Finite Group Databasebeta

← #13119294

Subgroups — #13119294

Order 1664.

568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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
3C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
4#11718649C211yesmaximal, characteristic, complemented
5#11718649C211yesmaximal, characteristic, complemented
6#11718638C211yesmaximal, characteristic, complemented
7#11718637C211yesmaximal, characteristic, complemented
8#11718620C214yesmaximal, complemented
9#11718601C214yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C13×#117—24no—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C42×C13C2212yes—
18C2×C22⋊Dic13C2212yes—
19#88184—24no—
20C2×#6103C2212yes—
21C2×#6103C2214yes—
22C2×#6103C2214yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2214yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2311yescharacteristic
30C23×D13C2312yes—
31C22×C4×C13—22no—
32C22×C4×C13—22no—
33C22×C4×C13D414yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—24no—
39C2×C22⋊D13—44no—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×D52—22no—
44C2×D52—22no—
45C2×D52—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C22⋊C4—24no—
49C42×C13—24no—
50C22⋊Dic13—24no—
51#6103—24no—
52#6103—28no—
53#6103—44no—
54C4⋊Dic13—22no—
55#6101—44no—
56C4×Dic13—22no—
57C4×Dic13—22no—
58#2500—131nomaximal, Sylow
59C23×C13—22no—
60C23×C13—21no—
61C23×C13—21no—
62C23×C13—22no—
63C23×C13C2×D412yes—
64C23×C13C2411yescharacteristic
65C22×D13—22no—
66C22×D13—24no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—24no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—28no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13—24no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C2×C4×C13#4112yes—
80C2×C4×C13#4112yes—
81C22⋊D13—48no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13—22no—
89C2×Dic13#4114yes—
90D52—44no—
91C2×#121—131no—
92C2×#117D1311yescharacteristic, complemented
93#394—134no—
94#390—131no—
95#390—131no—
96#388—134no—
97#384—131no—
98#382—131no—
99C4×C22⋊C4—131no—
100C22×C13—22no—
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13C22×D411yescharacteristic
106C22×C13C2×#4111yescharacteristic
107C22×C13C2×#4111yescharacteristic
108C22×C13C2×#4112yes—
109C22×C13H(5,𝔽2)12yes—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—44no—
114C2×D13—44no—
115C4×C13—22no—
116C4×C13—42no—
117C4×C13—42no—
118C4×C13#12314yes—
119Dic13—24no—
120Dic13—42no—
121Dic13—42no—
122C22×D4—132no—
123C22×D4—131no—
124C23×C4C2×D1311yescharacteristic
125#121—264no—
126#117—24no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4—134no—
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4—134no—
135C2×C22⋊C4C2×D1312yes—
136C2×C42—131no—
137C2×C42—131no—
138C2×C42C2×D1312yes—
139#95—132no—
140#95—134no—
141C2×C13—42no—
142C2×C13C2×#12311yescharacteristic
143C2×C13#53211yescharacteristic
144C2×C13#53511yescharacteristic
145C2×C13#55312yes—
146C2×C13#55512yes—
147D13—82no—
148C24—132no—
149C24C22×D1311yescharacteristic
150C2×D4—264no—
151C2×D4—262no—
152C2×D4—262no—
153C2×D4—262no—
154C2×D4—524no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—132no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4C22⋊D1314yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—262no—
168C4⋊C4—524no—
169C22⋊C4—24no—
170C22⋊C4—268no—
171C22⋊C4—264no—
172C22⋊C4—264no—
173C22⋊C4—524no—
174C42—24no—
175C42—262no—
176C42—262no—
177C13#250011yescharacteristic, complemented, Sylow
178C23—21no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23—262no—
183C23—262no—
184C23—264no—
185C23—264no—
186C23—262no—
187C23C2×C22⋊D1312yes—
188C23C23×D1311yescharacteristic
189D4—528no—
190D4—524no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—134no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—264no—
205C2×C4—262no—
206C2×C4#612712yes—
207C2×C4#612712yes—
208C2×C4C2×C22⋊D1312yes—
209C2×C4C2×C22⋊D1312yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—524no—
216C22—524no—
217C22—522no—
218C22—522no—
219C22—522no—
220C22C2×#612711yescharacteristic
221C22C2×#612711yescharacteristic
222C22#41×D1312yes—
223C22#8825612yes—
224C22C22×C22⋊D1311yescharacteristic
225C4—22no—
226C4—42no—
227C4—42no—
228C4—264no—
229C4—522no—
230C4—522no—
231C4#8818314yes—
232C2—42no—
233C2—1042no—
234C2#1171923512yes—
235C2#1171923712yes—
236C2C2×#8818311yescharacteristic
237C2#1171953511yescharacteristic
238C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#117C2
prime radicalC2×#88184C2
hypercenterC2×#117D13
hypocenterC13#2500
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. C4×C22⋊Dic13C2semidirect
4. #11718649C2semidirect
5. #11718649C2semidirect
6. #11718638C2semidirect
7. #11718637C2semidirect
8. #11718620C2semidirect
9. #11718601C2semidirect
92. C2×#117D13semidirect
177. C13#2500semidirect

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
C4×C22⋊Dic132
#117186492
#117186382
#117186372
#117186202
#117186012
#250013