Finite Group Databasebeta

← #13113322

Subgroups — #13113322

Order 1664.

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

normal subgroups only

This group has 238 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
2#11718593C211yesmaximal, characteristic, complemented
3#11718586C211yesmaximal, 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—
18#88071—21no—
19#88071C2212yes—
20C22⋊#1055C2212yes—
21C4⋊#1055—21no—
22C4×#1055—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—
48C2×#1055—22no—
49#1500—131nomaximal, Sylow
50C23×C13—21no—
51C23×C13C2×D411yescharacteristic
52Q8×C13—41no—
53D4×C13—41no—
54D4×C13—42no—
55C2×C4×C13—22no—
56C2×C4×C13—22no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—41no—
61C2×C4×C13—42no—
62C2×C4×C13C22⋊C411yescharacteristic
63C2×C4×C13C22⋊C411yescharacteristic
64C2×C4×C13C22⋊C411yescharacteristic
65C2×C4×C13C22⋊C411yescharacteristic
66C2×C4×C13C22×C411yescharacteristic
67C2×C4×C13C2×D411yescharacteristic
68C2×Dic13—24no—
69C2×Dic13—42no—
70C2×Dic13—42no—
71#1055—42no—
72#529D1311yescharacteristic
73#431—131no—
74#376—131no—
75#328—132no—
76#327—132no—
77C22×C13—21no—
78C22×C13—21no—
79C22×C13—41no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13C2×C22⋊C411yescharacteristic
83C22×C13#13512yes—
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—21no—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—41no—
90C4×C13—41no—
91C4×C13—41no—
92C4×C13#10412yes—
93Dic13—44no—
94#126—21no—
95#125Dic1311yescharacteristic, complemented
96#124Dic1311yescharacteristic, complemented
97#123—21no—
98C22⋊Q8C2×D1311yescharacteristic
99#121C2×D1311yescharacteristic
100C4×Q8Dic1311yescharacteristic, complemented
101C4×D4—21no—
102C4×D4Dic1311yescharacteristic, complemented
103#117—21no—
104C2×C42—261no—
105C2×C42C2×D1311yescharacteristic
106C4⋊C8—261no—
107C22⋊C8—132no—
108C4×C8—261no—
109#95—132no—
110#95—261no—
111C2×C13—22no—
112C2×C13—81no—
113C2×C13#41011yescharacteristic
114C2×C13#41611yescharacteristic
115C2×C13C2×#10411yescharacteristic
116C2×Q8C2×Dic1311yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic1311yescharacteristic
119C22×C4—21no—
120C22×C4—262no—
121C22×C4C22⋊D1311yescharacteristic
122C22×C4C22⋊D1311yescharacteristic
123C22×C4C22×D1311yescharacteristic
124C2×C8—262no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4C2×Dic1311yescharacteristic
130C4⋊C4C2×Dic1311yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42—264no—
138C42C2×Dic1311yescharacteristic
139C42C2×Dic1311yescharacteristic
140C42C22⋊D1311yescharacteristic
141C42C22⋊D1311yescharacteristic
142C13#150011yescharacteristic, complemented, Sylow
143C23—21no—
144C23C2×C22⋊D1311yescharacteristic
145Q8—41no—
146D4—41no—
147D4—42no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—264no—
156C2×C4—522no—
157C2×C4—522no—
158C2×C4C22⋊Dic1311yescharacteristic
159C2×C4C22⋊Dic1311yescharacteristic
160C2×C4C22⋊Dic1311yescharacteristic
161C2×C4C22⋊Dic1311yescharacteristic
162C2×C4C22×Dic1311yescharacteristic
163C2×C4C2×C22⋊D1311yescharacteristic
164C8—522no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22#8820412yes—
171C22C2×C22⋊Dic1311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—41no—
179C4—41no—
180C4—524no—
181C4#8807712yes—
182C2—22no—
183C2—81no—
184C2#1171889411yescharacteristic
185C2C2×#8807711yescharacteristic
186C2#1171890111yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#529C2
socleC22×C13C2×C22⋊C4
prime radicalC13×#121C22
cosocleC22×C4×C13C23
hypercenter#529D13
hypocenterC13#1500
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #11718593C2semidirect
3. #11718586C2semidirect
4. #11718130C2semidirect
7. C13×#125C4semidirect
8. C13×#124C4semidirect
12. C4×Q8×C13C4semidirect
14. C4×D4×C13C4semidirect
95. #125Dic13semidirect
96. #124Dic13semidirect
100. C4×Q8Dic13semidirect
102. C4×D4Dic13semidirect
142. C13#1500semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117185932
#117185862
#117181302
#117181292
#150013