Finite Group Databasebeta

← C127×#2190 #30635142

Subgroups — C127×#2190 #30635142

Order 16256.

226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 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#575×C127C211yesmaximal, characteristic, complemented
2#509×C127C212yesmaximal, complemented
3#469×C127C211yesmaximal, characteristic, complemented
4#360×C127C212yesmaximal, complemented
5#349×C127C211yesmaximal, characteristic, complemented
6C2×#41×C127—21no—
7#137×C127—22no—
8AGL(1,ℤ/8)×C127—22no—
9#135×C127—21no—
10#135×C127C2212yes—
11C2×D8×C127C2211yescharacteristic, complemented
12C2×M16×C127C2211yescharacteristic
13#121×C127—21no—
14SD32×C127—22no—
15D16×C127—22no—
16M32×C127C2212yescomplemented
17#106×C127C2211yescharacteristic, complemented
18#102×C127—21no—
19#41×C127—22no—
20#41×C127—22no—
21#41×C127—41no—
22#41×C127—41no—
23C2×Q8×C127—21no—
24C2×D4×C127—21no—
25C2×D4×C127—21no—
26C2×D4×C127—41no—
27C2×D4×C127—41no—
28C22×C4×C127—41no—
29C22×C4×C127D411yescharacteristic
30Q16×C127—21no—
31Q16×C127D412yescomplemented
32SD16×C127—22no—
33SD16×C127—22no—
34D8×C127—21no—
35D8×C127—22no—
36D8×C127D412yescomplemented
37M16×C127—22no—
38C2×C8×C127D411yescharacteristic
39C2×C8×C127C2311yescharacteristic
40C4⋊C4×C127—21no—
41C22⋊C4×C127—41no—
42C16×C127—22no—
43C23×C127—41no—
44C23×C127—41no—
45C23×C127D811yescharacteristic
46Q8×C127—22no—
47Q8×C127—41no—
48D4×C127—22no—
49D4×C127—41no—
50D4×C127—42no—
51D4×C127—42no—
52D4×C127—41no—
53D4×C127—41no—
54D4×C127—82no—
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—42no—
58C2×C4×C127—41no—
59C2×C4×C127—42no—
60C2×C4×C127—41no—
61C2×C4×C127D811yescharacteristic
62C2×C4×C127C2×D411yescharacteristic
63C8×C127—21no—
64C8×C127C2×D412yes—
65C22×C127—21no—
66C22×C127—41no—
67C22×C127—42no—
68C22×C127—81no—
69C22×C127—81no—
70C22×C127—82no—
71C22×C127—81no—
72C22×C127C2×D811yescharacteristic
73C4×C127—21no—
74C4×C127—42no—
75C4×C127—81no—
76C4×C127#12011yescharacteristic
77C4×C127AGL(1,ℤ/8)11yescharacteristic
78C2×C127—21no—
79C2×C127—41no—
80C2×C127—82no—
81C2×C127—161no—
82C2×C127#44711yescharacteristic
83#2190C12711yesmaximal, characteristic, direct product factor, Sylow
84C127#219011yescharacteristic, direct product factor, Sylow
85#575C2×C12711yescharacteristic, complemented
86#509C2×C12712yescomplemented
87#469C2×C12711yescharacteristic, complemented
88#360C2×C12712yescomplemented
89#349C2×C12711yescharacteristic, complemented
90C2×#41—21no—
91#137—22no—
92AGL(1,ℤ/8)—22no—
93#135—21no—
94#135C22×C12712yes—
95C2×D8C22×C12711yescharacteristic, complemented
96C2×M16C22×C12711yescharacteristic
97#121—21no—
98SD32—22no—
99D16—22no—
100M32C22×C12712yescomplemented
101#106C22×C12711yescharacteristic, complemented
102#102—21no—
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—21no—
110C2×D4—41no—
111C2×D4—41no—
112C22×C4—41no—
113C22×C4D4×C12711yescharacteristic
114Q16—21no—
115Q16D4×C12712yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—22no—
120D8D4×C12712yescomplemented
121M16—22no—
122C2×C8D4×C12711yescharacteristic
123C2×C8C23×C12711yescharacteristic
124C4⋊C4—21no—
125C22⋊C4—41no—
126C16—22no—
127C23—41no—
128C23—41no—
129C23D8×C12711yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—41no—
137D4—41no—
138D4—82no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—41no—
145C2×C4D8×C12711yescharacteristic
146C2×C4C2×D4×C12711yescharacteristic
147C8—21no—
148C8C2×D4×C12712yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—81no—
153C22—81no—
154C22—82no—
155C22—81no—
156C22C2×D8×C12711yescharacteristic
157C4—21no—
158C4—42no—
159C4—81no—
160C4#120×C12711yescharacteristic
161C4AGL(1,ℤ/8)×C12711yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—161no—
166C2#447×C12711yescharacteristic
subgroupG/H
center, socleC2×C127#447
commutator, Frattini, cosocleC2×C8C23×C127
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #575×C127C2semidirect
2. #509×C127C2semidirect
3. #469×C127C2semidirect
4. #360×C127C2semidirect
5. #349×C127C2semidirect
11. C2×D8×C127C22semidirect
16. M32×C127C22semidirect
17. #106×C127C22semidirect
31. Q16×C127D4semidirect
36. D8×C127D4semidirect
83. #2190C127direct (N × H)
84. C127#2190direct (N × H)
85. #575C2×C127semidirect
86. #509C2×C127semidirect
87. #469C2×C127semidirect
88. #360C2×C127semidirect
89. #349C2×C127semidirect
95. C2×D8C22×C127semidirect
100. M32C22×C127semidirect
101. #106C22×C127semidirect
115. Q16D4×C127semidirect
120. D8D4×C127semidirect

Maximal subgroups

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

subgroupindex
#575×C1272
#509×C1272
#469×C1272
#360×C1272
#349×C1272
#2190127