Finite Group Databasebeta

← #13130976

Subgroups — #13130976

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×#88149C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic, complemented
3C4×C22⋊#261C211yesmaximal, characteristic, complemented
4C2×#88107C214yesmaximal, complemented
5C22×D52C411yescharacteristic, complemented
6C22×D52C2212yes—
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261C2212yes—
9C2×C22⋊#261C2212yes—
10C2×C4⋊#261—21no—
11C2×C4×#261—21no—
12C2×C13×C4⋊C4C411yescharacteristic, complemented
13C2×#6103C412yescomplemented
14#88149—21no—
15#88149—21no—
16#88149—21no—
17#88149—21no—
18(C2×#261)⋊C4—21no—
19(C2×#261)⋊C4—21no—
20#88107—28no—
21C23×D13C2×C412yes—
22C23×D13C2311yescharacteristic
23C22×#261—22no—
24C22×#261—22no—
25C22×C4×C13C2×C412yes—
26C22×C4×C13C2×C411yescharacteristic
27C22×Dic13C2×C411yescharacteristic
28C2×D52—24no—
29C2×D52—22no—
30C2×D52—22no—
31C2×D52—24no—
32C2×D52—21no—
33C2×D52—21no—
34C2×D52—42no—
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—
45C13×C4⋊C4—21no—
46C13×C4⋊C4—21no—
47#6103—22no—
48#6103—22no—
49#1964—131nomaximal, Sylow
50C23×C13C22×C411yescharacteristic
51C22×D13—22no—
52C22×D13—24no—
53C22×D13—41no—
54C22×D13—41no—
55C22×D13—42no—
56C22×D13—42no—
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—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—24no—
70C2×C4×C13C22⋊C411yescharacteristic
71C2×C4×C13C22⋊C411yescharacteristic
72C2×Dic13—41no—
73C2×Dic13C22⋊C411yescharacteristic
74C2×Dic13C22⋊C411yescharacteristic
75D52—42no—
76D52—44no—
77D52—42no—
78D52—42no—
79D52—42no—
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×C13C2×C22⋊C411yescharacteristic
91C22×C13C4×D412yes—
92C2×D13—21no—
93C2×D13—21no—
94C2×D13—21no—
95C2×D13—21no—
96C2×D13—42no—
97C2×D13—42no—
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—42no—
101C2×D13—84no—
102C2×D13#12112yes—
103C2×D13#12411yescharacteristic
104C2×D13#12711yescharacteristic
105#261—44no—
106#261—82no—
107C4×C13—21no—
108C4×C13—42no—
109C4×C13#9912yescomplemented
110Dic13—21no—
111Dic13—21no—
112C22×D4—132no—
113C22×D4—131no—
114C23×C4—131no—
115#121—261no—
116#121—261no—
117#121—261no—
118#121—261no—
119C2×C4⋊C4—261no—
120C2×C4⋊C4#26111yescharacteristic, complemented
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#39011yescharacteristic
130C2×C13C2×#9911yescharacteristic
131C2×C13#41011yescharacteristic
132D13—22no—
133D13—21no—
134D13—21no—
135D13—82no—
136C24—131no—
137C24—132no—
138C2×D4—264no—
139C2×D4—262no—
140C2×D4—262no—
141C2×D4—264no—
142C2×D4—261no—
143C2×D4—261no—
144C2×D4—522no—
145C22×C4—131no—
146C22×C4—131no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—262no—
151C22×C4—262no—
152C22×C4—522no—
153C22×C4C2×#26112yes—
154C22×C4C2×#26111yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—21no—
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—131no—
166C23—131no—
167C23—132no—
168C23—132no—
169C23—262no—
170C23—264no—
171C23—521no—
172C23—521no—
173C23—522no—
174C23—522no—
175C23C22×#26111yescharacteristic
176D4—522no—
177D4—524no—
178D4—522no—
179D4—522no—
180D4—522no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—22no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—264no—
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—132no—
202C22—131no—
203C22—131no—
204C22—261no—
205C22—261no—
206C22—261no—
207C22—261no—
208C22—522no—
209C22—522no—
210C22—522no—
211C22—522no—
212C22—522no—
213C22—1044no—
214C22D4×#26112yes—
215C22C2×C22⋊#26111yescharacteristic
216C4—21no—
217C4—42no—
218C4—261no—
219C4—261no—
220C4—524no—
221C4—1042no—
222C4#8810712yescomplemented
223C2—22no—
224C2—262no—
225C2—261no—
226C2—261no—
227C2—1042no—
228C2C2×#8810711yescharacteristic
229C2#1171915111yescharacteristic
230C2#1171915611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#88149C2
cosocleC23×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1964
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11719136C2semidirect
3. C4×C22⋊#261C2semidirect
4. C2×#88107C2semidirect
5. C22×D52C4semidirect
12. C2×C13×C4⋊C4C4semidirect
13. C2×#6103C4semidirect
42. C22⋊#261D4semidirect
109. C4×C13#99semidirect
120. C2×C4⋊C4#261semidirect
164. C13#1964semidirect
222. C4#88107semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
#117191362
C4×C22⋊#2612
C2×#881072
#196413