Finite Group Databasebeta

← #13113465

Subgroups — #13113465

Order 1664.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#11719184C211yesmaximal, characteristic
2C13×#432C211yesmaximal, characteristic, complemented
3#11718587C211yesmaximal, characteristic, complemented
4#11718057C212yesmaximal, complemented
5#11718056C212yesmaximal, complemented
6C2×C42×C13C2211yescharacteristic
7#88184C411yescharacteristic
8#88183—21no—
9C4×C22⋊D13—21no—
10#88178C411yescharacteristic
11#88130—21no—
12#88129C2211yescharacteristic
13C4×D52C411yescharacteristic
14#88126—21no—
15#88124C2211yescharacteristic
16C4×Dic26C411yescharacteristic
17C13×C4⋊C8—21no—
18C13×C22⋊C8—21no—
19C13×#97C2212yes—
20C22⋊#1055—21no—
21C4⋊#1055—21no—
22#88043C2212yes—
23C22×C4×C13C2×C411yescharacteristic
24C22×C4×C13D411yescharacteristic
25C22×C4×C13D411yescharacteristic
26C2×C22⋊D13—21no—
27C2×D52C2×C411yescharacteristic
28C2×C4×D13—21no—
29C2×Dic26C2×C411yescharacteristic
30C2×C8×C13—22no—
31C42×C13C2×C411yescharacteristic
32C42×C13D411yescharacteristic
33C42×C13D411yescharacteristic
34C42×C13C2311yescharacteristic
35C22⋊Dic13—21no—
36#6103—21no—
37#6103—21no—
38#6103—21no—
39#6103—21no—
40C4⋊Dic13C2×C411yescharacteristic
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43#6101—21no—
44#6101—21no—
45#6101—21no—
46C4×Dic13—21no—
47C2×#1055—22no—
48#1535—131nomaximal, Sylow
49C23×C13C22⋊C411yescharacteristic
50C22×D13—21no—
51C2×C4×C13—41no—
52C2×C4×C13—41no—
53C2×C4×C13—41no—
54C2×C4×C13C22⋊C411yescharacteristic
55C2×C4×C13C22⋊C411yescharacteristic
56C2×C4×C13C22⋊C411yescharacteristic
57C2×C4×C13C22×C411yescharacteristic
58C2×C4×C13C2×D411yescharacteristic
59C2×C4×C13C2×D411yescharacteristic
60C22⋊D13—42no—
61C2×Dic13—21no—
62C2×Dic13—21no—
63C2×Dic13—21no—
64D52—41no—
65C4×D13—42no—
66Dic26—41no—
67C8×C13—42no—
68#1055—42no—
69#529—131no—
70#432—131no—
71#432D1311yescharacteristic, complemented
72#330—132no—
73#329—132no—
74C22×C13—21no—
75C22×C13—21no—
76C22×C13—21no—
77C22×C13C2×C22⋊C411yescharacteristic
78C2×D13—41no—
79C2×D13—41no—
80C2×D13—41no—
81C4×C13—21no—
82C4×C13—21no—
83C4×C13—21no—
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—21no—
87Dic13—41no—
88Dic13—41no—
89Dic13—41no—
90#126—261no—
91#125—131no—
92#124—131no—
93#123—261no—
94C22⋊Q8—131no—
95#121—131no—
96C4×Q8—131no—
97C4×D4—131no—
98C4×D4—261no—
99#117—261no—
100C2×C42C2×D1311yescharacteristic
101C4⋊C8—21no—
102C4⋊C8—261no—
103C22⋊C8—21no—
104C22⋊C8—261no—
105#97—132no—
106#97C2×D1312yes—
107C2×C13—41no—
108C2×C13#41311yescharacteristic
109C2×C13#42111yescharacteristic
110C2×C13#42111yescharacteristic
111D13—81no—
112C2×Q8—131no—
113C2×D4—131no—
114C2×D4—261no—
115C22×C4—261no—
116C22×C4C4×D1311yescharacteristic
117C22×C4D5211yescharacteristic
118C22×C4C22⋊D1311yescharacteristic
119C2×C8—22no—
120C2×C8—262no—
121C4⋊C4—131no—
122C4⋊C4—131no—
123C4⋊C4—261no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C22⋊C4—261no—
128C22⋊C4—261no—
129C22⋊C4—261no—
130C22⋊C4—261no—
131C22⋊C4—261no—
132C42—261no—
133C42C4×D1311yescharacteristic
134C42D5211yescharacteristic
135C42C22⋊D1311yescharacteristic
136C42C22×D1311yescharacteristic
137C13#153511yescharacteristic, complemented, Sylow
138C23—261no—
139C23#610311yescharacteristic
140Q8—521no—
141D4—521no—
142D4—522no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—261no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—522no—
150C2×C4#610311yescharacteristic
151C2×C4#610311yescharacteristic
152C2×C4#610311yescharacteristic
153C2×C4C2×C4×D1311yescharacteristic
154C2×C4C2×D5211yescharacteristic
155C2×C4C2×C22⋊D1311yescharacteristic
156C8—42no—
157C8—522no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—521no—
162C22—521no—
163C22—521no—
164C22C2×#610311yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—521no—
172C4—521no—
173C4—521no—
174C2—41no—
175C2—1041no—
176C2#1171866611yescharacteristic
177C2#1171879311yescharacteristic
178C2#1171880011yescharacteristic
subgroupG/H
centerC22C2×#6103
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#432C2
socleC22×C13C2×C22⋊C4
prime radical#88184C4
cosocleC42×C13C23
hypercenter#432D13
hypocenterC13#1535
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C13×#432C2semidirect
3. #11718587C2semidirect
4. #11718057C2semidirect
5. #11718056C2semidirect
71. #432D13semidirect
137. C13#1535semidirect

Maximal subgroups

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

subgroupindex
#117191842
C13×#4322
#117185872
#117180572
#117180562
#153513