Finite Group Databasebeta

← #13131107

Subgroups — #13131107

Order 1664.

258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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#11719537C211yesmaximal, characteristic
2#11719116C212yesmaximal, complemented
3#11718300C212yesmaximal, complemented
4#11718294C212yesmaximal, complemented
5C2×C13×#41C411yescharacteristic, complemented
6C2×#6127C2211yescharacteristic
7#88237—22no—
8#88201C2211yescharacteristic
9#88198C411yescharacteristic, complemented
10#88194C2211yescharacteristic
11#88193—22no—
12#88190C411yescharacteristic, complemented
13C4×C22⋊D13—22no—
14C2×C4×Dic13C411yescharacteristic, complemented
15#88119—22no—
16#88107C2214yes—
17C13×#41—41no—
18C13×#41—41no—
19C2×Q8×C13C2×C411yescharacteristic
20C2×D4×C13—21no—
21C2×D4×C13C2×C411yescharacteristic
22C22×C4×C13—21no—
23C22×C4×C13C2×C411yescharacteristic
24C2×C22⋊D13—22no—
25C2×C22⋊D13D412yes—
26C22×Dic13—21no—
27#6127—41no—
28#6127—41no—
29C2×D52C2311yescharacteristic
30C2×C4×D13D412yes—
31C2×Dic26C2×C411yescharacteristic
32C22⋊#261—24no—
33C4⋊#261—42no—
34C4×#261—42no—
35C22⋊Dic13—22no—
36#6103—22no—
37#6101—22no—
38C4×Dic13—21no—
39C4×Dic13C2×C411yescharacteristic
40C4×Dic13C2×C411yescharacteristic
41#2126—131nomaximal, Sylow
42C23×C13—21no—
43C23×C13C22⋊C411yescharacteristic
44C22×D13C2×D412yes—
45C2×#261—44no—
46Q8×C13—41no—
47D4×C13—41no—
48D4×C13—42no—
49C2×C4×C13—21no—
50C2×C4×C13—21no—
51C2×C4×C13—21no—
52C2×C4×C13—41no—
53C2×C4×C13—41no—
54C2×C4×C13C22⋊C411yescharacteristic
55C2×C4×C13C22×C411yescharacteristic
56C22⋊D13—42no—
57C22⋊D13—44no—
58C2×Dic13—21no—
59C2×Dic13—21no—
60C2×Dic13—42no—
61C2×Dic13C22⋊C412yes—
62D52—41no—
63C4×D13—22no—
64C4×D13—22no—
65Dic26—41no—
66#532—131no—
67#410—132no—
68#354—132no—
69#353—132no—
70C22×C13—21no—
71C22×C13—41no—
72C22×C13—42no—
73C22×C13—41no—
74C22×C13C2×C22⋊C411yescharacteristic
75C2×D13—22no—
76C2×D13—42no—
77#261—84no—
78C4×C13—21no—
79C4×C13—41no—
80C4×C13#9911yescharacteristic
81C4×C13#9911yescharacteristic
82Dic13—22no—
83Dic13—22no—
84Dic13—41no—
85C2×#41—131no—
86C2×#41#26111yescharacteristic, complemented
87C4⋊Q8—131no—
88#127—131no—
89#124—131no—
90#124—131no—
91#121—262no—
92C4×D4—262no—
93#117—262no—
94C2×C42—131no—
95#99—134no—
96#99—262no—
97C2×C13—21no—
98C2×C13—41no—
99C2×C13—81no—
100C2×C13C2×#9911yescharacteristic
101D13—42no—
102#41—41no—
103#41—41no—
104#41—521no—
105#41—521no—
106C2×Q8—131no—
107C2×Q8C2×#26111yescharacteristic
108C2×D4—21no—
109C2×D4—132no—
110C2×D4—131no—
111C2×D4—262no—
112C2×D4C2×#26111yescharacteristic
113C22×C4—21no—
114C22×C4—132no—
115C22×C4—261no—
116C22×C4C2×#26111yescharacteristic
117C4⋊C4—262no—
118C4⋊C4—522no—
119C22⋊C4—262no—
120C22⋊C4—262no—
121C22⋊C4—264no—
122C42—131no—
123C42—131no—
124C42—261no—
125C42—522no—
126C13#212611yescharacteristic, complemented, Sylow
127C23—21no—
128C23—132no—
129C23C22⋊#26111yescharacteristic
130Q8—41no—
131Q8—521no—
132D4—41no—
133D4—42no—
134D4—521no—
135D4—522no—
136D4—524no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—132no—
143C2×C4—261no—
144C2×C4—262no—
145C2×C4—262no—
146C2×C4—261no—
147C2×C4—522no—
148C2×C4—524no—
149C2×C4C22⋊#26111yescharacteristic
150C2×C4C22×#26111yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—262no—
156C22—522no—
157C22C2×C22⋊#26111yescharacteristic
158C4—21no—
159C4—41no—
160C4—262no—
161C4—262no—
162C4—521no—
163C4—1044no—
164C4#8811911yescharacteristic
165C4#8811911yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—522no—
170C2C2×#8811911yescharacteristic
subgroupG/H
centerC4#88119
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×#41C4
socleC2×C13C2×#99
prime radical#11719537C2
cosocleC2×D52C23
hypercenterC2×#41#261
hypocenterC13#2126
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11719116C2semidirect
3. #11718300C2semidirect
4. #11718294C2semidirect
5. C2×C13×#41C4semidirect
9. #88198C4semidirect
12. #88190C4semidirect
14. C2×C4×Dic13C4semidirect
86. C2×#41#261semidirect
126. C13#2126semidirect

Maximal subgroups

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

subgroupindex
#117195372
#117191162
#117183002
#117182942
#212613