Finite Group Databasebeta

← C127×#18603 #44582276

Subgroups — C127×#18603 #44582276

Order 32512.

866 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3507C211yesmaximal, characteristic
2C127×#3237C211yesmaximal, characteristic, complemented
3C127×#3182C211yesmaximal, characteristic
4C127×#3104C211yesmaximal, characteristic, complemented
5C127×#1648C212yesmaximal, complemented
6C127×#1640C212yesmaximal, complemented
7C127×#1636C212yesmaximal, complemented
8C127×#1630C212yesmaximal, complemented
9C127×#1553C211yesmaximal, characteristic
10C127×#1491C211yesmaximal, characteristic, complemented
11C127×#1485C211yesmaximal, characteristic, complemented
12#559×C127C2212yes—
13#557×C127C2212yes—
14#556×C127—21no—
15#556×C127—22no—
16#554×C127—21no—
17#552×C127—22no—
18#539×C127—22no—
19#536×C127—21no—
20#533×C127C2211yescharacteristic
21#533×C127C2211yescharacteristic
22#532×C127C2211yescharacteristic
23#529×C127—22no—
24#520×C127—21no—
25C2×C4×Q8×C127C2211yescharacteristic
26#501×C127—21no—
27#500×C127C2211yescharacteristic
28#492×C127C2211yescharacteristic
29#491×C127—21no—
30#487×C127C2211yescharacteristic
31#486×C127C2211yescharacteristic
32#485×C127—22no—
33#484×C127—21no—
34#477×C127C2212yes—
35#477×C127C2212yes—
36#475×C127C2212yes—
37#468×C127—22no—
38#462×C127C2212yes—
39#451×C127—21no—
40#440×C127—22no—
41C4×Q16×C127—22no—
42#432×C127C2211yescharacteristic
43#431×C127C2211yescharacteristic
44C4×M16×C127C2211yescharacteristic
45#332×C127C2212yes—
46#331×C127C2212yes—
47Q8⋊C8×C127C2212yes—
48Q8⋊C8×C127C2212yes—
49Q8⋊C8×C127C2212yes—
50Q8⋊C8×C127C2212yes—
51C2×#41×C127—21no—
52C22×Q8×C127D411yescharacteristic
53C2×Q16×C127—22no—
54C2×SD16×C127—22no—
55C2×M16×C127—21no—
56C4⋊Q8×C127—22no—
57C4⋊Q8×C127D411yescharacteristic
58C4⋊Q8×C127D411yescharacteristic
59C4⋊Q8×C127C2311yescharacteristic
60C4⋊Q8×C127C2311yescharacteristic
61C4⋊Q8×C127C2311yescharacteristic
62#127×C127C2311yescharacteristic
63#126×C127—24no—
64#126×C127—24no—
65#125×C127—22no—
66#125×C127—24no—
67#125×C127—21no—
68#125×C127—21no—
69#124×C127—22no—
70#124×C127—22no—
71#124×C127—21no—
72#123×C127—24no—
73#123×C127—24no—
74C22⋊Q8×C127—22no—
75C22⋊Q8×C127—22no—
76C22⋊Q8×C127—24no—
77C22⋊Q8×C127—21no—
78C22⋊Q8×C127—21no—
79C22⋊Q8×C127—21no—
80C22⋊Q8×C127D412yes—
81#121×C127—21no—
82#121×C127D412yes—
83C4×Q8×C127—22no—
84C4×Q8×C127—22no—
85C4×Q8×C127—21no—
86C4×Q8×C127—21no—
87C4×Q8×C127—21no—
88C4×Q8×C127—21no—
89C4×Q8×C127—21no—
90C4×Q8×C127D412yes—
91C4×Q8×C127C2312yes—
92C4×Q8×C127C2312yes—
93C4×D4×C127—24no—
94C4×D4×C127—22no—
95C4×D4×C127—22no—
96C4×D4×C127—21no—
97C4×D4×C127D412yes—
98#117×C127—22no—
99#117×C127—24no—
100#117×C127—21no—
101#117×C127—21no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—21no—
104C2×C4⋊C4×C127D411yescharacteristic
105C2×C42×C127—21no—
106C2×C42×C127C2311yescharacteristic
107#107×C127—22no—
108#107×C127—22no—
109#107×C127—22no—
110#106×C127—22no—
111C4⋊C8×C127C2312yes—
112C4⋊C8×C127C2312yes—
113#103×C127—22no—
114#103×C127—22no—
115#103×C127—22no—
116#103×C127—22no—
117#103×C127—22no—
118#102×C127—22no—
119C22⋊C8×C127—21no—
120C22⋊C8×C127—21no—
121#97×C127—21no—
122#97×C127—21no—
123C4×C8×C127—21no—
124C4×C8×C127C2311yescharacteristic
125C4×C8×C127C2311yescharacteristic
126#41×C127—44no—
127C2×Q8×C127—21no—
128C2×Q8×C127—21no—
129C2×Q8×C127—21no—
130C2×Q8×C127—21no—
131C2×Q8×C127—21no—
132C2×Q8×C127—42no—
133C2×Q8×C127C2×D412yes—
134C2×Q8×C127C2×D412yes—
135C2×D4×C127—22no—
136C2×D4×C127—21no—
137C2×D4×C127—21no—
138C2×D4×C127C2×D412yes—
139C22×C4×C127—21no—
140C22×C4×C127—24no—
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145C22×C4×C127C2×D411yescharacteristic
146Q16×C127—44no—
147SD16×C127—44no—
148M16×C127—42no—
