Finite Group Databasebeta

← C127×#2562 #30635514

Subgroups — C127×#2562 #30635514

Order 16256.

532 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×C127C211yesmaximal, characteristic, complemented
2C2×C4×D4×C127C211yesmaximal, characteristic
3#400×C127C212yesmaximal, complemented
4#394×C127C212yesmaximal
5#388×C127C214yesmaximal, complemented
6#380×C127C212yesmaximal, complemented
7#380×C127C212yesmaximal, complemented
8C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
9C22×D4×C127C2211yescharacteristic
10C23×C4×C127C2212yes—
11#125×C127—24no—
12C4×D4×C127—24no—
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C4⋊C4×C127C2211yescharacteristic
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C4⋊C4×C127C2212yes—
17C2×C4⋊C4×C127C2212yes—
18C2×C4⋊C4×C127C2212yes—
19C2×C22⋊C4×C127C2212yes—
20C2×C22⋊C4×C127C2214yes—
21C2×C22⋊C4×C127C2214yes—
22C2×C42×C127C2212yes—
23C2×C42×C127C2211yescharacteristic
24#95×C127C2212yes—
25#95×C127C2214yes—
26#95×C127C2214yes—
27C24×C127C2312yes—
28C2×D4×C127—24no—
29C2×D4×C127—22no—
30C22×C4×C127—24no—
31C22×C4×C127—24no—
32C22×C4×C127—24no—
33C22×C4×C127C2312yes—
34C22×C4×C127C2314yes—
35C22×C4×C127C2312yes—
36C22×C4×C127C2312yes—
37C22×C4×C127C2311yescharacteristic
38C22×C4×C127C2311yescharacteristic
39C22×C4×C127C2311yescharacteristic
40C4⋊C4×C127—22no—
41C4⋊C4×C127—24no—
42C4⋊C4×C127—24no—
43C4⋊C4×C127—22no—
44C4⋊C4×C127—22no—
45C4⋊C4×C127—24no—
46C22⋊C4×C127—28no—
47C22⋊C4×C127—24no—
48C22⋊C4×C127—44no—
49C42×C127—42no—
50C42×C127D414yes—
51C23×C127—22no—
52C23×C127—22no—
53C23×C127—22no—
54C23×C127—22no—
55C23×C127—22no—
56C23×C127—22no—
57C23×C127#4114yes—
58C23×C127C2411yescharacteristic
59D4×C127—28no—
60C2×C4×C127—22no—
61C2×C4×C127—21no—
62C2×C4×C127—21no—
63C2×C4×C127—22no—
64C2×C4×C127—22no—
65C2×C4×C127—22no—
66C2×C4×C127—24no—
67C2×C4×C127—24no—
68C2×C4×C127—24no—
69C2×C4×C127—22no—
70C2×C4×C127—22no—
71C2×C4×C127—24no—
72C2×C4×C127—22no—
73C2×C4×C127—22no—
74C2×C4×C127—48no—
75C2×C4×C127C2×D412yes—
76C2×C4×C127C2×D412yes—
77C2×C4×C127C2×D412yes—
78C2×C4×C127#4114yes—
79C22×C127—24no—
80C22×C127—24no—
81C22×C127—24no—
82C22×C127—42no—
83C22×C127—42no—
84C22×C127—42no—
85C22×C127—42no—
86C22×C127C22×D411yescharacteristic
87C22×C127C2×#4112yes—
88C22×C127C2×#4112yes—
89C22×C127H(5,𝔽2)11yescharacteristic
90C22×C1272−1+411yescharacteristic
91C4×C127—22no—
92C4×C127—22no—
93C4×C127—42no—
94C4×C127—42no—
95C4×C127—42no—
96C4×C127—44no—
97C4×C127#12414yes—
98C2×C127—44no—
99C2×C127#52511yescharacteristic
100C2×C127C2×#12411yescharacteristic
101C2×C127#53711yescharacteristic
102C2×C127#55212yes—
103C2×C127#55312yes—
104#2562C12711yesmaximal, characteristic, direct product factor, Sylow
105C127#256211yescharacteristic, direct product factor, Sylow
106C2×#125C2×C12711yescharacteristic, complemented
107C2×C4×D4C2×C12711yescharacteristic
108#400C2×C12712yescomplemented
109#394C2×C12712yes—
110#388C2×C12714yescomplemented
111#380C2×C12712yescomplemented
112#380C2×C12712yescomplemented
113C4×C4⋊C4C2×C12711yescharacteristic, complemented
114C22×D4C22×C12711yescharacteristic
115C23×C4C22×C12712yes—
116#125—24no—
117C4×D4—24no—
118C2×C4⋊C4C22×C12711yescharacteristic
119C2×C4⋊C4C22×C12711yescharacteristic
120C2×C4⋊C4C22×C12711yescharacteristic
121C2×C4⋊C4C22×C12712yes—
122C2×C4⋊C4C22×C12712yes—
123C2×C4⋊C4C22×C12712yes—
124C2×C22⋊C4C22×C12712yes—
125C2×C22⋊C4C22×C12714yes—
126C2×C22⋊C4C22×C12714yes—
127C2×C42C22×C12712yes—
128C2×C42C22×C12711yescharacteristic
129#95C22×C12712yes—
130#95C22×C12714yes—
131#95C22×C12714yes—
132C24C23×C12712yes—
133C2×D4—24no—
134C2×D4—22no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4C23×C12712yes—
139C22×C4C23×C12714yes—
140C22×C4C23×C12712yes—
141C22×C4C23×C12712yes—
142C22×C4C23×C12711yescharacteristic
143C22×C4C23×C12711yescharacteristic
144C22×C4C23×C12711yescharacteristic
145C4⋊C4—22no—
146C4⋊C4—24no—
147C4⋊C4—24no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—24no—
151C22⋊C4—28no—
152C22⋊C4—24no—
153C22⋊C4—44no—
154C42—42no—
155C42D4×C12714yes—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23#41×C12714yes—
163C23C24×C12711yescharacteristic
164D4—28no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—48no—
180C2×C4C2×D4×C12712yes—
181C2×C4C2×D4×C12712yes—
182C2×C4C2×D4×C12712yes—
183C2×C4#41×C12714yes—
184C22—24no—
185C22—24no—
186C22—24no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×D4×C12711yescharacteristic
192C22C2×#41×C12712yes—
193C22C2×#41×C12712yes—
194C22H(5,𝔽2)×C12711yescharacteristic
195C222−1+4×C12711yescharacteristic
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—42no—
201C4—44no—
202C4#124×C12714yes—
203C2—44no—
204C2#525×C12711yescharacteristic
205C2C2×#124×C12711yescharacteristic
206C2#537×C12711yescharacteristic
207C2#552×C12712yes—
208C2#553×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#125×C127C2semidirect
3. #400×C127C2semidirect
5. #388×C127C2semidirect
6. #380×C127C2semidirect
7. #380×C127C2semidirect
8. C4×C4⋊C4×C127C2semidirect
104. #2562C127direct (N × H)
105. C127#2562direct (N × H)
106. C2×#125C2×C127semidirect
108. #400C2×C127semidirect
110. #388C2×C127semidirect
111. #380C2×C127semidirect
112. #380C2×C127semidirect
113. C4×C4⋊C4C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#125×C1272
C2×C4×D4×C1272
#400×C1272
#394×C1272
#388×C1272
#380×C1272
C4×C4⋊C4×C1272
#2562127