Finite Group Databasebeta

← #13128614

Subgroups — #13128614

Order 1664.

1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.

normal subgroups only

This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 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
1C2×#88256C212yesmaximal, complemented
2C4×C13×#41C211yesmaximal, characteristic, complemented
3#11719282C214yesmaximal, complemented
4D4×D52C2112yesmaximal, complemented
5#11719230C216yesmaximal, complemented
6#11719182C213yesmaximal, complemented
7C2×#88128C213yesmaximal, complemented
8C2×C13×#41C2211yescharacteristic
9#88256—216no—
10C2×#6131C2214yescomplemented
11C2×D4×D13C22112yescomplemented
12C2×#6127C2216yescomplemented
13C22×D52C2216yescomplemented
14C22×D52C22112yescomplemented
15C4×Q8×C13C2212yescomplemented
16C4×D4×C13C2216yescomplemented
17C13×#117C2213yescomplemented
18C2×C42×C13C2213yescomplemented
19#88184C22112yescomplemented
20#88149C22124yescomplemented
21#88136C22124yescomplemented
22#88129C2216yescomplemented
23#88128C2213yescomplemented
24#88128C2216yescomplemented
25#88128C22112yescomplemented
26C4×D52C22112yescomplemented
27#88123C2211yescharacteristic, complemented
28C23×D13C23112yes—
29C13×#41D418yescomplemented
30C2×Q8×C13C2311yescharacteristic
31C2×D4×C13C2313yes—
32C22×C4×C13C2316yes—
33C22×C4×C13C2313yes—
34C2×C22⋊D13C23112yes—
35#6131—216no—
36D4×D13—248no—
37#6127—224no—
38C2×D52—224no—
39C2×D52—424no—
40C2×D52C23112yes—
41C2×D52C2316yes—
42C2×D52C23112yes—
43C2×D52C23124yes—
44C2×C4×D13C23112yes—
45C2×Dic26C2312yes—
46C13×C4⋊C4C2316yes—
47C13×C22⋊C4C2316yes—
48C42×C13C2311yescharacteristic
49C42×C13C2316yes—
50C42×C13C2313yes—
51#6103C23124yes—
52C4⋊Dic13C2314yes—
53#3498—131nomaximal, Sylow
54C23×C13C2413yes—
55C22×D13—224no—
56C22×D13—424no—
57C22×D13C24112yes—
58Q8×C13C2×D414yescomplemented
59D4×C13C2×D4112yescomplemented
60C2×C4×C13—212no—
61C2×C4×C13C2×D4112yescomplemented
62C2×C4×C13C2416yes—
63C2×C4×C13C2411yescharacteristic
64C2×C4×C13C2413yes—
65C2×C4×C13C2412yes—
66C22⋊D13—224no—
67C2×Dic13C2414yes—
68D52—212no—
69D52—224no—
70D52—224no—
71D52—424no—
72C4×D13—224no—
73Dic26—24no—
74C2×H(5,𝔽2)—132no—
75#550—134no—
76D42—1312no—
77#535—136no—
78#532—133no—
79C2×#127—133no—
80C4×#41D1311yescharacteristic, complemented
81C22×C13—26no—
82C22×C13C22×D416yes—
83C22×C13C2511yescharacteristic
84C2×D13—212no—
85C2×D13—224no—
86C2×D13—824no—
87C4×C13—26no—
88C4×C13C22×D412yes—
89C4×C13C22×D416yes—
90C4×C13H(5,𝔽2)14yescomplemented
91Dic13—24no—
92H(5,𝔽2)—2616no—
93C2×#41—134no—
94C2×#41—136no—
95C2×#41C2×D1311yescharacteristic
96C22×D4—1312no—
97C22×D4—136no—
98C22×D4—1312no—
99C4⋊Q8—131no—
100#127—133no—
101#127—136no—
102#127—1312no—
103#124—136no—
104#121—1312no—
105#121—1324no—
106#120—1324no—
107C4×Q8C2×D1312yescomplemented
