Finite Group Databasebeta

← #15765198

Subgroups — #15765198

Order 3328.

574 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125957C212yesmaximal, complemented
2#13125282C211yesmaximal, characteristic
3#13113395C212yesmaximal, complemented
4#13112681C211yesmaximal, characteristic, complemented
5C13×#1960C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×#88158—22no—
8#11719182C2212yes—
9C2×C13×#103—22no—
10C2×C13×#97C2211yescharacteristic
11C13×#382C2211yescharacteristic
12#11718749—22no—
13#11718748—24no—
14#11718739—22no—
15#11718628—24no—
16#11718586C2212yes—
17#11718376—22no—
18#11718373—22no—
19#11718043—24no—
20C22×Q8×C13—21no—
21C2×#6127—22no—
22C22×C8×C13D412yes—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—21no—
25C13×C4⋊Q8D412yes—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C42×C13C2311yescharacteristic
29#88184—22no—
30#88184—22no—
31C2×Dic52—22no—
32#88158—44no—
33#88158—44no—
34C2×D104—22no—
35C2×#6095—24no—
36#88129—22no—
37#88128D412yes—
38C4×D52—22no—
39C4×D52—22no—
40#88123D412yes—
41C13×#103—44no—
42C13×#97—22no—
43C13×#95—22no—
44C22⋊#1055D414yes—
45#88049—28no—
46#88047—28no—
47C4⋊#1055—22no—
48C4×#1055—22no—
49#10225—131nomaximal, Sylow
50C2×Q8×C13—22no—
51C2×Q8×C13—41no—
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C2×C22⋊D13—42no—
59#6127—44no—
60#6127—44no—
61C2×D52—22no—
62C2×D52—22no—
63C2×D52—22no—
64C2×C4×D13—42no—
65C2×Dic26—22no—
66C2×C8×C13—22no—
67C2×C8×C13—22no—
68C2×C8×C13D814yes—
69C13×C4⋊C4—24no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C42×C13C2×D411yescharacteristic
73C42×C13C2×D412yes—
74C42×C13#4111yescharacteristic
75#6103—42no—
76#6103—42no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79C2×#1055—24no—
80Dic52—44no—
81D104—44no—
82#6095—48no—
83#3226—132no—
84#3150—131no—
85#1960D1311yescharacteristic, complemented
86#1517—132no—
87#1281—131no—
88C23×C13#12711yescharacteristic
89C22×D13—42no—
90Q8×C13—44no—
91Q8×C13—82no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—81no—
95C2×C4×C13—81no—
96C2×C4×C13—82no—
97C2×C4×C13—81no—
98C2×C4×C13#12012yes—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13#12112yes—
101C2×C4×C13#12111yescharacteristic
102C2×C4×C13C2×D812yes—
103C2×C4×C13AGL(1,ℤ/8)12yes—
104C22⋊D13—82no—
105C22⋊D13—82no—
106C2×Dic13—42no—
107D52—44no—
108D52—44no—
109D52—82no—
110C4×D13—84no—
111Dic26—44no—
112C8×C13—24no—
113#1055—44no—
114C2×#135—262no—
115#532—132no—
116C2×C4⋊Q8C2×D1311yescharacteristic
117#500—262no—
118#497—262no—
119#496—262no—
120#486—262no—
121#480—264no—
122#474—264no—
123#431—132no—
124C2×#103—22no—
125C2×#97C2×D1311yescharacteristic
126#382C2×D1311yescharacteristic
127#327—264no—
128C22×C13—22no—
129C22×C13#39211yescharacteristic
130C22×C13#49311yescharacteristic
131C22×C13#49611yescharacteristic
132C2×D13—82no—
133C2×D13—82no—
134C2×D13—82no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—82no—
138C4×C13—161no—
139C4×C13#44712yes—
140C4×C13#45912yes—
141Dic13—82no—
142C2×#41—262no—
143C22×Q8—21no—
144#135—524no—
145#135—524no—
146C2×Q16—262no—
147C2×SD16—264no—
148C2×D8—262no—
149C22×C8C22⋊D1312yes—
150C4⋊Q8—21no—
151C4⋊Q8—22no—
152C4⋊Q8—132no—
153C4⋊Q8D5212yes—
154#127—132no—
155#124—262no—
156#121—262no—
157#121—262no—
158C4×D4—262no—
159C4×D4—262no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C42C22×D1311yescharacteristic
163#107—268no—
164C4⋊C8—262no—
165#103—44no—
166#102—268no—
167C22⋊C8—134no—
168#97—22no—
169C4×C8—262no—
170#95—22no—
171C2×C13—21no—
172C2×C13—21no—
173C2×C13#200912yes—
174C2×C13#201111yescharacteristic
175D13—162no—
176#41—524no—
177#41—524no—
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—262no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4—522no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—522no—
190C22×C4D4×D1312yes—
191C22×C4C2×C22⋊D1311yescharacteristic
192Q16—524no—
193SD16—528no—
194D8—524no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—264no—
198C2×C8#610414yes—
199C4⋊C4—24no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—262no—
203C4⋊C4—262no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C42C2×D5211yescharacteristic
207C42#612711yescharacteristic
208C42D4×D1312yes—
209C13#1022511yescharacteristic, complemented, Sylow
210C23—522no—
211C23#8819411yescharacteristic
212Q8—44no—
213Q8—82no—
214Q8—524no—
215D4—524no—
216D4—524no—
217D4—1042no—
218D4—1042no—
219D4—1042no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—522no—
227C2×C4—1044no—
228C2×C4#8813612yes—
229C2×C4#8813812yes—
230C2×C4#8818411yescharacteristic
231C2×C4C2×#610412yes—
232C2×C4#8819111yescharacteristic
233C2×C4#8820312yes—
234C8—24no—
235C8—524no—
236C22—22no—
237C22—1042no—
238C22—1042no—
239C22—1042no—
240C22#1171862111yescharacteristic
241C22#1171871911yescharacteristic
242C22#1171873411yescharacteristic
243C4—22no—
244C4—22no—
245C4—82no—
246C4—161no—
247C4—1042no—
248C4#1171867612yes—
249C4#1171869712yes—
250C2—21no—
251C2—21no—
252C2—2082no—
253C2#1311589812yes—
254C2#1311590611yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1960C2
socleC22×C13#392
prime radical#13125282C2
hypercenter#1960D13
hypocenterC13#10225
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
1. #13125957C2semidirect
3. #13113395C2semidirect
4. #13112681C2semidirect
5. C13×#1960C2semidirect
85. #1960D13semidirect
209. C13#10225semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131252822
#131133952
#131126812
C13×#19602
#1022513