Finite Group Databasebeta

← #13130816

Subgroups — #13130816

Order 1664.

408 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 92 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×#6118C211yesmaximal, characteristic, complemented
2C2×#88147C211yesmaximal, characteristic
3C2×#88111C211yesmaximal, characteristic, complemented
4C2×#88111C212yesmaximal, complemented
5#11718290C212yesmaximal, complemented
6C22×D52C411yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C22×C4×D13C2211yescharacteristic
9C22×#1057C2212yes—
10C22×#1057C2212yes—
11C2×#6118—22no—
12C2×#6118—24no—
13C2×C13×C4⋊C4C411yescharacteristic
14C2×#6103C411yescharacteristic
15C2×#6103C411yescharacteristic
16C2×C4×Dic13C2211yescharacteristic
17#88147—22no—
18#88147—22no—
19#88111—22no—
20#88111—24no—
21C23×D13C2×C411yescharacteristic
22C23×D13C2×C411yescharacteristic
23C22×C4×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C22×C4×C13C2×C411yescharacteristic
26C22×Dic13C2×C411yescharacteristic
27C22×Dic13C2311yescharacteristic
28C2×D52—22no—
29C2×D52—22no—
30C2×D52—22no—
31C2×C4×D13—22no—
32C2×C4×D13—22no—
33C2×C4×D13—22no—
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13—22no—
37C2×C4×D13D412yes—
38C2×C4×D13D412yes—
39C2×#1057—22no—
40C2×#1057—22no—
41C2×#1057—22no—
42C2×#1057—22no—
43C2×#1057—22no—
44C2×#1057D414yescomplemented
45#6118—28no—
46C13×C4⋊C4—22no—
47#6103—22no—
48#6103—22no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51#1870—131nomaximal, Sylow
52C23×C13C22×C411yescharacteristic
53C22×D13—21no—
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—21no—
57C22×D13—21no—
58C22×D13—21no—
59C22×D13—22no—
60C22×D13—22no—
61C22×D13C22⋊C412yes—
62C22×D13M1612yescomplemented
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13C22⋊C412yes—
69C2×C4×C13M1612yescomplemented
70C2×Dic13—21no—
71C2×Dic13—22no—
72C2×Dic13C2×D412yes—
73C2×Dic13C2×D411yescharacteristic
74C2×Dic13C2×D411yescharacteristic
75C2×Dic13#4112yes—
76D52—28no—
77C4×D13—22no—
78C4×D13—24no—
79C4×D13—22no—
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—132no—
88C2×C22⋊C8—131no—
89#336—132no—
90C22×C13C2×C22⋊C411yescharacteristic
91C22×C13C4×D412yes—
92C22×C13C2×M1611yescharacteristic
93C22×C13C2×M1611yescharacteristic
94C22×C13#13112yes—
95C2×D13—22no—
96C2×D13—22no—
97C2×D13—22no—
98C2×D13—22no—
99C2×D13—24no—
100C2×D13—41no—
101C2×D13—41no—
102C2×D13—42no—
103C2×D13—42no—
104C2×D13—42no—
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—41no—
108Dic13—41no—
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#26111yescharacteristic
122C2×C22⋊C4—131no—
123C2×C22⋊C4—131no—
124C2×C42—131no—
125C22⋊C8—264no—
126C22⋊C8—262no—
127C2×C13#38611yescharacteristic
128C2×C13#40711yescharacteristic
129C2×C13#40811yescharacteristic
130C2×C13#43512yes—
131C2×C13#43612yes—
132D13—42no—
133D13—42no—
134C24—131no—
135C24—131no—
136C2×D4—262no—
137C2×D4—262no—
138C2×D4—262no—
139C22×C4—131no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—131no—
143C22×C4—262no—
144C22×C4—262no—
145C22×C4—262no—
146C22×C4—261no—
147C22×C4—261no—
148C22×C4—262no—
149C22×C4C2×#26111yescharacteristic
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—22no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C42—261no—
163C42—261no—
164C13#187011yescharacteristic, complemented, Sylow
165C23—132no—
166C23—132no—
167C23—261no—
168C23—261no—
169C23—261no—
170C23—262no—
171C23—262no—
172C23—262no—
173C23—262no—
174C23—261no—
175C23C22×#26111yescharacteristic
176D4—268no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—132no—
183C2×C4—132no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—262no—
187C2×C4—264no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—261no—
191C2×C4—521no—
192C2×C4—522no—
193C2×C4—521no—
194C2×C4#611812yescomplemented
195C2×C4C22⋊#26112yes—
196C8—264no—
197C8—522no—
198C22—264no—
199C22—262no—
200C22—262no—
201C22—262no—
202C22—262no—
203C22—522no—
204C22—522no—
205C22—522no—
206C22—521no—
207C22—521no—
208C22C2×#611811yescharacteristic
209C22D13⋊M1611yescharacteristic
210C22D4×#26112yes—
211C22#8824012yes—
212C22C2×C22⋊#26111yescharacteristic
213C4—22no—
214C4—22no—
215C4—41no—
216C4—131no—
217C4—132no—
218C4—131no—
219C4—521no—
220C2—522no—
221C2—522no—
222C2#1171907512yes—
223C2#1171907612yes—
224C2#1171912711yescharacteristic
225C2#1171915011yescharacteristic
226C2#1171915911yescharacteristic
subgroupG/H
center, FrattiniC23C22×#261
commutator, socleC23×C13C22×C4
FittingC2×C13×C4⋊C4C4
prime radicalC22×D52C4
cosocleC22×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1870
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6118C2semidirect
3. C2×#88111C2semidirect
4. C2×#88111C2semidirect
5. #11718290C2semidirect
44. C2×#1057D4semidirect
62. C22×D13M16semidirect
69. C2×C4×C13M16semidirect
164. C13#1870semidirect
194. C2×C4#6118semidirect

Maximal subgroups

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

subgroupindex
C22×#61182
C2×#881472
C2×#881112
#117182902
#187013