Finite Group Databasebeta

← #13113361

Subgroups — #13113361

Order 1664.

242 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C13×#529C211yesmaximal, characteristic
2C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
3#11718587C211yesmaximal, characteristic, complemented
4#11718130C212yesmaximal, complemented
5#11718129C212yesmaximal
6C13×#126—21no—
7C13×#125C411yescharacteristic, complemented
8C13×#124C411yescharacteristic, complemented
9C13×#123—21no—
10C13×C22⋊Q8C2211yescharacteristic
11C13×#121C2211yescharacteristic
12C4×Q8×C13C411yescharacteristic, complemented
13C4×D4×C13—21no—
14C4×D4×C13C411yescharacteristic, complemented
15C13×#117—21no—
16C2×C42×C13C2211yescharacteristic
17C2×C4⋊Dic13—21no—
18C2×C4×Dic13—21no—
19#88071C2212yes—
20C22⋊#1055C2212yes—
21C4⋊#1055—21no—
22#88043—21no—
23C2×Q8×C13C2×C411yescharacteristic
24C2×D4×C13—21no—
25C2×D4×C13C2×C411yescharacteristic
26C22×C4×C13—21no—
27C22×C4×C13D411yescharacteristic
28C22×C4×C13D411yescharacteristic
29C22×C4×C13C2311yescharacteristic
30C22×Dic13—22no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4C2×C411yescharacteristic
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C22⋊C4—21no—
38C13×C22⋊C4—21no—
39C13×C22⋊C4—21no—
40C13×C22⋊C4—21no—
41C13×C22⋊C4—21no—
42C42×C13—21no—
43C42×C13C2×C411yescharacteristic
44C42×C13C2×C411yescharacteristic
45C42×C13D411yescharacteristic
46C42×C13D411yescharacteristic
47C4⋊Dic13—24no—
48C4×Dic13—42no—
49C2×#1055—22no—
50#1509—131nomaximal, Sylow
51C23×C13—21no—
52C23×C13C2×D411yescharacteristic
53Q8×C13—41no—
54D4×C13—41no—
55D4×C13—41no—
56D4×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—22no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—41no—
64C2×C4×C13—42no—
65C2×C4×C13C22⋊C411yescharacteristic
66C2×C4×C13C22⋊C411yescharacteristic
67C2×C4×C13C22⋊C411yescharacteristic
68C2×C4×C13C22⋊C411yescharacteristic
69C2×C4×C13C22×C411yescharacteristic
70C2×C4×C13C2×D411yescharacteristic
71C2×Dic13—24no—
72C2×Dic13—42no—
73C2×Dic13—42no—
74#1055—42no—
75#529D1311yescharacteristic
76#432—131no—
77C4×C4⋊C4—131no—
78#328—132no—
79#327—132no—
80C22×C13—21no—
81C22×C13—21no—
82C22×C13—41no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13C2×C22⋊C411yescharacteristic
86C22×C13AGL(1,ℤ/8)11yescharacteristic
87C22×C13#13711yescharacteristic
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13—41no—
94C4×C13—41no—
95C4×C13—41no—
96C4×C13#10412yes—
97Dic13—44no—
98#126—21no—
99#125Dic1311yescharacteristic, complemented
100#124Dic1311yescharacteristic, complemented
101#123—21no—
102C22⋊Q8C2×D1311yescharacteristic
103#121C2×D1311yescharacteristic
104C4×Q8Dic1311yescharacteristic, complemented
105C4×D4—21no—
106C4×D4Dic1311yescharacteristic, complemented
107#117—21no—
108C2×C4⋊C4—261no—
109C2×C42—261no—
110C2×C42C2×D1311yescharacteristic
111C4⋊C8—261no—
112C22⋊C8—132no—
113#97—261no—
114#95—132no—
115C2×C13—21no—
116C2×C13—21no—
117C2×C13—81no—
118C2×C13#41011yescharacteristic
119C2×C13#41711yescharacteristic
120C2×C13C2×#10411yescharacteristic
121C2×Q8C2×Dic1311yescharacteristic
122C2×D4—21no—
123C2×D4C2×Dic1311yescharacteristic
124C22×C4—21no—
125C22×C4—262no—
126C22×C4C22⋊D1311yescharacteristic
127C22×C4C22⋊D1311yescharacteristic
128C22×C4C22×D1311yescharacteristic
129C2×C8—262no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—264no—
135C4⋊C4C2×Dic1311yescharacteristic
136C4⋊C4C2×Dic1311yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42—522no—
144C42C2×Dic1311yescharacteristic
145C42C2×Dic1311yescharacteristic
146C42C22⋊D1311yescharacteristic
147C42C22⋊D1311yescharacteristic
148C13#150911yescharacteristic, complemented, Sylow
149C23—21no—
150C23C2×C22⋊D1311yescharacteristic
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—41no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—264no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4C22⋊Dic1311yescharacteristic
167C2×C4C22⋊Dic1311yescharacteristic
168C2×C4C22⋊Dic1311yescharacteristic
169C2×C4C22⋊Dic1311yescharacteristic
170C2×C4C22×Dic1311yescharacteristic
171C2×C4C2×C22⋊D1311yescharacteristic
172C8—522no—
173C22—21no—
174C22—21no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22#8820311yescharacteristic
179C22#8820511yescharacteristic
180C22C2×C22⋊Dic1311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—41no—
189C4—524no—
190C4#8807712yes—
191C2—21no—
192C2—21no—
193C2—81no—
194C2#1171889311yescharacteristic
195C2C2×#8807711yescharacteristic
196C2#1171890111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#529C2
socleC22×C13C2×C22⋊C4
prime radicalC13×#121C22
cosocleC22×C4×C13C23
hypercenter#529D13
hypocenterC13#1509
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic13C2semidirect
3. #11718587C2semidirect
4. #11718130C2semidirect
7. C13×#125C4semidirect
8. C13×#124C4semidirect
12. C4×Q8×C13C4semidirect
14. C4×D4×C13C4semidirect
99. #125Dic13semidirect
100. #124Dic13semidirect
104. C4×Q8Dic13semidirect
106. C4×D4Dic13semidirect
148. C13#1509semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
C4×C4⋊Dic132
#117185872
#117181302
#117181292
#150913