Finite Group Databasebeta

← C127×#19432 #44583105

Subgroups — C127×#19432 #44583105

Order 32512.

666 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3208C211yesmaximal, characteristic
2C127×#3078C211yesmaximal, characteristic, complemented
3C2×#460×C127C211yesmaximal, characteristic
4C127×#2983C211yesmaximal, characteristic, complemented
5C127×#1698C214yesmaximal, complemented
6C127×#1686C214yesmaximal, complemented
7C127×#1571C211yesmaximal, characteristic, complemented
8C127×#1545C211yesmaximal, characteristic
9C127×#1542C211yesmaximal, characteristic, complemented
10C22×SD16×C127—21no—
11#533×C127C2211yescharacteristic
12C2×#127×C127C2211yescharacteristic
13C2×C4×Q8×C127C2211yescharacteristic
14#492×C127C2212yes—
15#486×C127C2212yes—
16#479×C127—22no—
17#477×C127C2212yescomplemented
18#475×C127C2212yescomplemented
19#460×C127—22no—
20#460×C127—22no—
21#460×C127C2214yes—
22#450×C127—22no—
23#446×C127—22no—
24#446×C127C2214yescomplemented
25#432×C127—22no—
26#431×C127C2211yescharacteristic
27#431×C127C2211yescharacteristic
28#428×C127—21no—
29#423×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31#419×C127—21no—
32C2×#102×C127—21no—
33#335×C127C2214yescomplemented
34#333×C127C2212yescomplemented
35#332×C127C2212yescomplemented
36#331×C127C2214yes—
37C22×Q8×C127D411yescharacteristic
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127—21no—
41C2×SD16×C127—24no—
42C2×SD16×C127—24no—
43C2×SD16×C127—44no—
44C2×M16×C127—21no—
45C22×C8×C127—21no—
46C4⋊Q8×C127C2311yescharacteristic
47C4⋊Q8×C127C2311yescharacteristic
48#127×C127—21no—
49#127×C127—21no—
50#127×C127—21no—
51#127×C127C2312yes—
52#125×C127—21no—
53C22⋊Q8×C127—21no—
54C22⋊Q8×C127—21no—
55C4×Q8×C127—21no—
56C4×Q8×C127—21no—
57C4×Q8×C127—21no—
58C4×Q8×C127—21no—
59C4×Q8×C127D412yes—
60C4×Q8×C127C2312yes—
61#117×C127—21no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127D411yescharacteristic
64C2×C42×C127—21no—
65C2×C42×C127C2311yescharacteristic
66#107×C127—22no—
67#106×C127—22no—
68C4⋊C8×C127—24no—
69C4⋊C8×C127—21no—
70C4⋊C8×C127—21no—
71C4⋊C8×C127D412yes—
72C4⋊C8×C127C2312yes—
73C4⋊C8×C127C2312yes—
74C4⋊C8×C127C2312yes—
75#103×C127—22no—
76#103×C127—22no—
77#102×C127—24no—
78#102×C127—24no—
79C22⋊C8×C127—21no—
80C22⋊C8×C127D412yes—
81#97×C127—24no—
82C4×C8×C127—21no—
83C4×C8×C127C2312yes—
84C24×C127—41no—
85C2×Q8×C127—21no—
86C2×Q8×C127—22no—
87C2×Q8×C127—22no—
88C2×Q8×C127—21no—
89C2×Q8×C127—21no—
90C2×Q8×C127C2×D412yes—
91C2×D4×C127—22no—
92C2×D4×C127—22no—
93C2×D4×C127—22no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C2×D4×C127—42no—
98C2×D4×C127—42no—
99C2×D4×C127—82no—
100C2×D4×C127—82no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127C2×D411yescharacteristic
104C22×C4×C127C2×D411yescharacteristic
105C22×C4×C127#4111yescharacteristic
106SD16×C127—48no—
107SD16×C127—84no—
108M16×C127—42no—
109C2×C8×C127—22no—
110C2×C8×C127—22no—
111C2×C8×C127—22no—
112C2×C8×C127—42no—
113C2×C8×C127C2×D414yes—
114C4⋊C4×C127—22no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—22no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—41no—
122C4⋊C4×C127—41no—
123C4⋊C4×C127C2×D412yes—
124C22⋊C4×C127—41no—
125C42×C127—22no—