149C2×C8×C127—21no—
150C2×C8×C127—22no—
151C2×C8×C127—21no—
152C2×C8×C127—22no—
153C4⋊C4×C127—24no—
154C4⋊C4×C127—24no—
155C4⋊C4×C127—24no—
156C4⋊C4×C127—21no—
157C4⋊C4×C127—21no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127—21no—
160C4⋊C4×C127—22no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—21no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—21no—
166C4⋊C4×C127—21no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—21no—
169C4⋊C4×C127—41no—
170C4⋊C4×C127—41no—
171C4⋊C4×C127C2×D412yes—
172C4⋊C4×C127C2×D412yes—
173C4⋊C4×C127C2×D412yes—
174C22⋊C4×C127—24no—
175C22⋊C4×C127—24no—
176C22⋊C4×C127—24no—
177C22⋊C4×C127—22no—
178C22⋊C4×C127—22no—
179C22⋊C4×C127—22no—
180C22⋊C4×C127—41no—
181C42×C127—24no—
182C42×C127—22no—
183C42×C127—22no—
184C42×C127—22no—
185C42×C127—41no—
186C42×C127C2×D411yescharacteristic
187C42×C127C2×D411yescharacteristic
188C42×C127C2×D411yescharacteristic
189C42×C127C2411yescharacteristic
190C23×C127—22no—
191C23×C127#12011yescharacteristic
192Q8×C127—22no—
193Q8×C127—22no—
194Q8×C127—24no—
195Q8×C127—42no—
196Q8×C127—42no—
197Q8×C127—42no—
198Q8×C127—42no—
199Q8×C127—81no—
200D4×C127—42no—
201D4×C127—44no—
202D4×C127—42no—
203D4×C127—42no—
204C2×C4×C127—22no—
205C2×C4×C127—22no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—22no—
210C2×C4×C127—22no—
211C2×C4×C127—41no—
212C2×C4×C127—44no—
213C2×C4×C127—42no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—81no—
217C2×C4×C127—84no—
218C2×C4×C127#12011yescharacteristic
219C2×C4×C127#12011yescharacteristic
220C2×C4×C127#12011yescharacteristic
221C2×C4×C127C22×D411yescharacteristic
222C2×C4×C127C22×D411yescharacteristic
223C2×C4×C127C22×D411yescharacteristic
224C8×C127—22no—
225C8×C127—41no—
226C8×C127—42no—
227C8×C127—42no—
228C22×C127—21no—
229C22×C127—21no—
230C22×C127—21no—
231C22×C127—42no—
232C22×C127—42no—
233C22×C127—42no—
234C22×C127C2×#12011yescharacteristic
235C4×C127—21no—
236C4×C127—21no—
237C4×C127—21no—
238C4×C127—21no—
239C4×C127—42no—
240C4×C127—42no—
241C4×C127—42no—
242C4×C127—42no—
243C4×C127—42no—
244C4×C127—81no—
245C4×C127—81no—
246C4×C127#57512yes—
247C4×C127#57812yes—
248#18603C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—41no—
250C2×C127—82no—
251C2×C127#300511yescharacteristic
252C2×C127#301111yescharacteristic
253C2×C127#301811yescharacteristic
254#3507C2×C12711yescharacteristic
255#3237C2×C12711yescharacteristic, complemented
256#3182C2×C12711yescharacteristic
257#3104C2×C12711yescharacteristic, complemented
258#1648C2×C12712yescomplemented
259#1640C2×C12712yescomplemented
260#1636C2×C12712yescomplemented
261#1630C2×C12712yescomplemented
262#1553C2×C12711yescharacteristic
263#1491C2×C12711yescharacteristic, complemented
264#1485C2×C12711yescharacteristic, complemented
265C127#1860311yescharacteristic, direct product factor, Sylow
266#559C22×C12712yes—
267#557C22×C12712yes—
268#556—21no—
269#556—22no—
270#554—21no—
271#552—22no—
272#539—22no—
273#536—21no—
274#533C22×C12711yescharacteristic
275#533C22×C12711yescharacteristic
276#532C22×C12711yescharacteristic
277#529—22no—
278#520—21no—
279C2×C4×Q8C22×C12711yescharacteristic
280#501—21no—
281#500C22×C12711yescharacteristic
282#492C22×C12711yescharacteristic
283#491—21no—
284#487C22×C12711yescharacteristic
285#486C22×C12711yescharacteristic
286#485—22no—
287#484—21no—
288#477C22×C12712yes—
289#477C22×C12712yes—
290#475C22×C12712yes—
291#468—22no—
292#462C22×C12712yes—
293#451—21no—
294#440—22no—
295C4×Q16—22no—
296#432C22×C12711yescharacteristic
297#431C22×C12711yescharacteristic
298C4×M16C22×C12711yescharacteristic
299#332C22×C12712yes—
300#331C22×C12712yes—
301Q8⋊C8C22×C12712yes—
302Q8⋊C8C22×C12712yes—
303Q8⋊C8C22×C12712yes—
304Q8⋊C8C22×C12712yes—
