Finite Group Databasebeta

← C127×#14694 #44578367

Subgroups — C127×#14694 #44578367

Order 32512.

7034 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C127C211yesmaximal, characteristic, complemented
2C22×#120×C127C211yesmaximal, characteristic
3C2×#386×C127C216yesmaximal, complemented
4C2×#379×C127C211yesmaximal, characteristic, complemented
5C127×C22⋊#95C216yesmaximal, complemented
6C26×C127C2211yescharacteristic
7C23×D4×C127C2213yes—
8C24×C4×C127—24no—
9C24×C4×C127—224no—
10C24×C4×C127C2216yes—
11C2×#120×C127—24no—
12C2×#120×C127—24no—
13C2×#120×C127C418yescomplemented
14C22×C22⋊C4×C127C2216yes—
15C22×C22⋊C4×C127C2213yes—
16C22×C22⋊C4×C127C2214yescomplemented
17#386×C127—224no—
18#379×C127—24no—
19C2×#95×C127C22112yescomplemented
20C25×C127—212no—
21C25×C127—212no—
22C25×C127C2×C414yes—
23C25×C127D414yes—
24C25×C127D414yes—
25C25×C127C2311yescharacteristic
26C25×C127C2313yes—
27C22×D4×C127—26no—
28C22×D4×C127—26no—
29C22×D4×C127—212no—
30C22×D4×C127—212no—
31C22×D4×C127C2×C4112yescomplemented
32C23×C4×C127—296no—
33C23×C4×C127—2128no—
34C23×C4×C127—212no—
35C23×C4×C127—212no—
36C23×C4×C127—248no—
37C23×C4×C127D4124yescomplemented
38C23×C4×C127C2314yes—
39C23×C4×C127C2313yes—
40C23×C4×C127C2314yes—
41#120×C127—232no—
42C2×C22⋊C4×C127—26no—
43C2×C22⋊C4×C127—26no—
44C2×C22⋊C4×C127—212no—
45C2×C22⋊C4×C127—212no—
46C2×C22⋊C4×C127—212no—
47C2×C22⋊C4×C127—224no—
48C2×C22⋊C4×C127C2×C4112yescomplemented
49#95×C127—224no—
50C24×C127—232no—
51C24×C127—296no—
52C24×C127—248no—
53C24×C127—224no—
54C24×C127—248no—
55C24×C127—224no—
56C24×C127—212no—
57C24×C127—212no—
58C24×C127—26no—
59C24×C127—21no—
60C24×C127—21no—
61C24×C127—26no—
62C24×C127C22⋊C4116yescomplemented
63C24×C127C22×C416yes—
64C24×C127C22×C412yescomplemented
65C24×C127C2×D416yes—
66C24×C127C2×D416yes—
67C24×C127C2×D4112yes—
68C24×C127#41112yes—
69C24×C127C2411yescharacteristic
70C2×D4×C127—224no—
71C2×D4×C127—248no—
72C2×D4×C127—412no—
73C2×D4×C127—424no—
74C2×D4×C127—412no—
75C22×C4×C127—2256no—
76C22×C4×C127—296no—
77C22×C4×C127—296no—
78C22×C4×C127—248no—
79C22×C4×C127—24no—
80C22×C4×C127—212no—
81C22×C4×C127—296no—
82C22×C4×C127—26no—
83C22×C4×C127—23no—
84C22×C4×C127—23no—
85C22×C4×C127—26no—
86C22×C4×C127—212no—
87C22×C4×C127—24no—
88C22×C4×C127—212no—
89C22×C4×C127C22×C416yescomplemented
90C22×C4×C127C2×D4124yes—
91C22⋊C4×C127—224no—
92C22⋊C4×C127—424no—
93C22⋊C4×C127—416no—
94C23×C127—232no—
95C23×C127—2128no—
96C23×C127—296no—
97C23×C127—2128no—
98C23×C127—224no—
99C23×C127—224no—
100C23×C127—212no—
101C23×C127—224no—
102C23×C127—212no—
103C23×C127—224no—
104C23×C127—248no—
105C23×C127—296no—
106C23×C127—22no—
107C23×C127—212no—
108C23×C127—44no—
109C23×C127—43no—
110C23×C127—46no—
111C23×C127—43no—
112C23×C127—412no—
113C23×C127C2×C22⋊C4112yes—
114C23×C127C4×D4124yes—
115C23×C127#120112yes—
116C23×C127#121124yes—
117C23×C127#123112yes—
118C23×C127C23×C411yescharacteristic
