Finite Group Databasebeta

← C4×#379×C127 #44577442

Subgroups — C4×#379×C127 #44577442

Order 32512.

6734 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C127C211yesmaximal, characteristic
2C2×#379×C127C212yesmaximal
3C2×C4×C22⋊C4×C127C216yesmaximal, complemented
4C127×C22⋊#95C216yesmaximal, complemented
5C26×C127C2211yescharacteristic
6C24×C4×C127—224no—
7C24×C4×C127C418yescomplemented
8C24×C4×C127C2213yes—
9C24×C4×C127C2213yes—
10C22×C22⋊C4×C127C22112yes—
11C22×C42×C127C2214yescomplemented
12#379×C127C4116yesdirect product factor
13C4×C22⋊C4×C127—224no—
14C2×#95×C127C22112yescomplemented
15C25×C127—212no—
16C25×C127—212no—
17C25×C127C2×C414yes—
18C25×C127C2×C418yes—
19C25×C127C2313yes—
20C23×C4×C127—2128no—
21C23×C4×C127—212no—
22C23×C4×C127—296no—
23C23×C4×C127—224no—
24C23×C4×C127—224no—
25C23×C4×C127C2×C4112yes—
26C23×C4×C127C2×C4112yes—
27C23×C4×C127D4124yes—
28C23×C4×C127C2318yes—
29C23×C4×C127C2313yes—
30C23×C4×C127C2311yescharacteristic
31C2×C22⋊C4×C127—224no—
32C2×C22⋊C4×C127—224no—
33C2×C22⋊C4×C127C2×C4148yescomplemented
34C2×C42×C127—224no—
35#95×C127—224no—
36C24×C127—232no—
37C24×C127—296no—
38C24×C127—224no—
39C24×C127—224no—
40C24×C127—296no—
41C24×C127—212no—
42C24×C127—212no—
43C24×C127C42116yescomplemented
44C24×C127C22×C416yes—
45C24×C127C22×C4112yes—
46C24×C127C2×D4112yes—
47C24×C127#41112yes—
48C24×C127C2411yescharacteristic
49C22×C4×C127—296no—
50C22×C4×C127—2256no—
51C22×C4×C127—224no—
52C22×C4×C127—212no—
53C22×C4×C127—248no—
54C22×C4×C127—248no—
55C22×C4×C127—296no—
56C22×C4×C127—224no—
57C22×C4×C127—224no—
58C22×C4×C127C22⋊C4148yescomplemented
59C22×C4×C127C22×C416yes—
60C22×C4×C127C22×C412yes—
61C22×C4×C127C22×C4116yescomplemented
62C22×C4×C127C2×D4112yes—
63C22×C4×C127C2×D4112yes—
64C22⋊C4×C127—296no—
65C42×C127—416no—
66C23×C127—232no—
67C23×C127—296no—
68C23×C127—2256no—
69C23×C127—212no—
70C23×C127—212no—
71C23×C127—248no—
72C23×C127—224no—
73C23×C127—224no—
74C23×C127—248no—
75C23×C127—296no—
76C23×C127C2×C42112yes—
77C23×C127C2×C22⋊C4112yes—
78C23×C127#117112yes—
79C23×C127C4×D4148yes—
80C23×C127C23×C411yescharacteristic
81C23×C127C23×C412yes—
82C23×C127C22×D416yes—
83C23×C127C2×#4116yes—
84C2×C4×C127—296no—
85C2×C4×C127—212no—
86C2×C4×C127—224no—
87C2×C4×C127—296no—
88C2×C4×C127—248no—
89C2×C4×C127—48no—
90C2×C4×C127—424no—
91C2×C4×C127C2×C22⋊C4112yes—
92C2×C4×C127C2×C22⋊C4112yes—
93C2×C4×C127#120116yes—
94C22×C127—2128no—
95C22×C127—224no—
96C22×C127—212no—
97C22×C127—212no—
98C22×C127—224no—
99C22×C127—296no—
100C22×C127C4×C22⋊C4124yescomplemented
101C22×C127C22×C4211yescharacteristic
102C22×C127C22×C22⋊C413yes—
103C22×C127C2×#11713yes—
104C22×C127C2×C4×D4112yes—
105C22×C127C2×#12014yes—
106C22×C127#525112yes—
107C4×C127—212no—
108C4×C127—416no—
109C4×C127#37918yesdirect product factor
110C4×#379C12711yesmaximal, characteristic, direct product factor, Sylow
111C2×C127—224no—
112C2×C127C2×C4×C22⋊C413yes—
113C2×C127C2×#37911yescharacteristic
114C2×C127#228013yes—
115C2×C127C4×#12018yes—
116C25×C4C2×C12711yescharacteristic
117C2×#379C2×C12712yes—
118C2×C4×C22⋊C4C2×C12716yescomplemented
119C22⋊#95C2×C12716yescomplemented
120C127C4×#37911yescharacteristic, direct product factor, Sylow
121C26C22×C12711yescharacteristic
122C24×C4—224no—
123C24×C4C4×C12718yescomplemented
124C24×C4C22×C12713yes—
125C24×C4C22×C12713yes—
