Finite Group Databasebeta

← #13120086

Subgroups — #13120086

Order 1664.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C13×#400C211yesmaximal, characteristic, complemented
2#11718652C211yesmaximal, characteristic
3#11718651C212yesmaximal, complemented
4#11718635C211yesmaximal, characteristic, complemented
5#11718334C212yesmaximal, complemented
6#11718327C212yesmaximal, complemented
7#11718326C212yesmaximal
8#11718325C212yesmaximal, complemented
9#11718312C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C13×#95C2212yes—
23C13×#95C2211yescharacteristic
24C13×#95C2212yes—
25#88071C2211yescharacteristic
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C23×D13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×D52—24no—
41C2×D52—41no—
42C2×C4×D13—24no—
43C2×C4×D13—24no—
44C2×C4×D13—42no—
45C2×Dic26—22no—
46C2×Dic26—41no—
47C2×Dic26—41no—
48C13×C4⋊C4—41no—
49C13×C4⋊C4—41no—
50#6103—24no—
51#6103—24no—
52#6103—24no—
53#6103—42no—
54#6103—42no—
55C4×Dic13—24no—
56C4×Dic13—41no—
57#2572—131nomaximal, Sylow
58C23×C13C2411yescharacteristic
59C22×D13—22no—
60C22×D13—22no—
61C22×D13—22no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13#4114yes—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13#4112yes—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13#4114yes—
88D52—44no—
89C4×D13—48no—
90Dic26—44no—
91#400D1311yescharacteristic, complemented
92#394—131no—
93#393—132no—
94#391—131no—
95#388—132no—
96#386—132no—
97#383—132no—
98#381—132no—
99C4×C22⋊C4—132no—
100C22×C13C2×#4111yescharacteristic
101C22×C13C2×#4112yes—
102C22×C13C2×#4112yes—
103C22×C13H(5,𝔽2)11yescharacteristic
104C22×C13H(5,𝔽2)11yescharacteristic
105C2×D13—24no—
106C2×D13—24no—
107C2×D13—24no—
108C2×D13—42no—
109C2×D13—42no—
110C2×D13—42no—
111C2×D13—42no—
112C4×C13—22no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13—41no—
116C4×C13—42no—
117Dic13—24no—
118Dic13—42no—
119Dic13—42no—
120C22×Q8—131no—
121C22×D4—131no—
122C23×C4—132no—
123C2×C4⋊C4C2×D1311yescharacteristic
124C2×C4⋊C4C2×D1311yescharacteristic
125C2×C22⋊C4—132no—
126C2×C22⋊C4—132no—
127C2×C22⋊C4—132no—
128C2×C22⋊C4—132no—
129C2×C22⋊C4—132no—
130C2×C42—132no—
131C2×C42—131no—
132#95—132no—
133#95—132no—
134#95—132no—
135#95—131no—
136#95—132no—
137#95—132no—
138#95C2×D1312yes—
139#95C2×D1311yescharacteristic
140#95C2×D1312yes—
141C2×C13#52912yes—
142C2×C13#53811yescharacteristic
143C2×C13#55111yescharacteristic
144C2×C13#55112yes—
145C2×C13#55511yescharacteristic
146D13—44no—
147C24—132no—
148C2×Q8—262no—
149C2×Q8—521no—
150C2×Q8—521no—
151C2×D4—264no—
152C2×D4—521no—
153C22×C4—132no—
154C22×C4—132no—
155C22×C4—132no—
156C22×C4—264no—
157C22×C4—264no—
158C22×C4—522no—
159C22×C4C22×D1311yescharacteristic
160C22×C4C22×D1312yes—
161C22×C4C22×D1311yescharacteristic
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—41no—
166C22⋊C4—264no—
167C22⋊C4—264no—
168C22⋊C4—264no—
169C22⋊C4—522no—
170C22⋊C4—522no—
171C42—264no—
172C42—521no—
173C13#257211yescharacteristic, complemented, Sylow
174C23—134no—
175C23—262no—
176C23—262no—
177C23—262no—
178C23—262no—
179C23—262no—
180C23—262no—
181C23C23×D1311yescharacteristic
182Q8—524no—
183D4—524no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—134no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—528no—
206C2×C4#613112yes—
207C22—264no—
208C22—264no—
209C22—264no—
210C22—522no—
211C22—522no—
212C22—522no—
213C22—522no—
214C22#8825111yescharacteristic
215C22C2×#613111yescharacteristic
216C22#41×D1312yes—
217C22#41×D1312yes—
218C22#8825611yescharacteristic
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—264no—
225C4—522no—
226C4—522no—
227C2—524no—
228C2#1171934911yescharacteristic
229C2#1171936411yescharacteristic
230C2#1171937511yescharacteristic
231C2#1171939612yes—
232C2#1171941012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radicalC22×D52C22
hypercenter#400D13
hypocenterC13#2572
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C13×#400C2semidirect
3. #11718651C2semidirect
4. #11718635C2semidirect
5. #11718334C2semidirect
6. #11718327C2semidirect
8. #11718325C2semidirect
9. #11718312C2semidirect
91. #400D13semidirect
173. C13#2572semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186522
#117186512
#117186352
#117183342
#117183272
#117183262
#117183252
#117183122
#257213