Finite Group Databasebeta

← C127×#2050 #30635002

Subgroups — C127×#2050 #30635002

Order 16256.

266 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 80 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
2#423×C127C211yesmaximal, characteristic, complemented
3C2×#104×C127C212yesmaximal, complemented
4#413×C127C212yesmaximal, complemented
5#338×C127C211yesmaximal, characteristic, complemented
6C2×#41×C127C2212yes—
7#137×C127—22no—
8AGL(1,ℤ/8)×C127—22no—
9#135×C127—22no—
10C2×M16×C127C2212yes—
11C2×M16×C127C2211yescharacteristic
12C2×M16×C127C2211yescharacteristic
13C2×C42×C127C2211yescharacteristic
14C4⋊C8×C127—22no—
15#104×C127—22no—
16#104×C127—22no—
17#101×C127—22no—
18#100×C127—22no—
19#41×C127—22no—
20#41×C127—22no—
21#41×C127—22no—
22#41×C127—22no—
23C2×Q8×C127D412yes—
24C2×D4×C127—22no—
25C2×D4×C127D412yes—
26C22×C4×C127—21no—
27C22×C4×C127—22no—
28C22×C4×C127C2311yescharacteristic
29Q16×C127—22no—
30SD16×C127—24no—
31D8×C127—22no—
32M16×C127—22no—
33M16×C127—22no—
34M16×C127—22no—
35M16×C127—22no—
36C2×C8×C127—21no—
37C2×C8×C127—22no—
38C2×C8×C127D412yes—
39C42×C127—21no—
40C42×C127D411yescharacteristic
41C42×C127D411yescharacteristic
42C23×C127—22no—
43C23×C127#4111yescharacteristic
44Q8×C127—22no—
45Q8×C127—22no—
46D4×C127—22no—
47D4×C127—22no—
48D4×C127—42no—
49D4×C127—42no—
50C2×C4×C127—21no—
51C2×C4×C127—21no—
52C2×C4×C127—22no—
53C2×C4×C127—42no—
54C2×C4×C127—42no—
55C2×C4×C127—42no—
56C2×C4×C127C2×D412yes—
57C2×C4×C127C2×D411yescharacteristic
58C2×C4×C127C2×D411yescharacteristic
59C2×C4×C127#4112yes—
60C8×C127—22no—
61C8×C127—41no—
62C8×C127—42no—
63C22×C127—41no—
64C22×C127—42no—
65C22×C127—82no—
66C22×C127#12111yescharacteristic
67C22×C127#12312yes—
68C4×C127—22no—
69C4×C127—41no—
70C4×C127—42no—
71C4×C127#12011yescharacteristic
72C4×C127#12112yes—
73C4×C127#12411yescharacteristic
74C2×C127—21no—
75C2×C127—22no—
76C2×C127—82no—
77C2×C127#39411yescharacteristic
78#2050C12711yesmaximal, characteristic, direct product factor, Sylow
79C127#205011yescharacteristic, direct product factor, Sylow
80#575C2×C12711yescharacteristic
81#423C2×C12711yescharacteristic, complemented
82C2×#104C2×C12712yescomplemented
83#413C2×C12712yescomplemented
84#338C2×C12711yescharacteristic, complemented
85C2×#41C22×C12712yes—
86#137—22no—
87AGL(1,ℤ/8)—22no—
88#135—22no—
89C2×M16C22×C12712yes—
90C2×M16C22×C12711yescharacteristic
91C2×M16C22×C12711yescharacteristic
92C2×C42C22×C12711yescharacteristic
93C4⋊C8—22no—
94#104—22no—
95#104—22no—
96#101—22no—
97#100—22no—
98#41—22no—
99#41—22no—
100#41—22no—
101#41—22no—
102C2×Q8D4×C12712yes—
103C2×D4—22no—
104C2×D4D4×C12712yes—
105C22×C4—21no—
106C22×C4—22no—
107C22×C4C23×C12711yescharacteristic
108Q16—22no—
109SD16—24no—
110D8—22no—
111M16—22no—
112M16—22no—
113M16—22no—
114M16—22no—
115C2×C8—21no—
116C2×C8—22no—
117C2×C8D4×C12712yes—
118C42—21no—
119C42D4×C12711yescharacteristic
120C42D4×C12711yescharacteristic
121C23—22no—
122C23#41×C12711yescharacteristic
123Q8—22no—
124Q8—22no—
125D4—22no—
126D4—22no—
127D4—42no—
128D4—42no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4C2×D4×C12712yes—
136C2×C4C2×D4×C12711yescharacteristic
137C2×C4C2×D4×C12711yescharacteristic
138C2×C4#41×C12712yes—
139C8—22no—
140C8—41no—
141C8—42no—
142C22—41no—
143C22—42no—
144C22—82no—
145C22#121×C12711yescharacteristic
146C22#123×C12712yes—
147C4—22no—
148C4—41no—
149C4—42no—
150C4#120×C12711yescharacteristic
151C4#121×C12712yes—
152C4#124×C12711yescharacteristic
153C2—21no—
154C2—22no—
155C2—82no—
156C2#394×C12711yescharacteristic
subgroupG/H
centerC4×C127#124
commutator, Frattini, cosocleC22×C4C23×C127
socleC2×C127#394
prime radical#575×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #423×C127C2semidirect
3. C2×#104×C127C2semidirect
4. #413×C127C2semidirect
5. #338×C127C2semidirect
78. #2050C127direct (N × H)
79. C127#2050direct (N × H)
81. #423C2×C127semidirect
82. C2×#104C2×C127semidirect
83. #413C2×C127semidirect
84. #338C2×C127semidirect

Maximal subgroups

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

subgroupindex
#575×C1272
#423×C1272
C2×#104×C1272
#413×C1272
#338×C1272
#2050127