Finite Group Databasebeta

← C2×C127×#1630 #44582152

Subgroups — C2×C127×#1630 #44582152

Order 32512.

1074 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C127C211yesmaximal, characteristic
2C2×#492×C127C211yesmaximal, characteristic
3C2×#477×C127C212yesmaximal, complemented
4C127×#1630C218yesmaximal, direct product factor
5C2×#331×C127C211yesmaximal, characteristic
6C2×Q8⋊C8×C127C212yesmaximal, complemented
7C22×SD16×C127—22no—
8#559×C127—22no—
9#559×C127—24no—
10#559×C127C2214yes—
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×#127×C127C2211yescharacteristic
13C2×#124×C127—22no—
14C2×#123×C127—22no—
15C2×C4×Q8×C127C2212yes—
16C2×C4×D4×C127—22no—
17#492×C127—22no—
18#492×C127C2214yes—
19#477×C127—24no—
20#477×C127C2218yescomplemented
21C2×#107×C127—22no—
22C2×C4⋊C8×C127C2212yes—
23C2×#103×C127—22no—
24C2×C4×C8×C127C2211yescharacteristic
25#331×C127C2214yes—
26Q8⋊C8×C127C2218yescomplemented
27C22×Q8×C127—21no—
28C22×Q8×C127D412yes—
29C22×D4×C127—22no—
30C22×D4×C127D412yes—
31C23×C4×C127—22no—
32C2×SD16×C127—28no—
33C2×SD16×C127—48no—
34C22×C8×C127—21no—
35C22×C8×C127—22no—
36C4⋊Q8×C127—22no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127C2312yes—
39#127×C127—22no—
40#127×C127D412yes—
41#127×C127C2312yes—
42#124×C127—28no—
43#124×C127—28no—
44#123×C127—28no—
45#123×C127—28no—
46C4×Q8×C127—22no—
47C4×Q8×C127—22no—
48C4×Q8×C127D414yes—
49C4×Q8×C127C2314yes—
50C4×D4×C127—28no—
51C4×D4×C127—28no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127D412yes—
55C2×C22⋊C4×C127—24no—
56C2×C22⋊C4×C127—22no—
57C2×C42×C127—22no—
58C2×C42×C127C2311yescharacteristic
59#107×C127—28no—
60C4⋊C8×C127—22no—
61C4⋊C8×C127C2314yes—
62#103×C127—28no—
63C4×C8×C127—21no—
64C4×C8×C127C2312yes—
65C24×C127—22no—
66C2×Q8×C127—22no—
67C2×Q8×C127—24no—
68C2×Q8×C127—24no—
69C2×Q8×C127—22no—
70C2×Q8×C127—44no—
71C2×Q8×C127—41no—
72C2×Q8×C127C2×D414yes—
73C2×D4×C127—24no—
74C2×D4×C127—22no—
75C2×D4×C127—24no—
76C2×D4×C127—44no—
77C2×D4×C127—44no—
78C2×D4×C127—44no—
79C2×D4×C127C2×D414yes—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—28no—
83C22×C4×C127—41no—
84C22×C4×C127—84no—
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D412yes—
87SD16×C127—416no—
88C2×C8×C127—24no—
89C2×C8×C127—22no—
90C2×C8×C127—24no—
91C2×C8×C127—44no—
92C4⋊C4×C127—24no—
93C4⋊C4×C127—22no—
94C4⋊C4×C127—24no—
95C4⋊C4×C127—24no—
96C4⋊C4×C127—42no—
97C4⋊C4×C127C2×D414yes—
98C22⋊C4×C127—216no—
99C22⋊C4×C127—28no—
100C42×C127—24no—
101C42×C127—24no—
102C42×C127C2×D411yescharacteristic
103C42×C127C2×D412yes—
104C42×C127C2411yescharacteristic
105C23×C127—24no—
106C23×C127—48no—
107C23×C127—44no—
108C23×C127#12011yescharacteristic
109Q8×C127—24no—
110Q8×C127—24no—
111Q8×C127—44no—
112Q8×C127—44no—
113Q8×C127—82no—
114D4×C127—44no—
115D4×C127—44no—
116D4×C127—44no—
117D4×C127—48no—
118D4×C127—82no—
119C2×C4×C127—22no—
120C2×C4×C127—24no—
121C2×C4×C127—24no—
122C2×C4×C127—44no—
123C2×C4×C127—44no—
124C2×C4×C127—42no—
125C2×C4×C127—88no—
126C2×C4×C127—82no—
127C2×C4×C127#12011yescharacteristic
128C2×C4×C127#12012yes—
129C2×C4×C127#13514yes—
130C2×C4×C127#13714yes—
131C2×C4×C127C22×D411yescharacteristic
132C2×C4×C127C22×D412yes—
133C8×C127—24no—
134C8×C127—44no—
135C22×C127—48no—
136C22×C127—44no—
137C22×C127—88no—
138C22×C127#45214yes—
139C22×C127#45312yes—
140C22×C127C2×#12011yescharacteristic
141C4×C127—21no—
142C4×C127—21no—
143C4×C127—44no—
144C4×C127—44no—
145C4×C127—82no—
146C4×C127#45214yes—
147C4×C127C2×#13512yes—
148C4×C127C2×#13712yes—
149C2×#1630C12711yesmaximal, characteristic, direct product factor, Sylow
150C2×C127—84no—
151C2×C127#163014yesdirect product factor
152C2×C127C2×#45212yes—
153C2×C127C2×#45311yescharacteristic
