Finite Group Databasebeta

← C22×D8×D127 #30653444

Subgroups — C22×D8×D127 #30653444

Order 16256.

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×D127C212yesmaximal, complemented
2C22×D1016C211yesmaximal, characteristic, complemented
3C22×#14523233C212yesmaximal, complemented
4C2×D8×D127C2124yesmaximal, direct product factor
5C22×C8×D127C211yesmaximal, characteristic, complemented
6C22×D8×C127C211yesmaximal, characteristic, complemented
7C24×D127—22no—
8C22×D508C2212yescomplemented
9C22×C22⋊D127—22no—
10C2×D4×D127—212no—
11C2×D4×D127C22124yescomplemented
12C22×C4×D127C2211yescharacteristic
13C2×D1016C22112yescomplemented
14C2×#14523233C22124yescomplemented
15D8×D127C22164yesdirect product factor
16C22×C127⋊C8C2211yescharacteristic, complemented
17C2×C8×D127C22112yescomplemented
18C22×D4×C127C2212yescomplemented
19C2×D8×C127C22112yescomplemented
20C22×C8×C127C2211yescharacteristic, complemented
21C23×D127—224no—
22C23×D127—22no—
23C23×D127—416no—
24C23×D127D411yescharacteristic
25C2×D508—26no—
26C2×D508C23112yescomplemented
27C2×C22⋊D127—224no—
28D4×D127—248no—
29D4×D127C23132yescomplemented
30C22×Dic127D411yescharacteristic
31C2×C4×D127D416yes—
32C2×C4×D127C2316yes—
33D1016C23116yescomplemented
34#14523233C23132yescomplemented
35C2×C127⋊C8C2316yescomplemented
36C8×D127C23116yescomplemented
37C24×C127—22no—
38C2×D4×C127—26no—
39C2×D4×C127C23112yescomplemented
40C22×C4×C127C2311yescharacteristic
41D8×C127C23116yescomplemented
42C2×C8×C127C2316yescomplemented
43C22×D127—212no—
44C22×D127—232no—
45C22×D127—48no—
46C22×D127—496no—
47C22×D127D818yesdirect product factor
48C22×D127C2×D416yes—
49D508—212no—
50D508C2418yescomplemented
51C22⋊D127—232no—
52C2×Dic127C2×D416yes—
53C4×D127C2×D4112yes—
54C4×D127C2414yes—
55C127⋊C8C2414yescomplemented
56C23×C127—212no—
57C23×C127—48no—
58C23×C127C2×D411yescharacteristic
59D4×C127—212no—
60D4×C127C2418yescomplemented
61C2×C4×C127C2×D413yes—
62C2×C4×C127C2413yes—
63C8×C127C2414yescomplemented
64C22×C127—28no—
65C22×C127—424no—
66C22×C127C2×D814yescomplemented
67C22×C127C22×D413yes—
68C2×D127—28no—
69C2×D127—424no—
70C2×D127—464no—
71C2×D127C2×D8124yesdirect product factor
72C2×D127C22×D414yes—
73C4×C127C22×D413yes—
74C4×C127C2511yescharacteristic
75Dic127C22×D414yes—
76C2×C127—48no—
77C2×C127C22×D816yescomplemented
78C2×C127C23×D411yescharacteristic
79D127—48no—
80D127C22×D818yesdirect product factor
81C23×D8—1271nomaximal, Sylow
82C127C23×D811yescharacteristic, complemented, Sylow
83C23×D4—1272no—
84C22×D8—1272no—
85C22×D8—12724no—
86C22×D8—1271no—
87C22×D8D12711yescharacteristic, direct product factor
88C23×C8—1271no—
89C25—2542no—
90C22×D4—12724no—
91C22×D4—1272no—
92C22×D4—25412no—
93C22×D4—2542no—
94C22×D4C2×D12712yescomplemented
95C23×C4—1271no—
96C2×D8—12724no—
97C2×D8—12764no—
98C2×D8—12712no—
99C2×D8C2×D127112yesdirect product factor
100C22×C8—1271no—
