Finite Group Databasebeta

← #13130235

Subgroups — #13130235

Order 1664.

294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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×#88151C211yesmaximal, characteristic
2C4×C22⋊#261C211yesmaximal, characteristic
3#11719127C211yesmaximal, characteristic
4#11718241C214yesmaximal, complemented
5C22×C4×D13C2211yescharacteristic
6C22×Dic26C411yescharacteristic, complemented
7C2×C22⋊#261—21no—
8C2×C4×#261—21no—
9C2×#6118—21no—
10C2×C13×C4⋊C4C411yescharacteristic, complemented
11C2×#6103—21no—
12C2×C4⋊Dic13—21no—
13#88151—21no—
14#88151—21no—
15#88151C412yescomplemented
16#88151C2212yes—
17C22⋊#1057—21no—
18(C2×#261)⋊C4C2212yes—
19#88111C2212yes—
20C23×D13D411yescharacteristic
21C22×#261—22no—
22C22×C4×C13—21no—
23C22×C4×C13C2×C411yescharacteristic
24C22×Dic13—21no—
25C22×Dic13D411yescharacteristic
26C2×C4×D13—42no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13C2311yescharacteristic
31C2×Dic26—21no—
32C2×Dic26—42no—
33C2×Dic26C2×C412yes—
34C22⋊#261—24no—
35C2×#1057—22no—
36C4×#261—42no—
37#6118—42no—
38C13×C4⋊C4—21no—
39C13×C4⋊C4C2×C412yes—
40#6103—22no—
41#6103—22no—
42C4⋊Dic13—22no—
43C4⋊Dic13—22no—
44#1508—131nomaximal, Sylow
45C23×C13C22⋊C411yescharacteristic
46C22×D13—22no—
47C22×D13—22no—
48C22×D13—41no—
49C22×D13C22⋊C411yescharacteristic
50C22×D13C2×D411yescharacteristic
51C2×#261—24no—
52C2×#261—42no—
53C2×#261—42no—
54C2×C4×C13—22no—
55C2×C4×C13—22no—
56C2×C4×C13—42no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22×C411yescharacteristic
59C2×Dic13—22no—
60C2×Dic13—41no—
61C2×Dic13—42no—
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
64C4×D13—22no—
65C4×D13—22no—
66C4×D13—41no—
67C4×D13—41no—
68Dic26—42no—
69Dic26—42no—
70#1057—42no—
71C2×C22⋊Q8—131no—
72#407—131no—
73C4×C22⋊C4—131no—
74#328—134no—
75C22×C13—21no—
76C22×C13—21no—
77C22×C13#10412yes—
78C22×C13C2×C22⋊C411yescharacteristic
79C2×D13—21no—
80C2×D13—21no—
81C2×D13—21no—
82C2×D13—21no—
83C2×D13—21no—
84C2×D13—44no—
85C2×D13#13712yes—
86#261—44no—
87C4×C13—21no—
88C4×C13—42no—
89C4×C13#9912yes—
90Dic13—21no—
91Dic13—21no—
92Dic13—42no—
93C22×Q8—131no—
94C23×C4—131no—
95C2×M16—261no—
96C22⋊Q8—132no—
97C22⋊Q8—132no—
98C22⋊Q8—261no—
99C22⋊Q8—261no—
100C2×C4⋊C4—261no—
101C2×C4⋊C4#26111yescharacteristic, complemented
102C2×C22⋊C4—261no—
103C2×C22⋊C4—261no—
104C2×C42—261no—
105C22⋊C8—132no—
106C22⋊C8—261no—
107#95—132no—
108C2×C13—22no—
109C2×C13C2×#9911yescharacteristic
110C2×C13#41911yescharacteristic
111C2×C13C2×#10411yescharacteristic
112D13—22no—
113D13—41no—
114C24—131no—
115C2×Q8—132no—
116C2×Q8—261no—
117C2×Q8—522no—
118C22×C4—21no—
119C22×C4—131no—
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—262no—
125C22×C4—261no—
126C22×C4—522no—
127C22×C4C2×#26111yescharacteristic
128M16—522no—
129C2×C8—262no—
130C4⋊C4—21no—
131C4⋊C4—262no—
132C4⋊C4—262no—
133C4⋊C4C2×#26112yes—
134C22⋊C4—262no—
135C22⋊C4—262no—
136C22⋊C4—264no—
137C42—522no—
138C13#150811yescharacteristic, complemented, Sylow
139C23—131no—
140C23—131no—
141C23—262no—
142C23—262no—
143C23—521no—
144C23C22⋊#26111yescharacteristic
145Q8—522no—
146Q8—522no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—131no—
151C2×C4—131no—
152C2×C4—262no—
153C2×C4—262no—
154C2×C4—264no—
155C2×C4—262no—
156C2×C4—521no—
157C2×C4—521no—
158C2×C4—521no—
159C2×C4—522no—
160C2×C4—522no—
161C2×C4—522no—
162C2×C4C22⋊#26111yescharacteristic
163C2×C4C22×#26111yescharacteristic
164C8—522no—
165C22—21no—
166C22—21no—
167C22—132no—
168C22—261no—
169C22—261no—
170C22—261no—
171C22—261no—
172C22—261no—
173C22—524no—
174C22#8811612yes—
175C22C2×C22⋊#26111yescharacteristic
176C4—21no—
177C4—42no—
178C4—261no—
179C4—261no—
180C4—524no—
181C4—522no—
182C4#8810712yes—
183C2—22no—
184C2—262no—
185C2—521no—
186C2C2×#8810711yescharacteristic
187C2C2×#8811611yescharacteristic
188C2#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#1508
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11718241C2semidirect
6. C22×Dic26C4semidirect
10. C2×C13×C4⋊C4C4semidirect
15. #88151C4semidirect
101. C2×C4⋊C4#261semidirect
138. C13#1508semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C4×C22⋊#2612
#117191272
#117182412
#150813