154C2×#559C2×C12711yescharacteristic
155C2×#492C2×C12711yescharacteristic
156C2×#477C2×C12712yescomplemented
157#1630C2×C12718yesdirect product factor
158C2×#331C2×C12711yescharacteristic
159C2×Q8⋊C8C2×C12712yescomplemented
160C127C2×#163011yescharacteristic, direct product factor, Sylow
161C22×SD16—22no—
162#559—22no—
163#559—24no—
164#559C22×C12714yes—
165C2×C4⋊Q8C22×C12711yescharacteristic
166C2×#127C22×C12711yescharacteristic
167C2×#124—22no—
168C2×#123—22no—
169C2×C4×Q8C22×C12712yes—
170C2×C4×D4—22no—
171#492—22no—
172#492C22×C12714yes—
173#477—24no—
174#477C22×C12718yescomplemented
175C2×#107—22no—
176C2×C4⋊C8C22×C12712yes—
177C2×#103—22no—
178C2×C4×C8C22×C12711yescharacteristic
179#331C22×C12714yes—
180Q8⋊C8C22×C12718yescomplemented
181C22×Q8—21no—
182C22×Q8D4×C12712yes—
183C22×D4—22no—
184C22×D4D4×C12712yes—
185C23×C4—22no—
186C2×SD16—28no—
187C2×SD16—48no—
188C22×C8—21no—
189C22×C8—22no—
190C4⋊Q8—22no—
191C4⋊Q8—21no—
192C4⋊Q8C23×C12712yes—
193#127—22no—
194#127D4×C12712yes—
195#127C23×C12712yes—
196#124—28no—
197#124—28no—
198#123—28no—
199#123—28no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×Q8D4×C12714yes—
203C4×Q8C23×C12714yes—
204C4×D4—28no—
205C4×D4—28no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4D4×C12712yes—
209C2×C22⋊C4—24no—
210C2×C22⋊C4—22no—
211C2×C42—22no—
212C2×C42C23×C12711yescharacteristic
213#107—28no—
214C4⋊C8—22no—
215C4⋊C8C23×C12714yes—
216#103—28no—
217C4×C8—21no—
218C4×C8C23×C12712yes—
219C24—22no—
220C2×Q8—22no—
221C2×Q8—24no—
222C2×Q8—24no—
223C2×Q8—22no—
224C2×Q8—44no—
225C2×Q8—41no—
226C2×Q8C2×D4×C12714yes—
227C2×D4—24no—
228C2×D4—22no—
229C2×D4—24no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—44no—
233C2×D4C2×D4×C12714yes—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—28no—
237C22×C4—41no—
238C22×C4—84no—
239C22×C4C2×D4×C12711yescharacteristic
240C22×C4C2×D4×C12712yes—
241SD16—416no—
242C2×C8—24no—
243C2×C8—22no—
244C2×C8—24no—
245C2×C8—44no—
246C4⋊C4—24no—
247C4⋊C4—22no—
248C4⋊C4—24no—
249C4⋊C4—24no—
250C4⋊C4—42no—
251C4⋊C4C2×D4×C12714yes—
252C22⋊C4—216no—
253C22⋊C4—28no—
254C42—24no—
255C42—24no—
256C42C2×D4×C12711yescharacteristic
257C42C2×D4×C12712yes—
258C42C24×C12711yescharacteristic
259C23—24no—
260C23—48no—
261C23—44no—
262C23#120×C12711yescharacteristic
263Q8—24no—
264Q8—24no—
265Q8—44no—
266Q8—44no—
267Q8—82no—
268D4—44no—
269D4—44no—
270D4—44no—
271D4—48no—
272D4—82no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—88no—
280C2×C4—82no—
281C2×C4#120×C12711yescharacteristic
282C2×C4#120×C12712yes—
283C2×C4#135×C12714yes—
284C2×C4#137×C12714yes—
285C2×C4C22×D4×C12711yescharacteristic
286C2×C4C22×D4×C12712yes—
287C8—24no—
288C8—44no—
289C22—48no—
290C22—44no—
291C22—88no—
292C22#452×C12714yes—
293C22#453×C12712yes—
294C22C2×#120×C12711yescharacteristic
295C4—21no—
296C4—21no—
297C4—44no—
298C4—44no—
299C4—82no—
300C4#452×C12714yes—
301C4C2×#135×C12712yes—
302C4C2×#137×C12712yes—
303C2—84no—
304C2C127×#163014yesdirect product factor
305C2C2×#452×C12712yes—
306C2C2×#453×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#127×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#477×C127C2semidirect
4. C127×#1630C2direct (N × H)
6. C2×Q8⋊C8×C127C2semidirect
20. #477×C127C22semidirect
26. Q8⋊C8×C127C22semidirect
149. C2×#1630C127direct (N × H)
151. C2×C127#1630direct (N × H)
156. C2×#477C2×C127semidirect
157. #1630C2×C127direct (N × H)
159. C2×Q8⋊C8C2×C127semidirect
160. C127C2×#1630direct (N × H)
174. #477C22×C127semidirect
180. Q8⋊C8C22×C127semidirect
304. C2C127×#1630direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#559×C1272
C2×#492×C1272
C2×#477×C1272
C127×#16302
C2×#331×C1272
C2×Q8⋊C8×C1272
C2×#1630127