Finite Group Databasebeta

← C2×C127×#1634 #44582182

Subgroups — C2×C127×#1634 #44582182

Order 32512.

1074 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C127C211yesmaximal, characteristic
2C2×#494×C127C211yesmaximal, characteristic, complemented
3C2×#476×C127C212yesmaximal, complemented
4C127×#1634C218yesmaximal, direct product factor
5C2×#333×C127C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C127C212yesmaximal, complemented
7C22×Q16×C127—22no—
8#555×C127—22no—
9#555×C127—24no—
10#555×C127C2214yes—
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×C4⋊Q8×C127C2211yescharacteristic
13C2×#124×C127—22no—
14C2×#121×C127—22no—
15C2×C4×D4×C127C2212yes—
16C2×#117×C127—22no—
17#494×C127—22no—
18#494×C127C2214yescomplemented
19#476×C127—24no—
20#476×C127C2218yescomplemented
21C2×#106×C127—22no—
22C2×C4⋊C8×C127C2212yes—
23C2×#102×C127—22no—
24C2×C4×C8×C127C2211yescharacteristic
25#333×C127C2214yescomplemented
26D4⋊C8×C127C2218yescomplemented
27C22×Q8×C127—21no—
28C22×Q8×C127D412yes—
29C22×D4×C127—22no—
30C22×D4×C127D412yes—
31C23×C4×C127—22no—
32C2×Q16×C127—28no—
33C2×Q16×C127—48no—
34C22×C8×C127—21no—
35C22×C8×C127—22no—
36C4⋊Q8×C127—22no—
37C4⋊Q8×C127—22no—
38C4⋊Q8×C127—21no—
39C4⋊Q8×C127D412yes—
40C4⋊Q8×C127C2312yes—
41C4⋊Q8×C127C2312yes—
42#124×C127—28no—
43#124×C127—28no—
44#121×C127—28no—
45#121×C127—28no—
46C4×D4×C127—22no—
47C4×D4×C127—22no—
48C4×D4×C127D414yes—
49C4×D4×C127C2314yes—
50#117×C127—28no—
51#117×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#106×C127—28no—
60C4⋊C8×C127—22no—
61C4⋊C8×C127C2314yes—
62#102×C127—28no—
63C4×C8×C127—21no—
64C4×C8×C127C2312yes—
65C24×C127—22no—
66C2×Q8×C127—22no—
67C2×Q8×C127—22no—
68C2×Q8×C127—44no—
69C2×Q8×C127—44no—
70C2×Q8×C127—41no—
71C2×Q8×C127C2×D414yes—
72C2×D4×C127—28no—
73C2×D4×C127—22no—
74C2×D4×C127—24no—
75C2×D4×C127—24no—
76C2×D4×C127—84no—
77C2×D4×C127C2×D414yes—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—44no—
83C22×C4×C127—44no—
84C22×C4×C127—41no—
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D412yes—
87Q16×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—24no—
100C22⋊C4×C127—24no—
101C42×C127—28no—
102C42×C127C2×D411yescharacteristic
103C42×C127C2×D412yes—
104C42×C127C2411yescharacteristic
105C23×C127—24no—
106C23×C127—44no—
107C23×C127—44no—
108C23×C127—44no—
109C23×C127#12011yescharacteristic
110Q8×C127—44no—
111Q8×C127—44no—
112Q8×C127—82no—
113Q8×C127—82no—
114D4×C127—24no—
115D4×C127—24no—
116D4×C127—44no—
117D4×C127—88no—
118C2×C4×C127—22no—
119C2×C4×C127—24no—
120C2×C4×C127—24no—
121C2×C4×C127—44no—
122C2×C4×C127—44no—
123C2×C4×C127—44no—
124C2×C4×C127—44no—
125C2×C4×C127—48no—
126C2×C4×C127—42no—
127C2×C4×C127—82no—
128C2×C4×C127#12011yescharacteristic
129C2×C4×C127#12012yes—
130C2×C4×C127#13514yes—
131C2×C4×C127#13714yes—
132C2×C4×C127C22×D411yescharacteristic
133C2×C4×C127C22×D412yes—
134C8×C127—24no—
135C8×C127—44no—
136C22×C127—44no—
137C22×C127—44no—
138C22×C127—44no—
139C22×C127—88no—
140C22×C127#45214yes—
141C22×C127#45312yes—
142C22×C127C2×#12011yescharacteristic
143C4×C127—21no—
144C4×C127—21no—
145C4×C127—44no—
146C4×C127—44no—
147C4×C127—82no—
148C4×C127#45214yes—
149C4×C127C2×#13512yes—
150C4×C127C2×#13712yes—
151C2×#1634C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—84no—
153C2×C127#163414yesdirect product factor
154C2×C127C2×#45212yes—
155C2×C127C2×#45311yescharacteristic
156C2×#555C2×C12711yescharacteristic
157C2×#494C2×C12711yescharacteristic, complemented
158C2×#476C2×C12712yescomplemented
159#1634C2×C12718yesdirect product factor
160C2×#333C2×C12711yescharacteristic, complemented
161C2×D4⋊C8C2×C12712yescomplemented
