Finite Group Databasebeta

← C127×#14693 #44578366

Subgroups — C127×#14693 #44578366

Order 32512.

6494 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C127C211yesmaximal, characteristic
2C2×#385×C127C216yesmaximal, complemented
3C2×#379×C127C211yesmaximal, characteristic
4C2×#379×C127C211yesmaximal, characteristic
5C127×C22⋊#95C216yesmaximal, complemented
6C26×C127C2211yescharacteristic
7C24×C4×C127—24no—
8C24×C4×C127—224no—
9C24×C4×C127C2216yes—
10C22×C4⋊C4×C127C2214yescomplemented
11C22×C22⋊C4×C127C2213yes—
12C22×C22⋊C4×C127C2213yes—
13C22×C22⋊C4×C127C2216yes—
14#385×C127—224no—
15#379×C127—24no—
16#379×C127C418yescomplemented
17C2×#95×C127C22112yescomplemented
18C25×C127—212no—
19C25×C127—212no—
20C25×C127C2×C414yes—
21C25×C127D414yes—
22C25×C127Q814yes—
23C25×C127C2313yes—
24C23×C4×C127—296no—
25C23×C4×C127—2128no—
26C23×C4×C127—212no—
27C23×C4×C127—212no—
28C23×C4×C127—248no—
29C23×C4×C127D4124yes—
30C23×C4×C127C2311yescharacteristic
31C23×C4×C127C2313yes—
32C23×C4×C127C2314yes—
33C23×C4×C127C2314yes—
34C2×C4⋊C4×C127—224no—
35C2×C22⋊C4×C127—212no—
36C2×C22⋊C4×C127—212no—
37C2×C22⋊C4×C127—26no—
38C2×C22⋊C4×C127—26no—
39C2×C22⋊C4×C127—212no—
40C2×C22⋊C4×C127—212no—
41C2×C22⋊C4×C127C2×C4124yescomplemented
42#95×C127—224no—
43C24×C127—232no—
44C24×C127—296no—
45C24×C127—248no—
46C24×C127—224no—
47C24×C127—248no—
48C24×C127—224no—
49C24×C127—212no—
50C24×C127—212no—
51C24×C127C4⋊C4116yescomplemented
52C24×C127C22×C416yes—
53C24×C127C2×D416yes—
54C24×C127C2×D4112yes—
55C24×C127C2×Q816yes—
56C24×C127#41112yes—
57C24×C127C2411yescharacteristic
58C22×C4×C127—2256no—
59C22×C4×C127—296no—
60C22×C4×C127—296no—
61C22×C4×C127—248no—
62C22×C4×C127—24no—
63C22×C4×C127—212no—
64C22×C4×C127—296no—
65C22×C4×C127—212no—
66C22×C4×C127—212no—
67C22×C4×C127—26no—
68C22×C4×C127—21no—
69C22×C4×C127—23no—
70C22×C4×C127—26no—
71C22×C4×C127—212no—
72C22×C4×C127C22×C418yescomplemented
73C22×C4×C127C2×D4124yes—
74C4⋊C4×C127—416no—
75C22⋊C4×C127—248no—
76C22⋊C4×C127—412no—
77C22⋊C4×C127—412no—
78C23×C127—232no—
79C23×C127—2128no—
80C23×C127—296no—
81C23×C127—2128no—
82C23×C127—224no—
83C23×C127—224no—
84C23×C127—212no—
85C23×C127—224no—
86C23×C127—212no—
87C23×C127—224no—
88C23×C127—248no—
89C23×C127—296no—
90C23×C127C2×C4⋊C4112yes—
91C23×C127C4×D4124yes—
92C23×C127#120112yes—
93C23×C127C22⋊Q8124yes—
94C23×C127#123112yes—
95C23×C127C23×C411yescharacteristic
96C23×C127C22×D411yescharacteristic
97C23×C127C22×D416yes—
98C23×C127C22×Q811yescharacteristic
99C23×C127C2×#4116yes—
100C2×C4×C127—2192no—
101C2×C4×C127—224no—
102C2×C4×C127—224no—
103C2×C4×C127—224no—
104C2×C4×C127—44no—
105C2×C4×C127—412no—
106C2×C4×C127—43no—
107C2×C4×C127—43no—
108C2×C4×C127—44no—
109C2×C4×C127—46no—
110C2×C4×C127—412no—
111C2×C4×C127#120116yes—
112C22×C127—2128no—
113C22×C127—212no—
114C22×C127—248no—
115C22×C127—212no—
116C22×C127—224no—
117C22×C127—224no—
118C22×C127—248no—
119C22×C127#385124yescomplemented
120C22×C127C22×C4⋊C411yescharacteristic
121C22×C127C2×C4×D416yes—
122C22×C127C2×#12014yes—
123C22×C127C2×#12013yes—
124C22×C127C2×C22⋊Q816yes—
125C22×C127C2×#12313yes—
126C22×C127#525112yes—
127C4×C127—216no—
128C4×C127—48no—
129C4×C127—81no—
130C4×C127—83no—
131#14693C12711yesmaximal, characteristic, direct product factor, Sylow
132C2×C127—224no—
133C2×C127C2×#38513yes—
134C2×C127C4×#12014yes—
135C2×C127#284611yescharacteristic
136C2×C127#284814yes—
137C2×C127#284913yes—
138C25×C4C2×C12711yescharacteristic
139C2×#385C2×C12716yescomplemented
140C2×#379C2×C12711yescharacteristic
141C2×#379C2×C12711yescharacteristic
