Finite Group Databasebeta

← C127×#14664 #44578337

Subgroups — C127×#14664 #44578337

Order 32512.

1334 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C127C211yesmaximal, characteristic
2C2×#382×C127C212yesmaximal
3C127×#1445C214yesmaximal
4C127×#1441C218yesmaximal
5C2×#125×C127—28no—
6C2×#125×C127C418yescomplemented
7C22×C4⋊C4×C127C2214yes—
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2214yes—
10C22×C42×C127C2211yescharacteristic
11#382×C127—28no—
12C2×#95×C127C2214yes—
13C2×#95×C127C2214yes—
14C2×#95×C127C22116yes—
15C23×C4×C127C2318yes—
16C23×C4×C127C2314yes—
17C23×C4×C127C2312yes—
18C23×C4×C127C2311yescharacteristic
19#125×C127—232no—
20C2×C4⋊C4×C127—28no—
21C2×C4⋊C4×C127—24no—
22C2×C4⋊C4×C127—24no—
23C2×C4⋊C4×C127—28no—
24C2×C4⋊C4×C127—28no—
25C2×C4⋊C4×C127—48no—
26C2×C4⋊C4×C127C2×C4116yes—
27C2×C4⋊C4×C127C2×C418yes—
28C2×C42×C127C2×C414yes—
29C2×C42×C127D418yes—
30#95×C127—28no—
31#95×C127—28no—
32#95×C127—416no—
33C24×C127C2411yescharacteristic
34C22×C4×C127—24no—
35C22×C4×C127—24no—
36C22×C4×C127—24no—
37C22×C4×C127—24no—
38C22×C4×C127—24no—
39C22×C4×C127—28no—
40C22×C4×C127—28no—
41C22×C4×C127—28no—
42C22×C4×C127—28no—
43C22×C4×C127—216no—
44C22×C4×C127—216no—
45C22×C4×C127—28no—
46C22×C4×C127C22×C418yes—
47C22×C4×C127C22×C412yes—
48C22×C4×C127C22×C414yes—
49C22×C4×C127C2×D414yes—
50C22×C4×C127C2×D414yes—
51C22×C4×C127C2×D414yes—
52C4⋊C4×C127—216no—
53C4⋊C4×C127—232no—
54C4⋊C4×C127—416no—
55C42×C127C22⋊C4116yes—
56C23×C127C23×C411yescharacteristic
57C23×C127C22×D412yes—
58C23×C127H(5,𝔽2)14yes—
59C23×C1272−1+414yes—
60C23×C1272−1+414yes—
61C2×C4×C127—24no—
62C2×C4×C127—28no—
63C2×C4×C127—24no—
64C2×C4×C127—28no—
65C2×C4×C127—24no—
66C2×C4×C127—28no—
67C2×C4×C127—28no—
68C2×C4×C127—216no—
69C2×C4×C127—44no—
70C2×C4×C127—44no—
71C2×C4×C127—48no—
72C2×C4×C127—48no—
73C2×C4×C127—48no—
74C2×C4×C127—48no—
75C2×C4×C127—416no—
76C2×C4×C127—416no—
77C2×C4×C127C2×C22⋊C414yes—
78C2×C4×C127C2×C22⋊C418yes—
79C22×C127C22×C22⋊C411yescharacteristic
80C22×C127#51912yes—
81C22×C127#52014yes—
82C22×C127#53512yes—
83C22×C127#53614yes—
84C22×C127#53612yes—
85C22×C127#53714yes—
86C22×C127#56214yes—
87C22×C127#56318yes—
88C22×C127#56414yes—
89C4×C127—24no—
90C4×C127—28no—
91C4×C127—48no—
92C4×C127—88no—
93#14664C12711yesmaximal, characteristic, direct product factor, Sylow
94C2×C127#231011yescharacteristic
95C2×C127#231112yes—
96C2×C127#238214yes—
97C2×C127#282014yes—
98C2×C127#282214yes—
99C22×#125C2×C12711yescharacteristic
100C2×#382C2×C12712yes—
101#1445C2×C12714yes—
102#1441C2×C12718yes—
103C127#1466411yescharacteristic, direct product factor, Sylow
104C2×#125—28no—
105C2×#125C4×C12718yescomplemented
106C22×C4⋊C4C22×C12714yes—
107C22×C4⋊C4C22×C12712yes—
108C22×C4⋊C4C22×C12714yes—
109C22×C42C22×C12711yescharacteristic
110#382—28no—
111C2×#95C22×C12714yes—
112C2×#95C22×C12714yes—
113C2×#95C22×C127116yes—
114C23×C4C23×C12718yes—
115C23×C4C23×C12714yes—
116C23×C4C23×C12712yes—
117C23×C4C23×C12711yescharacteristic
118#125—232no—
119C2×C4⋊C4—28no—
120C2×C4⋊C4—24no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—28no—
123C2×C4⋊C4—28no—
124C2×C4⋊C4—48no—
125C2×C4⋊C4C2×C4×C127116yes—
126C2×C4⋊C4C2×C4×C12718yes—
127C2×C42C2×C4×C12714yes—
128C2×C42D4×C12718yes—
129#95—28no—
130#95—28no—
131#95—416no—
132C24C24×C12711yescharacteristic
133C22×C4—24no—
134C22×C4—24no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—28no—
139C22×C4—28no—
140C22×C4—28no—
141C22×C4—28no—
142C22×C4—216no—
143C22×C4—216no—
144C22×C4—28no—
145C22×C4C22×C4×C12718yes—
146C22×C4C22×C4×C12712yes—
147C22×C4C22×C4×C12714yes—
148C22×C4C2×D4×C12714yes—
149C22×C4C2×D4×C12714yes—
150C22×C4C2×D4×C12714yes—
151C4⋊C4—216no—
152C4⋊C4—232no—
153C4⋊C4—416no—
154C42C22⋊C4×C127116yes—
155C23C23×C4×C12711yescharacteristic
156C23C22×D4×C12712yes—
157C23H(5,𝔽2)×C12714yes—
158C232−1+4×C12714yes—
159C232−1+4×C12714yes—
160C2×C4—24no—
161C2×C4—28no—
162C2×C4—24no—
163C2×C4—28no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—28no—
167C2×C4—216no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4—48no—
171C2×C4—48no—
172C2×C4—48no—
173C2×C4—48no—
174C2×C4—416no—
175C2×C4—416no—
176C2×C4C2×C22⋊C4×C12714yes—
177C2×C4C2×C22⋊C4×C12718yes—
178C22C22×C22⋊C4×C12711yescharacteristic
179C22#519×C12712yes—
180C22#520×C12714yes—
181C22#535×C12712yes—
182C22#536×C12714yes—
183C22#536×C12712yes—
184C22#537×C12714yes—
185C22#562×C12714yes—
186C22#563×C12718yes—
187C22#564×C12714yes—
188C4—24no—
189C4—28no—
190C4—48no—
191C4—88no—
192C2C127×#231011yescharacteristic
193C2C127×#231112yes—
194C2C127×#238214yes—
195C2C127×#282014yes—
196C2C127×#282214yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C127C4semidirect
93. #14664C127direct (N × H)
103. C127#14664direct (N × H)
105. C2×#125C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C1272
C2×#382×C1272
C127×#14452
C127×#14412
#14664127