Finite Group Databasebeta

← #13125298

Subgroups — #13125298

Order 1664.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#11719537C211yesmaximal, characteristic, complemented
3C2×#88205C211yesmaximal, characteristic, complemented
4C2×#88190C211yesmaximal, characteristic, complemented
5C2×#88186C211yesmaximal, characteristic, complemented
6C2×#88163C211yesmaximal, characteristic, complemented
7#11718829C212yesmaximal, complemented
8#11718828C212yesmaximal, complemented
9#11718816C212yesmaximal, complemented
10#11718815C212yesmaximal, complemented
11M16×Dic13C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C13×AGL(1,ℤ/8)—24no—
17C2×C13×SD16C2212yes—
18C2×C13×D8C2212yes—
19C2×C13×M16C2211yescharacteristic
20C2×C22⋊Dic13—22no—
21#88205—24no—
22#88201C2211yescharacteristic, complemented
23#88198C2211yescharacteristic, complemented
24C2×#6107C2212yescomplemented
25#88194C2211yescharacteristic, complemented
26#88193—22no—
27#88190—22no—
28#88190C2212yes—
29#88190C2212yes—
30#88190C2211yescharacteristic, complemented
31C2×#6105C2212yes—
32C2×#6105C2212yescomplemented
33#88186—24no—
34C2×#6104C2212yes—
35C4×C22⋊D13—22no—
36C2×C4×Dic13C2211yescharacteristic
37C2×#6099C2211yescharacteristic
38#88163—24no—
39C2×Dic52C2212yescomplemented
40C2×#6095C2212yescomplemented
41#88055C2212yescomplemented
42C8×Dic13C2212yescomplemented
43C24×C13—21no—
44C13×#41—22no—
45C13×#41—22no—
46C2×Q8×C13C2311yescharacteristic
47C2×D4×C13—21no—
48C2×D4×C13—22no—
49C2×D4×C13—22no—
50C2×D4×C13—21no—
51C2×D4×C13C2312yes—
52C2×D4×C13C2311yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13C2311yescharacteristic
55C2×C22⋊D13—21no—
56C2×C22⋊D13—22no—
57C22×Dic13—21no—
58C22×Dic13D412yes—
59#6127—22no—
60#6127—22no—
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×Dic26—22no—
64C2×Dic26—22no—
65C2×Dic26—21no—
66C2×Dic26C2312yes—
67C2×Dic26C2311yescharacteristic
68C13×SD16—24no—
69C13×D8—24no—
70C13×M16D414yescomplemented
71C2×C8×C13C2312yes—
72C22⋊Dic13—22no—
73C22⋊Dic13—24no—
74C22⋊Dic13—24no—
75#6107—24no—
76#6105—24no—
77#6105—24no—
78#6104—24no—
79#6103—22no—
80#6101—22no—
81C4×Dic13D412yes—
82C4×Dic13C2311yescharacteristic
83C4×Dic13C2311yescharacteristic
84#6099D414yescomplemented
85C2×#1055C2312yes—
86Dic52—24no—
87#6095—24no—
88#3153—131nomaximal, Sylow
89C23×C13—22no—
90C23×C13—21no—
91C23×C13—44no—
92C23×C13—42no—
93C23×C13C2×D411yescharacteristic
94C22×D13—21no—
95Q8×C13—21no—
96Q8×C13—21no—
97D4×C13—22no—
98D4×C13—21no—
99D4×C13—21no—
100D4×C13—22no—
101D4×C13—42no—
102D4×C13—42no—
103C2×C4×C13—21no—
104C2×C4×C13—42no—
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2×D412yes—
107C2×C4×C13C2×D412yes—
108C2×C4×C13C2411yescharacteristic
109C22⋊D13—44no—
110C22⋊D13—42no—
111C2×Dic13—21no—
112C2×Dic13—22no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13C2×D412yes—
116C2×Dic13C2×D412yes—
117D52—21no—
118D52—21no—
119C4×D13—42no—
120Dic26—22no—
121Dic26—21no—
122Dic26—21no—
123Dic26—22no—
124Dic26—42no—
125C8×C13C2×D414yes—
126#1055C2×D414yes—
127C2×#137—131no—
128C2×#137—131no—
129C2×AGL(1,ℤ/8)—131no—
130C2×AGL(1,ℤ/8)D1311yescharacteristic, complemented
131#532—131no—
132C2×#124—131no—
133#497—132no—
134#496—132no—
135#495—132no—
136#495—132no—
137C4×M16—131no—
138C22×C13—22no—
139C22×C13—41no—
140C22×C13—42no—
141C22×C13—42no—
142C22×C13—44no—
143C22×C13—84no—
144C22×C13#12712yes—
145C22×C13C22×D411yescharacteristic
146C2×D13—41no—
147C2×D13—42no—
148C4×C13—41no—
149C4×C13#12712yes—
150C4×C13C22×D411yescharacteristic
151C4×C13C22×D411yescharacteristic
