Finite Group Databasebeta

← C127×#18325 #44581998

Subgroups — C127×#18325 #44581998

Order 32512.

1230 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C127C211yesmaximal, characteristic
2C127×#3193C212yesmaximal, complemented
3C127×#2583C211yesmaximal, characteristic, complemented
4C127×#1610C214yesmaximal, complemented
5C127×#1604C214yesmaximal, complemented
6C127×#1507C212yesmaximal, complemented
7C127×#1463C211yesmaximal, characteristic, complemented
8C22×#41×C127—21no—
9#537×C127—24no—
10#537×C127—22no—
11#537×C127C2214yes—
12C2×C22⋊Q8×C127—22no—
13C2×C22⋊Q8×C127C2211yescharacteristic
14C2×#121×C127—22no—
15C2×#121×C127—21no—
16C2×#121×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18#484×C127—22no—
19#480×C127C2214yescomplemented
20#468×C127—24no—
21#450×C127—22no—
22#448×C127C2214yescomplemented
23#407×C127C2212yes—
24#398×C127C2212yescomplemented
25#395×C127C2212yescomplemented
26#389×C127—22no—
27#385×C127—21no—
28#385×C127—21no—
29C4×C22⋊C4×C127C2211yescharacteristic
30#327×C127C2218yescomplemented
31#324×C127C2214yescomplemented
32C2×#41×C127—24no—
33C2×#41×C127—24no—
34C2×#41×C127—48no—
35C22×Q8×C127—21no—
36C22×Q8×C127C2311yescharacteristic
37C22×D4×C127—21no—
38C22×D4×C127—22no—
39C22×D4×C127—21no—
40C22×D4×C127D412yes—
41C23×C4×C127—22no—
42C23×C4×C127D411yescharacteristic
43C23×C4×C127D411yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C2×SD16×C127—24no—
46C2×M16×C127—22no—
47C22⋊Q8×C127—28no—
48C22⋊Q8×C127—28no—
49C22⋊Q8×C127—22no—
50C22⋊Q8×C127—22no—
51#121×C127—24no—
52#121×C127—28no—
53#121×C127—28no—
54#121×C127—24no—
55#121×C127—22no—
56#121×C127—22no—
57#121×C127D414yes—
58#121×C127C2314yes—
59C2×C4⋊C4×C127—21no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127D412yes—
66C2×C4⋊C4×C127D412yes—
67C2×C4⋊C4×C127C2311yescharacteristic
68C2×C4⋊C4×C127C2312yes—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—21no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—21no—
73C2×C42×C127—21no—
74#107×C127—24no—
75#103×C127—24no—
76#102×C127—24no—
77C22⋊C8×C127—22no—
78C22⋊C8×C127C2314yes—
79#95×C127—22no—
80#95×C127—22no—
81#95×C127C2312yes—
82C24×C127—22no—
83C24×C127C2×D411yescharacteristic
84#41×C127—416no—
85#41×C127—48no—
86#41×C127—48no—
87C2×Q8×C127—24no—
88C2×Q8×C127—22no—
89C2×Q8×C127—44no—
90C2×Q8×C127—81no—
91C2×D4×C127—24no—
92C2×D4×C127—24no—
93C2×D4×C127—24no—
94C2×D4×C127—24no—
95C2×D4×C127—22no—
96C2×D4×C127—44no—
97C2×D4×C127—48no—
98C2×D4×C127—82no—
99C2×D4×C127—82no—
100C2×D4×C127C2×D414yes—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—24no—
104C22×C4×C127—28no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—48no—
112C22×C4×C127—81no—
113C22×C4×C127—81no—
114C22×C4×C127C2×D412yes—
115C22×C4×C127C2×D412yes—
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D412yes—
118C22×C4×C127C2×D412yes—
119C22×C4×C127C2411yescharacteristic
120SD16×C127—84no—
121M16×C127—82no—
122C2×C8×C127—24no—
123C4⋊C4×C127—24no—
124C4⋊C4×C127—24no—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—24no—
127C4⋊C4×C127—22no—
128C4⋊C4×C127—42no—
129C4⋊C4×C127—44no—
