Finite Group Databasebeta

← C127×#8441 #44572114

Subgroups — C127×#8441 #44572114

Order 32512.

864 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3483C211yesmaximal, characteristic
2C127×#1962C211yesmaximal, characteristic, complemented
3C4×#104×C127C212yesmaximal, complemented
4C127×#1525C211yesmaximal, characteristic, complemented
5C127×#1489C212yesmaximal, complemented
6Q82×C127C411yescharacteristic, complemented
7#555×C127—22no—
8#555×C127—22no—
9#555×C127C411yescharacteristic, complemented
10#550×C127—22no—
11#550×C127C412yescomplemented
12#532×C127—22no—
13#532×C127—22no—
14#532×C127C2211yescharacteristic
15C4×#41×C127—22no—
16C4×#41×C127C2212yes—
17#423×C127C2211yescharacteristic
18C2×#104×C127—22no—
19C2×#104×C127—22no—
20C4×M16×C127C2212yes—
21C43×C127C2211yescharacteristic
22#339×C127—22no—
23#329×C127—22no—
24Q8⋊C8×C127—22no—
25D4⋊C8×C127—22no—
26C2×#41×C127—22no—
27C2×#41×C127—22no—
28C2×#41×C127D412yes—
29C2×#41×C127D412yes—
30C2×M16×C127—22no—
31C2×M16×C127—21no—
32C4⋊Q8×C127—22no—
33C4⋊Q8×C127—22no—
34C4⋊Q8×C127C2×C411yescharacteristic
35#127×C127—22no—
36#127×C127—22no—
37#127×C127C2×C411yescharacteristic
38#124×C127—22no—
39#124×C127—24no—
40#124×C127—22no—
41#124×C127D412yes—
42#121×C127—24no—
43#121×C127—24no—
44#121×C127—22no—
45#121×C127—24no—
46#121×C127—22no—
47#121×C127—22no—
48C4×Q8×C127—22no—
49C4×Q8×C127C2×C412yes—
50C4×Q8×C127D412yes—
51C4×D4×C127—24no—
52C4×D4×C127—24no—
53C4×D4×C127—22no—
54C4×D4×C127—22no—
55C4×D4×C127—22no—
56C4×D4×C127—22no—
57C4×D4×C127C2×C412yes—
58C4×D4×C127D412yes—
59#117×C127—24no—
60#117×C127—22no—
61#117×C127—22no—
62#117×C127D412yes—
63C2×C42×C127—22no—
64C2×C42×C127—22no—
65C2×C42×C127—22no—
66C2×C42×C127—21no—
67C2×C42×C127C2311yescharacteristic
68C4⋊C8×C127—22no—
69#104×C127—28no—
70#104×C127—44no—
71#97×C127—22no—
72C4×C8×C127—22no—
73#41×C127—24no—
74#41×C127—42no—
75#41×C127—42no—
76#41×C127—42no—
77#41×C127—44no—
78#41×C127—44no—
79#41×C127—82no—
80#41×C127—82no—
81C2×Q8×C127—22no—
82C2×Q8×C127C22⋊C412yes—
83C2×Q8×C127C22⋊C412yes—
84C2×D4×C127—24no—
85C2×D4×C127—22no—
86C2×D4×C127—22no—
87C2×D4×C127—24no—
88C2×D4×C127—22no—
89C2×D4×C127—22no—
90C2×D4×C127C22⋊C412yes—
91C2×D4×C127C22⋊C412yes—
92C22×C4×C127—24no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—41no—
98C22×C4×C127C2×D412yes—
99C22×C4×C127C2×D411yescharacteristic
100M16×C127—24no—
101M16×C127—42no—
102M16×C127—42no—
103C2×C8×C127—42no—
104C2×C8×C127—41no—
105C4⋊C4×C127—24no—
106C4⋊C4×C127—22no—
107C4⋊C4×C127—22no—
108C4⋊C4×C127—22no—
109C4⋊C4×C127C22⋊C412yes—
110C4⋊C4×C127C22⋊C412yes—
111C22⋊C4×C127—24no—
112C22⋊C4×C127—24no—
113C22⋊C4×C127—22no—
114C22⋊C4×C127—22no—
115C22⋊C4×C127—24no—
116C22⋊C4×C127—22no—
117C42×C127—22no—
118C42×C127—22no—
119C42×C127—22no—
120C42×C127—22no—
121C42×C127—22no—
