Finite Group Databasebeta

← #13122100

Subgroups — #13122100

Order 1664.

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

normal subgroups only

This group has 484 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#11718618C212yesmaximal, complemented
5#11718610C211yesmaximal, characteristic, complemented
6#11718336C212yesmaximal, complemented
7#11718333C212yesmaximal, complemented
8#11718331C212yesmaximal, complemented
9#11718313C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C2×C13×C22⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic13C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25C13×#95C2212yes—
26C13×#95C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C24×C13C2311yescharacteristic
32C23×D13C2312yes—
33C22×C4×C13—22no—
34C22×C4×C13—41no—
35C22×C4×C13—41no—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C2×C22⋊D13—24no—
41C2×C22⋊D13—24no—
42C2×C22⋊D13—42no—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C2×D52—42no—
47C2×D52—41no—
48C13×C22⋊C4—41no—
49C13×C22⋊C4—41no—
50C22⋊Dic13—42no—
51#6103—24no—
52#6103—42no—
53#6103—42no—
54#6103—42no—
55#6103—42no—
56C4⋊Dic13—41no—
57#6101—24no—
58#6101—42no—
59C4×Dic13—42no—
60#2752—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—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
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#4114yes—
95D52—44no—
96#399—131no—
97#397—132no—
98#394—132no—
99#392—131no—
100#390—132no—
101#388—132no—
102#387—132no—
103#386—132no—
104#381D1311yescharacteristic, complemented
105C22×C13—22no—
106C22×C13—24no—
107C22×C13—42no—
108C22×C13—41no—
109C22×C13—41no—
110C22×C13C2×#4111yescharacteristic
111C22×C13C2×#4112yes—
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C13H(5,𝔽2)11yescharacteristic
114C22×C13H(5,𝔽2)12yes—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—42no—
121C2×D13—42no—
122C4×C13—42no—
123C4×C13—42no—
124C4×C13—41no—
125C4×C13—41no—
126Dic13—24no—
127Dic13—42no—
128Dic13—42no—
129C22×D4—132no—
130C22×D4—131no—
131C23×C4C2×D1311yescharacteristic
132C2×C4⋊C4—132no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—131no—
135C2×C22⋊C4—132no—
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
143C2×C42—132no—
144#95—132no—
145#95—132no—
146#95—131no—
147#95—131no—
148#95C2×D1312yes—
149#95C2×D1312yes—
150C2×C13—42no—
151C2×C13#53811yescharacteristic
152C2×C13#54012yes—
153C2×C13#55112yes—
154C2×C13#55911yescharacteristic
155C2×C13#56011yescharacteristic
156D13—82no—
157C24—132no—
158C24C22×D1311yescharacteristic
159C2×D4—264no—
160C2×D4—264no—
161C2×D4—521no—
162C2×D4—522no—
163C2×D4—522no—
164C22×C4—22no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—132no—
168C22×C4—132no—
169C22×C4—132no—
170C22×C4C22×D1312yes—
171C22×C4C22×D1311yescharacteristic
172C22×C4C22×D1311yescharacteristic
173C22×C4C22×D1312yes—
174C4⋊C4—264no—
175C4⋊C4—522no—
176C4⋊C4—521no—
177C22⋊C4—41no—
178C22⋊C4—41no—
179C22⋊C4—264no—
180C22⋊C4—522no—
181C22⋊C4—522no—
182C22⋊C4—522no—
183C22⋊C4—522no—
184C22⋊C4—522no—
185C42—522no—
186C13#275211yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23—262no—
192C23—262no—
193C23—262no—
194C23—262no—
195C23—262no—
196C23—262no—
197C23—262no—
198C23#612712yes—
199C23C23×D1311yescharacteristic
200D4—524no—
201D4—528no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—134no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C22—22no—
223C22—24no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—522no—
228C22—522no—
229C22—522no—
230C22—522no—
231C22—522no—
232C22—522no—
233C22—522no—
234C22C2×#612711yescharacteristic
235C22#8825111yescharacteristic
236C22#8825111yescharacteristic
237C22#41×D1312yes—
238C22#8825612yes—
239C4—42no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—264no—
244C4—522no—
245C4—522no—
246C2—42no—
247C2—1042no—
248C2#1171919911yescharacteristic
249C2#1171923212yes—
250C2#1171936812yes—
251C2#1171936911yescharacteristic
252C2#1171937111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radical#11718621C2
hypercenter#381D13
hypocenterC13#2752
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. #11718618C2semidirect
5. #11718610C2semidirect
6. #11718336C2semidirect
7. #11718333C2semidirect
8. #11718331C2semidirect
9. #11718313C2semidirect
104. #381D13semidirect
186. C13#2752semidirect

Maximal subgroups

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

subgroupindex
C13×#3812
#117188742
#117186212
#117186182
#117186102
#117183362
#117183332
#117183312
#117183132
#275213