Finite Group Databasebeta

← #15775917

Subgroups — #15775917

Order 3328.

394 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116181C211yesmaximal, characteristic
2#13113843C212yesmaximal
3#13112842C212yesmaximal
4#13112782C211yesmaximal, characteristic
5C13×#2582C211yesmaximal, characteristic
6C2×C4×Q8×C13—21no—
7#11719205C2211yescharacteristic
8C13×#398—21no—
9C13×#398C2212yes—
10C13×#391—22no—
11C13×#389—22no—
12C13×#384C2211yescharacteristic
13#11718632—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13—21no—
20C4×Q8×C13—42no—
21C4×Q8×C13—42no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13—22no—
30C2×C42×C13D411yescharacteristic
31#88180—21no—
32#88178—22no—
33C2×#6099—21no—
34#88144—41no—
35#88142—41no—
36C13×#95—22no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95D412yes—
40C22⋊#1055—22no—
41#88050—42no—
42#88048—41no—
43#88048—42no—
44#88047—41no—
45#12247—131nomaximal, Sylow
46C2×Q8×C13—24no—
47C2×Q8×C13—42no—
48C2×Q8×C13—42no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—22no—
53C22×C4×C13C2×D411yescharacteristic
54C22×C4×C13C2×D412yes—
55C2×Dic26—22no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—44no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—81no—
64C42×C13—21no—
65C42×C13—44no—
66C42×C13SD1612yes—
67C22⋊Dic13—41no—
68C4⋊Dic13—21no—
69C4⋊Dic13—22no—
70C4⋊Dic13—21no—
71#6101—42no—
72C4×Dic13—41no—
73#6099—22no—
74#6099—41no—
75C2×#1055—41no—
76C2×#1055—42no—
77#2582D1311yescharacteristic
78#2060—131no—
79#1611—132no—
80#1346—132no—
81#1325—131no—
82C23×C13#12011yescharacteristic
83Q8×C13—48no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—24no—
90C2×C4×C13—22no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13C2×SD1611yescharacteristic
100C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
101C2×Dic13—41no—
102C2×Dic13—41no—
103Dic26—82no—
104#1055—42no—
105#1055—82no—
106#544—131no—
107C2×C4×Q8—21no—
108#483—262no—
109#428—261no—
110#398—21no—
111#398C2×D1312yes—
112#391—22no—
113#389—22no—
114#384C2×D1311yescharacteristic
115#343—131no—
116#339—261no—
117#328—262no—
118#324—132no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#45011yescharacteristic
122C22×C13#45611yescharacteristic
123C22×C13B(4,𝔽2)11yescharacteristic
124C4×C13—24no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—44no—
128C4×C13—42no—
129C4×C13—82no—
130C4×C13—81no—
131Dic13—81no—
132Dic13—81no—
133C22×Q8—21no—
134C2×M16—261no—
135C4⋊Q8—521no—
136#125—521no—
137C22⋊Q8—262no—
138C4×Q8—42no—
139C4×Q8—42no—
140#117—261no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4C22⋊D1311yescharacteristic
146C2×C4⋊C4C22⋊D1312yes—
147C2×C4⋊C4C22×D1311yescharacteristic
148C2×C42—22no—
149C2×C42C22⋊D1311yescharacteristic
150#107—521no—
151#106—521no—
152#106—522no—
153#103—522no—
154C22⋊C8—262no—
155#95—22no—
156#95—21no—
157#95—22no—
158#95C22⋊D1312yes—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13#160411yescharacteristic
162C2×C13#219811yescharacteristic
163C2×C13#220511yescharacteristic
164C2×Q8—24no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—262no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4C2×C22⋊D1311yescharacteristic
173C22×C4C2×C22⋊D1312yes—
174M16—262no—
175M16—521no—
176C2×C8—521no—
177C2×C8—522no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—44no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—81no—
186C4⋊C4—261no—
187C4⋊C4—262no—
188C4⋊C4—261no—
189C4⋊C4—522no—
190C22⋊C4—521no—
191C42—21no—
192C42—44no—
193C42—521no—
194C42#610512yes—
195C13#1224711yescharacteristic, complemented, Sylow
196C23#8820711yescharacteristic
197Q8—48no—
198Q8—1042no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—521no—
215C2×C4—521no—
216C2×C4#8818611yescharacteristic
217C2×C4C2×#610511yescharacteristic
218C8—522no—
219C8—1042no—
220C22—21no—
221C22—21no—
222C22#1171887911yescharacteristic
223C22#1171890511yescharacteristic
224C22#1171890711yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4—1041no—
233C4—1041no—
234C2—21no—
235C2—21no—
236C2#1311380511yescharacteristic
237C2#1311683211yescharacteristic
238C2#1311686611yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2582C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2582D13
hypocenterC13#12247
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

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

NH ≅ G/Ntype
195. C13#12247semidirect

Maximal subgroups

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

subgroupindex
#131161812
#131138432
#131128422
#131127822
C13×#25822
#1224713