Finite Group Databasebeta

← #15760330

Subgroups — #15760330

Order 3328.

486 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 123 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#13123921C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113508C212yesmaximal
4#13112739C212yesmaximal
5C13×#2546C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—21no—
7C2×C13×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C13×#398C414yes—
10C13×#391—21no—
11C13×#389—22no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88076—21no—
14#11718685—24no—
15#11718587—22no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718139—24no—
19#11718122—21no—
20C22×Q8×C13—21no—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—44no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—24no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13D412yes—
35C2×C42×C13C2311yescharacteristic
36C2×#6099—22no—
37C13×#95—24no—
38C13×#95C2×C412yes—
39#88076—42no—
40C22⋊#1055—22no—
41C4⋊#1055—24no—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44C4⋊#1055D414yes—
45#88043—24no—
46C4×#1055—22no—
47#9402—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—21no—
50C2×Q8×C13—22no—
51C2×Q8×C13—21no—
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C13×C4⋊C4—24no—
64C13×C4⋊C4—24no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—48no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13—42no—
73C42×C13C2×D412yes—
74C42×C13#4112yes—
75#6099—42no—
76#6099—42no—
77C2×#1055—24no—
78C2×#1055—42no—
79#2983—131no—
80#2546D1311yescharacteristic
81#1801—131no—
82#1546—132no—
83#1303—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87Q8×C13—82no—
88Q8×C13—82no—
89C2×C4×C13—22no—
90C2×C4×C13—24no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13C4×D412yes—
103C2×C4×C13#12011yescharacteristic
104C2×C4×C13#12112yes—
105C2×C4×C13#12311yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)12yes—
107C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C13#13711yescharacteristic
109#1055—44no—
110#1055—82no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8C2×D1311yescharacteristic
113C2×C4×Q8C2×D1311yescharacteristic
114#446—264no—
115#432—262no—
116#431—132no—
117#423—132no—
118C2×#101—261no—
119#398Dic1314yes—
120#391—21no—
121#389—22no—
122C4×C4⋊C4C2×D1311yescharacteristic
123#343—261no—
124#332—264no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#38611yescharacteristic
128C22×C13#41711yescharacteristic
129C22×C13#41811yescharacteristic
130C4×C13—21no—
131C4×C13—22no—
132C4×C13—44no—
133C4×C13—42no—
134C4×C13—42no—
135C4×C13—82no—
136C4×C13#45612yes—
137C4×C13#46812yes—
138C4×C13#46912yes—
139C22×Q8—21no—
140C22×Q8C22⋊D1311yescharacteristic
141C2×M16—262no—
142C4⋊Q8—22no—
143C4⋊Q8—22no—
144C4⋊Q8—44no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4C2×Dic1312yes—
151C2×C4⋊C4C2×Dic1312yes—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C42—21no—
154C2×C42C22⋊D1312yes—
155C2×C42C22×D1311yescharacteristic
156C4⋊C8—134no—
157C4⋊C8—264no—
158C4⋊C8—262no—
159C4⋊C8—262no—
160#101—522no—
161C22⋊C8—262no—
162#97—264no—
163C4×C8—262no—
164#95—24no—
165#95C2×Dic1312yes—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13#188611yescharacteristic
169C2×C13#189511yescharacteristic
170C2×C13#191511yescharacteristic
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8—41no—
178C2×Q8—41no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C22⋊Dic1312yes—
182C22×C4C22⋊Dic1312yes—
183C22×C4C22×Dic1311yescharacteristic
184C22×C4C2×C22⋊D1311yescharacteristic
185C22×C4C2×C22⋊D1311yescharacteristic
186M16—522no—
187M16—522no—
188C2×C8—264no—
189C2×C8—522no—
190C4⋊C4—24no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—24no—
194C4⋊C4—48no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C42—22no—
198C42—22no—
199C42—42no—
200C42D4×D1312yes—
201C42#612912yes—
202C13#940211yescharacteristic, complemented, Sylow
203C23C2×C22⋊Dic1311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—82no—
207Q8—82no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4#8818612yes—
222C2×C4D4×Dic1312yes—
223C2×C4#8818911yescharacteristic
224C2×C4#8819111yescharacteristic
225C2×C4#8819312yes—
226C2×C4#8820311yescharacteristic
227C2×C4#8820511yescharacteristic
228C8—524no—
229C8—1042no—
230C22—21no—
231C22—21no—
232C22#1171887611yescharacteristic
233C22#1171888111yescharacteristic
234C22#1171889311yescharacteristic
235C4—21no—
236C4—22no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4#1171870012yes—
242C4#1171870312yes—
243C4#1171875612yes—
244C2—21no—
245C2—21no—
246C2#1311523011yescharacteristic
247C2#1311527511yescharacteristic
248C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2546C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2546D13
hypocenterC13#9402
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
202. C13#9402semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131148322
#131135082
#131127392
C13×#25462
#940213