Finite Group Databasebeta

← C127×#7229 #44570902

Subgroups — C127×#7229 #44570902

Order 32512.

244 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 86 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×#2113C211yesmaximal, characteristic
2C127×#1813C212yesmaximal
3C2×#131×C127C2211yescharacteristic
4C2×M32×C127C411yescharacteristic
5C22×C16×C127C411yescharacteristic
6C2×#108×C127—22no—
7#413×C127—22no—
8C22⋊C16×C127—22no—
9#338×C127C414yes—
10C2×#41×C127D411yescharacteristic
11#131×C127—41no—
12#131×C127—41no—
13C2×M16×C127—24no—
14C2×M16×C127C2×C412yes—
15C2×M16×C127Q811yescharacteristic
16C22×C8×C127C2×C411yescharacteristic
17C22×C8×C127D412yes—
18M32×C127—41no—
19C2×C16×C127—21no—
20C2×C16×C127—21no—
21C2×C16×C127—41no—
22#108×C127—42no—
23#108×C127—42no—
24#101×C127—42no—
25#100×C127—42no—
26#41×C127—41no—
27#41×C127—41no—
28C2×Q8×C127D811yescharacteristic
29C2×D4×C127SD1612yes—
30C2×D4×C127Q1611yescharacteristic
31C22×C4×C127C22⋊C412yes—
32C22×C4×C127C4⋊C411yescharacteristic
33M16×C127—42no—
34M16×C127—41no—
35M16×C127—44no—
36M16×C127—44no—
37C2×C8×C127—22no—
38C2×C8×C127—22no—
39C2×C8×C127—21no—
40C2×C8×C127—21no—
41C2×C8×C127—44no—
42C2×C8×C127C4211yescharacteristic
43C2×C8×C127C22⋊C411yescharacteristic
44C2×C8×C127C4⋊C412yes—
45C16×C127—41no—
46C16×C127—41no—
47C23×C127#10312yes—
48C23×C127#10611yescharacteristic
49Q8×C127—41no—
50D4×C127—42no—
51D4×C127—41no—
52C2×C4×C127—22no—
53C2×C4×C127—21no—
54C2×C4×C127—22no—
55C2×C4×C127—21no—
56C2×C4×C127#9511yescharacteristic
57C2×C4×C127#10212yes—
58C2×C4×C127#10711yescharacteristic
59C8×C127—21no—
60C8×C127—22no—
61C8×C127—84no—
62C8×C127#9911yescharacteristic
63C8×C127#9911yescharacteristic
64C22×C127—22no—
65C22×C127—21no—
66C22×C127—42no—
67C22×C127—41no—
68C22×C127#34011yescharacteristic
69C4×C127—22no—
70C4×C127—21no—
71C4×C127H(3,ℤ/4)11yescharacteristic
72C4×C127#34211yescharacteristic
73#7229C12711yesmaximal, characteristic, direct product factor, Sylow
74C2×C127—21no—
75C2×C127—42no—
76C2×C127—41no—
77C2×C127#128911yescharacteristic
78#2113C2×C12711yescharacteristic
79#1813C2×C12712yes—
80C127#722911yescharacteristic, direct product factor, Sylow
81C2×#131C22×C12711yescharacteristic
82C2×M32C4×C12711yescharacteristic
83C22×C16C4×C12711yescharacteristic
84C2×#108—22no—
85#413—22no—
86C22⋊C16—22no—
87#338C4×C12714yes—
88C2×#41D4×C12711yescharacteristic
89#131—41no—
90#131—41no—
91C2×M16—24no—
92C2×M16C2×C4×C12712yes—
93C2×M16Q8×C12711yescharacteristic
94C22×C8C2×C4×C12711yescharacteristic
95C22×C8D4×C12712yes—
96M32—41no—
97C2×C16—21no—
98C2×C16—21no—
99C2×C16—41no—
100#108—42no—
101#108—42no—
102#101—42no—
103#100—42no—
104#41—41no—
105#41—41no—
106C2×Q8D8×C12711yescharacteristic
107C2×D4SD16×C12712yes—
108C2×D4Q16×C12711yescharacteristic
109C22×C4C22⋊C4×C12712yes—
110C22×C4C4⋊C4×C12711yescharacteristic
111M16—42no—
112M16—41no—
113M16—44no—
114M16—44no—
115C2×C8—22no—
116C2×C8—22no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—44no—
120C2×C8C42×C12711yescharacteristic
121C2×C8C22⋊C4×C12711yescharacteristic
122C2×C8C4⋊C4×C12712yes—
123C16—41no—
124C16—41no—
125C23#103×C12712yes—
126C23#106×C12711yescharacteristic
127Q8—41no—
128D4—42no—
129D4—41no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4#95×C12711yescharacteristic
135C2×C4#102×C12712yes—
136C2×C4#107×C12711yescharacteristic
137C8—21no—
138C8—22no—
139C8—84no—
140C8#99×C12711yescharacteristic
141C8#99×C12711yescharacteristic
142C22—22no—
143C22—21no—
144C22—42no—
145C22—41no—
146C22#340×C12711yescharacteristic
147C4—22no—
148C4—21no—
149C4H(3,ℤ/4)×C12711yescharacteristic
150C4#342×C12711yescharacteristic
151C2—21no—
152C2—42no—
153C2—41no—
154C2C127×#128911yescharacteristic
subgroupG/H
centerC4×C127H(3,ℤ/4)
commutatorC2×C8C42×C127
Frattini, cosocleC2×#131C22×C127
socleC2×C127#1289
prime radicalC2×#41×C127D4
LCSG ▷ C2×C8 ▷ C4 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
73. #7229C127direct (N × H)
80. C127#7229direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21132
C127×#18132
#7229127