Finite Group Databasebeta

← C22×D8×D131 #30680675

Subgroups — C22×D8×D131 #30680675

Order 16768.

1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C22×D4×D131C212yesmaximal, complemented
2C22×D1048C211yesmaximal, characteristic, complemented
3C22×#14523498C212yesmaximal, complemented
4C2×D8×D131C2124yesmaximal, direct product factor
5C22×C8×D131C211yesmaximal, characteristic, complemented
6C22×D8×C131C211yesmaximal, characteristic, complemented
7C24×D131—22no—
8C22×D524C2212yescomplemented
9C22×C22⋊D131—22no—
10C2×D4×D131—212no—
11C2×D4×D131C22124yescomplemented
12C22×C4×D131C2211yescharacteristic
13C2×D1048C22112yescomplemented
14C2×#14523498C22124yescomplemented
15D8×D131C22164yesdirect product factor
16C22×C131⋊C8C2211yescharacteristic, complemented
17C2×C8×D131C22112yescomplemented
18C22×D4×C131C2212yescomplemented
19C2×D8×C131C22112yescomplemented
20C22×C8×C131C2211yescharacteristic, complemented
21C23×D131—224no—
22C23×D131—22no—
23C23×D131—416no—
24C23×D131D411yescharacteristic
25C2×D524—26no—
26C2×D524C23112yescomplemented
27C2×C22⋊D131—224no—
28D4×D131—248no—
29D4×D131C23132yescomplemented
30C22×Dic131D411yescharacteristic
31C2×C4×D131D416yes—
32C2×C4×D131C2316yes—
33D1048C23116yescomplemented
34#14523498C23132yescomplemented
35C2×C131⋊C8C2316yescomplemented
36C8×D131C23116yescomplemented
37C24×C131—22no—
38C2×D4×C131—26no—
39C2×D4×C131C23112yescomplemented
40C22×C4×C131C2311yescharacteristic
41D8×C131C23116yescomplemented
42C2×C8×C131C2316yescomplemented
43C22×D131—212no—
44C22×D131—232no—
45C22×D131—48no—
46C22×D131—496no—
47C22×D131D818yesdirect product factor
48C22×D131C2×D416yes—
49D524—212no—
50D524C2418yescomplemented
51C22⋊D131—232no—
52C2×Dic131C2×D416yes—
53C4×D131C2×D4112yes—
54C4×D131C2414yes—
55C131⋊C8C2414yescomplemented
56C23×C131—212no—
57C23×C131—48no—
58C23×C131C2×D411yescharacteristic
59D4×C131—212no—
60D4×C131C2418yescomplemented
61C2×C4×C131C2×D413yes—
62C2×C4×C131C2413yes—
63C8×C131C2414yescomplemented
64C22×C131—28no—
65C22×C131—424no—
66C22×C131C2×D814yescomplemented
67C22×C131C22×D413yes—
68C2×D131—28no—
69C2×D131—424no—
70C2×D131—464no—
71C2×D131C2×D8124yesdirect product factor
72C2×D131C22×D414yes—
73C4×C131C22×D413yes—
74C4×C131C2511yescharacteristic
75Dic131C22×D414yes—
76C2×C131—48no—
77C2×C131C22×D816yescomplemented
78C2×C131C23×D411yescharacteristic
79D131—48no—
80D131C22×D818yesdirect product factor
81C131C23×D811yescharacteristic, complemented, Sylow
82C23×D8—1311nomaximal, Sylow
83C23×D4—1312no—
84C22×D8—1312no—
85C22×D8—13124no—
86C22×D8—1311no—
87C22×D8D13111yescharacteristic, direct product factor
88C23×C8—1311no—
89C25—2622no—
90C22×D4—26212no—
91C22×D4—2622no—
92C22×D4—13124no—
93C22×D4—1312no—
94C22×D4C2×D13112yescomplemented
95C23×C4—1311no—
96C2×D8—13124no—
97C2×D8—13164no—
98C2×D8—13112no—
99C2×D8C2×D131112yesdirect product factor
100C22×C8—1311no—
