Finite Group Databasebeta

← C127×#7340 #44571013

Subgroups — C127×#7340 #44571013

Order 32512.

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

normal subgroups only

This group has 452 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×#1783C211yesmaximal, characteristic
2C127×#1320C212yesmaximal, complemented
3C23×D4×C127C411yescharacteristic
4C2×#100×C127—22no—
5#407×C127C411yescharacteristic
6#407×C127C2211yescharacteristic
7#349×C127—22no—
8C25×C127C812yes—
9C22×D4×C127—21no—
10C22×D4×C127—21no—
11C22×D4×C127—41no—
12C22×D4×C127—41no—
13C22×D4×C127—44no—
14C23×C4×C127C2×C411yescharacteristic
15C2×M16×C127—21no—
16C2×M16×C127D412yes—
17M32×C127—42no—
18#100×C127—44no—
19C22⋊C8×C127—41no—
20C22⋊C8×C127—41no—
21C24×C127—22no—
22C24×C127—42no—
23C24×C127—44no—
24C24×C127—84no—
25C24×C127C2×C811yescharacteristic
26C2×D4×C127—24no—
27C2×D4×C127—42no—
28C2×D4×C127—42no—
29C2×D4×C127—44no—
30C2×D4×C127—48no—
31C2×D4×C127—44no—
32C2×D4×C127—44no—
33C2×D4×C127—41no—
34C2×D4×C127—41no—
35C22×C4×C127—21no—
36C22×C4×C127—21no—
37C22×C4×C127—42no—
38C22×C4×C127C22⋊C411yescharacteristic
39C22×C4×C127M1611yescharacteristic
40M16×C127—42no—
41M16×C127—42no—
42C2×C8×C127—22no—
43C2×C8×C127—41no—
44C16×C127—82no—
45C23×C127—21no—
46C23×C127—24no—
47C23×C127—41no—
48C23×C127—42no—
49C23×C127—42no—
50C23×C127—44no—
51C23×C127—44no—
52C23×C127—42no—
53C23×C127—84no—
54C23×C127—84no—
55C23×C127—88no—
56C23×C127—84no—
57C23×C127—88no—
58C23×C127C22⋊C811yescharacteristic
59D4×C127—44no—
60D4×C127—48no—
61D4×C127—44no—
62C2×C4×C127—22no—
63C2×C4×C127—21no—
64C2×C4×C127—42no—
65C2×C4×C127—42no—
66C2×C4×C127—41no—
67C2×C4×C127#9911yescharacteristic
68C2×C4×C127#10011yescharacteristic
69C8×C127—42no—
70C8×C127—81no—
71C22×C127—22no—
72C22×C127—21no—
73C22×C127—41no—
74C22×C127—41no—
75C22×C127—42no—
76C22×C127—42no—
77C22×C127—41no—
78C22×C127—44no—
79C22×C127—84no—
80C22×C127—84no—
81C22×C127—88no—
82C22×C127—84no—
83C22×C127—88no—
84C22×C127#32311yescharacteristic
85C4×C127—21no—
86C4×C127—41no—
87C4×C127AΣL(1,𝔽16)12yes—
88#7340C12711yesmaximal, characteristic, direct product factor, Sylow
89C2×C127—21no—
90C2×C127—42no—
91C2×C127—41no—
92C2×C127—84no—
93C2×C127#131611yescharacteristic
94#1783C2×C12711yescharacteristic
95#1320C2×C12712yescomplemented
96C127#734011yescharacteristic, direct product factor, Sylow
97C23×D4C4×C12711yescharacteristic
98C2×#100—22no—
99#407C4×C12711yescharacteristic
100#407C22×C12711yescharacteristic
101#349—22no—
102C25C8×C12712yes—
103C22×D4—21no—
104C22×D4—21no—
105C22×D4—41no—
106C22×D4—41no—
107C22×D4—44no—
108C23×C4C2×C4×C12711yescharacteristic
109C2×M16—21no—
110C2×M16D4×C12712yes—
111M32—42no—
112#100—44no—
113C22⋊C8—41no—
114C22⋊C8—41no—
115C24—22no—
116C24—42no—
117C24—44no—
118C24—84no—
119C24C2×C8×C12711yescharacteristic
120C2×D4—24no—
121C2×D4—42no—
122C2×D4—42no—
123C2×D4—44no—
124C2×D4—48no—
125C2×D4—44no—
126C2×D4—44no—
127C2×D4—41no—
128C2×D4—41no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—42no—
132C22×C4C22⋊C4×C12711yescharacteristic
133C22×C4M16×C12711yescharacteristic
134M16—42no—
135M16—42no—
136C2×C8—22no—
137C2×C8—41no—
138C16—82no—
139C23—21no—
140C23—24no—
141C23—41no—
142C23—42no—
143C23—42no—
144C23—44no—
145C23—44no—
146C23—42no—
147C23—84no—
148C23—84no—
149C23—88no—
150C23—84no—
151C23—88no—
152C23C22⋊C8×C12711yescharacteristic
153D4—44no—
154D4—48no—
155D4—44no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4#99×C12711yescharacteristic
162C2×C4#100×C12711yescharacteristic
163C8—42no—
164C8—81no—
165C22—22no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—41no—
172C22—44no—
173C22—84no—
174C22—84no—
175C22—88no—
176C22—84no—
177C22—88no—
178C22#323×C12711yescharacteristic
179C4—21no—
180C4—41no—
181C4AΣL(1,𝔽16)×C12712yes—
182C2—21no—
183C2—42no—
184C2—41no—
185C2—84no—
186C2C127×#131611yescharacteristic
subgroupG/H
center, socleC2×C127#1316
commutatorC24C2×C8×C127
Frattini, cosocle#407C22×C127
prime radicalC23×D4×C127C4
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
2. C127×#1320C2semidirect
88. #7340C127direct (N × H)
95. #1320C2×C127semidirect
96. C127#7340direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#17832
C127×#13202
#7340127