Finite Group Databasebeta

← C127×#2625 #30635577

Subgroups — C127×#2625 #30635577

Order 16256.

464 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×C127C211yesmaximal, characteristic
2C2×#117×C127C211yesmaximal, characteristic
3#400×C127C212yesmaximal, complemented
4#398×C127C212yesmaximal, complemented
5#397×C127C214yesmaximal
6#391×C127C212yesmaximal, complemented
7#389×C127C212yesmaximal, complemented
8#380×C127C211yesmaximal, characteristic
9C22×Q8×C127C2211yescharacteristic
10C23×C4×C127C2211yescharacteristic
11C22⋊Q8×C127—24no—
12#117×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×C127C2214yes—
19C2×C22⋊C4×C127C2212yes—
20C2×C22⋊C4×C127C2212yes—
21C2×C22⋊C4×C127C2212yes—
22C2×C42×C127C2212yes—
23#95×C127C2212yes—
24#95×C127C2214yes—
25#95×C127C2214yes—
26#95×C127C2214yes—
27C24×C127C2311yescharacteristic
28C2×Q8×C127—22no—
29C2×Q8×C127—24no—
30C22×C4×C127—24no—
31C22×C4×C127D414yes—
32C22×C4×C127C2312yes—
33C22×C4×C127C2314yes—
34C22×C4×C127C2312yes—
35C22×C4×C127C2312yes—
36C22×C4×C127C2312yes—
37C22×C4×C127C2311yescharacteristic
38C22×C4×C127C2311yescharacteristic
39C4⋊C4×C127—22no—
40C4⋊C4×C127—22no—
41C4⋊C4×C127—22no—
42C4⋊C4×C127—24no—
43C4⋊C4×C127—24no—
44C4⋊C4×C127—44no—
45C22⋊C4×C127—24no—
46C22⋊C4×C127—24no—
47C22⋊C4×C127—42no—
48C42×C127—24no—
49C23×C127—22no—
50C23×C127—21no—
51C23×C127—22no—
52C23×C127—21no—
53C23×C127C2×D412yes—
54C23×C127C2411yescharacteristic
55Q8×C127—44no—
56C2×C4×C127—22no—
57C2×C4×C127—28no—
58C2×C4×C127—22no—
59C2×C4×C127—22no—
60C2×C4×C127—22no—
61C2×C4×C127—22no—
62C2×C4×C127—24no—
63C2×C4×C127—24no—
64C2×C4×C127—24no—
65C2×C4×C127—22no—
66C2×C4×C127—22no—
67C2×C4×C127—24no—
68C2×C4×C127—22no—
69C2×C4×C127—22no—
70C2×C4×C127—24no—
71C2×C4×C127C2×D412yes—
72C2×C4×C127C2×D412yes—
73C2×C4×C127#4114yes—
74C22×C127—22no—
75C22×C127—22no—
76C22×C127—22no—
77C22×C127—42no—
78C22×C127—42no—
79C22×C127C22×D411yescharacteristic
80C22×C127C2×#4112yes—
81C22×C127H(5,𝔽2)11yescharacteristic
82C22×C1272−1+412yes—
83C22×C1272−1+411yescharacteristic
84C4×C127—22no—
85C4×C127—42no—
86C4×C127—42no—
87C4×C127—42no—
88C4×C127—42no—
89C4×C127—44no—
90C4×C127#12314yes—
91C2×C127—42no—
92C2×C127C2×#12311yescharacteristic
93C2×C127#53611yescharacteristic
94C2×C127#53711yescharacteristic
95C2×C127#54112yes—
96C2×C127#54212yes—
97#2625C12711yesmaximal, characteristic, direct product factor, Sylow
98C127#262511yescharacteristic, direct product factor, Sylow
99C2×C22⋊Q8C2×C12711yescharacteristic
100C2×#117C2×C12711yescharacteristic
101#400C2×C12712yescomplemented
102#398C2×C12712yescomplemented
103#397C2×C12714yes—
104#391C2×C12712yescomplemented
105#389C2×C12712yescomplemented
106#380C2×C12711yescharacteristic
107C22×Q8C22×C12711yescharacteristic
108C23×C4C22×C12711yescharacteristic
109C22⋊Q8—24no—
110#117—24no—
111C2×C4⋊C4C22×C12711yescharacteristic
112C2×C4⋊C4C22×C12711yescharacteristic
113C2×C4⋊C4C22×C12711yescharacteristic
114C2×C4⋊C4C22×C12712yes—
115C2×C4⋊C4C22×C12712yes—
116C2×C4⋊C4C22×C12714yes—
117C2×C22⋊C4C22×C12712yes—
118C2×C22⋊C4C22×C12712yes—
119C2×C22⋊C4C22×C12712yes—
120C2×C42C22×C12712yes—
121#95C22×C12712yes—
122#95C22×C12714yes—
123#95C22×C12714yes—
124#95C22×C12714yes—
125C24C23×C12711yescharacteristic
126C2×Q8—22no—
127C2×Q8—24no—
128C22×C4—24no—
129C22×C4D4×C12714yes—
130C22×C4C23×C12712yes—
131C22×C4C23×C12714yes—
132C22×C4C23×C12712yes—
133C22×C4C23×C12712yes—
134C22×C4C23×C12712yes—
135C22×C4C23×C12711yescharacteristic
136C22×C4C23×C12711yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4—22no—
140C4⋊C4—24no—
141C4⋊C4—24no—
142C4⋊C4—44no—
143C22⋊C4—24no—
144C22⋊C4—24no—
145C22⋊C4—42no—
146C42—24no—
147C23—22no—
148C23—21no—
149C23—22no—
150C23—21no—
151C23C2×D4×C12712yes—
152C23C24×C12711yescharacteristic
153Q8—44no—
154C2×C4—22no—
155C2×C4—28no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4C2×D4×C12712yes—
170C2×C4C2×D4×C12712yes—
171C2×C4#41×C12714yes—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—42no—
176C22—42no—
177C22C22×D4×C12711yescharacteristic
178C22C2×#41×C12712yes—
179C22H(5,𝔽2)×C12711yescharacteristic
180C222−1+4×C12712yes—
181C222−1+4×C12711yescharacteristic
182C4—22no—
183C4—42no—
184C4—42no—
185C4—42no—
186C4—42no—
187C4—44no—
188C4#123×C12714yes—
189C2—42no—
190C2C2×#123×C12711yescharacteristic
191C2#536×C12711yescharacteristic
192C2#537×C12711yescharacteristic
193C2#541×C12712yes—
194C2#542×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC24×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. #400×C127C2semidirect
4. #398×C127C2semidirect
6. #391×C127C2semidirect
7. #389×C127C2semidirect
97. #2625C127direct (N × H)
98. C127#2625direct (N × H)
101. #400C2×C127semidirect
102. #398C2×C127semidirect
104. #391C2×C127semidirect
105. #389C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C1272
C2×#117×C1272
#400×C1272
#398×C1272
#397×C1272
#391×C1272
#389×C1272
#380×C1272
#2625127