126C22×C22⋊C4C22×C127112yes—
127C22×C42C22×C12714yescomplemented
128#379C4×C127116yesdirect product factor
129C4×C22⋊C4—224no—
130C2×#95C22×C127112yescomplemented
131C25—212no—
132C25—212no—
133C25C2×C4×C12714yes—
134C25C2×C4×C12718yes—
135C25C23×C12713yes—
136C23×C4—2128no—
137C23×C4—212no—
138C23×C4—296no—
139C23×C4—224no—
140C23×C4—224no—
141C23×C4C2×C4×C127112yes—
142C23×C4C2×C4×C127112yes—
143C23×C4D4×C127124yes—
144C23×C4C23×C12718yes—
145C23×C4C23×C12713yes—
146C23×C4C23×C12711yescharacteristic
147C2×C22⋊C4—224no—
148C2×C22⋊C4—224no—
149C2×C22⋊C4C2×C4×C127148yescomplemented
150C2×C42—224no—
151#95—224no—
152C24—232no—
153C24—296no—
154C24—224no—
155C24—224no—
156C24—296no—
157C24—212no—
158C24—212no—
159C24C42×C127116yescomplemented
160C24C22×C4×C12716yes—
161C24C22×C4×C127112yes—
162C24C2×D4×C127112yes—
163C24#41×C127112yes—
164C24C24×C12711yescharacteristic
165C22×C4—296no—
166C22×C4—2256no—
167C22×C4—224no—
168C22×C4—212no—
169C22×C4—248no—
170C22×C4—248no—
171C22×C4—296no—
172C22×C4—224no—
173C22×C4—224no—
174C22×C4C22⋊C4×C127148yescomplemented
175C22×C4C22×C4×C12716yes—
176C22×C4C22×C4×C12712yes—
177C22×C4C22×C4×C127116yescomplemented
178C22×C4C2×D4×C127112yes—
179C22×C4C2×D4×C127112yes—
180C22⋊C4—296no—
181C42—416no—
182C23—232no—
183C23—296no—
184C23—2256no—
185C23—212no—
186C23—212no—
187C23—248no—
188C23—224no—
189C23—224no—
190C23—248no—
191C23—296no—
192C23C2×C42×C127112yes—
193C23C2×C22⋊C4×C127112yes—
194C23#117×C127112yes—
195C23C4×D4×C127148yes—
196C23C23×C4×C12711yescharacteristic
197C23C23×C4×C12712yes—
198C23C22×D4×C12716yes—
199C23C2×#41×C12716yes—
200C2×C4—296no—
201C2×C4—212no—
202C2×C4—224no—
203C2×C4—296no—
204C2×C4—248no—
205C2×C4—48no—
206C2×C4—424no—
207C2×C4C2×C22⋊C4×C127112yes—
208C2×C4C2×C22⋊C4×C127112yes—
209C2×C4#120×C127116yes—
210C22—2128no—
211C22—224no—
212C22—212no—
213C22—212no—
214C22—224no—
215C22—296no—
216C22C4×C22⋊C4×C127124yescomplemented
217C22C22×C42×C12711yescharacteristic
218C22C22×C22⋊C4×C12713yes—
219C22C2×#117×C12713yes—
220C22C2×C4×D4×C127112yes—
221C22C2×#120×C12714yes—
222C22#525×C127112yes—
223C4—212no—
224C4—416no—
225C4#379×C12718yesdirect product factor
226C2—224no—
227C2C2×C4×C22⋊C4×C12713yes—
228C2C2×#379×C12711yescharacteristic
229C2C127×#228013yes—
230C2C4×#120×C12718yes—
subgroupG/H
centerC23×C4×C127C23
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
socleC24×C127C24
prime radicalC26×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C127C2semidirect
4. C127×C22⋊#95C2semidirect
7. C24×C4×C127C4semidirect
11. C22×C42×C127C22semidirect
12. #379×C127C4direct (N × H)
14. C2×#95×C127C22semidirect
33. C2×C22⋊C4×C127C2×C4semidirect
43. C24×C127C42semidirect
58. C22×C4×C127C22⋊C4semidirect
61. C22×C4×C127C22×C4semidirect
100. C22×C127C4×C22⋊C4semidirect
109. C4×C127#379direct (N × H)
110. C4×#379C127direct (N × H)
118. C2×C4×C22⋊C4C2×C127semidirect
119. C22⋊#95C2×C127semidirect
120. C127C4×#379direct (N × H)
123. C24×C4C4×C127semidirect
127. C22×C42C22×C127semidirect
128. #379C4×C127direct (N × H)
130. C2×#95C22×C127semidirect
149. C2×C22⋊C4C2×C4×C127semidirect
159. C24C42×C127semidirect
174. C22×C4C22⋊C4×C127semidirect
177. C22×C4C22×C4×C127semidirect
216. C22C4×C22⋊C4×C127semidirect
225. C4#379×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4×C1272
C2×#379×C1272
C2×C4×C22⋊C4×C1272
C127×C22⋊#952
C4×#379127