Finite Group Databasebeta

← #13126316

Subgroups — #13126316

Order 1664.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×D8C211yesmaximal, characteristic, complemented
2#11719511C211yesmaximal, characteristic, complemented
3D4×C22⋊D13C211yesmaximal, characteristic, complemented
4C2×#88165C211yesmaximal, characteristic, complemented
5#11718879C211yesmaximal, characteristic, complemented
6#11718878C211yesmaximal, characteristic, complemented
7#11718820C211yesmaximal, characteristic, complemented
8#11718819C211yesmaximal, characteristic, complemented
9#11718817C211yesmaximal, characteristic, complemented
10#11718815C211yesmaximal, characteristic, complemented
11#11718814C211yesmaximal, characteristic, complemented
12#11718813C211yesmaximal, characteristic, complemented
13#11718811C211yesmaximal, characteristic, complemented
14#11718775C211yesmaximal, characteristic, complemented
15#11718772C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic, complemented
18C22×C22⋊D13—21no—
19C2×#6129C2211yescharacteristic, complemented
20C2×D4×D13C2211yescharacteristic, complemented
21C2×C13×D8—24no—
22C2×C13×D8C2211yescharacteristic
23C2×C13×D8C2211yescharacteristic
24C2×C13×D8C2211yescharacteristic, complemented
25C2×C13×D8C2211yescharacteristic, complemented
26C22×C8×C13C2211yescharacteristic, complemented
27#88207—21no—
28#88207—21no—
29C2×C22⋊Dic13—21no—
30#88194C2211yescharacteristic, complemented
31#88193—21no—
32#88193—21no—
33#88192C2211yescharacteristic, complemented
34#88192C2211yescharacteristic, complemented
35#88191—21no—
36#88190C2211yescharacteristic, complemented
37#88189—21no—
38D4×Dic13C2211yescharacteristic, complemented
39D4×Dic13C2211yescharacteristic, complemented
40C2×#6105C2211yescharacteristic, complemented
41C2×#6105C2211yescharacteristic, complemented
42C2×#6104C2211yescharacteristic, complemented
43C2×#6104C2211yescharacteristic, complemented
44#88184C2211yescharacteristic
45C4×C22⋊D13C2211yescharacteristic
46#88178C2211yescharacteristic, complemented
47#88165—24no—
48C2×#6095C2211yescharacteristic, complemented
49C2×#6094C2211yescharacteristic, complemented
50#88072C2211yescharacteristic, complemented
51#88072C2211yescharacteristic, complemented
52#88072C2211yescharacteristic, complemented
53#88072C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic, complemented
55#88061C2211yescharacteristic, complemented
56#88060C2211yescharacteristic, complemented
57#88057C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59#88055C2211yescharacteristic, complemented
60#88054C2211yescharacteristic, complemented
61C24×C13—21no—
62C24×C13—21no—
63C23×D13—21no—
64C2×D4×C13—22no—
65C2×D4×C13—22no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13C2311yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C2×D4×C13C2311yescharacteristic
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—21no—
81C2×C22⋊D13—21no—
82C2×C22⋊D13—44no—
83C2×C22⋊D13D411yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87#6129—22no—
88#6129—41no—
89D4×D13—22no—
90D4×D13—41no—
91C2×D52C2311yescharacteristic
92C2×C4×D13C2311yescharacteristic
93C2×Dic26C2311yescharacteristic
94C13×D8—22no—
95C13×D8—22no—
96C13×D8—22no—
97C13×D8D414yescomplemented
98C2×C8×C13—22no—
99C2×C8×C13C2311yescharacteristic
100C2×C8×C13C2311yescharacteristic
101C22⋊Dic13—21no—
102C22⋊Dic13—21no—
103C22⋊Dic13—21no—
104C22⋊Dic13—21no—
105C22⋊Dic13—21no—
106C22⋊Dic13—21no—
107C22⋊Dic13—21no—
108C22⋊Dic13D411yescharacteristic
109#6105—22no—
110#6105—41no—
111#6104—22no—
112#6104—41no—
113#6103—21no—
114#6103D411yescharacteristic
115C4⋊Dic13C2311yescharacteristic
116C4⋊Dic13C2311yescharacteristic
117#6101—21no—
118#6101D411yescharacteristic