130C4⋊C4×C127—82no—
131C4⋊C4×C127C2×D414yes—
132C22⋊C4×C127—24no—
133C22⋊C4×C127—28no—
134C22⋊C4×C127—24no—
135C22⋊C4×C127—24no—
136C22⋊C4×C127—41no—
137C22⋊C4×C127—41no—
138C42×C127—81no—
139C23×C127—22no—
140C23×C127—22no—
141C23×C127—24no—
142C23×C127—41no—
143C23×C127—44no—
144C23×C127—44no—
145C23×C127—44no—
146C23×C127#12011yescharacteristic
147C23×C127#12011yescharacteristic
148C23×C127C22×D411yescharacteristic
149Q8×C127—48no—
150Q8×C127—44no—
151D4×C127—44no—
152D4×C127—48no—
153D4×C127—48no—
154D4×C127—48no—
155D4×C127—82no—
156D4×C127—84no—
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—24no—
162C2×C4×C127—22no—
163C2×C4×C127—24no—
164C2×C4×C127—41no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—41no—
168C2×C4×C127—416no—
169C2×C4×C127—42no—
170C2×C4×C127—44no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—42no—
178C2×C4×C127—81no—
179C2×C4×C127#12012yes—
180C2×C4×C127AGL(1,ℤ/8)14yes—
181C2×C4×C127C22×D412yes—
182C8×C127—44no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—44no—
191C22×C127—44no—
192C22×C127—44no—
193C22×C127—44no—
194C22×C127—88no—
195C22×C127#45612yes—
196C22×C127C2×#12011yescharacteristic
197C22×C127C2×AGL(1,ℤ/8)12yes—
198C4×C127—24no—
199C4×C127—22no—
200C4×C127—22no—
201C4×C127—44no—
202C4×C127—44no—
203C4×C127—42no—
204C4×C127—81no—
205C4×C127—81no—
206#18325C12711yesmaximal, characteristic, direct product factor, Sylow
207C2×C127—22no—
208C2×C127—22no—
209C2×C127—41no—
210C2×C127—84no—
211C2×C127#300311yescharacteristic
212C2×C127C2×#45611yescharacteristic
213C2×C127#302611yescharacteristic
214C2×#537C2×C12711yescharacteristic
215#3193C2×C12712yescomplemented
216#2583C2×C12711yescharacteristic, complemented
217#1610C2×C12714yescomplemented
218#1604C2×C12714yescomplemented
219#1507C2×C12712yescomplemented
220#1463C2×C12711yescharacteristic, complemented
221C127#1832511yescharacteristic, direct product factor, Sylow
222C22×#41—21no—
223#537—24no—
224#537—22no—
225#537C22×C12714yes—
226C2×C22⋊Q8—22no—
227C2×C22⋊Q8C22×C12711yescharacteristic
228C2×#121—22no—
229C2×#121—21no—
230C2×#121C22×C12712yes—
231C22×C4⋊C4C22×C12711yescharacteristic
232#484—22no—
233#480C22×C12714yescomplemented
234#468—24no—
235#450—22no—
236#448C22×C12714yescomplemented
237#407C22×C12712yes—
238#398C22×C12712yescomplemented
239#395C22×C12712yescomplemented
240#389—22no—
241#385—21no—
242#385—21no—
243C4×C22⋊C4C22×C12711yescharacteristic
244#327C22×C12718yescomplemented
245#324C22×C12714yescomplemented
246C2×#41—24no—
247C2×#41—24no—
248C2×#41—48no—
249C22×Q8—21no—
250C22×Q8C23×C12711yescharacteristic
251C22×D4—21no—
252C22×D4—22no—
253C22×D4—21no—
254C22×D4D4×C12712yes—
255C23×C4—22no—
256C23×C4D4×C12711yescharacteristic
257C23×C4D4×C12711yescharacteristic
258C23×C4C23×C12711yescharacteristic
259C2×SD16—24no—
260C2×M16—22no—
261C22⋊Q8—28no—
262C22⋊Q8—28no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265#121—24no—
266#121—28no—
267#121—28no—
268#121—24no—
269#121—22no—
270#121—22no—
271#121D4×C12714yes—
272#121C23×C12714yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4D4×C12712yes—
