Finite Group Databasebeta

← C2×C127×#1347 #44575374

Subgroups — C2×C127×#1347 #44575374

Order 32512.

558 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C2×C22⋊C16×C127C211yesmaximal, characteristic, complemented
3C2×#340×C127C211yesmaximal, characteristic, complemented
4C127×#1347C214yesmaximal, direct product factor
5C22×D8×C127C411yescharacteristic, complemented
6C23×C8×C127C2211yescharacteristic
7C2×#121×C127—21no—
8C22×C4⋊C4×C127—21no—
9C22×C16×C127—21no—
10#466×C127—21no—
11#466×C127—21no—
12#466×C127C412yescomplemented
13#466×C127C2212yes—
14C2×#107×C127C411yescharacteristic, complemented
15C2×#102×C127—21no—
16C22⋊C16×C127—21no—
17C22⋊C16×C127C2212yescomplemented
18#340×C127—21no—
19#340×C127C2212yescomplemented
20C22×D4×C127—21no—
21C22×D4×C127—41no—
22C23×C4×C127—41no—
23C23×C4×C127D411yescharacteristic
24C2×D8×C127—21no—
25C2×D8×C127—42no—
26C2×D8×C127C2×C412yescomplemented
27C22×C8×C127—42no—
28C22×C8×C127C2×C411yescharacteristic
29C22×C8×C127C2×C411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C22×C8×C127D411yescharacteristic
32C22×C8×C127D411yescharacteristic
33C22×C8×C127C2311yescharacteristic
34#121×C127—22no—
35#121×C127—22no—
36#121×C127—41no—
37#121×C127—41no—
38C2×C4⋊C4×C127—24no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—42no—
42C2×C4⋊C4×C127—41no—
43C2×C22⋊C4×C127—41no—
44C2×C16×C127—22no—
45C2×C16×C127—42no—
46#107×C127—21no—
47#107×C127C2×C412yescomplemented
48#102×C127—22no—
49#102×C127—22no—
50C24×C127—41no—
51C24×C127D811yescharacteristic
52C2×D4×C127—22no—
53C2×D4×C127—42no—
54C2×D4×C127—42no—
55C2×D4×C127—42no—
56C2×D4×C127—41no—
57C2×D4×C127—42no—
58C2×D4×C127—82no—
59C2×D4×C127—82no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—44no—
63C22×C4×C127—41no—
64C22×C4×C127—42no—
65C22×C4×C127—82no—
66C22×C4×C127—82no—
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127D811yescharacteristic
70C22×C4×C127SD1611yescharacteristic
71C22×C4×C127SD1611yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73D8×C127—42no—
74D8×C127—42no—
75C2×C8×C127—22no—
76C2×C8×C127—22no—
77C2×C8×C127—41no—
78C2×C8×C127—41no—
79C2×C8×C127—41no—
80C2×C8×C127—41no—
81C2×C8×C127C22⋊C411yescharacteristic
82C2×C8×C127C22⋊C411yescharacteristic
83C2×C8×C127C22×C411yescharacteristic
84C2×C8×C127C2×D411yescharacteristic
85C4⋊C4×C127—24no—
86C4⋊C4×C127—22no—
87C4⋊C4×C127—44no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—41no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C16×C127—42no—
93C23×C127—22no—
94C23×C127—22no—
95C23×C127—42no—
96C23×C127—82no—
97C23×C127—82no—
98C23×C127—82no—
99C23×C127#10211yescharacteristic
100C23×C127#10211yescharacteristic
101C23×C127D1612yes—
102C23×C127SD3212yes—
103C23×C127C2×D811yescharacteristic
104D4×C127—42no—
105D4×C127—42no—
106D4×C127—84no—
107D4×C127—82no—
108D4×C127—82no—
109D4×C127—82no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—44no—
118C2×C4×C127—42no—
119C2×C4×C127—88no—
120C2×C4×C127—82no—
121C2×C4×C127—82no—
122C2×C4×C127—82no—
123C2×C4×C127#9912yes—
124C2×C4×C127#10211yescharacteristic
125C2×C4×C127#10211yescharacteristic
126C2×C4×C127#10412yes—
127C2×C4×C127C2×C22⋊C411yescharacteristic
128C2×C4×C127C2×SD1611yescharacteristic
129C8×C127—21no—
130C8×C127—21no—
131C8×C127—21no—
132C8×C127—21no—
133C22×C127—24no—
134C22×C127—24no—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—82no—
140C22×C127—82no—
141C22×C127—82no—
142C22×C127—164no—
143C22×C127#32712yes—
144C22×C127#35712yes—
145C22×C127#35712yes—
146C22×C127#36012yes—
147C22×C127C2×#10211yescharacteristic
148C22×C127C2×D1611yescharacteristic
149C22×C127C2×SD3211yescharacteristic
150C4×C127—21no—
151C4×C127—21no—
152C4×C127—84no—
153C4×C127—82no—
154C4×C127#32712yes—
155C4×C127C2×#9911yescharacteristic
156C4×C127C2×#10411yescharacteristic
157C2×#1347C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—22no—
160C2×C127—21no—
161C2×C127—162no—
162C2×C127#134714yesdirect product factor
163C2×C127C2×#32711yescharacteristic
164C2×C127C2×#35711yescharacteristic
165C2×C127C2×#36011yescharacteristic
166C2×#466C2×C12711yescharacteristic
167C2×C22⋊C16C2×C12711yescharacteristic, complemented
168C2×#340C2×C12711yescharacteristic, complemented
