Finite Group Databasebeta

← #13120423

Subgroups — #13120423

Order 1664.

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

normal subgroups only

This group has 604 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×C4×C22⋊D13C212yesmaximal, complemented
2C13×#381C211yesmaximal, characteristic, complemented
3#11718622C212yesmaximal, complemented
4#11718621C211yesmaximal, characteristic
5#11718614C211yesmaximal, characteristic, complemented
6#11718331C212yesmaximal, complemented
7#11718329C212yesmaximal, complemented
8#11718326C212yesmaximal, complemented
9#11718314C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C4×C22⋊D13—28no—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×C4×Dic13C2212yes—
26C13×#95C2212yes—
27C13×#95C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31#88071C2211yescharacteristic
32C24×C13C2311yescharacteristic
33C23×D13C2312yes—
34C22×C4×C13—41no—
35C22×C4×C13—41no—
36C22×C4×C13D414yescomplemented
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C2×C22⋊D13—24no—
42C2×C22⋊D13—24no—
43C2×C22⋊D13—24no—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C2×D52—24no—
48C2×D52—41no—
49C2×C4×D13—24no—
50C2×C4×D13—42no—
51C2×C4×D13—42no—
52C13×C22⋊C4—41no—
53C13×C22⋊C4—41no—
54C22⋊Dic13—24no—
55#6103—24no—
56#6103—24no—
57#6103—24no—
58#6103—42no—
59C4⋊Dic13—24no—
60C4⋊Dic13—41no—
61#6101—24no—
62C4×Dic13—24no—
63#2600—131nomaximal, Sylow
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—21no—
67C23×C13—21no—
68C23×C13C2×D412yes—
69C23×C13C2411yescharacteristic
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—22no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13#4114yes—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—44no—
87C2×C4×C13C2×D414yes—
88C22⋊D13—216no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13#4114yes—
98D52—44no—
99C4×D13—48no—
100C2×C4×D4—132no—
101#397—131no—
102#394—132no—
103#392—131no—
104#388—132no—
105#387—132no—
106#386—132no—
107#385—132no—
108#381D1311yescharacteristic, complemented
109C22×C13—24no—
110C22×C13—22no—
111C22×C13—41no—
112C22×C13—42no—
113C22×C13—41no—
114C22×C13C22×D411yescharacteristic
115C22×C13C2×#4112yes—
116C22×C13C2×#4112yes—
117C22×C13H(5,𝔽2)11yescharacteristic
118C22×C13H(5,𝔽2)11yescharacteristic
119C2×D13—24no—
120C2×D13—24no—
121C2×D13—24no—
122C2×D13—42no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C4×C13—24no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13—41no—
130Dic13—24no—
131Dic13—42no—
132Dic13—42no—
133C22×D4—132no—
134C22×D4—131no—
135C23×C4—132no—
136C23×C4C2×D1311yescharacteristic
137C4×D4—268no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—131no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C22⋊C4C2×D1311yescharacteristic
147C2×C22⋊C4C2×D1311yescharacteristic
148C2×C42—132no—
149#95—132no—
150#95—132no—
151#95—131no—
152#95—131no—
153#95C2×D1312yes—
154#95C2×D1312yes—
155C2×C13—42no—
156C2×C13#52512yes—
157C2×C13#53411yescharacteristic
158C2×C13#55111yescharacteristic
159C2×C13#55312yes—
160C2×C13#55911yescharacteristic
161D13—44no—
162C24—132no—
163C24C22×D1311yescharacteristic
164C2×D4—264no—
165C2×D4—264no—
166C2×D4—264no—
167C2×D4—264no—
168C2×D4—521no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—264no—
175C22×C4—522no—
176C22×C4—522no—
177C22×C4D5214yescomplemented
178C22×C4C22×D1311yescharacteristic
179C22×C4C22×D1312yes—
180C22×C4C22×D1311yescharacteristic
181C22×C4C22×D1312yes—
182C4⋊C4—264no—
183C4⋊C4—264no—
184C4⋊C4—521no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—264no—
188C22⋊C4—264no—
189C22⋊C4—264no—
190C22⋊C4—264no—
191C22⋊C4—522no—
192C42—264no—
193C13#260011yescharacteristic, complemented, Sylow
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—134no—
199C23—262no—
200C23—262no—
201C23—262no—
202C23—262no—
203C23—262no—
204C23—262no—
205C23C2×D5212yes—
206C23C23×D1311yescharacteristic
207D4—2616no—
208D4—524no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—134no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—528no—
229C2×C4C2×D5214yes—
230C22—22no—
231C22—24no—
232C22—41no—
233C22—42no—
234C22—41no—
235C22—264no—
236C22—264no—
237C22—264no—
238C22—522no—
239C22—522no—
240C22—522no—
241C22—522no—
242C22C22×D5211yescharacteristic
243C22#8825111yescharacteristic
244C22#8825111yescharacteristic
245C22#41×D1312yes—
246C22#41×D1312yes—
247C4—24no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—264no—
252C4—522no—
253C4—522no—
254C2—42no—
255C2—524no—
256C2#1171919811yescharacteristic
257C2#1171922912yes—
258C2#1171936411yescharacteristic
259C2#1171936612yes—
260C2#1171936911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radical#11718621C2
hypercenter#381D13
hypocenterC13#2600
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D13C2semidirect
2. C13×#381C2semidirect
3. #11718622C2semidirect
5. #11718614C2semidirect
6. #11718331C2semidirect
7. #11718329C2semidirect
8. #11718326C2semidirect
9. #11718314C2semidirect
36. C22×C4×C13D4semidirect
108. #381D13semidirect
177. C22×C4D52semidirect
193. C13#2600semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C13×#3812
#117186222
#117186212
#117186142
#117183312
#117183292
#117183262
#117183142
#260013