122C42×C127—24no—
123C42×C127—22no—
124C42×C127—42no—
125C42×C127—41no—
126C42×C127C22×C411yescharacteristic
127C42×C127C2×D411yescharacteristic
128C42×C127C2×D412yes—
129C23×C127—22no—
130C23×C127—22no—
131C23×C127#12011yescharacteristic
132Q8×C127—22no—
133Q8×C127—42no—
134Q8×C127—82no—
135Q8×C127#10414yescomplemented
136D4×C127—22no—
137D4×C127—22no—
138D4×C127—44no—
139D4×C127—42no—
140D4×C127—48no—
141D4×C127—42no—
142D4×C127—42no—
143D4×C127—82no—
144D4×C127—82no—
145D4×C127—84no—
146C2×C4×C127—22no—
147C2×C4×C127—22no—
148C2×C4×C127—22no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—22no—
154C2×C4×C127—44no—
155C2×C4×C127—48no—
156C2×C4×C127—42no—
157C2×C4×C127—44no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—42no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127C2×C22⋊C411yescharacteristic
165C2×C4×C127C2×C22⋊C412yes—
166C2×C4×C127#12012yes—
167C2×C4×C127#12011yescharacteristic
168C8×C127—44no—
169C8×C127—81no—
170C22×C127—21no—
171C22×C127—22no—
172C22×C127—42no—
173C22×C127—42no—
174C22×C127—42no—
175C22×C127—44no—
176C22×C127—42no—
177C22×C127#37911yescharacteristic
178C4×C127—21no—
179C4×C127—22no—
180C4×C127—24no—
181C4×C127—44no—
182C4×C127—42no—
183C4×C127—42no—
184C4×C127—42no—
185C4×C127C2×#10412yes—
186C4×C127#42112yes—
187C4×C127#45311yescharacteristic
188C4×C127#45511yescharacteristic
189#8441C12711yesmaximal, characteristic, direct product factor, Sylow
190C2×C127—41no—
191C2×C127—82no—
192C2×C127—82no—
193C2×C127#178912yes—
194C2×C127#179211yescharacteristic
195#3483C2×C12711yescharacteristic
196#1962C2×C12711yescharacteristic, complemented
197C4×#104C2×C12712yescomplemented
198#1525C2×C12711yescharacteristic, complemented
199#1489C2×C12712yescomplemented
200C127#844111yescharacteristic, direct product factor, Sylow
201Q82C4×C12711yescharacteristic, complemented
202#555—22no—
203#555—22no—
204#555C4×C12711yescharacteristic, complemented
205#550—22no—
206#550C4×C12712yescomplemented
207#532—22no—
208#532—22no—
209#532C22×C12711yescharacteristic
210C4×#41—22no—
211C4×#41C22×C12712yes—
212#423C22×C12711yescharacteristic
213C2×#104—22no—
214C2×#104—22no—
215C4×M16C22×C12712yes—
216C43C22×C12711yescharacteristic
217#339—22no—
218#329—22no—
219Q8⋊C8—22no—
220D4⋊C8—22no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41D4×C12712yes—
224C2×#41D4×C12712yes—
225C2×M16—22no—
226C2×M16—21no—
227C4⋊Q8—22no—
228C4⋊Q8—22no—
229C4⋊Q8C2×C4×C12711yescharacteristic
230#127—22no—
231#127—22no—
232#127C2×C4×C12711yescharacteristic
233#124—22no—
234#124—24no—
235#124—22no—
236#124D4×C12712yes—
237#121—24no—
238#121—24no—
239#121—22no—
240#121—24no—
241#121—22no—
242#121—22no—
243C4×Q8—22no—
244C4×Q8C2×C4×C12712yes—
245C4×Q8D4×C12712yes—
246C4×D4—24no—
247C4×D4—24no—
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4C2×C4×C12712yes—
