Finite Group Databasebeta

← #15767923

Subgroups — #15767923

Order 3328.

334 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115668C211yesmaximal, characteristic
2#13114956C211yesmaximal, characteristic, complemented
3#13113611C211yesmaximal, characteristic, complemented
4#13113607C211yesmaximal, characteristic, complemented
5#13113236C211yesmaximal, characteristic
6#13113236C211yesmaximal, characteristic
7C13×#1274C211yesmaximal, characteristic, complemented
8#11719182C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#376C2211yescharacteristic
12C2×#88045—22no—
13#11718585C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16#11718116—22no—
17#11718051—22no—
18#11718051—22no—
19#11718050—22no—
20#11718049—22no—
21C2×#6127—21no—
22C2×C42×C13D412yes—
23C2×C42×C13C2311yescharacteristic
24#88184—21no—
25#88184—21no—
26C2×#6099—21no—
27C22×#1055—21no—
28C22×#1055—21no—
29#88129—21no—
30#88128Q811yescharacteristic
31C4×D52—21no—
32C4×D52—21no—
33#88123Q811yescharacteristic
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C22⋊C8—21no—
37C13×C22⋊C8—21no—
38C4×C8×C13D412yes—
39C4×C8×C13D412yes—
40C13×#95—21no—
41C13×#95—21no—
42#88045—44no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49#10665—131nomaximal, Sylow
50C22×C4×C13—22no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×C4×C13#4111yescharacteristic
54C2×C22⋊D13—41no—
55#6127—42no—
56#6127—42no—
57C2×D52—21no—
58C2×D52—21no—
59C2×D52—21no—
60C2×C4×D13—41no—
61C2×Dic26—21no—
62C2×C8×C13—22no—
63C2×C8×C13—22no—
64C42×C13—22no—
65C42×C13—22no—
66C42×C13C2×D411yescharacteristic
67C42×C13C2×D411yescharacteristic
68C42×C13C2×Q811yescharacteristic
69C42×C13#4111yescharacteristic
70#6103—41no—
71#6103—41no—
72C4⋊Dic13—21no—
73C4⋊Dic13—21no—
74#6099—42no—
75C2×#1055—41no—
76C2×#1055—41no—
77C2×#1055—41no—
78C2×#1055—42no—
79C2×#1055—42no—
80#1963—131no—
81#1832—131no—
82#1571—131no—
83#1570—131no—
84#1480—131no—
85#1480—131no—
86#1274D1311yescharacteristic, complemented
87C23×C13#12311yescharacteristic
88C22×D13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13C22⋊Q811yescharacteristic
95C2×C4×C13C22⋊Q811yescharacteristic
96C2×C4×C13C22⋊Q811yescharacteristic
97C2×C4×C13#12311yescharacteristic
98C2×C4×C13#12311yescharacteristic
99C2×C4×C13#12711yescharacteristic
100C2×C4×C13#13512yes—
101C2×C4×C13AGL(1,ℤ/8)12yes—
102C22⋊D13—82no—
103C2×Dic13—41no—
104D52—42no—
105D52—42no—
106D52—42no—
107C4×D13—81no—
108C4×D13—81no—
109Dic26—42no—
110C8×C13—42no—
111C8×C13—42no—
112#1055—81no—
113#1055—81no—
114#1055—81no—
115#532—131no—
116#431C2×D1311yescharacteristic
117#431C2×D1311yescharacteristic
118#423—131no—
119C2×C4⋊C8—131no—
120C2×C4⋊C8—131no—
121C2×#104—262no—
122#376C2×D1311yescharacteristic
123#336—262no—
124#335—262no—
125#334—262no—
126D4⋊C8—262no—
127D4⋊C8—262no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#39911yescharacteristic
131C22×C13#48212yes—
132C2×D13—81no—
133C2×D13—81no—
134C2×D13—81no—
135C4×C13—21no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—82no—
140C4×C13#47812yes—
141C4×C13#49511yescharacteristic
142C4×C13#49611yescharacteristic
143Dic13—81no—
144C2×#41—261no—
145C2×M16—261no—
146C22×C8—261no—
147C22×C8—261no—
148C4⋊Q8—131no—
149#127—131no—
150#124—261no—
151#121—261no—
152#121—261no—
153C4×D4—261no—
154C4×D4—261no—
155C2×C42D5212yes—
156C2×C42C22×D1311yescharacteristic
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—261no—
160C4⋊C8—261no—
161C4⋊C8—261no—
162C4⋊C8—261no—
163C4⋊C8—261no—
164C4⋊C8—261no—
165#104—524no—
166C22⋊C8—21no—
167C22⋊C8—21no—
168C4×C8D5212yes—
169C4×C8D5212yes—
170#95—21no—
171#95—21no—
172C2×C13—22no—
173C2×C13#209211yescharacteristic
174C2×C13#209811yescharacteristic
175C2×C13#209811yescharacteristic
176D13—161no—
177#41—522no—
178#41—522no—
179C2×Q8—261no—
180C2×D4—261no—
181C2×D4—261no—
182C2×D4—261no—
183C2×D4—521no—
184C22×C4—22no—
185C22×C4—521no—
186C22×C4C2×D5211yescharacteristic
187C22×C4#612911yescharacteristic
188C22×C4#612911yescharacteristic
189M16—522no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—521no—
193C2×C8—521no—
194C2×C8—521no—
195C2×C8—522no—
196C2×C8—522no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C22⋊C4—521no—
200C22⋊C4—521no—
201C42—22no—
202C42—22no—
203C42C2×D5211yescharacteristic
204C42C2×D5211yescharacteristic
205C42#612911yescharacteristic
206C42Q8×D1311yescharacteristic
207C13#1066511yescharacteristic, complemented, Sylow
208C23—521no—
209C23#8814011yescharacteristic
210Q8—522no—
211D4—522no—
212D4—522no—
213D4—522no—
214D4—1042no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—521no—
221C2×C4—1041no—
222C2×C4—1041no—
223C2×C4#8812811yescharacteristic
224C2×C4#8814011yescharacteristic
225C2×C4#8814011yescharacteristic
226C2×C4#8815111yescharacteristic
227C2×C4#8815111yescharacteristic
228C2×C4#8815111yescharacteristic
229C2×C4#8815812yes—
230C2×C4#8816212yes—
231C8—42no—
232C8—42no—
233C8—1041no—
234C8—1041no—
235C8—1041no—
236C22—21no—
237C22—21no—
238C22—1041no—
239C22—1041no—
240C22—1041no—
241C22#1171833811yescharacteristic
242C22#1171839812yes—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—82no—
248C4—1041no—
249C4#1171835711yescharacteristic
250C4#1171837311yescharacteristic
251C4#1171850812yes—
252C2—22no—
253C2—2081no—
254C2#1311635611yescharacteristic
255C2#1311639011yescharacteristic
256C2#1311639011yescharacteristic
subgroupG/H
centerC2×C4#88128
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1274C2
socleC22×C13#399
prime radical#11719182C22
hypercenter#1274D13
hypocenterC13#10665
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #13114956C2semidirect
3. #13113611C2semidirect
4. #13113607C2semidirect
7. C13×#1274C2semidirect
86. #1274D13semidirect
207. C13#10665semidirect

Maximal subgroups

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

subgroupindex
#131156682
#131149562
#131136112
#131136072
#131132362
C13×#12742
#1066513