169#1347C2×C12714yesdirect product factor
170C127C2×#134711yescharacteristic, direct product factor, Sylow
171C22×D8C4×C12711yescharacteristic, complemented
172C23×C8C22×C12711yescharacteristic
173C2×#121—21no—
174C22×C4⋊C4—21no—
175C22×C16—21no—
176#466—21no—
177#466—21no—
178#466C4×C12712yescomplemented
179#466C22×C12712yes—
180C2×#107C4×C12711yescharacteristic, complemented
181C2×#102—21no—
182C22⋊C16—21no—
183C22⋊C16C22×C12712yescomplemented
184#340—21no—
185#340C22×C12712yescomplemented
186C22×D4—21no—
187C22×D4—41no—
188C23×C4—41no—
189C23×C4D4×C12711yescharacteristic
190C2×D8—21no—
191C2×D8—42no—
192C2×D8C2×C4×C12712yescomplemented
193C22×C8—42no—
194C22×C8C2×C4×C12711yescharacteristic
195C22×C8C2×C4×C12711yescharacteristic
196C22×C8D4×C12711yescharacteristic
197C22×C8D4×C12711yescharacteristic
198C22×C8D4×C12711yescharacteristic
199C22×C8C23×C12711yescharacteristic
200#121—22no—
201#121—22no—
202#121—41no—
203#121—41no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4—41no—
209C2×C22⋊C4—41no—
210C2×C16—22no—
211C2×C16—42no—
212#107—21no—
213#107C2×C4×C12712yescomplemented
214#102—22no—
215#102—22no—
216C24—41no—
217C24D8×C12711yescharacteristic
218C2×D4—22no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—82no—
225C2×D4—82no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—44no—
229C22×C4—41no—
230C22×C4—42no—
231C22×C4—82no—
232C22×C4—82no—
233C22×C4C22⋊C4×C12711yescharacteristic
234C22×C4C22⋊C4×C12711yescharacteristic
235C22×C4D8×C12711yescharacteristic
236C22×C4SD16×C12711yescharacteristic
237C22×C4SD16×C12711yescharacteristic
238C22×C4C2×D4×C12711yescharacteristic
239D8—42no—
240D8—42no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8C22⋊C4×C12711yescharacteristic
248C2×C8C22⋊C4×C12711yescharacteristic
249C2×C8C22×C4×C12711yescharacteristic
250C2×C8C2×D4×C12711yescharacteristic
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C16—42no—
259C23—22no—
260C23—22no—
261C23—42no—
262C23—82no—
263C23—82no—
264C23—82no—
265C23#102×C12711yescharacteristic
266C23#102×C12711yescharacteristic
267C23D16×C12712yes—
268C23SD32×C12712yes—
269C23C2×D8×C12711yescharacteristic
270D4—42no—
271D4—42no—
272D4—82no—
273D4—82no—
274D4—84no—
275D4—82no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—88no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4#99×C12712yes—
290C2×C4#102×C12711yescharacteristic
291C2×C4#102×C12711yescharacteristic
292C2×C4#104×C12712yes—
293C2×C4C2×C22⋊C4×C12711yescharacteristic
294C2×C4C2×SD16×C12711yescharacteristic
295C8—21no—
296C8—21no—
297C8—21no—
298C8—21no—
299C22—24no—
300C22—24no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—82no—
306C22—82no—
307C22—82no—
308C22—164no—
309C22#327×C12712yes—
310C22#357×C12712yes—
311C22#357×C12712yes—
312C22#360×C12712yes—
313C22C2×#102×C12711yescharacteristic
314C22C2×D16×C12711yescharacteristic
315C22C2×SD32×C12711yescharacteristic
316C4—21no—
317C4—21no—
318C4—84no—
319C4—82no—
320C4#327×C12712yes—
321C4C2×#99×C12711yescharacteristic
322C4C2×#104×C12711yescharacteristic
323C2—21no—
324C2—21no—
325C2—22no—
326C2—162no—
327C2C127×#134714yesdirect product factor
328C2C2×#327×C12711yescharacteristic
329C2C2×#357×C12711yescharacteristic
330C2C2×#360×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#466×C127C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C16×C127C2semidirect
3. C2×#340×C127C2semidirect
4. C127×#1347C2direct (N × H)
5. C22×D8×C127C4semidirect
12. #466×C127C4semidirect
14. C2×#107×C127C4semidirect
17. C22⋊C16×C127C22semidirect
19. #340×C127C22semidirect
26. C2×D8×C127C2×C4semidirect
47. #107×C127C2×C4semidirect
157. C2×#1347C127direct (N × H)
162. C2×C127#1347direct (N × H)
167. C2×C22⋊C16C2×C127semidirect
168. C2×#340C2×C127semidirect
169. #1347C2×C127direct (N × H)
170. C127C2×#1347direct (N × H)
171. C22×D8C4×C127semidirect
178. #466C4×C127semidirect
180. C2×#107C4×C127semidirect
183. C22⋊C16C22×C127semidirect
185. #340C22×C127semidirect
192. C2×D8C2×C4×C127semidirect
213. #107C2×C4×C127semidirect
327. C2C127×#1347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#466×C1272
C2×C22⋊C16×C1272
C2×#340×C1272
C127×#13472
C2×#1347127