Finite Group Databasebeta

← C127×#19082 #44582755

Subgroups — C127×#19082 #44582755

Order 32512.

864 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3553C211yesmaximal, characteristic, complemented
2C127×#3180C212yesmaximal, complemented
3C127×#3142C211yesmaximal, characteristic, complemented
4C127×#1664C212yesmaximal, complemented
5C127×#1663C211yesmaximal, characteristic, complemented
6C127×#1662C211yesmaximal, characteristic, complemented
7C127×#1658C211yesmaximal, characteristic, complemented
8C127×#1657C212yesmaximal, complemented
9C127×#1656C211yesmaximal, characteristic, complemented
10C127×#1524C212yesmaximal, complemented
11C2×#330×C127C211yesmaximal, characteristic, complemented
12#564×C127C2211yescharacteristic
13#563×C127C2212yes—
14#562×C127C2211yescharacteristic
15#554×C127—22no—
16#553×C127—22no—
17#552×C127—22no—
18#541×C127—22no—
19#539×C127—22no—
20#539×C127—22no—
21#532×C127C2211yescharacteristic
22#529×C127C2212yes—
23C2×#125×C127C2211yescharacteristic
24#501×C127C2212yes—
25#496×C127C2212yes—
26#491×C127C2211yescharacteristic
27#491×C127C2211yescharacteristic
28#490×C127C2211yescharacteristic
29#490×C127C2211yescharacteristic
30#490×C127C2212yes—
31#489×C127C2212yes—
32#488×C127—22no—
33#466×C127—22no—
34#465×C127—22no—
35#442×C127—22no—
36#440×C127—22no—
37#417×C127—22no—
38C4×M16×C127C2211yescharacteristic
39C2×#97×C127C2212yes—
40#330×C127C2211yescharacteristic
41#330×C127C2212yes—
42#330×C127C2212yes—
43#330×C127C2211yescharacteristic
44#330×C127C2212yes—
45#329×C127C2212yes—
46#329×C127C2212yes—
47C2×#41×C127—21no—
48C2×SD16×C127—22no—
49C2×D8×C127—22no—
50C2×M16×C127—21no—
51C22×C8×C127—22no—
52C4⋊Q8×C127—22no—
53C4⋊Q8×C127C2311yescharacteristic
54#127×C127C2311yescharacteristic
55#126×C127—22no—
56#126×C127—22no—
57#126×C127—22no—
58#126×C127—22no—
59#126×C127—22no—
60#125×C127—22no—
61#125×C127—22no—
62#125×C127—22no—
63#125×C127—22no—
64#125×C127—22no—
65#125×C127—22no—
66#125×C127D412yes—
67#125×C127C2312yes—
68#125×C127C2311yescharacteristic
69#125×C127C2311yescharacteristic
70#124×C127—21no—
71#124×C127C2312yes—
72#123×C127—22no—
73#123×C127—22no—
74#123×C127—22no—
75#123×C127—22no—
76#123×C127—22no—
77C22⋊Q8×C127—22no—
78C22⋊Q8×C127—22no—
79C22⋊Q8×C127—22no—
80C22⋊Q8×C127—22no—
81C22⋊Q8×C127—22no—
82C22⋊Q8×C127—22no—
83C22⋊Q8×C127D412yes—
84#121×C127—22no—
85#121×C127—22no—
86#121×C127—22no—
87#121×C127D412yes—
88C4×Q8×C127—22no—
89C4×Q8×C127D412yes—
90C4×D4×C127—22no—
91C4×D4×C127—22no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—22no—
95C4×D4×C127D412yes—
96#117×C127—22no—
97#117×C127—22no—
98C2×C4⋊C4×C127—22no—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127D412yes—
101C2×C42×C127C2311yescharacteristic
102#107×C127—22no—
103#106×C127—22no—
104#103×C127—22no—
105#103×C127—22no—
106#103×C127—22no—
107#102×C127—22no—
108#102×C127—22no—
109#102×C127—22no—
110#102×C127—22no—
111#102×C127—22no—
112#97×C127—22no—
113#97×C127C2312yes—
114#97×C127C2311yescharacteristic
115#97×C127C2311yescharacteristic
116#97×C127C2312yes—
117C4×C8×C127—21no—
118#41×C127—44no—
119C2×Q8×C127—22no—
120C2×Q8×C127—21no—
121C2×Q8×C127C2×D412yes—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—21no—
125C2×D4×C127—22no—
126C2×D4×C127—41no—
127C2×D4×C127C2×D412yes—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—41no—
