Finite Group Databasebeta

← #15760280

Subgroups — #15760280

Order 3328.

486 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 139 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#13114832C211yesmaximal, characteristic
3#13113517C212yesmaximal
4#13112739C212yesmaximal
5C13×#2567C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#395C414yes—
9C13×#391—21no—
10C13×#389—22no—
11C13×#384—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88076—21no—
14Q8×#1055—24no—
15#11718586—22no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718138—24no—
19#11718122—21no—
20C22×Q8×C13C2×C412yes—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—24no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13D412yes—
34C2×C42×C13C2311yescharacteristic
35C2×#6099—22no—
36C13×#95—24no—
37C13×#95C2×C412yes—
38#88076—42no—
39C22⋊#1055—22no—
40C4⋊#1055—24no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055D414yes—
44C4×#1055—24no—
45C4×#1055—22no—
46#9392—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13—24no—
50C2×Q8×C13—82no—
51C2×Q8×C13SD1612yes—
52C2×Q8×C13Q1612yes—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C13×C4⋊C4—24no—
61C13×C4⋊C4—24no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—84no—
67C42×C13—22no—
68C42×C13—22no—
69C42×C13—42no—
70C42×C13C2×D412yes—
71C42×C13#4112yes—
72#6099—42no—
73#6099—42no—
74C2×#1055—24no—
75C2×#1055—42no—
76#2982—131no—
77#2567D1311yescharacteristic
78#1801—131no—
79#1548—132no—
80#1303—132no—
81C23×C13C2×C22⋊C411yescharacteristic
82Q8×C13—24no—
83Q8×C13—24no—
84Q8×C13—84no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—24no—
89C2×C4×C13—22no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—44no—
95C2×C4×C13—42no—
96C2×C4×C13#10314yes—
97C2×C4×C13C4×D412yes—
98C2×C4×C13#12011yescharacteristic
99C2×C4×C13#12112yes—
100C2×C4×C13#12311yescharacteristic
101C2×C4×C13C2×SD1611yescharacteristic
102C2×C4×C13C2×Q1611yescharacteristic
103C2×C4×C13#13512yes—
104#1055—44no—
105#1055—82no—
106C2×C4⋊Q8C2×D1311yescharacteristic
107C2×C4×Q8C2×D1311yescharacteristic
108C8×Q8—264no—
109#431—132no—
110#431—262no—
111#423—132no—
112C2×#101—261no—
113#395Dic1314yes—
114#391—21no—
115#389—22no—
116#384—21no—
117C4×C4⋊C4C2×D1311yescharacteristic
118#343—261no—
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—44no—
129C4×C13—42no—
130C4×C13—82no—
131C4×C13#45612yes—
132C4×C13#46512yes—
133C4×C13#46712yes—
134C22×Q8C2×Dic1312yes—
135C22×Q8C22⋊D1311yescharacteristic
136C2×M16—262no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4C2×Dic1312yes—
146C2×C4⋊C4C22⋊D1311yescharacteristic
147C2×C42—21no—
148C2×C42C22⋊D1312yes—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—134no—
151C4⋊C8—264no—
152C4⋊C8—262no—
153C4⋊C8—262no—
154#101—522no—
155C22⋊C8—262no—
156C4×C8—264no—
157C4×C8—262no—
158#95—24no—
159#95C2×Dic1312yes—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13#188611yescharacteristic
163C2×C13#189211yescharacteristic
164C2×C13#191411yescharacteristic
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—24no—
168C2×Q8—82no—
169C2×Q8#610612yes—
170C2×Q8#610712yes—
171C22×C4—22no—
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—264no—
181C2×C8—522no—
182C4⋊C4—24no—
183C4⋊C4—24no—
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—84no—
189C42—22no—
190C42—22no—
191C42—42no—
192C42D4×D1312yes—
193C42#612912yes—
194C13#939211yescharacteristic, complemented, Sylow
195C23C2×C22⋊Dic1311yescharacteristic
196Q8—24no—
197Q8—24no—
198Q8—84no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4#8807514yes—
211C2×C4D4×Dic1312yes—
212C2×C4#8818911yescharacteristic
213C2×C4#8819111yescharacteristic
214C2×C4#8819312yes—
215C2×C4C2×#610611yescharacteristic
216C2×C4C2×#610711yescharacteristic
217C2×C4#8820412yes—
218C8—524no—
219C8—1042no—
220C22—21no—
221C22—21no—
222C22#1171888111yescharacteristic
223C22C2×#8807511yescharacteristic
224C22#1171889411yescharacteristic
225C4—21no—
226C4—24no—
227C4—22no—
228C4—44no—
229C4—42no—
230C4—82no—
231C4#1171870912yes—
232C4#1171871212yes—
233C4#1171875612yes—
234C2—21no—
235C2—21no—
236C2#1311523011yescharacteristic
237C2#1311526011yescharacteristic
238C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2567C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2567D13
hypocenterC13#9392
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

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
#131148322
#131135172
#131127392
C13×#25672
#939213