Finite Group Databasebeta

← #13122983

Subgroups — #13122983

Order 1664.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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×#398C211yesmaximal, characteristic, complemented
2#11718655C212yesmaximal, complemented
3#11718652C212yesmaximal
4#11718649C211yesmaximal, characteristic
5#11718642C212yesmaximal, complemented
6#11718640C211yesmaximal, characteristic, complemented
7#11718336C212yesmaximal, complemented
8#11718335C212yesmaximal, complemented
9#11718334C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24C13×#95C2212yes—
25C13×#95C2211yescharacteristic
26#88071C2212yes—
27#88071C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31C23×D13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×D52—22no—
41C2×D52—41no—
42C2×D52—41no—
43C2×Dic26—42no—
44C2×Dic26—41no—
45C13×C4⋊C4—24no—
46C13×C4⋊C4—41no—
47C13×C4⋊C4—41no—
48#6103—42no—
49#6103—42no—
50#6103—42no—
51#6103—42no—
52#6103—42no—
53#6103—42no—
54C4⋊Dic13—42no—
55#6101—42no—
56C4×Dic13—41no—
57#2830—131nomaximal, Sylow
58C23×C13C2411yescharacteristic
59C22×D13—22no—
60C22×D13—22no—
61C22×D13—22no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—22no—
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—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
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—22no—
88D52—44no—
89Dic26—44no—
90#398D1311yescharacteristic, complemented
91#397—132no—
92#397—132no—
93#396—132no—
94#395—131no—
95#394—132no—
96#393—132no—
97#390—131no—
98#387—132no—
99C22×C13C2×#4111yescharacteristic
100C22×C13H(5,𝔽2)11yescharacteristic
101C22×C13H(5,𝔽2)11yescharacteristic
102C22×C13H(5,𝔽2)12yes—
103C22×C132−1+412yes—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13—42no—
109C2×D13—42no—
110C2×D13—42no—
111C4×C13—22no—
112C4×C13—42no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13—41no—
116Dic13—42no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8—131no—
120C22×D4—131no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—132no—
123C2×C4⋊C4C2×D1312yes—
124C2×C4⋊C4C2×D1311yescharacteristic
125C2×C4⋊C4C2×D1311yescharacteristic
126C2×C22⋊C4—132no—
127C2×C22⋊C4—132no—
128C2×C22⋊C4—132no—
129C2×C22⋊C4—132no—
130C2×C22⋊C4—132no—
131C2×C22⋊C4—132no—
132C2×C42—131no—
133#95—132no—
134#95—132no—
135#95—132no—
136#95—132no—
137#95—131no—
138#95C2×D1312yes—
139#95C2×D1311yescharacteristic
140C2×C13#53811yescharacteristic
141C2×C13#54212yes—
142C2×C13#56011yescharacteristic
143C2×C13#56212yes—
144C2×C13#56311yescharacteristic
145D13—82no—
146C24—132no—
147C2×Q8—521no—
148C2×Q8—522no—
149C2×D4—262no—
150C2×D4—521no—
151C2×D4—521no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4—132no—
155C22×C4C22×D1312yes—
156C22×C4C22×D1311yescharacteristic
157C22×C4C22×D1312yes—
158C22×C4C22×D1311yescharacteristic
159C22×C4C22×D1311yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—522no—
164C4⋊C4—522no—
165C22⋊C4—522no—
166C22⋊C4—522no—
167C22⋊C4—522no—
168C22⋊C4—522no—
169C22⋊C4—522no—
170C22⋊C4—522no—
171C42—521no—
172C13#283011yescharacteristic, complemented, Sylow
173C23—262no—
174C23—262no—
175C23—262no—
176C23—262no—
177C23—262no—
178C23—262no—
179C23—262no—
180C23C23×D1311yescharacteristic
181Q8—524no—
182D4—524no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4#612912yes—
205C22—522no—
206C22—522no—
207C22—522no—
208C22—522no—
209C22—522no—
210C22—522no—
211C22—522no—
212C22C2×#612911yescharacteristic
213C22#8825111yescharacteristic
214C22#8825412yes—
215C22#8825611yescharacteristic
216C22#8825612yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—522no—
223C4—522no—
224C4—522no—
225C2—1042no—
226C2#1171932211yescharacteristic
227C2#1171934812yes—
228C2#1171937111yescharacteristic
229C2#1171940512yes—
230C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC22×D52C22
hypercenter#398D13
hypocenterC13#2830
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C13×#398C2semidirect
2. #11718655C2semidirect
5. #11718642C2semidirect
6. #11718640C2semidirect
7. #11718336C2semidirect
8. #11718335C2semidirect
9. #11718334C2semidirect
90. #398D13semidirect
172. C13#2830semidirect

Maximal subgroups

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

subgroupindex
C13×#3982
#117186552
#117186522
#117186492
#117186422
#117186402
#117183362
#117183352
#117183342
#283013