Finite Group Databasebeta

← #13125899

Subgroups — #13125899

Order 1664.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719240C211yesmaximal, characteristic, complemented
2#11719231C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718505C212yesmaximal, complemented
5#11718502C212yesmaximal, complemented
6#11718399C212yesmaximal, complemented
7#11718395C212yesmaximal, complemented
8#11718373C211yesmaximal, characteristic, complemented
9#11718364C211yesmaximal, characteristic, complemented
10#11718358C211yesmaximal, characteristic, complemented
11#11718354C211yesmaximal, characteristic, complemented
12C2×#6127C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C13×#117C2211yescharacteristic
15#88184C2212yes—
16C2×D104C2212yes—
17C2×#6095C2212yes—
18C2×#6095C2212yes—
19C2×#6095C2212yes—
20#88151—22no—
21#88148—22no—
22#88140—22no—
23#88138—22no—
24#88129C2211yescharacteristic
25#88129C2211yescharacteristic
26#88128C2211yescharacteristic
27C4×D52C2212yes—
28#88124C2211yescharacteristic
29#88123C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×C4⋊C8C2212yes—
32C13×C22⋊C8C2212yes—
33C13×#97C2211yescharacteristic
34C4×C8×C13C2211yescharacteristic
35#88061C2212yes—
36#88056C2212yes—
37#88056C2212yes—
38#88056C2212yes—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—21no—
41C2×C22⋊D13—22no—
42C22×Dic13—21no—
43#6127—42no—
44C2×D52—22no—
45C2×D52C2312yes—
46C2×D52C2311yescharacteristic
47C2×C4×D13—21no—
48C2×C4×D13—22no—
49C2×Dic26—21no—
50C2×Dic26—42no—
51C2×Dic26C2311yescharacteristic
52C2×Dic26C2311yescharacteristic
53C2×Dic26C2311yescharacteristic
54C2×C8×C13C2312yes—
55C2×C8×C13C2312yes—
56C13×C4⋊C4D412yes—
57C13×C22⋊C4D412yes—
58C42×C13C2311yescharacteristic
59C42×C13C2311yescharacteristic
60#6103—22no—
61#6103—22no—
62#6103—22no—
63#6103—22no—
64C4⋊Dic13—22no—
65C4⋊Dic13—22no—
66C4⋊Dic13C2312yes—
67#6101—22no—
68D104—42no—
69#6095—42no—
70#6095—42no—
71#6095—42no—
72#3221—131nomaximal, Sylow
73C23×C13C2×D411yescharacteristic
74C22×D13—21no—
75C22×D13—22no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—42no—
82C22⋊D13—82no—
83C2×Dic13—22no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—42no—
88D52—22no—
89D52—22no—
90D52—22no—
91D52—82no—
92C4×D13—42no—
93C4×D13—82no—
94Dic26—22no—
95Dic26—22no—
96Dic26—22no—
97Dic26—42no—
98C8×C13—22no—
99C8×C13—22no—
100#540—131no—
101#536—131no—
102#496—131no—
103#492—131no—
104#491—131no—
105#488—131no—
106#463—132no—
107#461—132no—
108#449—132no—
109#448—132no—
110#433D1311yescharacteristic, complemented
111C22×C13—21no—
112C22×C13—22no—
113C22×C13C22×D411yescharacteristic
114C2×D13—41no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13H(5,𝔽2)12yes—
123Dic13—41no—
124Dic13—41no—
125Dic13—41no—
126Dic13—42no—
127C2×#41—131no—
128C22×Q8—131no—
129C2×SD16—132no—
130C2×SD16—132no—
131C2×SD16—132no—
132C2×D8—132no—
133C4⋊Q8—131no—
134C4⋊Q8—131no—
135#127—131no—
136#125—131no—
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#117C2×D1311yescharacteristic
146C4⋊C8C2×D1312yes—
147#103—132no—
148#103—132no—
149#103—132no—
150#102—132no—
151C22⋊C8C2×D1312yes—
152#97C2×D1311yescharacteristic
153C4×C8C2×D1311yescharacteristic
154C2×C13—41no—
155C2×C13#53511yescharacteristic
156C2×C13#57712yes—
157D13—81no—
158D13—82no—
159#41—522no—
160C2×Q8—131no—
161C2×Q8—131no—
162C2×Q8—131no—
163C2×Q8—261no—
164C2×Q8—522no—
165C2×D4—131no—
166C2×D4—132no—
167C2×D4—261no—
168C2×D4—262no—
169C2×D4—262no—
170C22×C4—261no—
171C22×C4—261no—
172C22×C4—262no—
173C22×C4C22×D1311yescharacteristic
174SD16—522no—
175SD16—522no—
176SD16—522no—
177D8—522no—
178C2×C8C22×D1312yes—
179C2×C8C22×D1312yes—
180C4⋊C4—132no—
181C4⋊C4—262no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4D5212yes—
185C22⋊C4—262no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C22⋊C4D5212yes—
190C42C22×D1311yescharacteristic
191C42C22×D1311yescharacteristic
192C13#322111yescharacteristic, complemented, Sylow
193C23—261no—
194C23—262no—
195C23C2×D5211yescharacteristic
196Q8—262no—
197Q8—262no—
198Q8—262no—
199Q8—522no—
200D4—262no—
201D4—262no—
202D4—262no—
203D4—522no—
204D4—1042no—
205D4—1042no—
206C2×C4—22no—
207C2×C4—262no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—1042no—
214C2×C4C2×D5212yes—
215C2×C4C2×D5212yes—
216C2×C4C2×D5211yescharacteristic
217C2×C4C23×D1311yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—21no—
222C22—522no—
223C22—522no—
224C22—522no—
225C22—521no—
226C22—522no—
227C22C22×D5211yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—522no—
232C4—521no—
233C4—521no—
234C4—521no—
235C4#8825612yes—
236C2—41no—
237C2—1042no—
238C2—1041no—
239C2#1171923011yescharacteristic
240C2#1171945612yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
hypercenter#433D13
hypocenterC13#3221
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #11719240C2semidirect
2. #11719231C2semidirect
3. C13×#433C2semidirect
4. #11718505C2semidirect
5. #11718502C2semidirect
6. #11718399C2semidirect
7. #11718395C2semidirect
8. #11718373C2semidirect
9. #11718364C2semidirect
10. #11718358C2semidirect
11. #11718354C2semidirect
110. #433D13semidirect
192. C13#3221semidirect

Maximal subgroups

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

subgroupindex
#117192402
#117192312
C13×#4332
#117185052
#117185022
#117183992
#117183952
#117183732
#117183642
#117183582
#117183542
#322113