Finite Group Databasebeta

← C127×#21830 #44585503

Subgroups — C127×#21830 #44585503

Order 32512.

978 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C127C211yesmaximal, characteristic
2C127×#2920C212yesmaximal
3C127×#1998C218yesmaximal, complemented
4C127×#1821C214yesmaximal
5C2×#125×C127—24no—
6C2×#125×C127—24no—
7C2×#125×C127C414yes—
8C2×#125×C127C2214yes—
9C22×C4⋊C4×C127C414yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C42×C127C2211yescharacteristic
12#432×C127—24no—
13#431×C127—24no—
14#423×C127C2214yes—
15#407×C127C2214yes—
16C4×M16×C127C2214yes—
17#343×C127C22116yes—
18C23×C4×C127C2×C414yes—
19C23×C4×C127C2×C412yes—
20C23×C4×C127C2311yescharacteristic
21C2×M16×C127C2318yes—
22#125×C127—24no—
23#125×C127—28no—
24#125×C127—24no—
25#125×C127—24no—
26#125×C127—24no—
27#125×C127—28no—
28C2×C4⋊C4×C127—28no—
29C2×C4⋊C4×C127—24no—
30C2×C4⋊C4×C127—24no—
31C2×C4⋊C4×C127—24no—
32C2×C4⋊C4×C127—24no—
33C2×C4⋊C4×C127C2×C4116yes—
34C2×C4⋊C4×C127C2×C414yes—
35C2×C4⋊C4×C127C2314yes—
36C2×C42×C127C2×C412yes—
37C2×C42×C127D414yes—
38C2×C42×C127D414yes—
39C2×C42×C127C2312yes—
40C4⋊C8×C127—28no—
41C22⋊C8×C127—28no—
42#97×C127—24no—
43C4×C8×C127—24no—
44C24×C127C22×C411yescharacteristic
45C22×C4×C127—24no—
46C22×C4×C127—24no—
47C22×C4×C127—24no—
48C22×C4×C127—44no—
49C22×C4×C127—48no—
50C22×C4×C127C22⋊C414yes—
51C22×C4×C127C22⋊C412yes—
52C22×C4×C127C22⋊C412yes—
53C22×C4×C127C22×C411yescharacteristic
54C22×C4×C127C22×C418yes—
55C22×C4×C127C22×C414yes—
56C22×C4×C127C2×D414yes—
57C22×C4×C127C2411yescharacteristic
58M16×C127—216no—
59C2×C8×C127—28no—
60C4⋊C4×C127—28no—
61C4⋊C4×C127—216no—
62C4⋊C4×C127—216no—
63C4⋊C4×C127—28no—
64C42×C127C22⋊C412yes—
65C42×C127C22⋊C414yes—
66C42×C127C22⋊C412yes—
67C42×C127C2×D412yes—
68C42×C127C2×D412yes—
69C42×C127C2×D414yes—
70C23×C127—22no—
71C23×C127—24no—
72C23×C127C2×C22⋊C412yes—
73C23×C127C23×C411yescharacteristic
74C2×C4×C127—22no—
75C2×C4×C127—28no—
76C2×C4×C127—28no—
77C2×C4×C127—28no—
78C2×C4×C127—42no—
79C2×C4×C127—42no—
80C2×C4×C127—44no—
81C2×C4×C127—48no—
82C2×C4×C127—48no—
83C2×C4×C127—48no—
84C2×C4×C127C2×C22⋊C412yes—
85C2×C4×C127C2×C22⋊C414yes—
86C2×C4×C127C2×C22⋊C414yes—
87C2×C4×C127C22×D412yes—
88C2×C4×C1272−1+414yes—
89C8×C127—48no—
90C22×C127—28no—
91C22×C127—22no—
92C22×C127—22no—
93C22×C127—22no—
94C22×C127#41314yes—
95C22×C127C22×C22⋊C411yescharacteristic
96C22×C127#51912yes—
97C4×C127—22no—
98C4×C127—24no—
99C4×C127—24no—
100C4×C127—48no—
101C4×C127#53614yes—
102#21830C12711yesmaximal, characteristic, direct product factor, Sylow