126C42×C127—22no—
127C42×C127—41no—
128C42×C127C2×D411yescharacteristic
129C42×C127C2×D411yescharacteristic
130C42×C127#4111yescharacteristic
131C42×C127C2411yescharacteristic
132C23×C127—42no—
133C23×C127—82no—
134C23×C127—82no—
135C23×C127—82no—
136C23×C127#12111yescharacteristic
137Q8×C127—22no—
138Q8×C127—22no—
139Q8×C127—42no—
140Q8×C127—42no—
141Q8×C127—81no—
142D4×C127—42no—
143D4×C127—42no—
144D4×C127—44no—
145D4×C127—82no—
146D4×C127—82no—
147D4×C127—82no—
148D4×C127—82no—
149C2×C4×C127—22no—
150C2×C4×C127—22no—
151C2×C4×C127—22no—
152C2×C4×C127—41no—
153C2×C4×C127—42no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—81no—
157C2×C4×C127#12111yescharacteristic
158C2×C4×C127#12111yescharacteristic
159C2×C4×C127#12111yescharacteristic
160C2×C4×C127AGL(1,ℤ/8)12yes—
161C2×C4×C127#13712yes—
162C2×C4×C127C22×D411yescharacteristic
163C2×C4×C127C22×D411yescharacteristic
164C2×C4×C127C2×#4111yescharacteristic
165C8×C127—24no—
166C8×C127—42no—
167C8×C127—42no—
168C8×C127—42no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—82no—
172C22×C127—82no—
173C22×C127—82no—
174C22×C127—164no—
175C22×C127#46812yes—
176C22×C127C2×#12111yescharacteristic
177C4×C127—21no—
178C4×C127—21no—
179C4×C127—21no—
180C4×C127—42no—
181C4×C127—42no—
182C4×C127—81no—
183C4×C127—81no—
184C4×C127#46812yes—
185C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
186C4×C127C2×#13711yescharacteristic
187C4×C127#57712yes—
188#19432C12711yesmaximal, characteristic, direct product factor, Sylow
189C2×C127—22no—
190C2×C127—162no—
191C2×C127#304311yescharacteristic
192C2×C127C2×#46811yescharacteristic
193C2×C127#306811yescharacteristic
194#3208C2×C12711yescharacteristic
195#3078C2×C12711yescharacteristic, complemented
196C2×#460C2×C12711yescharacteristic
197#2983C2×C12711yescharacteristic, complemented
198#1698C2×C12714yescomplemented
199#1686C2×C12714yescomplemented
200#1571C2×C12711yescharacteristic, complemented
201#1545C2×C12711yescharacteristic
202#1542C2×C12711yescharacteristic, complemented
203C127#1943211yescharacteristic, direct product factor, Sylow
204C22×SD16—21no—
205#533C22×C12711yescharacteristic
206C2×#127C22×C12711yescharacteristic
207C2×C4×Q8C22×C12711yescharacteristic
208#492C22×C12712yes—
209#486C22×C12712yes—
210#479—22no—
211#477C22×C12712yescomplemented
212#475C22×C12712yescomplemented
213#460—22no—
214#460—22no—
215#460C22×C12714yes—
216#450—22no—
217#446—22no—
218#446C22×C12714yescomplemented
219#432—22no—
220#431C22×C12711yescharacteristic
221#431C22×C12711yescharacteristic
222#428—21no—
223#423C22×C12711yescharacteristic
224C2×C4⋊C8C22×C12711yescharacteristic
225#419—21no—
226C2×#102—21no—
227#335C22×C12714yescomplemented
228#333C22×C12712yescomplemented
229#332C22×C12712yescomplemented
230#331C22×C12714yes—
231C22×Q8D4×C12711yescharacteristic
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—21no—
235C2×SD16—24no—
236C2×SD16—24no—
237C2×SD16—44no—
238C2×M16—21no—
239C22×C8—21no—
240C4⋊Q8C23×C12711yescharacteristic
241C4⋊Q8C23×C12711yescharacteristic
242#127—21no—
243#127—21no—
244#127—21no—
245#127C23×C12712yes—
246#125—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8D4×C12712yes—
254C4×Q8C23×C12712yes—
