Finite Group Databasebeta

← C127×#2250 #30635202

Subgroups — C127×#2250 #30635202

Order 16256.

198 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×SD32×C127C212yesmaximal, complemented
2C2×D16×C127C212yesmaximal, complemented
3#495×C127C211yesmaximal, characteristic, complemented
4#493×C127C211yesmaximal, characteristic, complemented
5#346×C127C211yesmaximal, characteristic, complemented
6C2×Q16×C127C2211yescharacteristic
7C2×SD16×C127—21no—
8C2×D8×C127—21no—
9C2×D8×C127C2211yescharacteristic
10C2×D8×C127C2212yes—
11#127×C127—21no—
12#124×C127—21no—
13SD32×C127—24no—
14D16×C127—24no—
15C2×C16×C127C2212yes—
16C4×C8×C127C2211yescharacteristic
17C2×Q8×C127—21no—
18C2×D4×C127—21no—
19C2×D4×C127—22no—
20C2×D4×C127—42no—
21Q16×C127—22no—
22SD16×C127—42no—
23D8×C127—22no—
24D8×C127—22no—
25D8×C127—22no—
26D8×C127—42no—
27C2×C8×C127D411yescharacteristic
28C2×C8×C127C2311yescharacteristic
29C22⋊C4×C127—42no—
30C42×C127D411yescharacteristic
31C16×C127D414yescomplemented
32C23×C127—41no—
33C23×C127—42no—
34Q8×C127—41no—
35Q8×C127—41no—
36D4×C127—41no—
37D4×C127—42no—
38D4×C127—42no—
39D4×C127—41no—
40D4×C127—84no—
41C2×C4×C127—41no—
42C2×C4×C127D812yes—
43C2×C4×C127C2×D411yescharacteristic
44C8×C127D812yes—
45C8×C127C2×D412yes—
46C22×C127—82no—
47C22×C127—81no—
48C22×C127—84no—
49C22×C127—82no—
50C22×C127C2×D811yescharacteristic
51C4×C127—22no—
52C4×C127—81no—
53C4×C127#12711yescharacteristic
54C4×C127C2×D811yescharacteristic
55C2×C127—162no—
56C2×C127—161no—
57C2×C127#49311yescharacteristic
58C2×C127#50912yes—
59#2250C12711yesmaximal, characteristic, direct product factor, Sylow
60C127#225011yescharacteristic, direct product factor, Sylow
61C2×SD32C2×C12712yescomplemented
62C2×D16C2×C12712yescomplemented
63#495C2×C12711yescharacteristic, complemented
64#493C2×C12711yescharacteristic, complemented
65#346C2×C12711yescharacteristic, complemented
66C2×Q16C22×C12711yescharacteristic
67C2×SD16—21no—
68C2×D8—21no—
69C2×D8C22×C12712yes—
70C2×D8C22×C12711yescharacteristic
71#127—21no—
72#124—21no—
73SD32—24no—
74D16—24no—
75C2×C16C22×C12712yes—
76C4×C8C22×C12711yescharacteristic
77C2×Q8—21no—
78C2×D4—21no—
79C2×D4—22no—
80C2×D4—42no—
81Q16—22no—
82SD16—42no—
83D8—22no—
84D8—22no—
85D8—22no—
86D8—42no—
87C2×C8D4×C12711yescharacteristic
88C2×C8C23×C12711yescharacteristic
89C22⋊C4—42no—
90C42D4×C12711yescharacteristic
91C16D4×C12714yescomplemented
92C23—41no—
93C23—42no—
94Q8—41no—
95Q8—41no—
96D4—41no—
97D4—42no—
98D4—42no—
99D4—41no—
100D4—84no—
101C2×C4—41no—
102C2×C4D8×C12712yes—
103C2×C4C2×D4×C12711yescharacteristic
104C8D8×C12712yes—
105C8C2×D4×C12712yes—
106C22—84no—
107C22—82no—
108C22—82no—
109C22—81no—
110C22C2×D8×C12711yescharacteristic
111C4—22no—
112C4—81no—
113C4#127×C12711yescharacteristic
114C4C2×D8×C12711yescharacteristic
115C2—162no—
116C2—161no—
117C2#493×C12711yescharacteristic
118C2#509×C12712yes—
subgroupG/H
center, socleC22×C127C2×D8
commutator, Frattini, cosocleC2×C8C23×C127
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×SD32×C127C2semidirect
2. C2×D16×C127C2semidirect
3. #495×C127C2semidirect
4. #493×C127C2semidirect
5. #346×C127C2semidirect
31. C16×C127D4semidirect
59. #2250C127direct (N × H)
60. C127#2250direct (N × H)
61. C2×SD32C2×C127semidirect
62. C2×D16C2×C127semidirect
63. #495C2×C127semidirect
64. #493C2×C127semidirect
65. #346C2×C127semidirect
91. C16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×C1272
C2×D16×C1272
#495×C1272
#493×C1272
#346×C1272
#2250127