Finite Group Databasebeta

← #13130230

Subgroups — #13130230

Order 1664.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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#11719433C211yesmaximal, characteristic
2#11719057C211yesmaximal, characteristic
3#11719054C211yesmaximal, characteristic
4#11718298C214yesmaximal
5C2×C4×#261—21no—
6C13×C4⋊Q8C411yescharacteristic, complemented
7#88200C2212yes—
8Q8×Dic13C412yescomplemented
9#88151—21no—
10#88146—21no—
11#88144—21no—
12#88141—21no—
13C42×D13C2211yescharacteristic
14#88123C411yescharacteristic, complemented
15(C2×#261)⋊C4—21no—
16(C2×#261)⋊C4C2212yes—
17#88111C2212yes—
18#88110—21no—
19C4⋊#1057—21no—
20C22×#261—22no—
21C2×Q8×C13C2×C412yes—
22C2×C4×D13D411yescharacteristic
23C2×C4×D13D411yescharacteristic
24C2×C4×D13C2311yescharacteristic
25C2×Dic26—21no—
26C2×#1057—22no—
27C4×#261—24no—
28C13×C4⋊C4—21no—
29C13×C4⋊C4—21no—
30C42×C13C2×C411yescharacteristic
31#6103—22no—
32C4⋊Dic13—21no—
33C4⋊Dic13—22no—
34C4⋊Dic13C2×C412yes—
35#6101—22no—
36C4×Dic13—22no—
37C4×Dic13C2×C411yescharacteristic
38C4×Dic13D411yescharacteristic
39C4×Dic13D411yescharacteristic
40#1506—131nomaximal, Sylow
41C22×D13C2×D411yescharacteristic
42C2×#261—24no—
43C2×#261—42no—
44C2×#261—42no—
45Q8×C13—42no—
46C2×C4×C13—22no—
47C2×C4×C13C22⋊C411yescharacteristic
48C2×C4×C13C22⋊C411yescharacteristic
49C2×C4×C13C22×C411yescharacteristic
50C2×Dic13—22no—
51C2×Dic13C22⋊C411yescharacteristic
52C2×Dic13C22⋊C411yescharacteristic
53C2×Dic13C2×D411yescharacteristic
54C4×D13—22no—
55C4×D13—22no—
56C4×D13—41no—
57Dic26—42no—
58#1057—42no—
59#533—131no—
60#432—131no—
61#376—131no—
62#328—134no—
63C22×C13C2×C22⋊C411yescharacteristic
64C2×D13—21no—
65C2×D13—21no—
66C2×D13#13712yes—
67#261—44no—
68C4×C13—21no—
69C4×C13—21no—
70C4×C13—42no—
71C4×C13#10412yes—
72Dic13—21no—
73Dic13—21no—
74Dic13—21no—
75Dic13—42no—
76C4⋊Q8—131no—
77C4⋊Q8#26111yescharacteristic, complemented
78#125—261no—
79C22⋊Q8—132no—
80C22⋊Q8—261no—
81C4×Q8—132no—
82C4×Q8—261no—
83#117—261no—
84C2×C42—131no—
85C2×C42—261no—
86C4⋊C8—261no—
87C22⋊C8—132no—
88#97—261no—
89#95—132no—
90#95—261no—
91C2×C13#41011yescharacteristic
92C2×C13#41911yescharacteristic
93C2×C13C2×#10411yescharacteristic
94D13—22no—
95C2×Q8—261no—
96C2×Q8C2×#26112yes—
97C22×C4—131no—
98C22×C4—131no—
99C22×C4—131no—
100C22×C4—262no—
101C2×C8—262no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—132no—
105C4⋊C4—262no—
106C4⋊C4—262no—
107C4⋊C4—261no—
108C22⋊C4—262no—
109C42—131no—
110C42—131no—
111C42—131no—
112C42—262no—
113C42—264no—
114C42C2×#26111yescharacteristic
115C13#150611yescharacteristic, complemented, Sylow
116C23—131no—
117Q8—42no—
118Q8—522no—
119C2×C4—22no—
120C2×C4—131no—
121C2×C4—131no—
122C2×C4—131no—
123C2×C4—262no—
124C2×C4—262no—
125C2×C4—264no—
126C2×C4—262no—
127C2×C4—521no—
128C2×C4—522no—
129C2×C4—522no—
130C2×C4C22⋊#26111yescharacteristic
131C2×C4C22⋊#26111yescharacteristic
132C2×C4C22×#26111yescharacteristic
133C8—522no—
134C22—132no—
135C22—261no—
136C22—261no—
137C22C2×C22⋊#26111yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—261no—
142C4—261no—
143C4—261no—
144C4—524no—
145C4—522no—
146C4#8811812yes—
147C2—262no—
148C2#1171914211yescharacteristic
149C2#1171915311yescharacteristic
150C2C2×#8811811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
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
6. C13×C4⋊Q8C4semidirect
8. Q8×Dic13C4semidirect
14. #88123C4semidirect
77. C4⋊Q8#261semidirect
115. C13#1506semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117190572
#117190542
#117182982
#150613