Finite Group Databasebeta

← #16021067

Subgroups — #16021067

Order 3328.

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

normal subgroups only

This group has 472 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#13127974C212yesmaximal, complemented
2#13117150C214yesmaximal, complemented
3#13117148C212yesmaximal, complemented
4#13117146C212yesmaximal, complemented
5C2×D416C211yesmaximal, characteristic, complemented
6D13×D32C212yesmaximal, complemented
7#13117129C211yesmaximal, characteristic, complemented
8C13×#2262C211yesmaximal, characteristic, complemented
9#11719474—22no—
10C13×#508C2212yescomplemented
11#11718854—22no—
12#11718580C2214yescomplemented
13#11718575—24no—
14D13×D16C2214yescomplemented
15C2×D208C2212yescomplemented
16#11718562C2211yescharacteristic
17C13×Q64C2211yescharacteristic, complemented
18C13×SD64C2212yescomplemented
19C13×D32C2211yescharacteristic, complemented
20C2×C13×C32C2211yescharacteristic, complemented
21#11718113C2214yescomplemented
22#11718111C2214yescomplemented
23#11718091C2211yescharacteristic, complemented
24D416C2212yescomplemented
25D416C2212yescomplemented
26#11718039C2212yescomplemented
27D13×C32C2212yescomplemented
28#88256—42no—
29C13×#135—22no—
30#88203—42no—
31#88173—24no—
32#88168—44no—
33D8×D13—24no—
34C2×D104—22no—
35#88155D411yescharacteristic
36C13×Q32C2312yes—
37C13×SD32—22no—
38C13×D16C2312yes—
39C2×C13×C16C2311yescharacteristic
40#88068—24no—
41#88066—24no—
42#88052D411yescharacteristic
43D208—22no—
44D208C2314yes—
45#88038D412yes—
46C16×D13C2312yes—
47C13×C32C2311yescharacteristic
48C13×C32C2311yescharacteristic
49#88034C2312yes—
50#33982—131nomaximal, Sylow
51C13×#41—42no—
52#6131—44no—
53D4×D13—44no—
54D4×D13—84no—
55#6127—82no—
56#6127D811yescharacteristic
57C2×D52—42no—
58C2×D52—82no—
59C13×Q16—22no—
60C13×SD16—42no—
61C13×D8—22no—
62C2×C8×C13C2×D411yescharacteristic
63#6106—44no—
64#6104—44no—
65#6099D811yescharacteristic
66D104—24no—
67D104—42no—
68#6094D812yes—
69C8×D13C2×D412yes—
70C13×C16C2×D411yescharacteristic
71C13×C16C2411yescharacteristic
72#6090C2×D412yes—
73#3415—132no—
74#2263—132no—
75#2263—134no—
76#2262—132no—
77#2262D1311yescharacteristic, complemented
78C2×D32—132no—
79C2×D32—131no—
80#2258—131no—
81C22×D13—82no—
82C22×D13—84no—
83Q8×C13—42no—
84D4×C13—42no—
85D4×C13—82no—
86C2×C4×C13—82no—
87C2×C4×C13C2×D811yescharacteristic
88C22⋊D13—84no—
89C22⋊D13D1612yes—
90D52—44no—
91D52—84no—
92D52—82no—
93D52D1611yescharacteristic
94C4×D13—84no—
95C4×D13C2×D812yes—
96Dic26D1611yescharacteristic
97C8×C13C2×D811yescharacteristic
98C8×C13C22×D411yescharacteristic
99#1055C2×D812yes—
100#576—262no—
101#509—264no—
102#509—262no—
103#508—134no—
104#508C2×D1312yescomplemented
105C2×D16—134no—
106C2×D16—132no—
107#504—131no—
108Q64C2×D1311yescharacteristic, complemented
109SD64—134no—
110SD64C2×D1312yescomplemented
111D32—134no—
112D32—132no—
113D32—132no—
114D32C2×D1311yescharacteristic, complemented
115M64—131no—
116M64—132no—
117C2×C32—132no—
118C2×C32C2×D1311yescharacteristic, complemented
