Finite Group Databasebeta

← C127×#2487 #30635439

Subgroups — C127×#2487 #30635439

Order 16256.

584 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C127C211yesmaximal, characteristic
2C22×C4⋊C4×C127C211yesmaximal, characteristic, complemented
3#400×C127C212yesmaximal, complemented
4#399×C127C212yesmaximal, complemented
5#389×C127C212yesmaximal, complemented
6#386×C127C212yesmaximal
7#385×C127C212yesmaximal, complemented
8#380×C127C212yesmaximal, complemented
9#380×C127C211yesmaximal, characteristic, complemented
10C22×D4×C127C2211yescharacteristic
11C23×C4×C127C2211yescharacteristic
12C23×C4×C127C2211yescharacteristic
13C23×C4×C127C2212yes—
14C4×D4×C127—24no—
15C2×C4⋊C4×C127—24no—
16C2×C4⋊C4×C127C2212yes—
17C2×C4⋊C4×C127C2212yes—
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2212yes—
20C2×C4⋊C4×C127C2214yes—
21C2×C22⋊C4×C127C2211yescharacteristic
22C2×C22⋊C4×C127C2211yescharacteristic
23C2×C22⋊C4×C127C2212yes—
24C2×C22⋊C4×C127C2214yes—
25C2×C42×C127C2211yescharacteristic
26#95×C127C2214yes—
27#95×C127C2212yes—
28#95×C127C2214yes—
29C24×C127C2311yescharacteristic
30C24×C127C2311yescharacteristic
31C2×D4×C127—22no—
32C2×D4×C127—22no—
33C2×D4×C127Q814yes—
34C22×C4×C127—24no—
35C22×C4×C127—24no—
36C22×C4×C127—22no—
37C22×C4×C127—24no—
38C22×C4×C127—44no—
39C22×C4×C127D414yes—
40C22×C4×C127C2311yescharacteristic
41C22×C4×C127C2314yes—
42C22×C4×C127C2314yes—
43C22×C4×C127C2311yescharacteristic
44C22×C4×C127C2311yescharacteristic
45C22×C4×C127C2311yescharacteristic
46C22×C4×C127C2311yescharacteristic
47C4⋊C4×C127—24no—
48C4⋊C4×C127—24no—
49C4⋊C4×C127—22no—
50C4⋊C4×C127—24no—
51C4⋊C4×C127—44no—
52C22⋊C4×C127—22no—
53C22⋊C4×C127—24no—
54C22⋊C4×C127—22no—
55C22⋊C4×C127—44no—
56C42×C127—22no—
57C23×C127—22no—
58C23×C127—22no—
59C23×C127—21no—
60C23×C127—22no—
61C23×C127—21no—
62C23×C127—22no—
63C23×C127C2×D412yes—
64C23×C127C2×Q812yes—
65C23×C127C2×Q812yes—
66C23×C127#4112yes—
67C23×C127C2411yescharacteristic
68D4×C127—28no—
69C2×C4×C127—21no—
70C2×C4×C127—22no—
71C2×C4×C127—21no—
72C2×C4×C127—28no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—24no—
76C2×C4×C127—24no—
77C2×C4×C127—24no—
78C2×C4×C127—22no—
79C2×C4×C127—24no—
80C2×C4×C127—24no—
81C2×C4×C127—22no—
82C2×C4×C127—24no—
83C2×C4×C127—48no—
84C2×C4×C127—44no—
85C2×C4×C127C2×D412yes—
86C2×C4×C127C2×D412yes—
87C2×C4×C127C2×Q812yes—
88C2×C4×C127#4114yes—
89C22×C127—22no—
90C22×C127—22no—
91C22×C127—24no—
92C22×C127—24no—
93C22×C127—22no—
94C22×C127—24no—
95C22×C127—41no—
96C22×C127—41no—
97C22×C127—42no—
98C22×C127C22⋊Q814yes—
99C22×C127C22×D411yescharacteristic
100C22×C127C22×Q811yescharacteristic
101C22×C127C2×#4111yescharacteristic
102C22×C127C2×#4112yes—
103C22×C127H(5,𝔽2)12yes—
104C4×C127—22no—
105C4×C127—22no—
106C4×C127—41no—
107C4×C127—41no—
108C4×C127—44no—
109C4×C127—44no—
110C4×C127#12314yes—
111C2×C127—24no—
112C2×C127—42no—
113C2×C127C2×C22⋊Q811yescharacteristic
114C2×C127C2×#12311yescharacteristic
115C2×C127#53511yescharacteristic
116C2×C127#55312yes—
117C2×C127#55412yes—
118#2487C12711yesmaximal, characteristic, direct product factor, Sylow
119C127#248711yescharacteristic, direct product factor, Sylow
