Finite Group Databasebeta

← C127×#21395 #44585068

Subgroups — C127×#21395 #44585068

Order 32512.

1518 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C127C211yesmaximal, characteristic
2C2×#432×C127C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
4C127×#1987C212yesmaximal, complemented
5C127×#1982C212yesmaximal, complemented
6C127×#1874C214yesmaximal, complemented
7C127×#1762C214yesmaximal, complemented
8C22×#41×C127—21no—
9#532×C127—24no—
10#532×C127C418yescomplemented
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×#127×C127C2211yescharacteristic
13C2×#124×C127—21no—
14C2×#121×C127—21no—
15C2×#121×C127C2212yes—
16C2×C4×D4×C127—21no—
17C2×C4×D4×C127C2212yes—
18C22×C4⋊C4×C127C2212yes—
19C22×C42×C127—21no—
20C22×C42×C127C2211yescharacteristic
21#432×C127—24no—
22C2×C4⋊C8×C127C2212yes—
23C2×#102×C127C2218yes—
24C2×C22⋊C8×C127C2212yes—
25C2×#97×C127C2212yes—
26C4×C4⋊C4×C127—21no—
27C4×C4⋊C4×C127—21no—
28C4×C4⋊C4×C127C2212yes—
29C4×C4⋊C4×C127C2212yes—
30C2×#95×C127—21no—
31#340×C127C2218yes—
32C2×#41×C127—28no—
33C2×#41×C127—48no—
34C22×Q8×C127—21no—
35C22×D4×C127—22no—
36C22×D4×C127—21no—
37C22×D4×C127—21no—
38C22×D4×C127C2312yes—
39C23×C4×C127—22no—
40C23×C4×C127—22no—
41C23×C4×C127D411yescharacteristic
42C23×C4×C127D411yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C22×C8×C127C2314yes—
45C4⋊Q8×C127—22no—
46C4⋊Q8×C127C2×C414yescomplemented
47#127×C127—22no—
48#127×C127C2×C414yescomplemented
49#124×C127—28no—
50#121×C127—28no—
51#121×C127—24no—
52#121×C127C2×C418yes—
53C4×D4×C127—28no—
54C4×D4×C127—24no—
55C4×D4×C127C2×C418yescomplemented
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—21no—
58C2×C4⋊C4×C127—28no—
59C2×C4⋊C4×C127C2312yes—
60C2×C4⋊C4×C127C2314yes—
61C2×C22⋊C4×C127—22no—
62C2×C22⋊C4×C127—22no—
63C2×C42×C127—22no—
64C2×C42×C127—22no—
65C2×C42×C127—44no—
66C2×C42×C127C2×C414yes—
67C2×C42×C127D411yescharacteristic
68C2×C42×C127D411yescharacteristic
69C2×C42×C127D414yes—
70C2×C42×C127C2311yescharacteristic
71C2×C42×C127C2311yescharacteristic
72C4⋊C8×C127—24no—
73#102×C127—216no—
74C22⋊C8×C127—24no—
75#97×C127—24no—
76#95×C127—22no—
77#95×C127—22no—
78C24×C127—22no—
79C24×C127C2×D411yescharacteristic
80#41×C127—432no—
81C2×Q8×C127—24no—
82C2×Q8×C127—44no—
83C2×D4×C127—28no—
84C2×D4×C127—24no—
85C2×D4×C127—24no—
86C2×D4×C127—22no—
87C2×D4×C127—28no—
88C2×D4×C127—44no—
89C2×D4×C127—48no—
90C2×D4×C127—42no—
91C2×D4×C127—42no—
92C2×D4×C127C22×C414yes—
93C22×C4×C127—24no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—24no—
97C22×C4×C127—28no—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
100C22×C4×C127—28no—
101C22×C4×C127—48no—
102C22×C4×C127—44no—
103C22×C4×C127—44no—
104C22×C4×C127C22⋊C414yes—
105C22×C4×C127C22⋊C414yes—
106C22×C4×C127C22×C412yes—
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127C2×D411yescharacteristic
111C22×C4×C127C2×D412yes—
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127C2411yescharacteristic
114C2×C8×C127—24no—
115C2×C8×C127—28no—
116C4⋊C4×C127—28no—
117C4⋊C4×C127—24no—
118C4⋊C4×C127—22no—
119C4⋊C4×C127—24no—
120C4⋊C4×C127C22×C414yes—
121C4⋊C4×C127#4118yescomplemented
122C22⋊C4×C127—28no—
123C22⋊C4×C127—28no—
124C42×C127—44no—
125C42×C127—44no—
126C42×C127C22⋊C414yes—
127C42×C127C22⋊C414yes—
128C42×C127C22×C412yes—
129C42×C127C22×C412yes—
130C42×C127C2×D412yes—
131C42×C127C2×D412yes—
132C23×C127—22no—
133C23×C127—21no—
134C23×C127—21no—
135C23×C127—24no—
136C23×C127—44no—
137C23×C127—44no—
138C23×C127—42no—
139C23×C127—42no—
140C23×C127C2×C22⋊C412yes—
