Finite Group Databasebeta

← C127×#2053 #30635005

Subgroups — C127×#2053 #30635005

Order 16256.

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

normal subgroups only

This group has 264 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#424×C127C211yesmaximal, characteristic, complemented
3#416×C127C212yesmaximal, complemented
4#410×C127C212yesmaximal, complemented
5H(3,ℤ/4)×C127C211yesmaximal, characteristic, complemented
6C2×#41×C127C2212yes—
7#137×C127—22no—
8AGL(1,ℤ/8)×C127—22no—
9#135×C127—22no—
10C2×M16×C127C2211yescharacteristic
11C22×C8×C127C2211yescharacteristic
12#117×C127C2212yes—
13#117×C127C2211yescharacteristic
14C4⋊C8×C127—22no—
15#103×C127—22no—
16#102×C127—22no—
17#99×C127—24no—
18#41×C127—22no—
19#41×C127—22no—
20#41×C127—22no—
21#41×C127—22no—
22C2×Q8×C127D412yes—
23C2×D4×C127—22no—
24C2×D4×C127D412yes—
25C22×C4×C127—22no—
26C22×C4×C127C2311yescharacteristic
27Q16×C127—22no—
28SD16×C127—24no—
29D8×C127—22no—
30M16×C127—22no—
31C2×C8×C127—22no—
32C2×C8×C127—21no—
33C2×C8×C127D412yes—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—22no—
36C22⋊C4×C127—22no—
37C22⋊C4×C127D412yes—
38C42×C127—21no—
39C42×C127—22no—
40C23×C127—22no—
41C23×C127C2×D411yescharacteristic
42Q8×C127—22no—
43Q8×C127—22no—
44D4×C127—22no—
45D4×C127—22no—
46D4×C127—42no—
47D4×C127—42no—
48C2×C4×C127—22no—
49C2×C4×C127—22no—
50C2×C4×C127—42no—
51C2×C4×C127—42no—
52C2×C4×C127—42no—
53C2×C4×C127C2×D412yes—
54C2×C4×C127C2×D411yescharacteristic
55C2×C4×C127#4111yescharacteristic
56C2×C4×C127#4112yes—
57C8×C127—22no—
58C8×C127—41no—
59C22×C127—41no—
60C22×C127—42no—
61C22×C127—82no—
62C22×C127#12111yescharacteristic
63C22×C127#12112yes—
64C4×C127—42no—
65C4×C127—42no—
66C4×C127—82no—
67C4×C127#12011yescharacteristic
68C4×C127#12312yes—
69C4×C127#12411yescharacteristic
70C2×C127—21no—
71C2×C127—22no—
72C2×C127—82no—
73C2×C127#39411yescharacteristic
74#2053C12711yesmaximal, characteristic, direct product factor, Sylow
75C127#205311yescharacteristic, direct product factor, Sylow
76#575C2×C12711yescharacteristic
77#424C2×C12711yescharacteristic, complemented
78#416C2×C12712yescomplemented
79#410C2×C12712yescomplemented
80H(3,ℤ/4)C2×C12711yescharacteristic, complemented
81C2×#41C22×C12712yes—
82#137—22no—
83AGL(1,ℤ/8)—22no—
84#135—22no—
85C2×M16C22×C12711yescharacteristic
86C22×C8C22×C12711yescharacteristic
87#117C22×C12712yes—
88#117C22×C12711yescharacteristic
89C4⋊C8—22no—
90#103—22no—
91#102—22no—
92#99—24no—
93#41—22no—
94#41—22no—
95#41—22no—
96#41—22no—
97C2×Q8D4×C12712yes—
98C2×D4—22no—
99C2×D4D4×C12712yes—
100C22×C4—22no—
101C22×C4C23×C12711yescharacteristic
102Q16—22no—
103SD16—24no—
104D8—22no—
105M16—22no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8D4×C12712yes—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C22⋊C4—22no—
112C22⋊C4D4×C12712yes—
113C42—21no—
114C42—22no—
115C23—22no—
116C23C2×D4×C12711yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4—42no—
128C2×C4C2×D4×C12712yes—
129C2×C4C2×D4×C12711yescharacteristic
130C2×C4#41×C12711yescharacteristic
131C2×C4#41×C12712yes—
132C8—22no—
133C8—41no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#121×C12711yescharacteristic
138C22#121×C12712yes—
139C4—42no—
140C4—42no—
141C4—82no—
142C4#120×C12711yescharacteristic
143C4#123×C12712yes—
144C4#124×C12711yescharacteristic
145C2—21no—
146C2—22no—
147C2—82no—
148C2#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. #424×C127C2semidirect
3. #416×C127C2semidirect
4. #410×C127C2semidirect
5. H(3,ℤ/4)×C127C2semidirect
74. #2053C127direct (N × H)
75. C127#2053direct (N × H)
77. #424C2×C127semidirect
78. #416C2×C127semidirect
79. #410C2×C127semidirect
80. H(3,ℤ/4)C2×C127semidirect

Maximal subgroups

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

subgroupindex
#575×C1272
#424×C1272
#416×C1272
#410×C1272
H(3,ℤ/4)×C1272
#2053127