Finite Group Databasebeta

← #13126459

Subgroups — #13126459

Order 1664.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88165C212yesmaximal, complemented
2#11719423C211yesmaximal, characteristic, complemented
3D4×D52C211yesmaximal, characteristic, complemented
4C13×#459C211yesmaximal, characteristic, complemented
5#11718817C212yesmaximal, complemented
6#11718734C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic, complemented
8#11718509C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718443C212yesmaximal, complemented
11#11718442C212yesmaximal, complemented
12C2×#6129C2212yescomplemented
13C2×D4×D13C2212yes—
14C22×D52—21no—
15C2×C13×D8C2212yes—
16C13×#127C2211yescharacteristic, complemented
17C4×D4×C13C2211yescharacteristic
18#88194—21no—
19#88193—22no—
20#88192C2212yescomplemented
21D4×Dic13—21no—
22C2×#6105C2211yescharacteristic
23C2×#6104C2212yescomplemented
24C2×#6104C2212yescomplemented
25#88184—21no—
26#88165—28no—
27C2×#6095C2212yescomplemented
28C2×#6094C2212yescomplemented
29#88149C2212yes—
30#88136—22no—
31#88128C2211yescharacteristic
32C4×D52C2211yescharacteristic
33C4×Dic26C2211yescharacteristic, complemented
34C13×C4⋊C8C2211yescharacteristic, complemented
35C13×#102C2212yescomplemented
36#88072C2211yescharacteristic
37#88061C2212yescomplemented
38#88060C2212yescomplemented
39#88050C2211yescharacteristic, complemented
40#88048C2211yescharacteristic, complemented
41C4×#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13C2312yes—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C22×Dic13—22no—
52#6129—24no—
53#6129—42no—
54D4×D13—24no—
55D4×D13—42no—
56C2×D52—22no—
57C2×D52—21no—
58C2×D52—21no—
59C2×D52—44no—
60C2×D52D411yescharacteristic
61C2×D52C2312yes—
62C2×C4×D13C2312yes—
63C2×Dic26C2311yescharacteristic
64C13×D8—24no—
65C2×C8×C13C2312yes—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C42×C13C2311yescharacteristic
69C22⋊Dic13—22no—
70#6105D414yescomplemented
71#6104—24no—
72#6104—42no—
73#6103—22no—
74#6103D412yes—
75C4⋊Dic13D411yescharacteristic
76C4⋊Dic13C2311yescharacteristic
77#6101—21no—
78C4×Dic13—21no—
79C2×#1055C2311yescharacteristic
80C2×#1055C2311yescharacteristic
81#6095—24no—
82#6094—24no—
83#3274—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13—22no—
86C22×D13—22no—
87C22×D13—44no—
88C22×D13—44no—
89C22×D13—82no—
90C22×D13C2×D412yes—
91D4×C13—22no—
92D4×C13—21no—
93D4×C13—22no—
94D4×C13—42no—
95D4×C13—81no—
96D4×C13C2×D412yes—
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—44no—
103C22⋊D13—44no—
104C22⋊D13—82no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—44no—
108C2×Dic13C2×D412yes—
109D52—22no—
110D52—22no—
111D52—22no—
112D52—44no—
113D52—42no—
114D52—81no—
115C4×D13—22no—
116C4×D13—22no—
117Dic26—21no—
118Dic26C2×D412yescomplemented
119C8×C13—22no—
120#1055—21no—
121#1055C2×D412yescomplemented
122C2×AGL(1,ℤ/8)—132no—
123#550—131no—
124D42—131no—
125#493—131no—
126#469—132no—
127#460—131no—
128#459D1311yescharacteristic, complemented
129#449—132no—
130#447—132no—
131C4×SD16—131no—
132#436—131no—
133C22×C13—22no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13C22×D411yescharacteristic
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—22no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—88no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13AGL(1,ℤ/8)12yescomplemented
150C4×C13C22×D411yescharacteristic
151C4×C13H(5,𝔽2)11yescharacteristic
152Dic13—22no—
153Dic13—22no—
154Dic13—41no—
155C2×#41—132no—
156C22×D4—132no—
157C22×D4—261no—
158AGL(1,ℤ/8)—268no—
159C2×SD16—131no—
160C2×SD16—132no—
161C2×D8—132no—
162C2×D8—132no—
163C2×D8C2×D1312yes—
164C2×M16—132no—
165#127—131no—
166#127—261no—
