Finite Group Databasebeta

← #15775941

Subgroups — #15775941

Order 3328.

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

normal subgroups only

This group has 342 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#13116186C211yesmaximal, characteristic
2#13113843C212yesmaximal
3#13112842C212yesmaximal
4#13112780C211yesmaximal, characteristic
5C13×#2822C211yesmaximal, characteristic
6C2×C13×#125—21no—
7#11719205C2211yescharacteristic
8C13×#400—22no—
9C13×#398—21no—
10C13×#398—22no—
11C13×#398C2212yes—
12C13×#382C2211yescharacteristic
13#11718632—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C13×#125—42no—
20C13×#125—42no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13D411yescharacteristic
30#88180—21no—
31#88178—22no—
32C2×#6099—21no—
33#88144—41no—
34#88142—41no—
35C13×#95—22no—
36C13×#95—21no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95D412yes—
40C22⋊#1055—22no—
41#88050—42no—
42#88048—41no—
43#88048—42no—
44#88047—41no—
45#12251—131nomaximal, Sylow
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D412yes—
52C2×Dic26—22no—
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—44no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—81no—
62C42×C13—21no—
63C42×C13SD1612yes—
64C22⋊Dic13—41no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67C4⋊Dic13—21no—
68#6101—42no—
69C4×Dic13—41no—
70#6099—22no—
71#6099—41no—
72C2×#1055—41no—
73C2×#1055—42no—
74#2822D1311yescharacteristic
75#2061—131no—
76#1611—132no—
77#1346—132no—
78#1324—131no—
79C23×C13#12011yescharacteristic
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—41no—
95C2×C4×C13C2×SD1611yescharacteristic
96C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
97C2×Dic13—41no—
98C2×Dic13—41no—
99Dic26—82no—
100#1055—42no—
101#1055—82no—
102#544—131no—
103C2×#125—21no—
104#483—262no—
105#428—261no—
106#400—22no—
107#398—21no—
108#398—22no—
109#398C2×D1312yes—
110#382C2×D1311yescharacteristic
111#343—131no—
112#339—261no—
113#328—262no—
114#324—132no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#45011yescharacteristic
118C22×C13#45611yescharacteristic
119C22×C13B(4,𝔽2)11yescharacteristic
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—42no—
123C4×C13—42no—
124C4×C13—82no—
125C4×C13—82no—
126C4×C13—81no—
127Dic13—81no—
128Dic13—81no—
129C2×M16—261no—
130C4⋊Q8—521no—
131#125—42no—
132#125—42no—
133#125—521no—
134C22⋊Q8—262no—
135#117—261no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C22⋊D1311yescharacteristic
142C2×C4⋊C4C22⋊D1312yes—
143C2×C4⋊C4C22×D1311yescharacteristic
144C2×C42C22⋊D1311yescharacteristic
145#107—521no—
146#106—521no—
147#106—522no—
148#103—522no—
149C22⋊C8—262no—
150#95—22no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95C22⋊D1312yes—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#160411yescharacteristic
158C2×C13#220111yescharacteristic
159C2×C13#220311yescharacteristic
160C2×Q8—262no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4C2×C22⋊D1311yescharacteristic
166C22×C4C2×C22⋊D1312yes—
167M16—262no—
168M16—521no—
169C2×C8—521no—
170C2×C8—522no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—44no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—81no—
180C4⋊C4—261no—
181C4⋊C4—262no—
182C4⋊C4—261no—
183C4⋊C4—522no—
184C22⋊C4—521no—
185C42—21no—
186C42—521no—
187C42#610512yes—
188C13#1225111yescharacteristic, complemented, Sylow
189C23#8820711yescharacteristic
190Q8—1042no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—521no—
207C2×C4—521no—
208C2×C4#8818611yescharacteristic
209C2×C4C2×#610511yescharacteristic
210C8—522no—
211C8—1042no—
212C22—21no—
213C22—21no—
214C22#1171887911yescharacteristic
215C22#1171890511yescharacteristic
216C22#1171890711yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—81no—
223C4—82no—
224C4—1041no—
225C4—1041no—
226C2—21no—
227C2—21no—
228C2#1311380511yescharacteristic
229C2#1311684911yescharacteristic
230C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2822C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2822D13
hypocenterC13#12251
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2822

Complements

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

NH ≅ G/Ntype
188. C13#12251semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131138432
#131128422
#131127802
C13×#28222
#1225113