Finite Group Databasebeta

← #15775715

Subgroups — #15775715

Order 3328.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#13120501C211yesmaximal, characteristic
2#13113861C212yesmaximal
3#13112859C212yesmaximal
4#13112766C211yesmaximal, characteristic
5C13×#2030C211yesmaximal, characteristic
6C13×#543C2211yescharacteristic
7C13×#381—21no—
8C13×#381C2211yescharacteristic
9C4×C22⋊Dic13—21no—
10#11718705—22no—
11#11718610C2212yes—
12#11718608—21no—
13#11718316—22no—
14#11718307—22no—
15C13×#342—21no—
16C13×#342C2211yescharacteristic
17#11718130—22no—
18#11718117C2212yes—
19C23×C4×C13D411yescharacteristic
20C22×Dic26—21no—
21C13×C22⋊Q8—22no—
22C13×C22⋊Q8—42no—
23C2×C13×C22⋊C4—21no—
24C2×C13×C22⋊C4—21no—
25C2×C13×C22⋊C4D411yescharacteristic
26C2×C13×C22⋊C4C2311yescharacteristic
27C2×C22⋊Dic13—22no—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13—21no—
32C13×#95—22no—
33C13×#95—42no—
34#88075—42no—
35#88071—22no—
36#88071—22no—
37#88071—21no—
38#88071D412yes—
39C22⋊#1055—22no—
40#88047—42no—
41#12216—131nomaximal, Sylow
42C24×C13C2×D411yescharacteristic
43C2×Q8×C13—22no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13Q1612yes—
52C22×C4×C13C2×D412yes—
53C22×Dic13—22no—
54C22×Dic13—22no—
55C2×Dic26—44no—
56C2×Dic26—81no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—42no—
59C13×C22⋊C4—41no—
60C13×C22⋊C4—41no—
61C13×C22⋊C4—41no—
62C13×C22⋊C4—41no—
63C13×C22⋊C4—41no—
64C13×C22⋊C4—41no—
65C22⋊Dic13—44no—
66C4⋊Dic13—42no—
67#6101—44no—
68C4×Dic13—81no—
69C4×Dic13—81no—
70C2×#1055—42no—
71#2607—131no—
72#2030D1311yescharacteristic
73#1614—132no—
74#1352—132no—
75#1317—131no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—42no—
79C23×C13#12011yescharacteristic
80C23×C13C2×Q1611yescharacteristic
81C23×C13#13711yescharacteristic
82Q8×C13—82no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—81no—
93C2×C4×C13—82no—
94C2×C4×C13—81no—
95C2×C4×C13—82no—
96C2×Dic13—24no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102Dic26—84no—
103#1055—82no—
104#543C2×D1311yescharacteristic
105#484—262no—
106#399—132no—
107#393—261no—
108#391—262no—
109#387—262no—
110#381—21no—
111#381C2×D1311yescharacteristic
112C4×C22⋊C4—261no—
113#342—21no—
114#342C2×D1311yescharacteristic
115#328—262no—
116#323—132no—
117C22×C13—22no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13—42no—
123C22×C13—81no—
124C22×C13#45111yescharacteristic
125C22×C13#45511yescharacteristic
126C22×C13B(4,𝔽2)11yescharacteristic
127C4×C13—42no—
128C4×C13—42no—
129C4×C13—81no—
130C4×C13—82no—
131C4×C13—161no—
132Dic13—44no—
133Dic13—82no—
134C22×Q8—261no—
135C23×C4C22⋊D1311yescharacteristic
136C22⋊Q8—22no—
137C22⋊Q8—42no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—262no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—262no—
143C2×C22⋊C4C22⋊D1311yescharacteristic
144C2×C22⋊C4C22×D1311yescharacteristic
145C2×C42—261no—
146C2×C42—261no—
147#107—522no—
148#103—522no—
149C22⋊C8—262no—
150#95—22no—
151#95—42no—
152#95—132no—
153#95—262no—
154#95—261no—
155#95—262no—
156C2×C13—21no—
157C2×C13—21no—
158C2×C13—41no—
159C2×C13—41no—
160C2×C13#160211yescharacteristic
161C2×C13#219812yes—
162C24C2×C22⋊D1311yescharacteristic
163C2×Q8—22no—
164C2×Q8—524no—
165C2×Q8—1041no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—262no—
174C22×C4—262no—
175C22×C4#610712yes—
176C22×C4D4×D1312yes—
177C2×C8—522no—
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—522no—
181C4⋊C4—524no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—524no—
189C42—1041no—
190C42—1041no—
191C13#1221611yescharacteristic, complemented, Sylow
192C23—21no—
193C23—21no—
194C23—42no—
195C23#8819111yescharacteristic
196C23C2×#610711yescharacteristic
197C23#8820511yescharacteristic
198Q8—82no—
199Q8—1044no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—82no—
213C2×C4—264no—
214C2×C4—522no—
215C2×C4—522no—
216C2×C4—522no—
217C2×C4—522no—
218C2×C4—522no—
219C8—1042no—
220C22—22no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22#1171869311yescharacteristic
228C22#1171871111yescharacteristic
229C22#1171872211yescharacteristic
230C4—42no—
231C4—42no—
232C4—81no—
233C4—82no—
234C4—161no—
235C4—524no—
236C4—1042no—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2#1311379211yescharacteristic
242C2#1311683012yes—
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2030C2
socleC22×C13B(4,𝔽2)
prime radicalC24×C13C2×D4
hypercenter#2030D13
hypocenterC13#12216
LCSG ▷ C2×C13×C22⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
191. C13#12216semidirect

Maximal subgroups

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

subgroupindex
#131205012
#131138612
#131128592
#131127662
C13×#20302
#1221613