108C4×D4—1312no—
109C4×D4C2×D1316yescomplemented
110#117C2×D1313yescomplemented
111C2×C42C2×D1313yescomplemented
112C2×C13—26no—
113C2×C13C23×D411yescharacteristic
114C2×C13C2×H(5,𝔽2)12yes—
115D13—412no—
116C24—1312no—
117#41—2616no—
118#41—2624no—
119#41D5218yescomplemented
120C2×Q8—132no—
121C2×Q8C22×D1311yescharacteristic
122C2×D4—1312no—
123C2×D4—1312no—
124C2×D4—1312no—
125C2×D4—136no—
126C2×D4—1324no—
127C2×D4—2648no—
128C2×D4—2624no—
129C2×D4—5224no—
130C2×D4C22×D1313yes—
131C22×C4—1312no—
132C22×C4C22×D1316yes—
133C22×C4C22×D1313yes—
134C4⋊C4—134no—
135C4⋊C4C22×D1316yes—
136C22⋊C4—1324no—
137C22⋊C4C22×D1316yes—
138C42C22×D1311yescharacteristic
139C42C22×D1313yes—
140C42C22×D1316yes—
141C13#349811yescharacteristic, complemented, Sylow
142C23—1312no—
143C23—2624no—
144C23—5224no—
145C23C23×D1313yes—
146Q8—264no—
147Q8C2×D5214yescomplemented
148D4—2624no—
149D4—2624no—
150D4—2612no—
151D4—2624no—
152D4—5224no—
153D4C2×D52112yescomplemented
154C2×C4—212no—
155C2×C4—134no—
156C2×C4—2624no—
157C2×C4C2×D52112yescomplemented
158C2×C4C23×D1316yes—
159C2×C4C23×D1311yescharacteristic
160C2×C4C23×D1313yes—
161C2×C4C23×D1312yes—
162C22—26no—
163C22—2612no—
164C22—2624no—
165C22—10424no—
166C22C22×D5216yes—
167C22C24×D1311yescharacteristic
168C4—26no—
169C4—264no—
170C4C22×D5216yes—
171C4C22×D5212yes—
172C4#8825614yescomplemented
173C2—26no—
174C2—5212no—
175C2C23×D5211yescharacteristic
176C2C2×#8825612yes—
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC4×C13×#41C2
hypercenterC4×#41D13
hypocenterC13#3498
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#88256C2semidirect
2. C4×C13×#41C2semidirect
3. #11719282C2semidirect
4. D4×D52C2semidirect
5. #11719230C2semidirect
6. #11719182C2semidirect
7. C2×#88128C2semidirect
10. C2×#6131C22semidirect
11. C2×D4×D13C22semidirect
12. C2×#6127C22semidirect
13. C22×D52C22semidirect
14. C22×D52C22semidirect
15. C4×Q8×C13C22semidirect
16. C4×D4×C13C22semidirect
17. C13×#117C22semidirect
18. C2×C42×C13C22semidirect
19. #88184C22semidirect
20. #88149C22semidirect
21. #88136C22semidirect
22. #88129C22semidirect
23. #88128C22semidirect
24. #88128C22semidirect
25. #88128C22semidirect
26. C4×D52C22semidirect
27. #88123C22semidirect
29. C13×#41D4semidirect
58. Q8×C13C2×D4semidirect
59. D4×C13C2×D4semidirect
61. C2×C4×C13C2×D4semidirect
80. C4×#41D13semidirect
90. C4×C13H(5,𝔽2)semidirect
107. C4×Q8C2×D13semidirect
109. C4×D4C2×D13semidirect
110. #117C2×D13semidirect
111. C2×C42C2×D13semidirect
119. #41D52semidirect
141. C13#3498semidirect
147. Q8C2×D52semidirect
153. D4C2×D52semidirect
157. C2×C4C2×D52semidirect
172. C4#88256semidirect

Maximal subgroups

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

subgroupindex
C2×#882562
C4×C13×#412
#117192822
D4×D522
#117192302
#117191822
C2×#881282
#349813