Finite Group Databasebeta

← #13125231

Subgroups — #13125231

Order 1664.

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

normal subgroups only

This group has 424 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
1#11719430C211yesmaximal, characteristic
2D13×C4⋊Q8C211yesmaximal, characteristic, complemented
3C13×#487C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718742C211yesmaximal, characteristic, complemented
6#11718464C214yesmaximal, complemented
7#11718456C214yesmaximal, complemented
8#11718355C211yesmaximal, characteristic, complemented
9C4×#6094C211yesmaximal, characteristic, complemented
10C2×#6131C2212yes—
11C2×Q8×D13—21no—
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14#88201C2212yes—
15#88198—21no—
16C2×#6094C2212yes—
17#88149—21no—
18#88149—21no—
19#88147—21no—
20#88147—21no—
21C4⋊C4×D13—21no—
22C4⋊C4×D13C2212yes—
23#88142—21no—
24#88142C2212yes—
25#88128C2211yescharacteristic
26C42×D13C2211yescharacteristic
27#88123C2211yescharacteristic
28C13×#103C2214yes—
29C4×C8×C13C2211yescharacteristic
30#88075C2214yes—
31#88061C2214yes—
32#88055C2212yes—
33#88049C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37#6131—28no—
38Q8×D13—44no—
39C2×D52—22no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13D411yescharacteristic
46C2×C4×D13D411yescharacteristic
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26—22no—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C42×C13C2311yescharacteristic
56#6103—22no—
57#6103—22no—
58C4⋊Dic13—21no—
59C4⋊Dic13C2312yes—
60#6101—22no—
61#6101—22no—
62C4×Dic13D411yescharacteristic
63C4×Dic13D411yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055C2312yes—
66#6094—24no—
67#3141—131nomaximal, Sylow
68C22×D13—22no—
69C22×D13C2×D411yescharacteristic
70Q8×C13—24no—
71Q8×C13—42no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2411yescharacteristic
77C2×Dic13—22no—
78C2×Dic13C2×D411yescharacteristic
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—24no—
82D52—44no—
83D52—42no—
84D52—42no—
85C4×D13—22no—
86C4×D13—22no—
87C4×D13—44no—
88C4×D13—44no—
89C4×D13#4114yes—
90Dic26—44no—
91Dic26—42no—
92C8×C13—22no—
93#1055—22no—
94#532—131no—
95C2×C4⋊Q8—131no—
96#489—134no—
97#487—131no—
98#487D1311yescharacteristic, complemented
99#486—131no—
100#486—131no—
101#417—134no—
102C4×M16—131no—
103C22×C13C22×D411yescharacteristic
104C2×D13—21no—
105C2×D13—21no—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13—42no—
109C2×D13#12412yes—
110C4×C13—42no—
111C4×C13—42no—
112C4×C13AGL(1,ℤ/8)12yes—
113C4×C13#13712yes—
114C4×C13C2×#4112yes—
115Dic13—21no—
116Dic13—21no—
117Dic13—42no—
118Dic13#12412yes—
119C2×#41—132no—
120C22×Q8—261no—
121C2×M16—132no—
122C4⋊Q8—132no—
123C4⋊Q8—131no—
124C4⋊Q8—261no—
125C4⋊Q8—261no—
126C4⋊Q8C2×D1311yescharacteristic
127C4⋊Q8C2×D1311yescharacteristic
128#127—131no—
129#124—132no—
130#121—261no—
131#121—261no—
132C4×D4—261no—
133C4×D4—261no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—261no—
136C2×C42—131no—
137#103—134no—
138#103C2×D1314yes—
139#102—134no—
140#102—134no—
141#97—132no—
142C4×C8—131no—
143C4×C8C2×D1311yescharacteristic
144C2×C13C2×#12411yescharacteristic
145C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C13C2×#13711yescharacteristic
147D13—22no—
148D13—82no—
149#41—268no—
150C2×Q8—21no—
151C2×Q8—262no—
152C2×Q8—261no—
153C2×Q8—524no—
154C2×Q8C22×D1312yes—
155C2×D4—132no—
156C2×D4—262no—
157C2×D4—261no—
158C2×D4—261no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—262no—
163C22×C4—262no—
164M16—264no—
165C2×C8—132no—
166C2×C8C22×D1312yes—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—132no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—261no—
174C4⋊C4C22×D1312yes—
175C22⋊C4—262no—
176C22⋊C4—262no—
177C42—131no—
178C42—131no—
179C42—131no—
180C42C22×D1311yescharacteristic
181C13#314111yescharacteristic, complemented, Sylow
182C23—131no—
183C23—262no—
184Q8—24no—
185Q8—42no—
186Q8—524no—
187Q8—522no—
188D4—264no—
189D4—524no—
190D4—522no—
191D4—522no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—131no—
195C2×C4—134no—
196C2×C4—131no—
197C2×C4—131no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—524no—
202C2×C4—524no—
203C2×C4D4×D1311yescharacteristic
204C2×C4D4×D1311yescharacteristic
205C2×C4C23×D1311yescharacteristic
206C8—22no—
207C8—262no—
208C22—132no—
209C22—261no—
210C22—261no—
211C22—522no—
212C22—522no—
213C22—522no—
214C22C2×D4×D1311yescharacteristic
215C4—42no—
216C4—42no—
217C4—132no—
218C4—261no—
219C4—261no—
220C4—522no—
221C4#8816812yes—
222C4#8817212yes—
223C4#41×D1312yes—
224C2—262no—
225C2—1042no—
226C2D13×#12411yescharacteristic
227C2C2×#8816811yescharacteristic
228C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#487D13
hypocenterC13#3141
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. D13×C4⋊Q8C2semidirect
3. C13×#487C2semidirect
4. #11718749C2semidirect
5. #11718742C2semidirect
6. #11718464C2semidirect
7. #11718456C2semidirect
8. #11718355C2semidirect
9. C4×#6094C2semidirect
98. #487D13semidirect
181. C13#3141semidirect

Maximal subgroups

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

subgroupindex
#117194302
D13×C4⋊Q82
C13×#4872
#117187492
#117187422
#117184642
#117184562
#117183552
C4×#60942
#314113