Finite Group Databasebeta

← #15756500

Subgroups — #15756500

Order 3328.

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

normal subgroups only

This group has 422 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#13114832C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112739C212yesmaximal
4#13112694C212yesmaximal
5C13×#2351C211yesmaximal, characteristic
6C2×C4×Q8×C13—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#389—21no—
9C13×#389—22no—
10C13×#382C412yes—
11C13×#382C2211yescharacteristic
12C4×C13×C4⋊C4C412yes—
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88076—21no—
15#11718586C2212yes—
16#11718585C2212yes—
17#11718122—21no—
18#11718120—22no—
19C22×Q8×C13D411yescharacteristic
20C4×Q8×C13—22no—
21C4×Q8×C13—22no—
22C4×Q8×C13—44no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C42×C13—22no—
30C2×C42×C13—21no—
31C2×C42×C13C2×C412yes—
32C2×C42×C13C2311yescharacteristic
33C2×#6099—22no—
34C13×#95—22no—
35C13×#95—21no—
36C13×#95C2×C411yescharacteristic
37C13×#95C2×C412yes—
38C13×#95C2×C411yescharacteristic
39#88076—42no—
40C22⋊#1055—22no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44C4×#1055—22no—
45#8767—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C2×Q8×C13—22no—
48C2×Q8×C13SD1612yes—
49C2×Q8×C13Q1612yes—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—22no—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C13×C4⋊C4—24no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—44no—
62C13×C4⋊C4—44no—
63C13×C4⋊C4—42no—
64C42×C13—22no—
65C42×C13—22no—
66C42×C13—44no—
67C42×C13—42no—
68C42×C13#4112yes—
69C42×C13#4112yes—
70#6099—42no—
71#6099—42no—
72C2×#1055—42no—
73C2×#1055—42no—
74#2351D1311yescharacteristic
75#1801—131no—
76#1461—131no—
77#1303—132no—
78#1286—132no—
79C23×C13C2×C22⋊C411yescharacteristic
80Q8×C13—24no—
81Q8×C13—24no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13#10314yes—
98C2×C4×C13#11711yescharacteristic
99C2×C4×C13#11711yescharacteristic
100C2×C4×C13#12312yes—
101C2×C4×C13#12312yes—
102C2×C4×C13C2×SD1611yescharacteristic
103C2×C4×C13C2×Q1611yescharacteristic
104C2×C4×C13AGL(1,ℤ/8)12yes—
105#1055—82no—
106#1055—82no—
107C2×C4×Q8—21no—
108C2×C4×Q8C2×D1311yescharacteristic
109#431—132no—
110#423—132no—
111C2×#101—261no—
112#389—21no—
113#389—22no—
114#382Dic1312yes—
115#382C2×D1311yescharacteristic
116C4×C4⋊C4Dic1312yes—
117C4×C4⋊C4C2×D1311yescharacteristic
118#343—261no—
119#324—262no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#38111yescharacteristic
123C22×C13C2×#10311yescharacteristic
124C22×C13#41811yescharacteristic
125C4×C13—24no—
126C4×C13—22no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—42no—
131C4×C13—82no—
132C4×C13—81no—
133C4×C13#48112yes—
134C4×C13#48412yes—
135C22×Q8C22⋊D1311yescharacteristic
136C2×M16—262no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—44no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4C22⋊D1312yes—
145C2×C4⋊C4C22⋊D1311yescharacteristic
146C2×C42—22no—
147C2×C42—21no—
148C2×C42C2×Dic1312yes—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—262no—
151C4⋊C8—262no—
152C4⋊C8—262no—
153#101—522no—
154C22⋊C8—262no—
155C4×C8—262no—
156#95—22no—
157#95—21no—
158#95C2×Dic1311yescharacteristic
159#95C2×Dic1312yes—
160#95C2×Dic1311yescharacteristic
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#182411yescharacteristic
164C2×C13#182711yescharacteristic
165C2×C13#183011yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8#610612yes—
169C2×Q8#610712yes—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4C22⋊Dic1312yes—
174C22×C4C22⋊Dic1312yes—
175C22×C4C22×Dic1311yescharacteristic
176C22×C4C2×C22⋊D1311yescharacteristic
177C22×C4C2×C22⋊D1311yescharacteristic
178M16—522no—
179M16—522no—
180C2×C8—522no—
181C2×C8—522no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—44no—
185C4⋊C4—42no—
186C4⋊C4—44no—
187C4⋊C4—42no—
188C42—22no—
189C42—22no—
190C42—44no—
191C42—42no—
192C42#612712yes—
193C42#612712yes—
194C13#876711yescharacteristic, complemented, Sylow
195C23C2×C22⋊Dic1311yescharacteristic
196Q8—24no—
197Q8—24no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4#8807514yes—
214C2×C4#8818011yescharacteristic
215C2×C4#8818011yescharacteristic
216C2×C4#8818312yes—
217C2×C4#8818312yes—
218C2×C4#8818612yes—
219C2×C4C2×#610611yescharacteristic
220C2×C4C2×#610711yescharacteristic
221C8—1042no—
222C8—1042no—
223C22—21no—
224C22—21no—
225C22#1171887211yescharacteristic
226C22#1171887611yescharacteristic
227C22C2×#8807511yescharacteristic
228C4—24no—
229C4—22no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—42no—
234C4—82no—
235C4—81no—
236C4#1171862912yes—
237C4#1171863112yes—
238C2—21no—
239C2—21no—
240C2#1311492611yescharacteristic
241C2#1311494011yescharacteristic
242C2#1311495011yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2351C2
socleC22×C13#381
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2351D13
hypocenterC13#8767
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2351

Complements

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

NH ≅ G/Ntype
194. C13#8767semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131127392
#131126942
C13×#23512
#876713