Finite Group Databasebeta

← #13122213

Subgroups — #13122213

Order 1664.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#381C211yesmaximal, characteristic, complemented
2#11718874C212yesmaximal, complemented
3#11718621C211yesmaximal, characteristic
4#11718617C212yesmaximal, complemented
5#11718608C211yesmaximal, characteristic, complemented
6#11718334C212yesmaximal, complemented
7#11718326C212yesmaximal, complemented
8#11718325C212yesmaximal, complemented
9C13⋊#401C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C22×Dic26C2211yescharacteristic
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C13×#95C2212yes—
23C13×#95C2212yes—
24#88071C2211yescharacteristic
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C24×C13C2311yescharacteristic
32C23×D13C2312yes—
33C22×C4×C13—22no—
34C22×C4×C13—41no—
35C22×C4×C13—41no—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—24no—
41C2×C22⋊D13—24no—
42C2×C22⋊D13—42no—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C2×D52—24no—
47C2×D52—41no—
48C2×C4×D13—24no—
49C2×C4×D13—42no—
50C2×C4×D13—42no—
51C2×Dic26—41no—
52C2×Dic26—42no—
53C13×C22⋊C4—41no—
54C13×C22⋊C4—41no—
55C22⋊Dic13—42no—
56#6103—42no—
57#6103—42no—
58#6103—42no—
59#6103—42no—
60#2760—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—21no—
64C23×C13—21no—
65C23×C13#4112yes—
66C23×C13C2411yescharacteristic
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13#4114yes—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—44no—
85C22⋊D13—48no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95D52—44no—
96C4×D13—48no—
97Dic26—44no—
98#401—132no—
99#393—131no—
100#393—132no—
101#392—131no—
102#386—132no—
103#386—132no—
104#386—132no—
105#381—132no—
106#381D1311yescharacteristic, complemented
107C22×C13—22no—
108C22×C13—24no—
109C22×C13—42no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13C2×#4111yescharacteristic
113C22×C13C2×#4112yes—
114C22×C13H(5,𝔽2)11yescharacteristic
115C22×C13H(5,𝔽2)11yescharacteristic
116C22×C13H(5,𝔽2)12yes—
117C2×D13—24no—
118C2×D13—24no—
119C2×D13—24no—
120C2×D13—42no—
121C2×D13—42no—
122C2×D13—42no—
123C2×D13—42no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C13—41no—
128Dic13—42no—
129Dic13—42no—
130Dic13—42no—
131C22×Q8—131no—
132C22×D4—132no—
133C22×D4—131no—
134C23×C4—132no—
135C23×C4C2×D1311yescharacteristic
136C2×C22⋊C4—132no—
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4C2×D1311yescharacteristic
142C2×C22⋊C4C2×D1311yescharacteristic
143#95—131no—
144#95—132no—
145#95—132no—
146#95—132no—
147#95—132no—
148#95—132no—
149#95—131no—
150#95C2×D1312yes—
151#95C2×D1312yes—
152C2×C13—42no—
153C2×C13#53811yescharacteristic
154C2×C13#53812yes—
155C2×C13#55112yes—
156C2×C13#55111yescharacteristic
157C2×C13#56011yescharacteristic
158D13—44no—
159C24—132no—
160C24C22×D1311yescharacteristic
161C2×Q8—521no—
162C2×Q8—522no—
163C2×D4—264no—
164C2×D4—264no—
165C2×D4—264no—
166C2×D4—521no—
167C2×D4—522no—
168C22×C4—22no—
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×C4C22×D1311yescharacteristic
178C22×C4C22×D1312yes—
179C22×C4C22×D1312yes—
180C22×C4C22×D1311yescharacteristic
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—522no—
184C22⋊C4—522no—
185C22⋊C4—522no—
186C22⋊C4—522no—
187C22⋊C4—522no—
188C13#276011yescharacteristic, complemented, Sylow
189C23—21no—
190C23—21no—
191C23—22no—
192C23—22no—
193C23—134no—
194C23—262no—
195C23—262no—
196C23—262no—
197C23—262no—
198C23—262no—
199C23—262no—
200C23#612712yes—
201C23C23×D1311yescharacteristic
202Q8—524no—
203D4—524no—
204D4—528no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—528no—
226C22—22no—
227C22—24no—
228C22—42no—
229C22—41no—
230C22—41no—
231C22—264no—
232C22—264no—
233C22—264no—
234C22—522no—
235C22—522no—
236C22—522no—
237C22—522no—
238C22C2×#612711yescharacteristic
239C22#8825111yescharacteristic
240C22#8825111yescharacteristic
241C22#41×D1312yes—
242C22#8825612yes—
243C4—42no—
244C4—42no—
245C4—41no—
246C4—41no—
247C4—522no—
248C4—522no—
249C4—522no—
250C2—42no—
251C2—524no—
252C2#1171919911yescharacteristic
253C2#1171923212yes—
254C2#1171936212yes—
255C2#1171936411yescharacteristic
256C2#1171937111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radical#11718621C2
hypercenter#381D13
hypocenterC13#2760
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C13×#381C2semidirect
2. #11718874C2semidirect
4. #11718617C2semidirect
5. #11718608C2semidirect
6. #11718334C2semidirect
7. #11718326C2semidirect
8. #11718325C2semidirect
9. C13⋊#401C2semidirect
106. #381D13semidirect
188. C13#2760semidirect

Maximal subgroups

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

subgroupindex
C13×#3812
#117188742
#117186212
#117186172
#117186082
#117183342
#117183262
#117183252
C13⋊#4012
#276013