Finite Group Databasebeta

← #13126325

Subgroups — #13126325

Order 1664.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#11719536C211yesmaximal, characteristic, complemented
3D4×C22⋊D13C211yesmaximal, characteristic, complemented
4C2×SD16×D13C211yesmaximal, characteristic, complemented
5#11718899C211yesmaximal, characteristic, complemented
6#11718879C211yesmaximal, characteristic, complemented
7#11718831C211yesmaximal, characteristic, complemented
8#11718825C211yesmaximal, characteristic, complemented
9#11718824C211yesmaximal, characteristic, complemented
10#11718818C211yesmaximal, characteristic, complemented
11#11718817C211yesmaximal, characteristic, complemented
12#11718815C211yesmaximal, characteristic, complemented
13#11718814C211yesmaximal, characteristic, complemented
14#11718795C211yesmaximal, characteristic, complemented
15#11718788C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic, complemented
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13—21no—
19C2×Q8×D13C2211yescharacteristic, complemented
20C2×D4×D13C2211yescharacteristic
21C13×AGL(1,ℤ/8)—24no—
22C2×C13×SD16C2211yescharacteristic
23C2×C13×SD16C2211yescharacteristic, complemented
24C2×C13×D8C2211yescharacteristic
25C2×C13×D8C2211yescharacteristic, complemented
26C2×C13×M16C2211yescharacteristic, complemented
27#88207—21no—
28Q8×Dic13C2211yescharacteristic, complemented
29C2×#6106C2211yescharacteristic, complemented
30#88194C2211yescharacteristic
31#88193—21no—
32#88192—21no—
33#88192C2211yescharacteristic
34#88192C2211yescharacteristic, complemented
35#88191—21no—
36#88190—21no—
37#88190C2211yescharacteristic, complemented
38D4×Dic13C2211yescharacteristic
39C2×#6105C2211yescharacteristic
40C2×#6105C2211yescharacteristic, complemented
41C2×#6104C2211yescharacteristic, 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#88072C2211yescharacteristic
52#88072C2211yescharacteristic, complemented
53#88072C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic, complemented
55#88061C2211yescharacteristic, complemented
56#88060C2211yescharacteristic, complemented
57#88058C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59#88055C2211yescharacteristic, complemented
60#88054C2211yescharacteristic, complemented
61C24×C13—21no—
62C23×D13—21no—
63C13×#41—22no—
64C13×#41—41no—
65C2×Q8×C13C2311yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—41no—
70C2×D4×C13C2311yescharacteristic
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—21no—
81C2×C22⋊D13—44no—
82C2×C22⋊D13D411yescharacteristic
83C22×Dic13—21no—
84Q8×D13—22no—
85Q8×D13—41no—
86D4×D13—22no—
87D4×D13—41no—
88C2×D52C2311yescharacteristic
89C2×C4×D13—21no—
90C2×C4×D13C2311yescharacteristic
91C2×Dic26—21no—
92C2×Dic26C2311yescharacteristic
93C13×SD16—22no—
94C13×SD16D414yescomplemented
95C13×D8—22no—
96C13×D8—22no—
97C13×M16—22no—
98C2×C8×C13C2311yescharacteristic
99C2×C8×C13C2311yescharacteristic
100C22⋊Dic13—21no—
101C22⋊Dic13—21no—
102C22⋊Dic13—21no—
103C22⋊Dic13—21no—
104C22⋊Dic13—21no—
105C22⋊Dic13—21no—
106C22⋊Dic13D411yescharacteristic
107#6106—22no—
108#6105—22no—
109#6105—41no—
110#6104—41no—
111#6103—21no—
112#6103D411yescharacteristic
113C4⋊Dic13—21no—
114C4⋊Dic13C2311yescharacteristic
115C4⋊Dic13C2311yescharacteristic
116#6101—21no—
117#6101D411yescharacteristic
118C4×Dic13—21no—
119C4×Dic13C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122#6095—22no—
123C8×D13—22no—
124#3265—131nomaximal, Sylow
