Finite Group Databasebeta

← #13113374

Subgroups — #13113374

Order 1664.

222 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C13×#529C211yesmaximal, characteristic
2#11718597C211yesmaximal, characteristic, complemented
3#11718587C211yesmaximal, characteristic, complemented
4#11718130C212yesmaximal, complemented
5#11718129C212yesmaximal
6C13×#126—21no—
7C13×#125C411yescharacteristic, complemented
8C13×#124C411yescharacteristic, complemented
9C13×#123—21no—
10C13×C22⋊Q8C2211yescharacteristic
11C13×#121C2211yescharacteristic
12C4×Q8×C13C411yescharacteristic, complemented
13C4×D4×C13—21no—
14C4×D4×C13C411yescharacteristic, complemented
15C13×#117—21no—
16C2×C42×C13C2211yescharacteristic
17C2×C4⋊Dic13—21no—
18#88071—21no—
19#88071C2212yes—
20C22⋊#1055C2212yes—
21C4⋊#1055—21no—
22#88043—21no—
23C2×Q8×C13C2×C411yescharacteristic
24C2×D4×C13—21no—
25C2×D4×C13C2×C411yescharacteristic
26C22×C4×C13—21no—
27C22×C4×C13D411yescharacteristic
28C22×C4×C13D411yescharacteristic
29C22×C4×C13C2311yescharacteristic
30C22×Dic13—22no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4C2×C411yescharacteristic
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C22⋊C4—21no—
38C13×C22⋊C4—21no—
39C13×C22⋊C4—21no—
40C13×C22⋊C4—21no—
41C13×C22⋊C4—21no—
42C42×C13—21no—
43C42×C13C2×C411yescharacteristic
44C42×C13C2×C411yescharacteristic
45C42×C13D411yescharacteristic
46C42×C13D411yescharacteristic
47C4⋊Dic13—42no—
48C2×#1055—22no—
49#1512—131nomaximal, Sylow
50C23×C13—21no—
51C23×C13C2×D411yescharacteristic
52Q8×C13—41no—
53D4×C13—41no—
54D4×C13—41no—
55D4×C13—41no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—42no—
64C2×C4×C13C22⋊C411yescharacteristic
65C2×C4×C13C22⋊C411yescharacteristic
66C2×C4×C13C22⋊C411yescharacteristic
67C2×C4×C13C22⋊C411yescharacteristic
68C2×C4×C13C22×C411yescharacteristic
69C2×C4×C13C2×D411yescharacteristic
70C2×Dic13—42no—
71C2×Dic13—42no—
72C2×Dic13—42no—
73#1055—42no—
74#529D1311yescharacteristic
75#432—131no—
76#382—131no—
77#328—132no—
78#327—132no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13—41no—
82C22×C13—41no—
83C22×C13—41no—
84C22×C13C2×C22⋊C411yescharacteristic
85C22×C13AGL(1,ℤ/8)11yescharacteristic
86C22×C13#13711yescharacteristic
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13—41no—
94C4×C13—41no—
95C4×C13—41no—
96Dic13—82no—
97#126—21no—
98#125Dic1311yescharacteristic, complemented
99#124Dic1311yescharacteristic, complemented
100#123—21no—
101C22⋊Q8C2×D1311yescharacteristic
102#121C2×D1311yescharacteristic
103C4×Q8Dic1311yescharacteristic, complemented
104C4×D4—21no—
105C4×D4Dic1311yescharacteristic, complemented
106#117—21no—
107C2×C4⋊C4—261no—
108C2×C42C2×D1311yescharacteristic
109C4⋊C8—261no—
110C22⋊C8—132no—
111#97—261no—
112#95—132no—
113#95—261no—
114C2×C13—21no—
115C2×C13—21no—
116C2×C13—81no—
117C2×C13#41011yescharacteristic
118C2×C13#41711yescharacteristic
119C2×C13#42111yescharacteristic
120C2×Q8C2×Dic1311yescharacteristic
121C2×D4—21no—
122C2×D4C2×Dic1311yescharacteristic
123C22×C4—21no—
124C22×C4—262no—
125C22×C4C22⋊D1311yescharacteristic
126C22×C4C22⋊D1311yescharacteristic
127C22×C4C22×D1311yescharacteristic
128C2×C8—262no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—522no—
134C4⋊C4C2×Dic1311yescharacteristic
135C4⋊C4C2×Dic1311yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C42—21no—
142C42C2×Dic1311yescharacteristic
143C42C2×Dic1311yescharacteristic
144C42C22⋊D1311yescharacteristic
145C42C22⋊D1311yescharacteristic
146C13#151211yescharacteristic, complemented, Sylow
147C23—21no—
148C23C2×C22⋊D1311yescharacteristic
149Q8—41no—
150D4—41no—
151D4—41no—
152D4—41no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—522no—
162C2×C4—522no—
163C2×C4—522no—
164C2×C4C22⋊Dic1311yescharacteristic
165C2×C4C22⋊Dic1311yescharacteristic
166C2×C4C22⋊Dic1311yescharacteristic
167C2×C4C22⋊Dic1311yescharacteristic
168C2×C4C22×Dic1311yescharacteristic
169C2×C4C2×C22⋊D1311yescharacteristic
170C8—522no—
171C22—21no—
172C22—21no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#8820311yescharacteristic
177C22#8820511yescharacteristic
178C22C2×C22⋊Dic1311yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—1042no—
189C2—21no—
190C2—21no—
191C2—81no—
192C2#1171889311yescharacteristic
193C2#1171889711yescharacteristic
194C2#1171890111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#529C2
socleC22×C13C2×C22⋊C4
prime radicalC13×#121C22
cosocleC22×C4×C13C23
hypercenter#529D13
hypocenterC13#1512
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #11718597C2semidirect
3. #11718587C2semidirect
4. #11718130C2semidirect
7. C13×#125C4semidirect
8. C13×#124C4semidirect
12. C4×Q8×C13C4semidirect
14. C4×D4×C13C4semidirect
98. #125Dic13semidirect
99. #124Dic13semidirect
103. C4×Q8Dic13semidirect
105. C4×D4Dic13semidirect
146. C13#1512semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117185972
#117185872
#117181302
#117181292
#151213