Finite Group Databasebeta

← C2×C127×#1936 #44584758

Subgroups — C2×C127×#1936 #44584758

Order 32512.

1422 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#102×C127C211yesmaximal, characteristic
2C22×#102×C127C211yesmaximal, characteristic
3C22×#97×C127C211yesmaximal, characteristic, complemented
4C2×#390×C127C211yesmaximal, characteristic
5C2×#389×C127C211yesmaximal, characteristic, complemented
6C127×#1936C218yesmaximal, direct product factor
7C2×#340×C127C211yesmaximal, characteristic, complemented
8C2×#340×C127C211yesmaximal, characteristic, complemented
9C23×D4×C127C2211yescharacteristic
10C23×C8×C127C2211yescharacteristic
11C23×C8×C127C2211yescharacteristic
12C22×C4⋊C4×C127—21no—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127—21no—
17C22×C22⋊C4×C127—21no—
18C22×C42×C127C2211yescharacteristic
19C2×#102×C127—24no—
20C2×#102×C127C418yescomplemented
21C2×#102×C127C2214yes—
22C2×#102×C127C2214yes—
23C2×#97×C127—24no—
24C2×#97×C127C2214yescomplemented
25#390×C127—22no—
26#390×C127C2214yes—
27#389×C127—22no—
28#389×C127C2214yescomplemented
29C2×#95×C127—21no—
30#340×C127C2214yescomplemented
31#340×C127C2214yescomplemented
32C25×C127—21no—
33C22×D4×C127—22no—
34C22×D4×C127—21no—
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127C2×C414yes—
40C22×D4×C127C2312yes—
41C23×C4×C127—21no—
42C23×C4×C127—21no—
43C23×C4×C127—21no—
44C23×C4×C127D411yescharacteristic
45C23×C4×C127D411yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C22×C8×C127—22no—
48C22×C8×C127—22no—
49C22×C8×C127—22no—
50C22×C8×C127—22no—
51C22×C8×C127C2×C414yes—
52C22×C8×C127D414yes—
53C22×C8×C127C2312yes—
54C22×C8×C127C2312yes—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—44no—
65C2×C4⋊C4×C127C2×C414yes—
66C2×C4⋊C4×C127C2312yes—
67C2×C4⋊C4×C127C2312yes—
68C2×C4⋊C4×C127C2312yes—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127—24no—
71C2×C22⋊C4×C127—44no—
72C2×C22⋊C4×C127—44no—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127D412yes—
76C2×C42×C127C2312yes—
77#102×C127—28no—
78#102×C127C2×C4116yescomplemented
79#97×C127—28no—
80#95×C127—24no—
81C24×C127—24no—
82C24×C127—22no—
83C24×C127—42no—
84C24×C127—42no—
85C24×C127—42no—
86C24×C127—42no—
87C24×C127—42no—
88C24×C127—42no—
89C24×C127C2×D411yescharacteristic
90C2×D4×C127—28no—
91C2×D4×C127—28no—
92C2×D4×C127—24no—
93C2×D4×C127—22no—
94C2×D4×C127—22no—
95C2×D4×C127—22no—
96C2×D4×C127—22no—
97C2×D4×C127—22no—
98C2×D4×C127—42no—
99C2×D4×C127—44no—
100C2×D4×C127—42no—
101C2×D4×C127—44no—
102C2×D4×C127C22×C414yes—
103C22×C4×C127—24no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—42no—
114C22×C4×C127—42no—
115C22×C4×C127—42no—
116C22×C4×C127—42no—
117C22×C4×C127—42no—
118C22×C4×C127—42no—
119C22×C4×C127—42no—
120C22×C4×C127—42no—
121C22×C4×C127C22×C412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D412yes—
126C22×C4×C127#4112yes—
127C22×C4×C127#4112yes—
128C22×C4×C127#4112yes—
129C22×C4×C127#4112yes—
130C22×C4×C127C2411yescharacteristic
131C2×C8×C127—28no—
132C2×C8×C127—28no—
133C2×C8×C127—22no—
134C2×C8×C127—22no—
135C2×C8×C127—22no—
136C2×C8×C127—22no—
137C2×C8×C127C22×C414yes—
138C2×C8×C127C2×D414yes—
