Finite Group Databasebeta

← #13130328

Subgroups — #13130328

Order 1664.

194 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 56 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#11719055C211yesmaximal, characteristic
3#11719055C211yesmaximal, characteristic
4#11718242C214yesmaximal, complemented
5C13×C4⋊Q8C411yescharacteristic
6#88200—21no—
7Q8×Dic13—21no—
8#88151—21no—
9#88146C412yes—
10#88144C2212yes—
11#88141—21no—
12C42×D13C2211yescharacteristic
13#88123C411yescharacteristic
14#88112—21no—
15#88112—21no—
16#88111—21no—
17#88111—21no—
18#88110C2212yes—
19#88110C2212yes—
20C2×Q8×C13—21no—
21C2×C4×D13C2×C411yescharacteristic
22C2×C4×D13D411yescharacteristic
23C2×C4×D13D411yescharacteristic
24C2×Dic26—21no—
25C2×#1057—22no—
26C2×#1057—22no—
27C13×C4⋊C4—21no—
28C13×C4⋊C4C2×C412yes—
29C42×C13C2×C411yescharacteristic
30#6103—22no—
31C4⋊Dic13—21no—
32C4⋊Dic13—22no—
33C4⋊Dic13C2×C412yes—
34#6101—22no—
35C4×Dic13—22no—
36C4×Dic13D411yescharacteristic
37C4×Dic13D411yescharacteristic
38C4×Dic13C2311yescharacteristic
39#1537—131nomaximal, Sylow
40C22×D13C22⋊C411yescharacteristic
41Q8×C13—42no—
42C2×C4×C13—22no—
43C2×C4×C13C22⋊C411yescharacteristic
44C2×C4×C13C22⋊C411yescharacteristic
45C2×C4×C13C22×C411yescharacteristic
46C2×Dic13—22no—
47C2×Dic13C22⋊C411yescharacteristic
48C2×Dic13C2×D411yescharacteristic
49C2×Dic13C2×D411yescharacteristic
50C4×D13—22no—
51C4×D13—41no—
52C4×D13—41no—
53Dic26—42no—
54#1057—42no—
55#1057—42no—
56#533—131no—
57#432—131no—
58#432—131no—
59#330—134no—
60C22×C13C2×C22⋊C411yescharacteristic
61C2×D13—21no—
62C2×D13—21no—
63C2×D13—21no—
64C4×C13—21no—
65C4×C13—21no—
66C4×C13—21no—
67C4×C13—42no—
68Dic13—21no—
69Dic13—21no—
70Dic13—42no—
71Dic13#10112yes—
72C4⋊Q8—131no—
73C4⋊Q8#26111yescharacteristic
74#125—132no—
75C22⋊Q8—261no—
76C22⋊Q8—261no—
77C4×Q8—261no—
78C4×Q8—261no—
79#117—132no—
80C2×C42—131no—
81C4⋊C8—261no—
82C4⋊C8—261no—
83C22⋊C8—261no—
84C22⋊C8—261no—
85#97—132no—
86#97—132no—
87C2×C13C2×#10111yescharacteristic
88C2×C13#42111yescharacteristic
89C2×C13#42111yescharacteristic
90D13—41no—
91C2×Q8—21no—
92C2×Q8—261no—
93C22×C4—131no—
94C22×C4—131no—
95C22×C4—131no—
96C2×C8—262no—
97C2×C8—262no—
98C4⋊C4—21no—
99C4⋊C4—132no—
100C4⋊C4—262no—
101C4⋊C4—262no—
102C4⋊C4—261no—
103C4⋊C4C2×#26112yes—
104C22⋊C4—262no—
105C42—131no—
106C42—131no—
107C42—131no—
108C42—262no—
109C42C2×#26111yescharacteristic
110C13#153711yescharacteristic, complemented, Sylow
111C23—131no—
112Q8—42no—
113Q8—522no—
114C2×C4—22no—
115C2×C4—131no—
116C2×C4—131no—
117C2×C4—131no—
118C2×C4—262no—
119C2×C4—262no—
120C2×C4—521no—
121C2×C4—521no—
122C2×C4C22⋊#26111yescharacteristic
123C2×C4C22⋊#26111yescharacteristic
124C2×C4C22×#26111yescharacteristic
125C8—522no—
126C8—522no—
127C22—261no—
128C22—261no—
129C22—261no—
130C22C2×C22⋊#26111yescharacteristic
131C4—21no—
132C4—21no—
133C4—21no—
134C4—42no—
135C4—132no—
136C4—261no—
137C4—261no—
138C4—522no—
139C2—521no—
140C2#1171914011yescharacteristic
141C2#1171915511yescharacteristic
142C2D13⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC4×Dic13C23
hypercenterC4⋊Q8#261
hypocenterC13#1537
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
4. #11718242C2semidirect
110. C13#1537semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117190552
#117182422
#153713