Finite Group Databasebeta

← #13126237

Subgroups — #13126237

Order 1664.

354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719184C212yesmaximal, complemented
2C13×#423C211yesmaximal, characteristic, complemented
3#11718798C211yesmaximal, characteristic, complemented
4#11718796C211yesmaximal, characteristic
5#11718795C212yesmaximal, complemented
6#11718508C212yesmaximal, complemented
7#11718506C212yesmaximal, complemented
8#11718505C212yesmaximal, complemented
9#11718490C212yesmaximal, complemented
10C2×C13×M16C2211yescharacteristic
11C2×C13×M16C2211yescharacteristic
12C2×C42×C13C2211yescharacteristic
13#88184C2212yes—
14#88183—22no—
15C4×C22⋊D13—22no—
16#88178C2212yes—
17C2×Dic52C2211yescharacteristic
18C2×D104C2211yescharacteristic
19C2×#6095C2212yes—
20#88130—22no—
21#88129C2212yes—
22C4×D52C2212yes—
23#88126—22no—
24#88124C2212yes—
25C4×Dic26C2212yes—
26C13×C4⋊C8C2212yes—
27C13×C4⋊C8C2212yes—
28#88061C2212yes—
29#88061C2212yes—
30#88058C2212yes—
31#88057C2211yescharacteristic
32#88057C2211yescharacteristic
33#88056C2212yes—
34#88056C2212yes—
35C22×C4×C13D412yes—
36C22×C4×C13C2311yescharacteristic
37C2×C22⋊D13—22no—
38C2×D52C2312yes—
39C2×C4×D13—22no—
40C2×Dic26C2312yes—
41C13×M16—41no—
42C13×M16—41no—
43C2×C8×C13C2312yes—
44C2×C8×C13C2311yescharacteristic
45C2×C8×C13C2311yescharacteristic
46C42×C13D411yescharacteristic
47C42×C13D411yescharacteristic
48C42×C13C2312yes—
49C22⋊Dic13—22no—
50#6103—22no—
51#6103—22no—
52#6103—22no—
53#6103—22no—
54C4⋊Dic13C2312yes—
55C4⋊Dic13C2312yes—
56#6101—22no—
57#6101—22no—
58#6101—22no—
59#6101—22no—
60C4×Dic13—22no—
61Dic52—41no—
62D104—41no—
63#6095—42no—
64#3256—131nomaximal, Sylow
65C23×C13C2×D411yescharacteristic
66C22×D13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—42no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D412yes—
73C2×C4×C13C2411yescharacteristic
74C22⋊D13—44no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78D52—22no—
79D52—22no—
80C4×D13—44no—
81Dic26—22no—
82Dic26—22no—
83C8×C13—22no—
84C8×C13—21no—
85C8×C13—21no—
86#529—132no—
87#479—132no—
88#478—132no—
89#470—131no—
90#469—131no—
91#468—132no—
92#464—132no—
93#463—132no—
94#423D1311yescharacteristic, complemented
95C22×C13—21no—
96C22×C13—22no—
97C22×C13C22×D411yescharacteristic
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—42no—
101C4×C13—21no—
102C4×C13—22no—
103C4×C13—22no—
104C4×C13H(5,𝔽2)11yescharacteristic
105C4×C132−1+411yescharacteristic
106Dic13—42no—
107Dic13—42no—
108Dic13—42no—
109C2×Q16—131no—
110C2×SD16—132no—
111C2×D8—131no—
112C2×M16C2×D1311yescharacteristic
113C2×M16C2×D1311yescharacteristic
114#126—262no—
115#125—132no—
116#124—132no—
117#123—262no—
118C22⋊Q8—132no—
119#121—132no—
120C4×Q8—132no—
121C4×D4—132no—
122C4×D4—262no—
123#117—262no—
124C2×C42C2×D1311yescharacteristic
125#107—132no—
126#106—131no—
127#106—131no—
128C4⋊C8C2×D1312yes—
129C4⋊C8C2×D1312yes—
130#103—132no—
131#103—132no—
132#102—132no—
133#102—132no—
134C2×C13—41no—
135C2×C13#53711yescharacteristic
136C2×C13#57512yes—
137D13—82no—
138C2×Q8—132no—
139C2×D4—132no—
140C2×D4—262no—
141C22×C4—262no—
142C22×C4D5212yes—
143C22×C4C22×D1311yescharacteristic
144Q16—521no—
145SD16—522no—
146D8—521no—
147M16—41no—
148M16—41no—
149C2×C8C22×D1311yescharacteristic
150C2×C8C22×D1312yes—
151C2×C8C22×D1311yescharacteristic
152C4⋊C4—132no—
153C4⋊C4—132no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4—262no—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C22⋊C4—262no—
163C42—262no—
164C42D5211yescharacteristic
165C42D5211yescharacteristic
166C42C22×D1312yes—
167C13#325611yescharacteristic, complemented, Sylow
168C23—262no—
169C23C2×D5211yescharacteristic
170Q8—262no—
171Q8—262no—
172D4—262no—
173D4—262no—
174D4—524no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—524no—
182C2×C4C2×D5212yes—
183C2×C4C2×D5211yescharacteristic
184C2×C4C2×D5212yes—
185C2×C4C23×D1311yescharacteristic
186C8—21no—
187C8—22no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—522no—
192C22—522no—
193C22—522no—
194C22C22×D5211yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—522no—
199C4—522no—
200C4—522no—
201C4#8825111yescharacteristic
202C4#8825411yescharacteristic
203C2—41no—
204C2—1042no—
205C2#1171921511yescharacteristic
206C2#1171945312yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#423C2
socleC22×C13C22×D4
prime radical#11718796C2
hypercenter#423D13
hypocenterC13#3256
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #11719184C2semidirect
2. C13×#423C2semidirect
3. #11718798C2semidirect
5. #11718795C2semidirect
6. #11718508C2semidirect
7. #11718506C2semidirect
8. #11718505C2semidirect
9. #11718490C2semidirect
94. #423D13semidirect
167. C13#3256semidirect

Maximal subgroups

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

subgroupindex
#117191842
C13×#4232
#117187982
#117187962
#117187952
#117185082
#117185062
#117185052
#117184902
#325613