Finite Group Databasebeta

← #13130229

Subgroups — #13130229

Order 1664.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#11719283C211yesmaximal, characteristic
2#11719057C211yesmaximal, characteristic
3#11719055C211yesmaximal, characteristic
4#11718298C212yesmaximal
5#11718241C212yesmaximal
6C2×C4×#261—21no—
7C4×Q8×C13C411yescharacteristic, complemented
8#88200C2211yescharacteristic
9#88198C411yescharacteristic, complemented
10#88151C2211yescharacteristic
11#88150—21no—
12#88143—21no—
13#88142C411yescharacteristic, complemented
14#88126—21no—
15C42×D13C2211yescharacteristic
16C4×Dic26—21no—
17C4×Dic26C411yescharacteristic, complemented
18(C2×#261)⋊C4—21no—
19(C2×#261)⋊C4C2212yes—
20#88112—21no—
21#88111C2212yes—
22#88110—21no—
23C22×#261—22no—
24C2×Q8×C13C2×C411yescharacteristic
25C2×C4×D13D411yescharacteristic
26C2×C4×D13D411yescharacteristic
27C2×C4×D13C2311yescharacteristic
28C2×Dic26—21no—
29C2×Dic26C2×C411yescharacteristic
30C2×#1057—22no—
31C4×#261—24no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4C2×C411yescharacteristic
34C42×C13—21no—
35C42×C13C2×C411yescharacteristic
36#6103—21no—
37#6103—21no—
38C4⋊Dic13—21no—
39C4⋊Dic13C2×C411yescharacteristic
40#6101—21no—
41#6101—21no—
42#6101—21no—
43#6101—21no—
44#6101—21no—
45C4×Dic13—21no—
46C4×Dic13C2×C411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49#1506—131nomaximal, Sylow
50C22×D13C2×D411yescharacteristic
51C2×#261—24no—
52C2×#261—42no—
53C2×#261—42no—
54Q8×C13—41no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22×C411yescharacteristic
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65C4×D13—22no—
66C4×D13—22no—
67C4×D13—41no—
68Dic26—42no—
69Dic26—41no—
70#1057—42no—
71#533—131no—
72#432—131no—
73#376—131no—
74#328—132no—
75#328—132no—
76C22×C13C2×C22⋊C411yescharacteristic
77C2×D13—21no—
78C2×D13—21no—
79C2×D13#13712yes—
80#261—44no—
81C4×C13—21no—
82C4×C13—21no—
83C4×C13—21no—
84C4×C13—41no—
85C4×C13—41no—
86Dic13—21no—
87Dic13—21no—
88Dic13—41no—
89Dic13—41no—
90Dic13#10412yes—
91C4⋊Q8—131no—
92C4⋊Q8—131no—
93#125—261no—
94C22⋊Q8—131no—
95C22⋊Q8—131no—
96C22⋊Q8—261no—
97C4×Q8—131no—
98C4×Q8—261no—
99C4×Q8#26111yescharacteristic, complemented
100#117—261no—
101C2×C42—131no—
102C2×C42—261no—
103C4⋊C8—261no—
104C22⋊C8—132no—
105#97—261no—
106#95—132no—
107#95—261no—
108C2×C13#41011yescharacteristic
109C2×C13#41911yescharacteristic
110C2×C13C2×#10411yescharacteristic
111D13—22no—
112C2×Q8—131no—
113C2×Q8—261no—
114C2×Q8C2×#26111yescharacteristic
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—262no—
119C2×C8—262no—
120C4⋊C4—21no—
121C4⋊C4—131no—
122C4⋊C4—261no—
123C4⋊C4—261no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C4⋊C4—261no—
128C4⋊C4C2×#26111yescharacteristic
129C22⋊C4—261no—
130C22⋊C4—261no—
131C42—21no—
132C42—131no—
133C42—131no—
134C42—131no—
135C42—264no—
136C42—261no—
137C42C2×#26111yescharacteristic
138C13#150611yescharacteristic, complemented, Sylow
139C23—131no—
140Q8—41no—
141Q8—521no—
142Q8—522no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—131no—
146C2×C4—131no—
147C2×C4—131no—
148C2×C4—262no—
149C2×C4—262no—
150C2×C4—264no—
151C2×C4—261no—
152C2×C4—261no—
153C2×C4—521no—
154C2×C4—522no—
155C2×C4—522no—
156C2×C4C22⋊#26111yescharacteristic
157C2×C4C22⋊#26111yescharacteristic
158C2×C4C22×#26111yescharacteristic
159C8—522no—
160C22—132no—
161C22—261no—
162C22—261no—
163C22C2×C22⋊#26111yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—132no—
170C4—261no—
171C4—261no—
172C4—524no—
173C4—521no—
174C4—521no—
175C2—262no—
176C2#1171911611yescharacteristic
177C2#1171915311yescharacteristic
178C2D13⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC4×Q8#261
hypocenterC13#1506
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
7. C4×Q8×C13C4semidirect
9. #88198C4semidirect
13. #88142C4semidirect
17. C4×Dic26C4semidirect
99. C4×Q8#261semidirect
138. C13#1506semidirect

Maximal subgroups

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

subgroupindex
#117192832
#117190572
#117190552
#117182982
#117182412
#150613