Finite Group Databasebeta

← #13120705

Subgroups — #13120705

Order 1664.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×#125C211yesmaximal, characteristic, complemented
2C2×C4×D52C211yesmaximal, characteristic
3#11718654C212yesmaximal, complemented
4#11718653C212yesmaximal, complemented
5#11718652C212yesmaximal
6#11718650C214yesmaximal, complemented
7#11718644C212yesmaximal, complemented
8#11718598C211yesmaximal, characteristic, complemented
9C22×D52C2211yescharacteristic
10C22×C4×D13C2212yes—
11C13×#125—24no—
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2214yes—
19C2×#6103C2214yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2214yes—
22C4×D52—24no—
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2214yes—
27C23×D13C2312yes—
28C22×C4×C13C2312yes—
29C22×C4×C13C2312yes—
30C22×C4×C13C2311yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×Dic13C2314yes—
34C22×Dic13C2312yes—
35C2×D52—24no—
36C2×D52—22no—
37C2×C4×D13—24no—
38C2×C4×D13—44no—
39C13×C4⋊C4—24no—
40C13×C4⋊C4—22no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—24no—
43C42×C13D414yes—
44#6103—28no—
45#6103—24no—
46#6103—44no—
47C4⋊Dic13—22no—
48#6101—44no—
49#2633—131nomaximal, Sylow
50C23×C13C2411yescharacteristic
51C22×D13—22no—
52C22×D13—22no—
53C22×D13—24no—
54C22×D13—24no—
55C22×D13#4114yes—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—24no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13C2×D412yes—
65C2×C4×C13C2×D412yes—
66C2×C4×C13C2×D412yes—
67C2×Dic13—22no—
68C2×Dic13—24no—
69C2×Dic13—24no—
70C2×Dic13—24no—
71C2×Dic13—24no—
72D52—28no—
73C4×D13—48no—
74C2×#125D1311yescharacteristic, complemented
75C2×C4×D4—131no—
76#399—132no—
77#398—132no—
78#397—132no—
79#394—132no—
80#385—134no—
81#383—131no—
82C22×C13C22×D411yescharacteristic
83C22×C13C2×#4112yes—
84C22×C13H(5,𝔽2)12yes—
85C22×C132−1+412yes—
86C2×D13—24no—
87C2×D13—28no—
88C2×D13—42no—
89C2×D13—42no—
90C2×D13—44no—
91C4×C13—22no—
92C4×C13—22no—
93C4×C13—22no—
94C4×C13—42no—
95C4×C13—42no—
96Dic13—42no—
97Dic13—44no—
98C22×D4—131no—
99C23×C4—132no—
100#125—24no—
101C4×D4—264no—
102C2×C4⋊C4—131no—
103C2×C4⋊C4—134no—
104C2×C4⋊C4C2×D1312yes—
105C2×C4⋊C4C2×D1312yes—
106C2×C4⋊C4C2×D1311yescharacteristic
107C2×C4⋊C4C2×D1311yescharacteristic
108C2×C22⋊C4—132no—
109C2×C22⋊C4—134no—
110C2×C22⋊C4—134no—
111C2×C42C2×D1311yescharacteristic
112#95—132no—
113#95—132no—
114#95—132no—
115#95—134no—
116C2×C13#52511yescharacteristic
117C2×C13#53511yescharacteristic
118C2×C13#53611yescharacteristic
119C2×C13#53914yes—
120D13—44no—
121C24—132no—
122C2×D4—264no—
123C2×D4—262no—
124C22×C4—134no—
125C22×C4—132no—
126C22×C4—264no—
127C22×C4—524no—
128C22×C4C22×D1312yes—
129C22×C4C22×D1312yes—
130C22×C4C22×D1311yescharacteristic
131C22×C4C22×D1311yescharacteristic
132C22×C4C22×D1311yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—24no—
136C4⋊C4—24no—
137C4⋊C4—262no—
138C4⋊C4—524no—
139C22⋊C4—268no—
140C22⋊C4—264no—
141C22⋊C4—524no—
142C42C22⋊D1314yes—
143C13#263311yescharacteristic, complemented, Sylow
144C23—134no—
145C23—264no—
146C23—262no—
147C23—264no—
148C23—262no—
149C23C23×D1311yescharacteristic
150D4—268no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—264no—
160C2×C4—264no—
161C2×C4—264no—
162C2×C4—264no—
163C2×C4—262no—
164C2×C4—528no—
165C2×C4C2×C22⋊D1312yes—
166C2×C4C2×C22⋊D1312yes—
167C2×C4C2×C22⋊D1312yes—
168C22—264no—
169C22—268no—
170C22—522no—
171C22—522no—
172C22—524no—
173C22#8825412yes—
174C22#41×D1312yes—
175C22#8825612yes—
176C22C22×C22⋊D1311yescharacteristic
177C4—22no—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—522no—
183C4—524no—
184C2—524no—
185C2#1171939714yes—
186C2#1171952111yescharacteristic
187C2#1171953311yescharacteristic
188C2#1171953511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#125C2
prime radicalC22×D52C22
hypercenterC2×#125D13
hypocenterC13#2633
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C13×#125C2semidirect
3. #11718654C2semidirect
4. #11718653C2semidirect
6. #11718650C2semidirect
7. #11718644C2semidirect
8. #11718598C2semidirect
74. C2×#125D13semidirect
143. C13#2633semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
C2×C4×D522
#117186542
#117186532
#117186522
#117186502
#117186442
#117185982
#263313