Finite Group Databasebeta

← #16021062

Subgroups — #16021062

Order 3328.

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

normal subgroups only

This group has 466 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
1D13×#508C212yesmaximal, complemented
2#13117155C212yesmaximal, complemented
3#13117152C212yesmaximal, complemented
4#13117150C212yesmaximal, complemented
5#13117147C212yesmaximal, complemented
6#13117145C211yesmaximal, characteristic, complemented
7#13117143C212yesmaximal, complemented
8C2×#11718039C211yesmaximal, characteristic, complemented
9C13×#2262C211yesmaximal, characteristic, complemented
10D13×#135—22no—
11C13×#508C2212yescomplemented
12#11718855—22no—
13#11718580C2212yes—
14D13×Q32C2212yescomplemented
15#11718577—22no—
16D13×SD32—22no—
17#11718573C2212yes—
18D13×D16C2212yescomplemented
19#11718565C2212yescomplemented
20C2×C16×D13C2211yescharacteristic
21C13×Q64C2211yescharacteristic, complemented
22C13×SD64C2212yescomplemented
23C13×D32C2211yescharacteristic, complemented
24C2×C13×C32C2211yescharacteristic, complemented
25#11718114C2212yescomplemented
26#11718113C2212yescomplemented
27#11718112C2212yescomplemented
28#11718111C2212yescomplemented
29C2×#88034C2211yescharacteristic, complemented
30Dic208C2211yescharacteristic, complemented
31#11718041C2212yescomplemented
32D416C2211yescharacteristic, complemented
33#11718039C2212yescomplemented
34#11718039C2212yescomplemented
35#41×D13—42no—
36C13×#135—22no—
37#88204—42no—
38#88173—22no—
39Q16×D13—22no—
40#88170—42no—
41SD16×D13—42no—
42#88166—22no—
43D8×D13—22no—
44#88158—22no—
45C2×C8×D13D411yescharacteristic
46C13×Q32C2312yes—
47C13×SD32—22no—
48C13×D16C2312yes—
49C2×C13×C16C2311yescharacteristic
50#88069—22no—
51#88068—22no—
52#88067—22no—
53#88066—22no—
54C2×#6090D411yescharacteristic
55Dic104C2312yes—
56#88040—22no—
57D208C2312yes—
58C16×D13D412yes—
59C16×D13C2312yes—
60C13×C32C2311yescharacteristic
61C13×C32C2311yescharacteristic
62#88034C2312yes—
63#33981—131nomaximal, Sylow
64C13×#41—42no—
65#6131—42no—
66Q8×D13—42no—
67#6129—42no—
68#6129—82no—
69D4×D13—42no—
70D4×D13—82no—
71#6127—42no—
72#6127—82no—
73C2×C4×D13—82no—
74C2×C4×D13D811yescharacteristic
75C13×Q16—22no—
76C13×SD16—42no—
77C13×D8—22no—
78C2×C8×C13C2×D411yescharacteristic
79#6107—42no—
80#6106—42no—
81#6105—42no—
82#6104—42no—
83C2×#1055D811yescharacteristic
84Dic52—22no—
85D104—22no—
86#6095—42no—
87C8×D13D812yes—
88C8×D13C2×D412yes—
89C13×C16C2×D411yescharacteristic
90C13×C16C2411yescharacteristic
91#6090C2×D412yes—
92C2×#508—132no—
93#2264—132no—
94#2264—132no—
95#2263—132no—
96#2263—132no—
97#2262—132no—
98#2262—131no—
99#2262D1311yescharacteristic, complemented
100C2×M64—131no—
101C22×D13—82no—
102C22×D13D1611yescharacteristic
103Q8×C13—42no—
104D4×C13—42no—
105D4×C13—82no—
106C2×C4×C13—82no—
107C2×C4×C13C2×D811yescharacteristic
108C22⋊D13—82no—
109C22⋊D13—82no—
110C22⋊D13—82no—
111C2×Dic13—82no—
112C2×Dic13D1611yescharacteristic
113D52—42no—
114D52—82no—
115C4×D13—82no—
116C4×D13—82no—
117C4×D13—82no—
118C4×D13D1612yes—
119C4×D13C2×D812yes—
120Dic26—42no—
121Dic26—82no—
122C8×C13C2×D811yescharacteristic
123C8×C13C22×D411yescharacteristic
124#1055C2×D812yes—
125C2×#135—262no—
126#508—132no—
127#508—132no—
128#508—132no—
129#508—262no—
130#508—262no—
131#508C2×D1312yescomplemented
132C2×Q32—132no—
133C2×SD32—262no—
134C2×D16—132no—
135C22×C16—131no—
136Q64—132no—
137Q64—131no—
138Q64C2×D1311yescharacteristic, complemented
139SD64—132no—
140SD64—132no—
141SD64—132no—
142SD64C2×D1312yescomplemented
143D32—132no—
144D32—131no—
145D32C2×D1311yescharacteristic, complemented
146M64—132no—
147M64—132no—
148C2×C32—131no—
149C2×C32C2×D1311yescharacteristic, complemented
150C22×C13—82no—
151C22×C13C2×D1611yescharacteristic
152C2×D13—41no—
153C2×D13—82no—
154C2×D13—164no—
155C2×D13C2×D1612yes—
156C4×C13—82no—
157C4×C13C2×D1611yescharacteristic
158C4×C13C22×D811yescharacteristic
159Dic13—82no—
160Dic13C2×D1612yes—
161C2×#41—522no—
162#135—22no—
163#135—262no—
164#135—262no—
165#135—262no—
166#135—522no—
167#135—522no—
168C2×Q16—262no—
169C2×SD16—522no—
170C2×D8—262no—
171C22×C8—131no—
172Q32—132no—
173Q32—262no—
174Q32C22×D1312yes—
175SD32—22no—
176SD32—262no—
177SD32—262no—
178SD32—262no—
179D16—132no—
180D16—262no—
181D16C22×D1312yes—
182C2×C16—131no—
183C2×C16—132no—
184C2×C16—132no—
185C2×C16C22×D1311yescharacteristic
186C32—132no—
187C32C22×D1311yescharacteristic
188C32C22×D1311yescharacteristic
189C2×C13—21no—
190C2×C13—162no—
191C2×C13C22×D1611yescharacteristic
192D13—22no—
193D13—162no—
194#41—42no—
195#41—522no—
196#41—522no—
197#41—522no—
198#41—1042no—
199#41—1042no—
200C2×Q8—522no—
201C2×D4—522no—
202C2×D4—1042no—
203C22×C4—131no—
204C22×C4—1042no—
205Q16—22no—
206Q16—262no—
207Q16—522no—
208SD16—42no—
209SD16—522no—
210SD16—522no—
211SD16—522no—
212D8—22no—
213D8—262no—
214D8—522no—
215C2×C8—131no—
216C2×C8—132no—
217C2×C8—132no—
218C2×C8D4×D1311yescharacteristic
219C16—132no—
220C16D4×D1311yescharacteristic
221C16C23×D1311yescharacteristic
222C13#3398111yescharacteristic, complemented, Sylow
223C23—131no—
224C23—1042no—
225Q8—42no—
226Q8—522no—
227Q8—1042no—
228D4—42no—
229D4—82no—
230D4—522no—
231D4—1042no—
232D4—1042no—
233D4—1042no—
234D4—1042no—
235C2×C4—82no—
236C2×C4—131no—
237C2×C4—132no—
238C2×C4—132no—
239C2×C4—1042no—
240C2×C4—1042no—
241C2×C4—1042no—
242C2×C4—1042no—
243C2×C4D8×D1311yescharacteristic
244C8—132no—
245C8D8×D1311yescharacteristic
246C8C2×D4×D1311yescharacteristic
247C22—82no—
248C22—132no—
249C22—521no—
250C22—1042no—
251C22—2084no—
252C22D13×D1611yescharacteristic
253C4—82no—
254C4—132no—
255C4—1042no—
256C4D13×D1611yescharacteristic
257C4C2×D8×D1311yescharacteristic
258C2—21no—
259C2—162no—
260C2—262no—
261C2—2082no—
262C2C2×D13×D1611yescharacteristic
subgroupG/H
centerC4D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC13×#2262C2
socleC2×C13C22×D16
hypercenter#2262D13
hypocenterC13#33981
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2262

