Finite Group Databasebeta

← #13122907

Subgroups — #13122907

Order 1664.

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

normal subgroups only

This group has 456 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
1C2×#88133C212yesmaximal, complemented
2C13×#394C211yesmaximal, characteristic
3#11718883C212yesmaximal
4#11718644C211yesmaximal, characteristic, complemented
5#11718637C211yesmaximal, characteristic, complemented
6#11718609C212yesmaximal, complemented
7#11718609C212yesmaximal, complemented
8#11718609C212yesmaximal, complemented
9#11718318C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C22⋊C4C2212yes—
13C2×C13×C22⋊C4C2212yes—
14C2×C22⋊Dic13C2212yes—
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C4⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27#88133—28no—
28C13×#95C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31#88071C2211yescharacteristic
32C24×C13C2312yes—
33C2×D4×C13—42no—
34C2×D4×C13—41no—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C13×C4⋊C4—41no—
44C13×C22⋊C4—24no—
45C13×C22⋊C4—42no—
46C22⋊Dic13—24no—
47C22⋊Dic13—24no—
48C22⋊Dic13—42no—
49C22⋊Dic13—42no—
50C4⋊Dic13—24no—
51C4⋊Dic13—41no—
52C4⋊Dic13—41no—
53#6101—24no—
54#6101—24no—
55#6101—42no—
56#6101—42no—
57#6101—42no—
58C4×Dic13D414yescomplemented
59#2823—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—22no—
67C23×C13C2411yescharacteristic
68D4×C13—44no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
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×C13C2×D412yes—
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—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13C2×D414yes—
91C2×#126—132no—
92#398—131no—
93#398—132no—
94#396—132no—
95#396—132no—
96#396—132no—
97#394—132no—
98#394D1311yescharacteristic
99#384—131no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13C22×D411yescharacteristic
108C22×C13H(5,𝔽2)11yescharacteristic
109C22×C13H(5,𝔽2)12yes—
110C22×C132−1+411yescharacteristic
111C22×C132−1+412yes—
112C4×C13—22no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13—41no—
116Dic13—24no—
117Dic13—42no—
118Dic13—42no—
119Dic13—42no—
120C22×D4C2×D1311yescharacteristic
121#126—268no—
122C2×C4⋊C4—132no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C22⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4—132no—
135C2×C22⋊C4C2×D1312yes—
136C2×C22⋊C4C2×D1312yes—
137C2×C42—131no—
138#95—132no—
139#95—131no—
140#95—132no—
141#95C2×D1311yescharacteristic
142C2×C13—82no—
143C2×C13#53711yescharacteristic
144C2×C13#53712yes—
145C2×C13#56011yescharacteristic
146C2×C13#56312yes—
147C2×C13#56311yescharacteristic
148C24C22×D1312yes—
149C2×D4—41no—
150C2×D4—42no—
151C22×C4—132no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4—132no—
155C22×C4C22×D1311yescharacteristic
156C22×C4C22×D1312yes—
157C22×C4C22×D1311yescharacteristic
158C22×C4C22×D1311yescharacteristic
159C4⋊C4—41no—
160C4⋊C4—264no—
161C4⋊C4—264no—
162C4⋊C4—264no—
163C4⋊C4—522no—
164C4⋊C4—522no—
165C4⋊C4—522no—
166C4⋊C4—521no—
167C4⋊C4—521no—
168C22⋊C4—24no—
169C22⋊C4—42no—
170C22⋊C4—264no—
171C22⋊C4—264no—
172C22⋊C4—522no—
173C22⋊C4—522no—
174C42—134no—
175C13#282311yescharacteristic, complemented, Sylow
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23C23×D1311yescharacteristic
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—134no—
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—262no—
205C2×C4—262no—
206C2×C4D4×D1312yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×D4×D1311yescharacteristic
215C22#8825111yescharacteristic
216C22#8825112yes—
217C22#8825711yescharacteristic
218C22#8825712yes—
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—264no—
224C4—522no—
225C4—522no—
226C4—522no—
227C2—82no—
228C2#1171930011yescharacteristic
229C2#1171930211yescharacteristic
230C2#1171931312yes—
231C2#1171935612yes—
232C2#1171937711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2823
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#88133C2semidirect
4. #11718644C2semidirect
5. #11718637C2semidirect
6. #11718609C2semidirect
7. #11718609C2semidirect
8. #11718609C2semidirect
9. #11718318C2semidirect
58. C4×Dic13D4semidirect
175. C13#2823semidirect

Maximal subgroups

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

subgroupindex
C2×#881332
C13×#3942
#117188832
#117186442
#117186372
#117186092
#117183182
#282313