Finite Group Databasebeta

← #13113458

Subgroups — #13113458

Order 1664.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D13×#124C211yesmaximal, characteristic
2#11718366C212yesmaximal, complemented
3C13×#329C211yesmaximal, characteristic, complemented
4#11718132C211yesmaximal, characteristic, complemented
5#11718056C212yesmaximal, complemented
6C2×Q8×D13C411yescharacteristic
7C2×D4×D13C411yescharacteristic
8C13×#124C2211yescharacteristic
9#88201C411yescharacteristic
10#88190C411yescharacteristic
11#88139—22no—
12C22⋊C4×D13—22no—
13#88129C2211yescharacteristic
14C42×D13C2211yescharacteristic
15C13×#97C2212yescomplemented
16#88060—22no—
17#88054—22no—
18#88043C2212yescomplemented
19C23×D13—21no—
20C2×Q8×C13C2×C411yescharacteristic
21C2×D4×C13C2×C411yescharacteristic
22C2×C22⋊D13—21no—
23Q8×D13—42no—
24D4×D13—42no—
25C2×D52C2×C411yescharacteristic
26C2×C4×D13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D412yes—
29C2×Dic26—21no—
30C2×Dic26C2×C411yescharacteristic
31C2×C8×C13—22no—
32C13×C22⋊C4—22no—
33C42×C13C2311yescharacteristic
34C22⋊Dic13—22no—
35#6103—22no—
36#6103—22no—
37C4×Dic13C2×C411yescharacteristic
38C4×Dic13D412yes—
39C2×#1055—22no—
40#1533—131nomaximal, Sylow
41C23×C13—21no—
42C22×D13—21no—
43C22×D13—44no—
44C22×D13—42no—
45C22×D13C22⋊C411yescharacteristic
46Q8×C13—41no—
47D4×C13—41no—
48C2×C4×C13—21no—
49C2×C4×C13C22×C411yescharacteristic
50C2×C4×C13C2×D412yes—
51C22⋊D13—42no—
52C2×Dic13—21no—
53C2×Dic13C22⋊C412yes—
54C2×Dic13C22⋊C411yescharacteristic
55D52—41no—
56C4×D13—22no—
57C4×D13—42no—
58C4×D13—42no—
59Dic26—42no—
60Dic26—41no—
61C8×C13—42no—
62#1055—42no—
63C2×#124—131no—
64#432—132no—
65#329—131no—
66#329—132no—
67#329D1311yescharacteristic, complemented
68C22×C13—41no—
69C22×C13—42no—
70C22×C13C2×C22⋊C411yescharacteristic
71C2×D13—22no—
72C2×D13—41no—
73C2×D13—42no—
74C2×D13—84no—
75C2×D13#10012yes—
76C4×C13—21no—
77C4×C13—22no—
78C4×C13—41no—
79Dic13—21no—
80Dic13—22no—
81Dic13—41no—
82C22×Q8—131no—
83C22×D4—131no—
84#124—131no—
85#124—131no—
86#124—131no—
87#124—262no—
88#124C2×D1311yescharacteristic
89C2×C22⋊C4—262no—
90C2×C42—131no—
91C4⋊C8—262no—
92C22⋊C8—262no—
93#97—132no—
94#97C2×D1312yescomplemented
95C2×C13—81no—
96C2×C13C2×#10011yescharacteristic
97C2×C13#42112yes—
98D13—22no—
99D13—81no—
100C24—261no—
101C2×Q8—131no—
102C2×Q8—261no—
103C2×Q8—522no—
104C2×Q8C4×D1311yescharacteristic
105C2×D4—131no—
106C2×D4—261no—
107C2×D4—522no—
108C2×D4C4×D1311yescharacteristic
109C22×C4—131no—
110C22×C4—132no—
111C22×C4—261no—
112C2×C8—22no—
113C2×C8—262no—
114C22⋊C4—22no—
115C22⋊C4—262no—
116C22⋊C4—262no—
117C22⋊C4—262no—
118C42—131no—
119C42—132no—
120C42C22×D1311yescharacteristic
121C13#153311yescharacteristic, complemented, Sylow
122C23—21no—
123C23—131no—
124C23—261no—
125C23—522no—
126C23—524no—
127Q8—41no—
128Q8—521no—
129Q8—522no—
130D4—41no—
131D4—521no—
132D4—522no—
133C2×C4—21no—
134C2×C4—132no—
135C2×C4—131no—
136C2×C4—262no—
137C2×C4—261no—
138C2×C4—522no—
139C2×C4—522no—
140C2×C4C2×C4×D1311yescharacteristic
141C2×C4D4×D1312yes—
142C8—42no—
143C8—522no—
144C22—41no—
145C22—42no—
146C22—132no—
147C22—262no—
148C22—521no—
149C22—522no—
150C22—1044no—
151C22C22⋊C4×D1311yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—261no—
156C4—262no—
157C4—521no—
158C2—81no—
159C2—262no—
160C2—1041no—
161C2D13×#10011yescharacteristic
162C2#1171848212yes—
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#329C2
socleC22×C13C2×C22⋊C4
prime radicalC2×D4×D13C4
cosocleC42×C13C23
hypercenter#329D13
hypocenterC13#1533
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11718366C2semidirect
3. C13×#329C2semidirect
4. #11718132C2semidirect
5. #11718056C2semidirect
15. C13×#97C22semidirect
18. #88043C22semidirect
67. #329D13semidirect
94. #97C2×D13semidirect
121. C13#1533semidirect

Maximal subgroups

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

subgroupindex
D13×#1242
#117183662
C13×#3292
#117181322
#117180562
#153313