101C22×C8—13112no—
102C22×C8C2×D13111yescharacteristic, complemented
103C24—22no—
104C24—26224no—
105C24—2622no—
106C24—52416no—
107C24—1311no—
108C2×D4—26no—
109C2×D4—26248no—
110C2×D4—26224no—
111C2×D4—2626no—
112C2×D4—13132no—
113C2×D4—13112no—
114C2×D4C22×D131112yescomplemented
115C22×C4—1311no—
116C22×C4—1316no—
117C22×C4—1316no—
118C22×C4C22×D13111yescharacteristic
119D8—13132no—
120D8—13116no—
121D8C22×D131116yesdirect product factor
122C2×C8—1316no—
123C2×C8—13116no—
124C2×C8C22×D13116yescomplemented
125C23—212no—
126C23—48no—
127C23—26232no—
128C23—26212no—
129C23—52496no—
130C23—5248no—
131C23—1318no—
132C23—1316no—
133C23D4×D13111yescharacteristic
134D4—212no—
135D4—26232no—
136D4—26212no—
137D4—1318no—
138D4C23×D13118yescomplemented
139C2×C4—1316no—
140C2×C4—13112no—
141C2×C4—1314no—
142C2×C4D4×D13113yes—
143C2×C4C23×D13113yes—
144C8—1314no—
145C8C23×D13114yescomplemented
146C22—28no—
147C22—424no—
148C22—2628no—
149C22—52464no—
150C22—52424no—
151C22—1314no—
152C22—13124no—
153C22D8×D13114yesdirect product factor
154C22C2×D4×D13113yes—
155C4—1314no—
156C4C2×D4×D13113yes—
157C4C24×D13111yescharacteristic
158C2—48no—
159C2—5248no—
160C2—1318no—
161C2C2×D8×D13116yesdirect product factor
162C2C22×D4×D13111yescharacteristic
subgroupG/H
centerC23D4×D131
commutator, cosocleC4×C131C25
FrattiniC4C24×D131
FittingC22×D8×C131C2
socleC23×C131C2×D4
hypercenterC22×D8D131
hypocenterC131C23×D8
LCSG ▷ C4×C131 ▷ C2×C131 ▷ C131
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D131C2semidirect
2. C22×D1048C2semidirect
3. C22×#14523498C2semidirect
4. C2×D8×D131C2direct (N × H)
5. C22×C8×D131C2semidirect
6. C22×D8×C131C2semidirect
8. C22×D524C22semidirect
11. C2×D4×D131C22semidirect
13. C2×D1048C22semidirect
14. C2×#14523498C22semidirect
15. D8×D131C22direct (N × H)
16. C22×C131⋊C8C22semidirect
17. C2×C8×D131C22semidirect
18. C22×D4×C131C22semidirect
19. C2×D8×C131C22semidirect
20. C22×C8×C131C22semidirect
26. C2×D524C23semidirect
29. D4×D131C23semidirect
33. D1048C23semidirect
34. #14523498C23semidirect
35. C2×C131⋊C8C23semidirect
36. C8×D131C23semidirect
39. C2×D4×C131C23semidirect
41. D8×C131C23semidirect
42. C2×C8×C131C23semidirect
47. C22×D131D8direct (N × H)
50. D524C24semidirect
55. C131⋊C8C24semidirect
60. D4×C131C24semidirect
63. C8×C131C24semidirect
66. C22×C131C2×D8semidirect
71. C2×D131C2×D8direct (N × H)
77. C2×C131C22×D8semidirect
80. D131C22×D8direct (N × H)
81. C131C23×D8semidirect
87. C22×D8D131direct (N × H)
94. C22×D4C2×D131semidirect
99. C2×D8C2×D131direct (N × H)
102. C22×C8C2×D131semidirect
114. C2×D4C22×D131semidirect
121. D8C22×D131direct (N × H)
124. C2×C8C22×D131semidirect
138. D4C23×D131semidirect
145. C8C23×D131semidirect
153. C22D8×D131direct (N × H)
161. C2C2×D8×D131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1312
C22×D10482
C22×#145234982
C2×D8×D1312
C22×C8×D1312
C22×D8×C1312
C23×D8131