119C22×C13—82no—
120C22×C13C2×D1611yescharacteristic
121C2×D13—84no—
122C2×D13—324no—
123C2×D13—322no—
124C2×D13C2×D1612yes—
125C4×C13—82no—
126C4×C13C2×D1611yescharacteristic
127C4×C13C22×D811yescharacteristic
128Dic13C2×D1612yes—
129H(5,𝔽2)—522no—
130AGL(1,ℤ/8)—524no—
131AGL(1,ℤ/8)—522no—
132#135—22no—
133#135—264no—
134C2×D8—264no—
135C2×D8—262no—
136#131—131no—
137Q32C22×D1312yes—
138SD32—22no—
139SD32—264no—
140D16—134no—
141D16—264no—
142D16—262no—
143D16C22×D1312yes—
144M32—131no—
145M32—132no—
146C2×C16—132no—
147C2×C16C22×D1311yescharacteristic
148C32—132no—
149C32C22×D1311yescharacteristic
150C32C22×D1311yescharacteristic
151C2×C13—21no—
152C2×C13—162no—
153C2×C13C22×D1611yescharacteristic
154D13—22no—
155D13—164no—
156#41—42no—
157#41—131no—
158#41—524no—
159#41—1042no—
160C2×D4—524no—
161C2×D4—522no—
162C2×D4—1042no—
163C2×D4—1044no—
164Q16—22no—
165SD16—42no—
166SD16—524no—
167D8—22no—
168D8—264no—
169D8—524no—
170D8—522no—
171M16—131no—
172M16—132no—
173C2×C8—132no—
174C2×C8D4×D1311yescharacteristic
175C16—132no—
176C16D4×D1311yescharacteristic
177C16C23×D1311yescharacteristic
178C13#3398211yescharacteristic, complemented, Sylow
179C23—1044no—
180C23—1042no—
181Q8—42no—
182Q8—131no—
183D4—42no—
184D4—82no—
185D4—132no—
186D4—131no—
187D4—524no—
188D4—1044no—
189D4—1044no—
190D4—1042no—
191C2×C4—82no—
192C2×C4—132no—
193C2×C4—1044no—
194C2×C4D8×D1311yescharacteristic
195C8—132no—
196C8D8×D1311yescharacteristic
197C8C2×D4×D1311yescharacteristic
198C22—82no—
199C22—132no—
200C22—1044no—
201C22—4162no—
202C22—4164no—
203C22D13×D1611yescharacteristic
204C4—82no—
205C4—132no—
206C4D13×D1611yescharacteristic
207C4C2×D8×D1311yescharacteristic
208C2—21no—
209C2—162no—
210C2—262no—
211C2—2084no—
212C2C2×D13×D1611yescharacteristic
subgroupG/H
centerC2C2×D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC13×#2262C2
socleC2×C13C22×D16
hypercenter#2262D13
hypocenterC13#33982
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2262

Complements

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

NH ≅ G/Ntype
1. #13127974C2semidirect
2. #13117150C2semidirect
3. #13117148C2semidirect
4. #13117146C2semidirect
5. C2×D416C2semidirect
6. D13×D32C2semidirect
7. #13117129C2semidirect
8. C13×#2262C2semidirect
10. C13×#508C22semidirect
12. #11718580C22semidirect
14. D13×D16C22semidirect
15. C2×D208C22semidirect
17. C13×Q64C22semidirect
18. C13×SD64C22semidirect
19. C13×D32C22semidirect
20. C2×C13×C32C22semidirect
21. #11718113C22semidirect
22. #11718111C22semidirect
23. #11718091C22semidirect
24. D416C22semidirect
25. D416C22semidirect
26. #11718039C22semidirect
27. D13×C32C22semidirect
77. #2262D13semidirect
104. #508C2×D13semidirect
108. Q64C2×D13semidirect
110. SD64C2×D13semidirect
114. D32C2×D13semidirect
118. C2×C32C2×D13semidirect
178. C13#33982semidirect

Maximal subgroups

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

subgroupindex
#131279742
#131171502
#131171482
#131171462
C2×D4162
D13×D322
#131171292
C13×#22622
#3398213