Finite Group Databasebeta

← C127×#2337 #30635289

Subgroups — C127×#2337 #30635289

Order 16256.

540 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×#124×C127C211yesmaximal, characteristic
2#391×C127C212yesmaximal, complemented
3#388×C127C212yesmaximal, complemented
4#388×C127C212yesmaximal, complemented
5#386×C127C212yesmaximal
6#385×C127C212yesmaximal, complemented
7#383×C127C211yesmaximal, characteristic, complemented
8C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
9C4×C22⋊C4×C127C212yesmaximal, complemented
10C22×Q8×C127C2211yescharacteristic
11C22×D4×C127C2211yescharacteristic
12C23×C4×C127C2212yes—
13#124×C127C418yescomplemented
14C2×C4⋊C4×C127C2212yes—
15C2×C4⋊C4×C127C2212yes—
16C2×C22⋊C4×C127C2212yes—
17C2×C22⋊C4×C127C2212yes—
18C2×C22⋊C4×C127C2212yes—
19C2×C22⋊C4×C127C2212yes—
20C2×C22⋊C4×C127C2212yes—
21C2×C42×C127C2211yescharacteristic
22C2×C42×C127C2212yes—
23C2×C42×C127C2211yescharacteristic
24C2×C42×C127C2211yescharacteristic
25#95×C127C2212yes—
26#95×C127C2212yes—
27#95×C127C2212yes—
28#95×C127C2211yescharacteristic
29#95×C127C2212yes—
30#95×C127C2211yescharacteristic
31#95×C127C2212yes—
32C24×C127C2312yes—
33C2×Q8×C127—42no—
34C2×Q8×C127C2×C414yescomplemented
35C2×D4×C127—42no—
36C2×D4×C127C2×C414yes—
37C22×C4×C127—24no—
38C22×C4×C127—42no—
39C22×C4×C127—42no—
40C22×C4×C127C2312yes—
41C22×C4×C127C2312yes—
42C22×C4×C127C2312yes—
43C22×C4×C127C2311yescharacteristic
44C22×C4×C127C2311yescharacteristic
45C22×C4×C127C2311yescharacteristic
46C22×C4×C127C2312yes—
47C22×C4×C127C2312yes—
48C4⋊C4×C127—24no—
49C4⋊C4×C127—42no—
50C22⋊C4×C127—24no—
51C22⋊C4×C127—42no—
52C22⋊C4×C127—42no—
53C22⋊C4×C127C2×C418yescomplemented
54C22⋊C4×C127C2×C418yescomplemented
55C42×C127—41no—
56C42×C127—41no—
57C42×C127—42no—
58C42×C127C2×C414yescomplemented
59C23×C127—22no—
60C23×C127—22no—
61C23×C127—22no—
62C23×C127—22no—
63C23×C127—22no—
64C23×C127—22no—
65C23×C127C22×C414yes—
66C23×C127C2411yescharacteristic
67Q8×C127—44no—
68D4×C127—44no—
69C2×C4×C127—22no—
70C2×C4×C127—21no—
71C2×C4×C127—22no—
72C2×C4×C127—22no—
73C2×C4×C127—22no—
74C2×C4×C127—22no—
75C2×C4×C127—22no—
76C2×C4×C127—21no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—48no—
87C2×C4×C127C22×C412yes—
88C2×C4×C127C22×C412yes—
89C2×C4×C127C22×C412yes—
90C2×C4×C127C22×C414yes—
91C2×C4×C127#4114yes—
92C22×C127—24no—
93C22×C127—24no—
94C22×C127—24no—
95C22×C127—42no—
96C22×C127—42no—
97C22×C127—42no—
98C22×C127—42no—
99C22×C127C23×C411yescharacteristic
100C22×C127C2×#4112yes—
101C22×C127H(5,𝔽2)12yes—
102C22×C127H(5,𝔽2)11yescharacteristic
103C22×C1272−1+411yescharacteristic
104C4×C127—22no—
105C4×C127—22no—
106C4×C127—24no—
107C4×C127—22no—
108C4×C127—24no—
109C4×C127—42no—
110C4×C127—42no—
111C4×C127—42no—
112C2×C127—44no—
113C2×C127C4×#4111yescharacteristic
114C2×C127#51811yescharacteristic
115C2×C127#52011yescharacteristic
116C2×C127#53812yes—
117C2×C127#54212yes—
118#2337C12711yesmaximal, characteristic, direct product factor, Sylow
119C127#233711yescharacteristic, direct product factor, Sylow
120C2×#124C2×C12711yescharacteristic
121#391C2×C12712yescomplemented
122#388C2×C12712yescomplemented
123#388C2×C12712yescomplemented
124#386C2×C12712yes—