139C4⋊C4×C127—24no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—48no—
146C4⋊C4×C127—42no—
147C4⋊C4×C127—42no—
148C4⋊C4×C127C22×C414yes—
149C22⋊C4×C127—48no—
150C22⋊C4×C127—48no—
151C42×C127—24no—
152C42×C127—22no—
153C42×C127—22no—
154C23×C127—24no—
155C23×C127—42no—
156C23×C127—42no—
157C23×C127—42no—
158C23×C127—42no—
159C23×C127—42no—
160C23×C127—42no—
161C23×C127—48no—
162C23×C127—48no—
163C23×C127—48no—
164C23×C127—84no—
165C23×C127—84no—
166C23×C127—84no—
167C23×C127—84no—
168C23×C127C4×D412yes—
169C23×C127#12112yes—
170C23×C127#12412yes—
171C23×C127AGL(1,ℤ/8)12yes—
172C23×C127AGL(1,ℤ/8)12yes—
173C23×C127AGL(1,ℤ/8)12yes—
174C23×C127#13712yes—
175C23×C127C22×D411yescharacteristic
176D4×C127—24no—
177D4×C127—24no—
178D4×C127—42no—
179D4×C127—42no—
180D4×C127—48no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—48no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—84no—
200C2×C4×C127—84no—
201C2×C4×C127#11714yes—
202C2×C4×C127C4×D414yes—
203C2×C4×C127C4×D412yes—
204C2×C4×C127#12112yes—
205C2×C4×C127#12314yes—
206C2×C4×C127#12412yes—
207C2×C4×C127#12614yes—
208C2×C4×C127C23×C411yescharacteristic
209C2×C4×C127C22×D411yescharacteristic
210C2×C4×C127C2×#4111yescharacteristic
211C2×C4×C127C2×#4111yescharacteristic
212C2×C4×C127C2×#4111yescharacteristic
213C2×C4×C127C2×#4111yescharacteristic
214C8×C127—24no—
215C8×C127—24no—
216C22×C127—44no—
217C22×C127—44no—
218C22×C127—44no—
219C22×C127—82no—
220C22×C127—82no—
221C22×C127—816no—
222C22×C127—82no—
223C22×C127—82no—
224C22×C127#38814yes—
225C22×C127#44014yes—
226C22×C127#44214yes—
227C22×C127#46814yes—
228C22×C127#46914yes—
229C22×C127#48914yes—
230C22×C127#49014yes—
231C22×C127C2×C4×D411yescharacteristic
232C22×C127C2×#12111yescharacteristic
233C22×C127C2×#12411yescharacteristic
234C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
236C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
237C22×C127C2×#13711yescharacteristic
238C4×C127—44no—
239C4×C127—42no—
240C4×C127—42no—
241C4×C127—82no—
242C4×C127—82no—
243C4×C127#38814yes—
244C4×C127C2×#11711yescharacteristic
245C4×C127C2×C4×D411yescharacteristic
246C4×C127C2×#12311yescharacteristic
247C4×C127C2×#12611yescharacteristic
248C2×#1936C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—84no—
250C2×C127#193618yesdirect product factor
251C2×C127C2×#38811yescharacteristic
252C2×C127C2×#44011yescharacteristic
253C2×C127C2×#44211yescharacteristic
254C2×C127C2×#46811yescharacteristic
255C2×C127C2×#46911yescharacteristic
256C2×C127C2×#48911yescharacteristic
257C2×C127C2×#49011yescharacteristic
258C22×#102C2×C12711yescharacteristic
259C22×#102C2×C12711yescharacteristic
260C22×#97C2×C12711yescharacteristic, complemented
261C2×#390C2×C12711yescharacteristic
262C2×#389C2×C12711yescharacteristic, complemented
263#1936C2×C12718yesdirect product factor
264C2×#340C2×C12711yescharacteristic, complemented
265C2×#340C2×C12711yescharacteristic, complemented
266C127C2×#193611yescharacteristic, direct product factor, Sylow
267C23×D4C22×C12711yescharacteristic
268C23×C8C22×C12711yescharacteristic
269C23×C8C22×C12711yescharacteristic
270C22×C4⋊C4—21no—
271C22×C4⋊C4C22×C12711yescharacteristic
272C22×C4⋊C4C22×C12711yescharacteristic
