Finite Group Databasebeta

← #13125762

Subgroups — #13125762

Order 1664.

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

normal subgroups only

This group has 428 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#11718754C211yesmaximal, characteristic, complemented
5#11718746C211yesmaximal, characteristic, complemented
6#11718479C214yesmaximal, complemented
7#11718467C214yesmaximal, complemented
8#11718354C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic, complemented
10C2×#6131—21no—
11C2×Q8×D13C2212yes—
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14#88201—21no—
15#88198C2212yes—
16C2×#6106C2214yes—
17C2×#6095C2214yes—
18#88149—21no—
19#88149C2212yes—
20#88147—21no—
21#88147C2212yes—
22C4⋊C4×D13—21no—
23C4⋊C4×D13—21no—
24#88142—21no—
25#88142—21no—
26#88128C2211yescharacteristic
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#103C2214yes—
30C4×C8×C13C2211yescharacteristic
31#88060C2212yes—
32#88054C2212yes—
33#88050C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37#6131—44no—
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—22no—
49C2×Dic26C2312yes—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C42×C13C2311yescharacteristic
56#6106—44no—
57#6103—22no—
58#6103—22no—
59C4⋊Dic13—21no—
60C4⋊Dic13—21no—
61#6101—22no—
62#6101—22no—
63C4×Dic13D411yescharacteristic
64C4×Dic13D411yescharacteristic
65C4×Dic13C2311yescharacteristic
66C2×#1055C2312yes—
67#6095—44no—
68#3206—131nomaximal, Sylow
69C22×D13—22no—
70C22×D13C2×D411yescharacteristic
71Q8×C13—24no—
72Q8×C13—42no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2411yescharacteristic
78C2×Dic13—22no—
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82D52—24no—
83D52—44no—
84D52—42no—
85D52—42no—
86C4×D13—22no—
87C4×D13—22no—
88C4×D13—44no—
89C4×D13—44no—
90C4×D13SD1614yescomplemented
91Dic26—24no—
92Dic26—44no—
93C8×C13—22no—
94#1055—22no—
95#532—131no—
96C2×C4⋊Q8—131no—
97#492—131no—
98#492—131no—
99#487—131no—
100#487D1311yescharacteristic, complemented
101#461—134no—
102#448—134no—
103#431—131no—
104C22×C13C22×D411yescharacteristic
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—42no—
108C2×D13—42no—
109C2×D13—42no—
110C2×D13C2×SD1612yes—
111C4×C13—42no—
112C4×C13—42no—
113C4×C13C2×SD1612yes—
114C4×C13#13712yes—
115C4×C13H(5,𝔽2)12yes—
116Dic13—21no—
117Dic13—21no—
118Dic13—42no—
119Dic13C2×SD1612yes—
120C2×#41—261no—
121C22×Q8—132no—
122C2×SD16—134no—
123C2×SD16—134no—
124C4⋊Q8—132no—
125C4⋊Q8—131no—
126C4⋊Q8—261no—
127C4⋊Q8—261no—
128C4⋊Q8C2×D1311yescharacteristic
129C4⋊Q8C2×D1311yescharacteristic
130#127—131no—
131#124—261no—
132#121—132no—
133#121—261no—
134C4×D4—132no—
135C4×D4—261no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4—261no—
138C2×C42—131no—
139C4⋊C8—132no—
140#103—134no—
141#103C2×D1314yes—
142C22⋊C8—132no—
143C4×C8—131no—
144C4×C8C2×D1311yescharacteristic
145C2×C13#53511yescharacteristic
146C2×C13C22×SD1611yescharacteristic
147C2×C13C2×#13711yescharacteristic
148D13—22no—
149D13—82no—
150#41—524no—
151C2×Q8—21no—
152C2×Q8—132no—
153C2×Q8—262no—
154C2×Q8—524no—
155C2×Q8C22×D1312yes—
156C2×D4—132no—
157C2×D4—262no—
158C2×D4—261no—
159C2×D4—261no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—262no—
164C22×C4—262no—
165SD16—524no—
166SD16—524no—
167C2×C8—132no—
168C2×C8C22×D1312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C4⋊C4C22×D1312yes—
177C22⋊C4—262no—
178C22⋊C4—262no—
179C42—131no—
180C42—131no—
181C42—131no—
182C42C22×D1311yescharacteristic
183C13#320611yescharacteristic, complemented, Sylow
184C23—131no—
185C23—262no—
186Q8—24no—
187Q8—42no—
188Q8—264no—
189Q8—524no—
190D4—264no—
191D4—524no—
192D4—522no—
193D4—522no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—131no—
197C2×C4—134no—
198C2×C4—131no—
199C2×C4—131no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—524no—
204C2×C4—524no—
205C2×C4D4×D1311yescharacteristic
206C2×C4D4×D1311yescharacteristic
207C2×C4C23×D1311yescharacteristic
208C8—22no—
209C8—262no—
210C22—132no—
211C22—261no—
212C22—261no—
213C22—522no—
214C22—522no—
215C22—522no—
216C22C2×D4×D1311yescharacteristic
217C4—42no—
218C4—42no—
219C4—132no—
220C4—261no—
221C4—261no—
222C4—522no—
223C4SD16×D1312yes—
224C4#8817212yes—
225C4#8825612yes—
226C2—262no—
227C2—1042no—
228C2#1171937911yescharacteristic
229C2C2×SD16×D1311yescharacteristic
230C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#487D13
hypocenterC13#3206
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. #11718754C2semidirect
5. #11718746C2semidirect
6. #11718479C2semidirect
7. #11718467C2semidirect
8. #11718354C2semidirect
9. #11718346C2semidirect
90. C4×D13SD16semidirect
100. #487D13semidirect
183. C13#3206semidirect

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
#117187542
#117187462
#117184792
#117184672
#117183542
#117183462
#320613