Finite Group Databasebeta

← #13125580

Subgroups — #13125580

Order 1664.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#11719433C211yesmaximal, characteristic
2#11719433C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718753C211yesmaximal, characteristic, complemented
5#11718740C211yesmaximal, characteristic, complemented
6#11718477C214yesmaximal
7#11718450C214yesmaximal, complemented
8C4×#6094C211yesmaximal, characteristic
9#11718342C211yesmaximal, characteristic, complemented
10C13×C4⋊Q8C2211yescharacteristic
11C13×C4⋊Q8C2211yescharacteristic
12#88200—21no—
13#88200C2212yes—
14Q8×Dic13—21no—
15Q8×Dic13C2212yes—
16C2×#6107C2214yes—
17C2×#6094C2212yes—
18#88151—21no—
19#88151C2212yes—
20#88146—21no—
21#88146—21no—
22#88144—21no—
23#88144—21no—
24#88141—21no—
25#88141C2212yes—
26C42×D13C2211yescharacteristic
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#103C2214yes—
30C4×C8×C13C2211yescharacteristic
31#88056C2214yes—
32#88055C2212yes—
33#88048C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37C2×C4×D13D411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13C2311yescharacteristic
40C2×Dic26—21no—
41C2×Dic26C2312yes—
42C2×C8×C13C2312yes—
43C13×C4⋊C4—21no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4C2312yes—
47C42×C13C2311yescharacteristic
48#6107—28no—
49#6103—22no—
50#6103—22no—
51C4⋊Dic13—21no—
52C4⋊Dic13—21no—
53C4⋊Dic13—21no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13C2312yes—
57#6101—22no—
58#6101—22no—
59C4×Dic13—22no—
60C4×Dic13—22no—
61C4×Dic13D411yescharacteristic
62C4×Dic13D411yescharacteristic
63C4×Dic13C2311yescharacteristic
64C2×#1055C2312yes—
65#6094—24no—
66#3185—131nomaximal, Sylow
67C22×D13C2×D411yescharacteristic
68Q8×C13—24no—
69Q8×C13—42no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2411yescharacteristic
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13C2×D411yescharacteristic
78C2×Dic13C2×D411yescharacteristic
79C2×Dic13C2×D411yescharacteristic
80C4×D13—22no—
81C4×D13—22no—
82C4×D13—22no—
83Dic26—24no—
84Dic26—42no—
85C8×C13—22no—
86#1055#4114yes—
87#533—131no—
88#533—131no—
89#498—131no—
90#494—131no—
91#487—131no—
92#487D1311yescharacteristic, complemented
93#470—134no—
94#441—134no—
95C4×M16—131no—
96C22×C13C22×D411yescharacteristic
97C2×D13—21no—
98C2×D13—21no—
99C2×D13—21no—
100C4×C13—42no—
101C4×C13—42no—
102C4×C13#13712yes—
103C4×C13#13712yes—
104C4×C13C2×#4112yes—
105Dic13—21no—
106Dic13—21no—
107Dic13—21no—
108Dic13—42no—
109Dic13—42no—
110C2×Q16—134no—
111C2×M16—132no—
112C4⋊Q8—131no—
113C4⋊Q8—131no—
114C4⋊Q8C2×D1311yescharacteristic
115C4⋊Q8C2×D1311yescharacteristic
116#125—261no—
117#125—261no—
118C22⋊Q8—132no—
119C22⋊Q8—132no—
120C22⋊Q8—261no—
121C22⋊Q8—261no—
122C4×Q8—132no—
123C4×Q8—132no—
124C4×Q8—261no—
125C4×Q8—261no—
126#117—261no—
127#117—261no—
128C2×C42—131no—
129#106—134no—
130#103—134no—
131#103C2×D1314yes—
132#97—132no—
133C4×C8—131no—
134C4×C8C2×D1311yescharacteristic
135C2×C13#53211yescharacteristic
136C2×C13C2×#13711yescharacteristic
137C2×C13C2×#13711yescharacteristic
138D13—41no—
139C2×Q8—21no—
140C2×Q8—132no—
141C2×Q8—261no—
142C2×Q8C22×D1312yes—
143C22×C4—131no—
144C22×C4—131no—
145C22×C4—131no—
146Q16—268no—
147M16—264no—
148C2×C8—132no—
149C2×C8C22×D1312yes—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—132no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4—262no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C4⋊C4—261no—
161C4⋊C4C22×D1312yes—
162C22⋊C4—262no—
163C22⋊C4—262no—
164C42—131no—
165C42—131no—
166C42—131no—
167C42—262no—
168C42—262no—
169C42C22×D1311yescharacteristic
170C13#318511yescharacteristic, complemented, Sylow
171C23—131no—
172Q8—24no—
173Q8—42no—
174Q8—264no—
175Q8—522no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—131no—
179C2×C4—131no—
180C2×C4—131no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4D4×D1311yescharacteristic
187C2×C4D4×D1311yescharacteristic
188C2×C4C23×D1311yescharacteristic
189C8—22no—
190C8—134no—
191C22—261no—
192C22—261no—
193C22—261no—
194C22C2×D4×D1311yescharacteristic
195C4—42no—
196C4—42no—
197C4—261no—
198C4—261no—
199C4—261no—
200C4—522no—
201C4—522no—
202C4#8816912yes—
203C4#8817212yes—
204C4#41×D1312yes—
205C2—521no—
206C2#1171937311yescharacteristic
207C2C2×#8816911yescharacteristic
208C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#487D13
hypocenterC13#3185
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C13×#487C2semidirect
4. #11718753C2semidirect
5. #11718740C2semidirect
7. #11718450C2semidirect
9. #11718342C2semidirect
92. #487D13semidirect
170. C13#3185semidirect

Maximal subgroups

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

subgroupindex
#117194332
C13×#4872
#117187532
#117187402
#117184772
#117184502
C4×#60942
#117183422
#318513