Finite Group Databasebeta

← #13130739

Subgroups — #13130739

Order 1664.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×C4⋊C4×D13C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3D13⋊(C22⋊C8)C211yesmaximal, characteristic
4#11718246C214yesmaximal, complemented
5C22×C4×D13—21no—
6C22×C4×D13C2211yescharacteristic
7C2×C22⋊#261—21no—
8C2×C4⋊#261C2212yes—
9C2×D13⋊C8C2212yes—
10C2×C13×C4⋊C4C411yescharacteristic, complemented
11C2×C4⋊Dic13C411yescharacteristic, complemented
12C2×#6101—21no—
13C4⋊C4×D13—21no—
14C4⋊C4×D13—21no—
15C4⋊C4×D13C412yescomplemented
16C4⋊C4×D13C2212yes—
17C22⋊#1057—21no—
18(C2×#261)⋊C4—21no—
19#88111—21no—
20C23×D13D411yescharacteristic
21C22×#261—22no—
22C22×C4×C13—21no—
23C22×C4×C13C2×C411yescharacteristic
24C22×Dic13—21no—
25C22×Dic13D411yescharacteristic
26C2×C4×D13—24no—
27C2×C4×D13—22no—
28C2×C4×D13—22no—
29C2×C4×D13—42no—
30C2×C4×D13—42no—
31C2×C4×D13C2×C411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13C2311yescharacteristic
35C22⋊#261—42no—
36C2×#1057—22no—
37C4⋊#261—24no—
38D13⋊C8—24no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4C2×C412yes—
41C4⋊Dic13—21no—
42C4⋊Dic13C2×C412yes—
43#6101—22no—
44#6101—22no—
45#1823—131nomaximal, Sylow
46C23×C13C22⋊C411yescharacteristic
47C22×D13—22no—
48C22×D13—22no—
49C22×D13C22⋊C411yescharacteristic
50C22×D13D812yes—
51C22×D13SD1612yes—
52C22×D13C2×D411yescharacteristic
53C2×#261—42no—
54C2×#261—42no—
55C2×#261—42no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—42no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22×C411yescharacteristic
61C2×Dic13—22no—
62C2×Dic13—22no—
63C2×Dic13—42no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66C4×D13—22no—
67C4×D13—22no—
68C4×D13—22no—
69C4×D13—44no—
70C4×D13—42no—
71C4×D13—42no—
72C4×D13#4114yes—
73#1057—42no—
74C22×C4⋊C4—131no—
75C2×C22⋊C8—131no—
76#380—131no—
77#340—134no—
78C22×C13—21no—
79C22×C13—21no—
80C22×C13#10212yes—
81C22×C13C2×C22⋊C411yescharacteristic
82C2×D13—21no—
83C2×D13—21no—
84C2×D13—24no—
85C2×D13—24no—
86C2×D13#10212yes—
87C2×D13#12312yes—
88C2×D13C2×D811yescharacteristic
89C2×D13C2×SD1611yescharacteristic
90C2×D13#13712yes—
91#261—82no—
92C4×C13—21no—
93C4×C13—42no—
94C4×C13#11712yes—
95Dic13—21no—
96Dic13—42no—
97Dic13#12312yes—
98C23×C4—131no—
99C23×C4—261no—
100C22×C8—132no—
101C2×C4⋊C4—131no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—132no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—261no—
106C2×C4⋊C4—261no—
107C2×C4⋊C4—261no—
108C2×C4⋊C4#26111yescharacteristic, complemented
109C2×C22⋊C4—261no—
110C22⋊C8—261no—
111C22⋊C8—261no—
112#95—261no—
113C2×C13—22no—
114C2×C13#38111yescharacteristic
115C2×C13C2×#10211yescharacteristic
116C2×C13#41911yescharacteristic
117D13—22no—
118D13#48012yes—
119D13#48312yes—
120C24—131no—
121C22×C4—21no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—131no—
125C22×C4—131no—
126C22×C4—131no—
127C22×C4—264no—
128C22×C4—262no—
129C22×C4—262no—
130C22×C4—261no—
131C22×C4—262no—
132C22×C4—522no—
133C22×C4—522no—
134C22×C4C2×#26111yescharacteristic
135C2×C8—262no—
136C2×C8—264no—
137C4⋊C4—21no—
138C4⋊C4—132no—
139C4⋊C4—262no—
140C4⋊C4—262no—
141C4⋊C4—264no—
142C4⋊C4—261no—
143C4⋊C4C2×#26112yes—
144C22⋊C4—522no—
145C13#182311yescharacteristic, complemented, Sylow
146C23—131no—
147C23—132no—
148C23—132no—
149C23—131no—
150C23—262no—
151C23—262no—
152C23C22⋊#26111yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—131no—
157C2×C4—134no—
158C2×C4—131no—
159C2×C4—262no—
160C2×C4—262no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4—524no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4—522no—
171C2×C4C22⋊#26111yescharacteristic
172C2×C4C22×#26111yescharacteristic
173C8—522no—
174C22—21no—
175C22—21no—
176C22—132no—
177C22—131no—
178C22—131no—
179C22—132no—
180C22—132no—
181C22—264no—
182C22—264no—
183C22—261no—
184C22—261no—
185C22#8811512yes—
186C22C2×C22⋊#26111yescharacteristic
187C4—21no—
188C4—42no—
189C4—132no—
190C4—261no—
191C4—522no—
192C4—1042no—
193C4#8823712yes—
194C2—22no—
195C2—132no—
196C2—132no—
197C2—262no—
198C2#1171913511yescharacteristic
199C2C2×#8811511yescharacteristic
200C2#1171915311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1823
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11718246C2semidirect
10. C2×C13×C4⋊C4C4semidirect
11. C2×C4⋊Dic13C4semidirect
15. C4⋊C4×D13C4semidirect
108. C2×C4⋊C4#261semidirect
145. C13#1823semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D132
#117191362
D13⋊(C22⋊C8)2
#117182462
#182313