Finite Group Databasebeta

← #13124297

Subgroups — #13124297

Order 1664.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×D4×Dic13C211yesmaximal, characteristic, complemented
4C2×#88186C211yesmaximal, characteristic, complemented
5#11718893C211yesmaximal, characteristic, complemented
6#11718826C212yesmaximal, complemented
7#11718823C212yesmaximal, complemented
8#11718814C212yesmaximal, complemented
9#11718811C212yesmaximal, complemented
10#11718794C211yesmaximal, characteristic, complemented
11#11718779C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C23×Dic13—21no—
15C2×#6127C2211yescharacteristic
16C13×AGL(1,ℤ/8)—24no—
17C2×C13×SD16C2212yes—
18C2×C13×D8C2212yes—
19C2×C13×M16C2211yescharacteristic
20C2×C22⋊Dic13—21no—
21#88201C2211yescharacteristic, complemented
22#88198C2211yescharacteristic, complemented
23#88194C2211yescharacteristic, complemented
24#88193—21no—
25#88193—21no—
26#88190C2211yescharacteristic, complemented
27D4×Dic13—21no—
28D4×Dic13—21no—
29D4×Dic13C2212yes—
30D4×Dic13C2212yes—
31C2×#6105C2212yes—
32#88186—24no—
33C2×#6104C2212yes—
34C4×C22⋊D13—21no—
35C4×C22⋊D13—21no—
36C2×C4⋊Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×#6099C2211yescharacteristic
39#88075C2212yescomplemented
40#88072C2212yescomplemented
41#88061C2212yescomplemented
42#88056C2212yescomplemented
43#88054C2212yescomplemented
44#88054C2212yescomplemented
45C24×C13—21no—
46C13×#41—22no—
47C13×#41—22no—
48C2×Q8×C13C2311yescharacteristic
49C2×D4×C13—21no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13D414yescomplemented
53C2×D4×C13C2311yescharacteristic
54C2×D4×C13C2312yes—
55C22×C4×C13—21no—
56C22×C4×C13C2311yescharacteristic
57C2×C22⋊D13—21no—
58C2×C22⋊D13—21no—
59C2×C22⋊D13—21no—
60C22×Dic13—21no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—44no—
64C22×Dic13D411yescharacteristic
65C22×Dic13D411yescharacteristic
66#6127—22no—
67#6127—22no—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×Dic26C2311yescharacteristic
71C13×SD16—24no—
72C13×D8—24no—
73C13×M16—22no—
74C2×C8×C13C2312yes—
75C22⋊Dic13—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—22no—
78C22⋊Dic13—22no—
79#6105—24no—
80#6104—24no—
81#6103—21no—
82#6103—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13C2312yes—
85#6101—21no—
86#6101—21no—
87C4×Dic13D411yescharacteristic
88C4×Dic13D411yescharacteristic
89C4×Dic13C2311yescharacteristic
90C4×Dic13C2311yescharacteristic
91#6099—22no—
92C2×#1055C2312yes—
93#3036—131nomaximal, Sylow
94C23×C13—24no—
95C23×C13—22no—
96C23×C13—21no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13C2×D411yescharacteristic
100C22×D13—21no—
101Q8×C13—21no—
102Q8×C13—21no—
103D4×C13—24no—
104D4×C13—21no—
105D4×C13—22no—
106D4×C13—21no—
107D4×C13—42no—
108D4×C13C2×D414yes—
109C2×C4×C13—21no—
110C2×C4×C13—42no—
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D412yes—
113C2×C4×C13#4112yes—
114C2×C4×C13C2411yescharacteristic
115C22⋊D13—42no—
116C22⋊D13—42no—
117C22⋊D13—42no—
118C2×Dic13—22no—
119C2×Dic13—21no—
120C2×Dic13—22no—
121C2×Dic13—41no—
122C2×Dic13—44no—
123C2×Dic13—42no—
124C2×Dic13—44no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129D52—21no—
130D52—21no—
131C4×D13—42no—
132Dic26—21no—
133Dic26—21no—
134C8×C13—22no—
135#1055—22no—
136C2×AGL(1,ℤ/8)—131no—
137C2×AGL(1,ℤ/8)D1311yescharacteristic, complemented
138#532—131no—
139C2×C4×D4—131no—
140#463—132no—
141#463—132no—
142#461—132no—
143#459—132no—
144#423—131no—
145#417—131no—
146#417—131no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—24no—
150C22×C13—48no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13#12112yes—
157C22×C13C22×D411yescharacteristic
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—41no—
162C4×C13#12112yes—
163C4×C13C22×D411yescharacteristic
164C4×C13C2×#4111yescharacteristic