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—81no—
131C23×C13C2×D411yescharacteristic
132C22×D13—21no—
133C22×D13—42no—
134C22×D13—42no—
135C22×D13—81no—
136C22×D13C2×D411yescharacteristic
137Q8×C13—21no—
138Q8×C13C2×D412yescomplemented
139D4×C13—21no—
140D4×C13—21no—
141D4×C13—21no—
142D4×C13—21no—
143D4×C13—21no—
144D4×C13—42no—
145D4×C13—42no—
146D4×C13C2×D412yes—
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—22no—
154C22⋊D13—42no—
155C22⋊D13—42no—
156C22⋊D13—42no—
157C22⋊D13—42no—
158C22⋊D13—42no—
159C22⋊D13—81no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—42no—
164C2×Dic13C2×D411yescharacteristic
165C2×Dic13C2×D411yescharacteristic
166C2×Dic13C2×D411yescharacteristic
167D52—21no—
168D52—21no—
169C4×D13—21no—
170C4×D13—21no—
171C4×D13—42no—
172Dic26—21no—
173Dic26—21no—
174Dic26—42no—
175C8×C13—21no—
176C8×C13C2×D412yescomplemented
177#1055—21no—
178#1055—21no—
179C2×AGL(1,ℤ/8)D1311yescharacteristic, complemented
180C22×SD16—131no—
181#548—131no—
182D42—131no—
183#496—131no—
184#468—131no—
185#466—131no—
186#463—131no—
187#460—131no—
188#450—131no—
189#449—131no—
190#448—131no—
191#447—131no—
192#440—131no—
193#435—131no—
194C22×C13—22no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—84no—
207C22×C13C22×D411yescharacteristic
208C2×D13—21no—
209C2×D13—21no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C2×D13—84no—
214C2×D13AGL(1,ℤ/8)12yescomplemented
215C4×C13—22no—
216C4×C13—21no—
217C4×C13C22×D411yescharacteristic
218C4×C13H(5,𝔽2)11yescharacteristic
219Dic13—21no—
220Dic13—21no—
221Dic13—21no—
222Dic13—41no—
223Dic13—41no—
224Dic13—41no—
225C2×#41C2×D1311yescharacteristic, complemented
226C22×Q8—131no—
227C22×D4—131no—
228C22×D4—261no—
229C22×D4C2×D1311yescharacteristic
230AGL(1,ℤ/8)—24no—
231C2×SD16—131no—
232C2×SD16—131no—
233C2×SD16—131no—
234C2×SD16—131no—
235C2×SD16—264no—
236C2×SD16C2×D1311yescharacteristic
237C2×SD16C2×D1311yescharacteristic, complemented
238C2×D8—131no—
239C2×D8C2×D1311yescharacteristic
240C2×D8C2×D1311yescharacteristic, complemented
241C2×M16C2×D1311yescharacteristic, complemented
242C22×C8—131no—
243#127—131no—
244#124—131no—
245#124—261no—
246C22⋊Q8—131no—
247C22⋊Q8—261no—
248#121—131no—
249#121—131no—
250#121—131no—
251#121—261no—
252#121—261no—
253#120—261no—
254#120—261no—
255C4×Q8—131no—
256C4×D4—131no—
257C4×D4—131no—
258C4×D4—261no—
259#107—131no—
260C4⋊C8—131no—
261#103—131no—
262#103—131no—
263#102—131no—
264#102—131no—
265#102—131no—
266#102—131no—
267C22⋊C8—131no—
268C22⋊C8—131no—
269#97—131no—
270C2×C13—42no—
271C2×C13—41no—
272C2×C13—81no—
273C2×C13—81no—
274C2×C13D4211yescharacteristic
275C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
276C2×C13#57711yescharacteristic
277D13—22no—
278D13—81no—
279C24—21no—
280C24—261no—
281#41—22no—
282#41—41no—
283C2×Q8—131no—
284C2×Q8—261no—
285C2×Q8—262no—
286C2×Q8—521no—
287C2×Q8C22×D1311yescharacteristic
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—131no—
293C2×D4—131no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4—262no—
298C2×D4—261no—
299C2×D4—261no—
300C2×D4—261no—
301C2×D4—521no—
302C2×D4—524no—
303C2×D4C22×D1311yescharacteristic
304C2×D4C22×D1311yescharacteristic
305C2×D4C22×D1311yescharacteristic
306C22×C4—21no—
307C22×C4—131no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4C22×D1311yescharacteristic
311SD16—22no—
312SD16—262no—
313SD16—262no—
314SD16—262no—
315SD16—521no—
316SD16C22⋊D1314yescomplemented
317D8—22no—
318D8—22no—
319D8—521no—