162C127C2×#163411yescharacteristic, direct product factor, Sylow
163C22×Q16—22no—
164#555—22no—
165#555—24no—
166#555C22×C12714yes—
167C2×C4⋊Q8C22×C12711yescharacteristic
168C2×C4⋊Q8C22×C12711yescharacteristic
169C2×#124—22no—
170C2×#121—22no—
171C2×C4×D4C22×C12712yes—
172C2×#117—22no—
173#494—22no—
174#494C22×C12714yescomplemented
175#476—24no—
176#476C22×C12718yescomplemented
177C2×#106—22no—
178C2×C4⋊C8C22×C12712yes—
179C2×#102—22no—
180C2×C4×C8C22×C12711yescharacteristic
181#333C22×C12714yescomplemented
182D4⋊C8C22×C12718yescomplemented
183C22×Q8—21no—
184C22×Q8D4×C12712yes—
185C22×D4—22no—
186C22×D4D4×C12712yes—
187C23×C4—22no—
188C2×Q16—28no—
189C2×Q16—48no—
190C22×C8—21no—
191C22×C8—22no—
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—21no—
195C4⋊Q8D4×C12712yes—
196C4⋊Q8C23×C12712yes—
197C4⋊Q8C23×C12712yes—
198#124—28no—
199#124—28no—
200#121—28no—
201#121—28no—
202C4×D4—22no—
203C4×D4—22no—
204C4×D4D4×C12714yes—
205C4×D4C23×C12714yes—
206#117—28no—
207#117—28no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4D4×C12712yes—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—22no—
213C2×C42—22no—
214C2×C42C23×C12711yescharacteristic
215#106—28no—
216C4⋊C8—22no—
217C4⋊C8C23×C12714yes—
218#102—28no—
219C4×C8—21no—
220C4×C8C23×C12712yes—
221C24—22no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—44no—
225C2×Q8—44no—
226C2×Q8—41no—
227C2×Q8C2×D4×C12714yes—
228C2×D4—28no—
229C2×D4—22no—
230C2×D4—24no—
231C2×D4—24no—
232C2×D4—84no—
233C2×D4C2×D4×C12714yes—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—41no—
241C22×C4C2×D4×C12711yescharacteristic
242C22×C4C2×D4×C12712yes—
243Q16—416no—
244C2×C8—24no—
245C2×C8—22no—
246C2×C8—24no—
247C2×C8—44no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—42no—
253C4⋊C4C2×D4×C12714yes—
254C22⋊C4—216no—
255C22⋊C4—24no—
256C22⋊C4—24no—
257C42—28no—
258C42C2×D4×C12711yescharacteristic
259C42C2×D4×C12712yes—
260C42C24×C12711yescharacteristic
261C23—24no—
262C23—44no—
263C23—44no—
264C23—44no—
265C23#120×C12711yescharacteristic
266Q8—44no—
267Q8—44no—
268Q8—82no—
269Q8—82no—
270D4—24no—
271D4—24no—
272D4—44no—
273D4—88no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—48no—
282C2×C4—42no—
283C2×C4—82no—
284C2×C4#120×C12711yescharacteristic
285C2×C4#120×C12712yes—
286C2×C4#135×C12714yes—
287C2×C4#137×C12714yes—
288C2×C4C22×D4×C12711yescharacteristic
289C2×C4C22×D4×C12712yes—
290C8—24no—
291C8—44no—
292C22—44no—
293C22—44no—
294C22—44no—
295C22—88no—
296C22#452×C12714yes—
297C22#453×C12712yes—
298C22C2×#120×C12711yescharacteristic
299C4—21no—
300C4—21no—
301C4—44no—
302C4—44no—
303C4—82no—
304C4#452×C12714yes—
305C4C2×#135×C12712yes—
306C4C2×#137×C12712yes—
307C2—84no—
308C2C127×#163414yesdirect product factor
309C2C2×#452×C12712yes—
310C2C2×#453×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#555×C127C2
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
2. C2×#494×C127C2semidirect
3. C2×#476×C127C2semidirect
4. C127×#1634C2direct (N × H)
5. C2×#333×C127C2semidirect
6. C2×D4⋊C8×C127C2semidirect
18. #494×C127C22semidirect
20. #476×C127C22semidirect
25. #333×C127C22semidirect
26. D4⋊C8×C127C22semidirect
151. C2×#1634C127direct (N × H)
153. C2×C127#1634direct (N × H)
157. C2×#494C2×C127semidirect
158. C2×#476C2×C127semidirect
159. #1634C2×C127direct (N × H)
160. C2×#333C2×C127semidirect
161. C2×D4⋊C8C2×C127semidirect
162. C127C2×#1634direct (N × H)
174. #494C22×C127semidirect
176. #476C22×C127semidirect
181. #333C22×C127semidirect
182. D4⋊C8C22×C127semidirect
308. C2C127×#1634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#555×C1272
C2×#494×C1272
C2×#476×C1272
C127×#16342
C2×#333×C1272
C2×D4⋊C8×C1272
C2×#1634127