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—41no—
169Dic13—42no—
170Dic13AGL(1,ℤ/8)12yescomplemented
171C2×#41—131no—
172C2×#41C2×D1311yescharacteristic
173C22×D4C2×D1311yescharacteristic
174C23×C4—261no—
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—264no—
177C2×SD16—132no—
178C2×SD16C2×D1312yes—
179C2×D8—132no—
180C2×D8C2×D1312yes—
181C2×M16—131no—
182C2×M16C2×D1311yescharacteristic
183C4⋊Q8—131no—
184#127—131no—
185#124—131no—
186#124—131no—
187#121—261no—
188#121—261no—
189C4×D4—132no—
190C4×D4—132no—
191C4×D4—261no—
192C4×D4—261no—
193C4×D4—261no—
194C4×D4—261no—
195C2×C4⋊C4—131no—
196C2×C22⋊C4—261no—
197C2×C42—131no—
198C4⋊C8—132no—
199C4⋊C8—132no—
200#103—132no—
201#103—132no—
202#102—132no—
203#102—132no—
204C2×C13—22no—
205C2×C13—44no—
206C2×C13—81no—
207C2×C13C2×#12111yescharacteristic
208C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
209C2×C13#57511yescharacteristic
210D13—81no—
211C24—21no—
212#41—22no—
213#41—22no—
214#41—262no—
215#41—262no—
216C2×Q8—131no—
217C2×Q8C22×D1311yescharacteristic
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—22no—
221C2×D4—131no—
222C2×D4—261no—
223C2×D4—261no—
224C2×D4—261no—
225C2×D4C22⋊D1314yescomplemented
226C2×D4C22×D1311yescharacteristic
227C2×D4C22×D1312yes—
228C22×C4—21no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—524no—
236C22×C4C22×D1311yescharacteristic
237SD16—24no—
238SD16—264no—
239D8—24no—
240D8—264no—
241M16—22no—
242M16—262no—
243C2×C8—132no—
244C2×C8C22×D1312yes—
245C4⋊C4—132no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—262no—
252C22⋊C4—262no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C42—131no—
256C42—131no—
257C42—131no—
258C42—131no—
259C13#303611yescharacteristic, complemented, Sylow
260C23—24no—
261C23—22no—
262C23—21no—
263C23—42no—
264C23—42no—
265C23—261no—
266C23D4×D1311yescharacteristic
267Q8—21no—
268Q8—21no—
269Q8—261no—
270Q8—261no—
271D4—24no—
272D4—22no—
273D4—21no—
274D4—21no—
275D4—42no—
276D4—261no—
277D4—261no—
278D4—522no—
279D4—522no—
280D4—522no—
281D4C2×C22⋊D1314yes—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—262no—
289C2×C4—262no—
290C2×C4—261no—
291C2×C4—524no—
292C2×C4—521no—
293C2×C4—524no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4D4×D1311yescharacteristic
297C2×C4#612912yes—
298C2×C4C2×C22⋊D1312yes—
299C2×C4C23×D1311yescharacteristic
300C8—22no—
301C8—262no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—48no—
306C22—42no—
307C22—42no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—521no—
312C22—521no—
313C22—521no—
314C22#8819312yes—
315C22C2×D4×D1311yescharacteristic
316C4—41no—
317C4—132no—
318C4—261no—
319C4—261no—
320C4—261no—
321C4—522no—
322C4—521no—
323C4#8819312yes—
324C4C2×#612911yescharacteristic
325C4C22×C22⋊D1311yescharacteristic
326C2—22no—
327C2—44no—
328C2—81no—
329C2—1041no—
330C2D13×AGL(1,ℤ/8)11yescharacteristic
331C2#1171947811yescharacteristic
332C2C2×#8819311yescharacteristic
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#3036
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×D4×Dic13C2semidirect
4. C2×#88186C2semidirect
5. #11718893C2semidirect
6. #11718826C2semidirect
7. #11718823C2semidirect
8. #11718814C2semidirect
9. #11718811C2semidirect
10. #11718794C2semidirect
11. #11718779C2semidirect
21. #88201C22semidirect
22. #88198C22semidirect
23. #88194C22semidirect
26. #88190C22semidirect
39. #88075C22semidirect
40. #88072C22semidirect
41. #88061C22semidirect
42. #88056C22semidirect
43. #88054C22semidirect
44. #88054C22semidirect
52. C2×D4×C13D4semidirect
137. C2×AGL(1,ℤ/8)D13semidirect
170. Dic13AGL(1,ℤ/8)semidirect
225. C2×D4C22⋊D13semidirect
259. C13#3036semidirect

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×D4×Dic132
C2×#881862
#117188932
#117188262
#117188232
#117188142
#117188112
#117187942
#117187792
#303613