Finite Group Databasebeta

← #13126432

Subgroups — #13126432

Order 1664.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1D42×C13C211yesmaximal, characteristic, complemented
2C2×#88186C212yesmaximal, complemented
3#11719256C211yesmaximal, characteristic, complemented
4#11718879C212yesmaximal, complemented
5#11718737C211yesmaximal, characteristic, complemented
6#11718733C211yesmaximal, characteristic, complemented
7#11718703C212yesmaximal, complemented
8#11718698C212yesmaximal, complemented
9#11718680C211yesmaximal, characteristic, complemented
10C4×#6104C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic, complemented
12C22×D4×C13—21no—
13C22×D4×C13C2212yes—
14C2×#6127C2212yescomplemented
15C13×#127C2211yescharacteristic
16C13×#121—21no—
17C13×#121C2212yes—
18C13×#120—22no—
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88192—21no—
22C2×#6105C2212yes—
23C2×#6105C2212yescomplemented
24C2×#6105C2212yescomplemented
25#88186—28no—
26C2×#6104C2211yescharacteristic
27C2×#6104C2212yescomplemented
28#88178C2212yescomplemented
29C2×#6099C2212yescomplemented
30C4⋊C4×D13—21no—
31#88137—22no—
32C4×D52C2211yescharacteristic, complemented
33#88123C2211yescharacteristic, complemented
34#88072C2211yescharacteristic
35#88072C2212yescomplemented
36C22⋊#1055C2212yescomplemented
37#88050C2212yescomplemented
38#88049C2211yescharacteristic, complemented
39#88047C2211yescharacteristic, complemented
40C4⋊#1055C2211yescharacteristic, complemented
41C4×#1055C2211yescharacteristic, complemented
42C24×C13—22no—
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—42no—
49C2×D4×C13—44no—
50C2×D4×C13D411yescharacteristic
51C2×D4×C13C2312yes—
52C2×D4×C13C2311yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13C2312yes—
55C2×C22⋊D13—22no—
56#6127—24no—
57#6127—42no—
58C2×D52C2311yescharacteristic
59C2×C4×D13—21no—
60C2×C4×D13—22no—
61C2×Dic26C2312yes—
62C13×C4⋊C4D411yescharacteristic
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C13×C22⋊C4—22no—
66C13×C22⋊C4D412yes—
67C42×C13C2311yescharacteristic
68C22⋊Dic13—22no—
69#6105—24no—
70#6105—24no—
71#6105—42no—
72#6104—24no—
73#6104D414yescomplemented
74#6103—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13C2311yescharacteristic
78#6101—22no—
79#6099—24no—
80C2×#1055C2311yescharacteristic
81C2×#1055C2312yes—
82C2×#1055C2311yescharacteristic
83#3272—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13—22no—
86C23×C13—44no—
87C23×C13—44no—
88C23×C13—82no—
89C23×C13C2×D412yes—
90C22×D13—21no—
91D4×C13—22no—
92D4×C13—22no—
93D4×C13—21no—
94D4×C13—22no—
95D4×C13—44no—
96D4×C13—44no—
97D4×C13—42no—
98D4×C13—81no—
99D4×C13C2×D412yes—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—44no—
109C2×Dic13—21no—
110C2×Dic13—22no—
111D52—21no—
112D52C2×D412yescomplemented
113C4×D13—44no—
114C4×D13—42no—
115Dic26—22no—
116Dic26—22no—
117#1055—22no—
118#1055—21no—
119#1055C2×D412yescomplemented
120C2×AGL(1,ℤ/8)—132no—
121#547—131no—
122D42D1311yescharacteristic, complemented
123#492—131no—
124#468—132no—
125#461—131no—
126#459—131no—
127#450—132no—
128#449—132no—
129C4×D8—131no—
130#436—131no—
131C22×C13—22no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—88no—
141C22×C13C22×D411yescharacteristic
142C2×D13—22no—
143C2×D13—41no—
144C2×D13—41no—
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—41no—
148C4×C13AGL(1,ℤ/8)12yescomplemented
149C4×C13C22×D411yescharacteristic
150C4×C13H(5,𝔽2)11yescharacteristic
151Dic13—42no—
152Dic13—41no—
153C2×#41—132no—
154C22×D4—21no—
155C22×D4C2×D1312yes—
