Finite Group Databasebeta

← #16782232

Subgroups — #16782232

Order 3328.

418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 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#13130737C211yesmaximal, characteristic
2#13130733C211yesmaximal, characteristic
3#13129684C214yesmaximal
4#13117331C211yesmaximal, characteristic
5C2×#88126C2211yescharacteristic
6#11719135C2212yes—
7#11719126C2212yes—
8C13×#376C411yescharacteristic, complemented
9C4×#6103C2212yes—
10C4×#6101C412yescomplemented
11C42×Dic13C411yescharacteristic, complemented
12#11718330—22no—
13#11718313—22no—
14#11718291—22no—
15#11718289—22no—
16C22×C4×D13C2311yescharacteristic
17C2×C22⋊#261—22no—
18C2×#6122—22no—
19C2×C42×C13C2×C411yescharacteristic
20C2×C42×C13C2×C412yes—
21C2×#6103—22no—
22C2×#6103D412yes—
23C2×#6101—22no—
24C2×#6101D412yes—
25C2×C4×Dic13—22no—
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13C2×C412yes—
28#88126—24no—
29(C2×#261)⋊C4—24no—
30#88111—24no—
31C13×#95—22no—
32#88071—22no—
33#88071—22no—
34#8740—131nomaximal, Sylow
35C23×D13C2×D411yescharacteristic
36C22×#261—42no—
37C22×C4×C13—22no—
38C22×C4×C13C22⋊C412yes—
39C22×C4×C13C22×C411yescharacteristic
40C22×Dic13—22no—
41C22×Dic13C22⋊C412yes—
42C22×Dic13C2×D411yescharacteristic
43C2×C4×D13—42no—
44C2×C4×D13#4114yes—
45C22⋊#261—44no—
46#6122—44no—
47C2×#1057—42no—
48C42×C13—22no—
49C42×C13—42no—
50#6103—24no—
51#6103—44no—
52#6101—24no—
53#6101—44no—
54C4×Dic13—22no—
55C4×Dic13—44no—
56C4×Dic13—42no—
57#2298—131no—
58#1822—131no—
59#1820—131no—
60#1284—134no—
61C23×C13C2×C22⋊C411yescharacteristic
62C22×D13—22no—
63C22×D13—42no—
64C22×D13#12312yes—
65C2×#261—82no—
66C2×#261—84no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—42no—
73C2×C4×C13#11712yes—
74C2×Dic13—22no—
75C2×Dic13—24no—
76C2×Dic13—22no—
77C2×Dic13—42no—
78C2×Dic13—42no—
79C2×Dic13—42no—
80C2×Dic13#12312yes—
81C4×D13—44no—
82#1057—82no—
83C2×#117—131no—
84#407—132no—
85#388—262no—
86#387—262no—
87#381—132no—
88C4×C4⋊C4—132no—
89C4×C22⋊C4—132no—
90#376#26111yescharacteristic, complemented
91C43—131no—
92#343—262no—
93#342—262no—
94C22×C13—22no—
95C22×C13#38111yescharacteristic
96C22×C13#41012yes—
97C2×D13—22no—
98C2×D13—24no—
99C2×D13—82no—
100#261—162no—
101C4×C13—22no—
102C4×C13—42no—
103C4×C13—82no—
104Dic13—22no—
105Dic13—44no—
106Dic13—42no—
107C23×C4—131no—
108C2×M16—262no—
109#117—264no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—262no—
112C2×C22⋊C4—132no—
113C2×C22⋊C4—262no—
114C2×C22⋊C4—262no—
115C2×C42—131no—
116C2×C42—132no—
117C2×C42—262no—
118C2×C42C2×#26111yescharacteristic
119C2×C42C2×#26112yes—
120C22⋊C8—264no—
121#95—22no—
122#95—262no—
123#95—262no—
124#95—264no—
125C2×C13—22no—
126C2×C13#182011yescharacteristic
127C2×C13#182712yes—
128D13—42no—
129C24—131no—
130C22×C4—22no—
131C22×C4—131no—
132C22×C4—134no—
133C22×C4—132no—
134C22×C4—262no—
135C22×C4—522no—
136C22×C4—522no—
137C22×C4C22⋊#26112yes—
138C22×C4C22×#26111yescharacteristic
139M16—524no—
140C2×C8—522no—
141C4⋊C4—264no—
142C4⋊C4—524no—
143C22⋊C4—264no—
144C22⋊C4—524no—
145C22⋊C4—524no—
146C42—22no—
147C42—42no—
148C42—262no—
149C42—522no—
150C42—524no—
151C13#874011yescharacteristic, complemented, Sylow
152C23—132no—
153C23—262no—
154C23—522no—
155C23C2×C22⋊#26111yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—132no—
163C2×C4—262no—
164C2×C4—264no—
165C2×C4—262no—
166C2×C4—524no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4—1042no—
171C2×C4—1044no—
172C2×C4#8823712yes—
173C8—1042no—
174C22—22no—
175C22—262no—
176C22—264no—
177C22—1042no—
178C22#1171911612yes—
179C22#1171913511yescharacteristic
180C4—22no—
181C4—42no—
182C4—82no—
183C4—262no—
184C4—524no—
185C4—522no—
186C4—2082no—
187C2—22no—
188C2—522no—
189C2#1313073311yescharacteristic
190C2#1313074612yes—
subgroupG/H
centerC22#11719135
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#376C4
socleC22×C13#381
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#376#261
hypocenterC13#8740
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
8. C13×#376C4semidirect
10. C4×#6101C4semidirect
11. C42×Dic13C4semidirect
90. #376#261semidirect
151. C13#8740semidirect

Maximal subgroups

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

subgroupindex
#131307372
#131307332
#131296842
#131173312
#874013