Finite Group Databasebeta

← #13127434

Subgroups — #13127434

Order 1664.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#11719431C211yesmaximal, characteristic, complemented
2#11719268C211yesmaximal, characteristic, complemented
3C13×#474C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5C4×#6104C211yesmaximal, characteristic, complemented
6#11718546C212yesmaximal, complemented
7#11718542C212yesmaximal, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718443C212yesmaximal, complemented
11#11718438C212yesmaximal, complemented
12C2×#6131—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15#88200—21no—
16#88192C2212yes—
17C2×#6104C2211yescharacteristic
18#88184—21no—
19#88180—21no—
20C2×#6094C2212yes—
21#88149C2212yes—
22#88148—22no—
23#88146C2212yes—
24C4⋊C4×D13C2212yes—
25#88139—22no—
26C4×D52C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#107C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88061C2212yes—
34#88060C2212yes—
35#88057C2212yes—
36#88049C2211yescharacteristic
37#88048C2212yes—
38#88048C2212yes—
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×C22⋊D13—22no—
45#6131—44no—
46C2×D52—22no—
47C2×D52D411yescharacteristic
48C2×D52C2311yescharacteristic
49C2×C4×D13—22no—
50C2×C4×D13—21no—
51C2×C4×D13C2312yes—
52C2×Dic26—21no—
53C2×C8×C13C2312yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4C2312yes—
56C13×C4⋊C4C2311yescharacteristic
57C13×C22⋊C4—21no—
58C42×C13C2311yescharacteristic
59C22⋊Dic13—22no—
60#6104—22no—
61#6103—22no—
62#6103—21no—
63#6103—22no—
64#6103D412yes—
65C4⋊Dic13—21no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2312yes—
69#6101—22no—
70C4×Dic13—22no—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#6094—24no—
74#3354—131nomaximal, Sylow
75C23×C13—21no—
76C22×D13—21no—
77C22×D13C2×D412yes—
78Q8×C13—42no—
79D4×C13—21no—
80D4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—42no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—82no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91D52—22no—
92D52—21no—
93D52—21no—
94D52—44no—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—44no—
98C4×D13—42no—
99Dic26—81no—
100C8×C13—22no—
101#1055—21no—
102#1055#4112yescomplemented
103#555—131no—
104#547—131no—
105#498—131no—
106#482—132no—
107#481—132no—
108#476—131no—
109#474D1311yescharacteristic, complemented
110#469—132no—
111C4×D8—131no—
112#436—131no—
113#428—132no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—41no—
117C22×C13C22×D411yescharacteristic
118C2×D13—22no—
119C2×D13—22no—
120C2×D13—22no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—41no—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C13AGL(1,ℤ/8)12yes—
128C4×C13C2×#4111yescharacteristic
129C4×C132−1+411yescharacteristic
130Dic13—22no—
131Dic13—41no—
132Dic13—42no—
133C2×#41—261no—
134C2×D8—131no—
135C2×M16—132no—
136C4⋊Q8—131no—
137C4⋊Q8C2×D1311yescharacteristic
138#124—262no—
139#123—262no—
140C22⋊Q8—261no—
141#121—132no—
142#121—132no—
143#121—261no—
144C4×D4—131no—
145C4×D4—131no—
146C4×D4C2×D1311yescharacteristic
147#117—132no—
148#117—261no—
149C2×C4⋊C4—132no—
150#107—131no—
151#107C2×D1312yes—
152#106—132no—
153#106—132no—
154#106—132no—
155C4⋊C8C2×D1311yescharacteristic
156#102—131no—
157#102—132no—
158#102—131no—
159#102C2×D1312yes—
160C22⋊C8—132no—
161C4×C8—131no—
162C2×C13—81no—
163C2×C13#54711yescharacteristic
164C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C13#57711yescharacteristic
166D13—42no—
167D13—81no—
168#41—524no—
169C2×Q8—21no—
170C2×Q8—261no—
171C2×D4—131no—
172C2×D4—131no—
173C2×D4—262no—
174C2×D4—262no—
175C2×D4C22×D1311yescharacteristic
176C22×C4—21no—
177C22×C4—132no—
178C22×C4—262no—
179C22×C4—261no—
180D8—262no—
181M16—264no—
182C2×C8—131no—
183C2×C8—131no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—131no—
187C4⋊C4—132no—
188C4⋊C4—131no—
189C4⋊C4—262no—
190C4⋊C4—261no—
191C4⋊C4C22×D1311yescharacteristic
192C4⋊C4C22×D1312yes—
193C22⋊C4—21no—
194C22⋊C4—132no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C22⋊C4—261no—
199C42—262no—
200C42C22×D1311yescharacteristic
201C13#335411yescharacteristic, complemented, Sylow
202C23—21no—
203C23—132no—
204C23—261no—
205Q8—42no—
206Q8—1041no—
207D4—21no—
208D4—21no—
209D4—262no—
210D4—261no—
211D4—261no—
212D4—524no—
213D4—1042no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—132no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—524no—
223C2×C4—522no—
224C2×C4D4×D1311yescharacteristic
225C2×C4D4×D1311yescharacteristic
226C2×C4C23×D1311yescharacteristic
227C8—22no—
228C8—132no—
229C8—261no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—262no—
234C22—262no—
235C22—262no—
236C22—521no—
237C22—521no—
238C22—521no—
239C22C2×D4×D1311yescharacteristic
240C4—21no—
241C4—41no—
242C4—42no—
243C4—262no—
244C4—521no—
245C4—522no—
246C4#8816512yes—
247C4#8825411yescharacteristic
248C4#41×D1311yescharacteristic
249C2—81no—
250C2—522no—
251C2—1041no—
252C2#1171933611yescharacteristic
253C2C2×#8816511yescharacteristic
254C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
hypercenter#474D13
hypocenterC13#3354
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719431C2semidirect
2. #11719268C2semidirect
3. C13×#474C2semidirect
4. #11718740C2semidirect
5. C4×#6104C2semidirect
6. #11718546C2semidirect
7. #11718542C2semidirect
8. #11718503C2semidirect
9. #11718499C2semidirect
10. #11718443C2semidirect
11. #11718438C2semidirect
102. #1055#41semidirect
109. #474D13semidirect
201. C13#3354semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192682
C13×#4742
#117187402
C4×#61042
#117185462
#117185422
#117185032
#117184992
#117184432
#117184382
#335413