Finite Group Databasebeta

← #15760277

Subgroups — #15760277

Order 3328.

486 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 131 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#13123917C211yesmaximal, characteristic
2#13120041C211yesmaximal, characteristic
3#13113518C212yesmaximal
4#13112737C212yesmaximal
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#423C2212yes—
9C2×C13×#101—21no—
10#11718891—21no—
11Q8×#1055—24no—
12#11718640C414yes—
13#11718637—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718589—22no—
16#11718586—22no—
17#11718586C2212yes—
18C13×#343—21no—
19#11718073—24no—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26C2×C412yes—
22C2×C13×M16—22no—
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C42×C13D412yes—
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×#6101—24no—
33C2×C4×Dic13—21no—
34#88123—22no—
35#88123—22no—
36C13×C4⋊C8—22no—
37C13×C4⋊C8—22no—
38C13×#101—42no—
39#88071—24no—
40#88071C2×C412yes—
41C22⋊#1055—22no—
42C4⋊#1055—24no—
43C4⋊#1055D414yes—
44C4×#1055—24no—
45C4×#1055—22no—
46#9392—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13SD1612yes—
50C2×Q8×C13Q1612yes—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22×C411yescharacteristic
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13—22no—
58C2×Dic26—24no—
59C2×Dic26—82no—
60C13×M16—42no—
61C13×M16—42no—
62C2×C8×C13—42no—
63C13×C4⋊C4—24no—
64C13×C4⋊C4—22no—
65C42×C13—22no—
66C42×C13—22no—
67C42×C13C2×D412yes—
68C42×C13#4112yes—
69C4⋊Dic13—24no—
70C4⋊Dic13—41no—
71C4⋊Dic13—42no—
72C4⋊Dic13—41no—
73#6101—84no—
74C4×Dic13—42no—
75C2×#1055—24no—
76#2982—131no—
77#2567—131no—
78#1801D1311yescharacteristic
79#1548—132no—
80#1303—132no—
81C23×C13C2×C22⋊C411yescharacteristic
82Q8×C13—24no—
83Q8×C13—24no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13—42no—
90C2×C4×C13#10314yes—
91C2×C4×C13C4×D412yes—
92C2×C4×C13#12011yescharacteristic
93C2×C4×C13#12112yes—
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13C2×SD1611yescharacteristic
96C2×C4×C13C2×Q1611yescharacteristic
97C2×C4×C13#13512yes—
98C2×Dic13—24no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—44no—
102C2×Dic13—42no—
103Dic26—84no—
104C8×C13—82no—
105#1055—44no—
106C2×C4⋊Q8—131no—
107C2×C4×Q8C2×D1311yescharacteristic
108C8×Q8—264no—
109#431—132no—
110#431—262no—
111#423C2×D1312yes—
112C2×#101—21no—
113#395—134no—
114#391—261no—
115#389—262no—
116#384—261no—
117C4×C4⋊C4—131no—
118#343—21no—
119#333—264no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#38611yescharacteristic
123C22×C13C2×#10311yescharacteristic
124C22×C13#41611yescharacteristic
125C4×C13—21no—
126C4×C13—24no—
127C4×C13—22no—
128C4×C13—42no—
129C4×C13#45612yes—
130C4×C13#46512yes—
131C4×C13#46712yes—
132Dic13—44no—
133Dic13—82no—
134C22×Q8—132no—
135C22×Q8C22⋊D1311yescharacteristic
136C2×M16—22no—
137C4⋊Q8—262no—
138C4⋊Q8—262no—
139C4×Q8—22no—
140C4×Q8—22no—
141C2×C4⋊C4—261no—
142C2×C4⋊C4—261no—
143C2×C4⋊C4—261no—
144C2×C4⋊C4—264no—
145C2×C4⋊C4C4×D1312yes—
146C2×C4⋊C4C22⋊D1311yescharacteristic
147C2×C42—261no—
148C2×C42D5212yes—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—134no—
153C4⋊C8—264no—
154#101—42no—
155C22⋊C8—262no—
156C4×C8—264no—
157C4×C8—262no—
158#95—132no—
159#95—264no—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13#188611yescharacteristic
163C2×C13#189211yescharacteristic
164C2×C13#191411yescharacteristic
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—264no—
168C2×Q8—1042no—
169C2×Q8#610512yes—
170C2×Q8#610712yes—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4#610312yes—
174C22×C4#610312yes—
175C22×C4C2×C4×D1311yescharacteristic
176C22×C4C2×D5211yescharacteristic
177C22×C4C2×C22⋊D1311yescharacteristic
178M16—42no—
179M16—42no—
180C2×C8—42no—
181C2×C8—264no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—264no—
185C4⋊C4—521no—
186C4⋊C4—521no—
187C4⋊C4—522no—
188C4⋊C4—1044no—
189C42—22no—
190C42—22no—
191C42—522no—
192C42D4×D1312yes—
193C42#612912yes—
194C13#939211yescharacteristic, complemented, Sylow
195C23C2×#610311yescharacteristic
196Q8—24no—
197Q8—24no—
198Q8—1044no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—264no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—524no—
209C2×C4—522no—
210C2×C4#8805014yes—
211C2×C4#8813512yes—
212C2×C4#8813611yescharacteristic
213C2×C4#8814011yescharacteristic
214C2×C4C2×#610511yescharacteristic
215C2×C4#8819312yes—
216C2×C4C2×#610711yescharacteristic
217C2×C4#8820412yes—
218C8—82no—
219C8—524no—
220C22—21no—
221C22—21no—
222C22#1171861911yescharacteristic
223C22C2×#8805011yescharacteristic
224C22#1171866311yescharacteristic
225C4—21no—
226C4—24no—
227C4—22no—
228C4—42no—
229C4—524no—
230C4—1042no—
231C4#1171841312yes—
232C4#1171870212yes—
233C4#1171871212yes—
234C2—21no—
235C2—21no—
236C2#1311522711yescharacteristic
237C2#1311525711yescharacteristic
238C2#1311538111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1801D13
hypocenterC13#9392
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
194. C13#9392semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131200412
#131135182
#131127372
C13×#18012
#939213