255#117—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C12711yescharacteristic
258C2×C42—21no—
259C2×C42C23×C12711yescharacteristic
260#107—22no—
261#106—22no—
262C4⋊C8—24no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C12712yes—
266C4⋊C8C23×C12712yes—
267C4⋊C8C23×C12712yes—
268C4⋊C8C23×C12712yes—
269#103—22no—
270#103—22no—
271#102—24no—
272#102—24no—
273C22⋊C8—21no—
274C22⋊C8D4×C12712yes—
275#97—24no—
276C4×C8—21no—
277C4×C8C23×C12712yes—
278C24—41no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—22no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8C2×D4×C12712yes—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—82no—
294C2×D4—82no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4C2×D4×C12711yescharacteristic
298C22×C4C2×D4×C12711yescharacteristic
299C22×C4#41×C12711yescharacteristic
300SD16—48no—
301SD16—84no—
302M16—42no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8C2×D4×C12714yes—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4C2×D4×C12712yes—
318C22⋊C4—41no—
319C42—22no—
320C42—22no—
321C42—41no—
322C42C2×D4×C12711yescharacteristic
323C42C2×D4×C12711yescharacteristic
324C42#41×C12711yescharacteristic
325C42C24×C12711yescharacteristic
326C23—42no—
327C23—82no—
328C23—82no—
329C23—82no—
330C23#121×C12711yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336D4—42no—
337D4—42no—
338D4—44no—
339D4—82no—
340D4—82no—
341D4—82no—
342D4—82no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4#121×C12711yescharacteristic
352C2×C4#121×C12711yescharacteristic
353C2×C4#121×C12711yescharacteristic
354C2×C4AGL(1,ℤ/8)×C12712yes—
355C2×C4#137×C12712yes—
356C2×C4C22×D4×C12711yescharacteristic
357C2×C4C22×D4×C12711yescharacteristic
358C2×C4C2×#41×C12711yescharacteristic
359C8—24no—
360C8—42no—
361C8—42no—
362C8—42no—
363C22—21no—
364C22—21no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—164no—
369C22#468×C12712yes—
370C22C2×#121×C12711yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4#468×C12712yes—
379C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
380C4C2×#137×C12711yescharacteristic
381C4#577×C12712yes—
382C2—22no—
383C2—162no—
384C2C127×#304311yescharacteristic
385C2C2×#468×C12711yescharacteristic
386C2C127×#306811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#127×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3078C2semidirect
4. C127×#2983C2semidirect
5. C127×#1698C2semidirect
6. C127×#1686C2semidirect
7. C127×#1571C2semidirect
9. C127×#1542C2semidirect
17. #477×C127C22semidirect
18. #475×C127C22semidirect
24. #446×C127C22semidirect
33. #335×C127C22semidirect
34. #333×C127C22semidirect
35. #332×C127C22semidirect
188. #19432C127direct (N × H)
195. #3078C2×C127semidirect
197. #2983C2×C127semidirect
198. #1698C2×C127semidirect
199. #1686C2×C127semidirect
200. #1571C2×C127semidirect
202. #1542C2×C127semidirect
203. C127#19432direct (N × H)
211. #477C22×C127semidirect
212. #475C22×C127semidirect
218. #446C22×C127semidirect
227. #335C22×C127semidirect
228. #333C22×C127semidirect
229. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32082
C127×#30782
C2×#460×C1272
C127×#29832
C127×#16982
C127×#16862
C127×#15712
C127×#15452
C127×#15422
#19432127