Finite Group Databasebeta

← #15760764

Subgroups — #15760764

Order 3328.

474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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#13114832C211yesmaximal, characteristic
3#13113265C212yesmaximal
4#13112694C212yesmaximal
5C13×#2581C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#400C412yes—
9C13×#395C412yes—
10C13×#391—21no—
11C13×#389—21no—
12C13×#387—22no—
13C13×#382C2211yescharacteristic
14C2×#88076—21no—
15Q8×#1055—24no—
16#11718586—22no—
17#11718586C2212yes—
18#11718585C2212yes—
19Q8⋊#1055—24no—
20#11718122—21no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×Q8×C13D411yescharacteristic
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13D412yes—
35C2×C42×C13C2311yescharacteristic
36C2×#6099—22no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—21no—
41C13×#95C2×C412yes—
42#88076—42no—
43C22⋊#1055—22no—
44C4⋊#1055—24no—
45C4⋊#1055—22no—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48C4×#1055—24no—
49C4×#1055D414yes—
50#9484—131nomaximal, Sylow
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—42no—
55C2×Q8×C13SD1612yes—
56C2×Q8×C13Q1612yes—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C13×C4⋊C4—24no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—44no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—42no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—42no—
75C42×C13C2×D412yes—
76C42×C13#4112yes—
77#6099—42no—
78#6099—42no—
79C2×#1055—24no—
80C2×#1055—42no—
81#2982—131no—
82#2581D1311yescharacteristic
83#1801—131no—
84#1487—132no—
85#1286—132no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—24no—
88Q8×C13—24no—
89Q8×C13—24no—
90Q8×C13—42no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13#10314yes—
106C2×C4×C13C4×D412yes—
107C2×C4×C13#12011yescharacteristic
108C2×C4×C13#12112yes—
109C2×C4×C13#12311yescharacteristic
110C2×C4×C13C2×SD1611yescharacteristic
111C2×C4×C13C2×Q1611yescharacteristic
112C2×C4×C13#13512yes—
113#1055—44no—
114#1055—82no—
115C2×C4×Q8C2×D1311yescharacteristic
116C2×C4×Q8C2×D1311yescharacteristic
117C8×Q8—264no—
118#431—132no—
119#431—262no—
120#423—132no—
121C2×#101—261no—
122#400Dic1312yes—
123#395Dic1312yes—
124#391—21no—
125#389—21no—
126#387—22no—
127#382C2×D1311yescharacteristic
128#343—261no—
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—42no—
141C4×C13—82no—
142C4×C13—81no—
143C4×C13#46512yes—
144C4×C13#46712yes—
145C22×Q8C2×Dic1311yescharacteristic
146C22×Q8C22⋊D1311yescharacteristic
147C2×M16—262no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4C2×Dic1311yescharacteristic
156C2×C4⋊C4C2×Dic1312yes—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C42—21no—
159C2×C42C22⋊D1312yes—
160C2×C42C22×D1311yescharacteristic
161C4⋊C8—264no—
162C4⋊C8—262no—
163C4⋊C8—262no—
164C4⋊C8—262no—
165#101—522no—
166C22⋊C8—262no—
167C4×C8—134no—
168C4×C8—264no—
169#95—22no—
170#95—22no—
171#95—22no—
172#95—21no—
173#95C2×Dic1312yes—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13#189111yescharacteristic
177C2×C13#189211yescharacteristic
178C2×C13#191211yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8#610612yes—
184C2×Q8#610712yes—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—21no—
188C22×C4C22⋊Dic1312yes—
189C22×C4C22⋊Dic1312yes—
190C22×C4C22×Dic1311yescharacteristic
191C22×C4C2×C22⋊D1311yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193M16—522no—
194M16—522no—
195C2×C8—264no—
196C2×C8—522no—
197C4⋊C4—24no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—44no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C42—22no—
205C42—22no—
206C42—42no—
207C42D4×D1312yes—
208C42#612912yes—
209C13#948411yescharacteristic, complemented, Sylow
210C23C2×C22⋊Dic1311yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—24no—
214Q8—42no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4#8807514yes—
230C2×C4D4×Dic1312yes—
231C2×C4#8818911yescharacteristic
232C2×C4#8819111yescharacteristic
233C2×C4#8819312yes—
234C2×C4C2×#610611yescharacteristic
235C2×C4C2×#610711yescharacteristic
236C2×C4#8820412yes—
237C8—524no—
238C8—1042no—
239C22—21no—
240C22—21no—
241C22#1171888111yescharacteristic
242C22C2×#8807511yescharacteristic
243C22#1171889411yescharacteristic
244C4—22no—
245C4—24no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—82no—
251C4—81no—
252C4#1171870912yes—
253C4#1171871212yes—
254C2—21no—
255C2—21no—
256C2#1311525511yescharacteristic
257C2#1311526011yescharacteristic
258C2#1311537411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2581C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2581D13
hypocenterC13#9484
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

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
#131148322
#131132652
#131126942
C13×#25812
#948413