Finite Group Databasebeta

← #13126467

Subgroups — #13126467

Order 1664.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 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
3#11719511C211yesmaximal, characteristic, complemented
4C2×#88169C211yesmaximal, characteristic, complemented
5#11718900C211yesmaximal, characteristic, complemented
6#11718879C211yesmaximal, characteristic, complemented
7#11718831C211yesmaximal, characteristic, complemented
8#11718827C211yesmaximal, characteristic, complemented
9SD16×Dic13C211yesmaximal, characteristic, complemented
10#11718820C211yesmaximal, characteristic, complemented
11#11718819C211yesmaximal, characteristic, complemented
12#11718816C211yesmaximal, characteristic, complemented
13#11718814C211yesmaximal, characteristic, complemented
14#11718798C211yesmaximal, characteristic, complemented
15#11718789C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic, complemented
19C2×#6129C2211yescharacteristic
20C13×AGL(1,ℤ/8)—24no—
21C2×C13×SD16C2211yescharacteristic
22C2×C13×SD16C2211yescharacteristic
23C2×C13×D8C2211yescharacteristic
24C2×C13×D8C2211yescharacteristic
25C2×C13×M16C2211yescharacteristic
26#88207—21no—
27C2×C22⋊Dic13—21no—
28Q8×Dic13C2211yescharacteristic, complemented
29C2×#6107C2211yescharacteristic, complemented
30#88193—21no—
31#88192—21no—
32#88192C2211yescharacteristic
33#88192C2211yescharacteristic, complemented
34#88190—21no—
35#88190C2211yescharacteristic
36#88190C2211yescharacteristic, complemented
37#88189—21no—
38D4×Dic13C2211yescharacteristic
39C2×#6105C2211yescharacteristic
40C2×#6105C2211yescharacteristic
41C2×#6105C2211yescharacteristic, complemented
42C4×C22⋊D13—21no—
43C4×C22⋊D13C2211yescharacteristic
44#88178—21no—
45#88178C2211yescharacteristic
46#88178C2211yescharacteristic
47#88169—24no—
48C2×Dic52C2211yescharacteristic, complemented
49C2×#6094C2211yescharacteristic, complemented
50#88075C2211yescharacteristic, complemented
51#88072C2211yescharacteristic
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
54C22⋊#1055C2211yescharacteristic
55#88060C2211yescharacteristic, complemented
56#88057C2211yescharacteristic, complemented
57#88056C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59#88054C2211yescharacteristic, complemented
60C8×Dic13C2211yescharacteristic, complemented
61C24×C13—21no—
62C13×#41—22no—
63C13×#41—41no—
64C2×Q8×C13C2311yescharacteristic
65C2×D4×C13—22no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—41no—
69C2×D4×C13C2311yescharacteristic
70C2×D4×C13C2311yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13C2311yescharacteristic
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C2×C22⋊D13D411yescharacteristic
78C22×Dic13—21no—
79C22×Dic13—21no—
80Q8×D13—22no—
81Q8×D13—41no—
82#6129—22no—
83#6129—41no—
84C2×C4×D13—21no—
85C2×C4×D13C2311yescharacteristic
86C2×Dic26—21no—
87C2×Dic26C2311yescharacteristic
88C2×Dic26C2311yescharacteristic
89C13×SD16—22no—
90C13×SD16D414yescomplemented
91C13×D8—22no—
92C13×D8—22no—
93C13×M16—22no—
94C2×C8×C13C2311yescharacteristic
95C2×C8×C13C2311yescharacteristic
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—21no—
100C22⋊Dic13—21no—
101C22⋊Dic13—21no—
102C22⋊Dic13—21no—
103C22⋊Dic13—21no—
104C22⋊Dic13—21no—
105C22⋊Dic13D411yescharacteristic
106#6107—22no—
107#6105—22no—
108#6105—41no—
109#6105—41no—
110#6103D411yescharacteristic
111C4⋊Dic13—21no—
112C4⋊Dic13C2311yescharacteristic
113C4⋊Dic13C2311yescharacteristic
114#6101—21no—
115#6101—21no—
116#6101D411yescharacteristic
117C4×Dic13—21no—
118C4×Dic13C2311yescharacteristic
119C2×#1055C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121Dic52—22no—
122#6094—22no—
123#3275—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—81no—
130C23×C13C2×D411yescharacteristic
131C22×D13C2×D411yescharacteristic
132Q8×C13—21no—
133Q8×C13C2×D412yes—
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—21no—
137D4×C13—21no—
138D4×C13—21no—
139D4×C13—42no—
140D4×C13—42no—
141D4×C13C2×D412yes—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13C2×D411yescharacteristic
147C2×C4×C13C2411yescharacteristic
148C22⋊D13—41no—
149C22⋊D13—42no—
150C22⋊D13—42no—
151C22⋊D13—81no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—42no—
157C2×Dic13—81no—
158C2×Dic13C2×D411yescharacteristic
159C2×Dic13C2×D411yescharacteristic
160C2×Dic13C2×D411yescharacteristic
161C4×D13—21no—
162C4×D13—21no—
163C4×D13—42no—
164Dic26—21no—
165Dic26—21no—
166Dic26—21no—
167Dic26—21no—
168Dic26—42no—
169C8×C13—21no—
170C8×C13C2×D412yes—
171#1055—21no—
172#1055—21no—
173C2×#137—131no—
174C2×AGL(1,ℤ/8)D1311yescharacteristic, complemented
175#548—131no—
176#546—131no—
177#495—131no—
178#470—131no—
179#469—131no—
180#464—131no—
