Finite Group Databasebeta

← #13121788

Subgroups — #13121788

Order 1664.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88143C212yesmaximal
2C13×#389C211yesmaximal, characteristic
3#11718646C212yesmaximal
4#11718644C212yesmaximal
5#11718644C212yesmaximal
6#11718589C211yesmaximal, characteristic
7#11718589C211yesmaximal, characteristic
8#11718322C212yesmaximal
9#11718314C212yesmaximal
10C2×C13×C4⋊C4C2212yes—
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C42×C13C2211yescharacteristic
14C2×C4⋊Dic13C2212yes—
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25#88143—28no—
26C13×#95C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C13×C4⋊C4—24no—
42C13×C4⋊C4—41no—
43C13×C4⋊C4D414yes—
44C42×C13—41no—
45C4⋊Dic13—24no—
46C4⋊Dic13—22no—
47C4⋊Dic13—41no—
48C4⋊Dic13—41no—
49C4⋊Dic13—42no—
50C4⋊Dic13Q814yes—
51#6101—24no—
52#6101—24no—
53#6101—24no—
54#6101—24no—
55C4×Dic13—24no—
56#2726—131nomaximal, Sylow
57C23×C13C2411yescharacteristic
58C2×C4×C13—22no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13C2×D414yes—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×Q812yes—
72C2×C4×C13#4112yes—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13C2×Q814yes—
85C2×#125—132no—
86#398—132no—
87#398—132no—
88#398—132no—
89#389—132no—
90#389—131no—
91#389—131no—
92#389D1311yescharacteristic
93#387—132no—
94C22×C13C22×D411yescharacteristic
95C22×C13C22×Q811yescharacteristic
96C22×C13C2×#4111yescharacteristic
97C22×C13H(5,𝔽2)11yescharacteristic
98C22×C132−1+411yescharacteristic
99C22×C132−1+411yescharacteristic
100C22×C132−1+411yescharacteristic
101C4×C13—22no—
102C4×C13—22no—
103C4×C13—22no—
104C4×C13—24no—
105C4×C13—42no—
106Dic13—24no—
107Dic13—42no—
108Dic13—42no—
109Dic13—42no—
110#125—268no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—132no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—131no—
121C2×C4⋊C4C2×D1312yes—
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C4⋊C4C2×D1311yescharacteristic
124C2×C42—132no—
125C2×C42C2×D1311yescharacteristic
126#95—132no—
127#95—132no—
128#95—132no—
129#95—132no—
130#95—132no—
131#95C2×D1312yes—
132C2×C13#53711yescharacteristic
133C2×C13#53911yescharacteristic
134C2×C13#54411yescharacteristic
135C2×C13#54711yescharacteristic
136C2×C13D4×Q811yescharacteristic
137C2×C13#55711yescharacteristic
138C2×C13#56411yescharacteristic
139C22×C4—132no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—132no—
143C22×C4C22×D1312yes—
144C22×C4C22×D1312yes—
145C22×C4C22×D1311yescharacteristic
146C22×C4C22×D1311yescharacteristic
147C22×C4C22×D1311yescharacteristic
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—134no—
151C4⋊C4—264no—
152C4⋊C4—264no—
153C4⋊C4—264no—
154C4⋊C4—264no—
155C4⋊C4—264no—
156C4⋊C4—262no—
157C4⋊C4—521no—
158C4⋊C4—521no—
159C4⋊C4—522no—
160C4⋊C4D5214yes—
161C42—41no—
162C42—264no—
163C13#272611yescharacteristic, complemented, Sylow
164C23C23×D1311yescharacteristic
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—134no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4C2×D5214yes—
189C2×C4C2×D5212yes—
190C2×C4#612912yes—
191C2×C4Q8×D1312yes—
192C22C22×D5211yescharacteristic
193C22C2×#612911yescharacteristic
194C22#8825111yescharacteristic
195C22C2×Q8×D1311yescharacteristic
196C22#8825411yescharacteristic
197C22#8825711yescharacteristic
198C22#8825711yescharacteristic
199C4—22no—
200C4—24no—
201C4—22no—
202C4—22no—
203C4—42no—
204C4—264no—
205C4—522no—
206C4—522no—
207C4—522no—
208C2#1171921511yescharacteristic
209C2#1171926011yescharacteristic
210C2Q8×D5211yescharacteristic
211C2#1171930711yescharacteristic
212C2#1171932811yescharacteristic
213C2C13⋊#56411yescharacteristic
214C2#1171942611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#389C2
hypercenter#389D13
hypocenterC13#2726
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
163. C13#2726semidirect

Maximal subgroups

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

subgroupindex
C2×#881432
C13×#3892
#117186462
#117186442
#117185892
#117183222
#117183142
#272613