Finite Group Databasebeta

← C127×#2185 #30635137

Subgroups — C127×#2185 #30635137

Order 16256.

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

normal subgroups only

This group has 226 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
1C22×Q16×C127C211yesmaximal, characteristic, complemented
2C2×SD32×C127C212yesmaximal, complemented
3#466×C127C211yesmaximal, characteristic
4#358×C127C212yesmaximal, complemented
5C22⋊C16×C127C211yesmaximal, characteristic, complemented
6C22×Q8×C127—21no—
7C2×Q16×C127—24no—
8C2×Q16×C127—21no—
9C2×Q16×C127C2212yes—
10C2×D8×C127C2211yescharacteristic
11C22×C8×C127C2211yescharacteristic
12#121×C127—21no—
13SD32×C127—24no—
14C2×C16×C127C2212yes—
15#107×C127C2211yescharacteristic
16#102×C127—21no—
17C2×Q8×C127—24no—
18C2×Q8×C127—22no—
19C2×Q8×C127—42no—
20C2×Q8×C127—41no—
21C2×D4×C127—21no—
22C2×D4×C127—41no—
23C22×C4×C127—41no—
24C22×C4×C127D411yescharacteristic
25Q16×C127—24no—
26Q16×C127—22no—
27Q16×C127D414yescomplemented
28D8×C127—22no—
29C2×C8×C127—22no—
30C2×C8×C127D411yescharacteristic
31C2×C8×C127C2311yescharacteristic
32C4⋊C4×C127—21no—
33C22⋊C4×C127—41no—
34C16×C127—22no—
35C23×C127—41no—
36C23×C127D811yescharacteristic
37Q8×C127—24no—
38Q8×C127—44no—
39Q8×C127—42no—
40D4×C127—41no—
41D4×C127—41no—
42D4×C127—82no—
43C2×C4×C127—21no—
44C2×C4×C127—21no—
45C2×C4×C127—44no—
46C2×C4×C127—42no—
47C2×C4×C127—41no—
48C2×C4×C127D811yescharacteristic
49C2×C4×C127C2×D411yescharacteristic
50C8×C127—21no—
51C8×C127C2×D412yes—
52C22×C127—21no—
53C22×C127—21no—
54C22×C127—81no—
55C22×C127—81no—
56C22×C127—81no—
57C22×C127SD3212yescomplemented
58C22×C127C2×D811yescharacteristic
59C4×C127—21no—
60C4×C127—44no—
61C4×C127—81no—
62C4×C127#12011yescharacteristic
63C4×C127AGL(1,ℤ/8)11yescharacteristic
64C2×C127—22no—
65C2×C127—161no—
66C2×C127#44711yescharacteristic
67C2×C127C2×SD3211yescharacteristic
68C2×C127#51011yescharacteristic
69#2185C12711yesmaximal, characteristic, direct product factor, Sylow
70C127#218511yescharacteristic, direct product factor, Sylow
71C22×Q16C2×C12711yescharacteristic, complemented
72C2×SD32C2×C12712yescomplemented
73#466C2×C12711yescharacteristic
74#358C2×C12712yescomplemented
75C22⋊C16C2×C12711yescharacteristic, complemented
76C22×Q8—21no—
77C2×Q16—24no—
78C2×Q16—21no—
79C2×Q16C22×C12712yes—
80C2×D8C22×C12711yescharacteristic
81C22×C8C22×C12711yescharacteristic
82#121—21no—
83SD32—24no—
84C2×C16C22×C12712yes—
85#107C22×C12711yescharacteristic
86#102—21no—
87C2×Q8—24no—
88C2×Q8—22no—
89C2×Q8—42no—
90C2×Q8—41no—
91C2×D4—21no—
92C2×D4—41no—
93C22×C4—41no—
94C22×C4D4×C12711yescharacteristic
95Q16—24no—
96Q16—22no—
97Q16D4×C12714yescomplemented
98D8—22no—
99C2×C8—22no—
100C2×C8D4×C12711yescharacteristic
101C2×C8C23×C12711yescharacteristic
102C4⋊C4—21no—
103C22⋊C4—41no—
104C16—22no—
105C23—41no—
106C23D8×C12711yescharacteristic
107Q8—24no—
108Q8—44no—
109Q8—42no—
110D4—41no—
111D4—41no—
112D4—82no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—44no—
116C2×C4—42no—
117C2×C4—41no—
118C2×C4D8×C12711yescharacteristic
119C2×C4C2×D4×C12711yescharacteristic
120C8—21no—
121C8C2×D4×C12712yes—
122C22—21no—
123C22—21no—
124C22—81no—
125C22—81no—
126C22—81no—
127C22SD32×C12712yescomplemented
128C22C2×D8×C12711yescharacteristic
129C4—21no—
130C4—44no—
131C4—81no—
132C4#120×C12711yescharacteristic
133C4AGL(1,ℤ/8)×C12711yescharacteristic
134C2—22no—
135C2—161no—
136C2#447×C12711yescharacteristic
137C2C2×SD32×C12711yescharacteristic
138C2#510×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×D8
commutator, Frattini, cosocleC2×C8C23×C127
prime radical#466×C127C2
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
1. C22×Q16×C127C2semidirect
2. C2×SD32×C127C2semidirect
4. #358×C127C2semidirect
5. C22⋊C16×C127C2semidirect
27. Q16×C127D4semidirect
57. C22×C127SD32semidirect
69. #2185C127direct (N × H)
70. C127#2185direct (N × H)
71. C22×Q16C2×C127semidirect
72. C2×SD32C2×C127semidirect
74. #358C2×C127semidirect
75. C22⋊C16C2×C127semidirect
97. Q16D4×C127semidirect
127. C22SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×C1272
C2×SD32×C1272
#466×C1272
#358×C1272
C22⋊C16×C1272
#2185127