320M16—22no—
321C2×C8—131no—
322C2×C8—131no—
323C2×C8—262no—
324C2×C8C22×D1311yescharacteristic
325C2×C8C22×D1311yescharacteristic
326C4⋊C4—131no—
327C4⋊C4—131no—
328C4⋊C4—131no—
329C4⋊C4—261no—
330C4⋊C4—261no—
331C22⋊C4—131no—
332C22⋊C4—131no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C22⋊C4—261no—
337C22⋊C4—261no—
338C22⋊C4—261no—
339C22⋊C4—261no—
340C42—131no—
341C42—261no—
342C13#326511yescharacteristic, complemented, Sylow
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—131no—
350C23—261no—
351C23—522no—
352C23—522no—
353C23—1041no—
354C23D4×D1311yescharacteristic
355Q8—21no—
356Q8—261no—
357Q8—261no—
358Q8—522no—
359Q8C2×C22⋊D1312yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—42no—
367D4—262no—
368D4—261no—
369D4—261no—
370D4—522no—
371D4—522no—
372D4—522no—
373D4—522no—
374D4—522no—
375D4—1041no—
376D4C2×C22⋊D1312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—131no—
382C2×C4—131no—
383C2×C4—131no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4D4×D1311yescharacteristic
392C2×C4C23×D1311yescharacteristic
393C8—21no—
394C8—261no—
395C8—261no—
396C8C2×C22⋊D1312yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—84no—
410C22—132no—
411C22—261no—
412C22—261no—
413C22—521no—
414C22—521no—
415C22—521no—
416C22—1044no—
417C22C2×D4×D1311yescharacteristic
418C4—21no—
419C4—22no—
420C4—261no—
421C4—261no—
422C4—261no—
423C4—521no—
424C4—521no—
425C4—521no—
426C4#8825111yescharacteristic
427C4C22×C22⋊D1311yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—81no—
432C2—262no—
433C2—1041no—
434C2D13×AGL(1,ℤ/8)11yescharacteristic
435C2#1171948011yescharacteristic
436C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×AGL(1,ℤ/8)C2
socleC22×C13C22×D4
hypercenterC2×AGL(1,ℤ/8)D13
hypocenterC13#3265
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C13×AGL(1,ℤ/8)C2semidirect
2. #11719536C2semidirect
3. D4×C22⋊D13C2semidirect
4. C2×SD16×D13C2semidirect
5. #11718899C2semidirect
6. #11718879C2semidirect
7. #11718831C2semidirect
8. #11718825C2semidirect
9. #11718824C2semidirect
10. #11718818C2semidirect
11. #11718817C2semidirect
12. #11718815C2semidirect
13. #11718814C2semidirect
14. #11718795C2semidirect
15. #11718788C2semidirect
16. C2×C13×#41C22semidirect
19. C2×Q8×D13C22semidirect
23. C2×C13×SD16C22semidirect
25. C2×C13×D8C22semidirect
26. C2×C13×M16C22semidirect
28. Q8×Dic13C22semidirect
29. C2×#6106C22semidirect
34. #88192C22semidirect
37. #88190C22semidirect
40. C2×#6105C22semidirect
41. C2×#6104C22semidirect
46. #88178C22semidirect
48. C2×#6095C22semidirect
49. C2×C8×D13C22semidirect
50. #88075C22semidirect
52. #88072C22semidirect
53. #88072C22semidirect
54. C22⋊#1055C22semidirect
55. #88061C22semidirect
56. #88060C22semidirect
57. #88058C22semidirect
58. #88056C22semidirect
59. #88055C22semidirect
60. #88054C22semidirect
94. C13×SD16D4semidirect
138. Q8×C13C2×D4semidirect
176. C8×C13C2×D4semidirect
179. C2×AGL(1,ℤ/8)D13semidirect
214. C2×D13AGL(1,ℤ/8)semidirect
225. C2×#41C2×D13semidirect
237. C2×SD16C2×D13semidirect
240. C2×D8C2×D13semidirect
241. C2×M16C2×D13semidirect
316. SD16C22⋊D13semidirect
342. C13#3265semidirect
359. Q8C2×C22⋊D13semidirect
396. C8C2×C22⋊D13semidirect

Maximal subgroups

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

subgroupindex
C2×C13×AGL(1,ℤ/8)2
#117195362
D4×C22⋊D132
C2×SD16×D132
#117188992
#117188792
#117188312
#117188252
#117188242
#117188182
#117188172
#117188152
#117188142
#117187952
#117187882
#326513