Finite Group Databasebeta

← C2×#447×C127 #30635948

Subgroups — C2×#447×C127 #30635948

Order 16256.

1048 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×C127C211yesmaximal, characteristic, complemented
2C22×D8×C127C212yesmaximal, complemented
3C2×#121×C127C211yesmaximal, characteristic, complemented
4#447×C127C218yesmaximal, direct product factor
5C2×#102×C127C212yesmaximal, complemented
6C2×C22⋊C8×C127C211yesmaximal, characteristic, complemented
7C25×C127—21no—
8C22×D4×C127—28no—
9C22×D4×C127—21no—
10C22×D4×C127—22no—
11C22×D4×C127—21no—
12C22×D4×C127C2212yes—
13C22×D4×C127C2214yescomplemented
14C22×D4×C127C2211yescharacteristic, complemented
15C23×C4×C127C2211yescharacteristic
16C2×D8×C127—28no—
17C2×D8×C127C2218yescomplemented
18C22×C8×C127C2212yescomplemented
19#121×C127—22no—
20#121×C127C2214yescomplemented
21C2×C4⋊C4×C127C2211yescharacteristic, complemented
22C2×C22⋊C4×C127—21no—
23#102×C127C2218yescomplemented
24C22⋊C8×C127C2214yescomplemented
25C24×C127—28no—
26C24×C127—24no—
27C24×C127—22no—
28C24×C127—21no—
29C24×C127—44no—
30C24×C127—44no—
31C24×C127D411yescharacteristic
32C2×D4×C127—28no—
33C2×D4×C127—216no—
34C2×D4×C127—216no—
35C2×D4×C127—24no—
36C2×D4×C127—22no—
37C2×D4×C127—24no—
38C2×D4×C127—24no—
39C2×D4×C127—24no—
40C2×D4×C127—21no—
41C2×D4×C127—44no—
42C2×D4×C127D418yescomplemented
43C2×D4×C127C2314yes—
44C2×D4×C127C2312yescomplemented
45C22×C4×C127—24no—
46C22×C4×C127—21no—
47C22×C4×C127D412yes—
48C22×C4×C127D411yescharacteristic
49C22×C4×C127C2312yes—
50C22×C4×C127C2311yescharacteristic
51D8×C127—216no—
52C2×C8×C127—24no—
53C2×C8×C127C2314yescomplemented
54C4⋊C4×C127—21no—
55C4⋊C4×C127C2312yescomplemented
56C22⋊C4×C127—24no—
57C23×C127—22no—
58C23×C127—22no—
59C23×C127—216no—
60C23×C127—28no—
61C23×C127—24no—
62C23×C127—22no—
63C23×C127—48no—
64C23×C127—432no—
65C23×C127—44no—
66C23×C127—48no—
67C23×C127—44no—
68C23×C127—42no—
69C23×C127—42no—
70C23×C127—42no—
71C23×C127D814yescomplemented
72C23×C127C2×D412yes—
73C23×C127C2×D411yescharacteristic
74D4×C127—216no—
75D4×C127—28no—
76D4×C127—24no—
77D4×C127—24no—
78D4×C127—48no—
79D4×C127—42no—
80D4×C127C2×D418yescomplemented
81C2×C4×C127—22no—
82C2×C4×C127—24no—
83C2×C4×C127—24no—
84C2×C4×C127—22no—
85C2×C4×C127—42no—
86C2×C4×C127C2×D412yes—
87C2×C4×C127C2×D411yescharacteristic
88C2×C4×C127C2×D414yes—
89C2×C4×C127C2411yescharacteristic
90C8×C127—24no—
91C22×C127—22no—
92C22×C127—22no—
93C22×C127—28no—
94C22×C127—28no—
95C22×C127—432no—
96C22×C127—44no—
97C22×C127—44no—
98C22×C127—416no—
99C22×C127—42no—
100C22×C127—42no—
101C22×C127—42no—
102C22×C127—84no—
103C22×C127#12012yes—
104C22×C127C2×D812yes—
105C22×C127C2×D814yescomplemented
106C22×C127AGL(1,ℤ/8)12yes—
107C22×C127C22×D411yescharacteristic
108C4×C127—22no—
109C4×C127—42no—
110C4×C127#12012yes—
111C4×C127C22×D412yes—
112C2×C127—24no—
113C2×C127—48no—
114C2×C127—82no—
115C2×C127#44714yesdirect product factor
116C2×C127C2×#12011yescharacteristic
117C2×C127C22×D811yescharacteristic
118C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
119C2×#447C12711yesmaximal, characteristic, direct product factor, Sylow
120C127C2×#44711yescharacteristic, direct product factor, Sylow
121C23×D4C2×C12711yescharacteristic, complemented
122C22×D8C2×C12712yescomplemented
123C2×#121C2×C12711yescharacteristic, complemented
124#447C2×C12718yesdirect product factor
125C2×#102C2×C12712yescomplemented
126C2×C22⋊C8C2×C12711yescharacteristic, complemented
127C25—21no—
128C22×D4—28no—
129C22×D4—21no—
130C22×D4—21no—
131C22×D4—22no—
132C22×D4C22×C12712yes—
133C22×D4C22×C12714yescomplemented