119C23×C127C22×D411yescharacteristic
120C23×C127C22×D411yescharacteristic
121C23×C127C22×D416yes—
122C23×C127C2×#4116yes—
123D4×C127—448no—
124C2×C4×C127—2192no—
125C2×C4×C127—224no—
126C2×C4×C127—224no—
127C2×C4×C127—26no—
128C2×C4×C127—212no—
129C2×C4×C127—43no—
130C2×C4×C127—46no—
131C2×C4×C127—43no—
132C2×C4×C127—44no—
133C2×C4×C127—412no—
134C2×C4×C127—412no—
135C2×C4×C127#120116yescomplemented
136C22×C127—2128no—
137C22×C127—212no—
138C22×C127—248no—
139C22×C127—212no—
140C22×C127—224no—
141C22×C127—224no—
142C22×C127—248no—
143C22×C127—46no—
144C22×C127—48no—
145C22×C127—81no—
146C22×C127—84no—
147C22×C127—83no—
148C22×C127#386124yescomplemented
149C22×C127C22×C22⋊C411yescharacteristic
150C22×C127C2×C4×D416yes—
151C22×C127C2×#12014yes—
152C22×C127C2×#12013yes—
153C22×C127C2×#12116yes—
154C22×C127C2×#12313yes—
155C22×C127#525112yes—
156C4×C127—216no—
157C4×C127—46no—
158C4×C127—84no—
159#14694C12711yesmaximal, characteristic, direct product factor, Sylow
160C2×C127—224no—
161C2×C127—82no—
162C2×C127C2×#38613yes—
163C2×C127C4×#12014yes—
164C2×C127#284611yescharacteristic
165C2×C127#284714yes—
166C2×C127#284913yes—
167C25×C4C2×C12711yescharacteristic, complemented
168C22×#120C2×C12711yescharacteristic
169C2×#386C2×C12716yescomplemented
170C2×#379C2×C12711yescharacteristic, complemented
171C22⋊#95C2×C12716yescomplemented
172C127#1469411yescharacteristic, direct product factor, Sylow
173C26C22×C12711yescharacteristic
174C23×D4C22×C12713yes—
175C24×C4—24no—
176C24×C4—224no—
177C24×C4C22×C12716yes—
178C2×#120—24no—
179C2×#120—24no—
180C2×#120C4×C12718yescomplemented
181C22×C22⋊C4C22×C12716yes—
182C22×C22⋊C4C22×C12713yes—
183C22×C22⋊C4C22×C12714yescomplemented
184#386—224no—
185#379—24no—
186C2×#95C22×C127112yescomplemented
187C25—212no—
188C25—212no—
189C25C2×C4×C12714yes—
190C25D4×C12714yes—
191C25D4×C12714yes—
192C25C23×C12711yescharacteristic
193C25C23×C12713yes—
194C22×D4—26no—
195C22×D4—26no—
196C22×D4—212no—
197C22×D4—212no—
198C22×D4C2×C4×C127112yescomplemented
199C23×C4—296no—
200C23×C4—2128no—
201C23×C4—212no—
202C23×C4—212no—
203C23×C4—248no—
204C23×C4D4×C127124yescomplemented
205C23×C4C23×C12714yes—
206C23×C4C23×C12713yes—
207C23×C4C23×C12714yes—
208#120—232no—
209C2×C22⋊C4—26no—
210C2×C22⋊C4—26no—
211C2×C22⋊C4—212no—
212C2×C22⋊C4—212no—
213C2×C22⋊C4—212no—
214C2×C22⋊C4—224no—
215C2×C22⋊C4C2×C4×C127112yescomplemented
216#95—224no—
217C24—232no—
218C24—296no—
219C24—248no—
220C24—224no—
221C24—248no—
222C24—224no—
223C24—212no—
224C24—212no—
225C24—26no—
226C24—21no—
227C24—21no—
228C24—26no—
229C24C22⋊C4×C127116yescomplemented
230C24C22×C4×C12716yes—
231C24C22×C4×C12712yescomplemented
232C24C2×D4×C12716yes—
233C24C2×D4×C12716yes—
234C24C2×D4×C127112yes—
235C24#41×C127112yes—
236C24C24×C12711yescharacteristic
237C2×D4—224no—
238C2×D4—248no—
239C2×D4—412no—
240C2×D4—424no—
241C2×D4—412no—
242C22×C4—2256no—
243C22×C4—296no—
