Finite Group Databasebeta

← #13130815

Subgroups — #13130815

Order 1664.

408 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C22×#6122C211yesmaximal, characteristic, complemented
2C2×#88135C211yesmaximal, characteristic
3C2×C22⋊#1057C211yesmaximal, characteristic, complemented
4C2×#88111C212yesmaximal, complemented
5#11718290C212yesmaximal, complemented
6C22×C22⋊D13C411yescharacteristic
7C23×Dic13C2211yescharacteristic
8C22×C4×D13C2211yescharacteristic
9C2×#6122—22no—
10C2×#6122—24no—
11C22×#1057C2212yes—
12C22×#1057C2212yes—
13C2×C13×C22⋊C4C411yescharacteristic
14C2×#6103C411yescharacteristic
15C2×#6101C411yescharacteristic
16C2×C4×Dic13C2211yescharacteristic
17#88135—22no—
18#88135—22no—
19C22⋊#1057—22no—
20#88111—24no—
21C24×C13C2×C411yescharacteristic
22C23×D13C2×C411yescharacteristic
23C22×C4×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C2×C22⋊D13—22no—
26C2×C22⋊D13—22no—
27C2×C22⋊D13—22no—
28C22×Dic13—22no—
29C22×Dic13—22no—
30C22×Dic13C2×C411yescharacteristic
31C22×Dic13C2×C411yescharacteristic
32C22×Dic13D412yes—
33C22×Dic13D412yes—
34C22×Dic13C2311yescharacteristic
35C2×C4×D13—22no—
36C2×C4×D13—21no—
37C2×C4×D13—21no—
38C2×C4×D13—22no—
39#6122—28no—
40C2×#1057—22no—
41C2×#1057—22no—
42C2×#1057—22no—
43C2×#1057—22no—
44C2×#1057—22no—
45C2×#1057D414yescomplemented
46C13×C22⋊C4—22no—
47#6103—22no—
48#6101—22no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51#1870—131nomaximal, Sylow
52C23×C13—22no—
53C23×C13—21no—
54C23×C13—21no—
55C23×C13—22no—
56C23×C13C22⋊C412yes—
57C23×C13C22×C411yescharacteristic
58C22×D13—21no—
59C22×D13—22no—
60C22×D13—21no—
61C22×D13—22no—
62C22×D13M1612yescomplemented
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C22⋊D13—28no—
68C2×Dic13—21no—
69C2×Dic13—22no—
70C2×Dic13—21no—
71C2×Dic13—22no—
72C2×Dic13—24no—
73C2×Dic13—22no—
74C2×Dic13C22⋊C412yes—
75C2×Dic13M1612yescomplemented
76C2×Dic13C2×D412yes—
77C2×Dic13C2×D411yescharacteristic
78C2×Dic13C2×D411yescharacteristic
79C2×Dic13#4112yes—
80C4×D13—41no—
81C4×D13—42no—
82C4×D13—41no—
83#1057—24no—
84#1057—42no—
85C22×M16—131no—
86C2×C4×D4—131no—
87C2×C22⋊C8—131no—
88C2×C22⋊C8—132no—
89#336—132no—
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—22no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13C2×C22⋊C411yescharacteristic
96C22×C13C4×D412yes—
97C22×C13C2×M1611yescharacteristic
98C22×C13C2×M1611yescharacteristic
99C22×C13#13112yes—
100C2×D13—22no—
101C2×D13—24no—
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—42no—
105C4×C13—41no—
106C4×C13—41no—
107Dic13—22no—
108Dic13—22no—
109Dic13#12011yescharacteristic
110Dic13#12112yes—
111Dic13#12311yescharacteristic
112C22×D4—131no—
113C23×C4—131no—
114C23×C4—131no—
115C2×M16—264no—
116C2×M16—262no—
117C22×C8—132no—
118C22×C8—132no—
119C4×D4—262no—
120C4×D4—262no—
121C2×C4⋊C4—131no—
122C2×C22⋊C4—131no—
123C2×C22⋊C4#26111yescharacteristic
124C2×C42—131no—
125C22⋊C8—264no—
126C22⋊C8—262no—
127C2×C13—42no—
128C2×C13#38611yescharacteristic
129C2×C13#40711yescharacteristic
130C2×C13#40811yescharacteristic
131C2×C13#43512yes—
132C2×C13#43612yes—
133D13—42no—
134C24—131no—
135C24C2×#26111yescharacteristic
136C2×D4—262no—
137C2×D4—262no—
138C2×D4—262no—
139C22×C4—131no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—131no—
143C22×C4—131no—
144C22×C4—262no—
145C22×C4—261no—
146C22×C4—261no—
147C22×C4—262no—
148C22×C4—262no—
149C22×C4—262no—
150C22×C4C2×#26111yescharacteristic
151C22×C4C2×#26111yescharacteristic
152M16—268no—
153C2×C8—134no—
154C2×C8—262no—
155C2×C8—262no—
156C2×C8—262no—
157C2×C8—262no—
158C2×C8—262no—
159C4⋊C4—262no—
160C22⋊C4—22no—
161C22⋊C4—262no—
162C42—261no—
163C42—261no—
164C13#187011yescharacteristic, complemented, Sylow
165C23—21no—
166C23—21no—
167C23—22no—
168C23—22no—
169C23—132no—
170C23—261no—
171C23—262no—
172C23—262no—
173C23—261no—
174C23C22⋊#26112yes—
175C23C22×#26111yescharacteristic
176D4—268no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—132no—
182C2×C4—132no—
183C2×C4—131no—
184C2×C4—131no—
185C2×C4—132no—
186C2×C4—132no—
187C2×C4—262no—
188C2×C4—264no—
189C2×C4—262no—
190C2×C4—261no—
191C2×C4—262no—
192C2×C4—261no—
193C2×C4—521no—
194C2×C4—522no—
195C2×C4—521no—
196C8—264no—
197C8—522no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—264no—
204C22—262no—
205C22—522no—
206C22—521no—
207C22—521no—
208C22D13⋊M1611yescharacteristic
209C22D13⋊M1611yescharacteristic
210C22#8823812yes—
211C22D4×#26112yes—
212C22C2×C22⋊#26111yescharacteristic
213C4—41no—
214C4—41no—
215C4—131no—
216C4—132no—
217C4—131no—
218C4—262no—
219C4—262no—
220C2—42no—
221C2—522no—
222C2#1171906512yes—
223C2#1171906612yes—
224C2#1171912611yescharacteristic
225C2#1171914611yescharacteristic
226C2#1171915011yescharacteristic
subgroupG/H
center, FrattiniC23C22×#261
commutator, socleC23×C13C22×C4
FittingC2×C13×C22⋊C4C4
prime radicalC22×C22⋊D13C4
cosocleC22×Dic13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1870
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6122C2semidirect
3. C2×C22⋊#1057C2semidirect
4. C2×#88111C2semidirect
5. #11718290C2semidirect
45. C2×#1057D4semidirect
62. C22×D13M16semidirect
75. C2×Dic13M16semidirect
164. C13#1870semidirect

Maximal subgroups

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

subgroupindex
C22×#61222
C2×#881352
C2×C22⋊#10572
C2×#881112
#117182902
#187013