Finite Group Databasebeta

← #15776629

Subgroups — #15776629

Order 3328.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#13127725C211yesmaximal, characteristic
2#13117063C211yesmaximal, characteristic
3#13114203C211yesmaximal, characteristic
4#13112890C211yesmaximal, characteristic
5#13112814C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#2209C211yesmaximal, characteristic
8#11719275—21no—
9C2×C13×Q32—21no—
10C13×#494C2211yescharacteristic
11C4×C13×Q16C2211yescharacteristic
12Q16×Dic13—21no—
13#11718755—21no—
14#11718681—21no—
15#11718539—21no—
16#11718457—22no—
17#11718343C2211yescharacteristic
18C8×Dic26C2211yescharacteristic
19C13×C4⋊C16C2211yescharacteristic
20C13×#358—21no—
21#11718156—22no—
22#11718139—21no—
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16—21no—
26C2×C13×Q16—21no—
27C2×C13×Q16D411yescharacteristic
28C13×C4⋊Q8—21no—
29C4×Q8×C13—21no—
30Q8×Dic13—22no—
31#88144—22no—
32#88144—42no—
33#88123—21no—
34#88123—41no—
35C4×Dic26—41no—
36C4×Dic26D411yescharacteristic
37C13×Q32—42no—
38C2×C13×C16—21no—
39C13×#107D411yescharacteristic
40C13×#103—21no—
41C4×C8×C13C2311yescharacteristic
42#88075—22no—
43#88058—21no—
44#88058D412yes—
45#88054—21no—
46C8×Dic13—21no—
47C2×#6090—21no—
48#88050—41no—
49#88048—22no—
50#88048—41no—
51C4⋊#1055—21no—
52C4⋊#1055D411yescharacteristic
53#12357—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—41no—
56C2×Dic26—41no—
57C2×Dic26D811yescharacteristic
58C13×Q16—21no—
59C13×Q16—42no—
60C13×Q16—41no—
61C13×Q16—41no—
62C13×Q16SD1612yes—
63C2×C8×C13C2×D411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
65C13×C4⋊C4—21no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C42×C13—41no—
70C42×C13C2×D411yescharacteristic
71C4⋊Dic13—22no—
72C4⋊Dic13—42no—
73C4⋊Dic13—42no—
74C4⋊Dic13—41no—
75C4⋊Dic13D811yescharacteristic
76#6101—21no—
77#6101—42no—
78C4×Dic13—21no—
79C4×Dic13—42no—
80C2×#1055—21no—
81C2×#1055—41no—
82C13×C16—41no—
83#6090—41no—
84#3383—131no—
85#2241—131no—
86#2209D1311yescharacteristic
87#1670—131no—
88#1364—131no—
89Q8⋊C16—131no—
90#1332—131no—
91Q8×C13—22no—
92Q8×C13—41no—
93Q8×C13—81no—
94Q8×C13—81no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—81no—
98C2×C4×C13#12011yescharacteristic
99C2×C4×C13C2×D811yescharacteristic
100C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—42no—
104Dic26—21no—
105Dic26—21no—
106Dic26—81no—
107Dic26—81no—
108C8×C13—21no—
109C8×C13C2×SD1611yescharacteristic
110C8×C13#13711yescharacteristic
111#1055—41no—
112#1055—81no—
113#557—261no—
114C2×Q32—21no—
115#500—131no—
116#499—261no—
117#494C2×D1311yescharacteristic
118#479—262no—
119#475—261no—
120#475—261no—
121C8×Q8—131no—
122C4×Q16—261no—
123C4×Q16C2×D1311yescharacteristic
124C4⋊C16C2×D1311yescharacteristic
125#358—21no—
126#358—262no—
127C4×C16—131no—
128#335—131no—
129#332—261no—
130C22×C13#44711yescharacteristic
131C4×C13—21no—
132C4×C13—42no—
133C4×C13—81no—
134C4×C13—161no—
135C4×C13#44811yescharacteristic
136C4×C13#45411yescharacteristic
137C4×C13#50811yescharacteristic
138C4×C13#51011yescharacteristic
139Dic13—41no—
140Dic13—41no—
141Dic13—82no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×Q16C22⋊D1311yescharacteristic
145C4⋊Q8—21no—
146C4⋊Q8—261no—
147C4⋊Q8—521no—
148#125—262no—
149#125—522no—
150C4×Q8—21no—
151C4×Q8—131no—
152C4×Q8—262no—
153C4×Q8—521no—
154Q32—42no—
155C2×C16—21no—
156C2×C16—261no—
157#107—132no—
158#107—261no—
159#107C22⋊D1311yescharacteristic
160#106—262no—
161#106—521no—
162C4⋊C8—131no—
163C4⋊C8—261no—
164C4⋊C8—261no—
165#103—21no—
166#103—262no—
167#103—521no—
168C4×C8—261no—
169C4×C8C22×D1311yescharacteristic
170C2×C13#162711yescharacteristic
171C2×C13#218911yescharacteristic
172C2×C13#219511yescharacteristic
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—131no—
176C2×Q8—521no—
177Q16—21no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16#610512yes—
182C2×C8—261no—
183C2×C8—521no—
184C2×C8D4×D1311yescharacteristic
185C2×C8C2×C22⋊D1311yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—131no—
191C4⋊C4—261no—
192C4⋊C4—262no—
193C4⋊C4—522no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C4⋊C4—521no—
197C42—41no—
198C42—261no—
199C42—522no—
200C42D4×D1311yescharacteristic
201C16—41no—
202C16—521no—
203C13#1235711yescharacteristic, complemented, Sylow
204Q8—22no—
205Q8—41no—
206Q8—81no—
207Q8—81no—
208Q8—261no—
209Q8—261no—
210Q8—1041no—
211Q8—1041no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—522no—
218C2×C4D8×D1311yescharacteristic
219C2×C4#8816511yescharacteristic
220C2×C4#8819111yescharacteristic
221C8—21no—
222C8—521no—
223C8—1041no—
224C8C2×#610511yescharacteristic
225C8#8820511yescharacteristic
226C22#1171881711yescharacteristic
227C4—21no—
228C4—42no—
229C4—81no—
230C4—161no—
231C4—521no—
232C4—521no—
233C4—1042no—
234C4#1171857911yescharacteristic
235C4#1171858011yescharacteristic
236C4#1171870111yescharacteristic
237C4#1171886211yescharacteristic
238C2#1311393811yescharacteristic
239C2#1311677511yescharacteristic
240C2#1311681111yescharacteristic
subgroupG/H
centerC22#11718817
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2209C2
socle, prime radicalC22×C13#447
hypercenter#2209D13
hypocenterC13#12357
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
203. C13#12357semidirect

Maximal subgroups

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

subgroupindex
#131277252
#131170632
#131142032
#131128902
#131128142
#131128002
C13×#22092
#1235713