Complements

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

NH ≅ G/Ntype
1. D13×#508C2semidirect
2. #13117155C2semidirect
3. #13117152C2semidirect
4. #13117150C2semidirect
5. #13117147C2semidirect
6. #13117145C2semidirect
7. #13117143C2semidirect
8. C2×#11718039C2semidirect
9. C13×#2262C2semidirect
11. C13×#508C22semidirect
14. D13×Q32C22semidirect
18. D13×D16C22semidirect
19. #11718565C22semidirect
21. C13×Q64C22semidirect
22. C13×SD64C22semidirect
23. C13×D32C22semidirect
24. C2×C13×C32C22semidirect
25. #11718114C22semidirect
26. #11718113C22semidirect
27. #11718112C22semidirect
28. #11718111C22semidirect
29. C2×#88034C22semidirect
30. Dic208C22semidirect
31. #11718041C22semidirect
32. D416C22semidirect
33. #11718039C22semidirect
34. #11718039C22semidirect
99. #2262D13semidirect
131. #508C2×D13semidirect
138. Q64C2×D13semidirect
142. SD64C2×D13semidirect
145. D32C2×D13semidirect
149. C2×C32C2×D13semidirect
222. C13#33981semidirect

Maximal subgroups

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

subgroupindex
D13×#5082
#131171552
#131171522
#131171502
#131171472
#131171452
#131171432
C2×#117180392
C13×#22622
#3398113