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127C2×D412yes—
135SD16×C127—44no—
136D8×C127—44no—
137M16×C127—42no—
138C2×C8×C127—22no—
139C2×C8×C127—21no—
140C2×C8×C127—21no—
141C2×C8×C127—22no—
142C2×C8×C127—44no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127C2×D412yes—
160C4⋊C4×C127C2×D412yes—
161C4⋊C4×C127C2×D412yes—
162C4⋊C4×C127C2×D412yes—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—22no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—22no—
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—42no—
173C42×C127—22no—
174C42×C127—22no—
175C42×C127—22no—
176C42×C127C2×D411yescharacteristic
177C42×C127C2×D412yes—
178C42×C127C2411yescharacteristic
179C23×C127—22no—
180C23×C127—41no—
181C23×C127#12011yescharacteristic
182Q8×C127—42no—
183Q8×C127—42no—
184Q8×C127—82no—
185D4×C127—42no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—42no—
189D4×C127—44no—
190D4×C127—82no—
191D4×C127—82no—
192C2×C4×C127—22no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—42no—
199C2×C4×C127—41no—
200C2×C4×C127—82no—
201C2×C4×C127—82no—
202C2×C4×C127—82no—
203C2×C4×C127—82no—
204C2×C4×C127—82no—
205C2×C4×C127#12012yes—
206C2×C4×C127#12011yescharacteristic
207C2×C4×C127C22×D411yescharacteristic
208C2×C4×C127C22×D412yes—
209C8×C127—24no—
210C8×C127—42no—
211C8×C127—41no—
212C8×C127—41no—
213C22×C127—22no—
214C22×C127—42no—
215C22×C127—42no—
216C22×C127—42no—
217C22×C127—81no—
218C22×C127—82no—
219C22×C127#45412yes—
220C22×C127C2×#12011yescharacteristic
221C4×C127—21no—
222C4×C127—21no—
223C4×C127—22no—
224C4×C127—22no—
225C4×C127—42no—
226C4×C127—42no—
227C4×C127—42no—
228C4×C127—42no—
229C4×C127—42no—
230C4×C127—81no—
231#19082C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—22no—
233C2×C127—82no—
234C2×C127—161no—
235C2×C127C2×#45411yescharacteristic
236C2×C127#301812yes—
237#3553C2×C12711yescharacteristic, complemented
238#3180C2×C12712yescomplemented
239#3142C2×C12711yescharacteristic, complemented
240#1664C2×C12712yescomplemented
241#1663C2×C12711yescharacteristic, complemented
242#1662C2×C12711yescharacteristic, complemented
243#1658C2×C12711yescharacteristic, complemented
244#1657C2×C12712yescomplemented
245#1656C2×C12711yescharacteristic, complemented
246#1524C2×C12712yescomplemented
247C2×#330C2×C12711yescharacteristic, complemented
248C127#1908211yescharacteristic, direct product factor, Sylow
249#564C22×C12711yescharacteristic
250#563C22×C12712yes—
251#562C22×C12711yescharacteristic
252#554—22no—
253#553—22no—
254#552—22no—
255#541—22no—
256#539—22no—
257#539—22no—
258#532C22×C12711yescharacteristic
259#529C22×C12712yes—
260C2×#125C22×C12711yescharacteristic
261#501C22×C12712yes—
262#496C22×C12712yes—
263#491C22×C12711yescharacteristic
264#491C22×C12711yescharacteristic
265#490C22×C12711yescharacteristic
266#490C22×C12711yescharacteristic
267#490C22×C12712yes—
268#489C22×C12712yes—
269#488—22no—
270#466—22no—
271#465—22no—
272#442—22no—
273#440—22no—
274#417—22no—
275C4×M16C22×C12711yescharacteristic
276C2×#97C22×C12712yes—
277#330C22×C12711yescharacteristic
278#330C22×C12712yes—
279#330C22×C12712yes—
280#330C22×C12711yescharacteristic
281#330C22×C12712yes—
282#329C22×C12712yes—
283#329C22×C12712yes—
284C2×#41—21no—
285C2×SD16—22no—
286C2×D8—22no—
287C2×M16—21no—
288C22×C8—22no—
289C4⋊Q8—22no—
290C4⋊Q8C23×C12711yescharacteristic
291#127C23×C12711yescharacteristic
292#126—22no—