119C4×Dic13C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122#6095—22no—
123#6094—22no—
124#3264—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—81no—
134C23×C13—81no—
135C23×C13C2×D411yescharacteristic
136C22×D13—21no—
137C22×D13—42no—
138C22×D13—42no—
139C22×D13—81no—
140C22×D13C2×D411yescharacteristic
141D4×C13—21no—
142D4×C13—21no—
143D4×C13—21no—
144D4×C13—21no—
145D4×C13—21no—
146D4×C13—21no—
147D4×C13—42no—
148D4×C13—42no—
149D4×C13C2×D412yes—
150D4×C13C2×D412yescomplemented
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13C2×D411yescharacteristic
154C2×C4×C13C2411yescharacteristic
155C22⋊D13—22no—
156C22⋊D13—42no—
157C22⋊D13—42no—
158C22⋊D13—42no—
159C22⋊D13—42no—
160C22⋊D13—42no—
161C22⋊D13—81no—
162C22⋊D13—81no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—42no—
167C2×Dic13—42no—
168C2×Dic13—81no—
169C2×Dic13C2×D411yescharacteristic
170C2×Dic13C2×D411yescharacteristic
171C2×Dic13C2×D411yescharacteristic
172D52—21no—
173D52—21no—
174C4×D13—21no—
175C4×D13—21no—
176Dic26—21no—
177Dic26—21no—
178C8×C13—21no—
179C8×C13C2×D412yescomplemented
180#1055—21no—
181#1055—21no—
182C2×AGL(1,ℤ/8)—131no—
183C22×D8D1311yescharacteristic, complemented
184#546—131no—
185D42—131no—
186#496—131no—
187#469—131no—
188#465—131no—
189#463—131no—
190#459—131no—
191#450—131no—
192#449—131no—
193#447—131no—
194#447—131no—
195#442—131no—
196#435—131no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—84no—
212C22×C13—84no—
213C22×C13AGL(1,ℤ/8)12yescomplemented
214C22×C13C22×D411yescharacteristic
215C2×D13—21no—
216C2×D13—21no—
217C2×D13—21no—
218C2×D13—41no—
219C2×D13—41no—
220C2×D13—41no—
221C2×D13—84no—
222C4×C13—21no—
223C4×C13C22×D411yescharacteristic
224C4×C13H(5,𝔽2)11yescharacteristic
225Dic13—21no—
226Dic13—21no—
227Dic13—21no—
228Dic13—41no—
229Dic13—41no—
230Dic13—41no—
231C2×#41—131no—
232C22×D4—131no—
233C22×D4—261no—
234C22×D4C2×D1311yescharacteristic
235C22×D4C2×D1311yescharacteristic, complemented
236AGL(1,ℤ/8)—264no—
237C2×SD16—131no—
238C2×SD16—131no—
239C2×SD16—131no—
240C2×D8—24no—
241C2×D8—131no—
242C2×D8—131no—
243C2×D8C2×D1311yescharacteristic
244C2×D8C2×D1311yescharacteristic
245C2×D8C2×D1311yescharacteristic, complemented
246C2×D8C2×D1311yescharacteristic, complemented
247C2×M16—131no—
248C22×C8C2×D1311yescharacteristic, complemented
249#127—131no—
250#124—131no—
251#123—261no—
252C22⋊Q8—131no—
253#121—131no—
254#121—131no—
255#121—131no—
256#121—261no—
257#121—261no—
258#120—261no—
259#120—261no—
260#120—261no—
261C4×D4—131no—
262C4×D4—131no—
263C4×D4—131no—
264C2×C22⋊C4—261no—
265#106—131no—
266C4⋊C8—131no—
267#103—131no—
268#102—131no—
269#102—131no—
270#102—131no—
271#102—131no—
272#102—131no—
273C22⋊C8—131no—
274C22⋊C8—131no—
275#97—131no—
276C2×C13—22no—
277C2×C13—42no—
278C2×C13—42no—
279C2×C13—81no—
280C2×C13—81no—
281C2×C13D4211yescharacteristic
282C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
283C2×C13#57611yescharacteristic
284D13—41no—
285D13—81no—
286C24—21no—
287C24—21no—
288C24—261no—
289#41—262no—
290#41—521no—
291C2×Q8—131no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—131no—
299C2×D4—131no—
300C2×D4—261no—
301C2×D4—261no—
302C2×D4—261no—
303C2×D4—262no—
304C2×D4—261no—
305C2×D4—261no—
306C2×D4—261no—
307C2×D4—261no—
308C2×D4—521no—
309C2×D4—524no—
310C2×D4C22×D1311yescharacteristic
311C2×D4C22×D1311yescharacteristic
312C2×D4C22×D1311yescharacteristic
313C2×D4C22×D1311yescharacteristic
314C22×C4—131no—
315C22×C4—261no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4C22×D1311yescharacteristic
319SD16—262no—
320SD16—262no—
321SD16—521no—
322D8—22no—
323D8—22no—
324D8—22no—
325D8—262no—
326D8—521no—
