Finite Group Databasebeta

← #15760761

Subgroups — #15760761

Order 3328.

474 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 127 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#13123917C211yesmaximal, characteristic
2#13120198C211yesmaximal, characteristic
3#13113264C212yesmaximal
4#13112696C212yesmaximal
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#423C2212yes—
9C2×C13×#101—21no—
10#11718891—21no—
11Q8×#1055—24no—
12#11718647C412yes—
13#11718640C412yes—
14#11718634—21no—
15#11718597C2211yescharacteristic
16#11718594—22no—
17#11718586—22no—
18#11718586C2212yes—
19C13×#343—21no—
20#11718076—24no—
21C22×Q8×C13D411yescharacteristic
22C22×Dic26C2×C411yescharacteristic
23C2×C13×M16—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4C2×C412yes—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—22no—
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C4×Dic26—22no—
36C4×Dic26—22no—
37C13×C4⋊C8—22no—
38C13×C4⋊C8—22no—
39C13×#101—42no—
40#88071—22no—
41#88071—22no—
42#88071—22no—
43#88071—21no—
44#88071C2×C412yes—
45C22⋊#1055—22no—
46C4⋊#1055—24no—
47C4⋊#1055—22no—
48C4×#1055—24no—
49C4×#1055D414yes—
50#9484—131nomaximal, Sylow
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13SD1612yes—
54C2×Q8×C13Q1612yes—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—22no—
62C22×Dic13—21no—
63C2×Dic26—22no—
64C2×Dic26—42no—
65C13×M16—42no—
66C13×M16—42no—
67C2×C8×C13—42no—
68C13×C4⋊C4—24no—
69C13×C4⋊C4—22no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13C2×D412yes—
73C42×C13#4112yes—
74C4⋊Dic13—22no—
75C4⋊Dic13—42no—
76#6101—44no—
77#6101—41no—
78#6101—41no—
79C4×Dic13—42no—
80C2×#1055—24no—
81#2982—131no—
82#2581—131no—
83#1801D1311yescharacteristic
84#1487—132no—
85#1286—132no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—24no—
88Q8×C13—24no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13#10314yes—
96C2×C4×C13C4×D412yes—
97C2×C4×C13#12011yescharacteristic
98C2×C4×C13#12112yes—
99C2×C4×C13#12311yescharacteristic
100C2×C4×C13C2×SD1611yescharacteristic
101C2×C4×C13C2×Q1611yescharacteristic
102C2×C4×C13#13512yes—
103C2×Dic13—22no—
104C2×Dic13—41no—
105C2×Dic13—41no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—41no—
110C2×Dic13—42no—
111Dic26—24no—
112Dic26—42no—
113C8×C13—82no—
114#1055—44no—
115C2×C4×Q8—131no—
116C2×C4×Q8C2×D1311yescharacteristic
117C8×Q8—264no—
118#431—132no—
119#431—262no—
120#423C2×D1312yes—
121C2×#101—21no—
122#400—132no—
123#395—132no—
124#391—261no—
125#389—261no—
126#387—262no—
127#382—131no—
128#343—21no—
129Q8⋊C8—264no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#38611yescharacteristic
133C22×C13C2×#10311yescharacteristic
134C22×C13#41611yescharacteristic
135C4×C13—22no—
136C4×C13—24no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—42no—
140C4×C13#46512yes—
141C4×C13#46712yes—
142Dic13—42no—
143Dic13—82no—
144Dic13—81no—
145C22×Q8—131no—
146C22×Q8C22⋊D1311yescharacteristic
147C2×M16—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—262no—
151C4×Q8—262no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—262no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4C4×D1312yes—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C42—261no—
159C2×C42D5212yes—
160C2×C42C22×D1311yescharacteristic
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—264no—
164C4⋊C8—262no—
165#101—42no—
166C22⋊C8—262no—
167C4×C8—134no—
168C4×C8—264no—
169#95—132no—
170#95—262no—
171#95—262no—
172#95—262no—
173#95—261no—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13#189111yescharacteristic
177C2×C13#189211yescharacteristic
178C2×C13#191211yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—262no—
182C2×Q8—522no—
183C2×Q8#610512yes—
184C2×Q8#610712yes—
185C22×C4—261no—
186C22×C4—262no—
187C22×C4—261no—
188C22×C4#610312yes—
189C22×C4#610312yes—
190C22×C4C2×C4×D1311yescharacteristic
191C22×C4C2×D5211yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193M16—42no—
194M16—42no—
195C2×C8—42no—
196C2×C8—264no—
197C4⋊C4—24no—
198C4⋊C4—22no—
199C4⋊C4—262no—
200C4⋊C4—524no—
201C4⋊C4—521no—
202C4⋊C4—521no—
203C4⋊C4—522no—
204C42—22no—
205C42—22no—
206C42—522no—
207C42D4×D1312yes—
208C42#612912yes—
209C13#948411yescharacteristic, complemented, Sylow
210C23C2×#610311yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—264no—
214Q8—522no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—262no—
222C2×C4—521no—
223C2×C4—521no—
224C2×C4—522no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—521no—
229C2×C4#8805014yes—
230C2×C4#8813512yes—
231C2×C4#8813611yescharacteristic
232C2×C4#8814011yescharacteristic
233C2×C4C2×#610511yescharacteristic
234C2×C4#8819312yes—
235C2×C4C2×#610711yescharacteristic
236C2×C4#8820412yes—
237C8—82no—
238C8—524no—
239C22—21no—
240C22—21no—
241C22#1171861911yescharacteristic
242C22C2×#8805011yescharacteristic
243C22#1171866311yescharacteristic
244C4—22no—
245C4—24no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—522no—
250C4—1042no—
251C4—1041no—
252C4#1171870212yes—
253C4#1171871212yes—
254C2—21no—
255C2—21no—
256C2#1311525211yescharacteristic
257C2#1311525711yescharacteristic
258C2#1311537111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1801D13
hypocenterC13#9484
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
209. C13#9484semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131201982
#131132642
#131126962
C13×#18012
#948413