Finite Group Databasebeta

← #13130975

Subgroups — #13130975

Order 1664.

408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#88192C211yesmaximal, characteristic
2C2×#88119C214yesmaximal, complemented
3#11719136C211yesmaximal, characteristic, complemented
4C4×C22⋊#261C211yesmaximal, characteristic, complemented
5C22×D4×C13C411yescharacteristic, complemented
6C22×C22⋊D13C2212yes—
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261C2212yes—
9C2×C22⋊#261C2212yes—
10C2×C4⋊#261—21no—
11C2×C4×#261—21no—
12C2×C22⋊Dic13C412yescomplemented
13#88192—21no—
14#88192—21no—
15#88192—21no—
16#88192—21no—
17C2×C4⋊Dic13C411yescharacteristic, complemented
18#88119—28no—
19(C2×#261)⋊C4—21no—
20(C2×#261)⋊C4—21no—
21C24×C13C2×C412yes—
22C23×D13C2311yescharacteristic
23C22×#261—22no—
24C22×#261—22no—
25C2×D4×C13—21no—
26C2×D4×C13—21no—
27C2×D4×C13—42no—
28C22×C4×C13C2×C411yescharacteristic
29C2×C22⋊D13—24no—
30C2×C22⋊D13—22no—
31C2×C22⋊D13—22no—
32C2×C22⋊D13—24no—
33C22×Dic13C2×C412yes—
34C22×Dic13C2×C411yescharacteristic
35C2×C4×D13—42no—
36C2×C4×D13D411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13D411yescharacteristic
40C22⋊#261—22no—
41C22⋊#261—24no—
42C22⋊#261D414yescomplemented
43C4⋊#261—42no—
44C4×#261—42no—
45C22⋊Dic13—22no—
46C22⋊Dic13—22no—
47C4⋊Dic13—21no—
48C4⋊Dic13—21no—
49#1964—131nomaximal, Sylow
50C23×C13—22no—
51C23×C13—24no—
52C23×C13—42no—
53C23×C13—42no—
54C23×C13C22×C411yescharacteristic
55C22×D13—41no—
56C22×D13—41no—
57C22×D13C2×D411yescharacteristic
58C22×D13C2×D411yescharacteristic
59C22×D13C2×D412yes—
60C22×D13#4112yes—
61C2×#261—24no—
62C2×#261—42no—
63C2×#261—42no—
64C2×#261—42no—
65C2×#261—42no—
66C2×#261—42no—
67D4×C13—42no—
68D4×C13—42no—
69C2×C4×C13—22no—
70C2×C4×C13C22⋊C411yescharacteristic
71C2×C4×C13C22⋊C411yescharacteristic
72C22⋊D13—44no—
73C22⋊D13—42no—
74C22⋊D13—42no—
75C2×Dic13—22no—
76C2×Dic13—24no—
77C2×Dic13—41no—
78C2×Dic13C22⋊C411yescharacteristic
79C2×Dic13C22⋊C411yescharacteristic
80C4×D13—22no—
81C4×D13—22no—
82C4×D13—41no—
83C4×D13—41no—
84C2×#121—131no—
85C2×#99—134no—
86#380—131no—
87C4×C22⋊C4—131no—
88C22×C13—21no—
89C22×C13—21no—
90C22×C13—42no—
91C22×C13—42no—
92C22×C13—42no—
93C22×C13—84no—
94C22×C13C2×C22⋊C411yescharacteristic
95C22×C13C4×D412yes—
96C2×D13—21no—
97C2×D13—21no—
98C2×D13—21no—
99C2×D13—21no—
100C2×D13—42no—
101C2×D13—42no—
102C2×D13#12112yes—
103C2×D13#12411yescharacteristic
104C2×D13#12711yescharacteristic
105#261—44no—
106#261—82no—
107C4×C13—21no—
108C4×C13#9912yescomplemented
109Dic13—21no—
110Dic13—21no—
111Dic13—42no—
112C22×D4—132no—
113C22×D4#26111yescharacteristic, complemented
114C23×C4—131no—
115#121—261no—
116#121—261no—
117#121—261no—
118#121—261no—
119C2×C4⋊C4—131no—
120C2×C4⋊C4—261no—
121C2×C22⋊C4—132no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—132no—
124C2×C42—261no—
125#99—268no—
126#95—261no—
127#95—261no—
128C2×C13—22no—
129C2×C13—82no—
130C2×C13#39011yescharacteristic
131C2×C13C2×#9911yescharacteristic
132C2×C13#41011yescharacteristic
133D13—22no—
134D13—21no—
135D13—21no—
136C24—131no—
137C24C2×#26112yes—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—42no—
141C2×D4—264no—
142C2×D4—262no—
143C2×D4—262no—
144C2×D4—264no—
145C22×C4—131no—
146C22×C4—131no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—132no—
151C22×C4—262no—
152C22×C4—262no—
153C22×C4—522no—
154C22×C4C2×#26111yescharacteristic
155C4⋊C4—261no—
156C4⋊C4—261no—
157C4⋊C4—522no—
158C22⋊C4—134no—
159C22⋊C4—262no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C22⋊C4—264no—
163C42—522no—
164C13#196411yescharacteristic, complemented, Sylow
165C23—22no—
166C23—24no—
167C23—42no—
168C23—42no—
169C23—131no—
170C23—131no—
171C23—132no—
172C23—132no—
173C23—521no—
174C23—521no—
175C23C22×#26111yescharacteristic
176D4—42no—
177D4—42no—
178D4—524no—
179D4—522no—
180D4—522no—
181C2×C4—22no—
182C2×C4—131no—
183C2×C4—131no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—264no—
187C2×C4—264no—
188C2×C4—262no—
189C2×C4—521no—
190C2×C4—521no—
191C2×C4—521no—
192C2×C4—522no—
193C2×C4—522no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4C22⋊#26111yescharacteristic
198C2×C4C22⋊#26111yescharacteristic
199C22—21no—
200C22—21no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—84no—
205C22—132no—
206C22—131no—
207C22—131no—
208C22—261no—
209C22—261no—
210C22—261no—
211C22—261no—
212C22—522no—
213C22—522no—
214C22D4×#26112yes—
215C22C2×C22⋊#26111yescharacteristic
216C4—21no—
217C4—261no—
218C4—261no—
219C4—524no—
220C4—522no—
221C4—1042no—
222C4#8811912yescomplemented
223C2—22no—
224C2—82no—
225C2—262no—
226C2—261no—
227C2—261no—
228C2#1171914211yescharacteristic
229C2#1171915111yescharacteristic
230C2C2×#8811911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC22×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#88192C2
cosocleC23×D13C23
hypercenterC22×D4#261
hypocenterC13#1964
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#88119C2semidirect
3. #11719136C2semidirect
4. C4×C22⋊#261C2semidirect
5. C22×D4×C13C4semidirect
12. C2×C22⋊Dic13C4semidirect
17. C2×C4⋊Dic13C4semidirect
42. C22⋊#261D4semidirect
108. C4×C13#99semidirect
113. C22×D4#261semidirect
164. C13#1964semidirect
222. C4#88119semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
C2×#881192
#117191362
C4×C22⋊#2612
#196413