305C2×#41—21no—
306C22×Q8D4×C12711yescharacteristic
307C2×Q16—22no—
308C2×SD16—22no—
309C2×M16—21no—
310C4⋊Q8—22no—
311C4⋊Q8D4×C12711yescharacteristic
312C4⋊Q8D4×C12711yescharacteristic
313C4⋊Q8C23×C12711yescharacteristic
314C4⋊Q8C23×C12711yescharacteristic
315C4⋊Q8C23×C12711yescharacteristic
316#127C23×C12711yescharacteristic
317#126—24no—
318#126—24no—
319#125—22no—
320#125—24no—
321#125—21no—
322#125—21no—
323#124—22no—
324#124—22no—
325#124—21no—
326#123—24no—
327#123—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8D4×C12712yes—
335#121—21no—
336#121D4×C12712yes—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8D4×C12712yes—
345C4×Q8C23×C12712yes—
346C4×Q8C23×C12712yes—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—21no—
351C4×D4D4×C12712yes—
352#117—22no—
353#117—24no—
354#117—21no—
355#117—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4D4×C12711yescharacteristic
359C2×C42—21no—
360C2×C42C23×C12711yescharacteristic
361#107—22no—
362#107—22no—
363#107—22no—
364#106—22no—
365C4⋊C8C23×C12712yes—
366C4⋊C8C23×C12712yes—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#102—22no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375#97—21no—
376#97—21no—
377C4×C8—21no—
378C4×C8C23×C12711yescharacteristic
379C4×C8C23×C12711yescharacteristic
380#41—44no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8C2×D4×C12712yes—
388C2×Q8C2×D4×C12712yes—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×D4×C12712yes—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4C2×D4×C12711yescharacteristic
398C22×C4C2×D4×C12711yescharacteristic
399C22×C4C2×D4×C12711yescharacteristic
400Q16—44no—
401SD16—44no—
402M16—42no—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—21no—
406C2×C8—22no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4C2×D4×C12712yes—
426C4⋊C4C2×D4×C12712yes—
427C4⋊C4C2×D4×C12712yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C42—24no—
436C42—22no—
437C42—22no—
438C42—22no—
439C42—41no—
440C42C2×D4×C12711yescharacteristic
441C42C2×D4×C12711yescharacteristic
442C42C2×D4×C12711yescharacteristic
443C42C24×C12711yescharacteristic
444C23—22no—
445C23#120×C12711yescharacteristic
446Q8—22no—
447Q8—22no—
448Q8—24no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—81no—
454D4—42no—
455D4—44no—
456D4—42no—
457D4—42no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—84no—
472C2×C4#120×C12711yescharacteristic
473C2×C4#120×C12711yescharacteristic
474C2×C4#120×C12711yescharacteristic
475C2×C4C22×D4×C12711yescharacteristic
476C2×C4C22×D4×C12711yescharacteristic
477C2×C4C22×D4×C12711yescharacteristic
478C8—22no—
479C8—41no—
480C8—42no—
481C8—42no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22C2×#120×C12711yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—81no—
499C4—81no—
500C4#575×C12712yes—
501C4#578×C12712yes—
502C2—41no—
503C2—82no—
504C2C127×#300511yescharacteristic
505C2C127×#301111yescharacteristic
506C2C127×#301811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radical#532×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×#3237C2semidirect
4. C127×#3104C2semidirect
5. C127×#1648C2semidirect
6. C127×#1640C2semidirect
7. C127×#1636C2semidirect
8. C127×#1630C2semidirect
10. C127×#1491C2semidirect
11. C127×#1485C2semidirect
248. #18603C127direct (N × H)
255. #3237C2×C127semidirect
257. #3104C2×C127semidirect
258. #1648C2×C127semidirect
259. #1640C2×C127semidirect
260. #1636C2×C127semidirect
261. #1630C2×C127semidirect
263. #1491C2×C127semidirect
264. #1485C2×C127semidirect
265. C127#18603direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35072
C127×#32372
C127×#31822
C127×#31042
C127×#16482
C127×#16402
C127×#16362
C127×#16302
C127×#15532
C127×#14912
C127×#14852
#18603127