244C22×C4—296no—
245C22×C4—248no—
246C22×C4—24no—
247C22×C4—212no—
248C22×C4—296no—
249C22×C4—26no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—26no—
253C22×C4—212no—
254C22×C4—24no—
255C22×C4—212no—
256C22×C4C22×C4×C12716yescomplemented
257C22×C4C2×D4×C127124yes—
258C22⋊C4—224no—
259C22⋊C4—424no—
260C22⋊C4—416no—
261C23—232no—
262C23—2128no—
263C23—296no—
264C23—2128no—
265C23—224no—
266C23—224no—
267C23—212no—
268C23—224no—
269C23—212no—
270C23—224no—
271C23—248no—
272C23—296no—
273C23—22no—
274C23—212no—
275C23—44no—
276C23—43no—
277C23—46no—
278C23—43no—
279C23—412no—
280C23C2×C22⋊C4×C127112yes—
281C23C4×D4×C127124yes—
282C23#120×C127112yes—
283C23#121×C127124yes—
284C23#123×C127112yes—
285C23C23×C4×C12711yescharacteristic
286C23C22×D4×C12711yescharacteristic
287C23C22×D4×C12711yescharacteristic
288C23C22×D4×C12716yes—
289C23C2×#41×C12716yes—
290D4—448no—
291C2×C4—2192no—
292C2×C4—224no—
293C2×C4—224no—
294C2×C4—26no—
295C2×C4—212no—
296C2×C4—43no—
297C2×C4—46no—
298C2×C4—43no—
299C2×C4—44no—
300C2×C4—412no—
301C2×C4—412no—
302C2×C4#120×C127116yescomplemented
303C22—2128no—
304C22—212no—
305C22—248no—
306C22—212no—
307C22—224no—
308C22—224no—
309C22—248no—
310C22—46no—
311C22—48no—
312C22—81no—
313C22—84no—
314C22—83no—
315C22#386×C127124yescomplemented
316C22C22×C22⋊C4×C12711yescharacteristic
317C22C2×C4×D4×C12716yes—
318C22C2×#120×C12714yes—
319C22C2×#120×C12713yes—
320C22C2×#121×C12716yes—
321C22C2×#123×C12713yes—
322C22#525×C127112yes—
323C4—216no—
324C4—46no—
325C4—84no—
326C2—224no—
327C2—82no—
328C2C2×#386×C12713yes—
329C2C4×#120×C12714yes—
330C2C127×#284611yescharacteristic
331C2C127×#284714yes—
332C2C127×#284913yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#120×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C25×C4×C127C2semidirect
3. C2×#386×C127C2semidirect
4. C2×#379×C127C2semidirect
5. C127×C22⋊#95C2semidirect
13. C2×#120×C127C4semidirect
16. C22×C22⋊C4×C127C22semidirect
19. C2×#95×C127C22semidirect
31. C22×D4×C127C2×C4semidirect
37. C23×C4×C127D4semidirect
48. C2×C22⋊C4×C127C2×C4semidirect
62. C24×C127C22⋊C4semidirect
64. C24×C127C22×C4semidirect
89. C22×C4×C127C22×C4semidirect
135. C2×C4×C127#120semidirect
148. C22×C127#386semidirect
159. #14694C127direct (N × H)
167. C25×C4C2×C127semidirect
169. C2×#386C2×C127semidirect
170. C2×#379C2×C127semidirect
171. C22⋊#95C2×C127semidirect
172. C127#14694direct (N × H)
180. C2×#120C4×C127semidirect
183. C22×C22⋊C4C22×C127semidirect
186. C2×#95C22×C127semidirect
198. C22×D4C2×C4×C127semidirect
204. C23×C4D4×C127semidirect
215. C2×C22⋊C4C2×C4×C127semidirect
229. C24C22⋊C4×C127semidirect
231. C24C22×C4×C127semidirect
256. C22×C4C22×C4×C127semidirect
302. C2×C4#120×C127semidirect
315. C22#386×C127semidirect

Maximal subgroups

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

subgroupindex
C25×C4×C1272
C22×#120×C1272
C2×#386×C1272
C2×#379×C1272
C127×C22⋊#952
#14694127