103C2×C127—22no—
104C2×C127—24no—
105C2×C127#231011yescharacteristic
106C2×C127C2×#41312yes—
107C22×#125C2×C12711yescharacteristic
108#2920C2×C12712yes—
109#1998C2×C12718yescomplemented
110#1821C2×C12714yes—
111C127#2183011yescharacteristic, direct product factor, Sylow
112C2×#125—24no—
113C2×#125—24no—
114C2×#125C4×C12714yes—
115C2×#125C22×C12714yes—
116C22×C4⋊C4C4×C12714yes—
117C22×C4⋊C4C22×C12712yes—
118C22×C42C22×C12711yescharacteristic
119#432—24no—
120#431—24no—
121#423C22×C12714yes—
122#407C22×C12714yes—
123C4×M16C22×C12714yes—
124#343C22×C127116yes—
125C23×C4C2×C4×C12714yes—
126C23×C4C2×C4×C12712yes—
127C23×C4C23×C12711yescharacteristic
128C2×M16C23×C12718yes—
129#125—24no—
130#125—28no—
131#125—24no—
132#125—24no—
133#125—24no—
134#125—28no—
135C2×C4⋊C4—28no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4C2×C4×C127116yes—
141C2×C4⋊C4C2×C4×C12714yes—
142C2×C4⋊C4C23×C12714yes—
143C2×C42C2×C4×C12712yes—
144C2×C42D4×C12714yes—
145C2×C42D4×C12714yes—
146C2×C42C23×C12712yes—
147C4⋊C8—28no—
148C22⋊C8—28no—
149#97—24no—
150C4×C8—24no—
151C24C22×C4×C12711yescharacteristic
152C22×C4—24no—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—44no—
156C22×C4—48no—
157C22×C4C22⋊C4×C12714yes—
158C22×C4C22⋊C4×C12712yes—
159C22×C4C22⋊C4×C12712yes—
160C22×C4C22×C4×C12711yescharacteristic
161C22×C4C22×C4×C12718yes—
162C22×C4C22×C4×C12714yes—
163C22×C4C2×D4×C12714yes—
164C22×C4C24×C12711yescharacteristic
165M16—216no—
166C2×C8—28no—
167C4⋊C4—28no—
168C4⋊C4—216no—
169C4⋊C4—216no—
170C4⋊C4—28no—
171C42C22⋊C4×C12712yes—
172C42C22⋊C4×C12714yes—
173C42C22⋊C4×C12712yes—
174C42C2×D4×C12712yes—
175C42C2×D4×C12712yes—
176C42C2×D4×C12714yes—
177C23—22no—
178C23—24no—
179C23C2×C22⋊C4×C12712yes—
180C23C23×C4×C12711yescharacteristic
181C2×C4—22no—
182C2×C4—28no—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—48no—
189C2×C4—48no—
190C2×C4—48no—
191C2×C4C2×C22⋊C4×C12712yes—
192C2×C4C2×C22⋊C4×C12714yes—
193C2×C4C2×C22⋊C4×C12714yes—
194C2×C4C22×D4×C12712yes—
195C2×C42−1+4×C12714yes—
196C8—48no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22#413×C12714yes—
202C22C22×C22⋊C4×C12711yescharacteristic
203C22#519×C12712yes—
204C4—24no—
205C4—24no—
206C4—22no—
207C4—48no—
208C4#536×C12714yes—
209C2—22no—
210C2—24no—
211C2C127×#231011yescharacteristic
212C2C2×#413×C12712yes—
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1998C2semidirect
102. #21830C127direct (N × H)
109. #1998C2×C127semidirect
111. C127#21830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C1272
C127×#29202
C127×#19982
C127×#18212
#21830127