Finite Group Databasebeta

← #16781928

Subgroups — #16781928

Order 3328.

398 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 106 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#13130702C212yesmaximal
2#13130393C212yesmaximal
3#13129706C212yesmaximal
4C2×#11718491C211yesmaximal, characteristic
5C2×C4×Dic26C2211yescharacteristic
6C2×#88113—22no—
7#11719129C2214yes—
8C2×C13×C4⋊C8C411yescharacteristic
9C2×#88054C411yescharacteristic
10C2×#88054C2211yescharacteristic
11C2×C8×Dic13C411yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13C2×C4×#1055C411yescharacteristic
14#11718491—22no—
15#11718491—22no—
16#11718291—22no—
17#11718256—22no—
18#11718254—22no—
19C22×Dic26D411yescharacteristic
20C2×#6122—24no—
21C22×C8×C13C2×C411yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×C4⋊Dic13Q811yescharacteristic
25C2×#6101D411yescharacteristic
26C2×#6101Q811yescharacteristic
27C2×C4×Dic13C2×C411yescharacteristic
28C2×C4×Dic13C2311yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C4×Dic26—22no—
32C4×Dic26—22no—
33#88113—44no—
34#88112—24no—
35C4⋊#1057—24no—
36C13×C4⋊C8—22no—
37#88054—22no—
38#88054—22no—
39C8×Dic13—21no—
40C8×Dic13—21no—
41C8×Dic13D412yes—
42C8×Dic13D412yes—
43C4×#1055—21no—
44C4×#1055—21no—
45#8617—131nomaximal, Sylow
46C22×C4×C13C4⋊C411yescharacteristic
47C22×C4×C13C4⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C4⋊C411yescharacteristic
50C22×Dic13C4⋊C411yescharacteristic
51C22×Dic13C2×D411yescharacteristic
52C22×Dic13C2×Q811yescharacteristic
53C2×Dic26—22no—
54C2×Dic26—22no—
55C2×Dic26D812yes—
56C2×Dic26Q1612yes—
57#6122—44no—
58#6122—44no—
59C2×#1057—44no—
60C2×C8×C13—21no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C2×C8×C13C22⋊C412yes—
64C42×C13—21no—
65C42×C13—21no—
66C4⋊Dic13—22no—
67#6101—22no—
68#6101—22no—
69C4×Dic13—21no—
70C4×Dic13—21no—
71C4×Dic13C2×D412yes—
72C4×Dic13#4112yes—
73C2×#1055—22no—
74C2×#1055—21no—
75C2×#1055—41no—
76C2×#1055C22⋊C411yescharacteristic
77C2×#1055C22⋊C411yescharacteristic
78C2×C8×Q8—131no—
79#1801—132no—
80#1567—132no—
81#1292—132no—
82C23×C13C2×C4⋊C411yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—41no—
89C2×C4×C13#10712yes—
90C2×C4×C13C2×C22⋊C411yescharacteristic
91C2×C4×C13#11711yescharacteristic
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—41no—
96C2×Dic13—41no—
97C2×Dic13#10712yes—
98C2×Dic13#12112yes—
99C2×Dic13C22⋊Q812yes—
100C2×Dic13C2×D811yescharacteristic
101C2×Dic13C2×Q1611yescharacteristic
102C2×Dic13#13512yes—
103Dic26—24no—
104Dic26—24no—
105#1057—84no—
106C8×C13—22no—
107C8×C13—41no—
108#1055—21no—
109#1055—41no—
110#1055#10112yescomplemented
111C2×C4×Q8—131no—
112C8×Q8—262no—
113C8×Q8—262no—
114#423—134no—
115C2×C4⋊C8—131no—
116C2×C4⋊C8—131no—
117C2×C4⋊C8#26111yescharacteristic
118C2×#101—262no—
119C2×C4×C8—131no—
120C2×C4×C8—131no—
121C2×C4×C8—131no—
122#343—262no—
123#335—262no—
124#335—262no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#38011yescharacteristic
128C22×C13C2×#10711yescharacteristic
129C22×C13#42711yescharacteristic
130C4×C13—21no—
131C4×C13—22no—
132C4×C13—41no—
133C4×C13C2×#10111yescharacteristic
134C4×C13#41311yescharacteristic
135Dic13—22no—
136Dic13—22no—
137Dic13—41no—
138Dic13#46612yes—
139Dic13#46712yes—
140C22×Q8—131no—
141C2×M16—264no—
142C22×C8—131no—
143C22×C8—131no—
144C22×C8C2×#26111yescharacteristic
145C22×C8C2×#26111yescharacteristic
146C4×Q8—262no—
147C4×Q8—262no—
148C2×C4⋊C4—131no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—131no—
151C2×C42—131no—
152C2×C42—131no—
153C2×C42C2×#26111yescharacteristic
154C4⋊C8—22no—
155C4⋊C8—262no—
156C4⋊C8—264no—
157C4⋊C8—264no—
158C4⋊C8—262no—
159#101—524no—
160C4×C8—132no—
161C4×C8—132no—
162C4×C8—261no—
163C4×C8—261no—
164C4×C8—261no—
165C4×C8—261no—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13#180111yescharacteristic
169C2×C13#180811yescharacteristic
170C2×C13#181311yescharacteristic
171C2×Q8—132no—
172C2×Q8—132no—
173C2×Q8—262no—
174C2×Q8—262no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4C4⋊#26111yescharacteristic
180C22×C4C4⋊#26111yescharacteristic
181C22×C4C22×#26111yescharacteristic
182M16—524no—
183M16—524no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—131no—
188C2×C8—131no—
189C2×C8—262no—
190C2×C8—261no—
191C2×C8—521no—
192C2×C8—524no—
193C2×C8C22⋊#26112yes—
194C4⋊C4—262no—
195C4⋊C4—262no—
196C4⋊C4—262no—
197C42—21no—
198C42—21no—
199C42—132no—
200C42—132no—
201C42—261no—
202C42—261no—
203C13#861711yescharacteristic, complemented, Sylow
204C23C2×C4⋊#26111yescharacteristic
205Q8—264no—
206Q8—264no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—131no—
214C2×C4—131no—
215C2×C4—132no—
216C2×C4—132no—
217C2×C4—132no—
218C2×C4—132no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—521no—
223C2×C4—521no—
224C2×C4#8810212yes—
225C2×C4#8823711yescharacteristic
226C2×C4C2×C22⋊#26111yescharacteristic
227C8—22no—
228C8—41no—
229C8—132no—
230C8—261no—
231C8—521no—
232C8—1044no—
233C22—21no—
234C22—21no—
235C22C2×#8810211yescharacteristic
236C22#1171909211yescharacteristic
237C22#1171913611yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—132no—
242C4—132no—
243C4—262no—
244C4—262no—
245C4—521no—
246C4#1171914811yescharacteristic
247C4D13⋊#10111yescharacteristic
248C2—21no—
249C2—21no—
250C2#1313070311yescharacteristic
251C2#1313071311yescharacteristic
252C2#1313072111yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13#380
prime radicalC23×C13C2×C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊C8#261
hypocenterC13#8617
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
110. #1055#101semidirect
203. C13#8617semidirect

Maximal subgroups

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

subgroupindex
#131307022
#131303932
#131297062
C2×#117184912
#861713