156AGL(1,ℤ/8)—268no—
157C2×SD16—132no—
158C2×SD16—132no—
159C2×SD16—132no—
160C2×D8—131no—
161C2×D8—132no—
162C2×M16—132no—
163C4⋊Q8—131no—
164#127C2×D1311yescharacteristic
165#123—262no—
166C22⋊Q8—132no—
167#121—21no—
168#121—261no—
169#121C2×D1312yes—
170#120—22no—
171C4×D4—131no—
172C4×D4C2×D1311yescharacteristic
173C4×D4C2×D1311yescharacteristic
174C2×C4⋊C4—261no—
175#107—131no—
176C4⋊C8—131no—
177#103—132no—
178#102—131no—
179#102—132no—
180#102—131no—
181C22⋊C8—132no—
182C4×C8—131no—
183C2×C13—42no—
184C2×C13—42no—
185C2×C13—82no—
186C2×C13D4211yescharacteristic
187C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C13#57711yescharacteristic
189D13—42no—
190C24—22no—
191#41—264no—
192#41—522no—
193C2×Q8—132no—
194C2×D4—24no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—42no—
200C2×D4—44no—
201C2×D4—131no—
202C2×D4—262no—
203C2×D4C22⋊D1311yescharacteristic
204C2×D4C22×D1312yes—
205C2×D4C22×D1311yescharacteristic
206C22×C4—21no—
207C22×C4—261no—
208C22×C4—262no—
209C22×C4C22×D1312yes—
210SD16—264no—
211SD16—264no—
212SD16—522no—
213D8—134no—
214D8—264no—
215M16—264no—
216C2×C8—131no—
217C2×C8—131no—
218C2×C8—132no—
219C4⋊C4—131no—
220C4⋊C4—261no—
221C4⋊C4—262no—
222C4⋊C4—261no—
223C4⋊C4C22⋊D1311yescharacteristic
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—22no—
227C22⋊C4—262no—
228C22⋊C4—261no—
229C22⋊C4C22⋊D1312yes—
230C42C22×D1311yescharacteristic
231C13#327211yescharacteristic, complemented, Sylow
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—261no—
238C23C2×C22⋊D1312yes—
239Q8—262no—
240Q8—262no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—132no—
250D4—261no—
251D4—524no—
252D4D4×D1312yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—261no—
258C2×C4—262no—
259C2×C4—524no—
260C2×C4—522no—
261C2×C4C2×C22⋊D1311yescharacteristic
262C2×C4C2×C22⋊D1312yes—
263C2×C4C2×C22⋊D1311yescharacteristic
264C2×C4C23×D1311yescharacteristic
265C8—132no—
266C8—262no—
267C8—261no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—262no—
279C22—521no—
280C22—521no—
281C22C22×C22⋊D1311yescharacteristic
282C4—22no—
283C4—21no—
284C4—41no—
285C4—521no—
286C4—522no—
287C4#8818612yescomplemented
288C4C2×D4×D1311yescharacteristic
289C4#8825111yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—522no—
294C2C2×#8818611yescharacteristic
295C2D4×C22⋊D1311yescharacteristic
296C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3272
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. D42×C13C2semidirect
2. C2×#88186C2semidirect
3. #11719256C2semidirect
4. #11718879C2semidirect
5. #11718737C2semidirect
6. #11718733C2semidirect
7. #11718703C2semidirect
8. #11718698C2semidirect
9. #11718680C2semidirect
10. C4×#6104C2semidirect
11. #11718673C2semidirect
14. C2×#6127C22semidirect
23. C2×#6105C22semidirect
24. C2×#6105C22semidirect
27. C2×#6104C22semidirect
28. #88178C22semidirect
29. C2×#6099C22semidirect
32. C4×D52C22semidirect
33. #88123C22semidirect
35. #88072C22semidirect
36. C22⋊#1055C22semidirect
37. #88050C22semidirect
38. #88049C22semidirect
39. #88047C22semidirect
40. C4⋊#1055C22semidirect
41. C4×#1055C22semidirect
73. #6104D4semidirect
112. D52C2×D4semidirect
119. #1055C2×D4semidirect
122. D42D13semidirect
148. C4×C13AGL(1,ℤ/8)semidirect
231. C13#3272semidirect
287. C4#88186semidirect

Maximal subgroups

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

subgroupindex
D42×C132
C2×#881862
#117192562
#117188792
#117187372
#117187332
#117187032
#117186982
#117186802
C4×#61042
#117186732
#327213