Finite Group Databasebeta

← SD16×C22⋊D13 #13126526

Subgroups — SD16×C22⋊D13 #13126526

Order 1664.

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×C13×SD16C211yesmaximal, characteristic, complemented
2Q8×C22⋊D13C211yesmaximal, characteristic, complemented
3D4×C22⋊D13C211yesmaximal, characteristic
4C2×SD16×D13C211yesmaximal, characteristic, complemented
5#11718888C211yesmaximal, characteristic, complemented
6#11718879C211yesmaximal, characteristic, complemented
7#11718836C211yesmaximal, characteristic, complemented
8#11718832C211yesmaximal, characteristic, complemented
9#11718831C211yesmaximal, characteristic, complemented
10#11718830C211yesmaximal, characteristic, complemented
11#11718824C211yesmaximal, characteristic, complemented
12#11718823C211yesmaximal, characteristic, complemented
13SD16×Dic13C211yesmaximal, characteristic, complemented
14#11718775C211yesmaximal, characteristic, complemented
15C8×C22⋊D13C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic, complemented
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13—21no—
19C2×Q8×D13C2211yescharacteristic, complemented
20C2×D4×D13C2211yescharacteristic
21C2×C13×SD16—24no—
22C2×C13×SD16C2211yescharacteristic
23C2×C13×SD16C2211yescharacteristic
24C2×C13×SD16C2211yescharacteristic, complemented
25C2×C13×SD16C2211yescharacteristic, complemented
26C22×C8×C13C2211yescharacteristic, complemented
27#88207—21no—
28#88200—21no—
29#88200C2211yescharacteristic, complemented
30Q8×Dic13C2211yescharacteristic, complemented
31#88198—21no—
32#88198C2211yescharacteristic, complemented
33C2×#6106C2211yescharacteristic, complemented
34C2×#6106C2211yescharacteristic, complemented
35#88194C2211yescharacteristic
36#88193—21no—
37#88192C2211yescharacteristic
38#88191—21no—
39D4×Dic13C2211yescharacteristic
40C2×#6105C2211yescharacteristic
41C2×#6105C2211yescharacteristic, complemented
42#88184C2211yescharacteristic
43C4×C22⋊D13—21no—
44C4×C22⋊D13C2211yescharacteristic
45#88178—21no—
46#88178C2211yescharacteristic, complemented
47SD16×D13—24no—
48C2×#6095C2211yescharacteristic, complemented
49C2×C8×D13C2211yescharacteristic, complemented
50#88075C2211yescharacteristic, complemented
51#88075C2211yescharacteristic, complemented
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic, complemented
55#88061C2211yescharacteristic, complemented
56#88060C2211yescharacteristic, complemented
57#88057C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59#88054C2211yescharacteristic, complemented
60C8×Dic13C2211yescharacteristic, complemented
61C24×C13—21no—
62C23×D13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13—22no—
69C2×D4×C13—21no—
70C2×D4×C13—41no—
71C2×D4×C13C2311yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C22×C4×C13—21no—
74C22×C4×C13C2311yescharacteristic
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—21no—
80C2×C22⋊D13—44no—
81C2×C22⋊D13D411yescharacteristic
82C22×Dic13—21no—
83Q8×D13—22no—
84Q8×D13—41no—
85D4×D13—22no—
86D4×D13—41no—
87C2×D52C2311yescharacteristic
88C2×C4×D13—21no—
89C2×C4×D13C2311yescharacteristic
90C2×Dic26—21no—
91C2×Dic26C2311yescharacteristic
92C13×SD16—22no—
93C13×SD16—22no—
94C13×SD16—22no—
95C13×SD16D414yescomplemented
96C2×C8×C13—22no—
97C2×C8×C13C2311yescharacteristic
98C2×C8×C13C2311yescharacteristic
99C22⋊Dic13—21no—
100C22⋊Dic13—21no—
101C22⋊Dic13—21no—
102C22⋊Dic13D411yescharacteristic
103#6106—22no—
104#6106—41no—
105#6105—22no—
106#6105—41no—
107#6103—21no—
108#6103—21no—
109#6103D411yescharacteristic
110C4⋊Dic13—21no—
111C4⋊Dic13C2311yescharacteristic
112C4⋊Dic13C2311yescharacteristic
113#6101—21no—
114#6101—21no—
115#6101—21no—
116#6101—21no—
117#6101D411yescharacteristic
118C4×Dic13—21no—
