Finite Group Databasebeta

← #15760335

Subgroups — #15760335

Order 3328.

570 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 123 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#13123877C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13113521C212yesmaximal, complemented
4#13112739C212yesmaximal, complemented
5C13×#2542C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×C22⋊Q8—22no—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#399C414yes—
10C13×#390—21no—
11C13×#384—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88073—21no—
14#11718868—22no—
15#11718673—24no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718139—24no—
19#11718122—21no—
20C22×Q8×C13—21no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D412yes—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—22no—
25C13×C22⋊Q8—48no—
26C4×D4×C13—22no—
27C4×D4×C13—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—24no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4C2×C412yes—
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6099—24no—
38C2×#6099—22no—
39C13×#95C2×C412yes—
40#88073—42no—
41C22⋊#1055—24no—
42C22⋊#1055—22no—
43C4⋊#1055—22no—
44C4⋊#1055—22no—
45C4⋊#1055D414yes—
46C4×#1055—22no—
47#9403—131nomaximal, Sylow
48C24×C13C22⋊C412yes—
49C2×Q8×C13—44no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×D4×C13—22no—
53C2×D4×C13—21no—
54C2×D4×C13—22no—
55C2×D4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—44no—
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—24no—
68C13×C4⋊C4—48no—
69C13×C4⋊C4—42no—
70C13×C22⋊C4—24no—
71C13×C22⋊C4—48no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13C2×D412yes—
75C42×C13#4112yes—
76#6099—42no—
77#6099—42no—
78#6099—84no—
79C2×#1055—24no—
80C2×#1055—42no—
81#2975—131no—
82#2542D1311yescharacteristic
83#1800—131no—
84#1549—132no—
85#1303—132no—
86C23×C13—22no—
87C23×C13—22no—
88C23×C13—22no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13C2×C22⋊C411yescharacteristic
92Q8×C13—82no—
93Q8×C13—82no—
94D4×C13—42no—
95D4×C13—42no—
96C2×C4×C13—22no—
97C2×C4×C13—24no—
98C2×C4×C13—22no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—44no—
103C2×C4×C13—42no—
104C2×C4×C13—44no—
105C2×C4×C13—42no—
106C2×C4×C13—82no—
107C2×C4×C13C4×D412yes—
108C2×C4×C13#12011yescharacteristic
109C2×C4×C13#12112yes—
110C2×C4×C13#12311yescharacteristic
111C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C13#13712yes—
113C2×C4×C13#13711yescharacteristic
114#1055—44no—
115#1055—82no—
116C2×C4⋊Q8C2×D1311yescharacteristic
117C2×C22⋊Q8—22no—
118C2×C4×D4C2×D1311yescharacteristic
119#436—264no—
120#431—132no—
121#423—132no—
122C2×#100—261no—
123#407—262no—
124#399Dic1314yes—
125#390—21no—
126#384—21no—
127C4×C4⋊C4C2×D1311yescharacteristic
128#343—261no—
129#332—264no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—44no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—82no—
137C22×C13#38611yescharacteristic
138C22×C13#41711yescharacteristic
139C22×C13#41911yescharacteristic
140C4×C13—21no—
141C4×C13—22no—
142C4×C13—44no—
143C4×C13—42no—
144C4×C13—82no—
145C4×C13#45312yes—
146C4×C13#46812yes—
147C4×C13#47012yes—
148C22×Q8—21no—
149C22×D4C22⋊D1311yescharacteristic
150C23×C4C22⋊D1312yes—
151C2×M16—264no—
152C2×M16—262no—
153C4⋊Q8—22no—
154C4⋊Q8—22no—
155C22⋊Q8—48no—
156C4×D4—22no—
157C4×D4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4C2×Dic1312yes—
162C2×C4⋊C4C22⋊D1311yescharacteristic
163C2×C22⋊C4—24no—
164C2×C22⋊C4C2×Dic1312yes—
165C2×C42—21no—
166C2×C42C22×D1311yescharacteristic
167C4⋊C8—134no—
168C4⋊C8—262no—
169C4⋊C8—262no—
170#100—522no—
171C22⋊C8—264no—
172C22⋊C8—262no—
173C4×C8—262no—
174#95C2×Dic1312yes—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—82no—
178C2×C13#188711yescharacteristic
179C2×C13#189411yescharacteristic
180C2×C13#191511yescharacteristic
181C24C22⋊Dic1312yes—
182C2×Q8—44no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—44no—
194C22×C4C22⋊Dic1312yes—
195C22×C4C22×Dic1311yescharacteristic
196C22×C4C2×C22⋊D1311yescharacteristic
197C22×C4C2×C22⋊D1311yescharacteristic
198M16—522no—
199M16—522no—
200M16—1044no—
201C2×C8—264no—
202C2×C8—522no—
203C4⋊C4—24no—
204C4⋊C4—22no—
205C4⋊C4—24no—
206C4⋊C4—48no—
207C4⋊C4—42no—
208C22⋊C4—24no—
209C22⋊C4—48no—
210C42—41no—
211C42—41no—
212C42D4×D1312yes—
213C42#612912yes—
214C13#940311yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—22no—
218C23—42no—
219C23—42no—
220C23C2×C22⋊Dic1311yescharacteristic
221Q8—82no—
222Q8—82no—
223D4—42no—
224D4—42no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4D4×Dic1312yes—
237C2×C4#8818911yescharacteristic
238C2×C4#8819111yescharacteristic
239C2×C4#8819312yes—
240C2×C4#8819612yes—
241C2×C4#8820311yescharacteristic
242C2×C4#8820511yescharacteristic
243C8—524no—
244C8—1042no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22#1171888111yescharacteristic
253C22#1171888611yescharacteristic
254C22#1171889311yescharacteristic
255C4—21no—
256C4—22no—
257C4—44no—
258C4—42no—
259C4—82no—
260C4#1171871012yes—
261C4#1171871312yes—
262C4#1171873812yes—
263C2—21no—
264C2—21no—
265C2—82no—
266C2#1311523511yescharacteristic
267C2#1311527011yescharacteristic
268C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2542C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2542D13
hypocenterC13#9403
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
3. #13113521C2semidirect
4. #13112739C2semidirect
214. C13#9403semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131148282
#131135212
#131127392
C13×#25422
#940313