—21no—
170C4×D11—42no—
171Dic22—21no—
172Dic22—21no—
173Dic22—42no—
174C8×C11—21no—
175C8×C11C2×D412yescomplemented
176C11⋊C8—21no—
177C11⋊C8—21no—
178C22×SD16—111no—
179C22×SD16D1111yescharacteristic, complemented
180D4×Q8—111no—
181D42—111no—
182#492—111no—
183#465—111no—
184#465—111no—
185#461—111no—
186#460—111no—
187#450—111no—
188#450—111no—
189#448—111no—
190#448—111no—
191C4×SD16—111no—
192C8×D4—111no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—84no—
202C22×C11C2×SD1612yescomplemented
203C22×C11C22×D411yescharacteristic
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—84no—
210C2×D11C2×SD1612yescomplemented
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—41no—
214C4×C11C22×D411yescharacteristic
215C4×C11H(5,𝔽2)11yescharacteristic
216Dic11—21no—
217Dic11—21no—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221Dic11C2×SD1612yescomplemented
222C22×Q8—111no—
223C22×Q8C2×D1111yescharacteristic, complemented
224C22×D4—111no—
225C22×D4—221no—
226C22×D4C2×D1111yescharacteristic
227C2×SD16—24no—
228C2×SD16—111no—
229C2×SD16—111no—
230C2×SD16—111no—
231C2×SD16—111no—
232C2×SD16—111no—
233C2×SD16—224no—
234C2×SD16C2×D1111yescharacteristic
235C2×SD16C2×D1111yescharacteristic
236C2×SD16C2×D1111yescharacteristic, complemented
237C2×SD16C2×D1111yescharacteristic, complemented
238C22×C8—111no—
239C22×C8C2×D1111yescharacteristic, complemented
240C4⋊Q8—111no—
241C4⋊Q8—221no—
242#127—111no—
243C22⋊Q8—111no—
244C22⋊Q8—111no—
245C22⋊Q8—221no—
246C22⋊Q8—221no—
247#121—111no—
248#121—111no—
249#121—221no—
250#120—221no—
251#120—221no—
252C4×Q8—111no—
253C4×D4—111no—
254C4×D4—111no—
255C4×D4—221no—
256#106—111no—
257C4⋊C8—111no—
258#103—111no—
259#103—111no—
260#103—111no—
261#102—111no—
262#102—111no—
263#102—111no—
264C22⋊C8—111no—
265C22⋊C8—111no—
266C4×C8—111no—
267C2×C11—22no—
268C2×C11—42no—
269C2×C11—81no—
270C2×C11D4211yescharacteristic
271C2×C11C22×SD1611yescharacteristic
272C2×C11#57711yescharacteristic
273D11—22no—
274D11—81no—
275C24—21no—
276C24—221no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—111no—
281C2×Q8—221no—
282C2×Q8—222no—
283C2×Q8—441no—
284C2×Q8C22×D1111yescharacteristic
285C2×Q8C22×D1111yescharacteristic
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—111no—
290C2×D4—111no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—222no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—441no—
298C2×D4—444no—
299C2×D4C22×D1111yescharacteristic
300C2×D4C22×D1111yescharacteristic
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4C22×D1111yescharacteristic
306SD16—22no—
307SD16—22no—
308SD16—22no—
309SD16—222no—
310SD16—222no—
311SD16—222no—
312SD16—441no—
313SD16—441no—
314SD16C22⋊D1114yesdirect product factor
315C2×C8—22no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—222no—
319C2×C8C22×D1111yescharacteristic
320C2×C8C22×D1111yescharacteristic
321C4⋊C4—111no—
322C4⋊C4—111no—
323C4⋊C4—111no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C22⋊C4—111no—
330C22⋊C4—111no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C42—111no—
337C42—221no—
338C11D4×SD1611yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—111no—
345C23—221no—
346C23—442no—
347C23—442no—
348C23—881no—
349C23D4×D1111yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—221no—
355Q8—221no—
356Q8—442no—
357Q8C2×C22⋊D1112yescomplemented
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—114no—
363D4—221no—
364D4—221no—
365D4—442no—
366D4—442no—
367D4—442no—
368D4—442no—
369D4—881no—
370D4C2×C22⋊D1112yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—111no—
377C2×C4—111no—
378C2×C4—111no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4D4×D1111yescharacteristic
387C2×C4C23×D1111yescharacteristic
388C8—21no—
389C8—221no—
390C8—221no—
391C8C2×C22⋊D1112yescomplemented
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—112no—
402C22—221no—
403C22—221no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—884no—
408C22SD16×D1112yescomplemented
409C22C2×D4×D1111yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—112no—
414C4—221no—
415C4—221no—
416C4—441no—
417C4—441no—
418C4—441no—
419C4#6703711yescharacteristic
420C4C22×C22⋊D1111yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—222no—
425C2—881no—
426C2C2×SD16×D1111yescharacteristic
427C2#1062329311yescharacteristic
428C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC22×C11×SD16C2
socleC22×C11C22×D4
prime radicalD4×C22⋊D11C2
hypercenterC22×SD16D11
hypocenterC11D4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C11×SD16C2semidirect
2. Q8×C22⋊D11C2semidirect
4. C2×SD16×D11C2semidirect
5. #10622840C2semidirect
6. #10622831C2semidirect
7. #10622788C2semidirect
8. #10622784C2semidirect
9. #10622783C2semidirect
10. #10622782C2semidirect
11. #10622776C2semidirect
12. #10622775C2semidirect
13. SD16×Dic11C2semidirect
14. #10622727C2semidirect
15. C8×C22⋊D11C2semidirect
16. C22×Q8×C11C22semidirect
19. C2×Q8×D11C22semidirect
24. C2×C11×SD16C22semidirect
25. C2×C11×SD16C22semidirect
26. C22×C8×C11C22semidirect
29. #66999C22semidirect
30. Q8×Dic11C22semidirect
32. #66997C22semidirect
33. C2×#4325C22semidirect
34. C2×#4325C22semidirect
41. C2×#4324C22semidirect
46. #66977C22semidirect
48. C2×#4314C22semidirect
49. C2×C8×D11C22semidirect
50. #66899C22semidirect
51. #66899C22semidirect
53. #66896C22semidirect
54. C22⋊(C11⋊C8)C22semidirect
55. #66885C22semidirect
56. (C2×D11)⋊C8C22semidirect
57. #66881C22semidirect
58. #66880C22semidirect
59. Dic11⋊C8C22semidirect
60. C8×Dic11C22semidirect
95. C11×SD16D4semidirect
140. Q8×C11C2×D4semidirect
158. C22⋊D11SD16direct (N × H)
175. C8×C11C2×D4semidirect
179. C22×SD16D11semidirect
202. C22×C11C2×SD16semidirect
210. C2×D11C2×SD16semidirect
221. Dic11C2×SD16semidirect
223. C22×Q8C2×D11semidirect
236. C2×SD16C2×D11semidirect
237. C2×SD16C2×D11semidirect
239. C22×C8C2×D11semidirect
314. SD16C22⋊D11direct (N × H)
338. C11D4×SD16semidirect
357. Q8C2×C22⋊D11semidirect
391. C8C2×C22⋊D11semidirect
408. C22SD16×D11semidirect

Maximal subgroups

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

subgroupindex
C22×C11×SD162
Q8×C22⋊D112
D4×C22⋊D112
C2×SD16×D112
#106228402
#106228312
#106227882
#106227842
#106227832
#106227822
#106227762
#106227752
SD16×Dic112
#106227272
C8×C22⋊D112
D4×SD1611