125#385C2×C12712yescomplemented
126#383C2×C12711yescharacteristic, complemented
127C4×C4⋊C4C2×C12711yescharacteristic, complemented
128C4×C22⋊C4C2×C12712yescomplemented
129C22×Q8C22×C12711yescharacteristic
130C22×D4C22×C12711yescharacteristic
131C23×C4C22×C12712yes—
132#124C4×C12718yescomplemented
133C2×C4⋊C4C22×C12712yes—
134C2×C4⋊C4C22×C12712yes—
135C2×C22⋊C4C22×C12712yes—
136C2×C22⋊C4C22×C12712yes—
137C2×C22⋊C4C22×C12712yes—
138C2×C22⋊C4C22×C12712yes—
139C2×C22⋊C4C22×C12712yes—
140C2×C42C22×C12711yescharacteristic
141C2×C42C22×C12712yes—
142C2×C42C22×C12711yescharacteristic
143C2×C42C22×C12711yescharacteristic
144#95C22×C12712yes—
145#95C22×C12712yes—
146#95C22×C12712yes—
147#95C22×C12711yescharacteristic
148#95C22×C12712yes—
149#95C22×C12711yescharacteristic
150#95C22×C12712yes—
151C24C23×C12712yes—
152C2×Q8—42no—
153C2×Q8C2×C4×C12714yescomplemented
154C2×D4—42no—
155C2×D4C2×C4×C12714yes—
156C22×C4—24no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4C23×C12712yes—
160C22×C4C23×C12712yes—
161C22×C4C23×C12712yes—
162C22×C4C23×C12711yescharacteristic
163C22×C4C23×C12711yescharacteristic
164C22×C4C23×C12711yescharacteristic
165C22×C4C23×C12712yes—
166C22×C4C23×C12712yes—
167C4⋊C4—24no—
168C4⋊C4—42no—
169C22⋊C4—24no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4C2×C4×C12718yescomplemented
173C22⋊C4C2×C4×C12718yescomplemented
174C42—41no—
175C42—41no—
176C42—42no—
177C42C2×C4×C12714yescomplemented
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23C22×C4×C12714yes—
185C23C24×C12711yescharacteristic
186Q8—44no—
187D4—44no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—48no—
206C2×C4C22×C4×C12712yes—
207C2×C4C22×C4×C12712yes—
208C2×C4C22×C4×C12712yes—
209C2×C4C22×C4×C12714yes—
210C2×C4#41×C12714yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22C23×C4×C12711yescharacteristic
219C22C2×#41×C12712yes—
220C22H(5,𝔽2)×C12712yes—
221C22H(5,𝔽2)×C12711yescharacteristic
222C222−1+4×C12711yescharacteristic
223C4—22no—
224C4—22no—
225C4—24no—
226C4—22no—
227C4—24no—
228C4—42no—
229C4—42no—
230C4—42no—
231C2—44no—
232C2C4×#41×C12711yescharacteristic
233C2#518×C12711yescharacteristic
234C2#520×C12711yescharacteristic
235C2#538×C12712yes—
236C2#542×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutatorC22C23×C4×C127
Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #391×C127C2semidirect
3. #388×C127C2semidirect
4. #388×C127C2semidirect
6. #385×C127C2semidirect
7. #383×C127C2semidirect
8. C4×C4⋊C4×C127C2semidirect
9. C4×C22⋊C4×C127C2semidirect
13. #124×C127C4semidirect
34. C2×Q8×C127C2×C4semidirect
53. C22⋊C4×C127C2×C4semidirect
54. C22⋊C4×C127C2×C4semidirect
58. C42×C127C2×C4semidirect
118. #2337C127direct (N × H)
119. C127#2337direct (N × H)
121. #391C2×C127semidirect
122. #388C2×C127semidirect
123. #388C2×C127semidirect
125. #385C2×C127semidirect
126. #383C2×C127semidirect
127. C4×C4⋊C4C2×C127semidirect
128. C4×C22⋊C4C2×C127semidirect
132. #124C4×C127semidirect
153. C2×Q8C2×C4×C127semidirect
172. C22⋊C4C2×C4×C127semidirect
173. C22⋊C4C2×C4×C127semidirect
177. C42C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C1272
#391×C1272
#388×C1272
#386×C1272
#385×C1272
#383×C1272
C4×C4⋊C4×C1272
C4×C22⋊C4×C1272
#2337127