101C22×C8—12712no—
102C22×C8C2×D12711yescharacteristic, complemented
103C24—22no—
104C24—1271no—
105C24—50816no—
106C24—25424no—
107C24—2542no—
108C2×D4—26no—
109C2×D4—12732no—
110C2×D4—12712no—
111C2×D4—25448no—
112C2×D4—25424no—
113C2×D4—2546no—
114C2×D4C22×D127112yescomplemented
115C22×C4—1271no—
116C22×C4—1276no—
117C22×C4—1276no—
118C22×C4C22×D12711yescharacteristic
119D8—12732no—
120D8—12716no—
121D8C22×D127116yesdirect product factor
122C2×C8—1276no—
123C2×C8—12716no—
124C2×C8C22×D12716yescomplemented
125C23—212no—
126C23—48no—
127C23—1278no—
128C23—1276no—
129C23—50896no—
130C23—5088no—
131C23—25432no—
132C23—25412no—
133C23D4×D12711yescharacteristic
134D4—212no—
135D4—1278no—
136D4—25432no—
137D4—25412no—
138D4C23×D12718yescomplemented
139C2×C4—1276no—
140C2×C4—12712no—
141C2×C4—1274no—
142C2×C4D4×D12713yes—
143C2×C4C23×D12713yes—
144C8—1274no—
145C8C23×D12714yescomplemented
146C22—28no—
147C22—424no—
148C22—12724no—
149C22—1274no—
150C22—50864no—
151C22—50824no—
152C22—2548no—
153C22D8×D12714yesdirect product factor
154C22C2×D4×D12713yes—
155C4—1274no—
156C4C2×D4×D12713yes—
157C4C24×D12711yescharacteristic
158C2—48no—
159C2—1278no—
160C2—5088no—
161C2C2×D8×D12716yesdirect product factor
162C2C22×D4×D12711yescharacteristic
subgroupG/H
centerC23D4×D127
commutator, cosocleC4×C127C25
FrattiniC4C24×D127
FittingC22×D8×C127C2
socleC23×C127C2×D4
hypercenterC22×D8D127
hypocenterC127C23×D8
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D127C2semidirect
2. C22×D1016C2semidirect
3. C22×#14523233C2semidirect
4. C2×D8×D127C2direct (N × H)
5. C22×C8×D127C2semidirect
6. C22×D8×C127C2semidirect
8. C22×D508C22semidirect
11. C2×D4×D127C22semidirect
13. C2×D1016C22semidirect
14. C2×#14523233C22semidirect
15. D8×D127C22direct (N × H)
16. C22×C127⋊C8C22semidirect
17. C2×C8×D127C22semidirect
18. C22×D4×C127C22semidirect
19. C2×D8×C127C22semidirect
20. C22×C8×C127C22semidirect
26. C2×D508C23semidirect
29. D4×D127C23semidirect
33. D1016C23semidirect
34. #14523233C23semidirect
35. C2×C127⋊C8C23semidirect
36. C8×D127C23semidirect
39. C2×D4×C127C23semidirect
41. D8×C127C23semidirect
42. C2×C8×C127C23semidirect
47. C22×D127D8direct (N × H)
50. D508C24semidirect
55. C127⋊C8C24semidirect
60. D4×C127C24semidirect
63. C8×C127C24semidirect
66. C22×C127C2×D8semidirect
71. C2×D127C2×D8direct (N × H)
77. C2×C127C22×D8semidirect
80. D127C22×D8direct (N × H)
82. C127C23×D8semidirect
87. C22×D8D127direct (N × H)
94. C22×D4C2×D127semidirect
99. C2×D8C2×D127direct (N × H)
102. C22×C8C2×D127semidirect
114. C2×D4C22×D127semidirect
121. D8C22×D127direct (N × H)
124. C2×C8C22×D127semidirect
138. D4C23×D127semidirect
145. C8C23×D127semidirect
153. C22D8×D127direct (N × H)
161. C2C2×D8×D127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1272
C22×D10162
C22×#145232332
C2×D8×D1272
C22×C8×D1272
C22×D8×C1272
C23×D8127