141C23×C127AGL(1,ℤ/8)14yes—
142C23×C127C22×D411yescharacteristic
143Q8×C127—48no—
144D4×C127—28no—
145D4×C127—48no—
146D4×C127—416no—
147D4×C127—44no—
148D4×C127—48no—
149C2×C4×C127—22no—
150C2×C4×C127—21no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—21no—
154C2×C4×C127—28no—
155C2×C4×C127—24no—
156C2×C4×C127—24no—
157C2×C4×C127—28no—
158C2×C4×C127—24no—
159C2×C4×C127—28no—
160C2×C4×C127—416no—
161C2×C4×C127—416no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127C2×C22⋊C412yes—
166C2×C4×C127C2×C22⋊C412yes—
167C2×C4×C127C2×C22⋊C412yes—
168C2×C4×C127C2×C22⋊C412yes—
169C2×C4×C127C2×C22⋊C412yes—
170C2×C4×C127AGL(1,ℤ/8)12yes—
171C2×C4×C127#13712yes—
172C2×C4×C127C23×C411yescharacteristic
173C2×C4×C127C22×D411yescharacteristic
174C2×C4×C127C2×#4114yes—
175C8×C127—44no—
176C22×C127—24no—
177C22×C127—24no—
178C22×C127—22no—
179C22×C127—22no—
180C22×C127—44no—
181C22×C127—44no—
182C22×C127—44no—
183C22×C127—84no—
184C22×C127—84no—
185C22×C127#41814yes—
186C22×C127C22×C22⋊C411yescharacteristic
187C22×C127#52512yes—
188C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
189C22×C127C2×AGL(1,ℤ/8)12yes—
190C22×C127C2×#13711yescharacteristic
191C4×C127—22no—
192C4×C127—22no—
193C4×C127—22no—
194C4×C127—22no—
195C4×C127—48no—
196C4×C127—44no—
197C4×C127#41714yes—
198C4×C127C4×#4112yes—
199C4×C127#53212yes—
200#21395C12711yesmaximal, characteristic, direct product factor, Sylow
201C2×C127—24no—
202C2×C127—84no—
203C2×C127#229711yescharacteristic
204C2×C127C2×#41811yescharacteristic
205C2×C127C2×#41711yescharacteristic
206C2×C127#310912yes—
207C2×C127#311212yes—
208C2×#532C2×C12711yescharacteristic
209C2×#432C2×C12711yescharacteristic, complemented
210C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
211#1987C2×C12712yescomplemented
212#1982C2×C12712yescomplemented
213#1874C2×C12714yescomplemented
214#1762C2×C12714yescomplemented
215C127#2139511yescharacteristic, direct product factor, Sylow
216C22×#41—21no—
217#532—24no—
218#532C4×C12718yescomplemented
219C2×C4⋊Q8C22×C12711yescharacteristic
220C2×#127C22×C12711yescharacteristic
221C2×#124—21no—
222C2×#121—21no—
223C2×#121C22×C12712yes—
224C2×C4×D4—21no—
225C2×C4×D4C22×C12712yes—
226C22×C4⋊C4C22×C12712yes—
227C22×C42—21no—
228C22×C42C22×C12711yescharacteristic
229#432—24no—
230C2×C4⋊C8C22×C12712yes—
231C2×#102C22×C12718yes—
232C2×C22⋊C8C22×C12712yes—
233C2×#97C22×C12712yes—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4C22×C12712yes—
237C4×C4⋊C4C22×C12712yes—
238C2×#95—21no—
239#340C22×C12718yes—
240C2×#41—28no—
241C2×#41—48no—
242C22×Q8—21no—
243C22×D4—22no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4C23×C12712yes—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4D4×C12711yescharacteristic
250C23×C4D4×C12711yescharacteristic
251C23×C4C23×C12711yescharacteristic
252C22×C8C23×C12714yes—
253C4⋊Q8—22no—
254C4⋊Q8C2×C4×C12714yescomplemented
255#127—22no—
256#127C2×C4×C12714yescomplemented
257#124—28no—
258#121—28no—
259#121—24no—
260#121C2×C4×C12718yes—
261C4×D4—28no—
262C4×D4—24no—
263C4×D4C2×C4×C12718yescomplemented
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4C23×C12712yes—
268C2×C4⋊C4C23×C12714yes—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—44no—
274C2×C42C2×C4×C12714yes—
275C2×C42D4×C12711yescharacteristic
276C2×C42D4×C12711yescharacteristic
277C2×C42D4×C12714yes—
278C2×C42C23×C12711yescharacteristic
279C2×C42C23×C12711yescharacteristic
280C4⋊C8—24no—
281#102—216no—
282C22⋊C8—24no—
283#97—24no—
284#95—22no—
285#95—22no—
286C24—22no—
