Finite Group Databasebeta

← C127×#2236 #30635188

Subgroups — C127×#2236 #30635188

Order 16256.

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

normal subgroups only

This group has 140 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#467×C127C211yesmaximal, characteristic
2C2×#107×C127C211yesmaximal, characteristic
3#366×C127C212yesmaximal, complemented
4#358×C127C212yesmaximal, complemented
5C22⋊C16×C127C211yesmaximal, characteristic
6C2×Q16×C127C2211yescharacteristic
7C22×C8×C127C2211yescharacteristic
8C22⋊Q8×C127—21no—
9C2×C4⋊C4×C127—21no—
10C2×C16×C127C2212yes—
11#107×C127—21no—
12#107×C127C2212yes—
13#107×C127C2211yescharacteristic
14#103×C127—21no—
15C2×Q8×C127—21no—
16C22×C4×C127—41no—
17C22×C4×C127D411yescharacteristic
18Q16×C127—22no—
19C2×C8×C127—22no—
20C2×C8×C127D411yescharacteristic
21C2×C8×C127C2311yescharacteristic
22C4⋊C4×C127—21no—
23C4⋊C4×C127—22no—
24C4⋊C4×C127—41no—
25C4⋊C4×C127—41no—
26C22⋊C4×C127—41no—
27C16×C127—22no—
28C23×C127D811yescharacteristic
29Q8×C127—41no—
30Q8×C127—41no—
31C2×C4×C127—21no—
32C2×C4×C127—21no—
33C2×C4×C127—41no—
34C2×C4×C127—41no—
35C2×C4×C127—42no—
36C2×C4×C127—82no—
37C2×C4×C127D811yescharacteristic
38C2×C4×C127C2×D411yescharacteristic
39C8×C127—21no—
40C8×C127#4112yes—
41C22×C127—21no—
42C22×C127—21no—
43C22×C127Q3212yes—
44C22×C127C2×D811yescharacteristic
45C4×C127—21no—
46C4×C127—81no—
47C4×C127—81no—
48C4×C127—82no—
49C4×C127#12311yescharacteristic
50C4×C127#13711yescharacteristic
51C2×C127—22no—
52C2×C127#48011yescharacteristic
53C2×C127C2×Q3211yescharacteristic
54C2×C127#50911yescharacteristic
55#2236C12711yesmaximal, characteristic, direct product factor, Sylow
56C127#223611yescharacteristic, direct product factor, Sylow
57#467C2×C12711yescharacteristic
58C2×#107C2×C12711yescharacteristic
59#366C2×C12712yescomplemented
60#358C2×C12712yescomplemented
61C22⋊C16C2×C12711yescharacteristic
62C2×Q16C22×C12711yescharacteristic
63C22×C8C22×C12711yescharacteristic
64C22⋊Q8—21no—
65C2×C4⋊C4—21no—
66C2×C16C22×C12712yes—
67#107—21no—
68#107C22×C12712yes—
69#107C22×C12711yescharacteristic
70#103—21no—
71C2×Q8—21no—
72C22×C4—41no—
73C22×C4D4×C12711yescharacteristic
74Q16—22no—
75C2×C8—22no—
76C2×C8D4×C12711yescharacteristic
77C2×C8C23×C12711yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—22no—
80C4⋊C4—41no—
81C4⋊C4—41no—
82C22⋊C4—41no—
83C16—22no—
84C23D8×C12711yescharacteristic
85Q8—41no—
86Q8—41no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—42no—
92C2×C4—82no—
93C2×C4D8×C12711yescharacteristic
94C2×C4C2×D4×C12711yescharacteristic
95C8—21no—
96C8#41×C12712yes—
97C22—21no—
98C22—21no—
99C22Q32×C12712yes—
100C22C2×D8×C12711yescharacteristic
101C4—21no—
102C4—82no—
103C4—81no—
104C4—81no—
105C4#123×C12711yescharacteristic
106C4#137×C12711yescharacteristic
107C2—22no—
108C2#480×C12711yescharacteristic
109C2C2×Q32×C12711yescharacteristic
110C2#509×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×D8
commutator, Frattini, cosocleC2×C8C23×C127
prime radicalC23×C127D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. #366×C127C2semidirect
4. #358×C127C2semidirect
55. #2236C127direct (N × H)
56. C127#2236direct (N × H)
59. #366C2×C127semidirect
60. #358C2×C127semidirect

Maximal subgroups

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

subgroupindex
#467×C1272
C2×#107×C1272
#366×C1272
#358×C1272
C22⋊C16×C1272
#2236127