Finite Group Databasebeta

← #13119295

Subgroups — #13119295

Order 1664.

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

normal subgroups only

This group has 568 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×#88149C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic, complemented
3C13×#384C211yesmaximal, characteristic, complemented
4#11718652C214yesmaximal, complemented
5#11718651C214yesmaximal, complemented
6#11718649C211yesmaximal, characteristic, complemented
7#11718638C211yesmaximal, characteristic, complemented
8#11718600C211yesmaximal, characteristic, complemented
9C4×#6103C211yesmaximal, characteristic, complemented
10C22×D52C2211yescharacteristic
11C22×D52C2212yes—
12C22×C4×D13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2214yes—
21C2×#6103C2214yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4×Dic13C2212yes—
24C2×C4×Dic13C2211yescharacteristic
25#88149—24no—
26#88146—24no—
27#88071C2212yes—
28#88071C2214yes—
29C23×D13C2312yes—
30C23×D13C2311yescharacteristic
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×Dic13C2312yes—
36C22×Dic13C2312yes—
37C22×Dic13C2311yescharacteristic
38C2×D52—24no—
39C2×D52—22no—
40C2×D52—22no—
41C2×D52—22no—
42C2×D52—44no—
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13D414yes—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—44no—
49C42×C13—22no—
50#6103—24no—
51#6103—24no—
52#6103—28no—
53#6103—24no—
54#6103—44no—
55C4⋊Dic13—22no—
56C4×Dic13—22no—
57C4×Dic13—24no—
58#2500—131nomaximal, Sylow
59C23×C13C2411yescharacteristic
60C22×D13—22no—
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—24no—
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—24no—
69C22×D13C2×D412yes—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—24no—
75C2×C4×C13—24no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13#4114yes—
78C2×C4×C13#4112yes—
79C2×C4×C13#4112yes—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—24no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13C2×D412yes—
88D52—48no—
89D52—44no—
90C4×D13—28no—
91C2×#121—131no—
92C2×#117—131no—
93#394—134no—
94#390—131no—
95#390—131no—
96#388—134no—
97#384D1311yescharacteristic, complemented
98#382—131no—
99C4×C22⋊C4—131no—
100C22×C13C22×D411yescharacteristic
101C22×C13C2×#4111yescharacteristic
102C22×C13C2×#4111yescharacteristic
103C22×C13C2×#4112yes—
104C22×C13H(5,𝔽2)12yes—
105C2×D13—22no—
106C2×D13—22no—
107C2×D13—22no—
108C2×D13—42no—
109C2×D13—42no—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—44no—
114C2×D13—44no—
115C4×C13—24no—
116C4×C13—42no—
117C4×C13—42no—
118C4×C13#12314yes—
119Dic13—22no—
120Dic13—42no—
121Dic13—42no—
122C22×D4—131no—
123C22×D4—132no—
124C23×C4—131no—
125#121—264no—
126#117—264no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4C2×D1311yescharacteristic
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C4⋊C4C2×D1314yes—
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—134no—
135C2×C22⋊C4—134no—
136C2×C42—132no—
137C2×C42—131no—
138C2×C42C2×D1311yescharacteristic
139#95—132no—
140#95—134no—
141C2×C13C2×#12311yescharacteristic
142C2×C13#53211yescharacteristic
143C2×C13#53511yescharacteristic
144C2×C13#55312yes—
145C2×C13#55512yes—
146D13—42no—
147D13—82no—
148C24—131no—
149C24—132no—
150C2×D4—264no—
151C2×D4—262no—
152C2×D4—262no—
153C2×D4—262no—
154C2×D4—524no—
155C22×C4—131no—
156C22×C4—134no—
157C22×C4—132no—
158C22×C4—132no—
159C22×C4—262no—
160C22×C4—262no—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1312yes—
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—44no—
168C4⋊C4—262no—
169C22⋊C4—264no—
170C22⋊C4—264no—
171C22⋊C4—264no—
172C22⋊C4—268no—
173C22⋊C4—524no—
174C42—22no—
175C42—264no—
176C42—262no—
177C13#250011yescharacteristic, complemented, Sylow
178C23—132no—
179C23—261no—
180C23—262no—
181C23—262no—
182C23—261no—
183C23—262no—
184C23—262no—
185C23—264no—
186C23—264no—
187C23—262no—
188C23C23×D1311yescharacteristic
189D4—528no—
190D4—524no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—132no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—268no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—264no—
205C2×C4—262no—
206C2×C4#612712yes—
207C2×C4D4×D1312yes—
208C2×C4#613114yes—
209C2×C4#613112yes—
210C22—262no—
211C22—262no—
212C22—262no—
213C22—522no—
214C22—522no—
215C22—522no—
216C22—524no—
217C22—522no—
218C22—524no—
219C22—522no—
220C22C2×#612711yescharacteristic
221C22C2×D4×D1311yescharacteristic
222C22#8825112yes—
223C22C2×#613112yes—
224C22C2×#613111yescharacteristic
225C4—24no—
226C4—42no—
227C4—42no—
228C4—262no—
229C4—522no—
230C4—522no—
231C4#8814814yes—
232C2—522no—
233C2—1042no—
234C2C2×#8814811yescharacteristic
235C2#1171921912yes—
236C2#1171942011yescharacteristic
237C2#1171943011yescharacteristic
238C2#1171943912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#384C2
prime radicalC2×#88149C2
hypercenter#384D13
hypocenterC13#2500
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#88146C2semidirect
3. C13×#384C2semidirect
4. #11718652C2semidirect
5. #11718651C2semidirect
6. #11718649C2semidirect
7. #11718638C2semidirect
8. #11718600C2semidirect
9. C4×#6103C2semidirect
97. #384D13semidirect
177. C13#2500semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×#881462
C13×#3842
#117186522
#117186512
#117186492
#117186382
#117186002
C4×#61032
#250013