Finite Group Databasebeta

← #15776643

Subgroups — #15776643

Order 3328.

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

normal subgroups only

This group has 296 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#13127701C211yesmaximal, characteristic
2#13117063C211yesmaximal, characteristic, complemented
3#13114203C211yesmaximal, characteristic, complemented
4#13112893C211yesmaximal, characteristic, complemented
5#13112814C211yesmaximal, characteristic, complemented
6#13112797C211yesmaximal, characteristic
7C13×#2208C211yesmaximal, characteristic
8#11719248—21no—
9C2×C13×SD32—21no—
10C13×#494C2211yescharacteristic
11C4×C13×D8C2211yescharacteristic
12D8×Dic13—21no—
13#11718755—21no—
14#11718669—21no—
15#11718539—21no—
16#11718427—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×D8D411yescharacteristic
28C13×C4⋊Q8—21no—
29C4×D4×C13—21no—
30D4×Dic13—22no—
31C2×C4⋊Dic13—41no—
32#88178—41no—
33#88144—22no—
34#88132—42no—
35#88123—21no—
36C4×Dic26D411yescharacteristic
37C13×SD32—42no—
38C2×C13×C16—21no—
39C13×#107D411yescharacteristic
40C13×#102—21no—
41C4×C8×C13C2311yescharacteristic
42#88072—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#12359—131nomaximal, Sylow
54C2×Q8×C13—41no—
55C2×D4×C13—21no—
56C22×C4×C13—41no—
57C22×Dic13—42no—
58C2×Dic26—41no—
59C2×Dic26D811yescharacteristic
60C13×Q16—42no—
61C13×Q16—41no—
62C13×Q16—41no—
63C13×D8—21no—
64C13×D8SD1612yes—
65C2×C8×C13C2×D411yescharacteristic
66C2×C8×C13C2×D411yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C22⋊C4—41no—
71C42×C13C2×D411yescharacteristic
72C22⋊Dic13—42no—
73C4⋊Dic13—22no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76C4⋊Dic13D811yescharacteristic
77#6101—21no—
78#6101—42no—
79C4×Dic13—21no—
80C2×#1055—21no—
81C2×#1055—41no—
82C13×C16—41no—
83#6090—41no—
84#3380—131no—
85#2241—131no—
86#2208D1311yescharacteristic
87#1670—131no—
88#1365—131no—
89Q8⋊C16—131no—
90#1331—131no—
91C23×C13—41no—
92Q8×C13—81no—
93Q8×C13—81no—
94D4×C13—22no—
95D4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—81no—
98C2×C4×C13—81no—
99C2×C4×C13—81no—
100C2×C4×C13#12011yescharacteristic
101C2×C4×C13C2×D811yescharacteristic
102C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—42no—
106C2×Dic13—162no—
107Dic26—21no—
108Dic26—21no—
109Dic26—161no—
110C8×C13—21no—
111C8×C13C2×SD1611yescharacteristic
112C8×C13#13711yescharacteristic
113#1055—41no—
114#1055—81no—
115#554—261no—
116C2×SD32—21no—
117#500—131no—
118#499—261no—
119#494C2×D1311yescharacteristic
120#478—262no—
121#476—261no—
122#475—261no—
123C8×Q8—131no—
124C4×D8—261no—
125C4×D8C2×D1311yescharacteristic
126C4⋊C16C2×D1311yescharacteristic
127#358—21no—
128#358—262no—
129C4×C16—131no—
130#335—131no—
131#332—261no—
132C22×C13—42no—
133C22×C13—81no—
134C22×C13—81no—
135C22×C13#44711yescharacteristic
136C4×C13—21no—
137C4×C13—81no—
138C4×C13—161no—
139C4×C13#44811yescharacteristic
140C4×C13#45411yescharacteristic
141C4×C13#50811yescharacteristic
142C4×C13#51011yescharacteristic
143Dic13—41no—
144Dic13—41no—
145Dic13—82no—
146C2×Q16—21no—
147C2×Q16—21no—
148C2×D8C22⋊D1311yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—261no—
151#125—262no—
152C22⋊Q8—522no—
153C22⋊Q8—521no—
154C4×Q8—131no—
155C4×D4—21no—
156C4×D4—262no—
157C2×C4⋊C4—521no—
158SD32—42no—
159C2×C16—21no—
160C2×C16—261no—
161#107—132no—
162#107—261no—
163#107C22⋊D1311yescharacteristic
164#106—262no—
165#106—521no—
166C4⋊C8—131no—
167C4⋊C8—261no—
168C4⋊C8—261no—
169#103—521no—
170#102—21no—
171#102—262no—
172C4×C8—261no—
173C4×C8C22×D1311yescharacteristic
174C2×C13—82no—
175C2×C13#162711yescharacteristic
176C2×C13#218911yescharacteristic
177C2×C13#219411yescharacteristic
178C2×Q8—41no—
179C2×Q8—131no—
180C2×Q8—521no—
181C2×D4—21no—
182C22×C4—41no—
183C22×C4—522no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187D8—21no—
188D8#610512yes—
189C2×C8—261no—
190C2×C8—521no—
191C2×C8D4×D1311yescharacteristic
192C2×C8C2×C22⋊D1311yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—131no—
197C4⋊C4—261no—
198C4⋊C4—262no—
199C4⋊C4—522no—
200C4⋊C4—522no—
201C4⋊C4—521no—
202C22⋊C4—41no—
203C22⋊C4—522no—
204C42—261no—
205C42D4×D1311yescharacteristic
206C16—41no—
207C16—521no—
208C13#1235911yescharacteristic, complemented, Sylow
209C23—41no—
210Q8—81no—
211Q8—81no—
212Q8—261no—
213Q8—261no—
214Q8—2081no—
215D4—22no—
216D4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—522no—
224C2×C4—2082no—
225C2×C4D8×D1311yescharacteristic
226C2×C4#8816511yescharacteristic
227C2×C4#8819111yescharacteristic
228C8—21no—
229C8—521no—
230C8—1041no—
231C8C2×#610511yescharacteristic
232C8#8820511yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1171881711yescharacteristic
237C4—21no—
238C4—81no—
239C4—161no—
240C4—521no—
241C4—521no—
242C4—1042no—
243C4#1171857611yescharacteristic
244C4#1171857711yescharacteristic
245C4#1171870111yescharacteristic
246C4#1171886211yescharacteristic
247C2—82no—
248C2#1311393811yescharacteristic
249C2#1311677311yescharacteristic
250C2#1311680411yescharacteristic
subgroupG/H
centerC22#11718817
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2208C2
socleC22×C13#447
prime radicalC2×C13×D8D4
hypercenter#2208D13
hypocenterC13#12359
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #13117063C2semidirect
3. #13114203C2semidirect
4. #13112893C2semidirect
5. #13112814C2semidirect
208. C13#12359semidirect

Maximal subgroups

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

subgroupindex
#131277012
#131170632
#131142032
#131128932
#131128142
#131127972
C13×#22082
#1235913