Finite Group Databasebeta

← #15775997

Subgroups — #15775997

Order 3328.

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

normal subgroups only

This group has 342 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#13123108C211yesmaximal, characteristic
2#13113810C212yesmaximal
3#13112865C212yesmaximal
4#13112780C211yesmaximal, characteristic
5C13×#2061C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C13×#428—21no—
8C13×#382C2211yescharacteristic
9#11718711—22no—
10#11718647—21no—
11#11718640C2212yes—
12#11718597—21no—
13#11718321—22no—
14#11718317—22no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17#11718130—22no—
18#11718120C2212yes—
19C22×Dic26D412yes—
20C2×C13×M16—21no—
21C13×C4⋊Q8—41no—
22C13×#125—41no—
23C13×C22⋊Q8—22no—
24C13×#117—21no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×#6107—42no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×#6101—22no—
33C13×#107—41no—
34C13×#106—41no—
35C13×#95—22no—
36#88071—22no—
37#88071—22no—
38#88071—21no—
39#88071—22no—
40#88071D412yes—
41C22⋊#1055—22no—
42#88050—42no—
43#12260—131nomaximal, Sylow
44C2×Q8×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C2×D412yes—
48C22×C4×C13C2×D411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13—22no—
51C2×Dic26—42no—
52C2×Dic26—82no—
53C13×M16—22no—
54C13×M16—41no—
55C2×C8×C13—41no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C22⋊C4—41no—
63C42×C13—21no—
64C42×C13—41no—
65C42×C13Q1612yescomplemented
66#6107—84no—
67C4⋊Dic13—81no—
68C4⋊Dic13—81no—
69C4⋊Dic13—81no—
70#6101—82no—
71C2×#1055—42no—
72#2844—131no—
73#2061D1311yescharacteristic
74#1605—132no—
75#1354—132no—
76#1324—131no—
77C23×C13#12011yescharacteristic
78Q8×C13—82no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13C2×Q1611yescharacteristic
91C2×C4×C13#13711yescharacteristic
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98Dic26—44no—
99Dic26—82no—
100C8×C13—42no—
101#1055—82no—
102#544C2×D1311yescharacteristic
103#451—262no—
104#428—21no—
105#400—262no—
106#400—261no—
107#395—132no—
108#395—262no—
109#382—261no—
110#382C2×D1311yescharacteristic
111#343C2×D1311yescharacteristic
112#339—21no—
113#328—262no—
114#324—132no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#45111yescharacteristic
118C22×C13#45611yescharacteristic
119C22×C13B(4,𝔽2)11yescharacteristic
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—42no—
123C4×C13—42no—
124C4×C13—81no—
125C4×C13—81no—
126C4×C13—81no—
127Dic13—82no—
128Dic13—82no—
129C22×Q8—132no—
130C2×Q16—522no—
131C2×M16—21no—
132C4⋊Q8—41no—
133#125—41no—
134C22⋊Q8—22no—
135#117—21no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4—261no—
138C2×C4⋊C4—261no—
139C2×C4⋊C4—262no—
140C2×C4⋊C4C22⋊D1311yescharacteristic
141C2×C4⋊C4C22×D1311yescharacteristic
142C2×C42C22⋊D1311yescharacteristic
143#107—41no—
144#106—41no—
145#103—522no—
146C22⋊C8—262no—
147#95—22no—
148#95—132no—
149#95—262no—
150#95—262no—
151#95—261no—
152#95—262no—
153C2×C13—21no—
154C2×C13—21no—
155C2×C13#160511yescharacteristic
156C2×C13#219911yescharacteristic
157C2×C13#220311yescharacteristic
158C2×Q8—22no—
159C2×Q8—522no—
160C2×Q8—1042no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—262no—
164C22×C4—262no—
165C22×C4D4×D1312yes—
166C22×C4C2×C22⋊D1311yescharacteristic
167Q16—1044no—
168M16—22no—
169M16—41no—
170C2×C8—41no—
171C2×C8—522no—
172C4⋊C4—22no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—1042no—
179C4⋊C4—1041no—
180C4⋊C4—1041no—
181C4⋊C4—1041no—
182C22⋊C4—41no—
183C42—21no—
184C42—41no—
185C42#610712yescomplemented
186C13#1226011yescharacteristic, complemented, Sylow
187C23#8819111yescharacteristic
188Q8—82no—
189Q8—524no—
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—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4C2×#610711yescharacteristic
209C2×C4#8820511yescharacteristic
210C8—42no—
211C8—1042no—
212C22—21no—
213C22—21no—
214C22#1171869311yescharacteristic
215C22#1171871111yescharacteristic
216C22#1171875611yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—81no—
222C4—81no—
223C4—81no—
224C4—1042no—
225C4—1042no—
226C2—21no—
227C2—21no—
228C2#1311380911yescharacteristic
229C2#1311683611yescharacteristic
230C2#1311685611yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2061C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2061D13
hypocenterC13#12260
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
65. C42×C13Q16semidirect
185. C42#6107semidirect
186. C13#12260semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131138102
#131128652
#131127802
C13×#20612
#1226013