Finite Group Databasebeta

← C127×#7341 #44571014

Subgroups — C127×#7341 #44571014

Order 32512.

324 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1784C211yesmaximal, characteristic
2C127×#1320C212yesmaximal
3C23×Q8×C127C411yescharacteristic
4C2×#101×C127—22no—
5#407×C127C411yescharacteristic
6#407×C127C2211yescharacteristic
7#349×C127—22no—
8C22×Q8×C127—21no—
9C22×Q8×C127—21no—
10C22×Q8×C127—41no—
11C22×Q8×C127—41no—
12C22×Q8×C127—44no—
13C23×C4×C127C812yes—
14C23×C4×C127C2×C411yescharacteristic
15C2×M16×C127—21no—
16C2×M16×C127D412yes—
17M32×C127—42no—
18#101×C127—44no—
19C22⋊C8×C127—41no—
20C22⋊C8×C127—41no—
21C24×C127C2×C811yescharacteristic
22C2×Q8×C127—24no—
23C2×Q8×C127—42no—
24C2×Q8×C127—44no—
25C2×Q8×C127—42no—
26C2×Q8×C127—44no—
27C2×Q8×C127—48no—
28C2×Q8×C127—44no—
29C2×Q8×C127—41no—
30C2×Q8×C127—41no—
31C22×C4×C127—22no—
32C22×C4×C127—21no—
33C22×C4×C127—21no—
34C22×C4×C127—44no—
35C22×C4×C127—42no—
36C22×C4×C127—42no—
37C22×C4×C127C22⋊C411yescharacteristic
38C22×C4×C127M1611yescharacteristic
39M16×C127—42no—
40M16×C127—42no—
41C2×C8×C127—22no—
42C2×C8×C127—41no—
43C16×C127—82no—
44C23×C127—21no—
45C23×C127—41no—
46C23×C127—42no—
47C23×C127C22⋊C811yescharacteristic
48Q8×C127—44no—
49Q8×C127—48no—
50Q8×C127—44no—
51C2×C4×C127—22no—
52C2×C4×C127—24no—
53C2×C4×C127—21no—
54C2×C4×C127—42no—
55C2×C4×C127—42no—
56C2×C4×C127—44no—
57C2×C4×C127—42no—
58C2×C4×C127—42no—
59C2×C4×C127—41no—
60C2×C4×C127—44no—
61C2×C4×C127#9911yescharacteristic
62C2×C4×C127#10011yescharacteristic
63C8×C127—42no—
64C8×C127—81no—
65C22×C127—22no—
66C22×C127—21no—
67C22×C127—41no—
68C22×C127—41no—
69C22×C127—42no—
70C22×C127—42no—
71C22×C127—41no—
72C22×C127#32311yescharacteristic
73C4×C127—21no—
74C4×C127—44no—
75C4×C127—41no—
76C4×C127AΣL(1,𝔽16)12yes—
77#7341C12711yesmaximal, characteristic, direct product factor, Sylow
78C2×C127—21no—
79C2×C127—42no—
80C2×C127—41no—
81C2×C127#131611yescharacteristic
82#1784C2×C12711yescharacteristic
83#1320C2×C12712yes—
84C127#734111yescharacteristic, direct product factor, Sylow
85C23×Q8C4×C12711yescharacteristic
86C2×#101—22no—
87#407C4×C12711yescharacteristic
88#407C22×C12711yescharacteristic
89#349—22no—
90C22×Q8—21no—
91C22×Q8—21no—
92C22×Q8—41no—
93C22×Q8—41no—
94C22×Q8—44no—
95C23×C4C8×C12712yes—
96C23×C4C2×C4×C12711yescharacteristic
97C2×M16—21no—
98C2×M16D4×C12712yes—
99M32—42no—
100#101—44no—
101C22⋊C8—41no—
102C22⋊C8—41no—
103C24C2×C8×C12711yescharacteristic
104C2×Q8—24no—
105C2×Q8—42no—
106C2×Q8—44no—
107C2×Q8—42no—
108C2×Q8—44no—
109C2×Q8—48no—
110C2×Q8—44no—
111C2×Q8—41no—
112C2×Q8—41no—
113C22×C4—22no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—44no—
117C22×C4—42no—
118C22×C4—42no—
119C22×C4C22⋊C4×C12711yescharacteristic
120C22×C4M16×C12711yescharacteristic
121M16—42no—
122M16—42no—
123C2×C8—22no—
124C2×C8—41no—
125C16—82no—
126C23—21no—
127C23—41no—
128C23—42no—
129C23C22⋊C8×C12711yescharacteristic
130Q8—44no—
131Q8—48no—
132Q8—44no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—21no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—44no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4#99×C12711yescharacteristic
144C2×C4#100×C12711yescharacteristic
145C8—42no—
146C8—81no—
147C22—22no—
148C22—21no—
149C22—41no—
150C22—41no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22#323×C12711yescharacteristic
155C4—21no—
156C4—44no—
157C4—41no—
158C4AΣL(1,𝔽16)×C12712yes—
159C2—21no—
160C2—42no—
161C2—41no—
162C2C127×#131611yescharacteristic
subgroupG/H
center, socleC2×C127#1316
commutatorC24C2×C8×C127
Frattini, cosocle#407C22×C127
prime radicalC24×C127C2×C8
LCSG ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ #407×C127 ◁ G

Complements

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

NH ≅ G/Ntype
77. #7341C127direct (N × H)
84. C127#7341direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#17842
C127×#13202
#7341127