280C2×C4⋊C4D4×C12712yes—
281C2×C4⋊C4C23×C12711yescharacteristic
282C2×C4⋊C4C23×C12712yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—21no—
287C2×C42—21no—
288#107—24no—
289#103—24no—
290#102—24no—
291C22⋊C8—22no—
292C22⋊C8C23×C12714yes—
293#95—22no—
294#95—22no—
295#95C23×C12712yes—
296C24—22no—
297C24C2×D4×C12711yescharacteristic
298#41—416no—
299#41—48no—
300#41—48no—
301C2×Q8—24no—
302C2×Q8—22no—
303C2×Q8—44no—
304C2×Q8—81no—
305C2×D4—24no—
306C2×D4—24no—
307C2×D4—24no—
308C2×D4—24no—
309C2×D4—22no—
310C2×D4—44no—
311C2×D4—48no—
312C2×D4—82no—
313C2×D4—82no—
314C2×D4C2×D4×C12714yes—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—28no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—48no—
326C22×C4—81no—
327C22×C4—81no—
328C22×C4C2×D4×C12712yes—
329C22×C4C2×D4×C12712yes—
330C22×C4C2×D4×C12711yescharacteristic
331C22×C4C2×D4×C12712yes—
332C22×C4C2×D4×C12712yes—
333C22×C4C24×C12711yescharacteristic
334SD16—84no—
335M16—82no—
336C2×C8—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—24no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—44no—
344C4⋊C4—82no—
345C4⋊C4C2×D4×C12714yes—
346C22⋊C4—24no—
347C22⋊C4—28no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—81no—
353C23—22no—
354C23—22no—
355C23—24no—
356C23—41no—
357C23—44no—
358C23—44no—
359C23—44no—
360C23#120×C12711yescharacteristic
361C23#120×C12711yescharacteristic
362C23C22×D4×C12711yescharacteristic
363Q8—48no—
364Q8—44no—
365D4—44no—
366D4—48no—
367D4—48no—
368D4—48no—
369D4—82no—
370D4—84no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—416no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4#120×C12712yes—
394C2×C4AGL(1,ℤ/8)×C12714yes—
395C2×C4C22×D4×C12712yes—
396C8—44no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—44no—
405C22—44no—
406C22—44no—
407C22—44no—
408C22—88no—
409C22#456×C12712yes—
410C22C2×#120×C12711yescharacteristic
411C22C2×AGL(1,ℤ/8)×C12712yes—
412C4—24no—
413C4—22no—
414C4—22no—
415C4—44no—
416C4—44no—
417C4—42no—
418C4—81no—
419C4—81no—
420C2—22no—
421C2—22no—
422C2—41no—
423C2—84no—
424C2C127×#300311yescharacteristic
425C2C2×#456×C12711yescharacteristic
426C2C127×#302611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC2×#537×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3193C2semidirect
3. C127×#2583C2semidirect
4. C127×#1610C2semidirect
5. C127×#1604C2semidirect
6. C127×#1507C2semidirect
7. C127×#1463C2semidirect
19. #480×C127C22semidirect
22. #448×C127C22semidirect
24. #398×C127C22semidirect
25. #395×C127C22semidirect
30. #327×C127C22semidirect
31. #324×C127C22semidirect
206. #18325C127direct (N × H)
215. #3193C2×C127semidirect
216. #2583C2×C127semidirect
217. #1610C2×C127semidirect
218. #1604C2×C127semidirect
219. #1507C2×C127semidirect
220. #1463C2×C127semidirect
221. C127#18325direct (N × H)
233. #480C22×C127semidirect
236. #448C22×C127semidirect
238. #398C22×C127semidirect
239. #395C22×C127semidirect
244. #327C22×C127semidirect
245. #324C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1272
C127×#31932
C127×#25832
C127×#16102
C127×#16042
C127×#15072
C127×#14632
#18325127