Finite Group Databasebeta

← C127×#14342 #44578015

Subgroups — C127×#14342 #44578015

Order 32512.

1998 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C127C211yesmaximal, characteristic
2C2×#381×C127C212yesmaximal
3C127×#1445C218yesmaximal, complemented
4C127×C22⋊#95C214yesmaximal
5C24×C4×C127C2211yescharacteristic
6C24×C4×C127C2212yes—
7C22×C4⋊C4×C127—28no—
8C22×C4⋊C4×C127C418yescomplemented
9C22×C4⋊C4×C127C2214yes—
10C22×C22⋊C4×C127C2214yes—
11#381×C127—28no—
12C2×#95×C127C2218yes—
13C2×#95×C127C22116yes—
14C25×C127C2311yescharacteristic
15C23×C4×C127—28no—
16C23×C4×C127—28no—
17C23×C4×C127—48no—
18C23×C4×C127C2×C414yes—
19C23×C4×C127C2×C418yes—
20C23×C4×C127D418yes—
21C23×C4×C127C2318yes—
22C23×C4×C127C2314yes—
23C23×C4×C127C2312yes—
24C2×C4⋊C4×C127—232no—
25C2×C4⋊C4×C127—216no—
26C2×C4⋊C4×C127C2×C4116yes—
27C2×C22⋊C4×C127—28no—
28C2×C22⋊C4×C127—216no—
29#95×C127—216no—
30#95×C127—416no—
31C24×C127—24no—
32C24×C127—24no—
33C24×C127C22×C412yes—
34C24×C127C2×D414yes—
35C24×C127#4118yes—
36C24×C127C2411yescharacteristic
37C22×C4×C127—216no—
38C22×C4×C127—232no—
39C22×C4×C127—28no—
40C22×C4×C127—216no—
41C22×C4×C127—28no—
42C22×C4×C127—216no—
43C22×C4×C127—28no—
44C22×C4×C127—216no—
45C22×C4×C127—216no—
46C22×C4×C127—216no—
47C22×C4×C127—416no—
48C22×C4×C127—432no—
49C22×C4×C127C22⋊C4116yes—
50C22×C4×C127C22×C418yes—
51C22×C4×C127C22×C414yes—
52C22×C4×C127C2×D418yes—
53C4⋊C4×C127—232no—
54C22⋊C4×C127—416no—
55C23×C127—24no—
56C23×C127—24no—
57C23×C127—28no—
58C23×C127—28no—
59C23×C127—232no—
60C23×C127C2×C22⋊C414yes—
61C23×C127#11718yes—
62C23×C127#123116yes—
63C23×C127C23×C411yescharacteristic
64C23×C127C22×D412yes—
65C23×C127C2×#4114yes—
66C23×C127H(5,𝔽2)14yes—
67C23×C1272−1+414yes—
68C2×C4×C127—28no—
69C2×C4×C127—216no—
70C2×C4×C127—232no—
71C2×C4×C127—28no—
72C2×C4×C127—216no—
73C2×C4×C127—432no—
74C2×C4×C127—416no—
75C2×C4×C127—48no—
76C2×C4×C127—48no—
77C2×C4×C127—48no—
78C2×C4×C127—432no—
79C2×C4×C127C2×C22⋊C418yes—
80C22×C127—24no—
81C22×C127—24no—
82C22×C127—216no—
83C22×C127—232no—
84C22×C127#38118yes—
85C22×C127C22×C22⋊C411yescharacteristic
86C22×C127C2×#11712yes—
87C22×C127#51812yes—
88C22×C127#51912yes—
89C22×C127C2×#12314yes—
90C22×C127#53514yes—
91C22×C127#53614yes—
92C22×C127#539116yes—
93C4×C127—28no—
94C4×C127—48no—
95C4×C127—88no—
96#14342C12711yesmaximal, characteristic, direct product factor, Sylow
97C2×C127—28no—
98C2×C127C2×#38111yescharacteristic
99C2×C127#230911yescharacteristic
100C2×C127#231011yescharacteristic
101C2×C127#231314yes—
102C2×C127#262318yes—
