Finite Group Databasebeta

← #13125898

Subgroups — #13125898

Order 1664.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719429C211yesmaximal, characteristic, complemented
2#11719403C211yesmaximal, characteristic, complemented
3C13×#491C211yesmaximal, characteristic, complemented
4#11718746C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718480C212yesmaximal, complemented
7#11718479C212yesmaximal, complemented
8#11718472C212yesmaximal, complemented
9#11718467C212yesmaximal, complemented
10#11718373C211yesmaximal, characteristic, complemented
11#11718370C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C2×Q8×D13C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15C13×#125C2211yescharacteristic
16#88201C2211yescharacteristic
17#88198C2211yescharacteristic
18C2×#6106C2212yes—
19C2×#6106C2212yes—
20C2×D104C2212yes—
21C2×#6095C2212yes—
22#88150—22no—
23#88149—22no—
24#88149C2212yes—
25#88148—22no—
26#88148—22no—
27#88147C2212yes—
28#88129C2211yescharacteristic
29#88128C2211yescharacteristic
30#88126C2211yescharacteristic
31C13×#103C2212yes—
32C13×#103C2212yes—
33C13×#97C2211yescharacteristic
34#88060C2212yes—
35#88054C2212yes—
36#88050C2212yes—
37#88049C2212yes—
38C4×#1055C2211yescharacteristic
39C2×Q8×C13C2311yescharacteristic
40C2×Q8×C13C2311yescharacteristic
41#6131—42no—
42Q8×D13—42no—
43C2×D52—21no—
44C2×D52—22no—
45C2×D52—22no—
46C2×D52C2312yes—
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×C4×D13—21no—
50C2×C4×D13—22no—
51C2×C4×D13C2311yescharacteristic
52C2×Dic26—21no—
53C2×Dic26C2311yescharacteristic
54C2×C8×C13C2312yes—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4C2312yes—
58C42×C13C2311yescharacteristic
59#6106—42no—
60#6106—42no—
61#6103—22no—
62#6103—22no—
63#6103—22no—
64#6103—22no—
65#6103D412yes—
66#6101—22no—
67#6101D412yes—
68C4×Dic13C2311yescharacteristic
69C2×#1055C2312yes—
70D104—42no—
71#6095—42no—
72#3221—131nomaximal, Sylow
73C22×D13—21no—
74C22×D13—22no—
75C22×D13C2×D411yescharacteristic
76Q8×C13—22no—
77Q8×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13C2×D412yes—
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13C2×D412yes—
85C2×Dic13C2×D411yescharacteristic
86D52—22no—
87D52—22no—
88D52—22no—
89D52—42no—
90D52—82no—
91D52—82no—
92C4×D13—22no—
93C4×D13—42no—
94C4×D13—42no—
95C4×D13—82no—
96Dic26—22no—
97Dic26—42no—
98C8×C13—22no—
99#1055—22no—
100#540—131no—
101#536—131no—
102#496—131no—
103#492—131no—
104#491D1311yescharacteristic, complemented
105#488—131no—
106#463—132no—
107#461—132no—
108#449—132no—
109#448—132no—
110#433—131no—
111C22×C13C22×D411yescharacteristic
112C2×D13—21no—
113C2×D13—22no—
114C2×D13—41no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C4×C13—22no—
120C4×C13—41no—
121C4×C13—41no—
122C4×C13—42no—
123C4×C13H(5,𝔽2)12yes—
124Dic13—21no—
125Dic13—22no—
126Dic13—41no—
127C2×#41—131no—
128C22×Q8—131no—
129C2×SD16—132no—
130C2×SD16—132no—
131C2×SD16—132no—
132C2×D8—132no—
133C4⋊Q8—131no—
134C4⋊Q8C2×D1311yescharacteristic
135#127—131no—
136#125C2×D1311yescharacteristic
137#124—131no—
138#124—131no—
139#123—262no—
140#123—262no—
141C22⋊Q8—262no—
142#121—132no—
143#121—262no—
144C4×D4—132no—
145#117—131no—
146C4⋊C8—132no—
147#103—132no—
148#103C2×D1312yes—
149#103C2×D1312yes—
150#102—132no—
151C22⋊C8—132no—
152#97C2×D1311yescharacteristic
153C4×C8—131no—
154C2×C13#53511yescharacteristic
155C2×C13#57712yes—
156D13—41no—
157D13—81no—
158D13—82no—
159#41—522no—
160C2×Q8—131no—
161C2×Q8—261no—
162C2×Q8—522no—
163C2×Q8C22×D1311yescharacteristic
164C2×Q8C22×D1311yescharacteristic
165C2×D4—131no—
166C2×D4—132no—
167C2×D4—261no—
168C2×D4—262no—
169C2×D4—262no—
170C22×C4—131no—
171C22×C4—261no—
172C22×C4—262no—
173C22×C4—261no—
174SD16—522no—
175SD16—522no—
176SD16—522no—
177D8—522no—
178C2×C8—132no—
179C2×C8C22×D1312yes—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—132no—
183C4⋊C4—262no—
184C4⋊C4C22×D1312yes—
185C22⋊C4—132no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C42—131no—
191C42C22×D1311yescharacteristic
192C13#322111yescharacteristic, complemented, Sylow
193C23—131no—
194C23—261no—
195C23—262no—
196Q8—22no—
197Q8—22no—
198Q8—262no—
199Q8—522no—
200D4—262no—
201D4—262no—
202D4—262no—
203D4—522no—
204D4—1042no—
205D4—1042no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—132no—
210C2×C4—131no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—1042no—
216C2×C4D4×D1312yes—
217C2×C4C23×D1311yescharacteristic
218C8—22no—
219C8—262no—
220C22—262no—
221C22—261no—
222C22—522no—
223C22—522no—
224C22—522no—
225C22—521no—
226C22—522no—
227C22C2×D4×D1311yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—262no—
233C4—261no—
234C4—521no—
235C4#8825612yes—
236C2—521no—
237C2—1042no—
238C2—1041no—
239C2#1171937911yescharacteristic
240C2#1171948312yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
hypercenter#491D13
hypocenterC13#3221
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #11719429C2semidirect
2. #11719403C2semidirect
3. C13×#491C2semidirect
4. #11718746C2semidirect
5. #11718729C2semidirect
6. #11718480C2semidirect
7. #11718479C2semidirect
8. #11718472C2semidirect
9. #11718467C2semidirect
10. #11718373C2semidirect
11. #11718370C2semidirect
104. #491D13semidirect
192. C13#3221semidirect

Maximal subgroups

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

subgroupindex
#117194292
#117194032
C13×#4912
#117187462
#117187292
#117184802
#117184792
#117184722
#117184672
#117183732
#117183702
#322113