293#126—22no—
294#126—22no—
295#126—22no—
296#126—22no—
297#125—22no—
298#125—22no—
299#125—22no—
300#125—22no—
301#125—22no—
302#125—22no—
303#125D4×C12712yes—
304#125C23×C12711yescharacteristic
305#125C23×C12711yescharacteristic
306#125C23×C12712yes—
307#124—21no—
308#124C23×C12712yes—
309#123—22no—
310#123—22no—
311#123—22no—
312#123—22no—
313#123—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8D4×C12712yes—
321#121—22no—
322#121—22no—
323#121—22no—
324#121D4×C12712yes—
325C4×Q8—22no—
326C4×Q8D4×C12712yes—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4D4×C12712yes—
333#117—22no—
334#117—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4D4×C12712yes—
338C2×C42C23×C12711yescharacteristic
339#107—22no—
340#106—22no—
341#103—22no—
342#103—22no—
343#103—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—22no—
349#97—22no—
350#97C23×C12711yescharacteristic
351#97C23×C12711yescharacteristic
352#97C23×C12712yes—
353#97C23×C12712yes—
354C4×C8—21no—
355#41—44no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8C2×D4×C12712yes—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—41no—
364C2×D4C2×D4×C12712yes—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—41no—
370C22×C4C2×D4×C12711yescharacteristic
371C22×C4C2×D4×C12712yes—
372SD16—44no—
373D8—44no—
374M16—42no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—44no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4C2×D4×C12712yes—
397C4⋊C4C2×D4×C12712yes—
398C4⋊C4C2×D4×C12712yes—
399C4⋊C4C2×D4×C12712yes—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—42no—
410C42—22no—
411C42—22no—
412C42—22no—
413C42C2×D4×C12711yescharacteristic
414C42C2×D4×C12712yes—
415C42C24×C12711yescharacteristic
416C23—22no—
417C23—41no—
418C23#120×C12711yescharacteristic
419Q8—42no—
420Q8—42no—
421Q8—82no—
422D4—42no—
423D4—42no—
424D4—42no—
425D4—42no—
426D4—44no—
427D4—82no—
428D4—82no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4#120×C12712yes—
443C2×C4#120×C12711yescharacteristic
444C2×C4C22×D4×C12711yescharacteristic
445C2×C4C22×D4×C12712yes—
446C8—24no—
447C8—42no—
448C8—41no—
449C8—41no—
450C22—22no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—81no—
455C22—82no—
456C22#454×C12712yes—
457C22C2×#120×C12711yescharacteristic
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—81no—
468C2—22no—
469C2—82no—
470C2—161no—
471C2C2×#454×C12711yescharacteristic
472C2C127×#301812yes—
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
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
1. C127×#3553C2semidirect
2. C127×#3180C2semidirect
3. C127×#3142C2semidirect
4. C127×#1664C2semidirect
5. C127×#1663C2semidirect
6. C127×#1662C2semidirect
7. C127×#1658C2semidirect
8. C127×#1657C2semidirect
9. C127×#1656C2semidirect
10. C127×#1524C2semidirect
11. C2×#330×C127C2semidirect
231. #19082C127direct (N × H)
237. #3553C2×C127semidirect
238. #3180C2×C127semidirect
239. #3142C2×C127semidirect
240. #1664C2×C127semidirect
241. #1663C2×C127semidirect
242. #1662C2×C127semidirect
243. #1658C2×C127semidirect
244. #1657C2×C127semidirect
245. #1656C2×C127semidirect
246. #1524C2×C127semidirect
247. C2×#330C2×C127semidirect
248. C127#19082direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35532
C127×#31802
C127×#31422
C127×#16642
C127×#16632
C127×#16622
C127×#16582
C127×#16572
C127×#16562
C127×#15242
C2×#330×C1272
#19082127