Finite Group Databasebeta

← #13120513

Subgroups — #13120513

Order 1664.

540 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88126C212yesmaximal, complemented
2C13×#382C211yesmaximal, characteristic, complemented
3#11718655C212yesmaximal, complemented
4#11718652C211yesmaximal, characteristic
5#11718644C211yesmaximal, characteristic, complemented
6#11718331C212yesmaximal, complemented
7#11718329C212yesmaximal, complemented
8#11718326C212yesmaximal
9#11718314C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×C4⋊Dic13C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25#88126—28no—
26C13×#95C2212yes—
27C13×#95C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31#88071C2211yescharacteristic
32C23×D13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×D52—24no—
42C2×D52—41no—
43C2×C4×D13—24no—
44C2×C4×D13—24no—
45C2×C4×D13—24no—
46C13×C4⋊C4—41no—
47C13×C4⋊C4—41no—
48C42×C13D414yescomplemented
49#6103—24no—
50#6103—24no—
51#6103—24no—
52#6103—24no—
53#6103—42no—
54C4⋊Dic13—24no—
55C4⋊Dic13—41no—
56#6101—24no—
57#6101—24no—
58C4×Dic13—24no—
59#2609—131nomaximal, Sylow
60C23×C13C2411yescharacteristic
61C22×D13—22no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13#4114yes—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13C2×D414yes—
80C2×C4×C13C2×D412yes—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13#4114yes—
90D52—44no—
91C4×D13—216no—
92C2×#117—132no—
93#398—131no—
94#396—132no—
95#394—131no—
96#388—132no—
97#387—132no—
98#386—132no—
99#385—132no—
100#382D1311yescharacteristic, complemented
101C22×C13C22×D411yescharacteristic
102C22×C13C2×#4112yes—
103C22×C13C2×#4112yes—
104C22×C13H(5,𝔽2)11yescharacteristic
105C22×C132−1+411yescharacteristic
106C2×D13—24no—
107C2×D13—24no—
108C2×D13—24no—
109C2×D13—42no—
110C2×D13—42no—
111C2×D13—42no—
112C2×D13—42no—
113C4×C13—24no—
114C4×C13—22no—
115C4×C13—41no—
116C4×C13—41no—
117C4×C13—42no—
118Dic13—24no—
119Dic13—42no—
120Dic13—42no—
121C22×D4—131no—
122C23×C4—132no—
123#117—268no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4C2×D1311yescharacteristic
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C22⋊C4—132no—
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—132no—
135C2×C42—132no—
136C2×C42C2×D1311yescharacteristic
137#95—131no—
138#95—132no—
139#95—131no—
140#95—132no—
141#95C2×D1312yes—
142#95C2×D1312yes—
143C2×C13#52512yes—
144C2×C13#53711yescharacteristic
145C2×C13#55111yescharacteristic
146C2×C13#55212yes—
147C2×C13#55511yescharacteristic
148D13—44no—
149C24—132no—
150C2×D4—264no—
151C2×D4—521no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4—132no—
155C22×C4—264no—
156C22×C4—264no—
157C22×C4—264no—
158C22×C4C22×D1311yescharacteristic
159C22×C4C22×D1312yes—
160C22×C4C22×D1311yescharacteristic
161C22×C4C22×D1312yes—
162C22×C4C22×D1311yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—264no—
166C4⋊C4—264no—
167C4⋊C4—264no—
168C4⋊C4—521no—
169C22⋊C4—264no—
170C22⋊C4—264no—
171C22⋊C4—264no—
172C22⋊C4—264no—
173C22⋊C4—522no—
174C42—264no—
175C42D5214yescomplemented
176C13#260911yescharacteristic, complemented, Sylow
177C23—134no—
178C23—262no—
179C23—262no—
180C23—262no—
181C23—262no—
182C23—262no—
183C23—262no—
184C23C23×D1311yescharacteristic
185D4—524no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—134no—
198C2×C4—2616no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4C2×D5214yes—
208C2×C4C2×D5212yes—
209C22—264no—
210C22—264no—
211C22—264no—
212C22—522no—
213C22—522no—
214C22—522no—
215C22—522no—
216C22C22×D5211yescharacteristic
217C22#8825111yescharacteristic
218C22#8825411yescharacteristic
219C22#41×D1312yes—
220C22#41×D1312yes—
221C4—22no—
222C4—24no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—264no—
227C4—522no—
228C4—522no—
229C2—524no—
230C2#1171921511yescharacteristic
231C2#1171922912yes—
232C2#1171937511yescharacteristic
233C2#1171938411yescharacteristic
234C2#1171939812yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#382C2
prime radicalC22×D52C22
hypercenter#382D13
hypocenterC13#2609
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#88126C2semidirect
2. C13×#382C2semidirect
3. #11718655C2semidirect
5. #11718644C2semidirect
6. #11718331C2semidirect
7. #11718329C2semidirect
9. #11718314C2semidirect
48. C42×C13D4semidirect
100. #382D13semidirect
175. C42D52semidirect
176. C13#2609semidirect

Maximal subgroups

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

subgroupindex
C2×#881262
C13×#3822
#117186552
#117186522
#117186442
#117183312
#117183292
#117183262
#117183142
#260913