167#127C2×D1311yescharacteristic, complemented
168#121—132no—
169#121—132no—
170#121—262no—
171#121—261no—
172#120—262no—
173C4×Q8—131no—
174C4×D4—131no—
175C4×D4—261no—
176C4×D4C2×D1311yescharacteristic
177#106—131no—
178C4⋊C8C2×D1311yescharacteristic, complemented
179#103—131no—
180#102—131no—
181#102—132no—
182#102C2×D1312yescomplemented
183C22⋊C8—132no—
184C4×C8—131no—
185C2×C13—42no—
186C2×C13—82no—
187C2×C13D4211yescharacteristic
188C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C13#57611yescharacteristic
190D13—42no—
191D13—82no—
192C24—262no—
193#41—264no—
194#41—522no—
195C2×Q8—131no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—131no—
199C2×D4—132no—
200C2×D4—262no—
201C2×D4—262no—
202C2×D4—264no—
203C2×D4—262no—
204C2×D4—262no—
205C2×D4—261no—
206C2×D4—261no—
207C2×D4—524no—
208C2×D4—522no—
209C2×D4C22×D1312yes—
210C2×D4C22×D1311yescharacteristic
211C22×C4—21no—
212C22×C4—132no—
213C22×C4—262no—
214SD16—134no—
215SD16—264no—
216D8—24no—
217D8—264no—
218D8—522no—
219M16—264no—
220C2×C8—131no—
221C2×C8—131no—
222C2×C8C22×D1312yes—
223C4⋊C4—131no—
224C4⋊C4—131no—
225C4⋊C4—261no—
226C4⋊C4C22×D1311yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—132no—
229C22⋊C4—262no—
230C22⋊C4—262no—
231C42—261no—
232C42C22×D1311yescharacteristic
233C13#327411yescharacteristic, complemented, Sylow
234C23—21no—
235C23—22no—
236C23—132no—
237C23—262no—
238C23—524no—
239C23—524no—
240C23—1042no—
241Q8—132no—
242Q8—261no—
243D4—22no—
244D4—21no—
245D4—22no—
246D4—42no—
247D4—81no—
248D4—262no—
249D4—262no—
250D4—262no—
251D4—524no—
252D4—524no—
253D4—524no—
254D4—522no—
255D4—1041no—
256D4—1042no—
257D4D4×D1312yes—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—132no—
261C2×C4—261no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—524no—
266C2×C4D4×D1311yescharacteristic
267C2×C4D4×D1311yescharacteristic
268C2×C4C23×D1311yescharacteristic
269C8—22no—
270C8—132no—
271C8—261no—
272C22—22no—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—262no—
279C22—262no—
280C22—262no—
281C22—522no—
282C22—522no—
283C22—522no—
284C22—1048no—
285C22C2×D4×D1311yescharacteristic
286C4—21no—
287C4—41no—
288C4—262no—
289C4—262no—
290C4—521no—
291C4#8816512yescomplemented
292C4C2×D4×D1311yescharacteristic
293C4#8825611yescharacteristic
294C2—42no—
295C2—82no—
296C2—522no—
297C2—1042no—
298C2#1171931411yescharacteristic
299C2C2×#8816511yescharacteristic
300C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#459C2
socleC22×C13C22×D4
hypercenter#459D13
hypocenterC13#3274
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#88165C2semidirect
2. #11719423C2semidirect
3. D4×D52C2semidirect
4. C13×#459C2semidirect
5. #11718817C2semidirect
6. #11718734C2semidirect
7. C4×#6105C2semidirect
8. #11718509C2semidirect
9. #11718499C2semidirect
10. #11718443C2semidirect
11. #11718442C2semidirect
12. C2×#6129C22semidirect
16. C13×#127C22semidirect
20. #88192C22semidirect
23. C2×#6104C22semidirect
24. C2×#6104C22semidirect
27. C2×#6095C22semidirect
28. C2×#6094C22semidirect
33. C4×Dic26C22semidirect
34. C13×C4⋊C8C22semidirect
35. C13×#102C22semidirect
37. #88061C22semidirect
38. #88060C22semidirect
39. #88050C22semidirect
40. #88048C22semidirect
41. C4×#1055C22semidirect
70. #6105D4semidirect
118. Dic26C2×D4semidirect
121. #1055C2×D4semidirect
128. #459D13semidirect
149. C4×C13AGL(1,ℤ/8)semidirect
167. #127C2×D13semidirect
178. C4⋊C8C2×D13semidirect
182. #102C2×D13semidirect
233. C13#3274semidirect
291. C4#88165semidirect

Maximal subgroups

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

subgroupindex
C2×#881652
#117194232
D4×D522
C13×#4592
#117188172
#117187342
C4×#61052
#117185092
#117184992
#117184432
#117184422
#327413