Finite Group Databasebeta

← #13120625

Subgroups — #13120625

Order 1664.

548 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×C13×#117C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic
3#11718873C211yesmaximal, characteristic, complemented
4#11718654C212yesmaximal, complemented
5#11718653C212yesmaximal, complemented
6#11718620C214yesmaximal, complemented
7#11718600C212yesmaximal, complemented
8#11718589C212yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C22×C22⋊D13C2212yes—
11C22×D52C2211yescharacteristic
12C13×#117—24no—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C42×C13C2212yes—
17C2×C22⋊Dic13C2212yes—
18#88184—24no—
19C2×#6103C2212yes—
20C2×#6103C2214yes—
21C2×#6103C2214yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2214yes—
25#88071C2214yes—
26#88071C2212yes—
27C24×C13C2311yescharacteristic
28C23×D13C2312yes—
29C22×C4×C13—24no—
30C22×C4×C13D414yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2311yescharacteristic
35C2×C22⋊D13—24no—
36C2×C22⋊D13—44no—
37C22×Dic13C2312yes—
38C22×Dic13C2314yes—
39C2×D52—22no—
40C2×D52—24no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—22no—
43C13×C22⋊C4—24no—
44C42×C13—24no—
45C22⋊Dic13—42no—
46#6103—24no—
47#6103—44no—
48#6103—44no—
49C4⋊Dic13—22no—
50C4⋊Dic13—24no—
51#6101—44no—
52#2624—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—21no—
55C23×C13—22no—
56C23×C13—21no—
57C23×C13C2×D412yes—
58C23×C13C2411yescharacteristic
59C22×D13—22no—
60C22×D13—24no—
61C22×D13—22no—
62C22×D13—24no—
63C22×D13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—28no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13C2×D412yes—
73C2×C4×C13C2×D412yes—
74C2×C4×C13#4114yes—
75C22⋊D13—48no—
76C2×Dic13—22no—
77C2×Dic13—24no—
78C2×Dic13—24no—
79C2×Dic13—24no—
80C2×Dic13—24no—
81D52—44no—
82C2×#121—131no—
83C2×#117D1311yescharacteristic, complemented
84#399—132no—
85#397—132no—
86#394—134no—
87#390—132no—
88#389—132no—
89#380—131no—
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—22no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13C22×D411yescharacteristic
96C22×C13C2×#4112yes—
97C22×C13H(5,𝔽2)12yes—
98C22×C13H(5,𝔽2)11yescharacteristic
99C22×C132−1+411yescharacteristic
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—42no—
103C2×D13—44no—
104C2×D13—44no—
105C4×C13—22no—
106C4×C13—42no—
107C4×C13—42no—
108C4×C13#12314yes—
109Dic13—42no—
110Dic13—44no—
111C22×D4—132no—
112C22×D4—131no—
113C23×C4C2×D1311yescharacteristic
114#121—264no—
115#117—24no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—134no—
119C2×C4⋊C4C2×D1311yescharacteristic
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C22⋊C4—132no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4—134no—
125C2×C22⋊C4C2×D1312yes—
126C2×C42C2×D1312yes—
127#95—132no—
128#95—134no—
129C2×C13—42no—
130C2×C13C2×#12311yescharacteristic
131C2×C13#53511yescharacteristic
132C2×C13#53711yescharacteristic
133C2×C13#54012yes—
134C2×C13#54212yes—
135D13—82no—
136C24—132no—
137C24C22×D1311yescharacteristic
138C2×D4—264no—
139C2×D4—264no—
140C2×D4—262no—
141C2×D4—524no—
142C22×C4—24no—
143C22×C4—134no—
144C22×C4—132no—
145C22×C4C22⋊D1314yes—
146C22×C4C22×D1312yes—
147C22×C4C22×D1312yes—
148C22×C4C22×D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—264no—
153C4⋊C4—262no—
154C4⋊C4—524no—
155C22⋊C4—24no—
156C22⋊C4—264no—
157C22⋊C4—524no—
158C22⋊C4—524no—
159C22⋊C4—522no—
160C42—24no—
161C13#262411yescharacteristic, complemented, Sylow
162C23—22no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—264no—
167C23—262no—
168C23—264no—
169C23—262no—
170C23—262no—
171C23C2×C22⋊D1312yes—
172C23C23×D1311yescharacteristic
173D4—528no—
174D4—524no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—264no—
184C2×C4—264no—
185C2×C4—264no—
186C2×C4—264no—
187C2×C4—262no—
188C2×C4#612714yes—
189C2×C4C2×C22⋊D1312yes—
190C2×C4C2×C22⋊D1312yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—522no—
197C22—524no—
198C22—524no—
199C22—522no—
200C22—522no—
201C22C2×#612712yes—
202C22#8825612yes—
203C22#8825611yescharacteristic
204C22#8825711yescharacteristic
205C22C22×C22⋊D1311yescharacteristic
206C4—22no—
207C4—42no—
208C4—42no—
209C4—524no—
210C4—522no—
211C4#8818314yes—
212C2—42no—
213C2—1042no—
214C2#1171923912yes—
215C2#1171924012yes—
216C2C2×#8818311yescharacteristic
217C2#1171953511yescharacteristic
218C2#1171953811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#117C2
prime radicalC2×#88184C2
hypercenterC2×#117D13
hypocenterC13#2624
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C13×#117C2semidirect
3. #11718873C2semidirect
4. #11718654C2semidirect
5. #11718653C2semidirect
6. #11718620C2semidirect
7. #11718600C2semidirect
8. #11718589C2semidirect
83. C2×#117D13semidirect
161. C13#2624semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1172
C2×#881842
#117188732
#117186542
#117186532
#117186202
#117186002
#117185892
#262413