Finite Group Databasebeta

← C127×#13692 #44577365

Subgroups — C127×#13692 #44577365

Order 32512.

216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C127×#2263C212yesmaximal, complemented
2C127×#2246C211yesmaximal, characteristic, complemented
3C127×#2178C211yesmaximal, characteristic, complemented
4C127×#1422C211yesmaximal, characteristic, complemented
5C127×#1419C212yesmaximal, complemented
6#508×C127C2211yescharacteristic
7C2×D16×C127—21no—
8C2×D16×C127C2212yes—
9#493×C127—21no—
10#443×C127—21no—
11SD64×C127—22no—
12D32×C127—22no—
13M64×C127C2212yes—
14#368×C127C2211yescharacteristic
15#359×C127—21no—
16C4×C16×C127C2211yescharacteristic
17#135×C127—21no—
18C2×D8×C127—22no—
19C2×D8×C127—41no—
20#131×C127—41no—
21#127×C127—41no—
22Q32×C127D411yescharacteristic, complemented
23SD32×C127—21no—
24D16×C127—22no—
25D16×C127—22no—
26D16×C127—42no—
27D16×C127D411yescharacteristic, complemented
28C2×C16×C127D411yescharacteristic
29C2×C16×C127C2311yescharacteristic
30#108×C127—21no—
31#104×C127—41no—
32C4×C8×C127D411yescharacteristic
33C32×C127—22no—
34#41×C127—41no—
35C2×D4×C127—42no—
36C2×D4×C127—82no—
37Q16×C127—21no—
38SD16×C127—41no—
39D8×C127—21no—
40D8×C127—42no—
41D8×C127—42no—
42D8×C127—81no—
43D8×C127—81no—
44M16×C127—41no—
45M16×C127—81no—
46C2×C8×C127—81no—
47C2×C8×C127D811yescharacteristic
48C2×C8×C127C2×D411yescharacteristic
49C42×C127D811yescharacteristic
50C16×C127—21no—
51C16×C127C2×D411yescharacteristic
52C16×C127#4111yescharacteristic
53C23×C127—82no—
54Q8×C127—41no—
55D4×C127—41no—
56D4×C127—81no—
57D4×C127—82no—
58D4×C127—82no—
59D4×C127—164no—
60C2×C4×C127—21no—
61C2×C4×C127—81no—
62C2×C4×C127C2×D811yescharacteristic
63C8×C127—81no—
64C8×C127D1611yescharacteristic
65C8×C127D1611yescharacteristic
66C8×C127#12111yescharacteristic
67C8×C127AGL(1,ℤ/8)11yescharacteristic
68C22×C127—81no—
69C22×C127—164no—
70C22×C127—162no—
71C22×C127#50911yescharacteristic
72C4×C127—22no—
73C4×C127—81no—
74C4×C127#45911yescharacteristic
75C4×C127C2×D1611yescharacteristic
76#13692C12711yesmaximal, characteristic, direct product factor, Sylow
77C2×C127—21no—
78C2×C127—161no—
79C2×C127—322no—
80C2×C127#220611yescharacteristic
81#2263C2×C12712yescomplemented
82#2246C2×C12711yescharacteristic, complemented
83#2178C2×C12711yescharacteristic, complemented
84#1422C2×C12711yescharacteristic, complemented
85#1419C2×C12712yescomplemented
86C127#1369211yescharacteristic, direct product factor, Sylow
87#508C22×C12711yescharacteristic
88C2×D16—21no—
89C2×D16C22×C12712yes—
90#493—21no—
91#443—21no—
92SD64—22no—
93D32—22no—
94M64C22×C12712yes—
95#368C22×C12711yescharacteristic
96#359—21no—
97C4×C16C22×C12711yescharacteristic
98#135—21no—
99C2×D8—22no—
100C2×D8—41no—
101#131—41no—
102#127—41no—
103Q32D4×C12711yescharacteristic, complemented
104SD32—21no—
105D16—22no—
106D16—22no—
107D16—42no—
108D16D4×C12711yescharacteristic, complemented
109C2×C16D4×C12711yescharacteristic
110C2×C16C23×C12711yescharacteristic
111#108—21no—
112#104—41no—
113C4×C8D4×C12711yescharacteristic
114C32—22no—
115#41—41no—
116C2×D4—42no—
117C2×D4—82no—
118Q16—21no—
119SD16—41no—
120D8—21no—
121D8—42no—
122D8—42no—
123D8—81no—
124D8—81no—
125M16—41no—
126M16—81no—
127C2×C8—81no—
128C2×C8D8×C12711yescharacteristic
129C2×C8C2×D4×C12711yescharacteristic
130C42D8×C12711yescharacteristic
131C16—21no—
132C16C2×D4×C12711yescharacteristic
133C16#41×C12711yescharacteristic
134C23—82no—
135Q8—41no—
136D4—41no—
137D4—81no—
138D4—82no—
139D4—82no—
140D4—164no—
141C2×C4—21no—
142C2×C4—81no—
143C2×C4C2×D8×C12711yescharacteristic
144C8—81no—
145C8D16×C12711yescharacteristic
146C8D16×C12711yescharacteristic
147C8#121×C12711yescharacteristic
148C8AGL(1,ℤ/8)×C12711yescharacteristic
149C22—81no—
150C22—164no—
151C22—162no—
152C22#509×C12711yescharacteristic
153C4—22no—
154C4—81no—
155C4#459×C12711yescharacteristic
156C4C2×D16×C12711yescharacteristic
157C2—21no—
158C2—161no—
159C2—322no—
160C2C127×#220611yescharacteristic
subgroupG/H
center, socleC2×C127#2206
commutator, Frattini, cosocleC2×C16C23×C127
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ C4×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2263C2semidirect
2. C127×#2246C2semidirect
3. C127×#2178C2semidirect
4. C127×#1422C2semidirect
5. C127×#1419C2semidirect
22. Q32×C127D4semidirect
27. D16×C127D4semidirect
76. #13692C127direct (N × H)
81. #2263C2×C127semidirect
82. #2246C2×C127semidirect
83. #2178C2×C127semidirect
84. #1422C2×C127semidirect
85. #1419C2×C127semidirect
86. C127#13692direct (N × H)
103. Q32D4×C127semidirect
108. D16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22632
C127×#22462
C127×#21782
C127×#14222
C127×#14192
#13692127