Finite Group Databasebeta

← #13122858

Subgroups — #13122858

Order 1664.

644 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 133 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×#121C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic, complemented
3#11718884C214yesmaximal, complemented
4#11718884C212yesmaximal, complemented
5#11718872C211yesmaximal, characteristic, complemented
6#11718654C212yesmaximal, complemented
7#11718621C212yesmaximal, complemented
8#11718614C212yesmaximal, complemented
9C22×D4×C13C2212yes—
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13C2212yes—
13C22×C22⋊D13C2214yes—
14C22×D52C2211yescharacteristic
15C13×#121—24no—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2214yes—
19C2×C22⋊Dic13C2212yes—
20#88184—24no—
21C2×#6103C2212yes—
22C2×#6103C2214yes—
23C2×C4⋊Dic13C2211yescharacteristic
24#88071C2212yes—
25#88071C2214yes—
26#88071C2212yes—
27C24×C13C2312yes—
28C24×C13C2311yescharacteristic
29C23×D13C2312yes—
30C2×D4×C13—24no—
31C2×D4×C13—22no—
32C2×D4×C13—42no—
33C2×D4×C13—44no—
34C22×C4×C13—42no—
35C22×C4×C13D414yescomplemented
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C2×C22⋊D13—24no—
40C2×C22⋊D13—44no—
41C2×C22⋊D13—44no—
42C2×C22⋊D13—44no—
43C2×C22⋊D13—44no—
44C22×Dic13C2314yes—
45C22×Dic13C2312yes—
46C2×D52—22no—
47C2×D52—42no—
48C13×C4⋊C4—22no—
49C13×C22⋊C4—24no—
50C22⋊Dic13—42no—
51C22⋊Dic13—44no—
52#6103—24no—
53#6103—44no—
54C4⋊Dic13—22no—
55#2815—131nomaximal, Sylow
56C23×C13—22no—
57C23×C13—22no—
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—24no—
63C23×C13—24no—
64C23×C13C2×D412yes—
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—24no—
69C22×D13—24no—
70C22×D13—22no—
71D4×C13—44no—
72D4×C13—48no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—24no—
77C2×C4×C13—44no—
78C2×C4×C13C2×D412yes—
79C2×C4×C13C2×D412yes—
80C22⋊D13—48no—
81C22⋊D13—416no—
82C2×Dic13—22no—
83C2×Dic13—24no—
84C2×Dic13—24no—
85C2×Dic13—24no—
86C2×Dic13—24no—
87D52—44no—
88C2×#121—131no—
89C2×#121D1311yescharacteristic, complemented
90#397—132no—
91#397—132no—
92#392—132no—
93#392—134no—
94#392—132no—
95#381—131no—
96C22×C13—22no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—44no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—44no—
104C22×C13—44no—
105C22×C13C22×D411yescharacteristic
106C22×C13H(5,𝔽2)12yes—
107C22×C13H(5,𝔽2)12yes—
108C22×C13H(5,𝔽2)12yes—
109C2×D13—42no—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—44no—
113C2×D13—44no—
114C4×C13—22no—
115C4×C13—22no—
116C4×C13—42no—
117Dic13—42no—
118Dic13—44no—
119C22×D4—132no—
120C22×D4—134no—
121C22×D4—131no—
122C22×D4C2×D1312yes—
123C22×D4C2×D1311yescharacteristic
124C23×C4C2×D1311yescharacteristic
125#121—24no—
126#121—264no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4C2×D1311yescharacteristic
129C2×C22⋊C4—132no—
130C2×C22⋊C4—132no—
131C2×C22⋊C4—134no—
132C2×C22⋊C4—134no—
133C2×C22⋊C4C2×D1312yes—
134#95—132no—
135#95—132no—
136#95—134no—
137C2×C13—42no—
138C2×C13—82no—
139C2×C13#53411yescharacteristic
140C2×C13#53511yescharacteristic
141C2×C13#53511yescharacteristic
142C2×C13#56014yes—
143D13—82no—
144C24—132no—
145C24C22×D1312yes—
146C24C22×D1311yescharacteristic
147C2×D4—24no—
148C2×D4—22no—
149C2×D4—42no—
150C2×D4—44no—
151C2×D4—264no—
152C2×D4—262no—
153C2×D4—522no—
154C2×D4—524no—
155C2×D4—524no—
156C2×D4—524no—
157C2×D4—524no—
158C22×C4—42no—
159C22×C4—134no—
160C22×C4—132no—
161C22×C4C22⋊D1314yescomplemented
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—262no—
167C22⋊C4—24no—
168C22⋊C4—264no—
169C22⋊C4—524no—
170C22⋊C4—522no—
171C22⋊C4—524no—
172C13#281511yescharacteristic, complemented, Sylow
173C23—22no—
174C23—22no—
175C23—22no—
176C23—24no—
177C23—24no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—262no—
182C23—264no—
183C23—262no—
184C23—264no—
185C23—262no—
186C23C2×C22⋊D1312yes—
187C23C23×D1311yescharacteristic
188D4—44no—
189D4—48no—
190D4—524no—
191D4—528no—
192D4—5216no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—44no—
198C2×C4—264no—
199C2×C4—264no—
200C2×C4—264no—
201C2×C4—264no—
202C2×C4—262no—
203C2×C4C2×C22⋊D1312yes—
204C2×C4C2×C22⋊D1312yes—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—44no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—44no—
213C22—44no—
214C22—522no—
215C22—522no—
216C22—522no—
217C22—524no—
218C22—524no—
219C22#8825112yes—
220C22#8825112yes—
221C22#8825612yes—
222C22C22×C22⋊D1311yescharacteristic
223C4—22no—
224C4—22no—
225C4—42no—
226C4—522no—
227C4—524no—
228C2—42no—
229C2—82no—
230C2—1042no—
231C2#1171932514yes—
232C2#1171950911yescharacteristic
233C2#1171951011yescharacteristic
234C2#1171953511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2815
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C13×#121C2semidirect
2. C2×#88184C2semidirect
3. #11718884C2semidirect
4. #11718884C2semidirect
5. #11718872C2semidirect
6. #11718654C2semidirect
7. #11718621C2semidirect
8. #11718614C2semidirect
35. C22×C4×C13D4semidirect
89. C2×#121D13semidirect
161. C22×C4C22⋊D13semidirect
172. C13#2815semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881842
#117188842
#117188722
#117186542
#117186212
#117186142
#281513