Finite Group Databasebeta

← #15756399

Subgroups — #15756399

Order 3328.

418 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 91 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#13117334C211yesmaximal, characteristic
2#13114913C211yesmaximal, characteristic
3#13112690C214yesmaximal
4C13×#1822C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C13×#407C2212yes—
7#11718872C2212yes—
8C4×C22⋊Dic13C2212yes—
9#11718642—22no—
10#11718612—22no—
11C4×C4⋊Dic13C412yescomplemented
12#11718593C411yescharacteristic, complemented
13C42×Dic13C411yescharacteristic, complemented
14C13×#343—22no—
15#11718118—22no—
16C23×C4×C13C2311yescharacteristic
17C2×C13×M16—22no—
18C13×#117—24no—
19C2×C13×C4⋊C4D412yes—
20C2×C13×C22⋊C4D412yes—
21C2×C42×C13C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×C22⋊Dic13—22no—
24C2×C22⋊Dic13—22no—
25C2×C4⋊Dic13—22no—
26C2×C4×Dic13—22no—
27C2×C4×Dic13C2×C412yes—
28C2×C4×Dic13C2×C412yes—
29C13×C22⋊C8—24no—
30#88071—22no—
31#88071—22no—
32#88071—22no—
33#88071—24no—
34#8740—131nomaximal, Sylow
35C24×C13C2×D411yescharacteristic
36C22×C4×C13—42no—
37C22×C4×C13C22⋊C412yes—
38C22×C4×C13C22⋊C412yes—
39C22×C4×C13C22×C411yescharacteristic
40C22×C4×C13C2×D411yescharacteristic
41C22×C4×C13#4114yes—
42C22×Dic13—22no—
43C22×Dic13—22no—
44C22×Dic13—42no—
45C13×M16—44no—
46C2×C8×C13—42no—
47C13×C4⋊C4—24no—
48C13×C22⋊C4—24no—
49C42×C13—22no—
50C42×C13—22no—
51C22⋊Dic13—44no—
52C22⋊Dic13—44no—
53C4⋊Dic13—44no—
54C4×Dic13—44no—
55C4×Dic13—42no—
56C4×Dic13—42no—
57#2298—131no—
58#1822D1311yescharacteristic
59#1820—131no—
60#1284—134no—
61C23×C13—22no—
62C23×C13—42no—
63C23×C13C2×C22⋊C411yescharacteristic
64C23×C13#12312yes—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—44no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13#11712yes—
73C2×C4×C13#12312yes—
74C2×Dic13—24no—
75C2×Dic13—42no—
76C2×Dic13—42no—
77C2×Dic13—42no—
78C2×Dic13—42no—
79C2×Dic13—42no—
80C2×Dic13—82no—
81C2×Dic13—84no—
82C8×C13—82no—
83C2×#117C2×D1311yescharacteristic
84#407C2×D1312yes—
85#388—262no—
86#387—262no—
87#381—132no—
88C4×C4⋊C4—132no—
89C4×C22⋊C4—132no—
90#376—131no—
91C43—131no—
92#343—22no—
93#342—262no—
94C22×C13—22no—
95C22×C13—22no—
96C22×C13—24no—
97C22×C13—82no—
98C22×C13#38111yescharacteristic
99C22×C13#41012yes—
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—42no—
103C4×C13—42no—
104Dic13—44no—
105Dic13—82no—
106Dic13—162no—
107C23×C4C22×D1311yescharacteristic
108C2×M16—22no—
109#117—24no—
110C2×C4⋊C4—262no—
111C2×C4⋊C4C22⋊D1312yes—
112C2×C22⋊C4—262no—
113C2×C22⋊C4—262no—
114C2×C22⋊C4D5212yes—
115C2×C42—132no—
116C2×C42—132no—
117C2×C42—262no—
118C2×C42C4×D1311yescharacteristic
119C2×C42C4×D1311yescharacteristic
120C22⋊C8—24no—
121#95—262no—
122#95—262no—
123#95—262no—
124#95—264no—
125C2×C13—22no—
126C2×C13—42no—
127C2×C13#182011yescharacteristic
128C2×C13#182712yes—
129C24C2×D5211yescharacteristic
130C22×C4—42no—
131C22×C4—262no—
132C22×C4—262no—
133C22×C4—522no—
134C22×C4#610312yes—
135C22×C4#610312yes—
136C22×C4C2×C4×D1311yescharacteristic
137C22×C4#612914yes—
138C22×C4C2×C22⋊D1311yescharacteristic
139M16—44no—
140C2×C8—42no—
141C4⋊C4—24no—
142C4⋊C4—524no—
143C22⋊C4—24no—
144C22⋊C4—524no—
145C22⋊C4—524no—
146C42—22no—
147C42—22no—
148C42—522no—
149C42—522no—
150C42—524no—
151C13#874011yescharacteristic, complemented, Sylow
152C23—22no—
153C23—42no—
154C23#8814012yes—
155C23C2×#610311yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—264no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4—522no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4—1042no—
170C2×C4—1044no—
171C2×C4#8813112yes—
172C2×C4#8818912yes—
173C8—82no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—82no—
178C22#1171860411yescharacteristic
179C22#1171866712yes—
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—524no—
185C4—1042no—
186C4—2082no—
187C2—22no—
188C2—42no—
189C2#1311491111yescharacteristic
190C2#1311494112yes—
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1822C2
socleC22×C13#381
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1822D13
hypocenterC13#8740
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
11. C4×C4⋊Dic13C4semidirect
12. #11718593C4semidirect
13. C42×Dic13C4semidirect
151. C13#8740semidirect

Maximal subgroups

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

subgroupindex
#131173342
#131149132
#131126902
C13×#18222
#874013