Finite Group Databasebeta

← #13113469

Subgroups — #13113469

Order 1664.

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

normal subgroups only

This group has 238 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
1#11719373C211yesmaximal, characteristic
2#11718366C212yesmaximal, complemented
3C13×#329C211yesmaximal, characteristic, complemented
4#11718132C211yesmaximal, characteristic, complemented
5#11718056C212yesmaximal, complemented
6C2×#6131C411yescharacteristic
7C2×#6129C411yescharacteristic
8C13×#124C2211yescharacteristic
9#88198C411yescharacteristic
10#88194C411yescharacteristic
11#88138—22no—
12#88135—22no—
13#88129C2211yescharacteristic
14C42×D13C2211yescharacteristic
15C13×#97C2212yes—
16#88060—22no—
17#88054—22no—
18#88043C2212yes—
19C2×Q8×C13C2×C411yescharacteristic
20C2×D4×C13C2×C411yescharacteristic
21C2×C22⋊D13—21no—
22C2×C22⋊D13—22no—
23C22×Dic13—21no—
24#6131—42no—
25#6129—42no—
26C2×D52—21no—
27C2×D52C2×C411yescharacteristic
28C2×C4×D13—21no—
29C2×C4×D13C2×C411yescharacteristic
30C2×C4×D13D412yes—
31C2×Dic26C2×C411yescharacteristic
32C2×C8×C13—22no—
33C13×C22⋊C4—22no—
34C42×C13C2311yescharacteristic
35#6103—22no—
36#6101—22no—
37C4×Dic13C2×C411yescharacteristic
38C4×Dic13D412yes—
39C2×#1055—22no—
40#1536—131nomaximal, Sylow
41C23×C13—21no—
42C22×D13—21no—
43C22×D13C22⋊C411yescharacteristic
44Q8×C13—41no—
45D4×C13—41no—
46C2×C4×C13—21no—
47C2×C4×C13C22×C411yescharacteristic
48C2×C4×C13C2×D412yes—
49C22⋊D13—44no—
50C22⋊D13—42no—
51C2×Dic13—21no—
52C2×Dic13—42no—
53C2×Dic13C22⋊C412yes—
54C2×Dic13C22⋊C411yescharacteristic
55D52—41no—
56D52—42no—
57C4×D13—22no—
58C4×D13—42no—
59C4×D13—42no—
60Dic26—41no—
61C8×C13—42no—
62#1055—42no—
63#532—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—21no—
72C2×D13—22no—
73C2×D13—41no—
74C2×D13—42no—
75C4×C13—21no—
76C4×C13—22no—
77C4×C13—41no—
78Dic13—22no—
79Dic13—41no—
80Dic13#10012yes—
81C2×#41—131no—
82C2×#41—131no—
83C4⋊Q8—131no—
84#127—131no—
85#124—131no—
86#124C2×D1311yescharacteristic
87#121—262no—
88C4×D4—262no—
89C2×C42—131no—
90C4⋊C8—262no—
91C22⋊C8—262no—
92#97—132no—
93#97C2×D1312yes—
94C2×C13—81no—
95C2×C13C2×#10011yescharacteristic
96C2×C13#42112yes—
97D13—41no—
98D13—81no—
99#41—522no—
100#41—522no—
101C2×Q8—131no—
102C2×Q8C4×D1311yescharacteristic
103C2×D4—131no—
104C2×D4—261no—
105C2×D4—262no—
106C2×D4—261no—
107C2×D4C4×D1311yescharacteristic
108C22×C4—131no—
109C22×C4—132no—
110C22×C4—261no—
111C22×C4—261no—
112C2×C8—22no—
113C2×C8—262no—
114C4⋊C4—262no—
115C22⋊C4—22no—
116C22⋊C4—262no—
117C42—131no—
118C42—132no—
119C42C22×D1311yescharacteristic
120C13#153611yescharacteristic, complemented, Sylow
121C23—21no—
122C23—131no—
123C23—261no—
124Q8—41no—
125Q8—521no—
126D4—41no—
127D4—521no—
128D4—522no—
129D4—524no—
130D4—522no—
131C2×C4—21no—
132C2×C4—131no—
133C2×C4—132no—
134C2×C4—262no—
135C2×C4—261no—
136C2×C4—522no—
137C2×C4—522no—
138C2×C4—522no—
139C2×C4C2×C4×D1311yescharacteristic
140C2×C4D4×D1312yes—
141C8—42no—
142C8—522no—
143C22—41no—
144C22—42no—
145C22—261no—
146C22—262no—
147C22—521no—
148C22—522no—
149C22C22⋊C4×D1311yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—132no—
154C4—262no—
155C4—521no—
156C2—81no—
157C2—521no—
158C2—1041no—
159C2D13×#10011yescharacteristic
160C2#1171848212yes—
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#329C2
socleC22×C13C2×C22⋊C4
prime radical#11719373C2
cosocleC42×C13C23
hypercenter#329D13
hypocenterC13#1536
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
67. #329D13semidirect
120. C13#1536semidirect

Maximal subgroups

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

subgroupindex
#117193732
#117183662
C13×#3292
#117181322
#117180562
#153613