287C24C2×D4×C12711yescharacteristic
288#41—432no—
289C2×Q8—24no—
290C2×Q8—44no—
291C2×D4—28no—
292C2×D4—24no—
293C2×D4—24no—
294C2×D4—22no—
295C2×D4—28no—
296C2×D4—44no—
297C2×D4—48no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4C22×C4×C12714yes—
301C22×C4—24no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—28no—
306C22×C4—24no—
307C22×C4—22no—
308C22×C4—28no—
309C22×C4—48no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4C22⋊C4×C12714yes—
313C22×C4C22⋊C4×C12714yes—
314C22×C4C22×C4×C12712yes—
315C22×C4C2×D4×C12711yescharacteristic
316C22×C4C2×D4×C12711yescharacteristic
317C22×C4C2×D4×C12711yescharacteristic
318C22×C4C2×D4×C12711yescharacteristic
319C22×C4C2×D4×C12712yes—
320C22×C4C2×D4×C12711yescharacteristic
321C22×C4C24×C12711yescharacteristic
322C2×C8—24no—
323C2×C8—28no—
324C4⋊C4—28no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4C22×C4×C12714yes—
329C4⋊C4#41×C12718yescomplemented
330C22⋊C4—28no—
331C22⋊C4—28no—
332C42—44no—
333C42—44no—
334C42C22⋊C4×C12714yes—
335C42C22⋊C4×C12714yes—
336C42C22×C4×C12712yes—
337C42C22×C4×C12712yes—
338C42C2×D4×C12712yes—
339C42C2×D4×C12712yes—
340C23—22no—
341C23—21no—
342C23—21no—
343C23—24no—
344C23—44no—
345C23—44no—
346C23—42no—
347C23—42no—
348C23C2×C22⋊C4×C12712yes—
349C23AGL(1,ℤ/8)×C12714yes—
350C23C22×D4×C12711yescharacteristic
351Q8—48no—
352D4—28no—
353D4—48no—
354D4—416no—
355D4—44no—
356D4—48no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—28no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—28no—
366C2×C4—24no—
367C2×C4—28no—
368C2×C4—416no—
369C2×C4—416no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4C2×C22⋊C4×C12712yes—
374C2×C4C2×C22⋊C4×C12712yes—
375C2×C4C2×C22⋊C4×C12712yes—
376C2×C4C2×C22⋊C4×C12712yes—
377C2×C4C2×C22⋊C4×C12712yes—
378C2×C4AGL(1,ℤ/8)×C12712yes—
379C2×C4#137×C12712yes—
380C2×C4C23×C4×C12711yescharacteristic
381C2×C4C22×D4×C12711yescharacteristic
382C2×C4C2×#41×C12714yes—
383C8—44no—
384C22—24no—
385C22—24no—
386C22—22no—
387C22—22no—
388C22—44no—
389C22—44no—
390C22—44no—
391C22—84no—
392C22—84no—
393C22#418×C12714yes—
394C22C22×C22⋊C4×C12711yescharacteristic
395C22#525×C12712yes—
396C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
397C22C2×AGL(1,ℤ/8)×C12712yes—
398C22C2×#137×C12711yescharacteristic
399C4—22no—
400C4—22no—
401C4—22no—
402C4—22no—
403C4—48no—
404C4—44no—
405C4#417×C12714yes—
406C4C4×#41×C12712yes—
407C4#532×C12712yes—
408C2—24no—
409C2—84no—
410C2C127×#229711yescharacteristic
411C2C2×#418×C12711yescharacteristic
412C2C2×#417×C12711yescharacteristic
413C2C127×#310912yes—
414C2C127×#311212yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#532×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#432×C127C2semidirect
3. C2×C4×C4⋊C4×C127C2semidirect
4. C127×#1987C2semidirect
5. C127×#1982C2semidirect
6. C127×#1874C2semidirect
7. C127×#1762C2semidirect
10. #532×C127C4semidirect
46. C4⋊Q8×C127C2×C4semidirect
48. #127×C127C2×C4semidirect
55. C4×D4×C127C2×C4semidirect
121. C4⋊C4×C127#41semidirect
200. #21395C127direct (N × H)
209. C2×#432C2×C127semidirect
210. C2×C4×C4⋊C4C2×C127semidirect
211. #1987C2×C127semidirect
212. #1982C2×C127semidirect
213. #1874C2×C127semidirect
214. #1762C2×C127semidirect
215. C127#21395direct (N × H)
218. #532C4×C127semidirect
254. C4⋊Q8C2×C4×C127semidirect
256. #127C2×C4×C127semidirect
263. C4×D4C2×C4×C127semidirect
329. C4⋊C4#41×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1272
C2×#432×C1272
C2×C4×C4⋊C4×C1272
C127×#19872
C127×#19822
C127×#18742
C127×#17622
#21395127