253C4×D4D4×C12712yes—
254#117—24no—
255#117—22no—
256#117—22no—
257#117D4×C12712yes—
258C2×C42—22no—
259C2×C42—22no—
260C2×C42—22no—
261C2×C42—21no—
262C2×C42C23×C12711yescharacteristic
263C4⋊C8—22no—
264#104—28no—
265#104—44no—
266#97—22no—
267C4×C8—22no—
268#41—24no—
269#41—42no—
270#41—42no—
271#41—42no—
272#41—44no—
273#41—44no—
274#41—82no—
275#41—82no—
276C2×Q8—22no—
277C2×Q8C22⋊C4×C12712yes—
278C2×Q8C22⋊C4×C12712yes—
279C2×D4—24no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4C22⋊C4×C12712yes—
286C2×D4C22⋊C4×C12712yes—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4C2×D4×C12712yes—
294C22×C4C2×D4×C12711yescharacteristic
295M16—24no—
296M16—42no—
297M16—42no—
298C2×C8—42no—
299C2×C8—41no—
300C4⋊C4—24no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4C22⋊C4×C12712yes—
305C4⋊C4C22⋊C4×C12712yes—
306C22⋊C4—24no—
307C22⋊C4—24no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—24no—
311C22⋊C4—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—24no—
318C42—22no—
319C42—42no—
320C42—41no—
321C42C22×C4×C12711yescharacteristic
322C42C2×D4×C12712yes—
323C42C2×D4×C12711yescharacteristic
324C23—22no—
325C23—22no—
326C23#120×C12711yescharacteristic
327Q8—22no—
328Q8—42no—
329Q8—82no—
330Q8#104×C12714yescomplemented
331D4—22no—
332D4—22no—
333D4—44no—
334D4—42no—
335D4—48no—
336D4—42no—
337D4—42no—
338D4—82no—
339D4—82no—
340D4—84no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—44no—
350C2×C4—48no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4C2×C22⋊C4×C12711yescharacteristic
360C2×C4C2×C22⋊C4×C12712yes—
361C2×C4#120×C12712yes—
362C2×C4#120×C12711yescharacteristic
363C8—44no—
364C8—81no—
365C22—22no—
366C22—21no—
367C22—42no—
368C22—44no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22#379×C12711yescharacteristic
373C4—22no—
374C4—24no—
375C4—21no—
376C4—44no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4C2×#104×C12712yes—
381C4#421×C12712yes—
382C4#453×C12711yescharacteristic
383C4#455×C12711yescharacteristic
384C2—41no—
385C2—82no—
386C2—82no—
387C2C127×#178912yes—
388C2C127×#179211yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#379
prime radicalC127×#3483C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1962C2semidirect
3. C4×#104×C127C2semidirect
4. C127×#1525C2semidirect
5. C127×#1489C2semidirect
6. Q82×C127C4semidirect
9. #555×C127C4semidirect
11. #550×C127C4semidirect
135. Q8×C127#104semidirect
189. #8441C127direct (N × H)
196. #1962C2×C127semidirect
197. C4×#104C2×C127semidirect
198. #1525C2×C127semidirect
199. #1489C2×C127semidirect
200. C127#8441direct (N × H)
201. Q82C4×C127semidirect
204. #555C4×C127semidirect
206. #550C4×C127semidirect
330. Q8#104×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34832
C127×#19622
C4×#104×C1272
C127×#15252
C127×#14892
#8441127