327D8C22⋊D1314yescomplemented
328M16—262no—
329C2×C8—22no—
330C2×C8—131no—
331C2×C8—131no—
332C2×C8C22×D1311yescharacteristic
333C2×C8C22×D1311yescharacteristic
334C4⋊C4—131no—
335C4⋊C4—131no—
336C4⋊C4—131no—
337C4⋊C4—261no—
338C22⋊C4—131no—
339C22⋊C4—131no—
340C22⋊C4—261no—
341C22⋊C4—261no—
342C22⋊C4—261no—
343C22⋊C4—261no—
344C22⋊C4—261no—
345C22⋊C4—261no—
346C22⋊C4—261no—
347C22⋊C4—261no—
348C42—131no—
349C13#326411yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23—131no—
361C23—261no—
362C23—522no—
363C23—522no—
364C23—1041no—
365C23D4×D1311yescharacteristic
366Q8—261no—
367Q8—261no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—262no—
377D4—261no—
378D4—261no—
379D4—522no—
380D4—522no—
381D4—522no—
382D4—522no—
383D4—522no—
384D4—1041no—
385D4—1041no—
386D4C2×C22⋊D1312yes—
387D4C2×C22⋊D1312yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—131no—
391C2×C4—131no—
392C2×C4—131no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—522no—
399C2×C4—522no—
400C2×C4—1041no—
401C2×C4D4×D1311yescharacteristic
402C2×C4C23×D1311yescharacteristic
403C8—21no—
404C8—261no—
405C8—261no—
406C8C2×C22⋊D1312yescomplemented
407C22—21no—
408C22—21no—
409C22—22no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—261no—
424C22—261no—
425C22—261no—
426C22—521no—
427C22—521no—
428C22—521no—
429C22—1044no—
430C22#8816512yescomplemented
431C22C2×D4×D1311yescharacteristic
432C4—21no—
433C4—261no—
434C4—261no—
435C4—261no—
436C4—521no—
437C4—521no—
438C4—521no—
439C4#8825111yescharacteristic
440C4C22×C22⋊D1311yescharacteristic
441C2—22no—
442C2—42no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—521no—
447C2—1041no—
448C2C2×#8816511yescharacteristic
449C2#1171946211yescharacteristic
450C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×D8C2
socleC22×C13C22×D4
hypercenterC22×D8D13
hypocenterC13#3264
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C13×D8C2semidirect
2. #11719511C2semidirect
3. D4×C22⋊D13C2semidirect
4. C2×#88165C2semidirect
5. #11718879C2semidirect
6. #11718878C2semidirect
7. #11718820C2semidirect
8. #11718819C2semidirect
9. #11718817C2semidirect
10. #11718815C2semidirect
11. #11718814C2semidirect
12. #11718813C2semidirect
13. #11718811C2semidirect
14. #11718775C2semidirect
15. #11718772C2semidirect
17. C22×D4×C13C22semidirect
19. C2×#6129C22semidirect
20. C2×D4×D13C22semidirect
24. C2×C13×D8C22semidirect
25. C2×C13×D8C22semidirect
26. C22×C8×C13C22semidirect
30. #88194C22semidirect
33. #88192C22semidirect
34. #88192C22semidirect
36. #88190C22semidirect
38. D4×Dic13C22semidirect
39. D4×Dic13C22semidirect
40. C2×#6105C22semidirect
41. C2×#6105C22semidirect
42. C2×#6104C22semidirect
43. C2×#6104C22semidirect
46. #88178C22semidirect
48. C2×#6095C22semidirect
49. C2×#6094C22semidirect
50. #88072C22semidirect
51. #88072C22semidirect
52. #88072C22semidirect
53. #88072C22semidirect
54. C22⋊#1055C22semidirect
55. #88061C22semidirect
56. #88060C22semidirect
57. #88057C22semidirect
58. #88056C22semidirect
59. #88055C22semidirect
60. #88054C22semidirect
97. C13×D8D4semidirect
150. D4×C13C2×D4semidirect
179. C8×C13C2×D4semidirect
183. C22×D8D13semidirect
213. C22×C13AGL(1,ℤ/8)semidirect
235. C22×D4C2×D13semidirect
245. C2×D8C2×D13semidirect
246. C2×D8C2×D13semidirect
248. C22×C8C2×D13semidirect
327. D8C22⋊D13semidirect
349. C13#3264semidirect
387. D4C2×C22⋊D13semidirect
406. C8C2×C22⋊D13semidirect
430. C22#88165semidirect

Maximal subgroups

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

subgroupindex
C22×C13×D82
#117195112
D4×C22⋊D132
C2×#881652
#117188792
#117188782
#117188202
#117188192
#117188172
#117188152
#117188142
#117188132
#117188112
#117187752
#117187722
#326413