142C22⋊#95C2×C12716yescomplemented
143C127#1469311yescharacteristic, direct product factor, Sylow
144C26C22×C12711yescharacteristic
145C24×C4—24no—
146C24×C4—224no—
147C24×C4C22×C12716yes—
148C22×C4⋊C4C22×C12714yescomplemented
149C22×C22⋊C4C22×C12713yes—
150C22×C22⋊C4C22×C12713yes—
151C22×C22⋊C4C22×C12716yes—
152#385—224no—
153#379—24no—
154#379C4×C12718yescomplemented
155C2×#95C22×C127112yescomplemented
156C25—212no—
157C25—212no—
158C25C2×C4×C12714yes—
159C25D4×C12714yes—
160C25Q8×C12714yes—
161C25C23×C12713yes—
162C23×C4—296no—
163C23×C4—2128no—
164C23×C4—212no—
165C23×C4—212no—
166C23×C4—248no—
167C23×C4D4×C127124yes—
168C23×C4C23×C12711yescharacteristic
169C23×C4C23×C12713yes—
170C23×C4C23×C12714yes—
171C23×C4C23×C12714yes—
172C2×C4⋊C4—224no—
173C2×C22⋊C4—212no—
174C2×C22⋊C4—212no—
175C2×C22⋊C4—26no—
176C2×C22⋊C4—26no—
177C2×C22⋊C4—212no—
178C2×C22⋊C4—212no—
179C2×C22⋊C4C2×C4×C127124yescomplemented
180#95—224no—
181C24—232no—
182C24—296no—
183C24—248no—
184C24—224no—
185C24—248no—
186C24—224no—
187C24—212no—
188C24—212no—
189C24C4⋊C4×C127116yescomplemented
190C24C22×C4×C12716yes—
191C24C2×D4×C12716yes—
192C24C2×D4×C127112yes—
193C24C2×Q8×C12716yes—
194C24#41×C127112yes—
195C24C24×C12711yescharacteristic
196C22×C4—2256no—
197C22×C4—296no—
198C22×C4—296no—
199C22×C4—248no—
200C22×C4—24no—
201C22×C4—212no—
202C22×C4—296no—
203C22×C4—212no—
204C22×C4—212no—
205C22×C4—26no—
206C22×C4—21no—
207C22×C4—23no—
208C22×C4—26no—
209C22×C4—212no—
210C22×C4C22×C4×C12718yescomplemented
211C22×C4C2×D4×C127124yes—
212C4⋊C4—416no—
213C22⋊C4—248no—
214C22⋊C4—412no—
215C22⋊C4—412no—
216C23—232no—
217C23—2128no—
218C23—296no—
219C23—2128no—
220C23—224no—
221C23—224no—
222C23—212no—
223C23—224no—
224C23—212no—
225C23—224no—
226C23—248no—
227C23—296no—
228C23C2×C4⋊C4×C127112yes—
229C23C4×D4×C127124yes—
230C23#120×C127112yes—
231C23C22⋊Q8×C127124yes—
232C23#123×C127112yes—
233C23C23×C4×C12711yescharacteristic
234C23C22×D4×C12711yescharacteristic
235C23C22×D4×C12716yes—
236C23C22×Q8×C12711yescharacteristic
237C23C2×#41×C12716yes—
238C2×C4—2192no—
239C2×C4—224no—
240C2×C4—224no—
241C2×C4—224no—
242C2×C4—44no—
243C2×C4—412no—
244C2×C4—43no—
245C2×C4—43no—
246C2×C4—44no—
247C2×C4—46no—
248C2×C4—412no—
249C2×C4#120×C127116yes—
250C22—2128no—
251C22—212no—
252C22—248no—
253C22—212no—
254C22—224no—
255C22—224no—
256C22—248no—
257C22#385×C127124yescomplemented
258C22C22×C4⋊C4×C12711yescharacteristic
259C22C2×C4×D4×C12716yes—
260C22C2×#120×C12714yes—
261C22C2×#120×C12713yes—
262C22C2×C22⋊Q8×C12716yes—
263C22C2×#123×C12713yes—
264C22#525×C127112yes—
265C4—216no—
266C4—48no—
267C4—81no—
268C4—83no—
269C2—224no—
270C2C2×#385×C12713yes—
271C2C4×#120×C12714yes—
272C2C127×#284611yescharacteristic
273C2C127×#284814yes—
274C2C127×#284913yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#385×C127C2semidirect
5. C127×C22⋊#95C2semidirect
10. C22×C4⋊C4×C127C22semidirect
16. #379×C127C4semidirect
17. C2×#95×C127C22semidirect
41. C2×C22⋊C4×C127C2×C4semidirect
51. C24×C127C4⋊C4semidirect
72. C22×C4×C127C22×C4semidirect
119. C22×C127#385semidirect
131. #14693C127direct (N × H)
139. C2×#385C2×C127semidirect
142. C22⋊#95C2×C127semidirect
143. C127#14693direct (N × H)
148. C22×C4⋊C4C22×C127semidirect
154. #379C4×C127semidirect
155. C2×#95C22×C127semidirect
179. C2×C22⋊C4C2×C4×C127semidirect
189. C24C4⋊C4×C127semidirect
210. C22×C4C22×C4×C127semidirect
257. C22#385×C127semidirect

Maximal subgroups

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

subgroupindex
C25×C4×C1272
C2×#385×C1272
C2×#379×C1272
C127×C22⋊#952
#14693127