Finite Group Databasebeta

← C127×#3184 #30636136

Subgroups — C127×#3184 #30636136

Order 16256.

446 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 184 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#532×C127C212yesmaximal, complemented
2#498×C127C211yesmaximal, characteristic, complemented
3#493×C127C211yesmaximal, characteristic, complemented
4#486×C127C212yesmaximal, complemented
5#469×C127C214yesmaximal, complemented
6#442×C127C214yesmaximal, complemented
7C4×M16×C127C211yesmaximal, characteristic, complemented
8C2×#41×C127—22no—
9C2×D8×C127C2214yes—
10C2×M16×C127C2212yes—
11C4⋊Q8×C127C2212yes—
12#127×C127C2212yes—
13#124×C127—22no—
14#121×C127—22no—
15#121×C127C2214yes—
16C4×D4×C127—22no—
17C4×D4×C127C2214yes—
18C2×C42×C127C2211yescharacteristic
19#106×C127C2214yes—
20#102×C127C2218yes—
21#97×C127C2212yes—
22C4×C8×C127C2211yescharacteristic
23C4×C8×C127C2211yescharacteristic
24#41×C127—48no—
25C2×Q8×C127—22no—
26C2×D4×C127—24no—
27C2×D4×C127—22no—
28C2×D4×C127—22no—
29C2×D4×C127C2314yes—
30C22×C4×C127—24no—
31C22×C4×C127D412yes—
32C22×C4×C127C2311yescharacteristic
33D8×C127—28no—
34M16×C127—24no—
35C2×C8×C127C2312yes—
36C2×C8×C127C2312yes—
37C4⋊C4×C127—22no—
38C4⋊C4×C127C2314yes—
39C22⋊C4×C127—24no—
40C22⋊C4×C127—24no—
41C42×C127D412yes—
42C42×C127C2311yescharacteristic
43C42×C127C2311yescharacteristic
44C23×C127—24no—
45C23×C127C2×D411yescharacteristic
46Q8×C127—44no—
47D4×C127—28no—
48D4×C127—48no—
49D4×C127—44no—
50D4×C127—44no—
51C2×C4×C127—24no—
52C2×C4×C127—22no—
53C2×C4×C127—24no—
54C2×C4×C127—48no—
55C2×C4×C127C2×D411yescharacteristic
56C2×C4×C127C2×D412yes—
57C2×C4×C127C2×D412yes—
58C2×C4×C127C2411yescharacteristic
59C8×C127—22no—
60C8×C127#4114yescomplemented
61C22×C127—21no—
62C22×C127—22no—
63C22×C127—44no—
64C22×C127—44no—
65C22×C127—44no—
66C22×C127C22×D411yescharacteristic
67C4×C127—21no—
68C4×C127—22no—
69C4×C127—44no—
70C4×C127AGL(1,ℤ/8)14yes—
71C4×C127C2×#4112yes—
72C2×C127—41no—
73C2×C127—84no—
74C2×C127#53211yescharacteristic
75C2×C127C2×AGL(1,ℤ/8)12yes—
76#3184C12711yesmaximal, characteristic, direct product factor, Sylow
77C127#318411yescharacteristic, direct product factor, Sylow
78#532C2×C12712yescomplemented
79#498C2×C12711yescharacteristic, complemented
80#493C2×C12711yescharacteristic, complemented
81#486C2×C12712yescomplemented
82#469C2×C12714yescomplemented
83#442C2×C12714yescomplemented
84C4×M16C2×C12711yescharacteristic, complemented
85C2×#41—22no—
86C2×D8C22×C12714yes—
87C2×M16C22×C12712yes—
88C4⋊Q8C22×C12712yes—
89#127C22×C12712yes—
90#124—22no—
91#121—22no—
92#121C22×C12714yes—
93C4×D4—22no—
94C4×D4C22×C12714yes—
95C2×C42C22×C12711yescharacteristic
96#106C22×C12714yes—
97#102C22×C12718yes—
98#97C22×C12712yes—
99C4×C8C22×C12711yescharacteristic
100C4×C8C22×C12711yescharacteristic
101#41—48no—
102C2×Q8—22no—
103C2×D4—24no—
104C2×D4—22no—
105C2×D4—22no—
106C2×D4C23×C12714yes—
107C22×C4—24no—
108C22×C4D4×C12712yes—
109C22×C4C23×C12711yescharacteristic
110D8—28no—
111M16—24no—
112C2×C8C23×C12712yes—
113C2×C8C23×C12712yes—
114C4⋊C4—22no—
115C4⋊C4C23×C12714yes—
116C22⋊C4—24no—
117C22⋊C4—24no—
118C42D4×C12712yes—
119C42C23×C12711yescharacteristic
120C42C23×C12711yescharacteristic
121C23—24no—
122C23C2×D4×C12711yescharacteristic
123Q8—44no—
124D4—28no—
125D4—48no—
126D4—44no—
127D4—44no—
128C2×C4—24no—
129C2×C4—22no—
130C2×C4—24no—
131C2×C4—48no—
132C2×C4C2×D4×C12711yescharacteristic
133C2×C4C2×D4×C12712yes—
134C2×C4C2×D4×C12712yes—
135C2×C4C24×C12711yescharacteristic
136C8—22no—
137C8#41×C12714yescomplemented
138C22—21no—
139C22—22no—
140C22—44no—
141C22—44no—
142C22—44no—
143C22C22×D4×C12711yescharacteristic
144C4—21no—
145C4—22no—
146C4—44no—
147C4AGL(1,ℤ/8)×C12714yes—
148C4C2×#41×C12712yes—
149C2—41no—
150C2—84no—
151C2#532×C12711yescharacteristic
152C2C2×AGL(1,ℤ/8)×C12712yes—
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #532×C127C2semidirect
2. #498×C127C2semidirect
3. #493×C127C2semidirect
4. #486×C127C2semidirect
5. #469×C127C2semidirect
6. #442×C127C2semidirect
7. C4×M16×C127C2semidirect
60. C8×C127#41semidirect
76. #3184C127direct (N × H)
77. C127#3184direct (N × H)
78. #532C2×C127semidirect
79. #498C2×C127semidirect
80. #493C2×C127semidirect
81. #486C2×C127semidirect
82. #469C2×C127semidirect
83. #442C2×C127semidirect
84. C4×M16C2×C127semidirect
137. C8#41×C127semidirect

Maximal subgroups

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

subgroupindex
#532×C1272
#498×C1272
#493×C1272
#486×C1272
#469×C1272
#442×C1272
C4×M16×C1272
#3184127