Finite Group Databasebeta

← #13122905

Subgroups — #13122905

Order 1664.

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

normal subgroups only

This group has 380 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×#88144C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic
3C13×#400C211yesmaximal, characteristic
4#11718644C211yesmaximal, characteristic
5#11718643C211yesmaximal, characteristic
6#11718322C211yesmaximal, characteristic
7#11718322C212yesmaximal
8#11718319C212yesmaximal
9#11718318C212yesmaximal
10#11718318C212yesmaximal
11#11718311C211yesmaximal, characteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×#6101C2211yescharacteristic
19C2×#6101C2211yescharacteristic
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26#88144—24no—
27#88143—24no—
28C13×#95C2211yescharacteristic
29C13×#95C2212yes—
30C13×#95C2212yes—
31#88071C2212yes—
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C13×C4⋊C4—22no—
49C13×C4⋊C4—22no—
50C4⋊Dic13—22no—
51C4⋊Dic13—22no—
52C4⋊Dic13—24no—
53C4⋊Dic13—42no—
54#6101—22no—
55#6101—22no—
56#6101—22no—
57#6101—22no—
58#6101—24no—
59#6101—42no—
60#6101—42no—
61C4×Dic13D414yes—
62#2822—131nomaximal, Sylow
63C23×C13C2411yescharacteristic
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—24no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D412yes—
76C2×Dic13—21no—
77C2×Dic13—22no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92C2×#125—131no—
93C2×#125—131no—
94#400—131no—
95#400—132no—
96#400D1311yescharacteristic
97#398—131no—
98#398—132no—
99#398—132no—
100#398—131no—
101#398—132no—
102#382—131no—
103C22×C13C22×D411yescharacteristic
104C22×C13H(5,𝔽2)11yescharacteristic
105C22×C132−1+411yescharacteristic
106C22×C132−1+412yes—
107C22×C132−1+412yes—
108C4×C13—22no—
109C4×C13—41no—
110C4×C13—42no—
111C4×C13—41no—
112C4×C13—42no—
113Dic13—22no—
114Dic13—22no—
115Dic13—41no—
116Dic13—41no—
117Dic13—42no—
118Dic13—42no—
119#125—264no—
120#125—264no—
121C2×C4⋊C4—131no—
122C2×C4⋊C4—131no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—131no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4C2×D1311yescharacteristic
133C2×C4⋊C4C2×D1311yescharacteristic
134C2×C42—131no—
135#95—132no—
136#95—131no—
137#95—132no—
138#95—132no—
139#95—132no—
140#95—132no—
141#95C2×D1311yescharacteristic
142#95C2×D1312yes—
143#95C2×D1312yes—
144C2×C13#53611yescharacteristic
145C2×C13#53611yescharacteristic
146C2×C13#53711yescharacteristic
147C2×C13#56312yes—
148C2×C13#56412yes—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—132no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—132no—
155C22×C4C22×D1312yes—
156C22×C4C22×D1311yescharacteristic
157C22×C4C22×D1312yes—
158C22×C4C22×D1311yescharacteristic
159C22×C4C22×D1311yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C4⋊C4—264no—
165C4⋊C4—262no—
166C4⋊C4—262no—
167C4⋊C4—264no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—522no—
171C4⋊C4—522no—
172C4⋊C4—522no—
173C42—134no—
174C13#282211yescharacteristic, complemented, Sylow
175C23C23×D1311yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—132no—
188C2×C4—132no—
189C2×C4—261no—
190C2×C4—261no—
191C2×C4—262no—
192C2×C4—261no—
193C2×C4—262no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—261no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4D4×D1312yes—
204C22C2×D4×D1311yescharacteristic
205C22#8825411yescharacteristic
206C22#8825611yescharacteristic
207C22#8825712yes—
208C22#8825712yes—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—42no—
214C4—262no—
215C4—262no—
216C4—521no—
217C4—522no—
218C4—521no—
219C4—522no—
220C2#1171933411yescharacteristic
221C2#1171935311yescharacteristic
222C2#1171938011yescharacteristic
223C2C13⋊#56412yes—
224C2#1171941712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#400C2
hypercenter#400D13
hypocenterC13#2822
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
174. C13#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#881442
C2×#881432
C13×#4002
#117186442
#117186432
#117183222
#117183192
#117183182
#117183112
#282213