Finite Group Databasebeta

← C127×#7433 #44571106

Subgroups — C127×#7433 #44571106

Order 32512.

182 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2091C211yesmaximal, characteristic
2C127×#1320C211yesmaximal, characteristic
3C127×#1298C211yesmaximal, characteristic
4#430×C127—21no—
5#430×C127C411yescharacteristic
6#407×C127—21no—
7#407×C127C2211yescharacteristic
8C2×C22⋊C8×C127—21no—
9#349×C127—21no—
10#338×C127C411yescharacteristic
11C23×C4×C127D411yescharacteristic
12C2×M16×C127—21no—
13C2×M16×C127—21no—
14C2×M16×C127C2×C411yescharacteristic
15C2×M16×C127D411yescharacteristic
16C22×C8×C127—41no—
17M32×C127—41no—
18#108×C127—42no—
19#108×C127—41no—
20C22⋊C8×C127—22no—
21C22⋊C8×C127—41no—
22C22⋊C8×C127—42no—
23C22⋊C8×C127—41no—
24C24×C127Q1611yescharacteristic
25C22×C4×C127—21no—
26C22×C4×C127—21no—
27C22×C4×C127—41no—
28C22×C4×C127—41no—
29C22×C4×C127C22⋊C411yescharacteristic
30C22×C4×C127SD1611yescharacteristic
31M16×C127—41no—
32M16×C127—41no—
33M16×C127—41no—
34M16×C127—41no—
35M16×C127—41no—
36M16×C127—41no—
37C2×C8×C127—22no—
38C2×C8×C127—21no—
39C2×C8×C127—21no—
40C2×C8×C127—42no—
41C2×C8×C127—41no—
42C2×C8×C127—81no—
43C2×C8×C127—81no—
44C16×C127—81no—
45C23×C127—21no—
46C23×C127—41no—
47C23×C127—42no—
48C23×C127#10311yescharacteristic
49C2×C4×C127—21no—
50C2×C4×C127—21no—
51C2×C4×C127—21no—
52C2×C4×C127—41no—
53C2×C4×C127—41no—
54C2×C4×C127—41no—
55C2×C4×C127—81no—
56C2×C4×C127#9911yescharacteristic
57C2×C4×C127#10411yescharacteristic
58C8×C127—42no—
59C8×C127—41no—
60C8×C127—41no—
61C8×C127—82no—
62C8×C127—81no—
63C22×C127—22no—
64C22×C127—21no—
65C22×C127—41no—
66C22×C127—41no—
67C22×C127—42no—
68C22×C127—41no—
69C22×C127—81no—
70C22×C127#32811yescharacteristic
71C4×C127—21no—
72C4×C127—41no—
73C4×C127#35211yescharacteristic
74C4×C127#35311yescharacteristic
75#7433C12711yesmaximal, characteristic, direct product factor, Sylow
76C2×C127—21no—
77C2×C127—42no—
78C2×C127—41no—
79C2×C127#135211yescharacteristic
80#2091C2×C12711yescharacteristic
81#1320C2×C12711yescharacteristic
82#1298C2×C12711yescharacteristic
83C127#743311yescharacteristic, direct product factor, Sylow
84#430—21no—
85#430C4×C12711yescharacteristic
86#407—21no—
87#407C22×C12711yescharacteristic
88C2×C22⋊C8—21no—
89#349—21no—
90#338C4×C12711yescharacteristic
91C23×C4D4×C12711yescharacteristic
92C2×M16—21no—
93C2×M16—21no—
94C2×M16C2×C4×C12711yescharacteristic
95C2×M16D4×C12711yescharacteristic
96C22×C8—41no—
97M32—41no—
98#108—41no—
99#108—42no—
100C22⋊C8—22no—
101C22⋊C8—41no—
102C22⋊C8—42no—
103C22⋊C8—41no—
104C24Q16×C12711yescharacteristic
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—41no—
108C22×C4—41no—
109C22×C4C22⋊C4×C12711yescharacteristic
110C22×C4SD16×C12711yescharacteristic
111M16—41no—
112M16—41no—
113M16—41no—
114M16—41no—
115M16—41no—
116M16—41no—
117C2×C8—22no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—42no—
121C2×C8—41no—
122C2×C8—81no—
123C2×C8—81no—
124C16—81no—
125C23—21no—
126C23—41no—
127C23—42no—
128C23#103×C12711yescharacteristic
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—81no—
136C2×C4#99×C12711yescharacteristic
137C2×C4#104×C12711yescharacteristic
138C8—42no—
139C8—41no—
140C8—41no—
141C8—82no—
142C8—81no—
143C22—22no—
144C22—21no—
145C22—41no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22—81no—
150C22#328×C12711yescharacteristic
151C4—21no—
152C4—41no—
153C4#352×C12711yescharacteristic
154C4#353×C12711yescharacteristic
155C2—21no—
156C2—42no—
157C2—41no—
158C2C127×#135211yescharacteristic
subgroupG/H
centerC4×C127#353
commutatorC2×M16C2×C4×C127
Frattini, cosocle#407C22×C127
socleC2×C127#1352
prime radicalC24×C127Q16
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ #407×C127 ◁ G

Complements

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

NH ≅ G/Ntype
75. #7433C127direct (N × H)
83. C127#7433direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#20912
C127×#13202
C127×#12982
#7433127