134C22×D4C22×C12711yescharacteristic, complemented
135C23×C4C22×C12711yescharacteristic
136C2×D8—28no—
137C2×D8C22×C12718yescomplemented
138C22×C8C22×C12712yescomplemented
139#121—22no—
140#121C22×C12714yescomplemented
141C2×C4⋊C4C22×C12711yescharacteristic, complemented
142C2×C22⋊C4—21no—
143#102C22×C12718yescomplemented
144C22⋊C8C22×C12714yescomplemented
145C24—28no—
146C24—22no—
147C24—24no—
148C24—21no—
149C24—44no—
150C24—44no—
151C24D4×C12711yescharacteristic
152C2×D4—28no—
153C2×D4—216no—
154C2×D4—216no—
155C2×D4—24no—
156C2×D4—22no—
157C2×D4—24no—
158C2×D4—24no—
159C2×D4—24no—
160C2×D4—21no—
161C2×D4—44no—
162C2×D4D4×C12718yescomplemented
163C2×D4C23×C12714yes—
164C2×D4C23×C12712yescomplemented
165C22×C4—24no—
166C22×C4—21no—
167C22×C4D4×C12711yescharacteristic
168C22×C4D4×C12712yes—
169C22×C4C23×C12712yes—
170C22×C4C23×C12711yescharacteristic
171D8—216no—
172C2×C8—24no—
173C2×C8C23×C12714yescomplemented
174C4⋊C4—21no—
175C4⋊C4C23×C12712yescomplemented
176C22⋊C4—24no—
177C23—22no—
178C23—22no—
179C23—216no—
180C23—28no—
181C23—24no—
182C23—22no—
183C23—48no—
184C23—432no—
185C23—44no—
186C23—48no—
187C23—44no—
188C23—42no—
189C23—42no—
190C23—42no—
191C23D8×C12714yescomplemented
192C23C2×D4×C12712yes—
193C23C2×D4×C12711yescharacteristic
194D4—216no—
195D4—28no—
196D4—24no—
197D4—24no—
198D4—48no—
199D4—42no—
200D4C2×D4×C12718yescomplemented
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4C2×D4×C12712yes—
207C2×C4C2×D4×C12711yescharacteristic
208C2×C4C2×D4×C12714yes—
209C2×C4C24×C12711yescharacteristic
210C8—24no—
211C22—22no—
212C22—22no—
213C22—28no—
214C22—28no—
215C22—432no—
216C22—44no—
217C22—44no—
218C22—416no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—84no—
223C22#120×C12712yes—
224C22C2×D8×C12712yes—
225C22C2×D8×C12714yescomplemented
226C22AGL(1,ℤ/8)×C12712yes—
227C22C22×D4×C12711yescharacteristic
228C4—22no—
229C4—42no—
230C4#120×C12712yes—
231C4C22×D4×C12712yes—
232C2—24no—
233C2—48no—
234C2—82no—
235C2#447×C12714yesdirect product factor
236C2C2×#120×C12711yescharacteristic
237C2C22×D8×C12711yescharacteristic
238C2C2×AGL(1,ℤ/8)×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×D4×C127C2semidirect
2. C22×D8×C127C2semidirect
3. C2×#121×C127C2semidirect
4. #447×C127C2direct (N × H)
5. C2×#102×C127C2semidirect
6. C2×C22⋊C8×C127C2semidirect
13. C22×D4×C127C22semidirect
14. C22×D4×C127C22semidirect
17. C2×D8×C127C22semidirect
18. C22×C8×C127C22semidirect
20. #121×C127C22semidirect
21. C2×C4⋊C4×C127C22semidirect
23. #102×C127C22semidirect
24. C22⋊C8×C127C22semidirect
42. C2×D4×C127D4semidirect
44. C2×D4×C127C23semidirect
53. C2×C8×C127C23semidirect
55. C4⋊C4×C127C23semidirect
71. C23×C127D8semidirect
80. D4×C127C2×D4semidirect
105. C22×C127C2×D8semidirect
115. C2×C127#447direct (N × H)
119. C2×#447C127direct (N × H)
120. C127C2×#447direct (N × H)
121. C23×D4C2×C127semidirect
122. C22×D8C2×C127semidirect
123. C2×#121C2×C127semidirect
124. #447C2×C127direct (N × H)
125. C2×#102C2×C127semidirect
126. C2×C22⋊C8C2×C127semidirect
133. C22×D4C22×C127semidirect
134. C22×D4C22×C127semidirect
137. C2×D8C22×C127semidirect
138. C22×C8C22×C127semidirect
140. #121C22×C127semidirect
141. C2×C4⋊C4C22×C127semidirect
143. #102C22×C127semidirect
144. C22⋊C8C22×C127semidirect
162. C2×D4D4×C127semidirect
164. C2×D4C23×C127semidirect
173. C2×C8C23×C127semidirect
175. C4⋊C4C23×C127semidirect
191. C23D8×C127semidirect
200. D4C2×D4×C127semidirect
225. C22C2×D8×C127semidirect
235. C2#447×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×C1272
C22×D8×C1272
C2×#121×C1272
#447×C1272
C2×#102×C1272
C2×C22⋊C8×C1272
C2×#447127