181#463—131no—
182#452—131no—
183#450—131no—
184#449—131no—
185#448—131no—
186C4×SD16—131no—
187#436—131no—
188C22×C13—22no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—84no—
201C22×C13C22×D411yescharacteristic
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—21no—
205C4×C13—22no—
206C4×C13—21no—
207C4×C13C22×D411yescharacteristic
208C4×C13H(5,𝔽2)11yescharacteristic
209Dic13—21no—
210Dic13—21no—
211Dic13—21no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216C2×#41—131no—
217C2×#41C2×D1311yescharacteristic
218C22×Q8—131no—
219C22×D4C2×D1311yescharacteristic
220#137—264no—
221AGL(1,ℤ/8)—24no—
222C2×Q16—131no—
223C2×Q16—131no—
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16C2×D1311yescharacteristic
228C2×SD16C2×D1311yescharacteristic
229C2×D8C2×D1311yescharacteristic
230C2×D8C2×D1311yescharacteristic
231C2×M16—131no—
232C2×M16C2×D1311yescharacteristic
233#124—131no—
234#124—131no—
235#124—261no—
236#123—261no—
237C22⋊Q8—131no—
238C22⋊Q8—131no—
239C22⋊Q8—261no—
240#121—131no—
241#121—131no—
242#121—261no—
243#121—261no—
244#120—261no—
245C4×Q8—131no—
246C4×D4—131no—
247C4×D4—131no—
248C4×D4—261no—
249C2×C22⋊C4—261no—
250#106—131no—
251C4⋊C8—131no—
252#103—131no—
253#103—131no—
254#103—131no—
255#102—131no—
256#102—131no—
257#102—131no—
258C22⋊C8—131no—
259C22⋊C8—131no—
260C4×C8—131no—
261C2×C13—41no—
262C2×C13—42no—
263C2×C13—81no—
264C2×C13—81no—
265C2×C13D4211yescharacteristic
266C2×C13#57511yescharacteristic
267C2×C13#57711yescharacteristic
268D13—41no—
269C24—21no—
270#41—22no—
271#41—41no—
272#41—262no—
273#41—521no—
274C2×Q8—131no—
275C2×Q8—131no—
276C2×Q8—261no—
277C2×Q8—262no—
278C2×Q8—521no—
279C2×Q8C22×D1311yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—131no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4C22×D1311yescharacteristic
289C2×D4C22×D1311yescharacteristic
290C2×D4C22×D1311yescharacteristic
291C22×C4—21no—
292C22×C4—131no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4C22×D1311yescharacteristic
297Q16—262no—
298Q16—262no—
299SD16—22no—
300SD16—262no—
301SD16—521no—
302SD16—521no—
303SD16C22⋊D1314yescomplemented
304D8—22no—
305D8—22no—
306M16—22no—
307M16—262no—
308C2×C8—131no—
309C2×C8—131no—
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—131no—
313C4⋊C4—131no—
314C4⋊C4—131no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4—261no—
318C22⋊C4—131no—
319C22⋊C4—131no—
320C22⋊C4—261no—
321C22⋊C4—261no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C22⋊C4—261no—
329C42—131no—
330C42—261no—
331C13#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—131no—
339C23D4×D1311yescharacteristic
340Q8—21no—
341Q8—261no—
342Q8—261no—
343Q8—261no—
344Q8—261no—
345Q8—522no—
346Q8C2×C22⋊D1312yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—521no—
355D4—522no—
356D4—522no—
357D4—1041no—
358D4C2×C22⋊D1312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—131no—
364C2×C4—131no—
365C2×C4—131no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—1041no—
375C2×C4D4×D1311yescharacteristic
376C2×C4C23×D1311yescharacteristic
377C8—21no—
378C8—261no—
379C8—261no—
380C8C2×C22⋊D1312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—261no—
395C22—261no—
396C22—261no—
397C22C2×D4×D1311yescharacteristic
398C4—21no—
399C4—22no—
400C4—261no—
401C4—261no—
402C4—261no—
403C4—521no—
404C4—521no—
405C4—521no—
406C4—521no—
407C4#8825111yescharacteristic
408C4C22×C22⋊D1311yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—521no—
414C2#1171947811yescharacteristic
415C2#1171948011yescharacteristic
416C2D4×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#3275
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. #11719511C2semidirect
4. C2×#88169C2semidirect
5. #11718900C2semidirect
6. #11718879C2semidirect
7. #11718831C2semidirect
8. #11718827C2semidirect
9. SD16×Dic13C2semidirect
10. #11718820C2semidirect
11. #11718819C2semidirect
12. #11718816C2semidirect
13. #11718814C2semidirect
14. #11718798C2semidirect
15. #11718789C2semidirect
18. C2×Q8×D13C22semidirect
28. Q8×Dic13C22semidirect
29. C2×#6107C22semidirect
33. #88192C22semidirect
36. #88190C22semidirect
41. C2×#6105C22semidirect
48. C2×Dic52C22semidirect
49. C2×#6094C22semidirect
50. #88075C22semidirect
53. #88072C22semidirect
55. #88060C22semidirect
56. #88057C22semidirect
57. #88056C22semidirect
58. #88056C22semidirect
59. #88054C22semidirect
60. C8×Dic13C22semidirect
90. C13×SD16D4semidirect
174. C2×AGL(1,ℤ/8)D13semidirect
303. SD16C22⋊D13semidirect
331. C13#3275semidirect

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
#117195112
C2×#881692
#117189002
#117188792
#117188312
#117188272
SD16×Dic132
#117188202
#117188192
#117188162
#117188142
#117187982
#117187892
#327513