152Dic13—22no—
153Dic13—22no—
154Dic13—42no—
155Dic13—41no—
156C2×#41—131no—
157C2×#41C2×D1311yescharacteristic
158C22×Q8—131no—
159C22×D4C2×D1311yescharacteristic
160#137—264no—
161#137—264no—
162AGL(1,ℤ/8)—24no—
163AGL(1,ℤ/8)—264no—
164C2×Q16—132no—
165C2×Q16—132no—
166C2×SD16—132no—
167C2×SD16—132no—
168C2×SD16—132no—
169C2×SD16C2×D1312yes—
170C2×D8—132no—
171C2×D8C2×D1312yes—
172C2×M16—131no—
173C2×M16C2×D1311yescharacteristic
174C4⋊Q8—131no—
175#127—131no—
176#124—131no—
177#124—132no—
178#124—132no—
179#124—131no—
180#124—262no—
181#121—262no—
182C4×D4—262no—
183C2×C22⋊C4—262no—
184C2×C42—131no—
185#97—132no—
186C4×C8—132no—
187C2×C13—22no—
188C2×C13—81no—
189C2×C13—82no—
190C2×C13C2×#12711yescharacteristic
191C2×C13#57512yes—
192D13—81no—
193C24—21no—
194#41—22no—
195#41—22no—
196#41—262no—
197#41—262no—
198C2×Q8—132no—
199C2×Q8—131no—
200C2×Q8—261no—
201C2×Q8—262no—
202C2×Q8—262no—
203C2×Q8C22×D1311yescharacteristic
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—131no—
209C2×D4—262no—
210C2×D4—261no—
211C2×D4C22×D1312yes—
212C2×D4C22×D1311yescharacteristic
213C22×C4—21no—
214C22×C4—132no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4C22×D1311yescharacteristic
218Q16—264no—
219Q16—264no—
220SD16—24no—
221SD16—264no—
222SD16—264no—
223SD16—264no—
224D8—24no—
225D8—264no—
226M16—134no—
227M16C22⋊D1314yescomplemented
228C2×C8—132no—
229C2×C8C22×D1312yes—
230C4⋊C4—262no—
231C22⋊C4—262no—
232C22⋊C4—264no—
233C22⋊C4—264no—
234C22⋊C4—262no—
235C42—132no—
236C42—131no—
237C42—131no—
238C13#315311yescharacteristic, complemented, Sylow
239C23—22no—
240C23—21no—
241C23—44no—
242C23—42no—
243C23—261no—
244C23D4×D1311yescharacteristic
245Q8—21no—
246Q8—21no—
247Q8—261no—
248Q8—262no—
249Q8—262no—
250Q8—261no—
251Q8—522no—
252D4—22no—
253D4—21no—
254D4—21no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—261no—
259D4—261no—
260D4—524no—
261D4—522no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—132no—
265C2×C4—132no—
266C2×C4—262no—
267C2×C4—261no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4D4×D1311yescharacteristic
272C2×C4D4×D1312yes—
273C2×C4C2×C22⋊D1312yes—
274C2×C4C23×D1311yescharacteristic
275C8—134no—
276C8C2×C22⋊D1314yes—
277C22—22no—
278C22—42no—
279C22—44no—
280C22—41no—
281C22—42no—
282C22—84no—
283C22—522no—
284C22—521no—
285C22#8819412yes—
286C22C2×D4×D1311yescharacteristic
287C4—41no—
288C4—262no—
289C4—262no—
290C4—521no—
291C4—522no—
292C4#8819412yes—
293C4C2×D4×D1311yescharacteristic
294C4C22×C22⋊D1311yescharacteristic
295C2—22no—
296C2—82no—
297C2—81no—
298C2—1041no—
299C2#1171947812yes—
300C2C2×#8819411yescharacteristic
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#3153
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. #11719537C2semidirect
3. C2×#88205C2semidirect
4. C2×#88190C2semidirect
5. C2×#88186C2semidirect
6. C2×#88163C2semidirect
7. #11718829C2semidirect
8. #11718828C2semidirect
9. #11718816C2semidirect
10. #11718815C2semidirect
11. M16×Dic13C2semidirect
22. #88201C22semidirect
23. #88198C22semidirect
24. C2×#6107C22semidirect
25. #88194C22semidirect
30. #88190C22semidirect
32. C2×#6105C22semidirect
39. C2×Dic52C22semidirect
40. C2×#6095C22semidirect
41. #88055C22semidirect
42. C8×Dic13C22semidirect
70. C13×M16D4semidirect
84. #6099D4semidirect
130. C2×AGL(1,ℤ/8)D13semidirect
227. M16C22⋊D13semidirect
238. C13#3153semidirect

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
#117195372
C2×#882052
C2×#881902
C2×#881862
C2×#881632
#117188292
#117188282
#117188162
#117188152
M16×Dic132
#315313