119C4×Dic13C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122#6095—22no—
123C8×D13—22no—
124D4×SD16—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—81no—
130C23×C13C2×D411yescharacteristic
131C22×D13—21no—
132C22×D13—42no—
133C22×D13—42no—
134C22×D13—81no—
135C22×D13C2×D411yescharacteristic
136Q8×C13—21no—
137Q8×C13—21no—
138Q8×C13—21no—
139Q8×C13—42no—
140Q8×C13C2×D412yescomplemented
141D4×C13—21no—
142D4×C13—21no—
143D4×C13—21no—
144D4×C13—42no—
145D4×C13C2×D412yes—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—42no—
151C2×C4×C13C2×D411yescharacteristic
152C2×C4×C13C2411yescharacteristic
153C22⋊D13—42no—
154C22⋊D13—42no—
155C22⋊D13—42no—
156C22⋊D13—42no—
157C22⋊D13—81no—
158C22⋊D13SD1614yesdirect product factor
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—42no—
163C2×Dic13C2×D411yescharacteristic
164C2×Dic13C2×D411yescharacteristic
165C2×Dic13C2×D411yescharacteristic
166D52—21no—
167D52—21no—
168C4×D13—21no—
169C4×D13—21no—
170C4×D13—42no—
171Dic26—21no—
172Dic26—21no—
173Dic26—42no—
174C8×C13—21no—
175C8×C13C2×D412yescomplemented
176#1055—21no—
177#1055—21no—
178C22×SD16—131no—
179C22×SD16D1311yescharacteristic, complemented
180D4×Q8—131no—
181D42—131no—
182#492—131no—
183#465—131no—
184#465—131no—
185#461—131no—
186#460—131no—
187#450—131no—
188#450—131no—
189#448—131no—
190#448—131no—
191C4×SD16—131no—
192C8×D4—131no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—22no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—84no—
202C22×C13C2×SD1612yescomplemented
203C22×C13C22×D411yescharacteristic
204C2×D13—21no—
205C2×D13—21no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—84no—
210C2×D13C2×SD1612yescomplemented
211C4×C13—22no—
212C4×C13—21no—
213C4×C13—41no—
214C4×C13C22×D411yescharacteristic
215C4×C13H(5,𝔽2)11yescharacteristic
216Dic13—21no—
217Dic13—21no—
218Dic13—41no—
219Dic13—41no—
220Dic13—41no—
221Dic13C2×SD1612yescomplemented
222C22×Q8—131no—
223C22×Q8C2×D1311yescharacteristic, complemented
224C22×D4—131no—
225C22×D4—261no—
226C22×D4C2×D1311yescharacteristic
227C2×SD16—24no—
228C2×SD16—131no—
229C2×SD16—131no—
230C2×SD16—131no—
231C2×SD16—131no—
232C2×SD16—131no—
233C2×SD16—264no—
234C2×SD16C2×D1311yescharacteristic
235C2×SD16C2×D1311yescharacteristic
236C2×SD16C2×D1311yescharacteristic, complemented
237C2×SD16C2×D1311yescharacteristic, complemented
238C22×C8—131no—
239C22×C8C2×D1311yescharacteristic, complemented
240C4⋊Q8—131no—
241C4⋊Q8—261no—
242#127—131no—
243C22⋊Q8—131no—
244C22⋊Q8—131no—
245C22⋊Q8—261no—
246C22⋊Q8—261no—
247#121—131no—
248#121—131no—
249#121—261no—
250#120—261no—
251#120—261no—
252C4×Q8—131no—
253C4×D4—131no—
254C4×D4—131no—
255C4×D4—261no—
256#106—131no—
257C4⋊C8—131no—
258#103—131no—
259#103—131no—
260#103—131no—
261#102—131no—
262#102—131no—
263#102—131no—
264C22⋊C8—131no—
265C22⋊C8—131no—
266C4×C8—131no—
267C2×C13—22no—
268C2×C13—42no—
269C2×C13—81no—
270C2×C13D4211yescharacteristic
271C2×C13C22×SD1611yescharacteristic
272C2×C13#57711yescharacteristic
273D13—22no—
274D13—81no—
275C24—21no—
276C24—261no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—131no—
281C2×Q8—261no—
282C2×Q8—262no—
283C2×Q8—521no—
284C2×Q8C22×D1311yescharacteristic
285C2×Q8C22×D1311yescharacteristic
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—131no—
290C2×D4—131no—
291C2×D4—261no—
292C2×D4—261no—
293C2×D4—261no—
294C2×D4—262no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4—521no—
298C2×D4—524no—
299C2×D4C22×D1311yescharacteristic
300C2×D4C22×D1311yescharacteristic
301C22×C4—21no—
302C22×C4—131no—
303C22×C4—261no—
304C22×C4—261no—
305C22×C4C22×D1311yescharacteristic
306SD16—22no—
307SD16—22no—
308SD16—22no—
309SD16—262no—