103C23×C4⋊C4C2×C12711yescharacteristic
104C2×#381C2×C12712yes—
105#1445C2×C12718yescomplemented
106C22⋊#95C2×C12714yes—
107C127#1434211yescharacteristic, direct product factor, Sylow
108C24×C4C22×C12711yescharacteristic
109C24×C4C22×C12712yes—
110C22×C4⋊C4—28no—
111C22×C4⋊C4C4×C12718yescomplemented
112C22×C4⋊C4C22×C12714yes—
113C22×C22⋊C4C22×C12714yes—
114#381—28no—
115C2×#95C22×C12718yes—
116C2×#95C22×C127116yes—
117C25C23×C12711yescharacteristic
118C23×C4—28no—
119C23×C4—28no—
120C23×C4—48no—
121C23×C4C2×C4×C12714yes—
122C23×C4C2×C4×C12718yes—
123C23×C4D4×C12718yes—
124C23×C4C23×C12718yes—
125C23×C4C23×C12714yes—
126C23×C4C23×C12712yes—
127C2×C4⋊C4—232no—
128C2×C4⋊C4—216no—
129C2×C4⋊C4C2×C4×C127116yes—
130C2×C22⋊C4—28no—
131C2×C22⋊C4—216no—
132#95—216no—
133#95—416no—
134C24—24no—
135C24—24no—
136C24C22×C4×C12712yes—
137C24C2×D4×C12714yes—
138C24#41×C12718yes—
139C24C24×C12711yescharacteristic
140C22×C4—216no—
141C22×C4—232no—
142C22×C4—28no—
143C22×C4—216no—
144C22×C4—28no—
145C22×C4—216no—
146C22×C4—28no—
147C22×C4—216no—
148C22×C4—216no—
149C22×C4—216no—
150C22×C4—416no—
151C22×C4—432no—
152C22×C4C22⋊C4×C127116yes—
153C22×C4C22×C4×C12718yes—
154C22×C4C22×C4×C12714yes—
155C22×C4C2×D4×C12718yes—
156C4⋊C4—232no—
157C22⋊C4—416no—
158C23—24no—
159C23—24no—
160C23—28no—
161C23—28no—
162C23—232no—
163C23C2×C22⋊C4×C12714yes—
164C23#117×C12718yes—
165C23#123×C127116yes—
166C23C23×C4×C12711yescharacteristic
167C23C22×D4×C12712yes—
168C23C2×#41×C12714yes—
169C23H(5,𝔽2)×C12714yes—
170C232−1+4×C12714yes—
171C2×C4—28no—
172C2×C4—216no—
173C2×C4—232no—
174C2×C4—28no—
175C2×C4—216no—
176C2×C4—432no—
177C2×C4—416no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—48no—
181C2×C4—432no—
182C2×C4C2×C22⋊C4×C12718yes—
183C22—216no—
184C22—232no—
185C22—24no—
186C22—24no—
187C22#381×C12718yes—
188C22C22×C22⋊C4×C12711yescharacteristic
189C22C2×#117×C12712yes—
190C22#518×C12712yes—
191C22#519×C12712yes—
192C22C2×#123×C12714yes—
193C22#535×C12714yes—
194C22#536×C12714yes—
195C22#539×C127116yes—
196C4—28no—
197C4—48no—
198C4—88no—
199C2—28no—
200C2C2×#381×C12711yescharacteristic
201C2C127×#230911yescharacteristic
202C2C127×#231011yescharacteristic
203C2C127×#231314yes—
204C2C127×#262318yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1445C2semidirect
8. C22×C4⋊C4×C127C4semidirect
96. #14342C127direct (N × H)
105. #1445C2×C127semidirect
107. C127#14342direct (N × H)
111. C22×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C1272
C2×#381×C1272
C127×#14452
C127×C22⋊#952
#14342127