Finite Group Databasebeta

← #13130839

Subgroups — #13130839

Order 1664.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#11719621C211yesmaximal, characteristic, complemented
2#11719421C211yesmaximal, characteristic
3#11719142C211yesmaximal, characteristic, complemented
4#11719140C212yesmaximal, complemented
5#11718234C212yesmaximal, complemented
6C2×#6129C2211yescharacteristic
7C2×#6129C2211yescharacteristic
8C2×#6122—22no—
9#88238—24no—
10#88237C2212yes—
11D13⋊M16C2212yes—
12C13×#127C411yescharacteristic, complemented
13#88192—22no—
14#88190C411yescharacteristic, complemented
15#88190C411yescharacteristic, complemented
16D4×Dic13—22no—
17C42×D13C2211yescharacteristic
18#88123C411yescharacteristic, complemented
19#88119—22no—
20#88116—24no—
21C2×D4×C13—22no—
22C2×D4×C13C2×C411yescharacteristic
23C2×D4×C13C2×C411yescharacteristic
24C2×C22⋊D13—21no—
25C2×C22⋊D13D412yes—
26C22×Dic13—21no—
27C22×Dic13D412yes—
28#6129—22no—
29#6129—22no—
30#6129—22no—
31#6129—22no—
32C2×C4×D13—21no—
33C2×C4×D13C2311yescharacteristic
34C2×Dic26C2×C411yescharacteristic
35C2×Dic26C2×C411yescharacteristic
36C22⋊#261—22no—
37#6122—24no—
38#6122—22no—
39C2×#1057—24no—
40C4⋊#261—22no—
41C4×#261—22no—
42#6118D414yescomplemented
43D13⋊C8—22no—
44C42×C13C2×C411yescharacteristic
45C22⋊Dic13—22no—
46C22⋊Dic13—22no—
47C4⋊Dic13—22no—
48C4×Dic13—21no—
49C4×Dic13C2×C411yescharacteristic
50#1884—131nomaximal, Sylow
51C23×C13—21no—
52C23×C13C22⋊C412yes—
53C22×D13C2×D411yescharacteristic
54C2×#261—42no—
55D4×C13—22no—
56D4×C13—22no—
57D4×C13—44no—
58C2×C4×C13—21no—
59C2×C4×C13C22×C411yescharacteristic
60C22⋊D13—24no—
61C22⋊D13—42no—
62C2×Dic13—22no—
63C2×Dic13—22no—
64C2×Dic13—21no—
65C2×Dic13—21no—
66C2×Dic13—41no—
67C2×Dic13—41no—
68C2×Dic13C22⋊C412yes—
69C2×Dic13C2×D411yescharacteristic
70C4×D13—42no—
71C4×D13C2×D412yes—
72C4×D13#4112yes—
73Dic26—22no—
74Dic26—22no—
75#1057—24no—
76#568—131no—
77#532—131no—
78#421—132no—
79#410—131no—
80#339—132no—
81C22×C13—22no—
82C22×C13—42no—
83C22×C13—42no—
84C22×C13—41no—
85C22×C13C2×C22⋊C411yescharacteristic
86C2×D13—41no—
87C2×D13#12112yes—
88#261—82no—
89C4×C13—22no—
90C4×C13C4×D412yes—
91Dic13—22no—
92Dic13—41no—
93Dic13—41no—
94Dic13#12011yescharacteristic
95Dic13#12311yescharacteristic
96C2×#41—131no—
97C2×#41—131no—
98#131—264no—
99C2×M16—132no—
100C2×M16—262no—
101C4⋊Q8—131no—
102#127#26111yescharacteristic, complemented
103#124—131no—
104#124—131no—
105#121—262no—
106C4×D4—262no—
107#117—132no—
108C2×C42—131no—
109#104—264no—
110#99—262no—
111C2×C13—21no—
112C2×C13—42no—
113C2×C13—81no—
114C2×C13#38611yescharacteristic
115D13—22no—
116#41—262no—
117#41—262no—
118#41—262no—
119#41—262no—
120C2×Q8—131no—
121C2×Q8—131no—
122C2×D4—22no—
123C2×D4—132no—
124C2×D4—261no—
125C2×D4C2×#26111yescharacteristic
126C2×D4C2×#26111yescharacteristic
127C22×C4—131no—
128C22×C4—132no—
129C22×C4—261no—
130C22×C4—261no—
131M16—134no—
132M16—262no—
133M16—264no—
134C2×C8—262no—
135C2×C8—264no—
136C4⋊C4—262no—
137C4⋊C4—262no—
138C22⋊C4—262no—
139C22⋊C4—262no—
140C22⋊C4—262no—
141C42—131no—
142C42—261no—
143C42—262no—
144C42C2×#26111yescharacteristic
145C13#188411yescharacteristic, complemented, Sylow
146C23—21no—
147C23—131no—
148C23C22⋊#26112yes—
149Q8—262no—
150Q8—262no—
151D4—22no—
152D4—22no—
153D4—44no—
154D4—264no—
155D4—522no—
156C2×C4—21no—
157C2×C4—131no—
158C2×C4—132no—
159C2×C4—132no—
160C2×C4—132no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—261no—
164C2×C4—261no—
165C2×C4—522no—
166C2×C4—521no—
167C2×C4—521no—
168C2×C4—522no—
169C2×C4C22×#26111yescharacteristic
170C8—264no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—41no—
175C22—132no—
176C22—521no—
177C22C2×C22⋊#26111yescharacteristic
178C4—22no—
179C4—131no—
180C4—131no—
181C4—262no—
182C4—521no—
183C4—521no—
184C4—1042no—
185C4D4×#26112yes—
186C2—21no—
187C2—42no—
188C2—81no—
189C2—262no—
190C2#1171915011yescharacteristic
subgroupG/H
centerC2#11719150
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#127C4
socleC2×C13#386
prime radical#11719421C2
cosocleC2×C4×D13C23
hypercenter#127#261
hypocenterC13#1884
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11719621C2semidirect
3. #11719142C2semidirect
4. #11719140C2semidirect
5. #11718234C2semidirect
12. C13×#127C4semidirect
14. #88190C4semidirect
15. #88190C4semidirect
18. #88123C4semidirect
42. #6118D4semidirect
102. #127#261semidirect
145. C13#1884semidirect

Maximal subgroups

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

subgroupindex
#117196212
#117194212
#117191422
#117191402
#117182342
#188413