Finite Group Databasebeta

← #13120316

Subgroups — #13120316

Order 1664.

596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic
3#11718874C212yesmaximal, complemented
4#11718874C212yesmaximal, complemented
5C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
6#11718652C212yesmaximal, complemented
7#11718651C214yesmaximal, complemented
8#11718647C212yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13C2212yes—
13C22×D52C2211yescharacteristic
14C2×C13×C4⋊C4—24no—
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2212yes—
17C2×C22⋊Dic13C2212yes—
18#88184—24no—
19C2×#6103C2212yes—
20C2×#6103C2214yes—
21C2×#6103C2214yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4×Dic13C2212yes—
24#88071C2212yes—
25#88071C2214yes—
26#88071C2214yes—
27C24×C13C2311yescharacteristic
28C23×D13C2312yes—
29C22×C4×C13—22no—
30C22×C4×C13—24no—
31C22×C4×C13—22no—
32C22×C4×C13—42no—
33C22×C4×C13—42no—
34C22×C4×C13D414yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C2×C22⋊D13—24no—
40C2×C22⋊D13—28no—
41C22×Dic13C2312yes—
42C22×Dic13C2314yes—
43C2×D52—22no—
44C2×D52—42no—
45C13×C4⋊C4—24no—
46C13×C4⋊C4—24no—
47C22⋊Dic13—24no—
48#6103—24no—
49#6103—28no—
50#6103—44no—
51C4⋊Dic13—22no—
52C4×Dic13—42no—
53#2591—131nomaximal, Sylow
54C23×C13—22no—
55C23×C13—22no—
56C23×C13C2×D412yes—
57C23×C13#4114yes—
58C23×C13C2411yescharacteristic
59C22×D13—22no—
60C22×D13—24no—
61C22×D13—24no—
62C22×D13—24no—
63C2×C4×C13—28no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—24no—
70C2×C4×C13—44no—
71C2×C4×C13—44no—
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—
83C22×C4⋊C4D1311yescharacteristic, complemented
84#400—132no—
85#394—132no—
86#388—134no—
87#386—132no—
88#386—132no—
89C4×C22⋊C4—131no—
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—28no—
93C22×C13#12414yes—
94C22×C13C22×D411yescharacteristic
95C22×C13C2×#4112yes—
96C22×C13C2×#4112yes—
97C22×C13H(5,𝔽2)12yes—
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—42no—
101C2×D13—48no—
102C4×C13—24no—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—42no—
106Dic13—42no—
107Dic13—44no—
108C22×D4—132no—
109C22×D4—131no—
110C23×C4C2×D1311yescharacteristic
111C23×C4C2×D1311yescharacteristic
112C23×C4C2×D1311yescharacteristic
113#121—264no—
114C2×C4⋊C4—24no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4C2×D1312yes—
117C2×C4⋊C4C2×D1312yes—
118C2×C22⋊C4—132no—
119C2×C22⋊C4—132no—
120C2×C22⋊C4—134no—
121C2×C22⋊C4—134no—
122C2×C42—132no—
123#95—132no—
124#95—134no—
125#95—134no—
126C2×C13—24no—
127C2×C13#52511yescharacteristic
128C2×C13C2×#12411yescharacteristic
129C2×C13#53411yescharacteristic
130C2×C13#55314yes—
131D13—82no—
132C24—132no—
133C24C22×D1311yescharacteristic
134C2×D4—268no—
135C2×D4—264no—
136C2×D4—262no—
137C2×D4—522no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—22no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—132no—
144C22×C4—134no—
145C22×C4C22⋊D1314yes—
146C22×C4C22×D1312yes—
147C22×C4C22×D1312yes—
148C22×C4C22×D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—24no—
152C4⋊C4—262no—
153C22⋊C4—264no—
154C22⋊C4—268no—
155C22⋊C4—264no—
156C22⋊C4—524no—
157C42—522no—
158C13#259111yescharacteristic, complemented, Sylow
159C23—22no—
160C23—22no—
161C23—264no—
162C23—264no—
163C23—264no—
164C23—262no—
165C23#613114yes—
166C23C2×C22⋊D1312yes—
167C23C23×D1311yescharacteristic
168D4—524no—
169D4—528no—
170C2×C4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—264no—
180C2×C4—264no—
181C2×C4—264no—
182C2×C4—264no—
183C2×C4—262no—
184C2×C4#612714yes—
185C2×C4C2×C22⋊D1312yes—
186C2×C4C2×C22⋊D1312yes—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—528no—
191C22—522no—
192C22—522no—
193C22—522no—
194C22#8820114yes—
195C22C2×#612712yes—
196C22#8825112yes—
197C22C2×#613112yes—
198C22C22×C22⋊D1311yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—524no—
204C4—522no—
205C2—24no—
206C2—1042no—
207C2#1171921914yes—
208C2#1171949611yescharacteristic
209C2#1171950911yescharacteristic
210C2C2×#8820111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC22×C13×C4⋊C4C2
prime radicalC2×#88184C2
hypercenterC22×C4⋊C4D13
hypocenterC13#2591
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
3. #11718874C2semidirect
4. #11718874C2semidirect
5. C4×C22⋊Dic13C2semidirect
6. #11718652C2semidirect
7. #11718651C2semidirect
8. #11718647C2semidirect
83. C22×C4⋊C4D13semidirect
158. C13#2591semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
C2×#881842
#117188742
C4×C22⋊Dic132
#117186522
#117186512
#117186472
#259113