120C2×C4×D4C2×C12711yescharacteristic
121C22×C4⋊C4C2×C12711yescharacteristic, complemented
122#400C2×C12712yescomplemented
123#399C2×C12712yescomplemented
124#389C2×C12712yescomplemented
125#386C2×C12712yes—
126#385C2×C12712yescomplemented
127#380C2×C12712yescomplemented
128#380C2×C12711yescharacteristic, complemented
129C22×D4C22×C12711yescharacteristic
130C23×C4C22×C12711yescharacteristic
131C23×C4C22×C12711yescharacteristic
132C23×C4C22×C12712yes—
133C4×D4—24no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4C22×C12712yes—
136C2×C4⋊C4C22×C12712yes—
137C2×C4⋊C4C22×C12711yescharacteristic
138C2×C4⋊C4C22×C12712yes—
139C2×C4⋊C4C22×C12714yes—
140C2×C22⋊C4C22×C12711yescharacteristic
141C2×C22⋊C4C22×C12711yescharacteristic
142C2×C22⋊C4C22×C12712yes—
143C2×C22⋊C4C22×C12714yes—
144C2×C42C22×C12711yescharacteristic
145#95C22×C12714yes—
146#95C22×C12712yes—
147#95C22×C12714yes—
148C24C23×C12711yescharacteristic
149C24C23×C12711yescharacteristic
150C2×D4—22no—
151C2×D4—22no—
152C2×D4Q8×C12714yes—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4—44no—
158C22×C4D4×C12714yes—
159C22×C4C23×C12711yescharacteristic
160C22×C4C23×C12714yes—
161C22×C4C23×C12714yes—
162C22×C4C23×C12711yescharacteristic
163C22×C4C23×C12711yescharacteristic
164C22×C4C23×C12711yescharacteristic
165C22×C4C23×C12711yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—24no—
168C4⋊C4—22no—
169C4⋊C4—24no—
170C4⋊C4—44no—
171C22⋊C4—22no—
172C22⋊C4—24no—
173C22⋊C4—22no—
174C22⋊C4—44no—
175C42—22no—
176C23—22no—
177C23—22no—
178C23—21no—
179C23—22no—
180C23—21no—
181C23—22no—
182C23C2×D4×C12712yes—
183C23C2×Q8×C12712yes—
184C23C2×Q8×C12712yes—
185C23#41×C12712yes—
186C23C24×C12711yescharacteristic
187D4—28no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—28no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—48no—
203C2×C4—44no—
204C2×C4C2×D4×C12712yes—
205C2×C4C2×D4×C12712yes—
206C2×C4C2×Q8×C12712yes—
207C2×C4#41×C12714yes—
208C22—22no—
209C22—22no—
210C22—24no—
211C22—24no—
212C22—22no—
213C22—24no—
214C22—41no—
215C22—41no—
216C22—42no—
217C22C22⋊Q8×C12714yes—
218C22C22×D4×C12711yescharacteristic
219C22C22×Q8×C12711yescharacteristic
220C22C2×#41×C12711yescharacteristic
221C22C2×#41×C12712yes—
222C22H(5,𝔽2)×C12712yes—
223C4—22no—
224C4—22no—
225C4—41no—
226C4—44no—
227C4—41no—
228C4—44no—
229C4#123×C12714yes—
230C2—24no—
231C2—42no—
232C2C2×C22⋊Q8×C12711yescharacteristic
233C2C2×#123×C12711yescharacteristic
234C2#535×C12711yescharacteristic
235C2#553×C12712yes—
236C2#554×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
2. C22×C4⋊C4×C127C2semidirect
3. #400×C127C2semidirect
4. #399×C127C2semidirect
5. #389×C127C2semidirect
7. #385×C127C2semidirect
8. #380×C127C2semidirect
9. #380×C127C2semidirect
118. #2487C127direct (N × H)
119. C127#2487direct (N × H)
121. C22×C4⋊C4C2×C127semidirect
122. #400C2×C127semidirect
123. #399C2×C127semidirect
124. #389C2×C127semidirect
126. #385C2×C127semidirect
127. #380C2×C127semidirect
128. #380C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C1272
C22×C4⋊C4×C1272
#400×C1272
#399×C1272
#389×C1272
#386×C1272
#385×C1272
#380×C1272
#2487127