Finite Group Databasebeta

← #15756443

Subgroups — #15756443

Order 3328.

566 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 87 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#13117421C211yesmaximal, characteristic
2#13114759C212yesmaximal
3#13112745C212yesmaximal
4#13112744C211yesmaximal, characteristic
5C13×#1306C211yesmaximal, characteristic
6C23×Dic26C2211yescharacteristic
7C2×#88131C412yes—
8C13×#407C2212yes—
9C13×#381C2211yescharacteristic
10#11718872C2211yescharacteristic
11#11718868C2212yes—
12C2×#88064—24no—
13#11718604C412yes—
14#11718307—24no—
15C23×C4×C13C2311yescharacteristic
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C411yescharacteristic
18C22×Dic26—22no—
19C22×Dic26—21no—
20C22×Dic26—21no—
21C22×Dic26—44no—
22C22×Dic26D414yes—
23C2×C13×M16—22no—
24C2×C13×C22⋊C4C2×C412yes—
25C2×C22⋊Dic13C2×C412yes—
26C2×#6101—22no—
27C2×C4×Dic13—22no—
28C2×#6099—22no—
29#88131—44no—
30C13×C22⋊C8—22no—
31C13×C22⋊C8—22no—
32C13×#95—22no—
33#88071—22no—
34#88071—24no—
35C22⋊#1055—22no—
36C22⋊#1055—22no—
37#88064—48no—
38#8754—131nomaximal, Sylow
39C24×C13C22×C411yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13—42no—
42C22×C4×C13C2×D412yes—
43C22×C4×C13#4112yes—
44C22×C4×C13#4111yescharacteristic
45C22×C4×C13#4111yescharacteristic
46C22×Dic13—21no—
47C22×Dic13—21no—
48C22×Dic13—24no—
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13—22no—
52C22×Dic13—42no—
53C22×Dic13C22⋊C412yes—
54C22×Dic13C22⋊C412yes—
55C2×Dic26—24no—
56C2×Dic26—24no—
57C2×Dic26—28no—
58C2×Dic26—44no—
59C2×Dic26—44no—
60C2×Dic26—48no—
61C2×Dic26—44no—
62C13×M16—44no—
63C2×C8×C13—42no—
64C13×C22⋊C4—42no—
65C22⋊Dic13—42no—
66#6101—44no—
67C4×Dic13—44no—
68#6099—44no—
69C2×#1055—42no—
70#2310—131no—
71#1784—132no—
72#1306—132no—
73#1306—131no—
74#1306D1311yescharacteristic
75C23×C13—22no—
76C23×C13—42no—
77C23×C13C2×C22⋊C411yescharacteristic
78C23×C13#11711yescharacteristic
79C23×C13#11711yescharacteristic
80C2×C4×C13—24no—
81C2×C4×C13—41no—
82C2×C4×C13—42no—
83C2×C4×C13—41no—
84C2×C4×C13—44no—
85C2×C4×C13—42no—
86C2×C4×C13#12312yes—
87C2×C4×C13#12312yes—
88C2×Dic13—24no—
89C2×Dic13—24no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—24no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—44no—
97C2×Dic13—42no—
98C2×Dic13#9914yes—
99Dic26—48no—
100Dic26—48no—
101C8×C13—82no—
102#1055—82no—
103C23×Q8—131no—
104C2×#117—132no—
105C2×#101—264no—
106#407—132no—
107#407C2×D1312yes—
108#391—264no—
109#381—131no—
110#381—132no—
111#381C2×D1311yescharacteristic
112C22×C13—22no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13—22no—
116C22×C13—22no—
117C22×C13—44no—
118C22×C13#38111yescharacteristic
119C22×C13C2×#9912yes—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—82no—
123Dic13—24no—
124Dic13—42no—
125Dic13—82no—
126C22×Q8—134no—
127C22×Q8—262no—
128C22×Q8—261no—
129C22×Q8—261no—
130C22×Q8—524no—
131C23×C4—131no—
132C23×C4—131no—
133C23×C4C22×D1311yescharacteristic
134C2×M16—22no—
135C2×M16—262no—
136#117—524no—
137C2×C4⋊C4—262no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4C4×D1312yes—
140C2×C42—262no—
141#101—528no—
142C22⋊C8—22no—
143C22⋊C8—22no—
144C22⋊C8—262no—
145C22⋊C8—262no—
146#95—22no—
147#95—264no—
148#95—262no—
149C2×C13—22no—
150C2×C13—41no—
151C2×C13—41no—
152C2×C13#181911yescharacteristic
153C2×C13#183012yes—
154C24C2×C4×D1311yescharacteristic
155C2×Q8—268no—
156C2×Q8—264no—
157C2×Q8—264no—
158C2×Q8—524no—
159C2×Q8—528no—
160C2×Q8—524no—
161C2×Q8—524no—
162C22×C4—22no—
163C22×C4—42no—
164C22×C4—132no—
165C22×C4—132no—
166C22×C4—264no—
167C22×C4—261no—
168C22×C4—261no—
169C22×C4—261no—
170C22×C4—261no—
171C22×C4—262no—
172C22×C4—522no—
173C22×C4#612712yes—
174C22×C4D4×D1312yes—
175C22×C4#612911yescharacteristic
176C22×C4#613111yescharacteristic
177M16—44no—
178M16—524no—
179C2×C8—42no—
180C2×C8—522no—
181C4⋊C4—524no—
182C22⋊C4—42no—
183C22⋊C4—522no—
184C42—524no—
185C13#875411yescharacteristic, complemented, Sylow
186C23—22no—
187C23—42no—
188C23#8812611yescharacteristic
189C23C22⋊C4×D1311yescharacteristic
190C23#8814611yescharacteristic
191Q8—528no—
192Q8—528no—
193C2×C4—24no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—44no—
198C2×C4—42no—
199C2×C4—134no—
200C2×C4—264no—
201C2×C4—264no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—264no—
205C2×C4—262no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—524no—
209C2×C4—522no—
210C2×C4#8813712yes—
211C2×C4#8814812yes—
212C8—82no—
213C8—1042no—
214C22—22no—
215C22—21no—
216C22—21no—
217C22—22no—
218C22—22no—
219C22—44no—
220C22#1171832511yescharacteristic
221C22D13×#9912yes—
222C4—22no—
223C4—22no—
224C4—82no—
225C4—264no—
226C4—522no—
227C4—1042no—
228C2—22no—
229C2—41no—
230C2—41no—
231C2#1311490911yescharacteristic
232C2#1311494912yes—
subgroupG/H
centerC22#11718325
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1306C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#1306D13
hypocenterC13#8754
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
185. C13#8754semidirect

Maximal subgroups

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

subgroupindex
#131174212
#131147592
#131127452
#131127442
C13×#13062
#875413