310SD16—262no—
311SD16—262no—
312SD16—521no—
313SD16—521no—
314SD16C22⋊D1314yesdirect product factor
315C2×C8—22no—
316C2×C8—131no—
317C2×C8—131no—
318C2×C8—262no—
319C2×C8C22×D1311yescharacteristic
320C2×C8C22×D1311yescharacteristic
321C4⋊C4—131no—
322C4⋊C4—131no—
323C4⋊C4—131no—
324C4⋊C4—261no—
325C4⋊C4—261no—
326C4⋊C4—261no—
327C4⋊C4—261no—
328C4⋊C4—261no—
329C22⋊C4—131no—
330C22⋊C4—131no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C42—131no—
337C42—261no—
338C13D4×SD1611yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—131no—
345C23—261no—
346C23—522no—
347C23—522no—
348C23—1041no—
349C23D4×D1311yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—261no—
355Q8—261no—
356Q8—522no—
357Q8C2×C22⋊D1312yescomplemented
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—134no—
363D4—261no—
364D4—261no—
365D4—522no—
366D4—522no—
367D4—522no—
368D4—522no—
369D4—1041no—
370D4C2×C22⋊D1312yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—131no—
377C2×C4—131no—
378C2×C4—131no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—522no—
385C2×C4—522no—
386C2×C4D4×D1311yescharacteristic
387C2×C4C23×D1311yescharacteristic
388C8—21no—
389C8—261no—
390C8—261no—
391C8C2×C22⋊D1312yescomplemented
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—132no—
402C22—261no—
403C22—261no—
404C22—521no—
405C22—521no—
406C22—521no—
407C22—1044no—
408C22SD16×D1312yescomplemented
409C22C2×D4×D1311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—132no—
414C4—261no—
415C4—261no—
416C4—521no—
417C4—521no—
418C4—521no—
419C4#8825111yescharacteristic
420C4C22×C22⋊D1311yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—262no—
425C2—1041no—
426C2C2×SD16×D1311yescharacteristic
427C2#1171946711yescharacteristic
428C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×SD16C2
socleC22×C13C22×D4
prime radicalD4×C22⋊D13C2
hypercenterC22×SD16D13
hypocenterC13D4×SD16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C13×SD16C2semidirect
2. Q8×C22⋊D13C2semidirect
4. C2×SD16×D13C2semidirect
5. #11718888C2semidirect
6. #11718879C2semidirect
7. #11718836C2semidirect
8. #11718832C2semidirect
9. #11718831C2semidirect
10. #11718830C2semidirect
11. #11718824C2semidirect
12. #11718823C2semidirect
13. SD16×Dic13C2semidirect
14. #11718775C2semidirect
15. C8×C22⋊D13C2semidirect
16. C22×Q8×C13C22semidirect
19. C2×Q8×D13C22semidirect
24. C2×C13×SD16C22semidirect
25. C2×C13×SD16C22semidirect
26. C22×C8×C13C22semidirect
29. #88200C22semidirect
30. Q8×Dic13C22semidirect
32. #88198C22semidirect
33. C2×#6106C22semidirect
34. C2×#6106C22semidirect
41. C2×#6105C22semidirect
46. #88178C22semidirect
48. C2×#6095C22semidirect
49. C2×C8×D13C22semidirect
50. #88075C22semidirect
51. #88075C22semidirect
53. #88072C22semidirect
54. C22⋊#1055C22semidirect
55. #88061C22semidirect
56. #88060C22semidirect
57. #88057C22semidirect
58. #88056C22semidirect
59. #88054C22semidirect
60. C8×Dic13C22semidirect
95. C13×SD16D4semidirect
140. Q8×C13C2×D4semidirect
158. C22⋊D13SD16direct (N × H)
175. C8×C13C2×D4semidirect
179. C22×SD16D13semidirect
202. C22×C13C2×SD16semidirect
210. C2×D13C2×SD16semidirect
221. Dic13C2×SD16semidirect
223. C22×Q8C2×D13semidirect
236. C2×SD16C2×D13semidirect
237. C2×SD16C2×D13semidirect
239. C22×C8C2×D13semidirect
314. SD16C22⋊D13direct (N × H)
338. C13D4×SD16semidirect
357. Q8C2×C22⋊D13semidirect
391. C8C2×C22⋊D13semidirect
408. C22SD16×D13semidirect

Maximal subgroups

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

subgroupindex
C22×C13×SD162
Q8×C22⋊D132
D4×C22⋊D132
C2×SD16×D132
#117188882
#117188792
#117188362
#117188322
#117188312
#117188302
#117188242
#117188232
SD16×Dic132
#117187752
C8×C22⋊D132
D4×SD1613