273C22×C4⋊C4C22×C12711yescharacteristic
274C22×C22⋊C4—21no—
275C22×C22⋊C4—21no—
276C22×C42C22×C12711yescharacteristic
277C2×#102—24no—
278C2×#102C4×C12718yescomplemented
279C2×#102C22×C12714yes—
280C2×#102C22×C12714yes—
281C2×#97—24no—
282C2×#97C22×C12714yescomplemented
283#390—22no—
284#390C22×C12714yes—
285#389—22no—
286#389C22×C12714yescomplemented
287C2×#95—21no—
288#340C22×C12714yescomplemented
289#340C22×C12714yescomplemented
290C25—21no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4C2×C4×C12714yes—
298C22×D4C23×C12712yes—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4D4×C12711yescharacteristic
303C23×C4D4×C12711yescharacteristic
304C23×C4C23×C12711yescharacteristic
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8C2×C4×C12714yes—
310C22×C8D4×C12714yes—
311C22×C8C23×C12712yes—
312C22×C8C23×C12712yes—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4C2×C4×C12714yes—
324C2×C4⋊C4C23×C12712yes—
325C2×C4⋊C4C23×C12712yes—
326C2×C4⋊C4C23×C12712yes—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42D4×C12712yes—
334C2×C42C23×C12712yes—
335#102—28no—
336#102C2×C4×C127116yescomplemented
337#97—28no—
338#95—24no—
339C24—24no—
340C24—22no—
341C24—42no—
342C24—42no—
343C24—42no—
344C24—42no—
345C24—42no—
346C24—42no—
347C24C2×D4×C12711yescharacteristic
348C2×D4—28no—
349C2×D4—28no—
350C2×D4—24no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—42no—
357C2×D4—44no—
358C2×D4—42no—
359C2×D4—44no—
360C2×D4C22×C4×C12714yes—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4C22×C4×C12712yes—
380C22×C4C2×D4×C12712yes—
381C22×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12711yescharacteristic
383C22×C4C2×D4×C12712yes—
384C22×C4#41×C12712yes—
385C22×C4#41×C12712yes—
386C22×C4#41×C12712yes—
387C22×C4#41×C12712yes—
388C22×C4C24×C12711yescharacteristic
389C2×C8—28no—
390C2×C8—28no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8C22×C4×C12714yes—
396C2×C8C2×D4×C12714yes—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—48no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4C22×C4×C12714yes—
407C22⋊C4—48no—
408C22⋊C4—48no—
409C42—24no—
410C42—22no—
411C42—22no—
412C23—24no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—48no—
420C23—48no—
421C23—48no—
422C23—84no—
423C23—84no—
424C23—84no—
425C23—84no—
426C23C4×D4×C12712yes—
427C23#121×C12712yes—
428C23#124×C12712yes—
429C23AGL(1,ℤ/8)×C12712yes—
430C23AGL(1,ℤ/8)×C12712yes—
431C23AGL(1,ℤ/8)×C12712yes—
432C23#137×C12712yes—
433C23C22×D4×C12711yescharacteristic
434D4—24no—
435D4—24no—
436D4—42no—
437D4—42no—
438D4—48no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—48no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—84no—
458C2×C4—84no—
459C2×C4#117×C12714yes—
460C2×C4C4×D4×C12714yes—
461C2×C4C4×D4×C12712yes—
462C2×C4#121×C12712yes—
463C2×C4#123×C12714yes—
464C2×C4#124×C12712yes—
465C2×C4#126×C12714yes—
466C2×C4C23×C4×C12711yescharacteristic
467C2×C4C22×D4×C12711yescharacteristic
468C2×C4C2×#41×C12711yescharacteristic
469C2×C4C2×#41×C12711yescharacteristic
470C2×C4C2×#41×C12711yescharacteristic
471C2×C4C2×#41×C12711yescharacteristic
472C8—24no—
473C8—24no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—82no—
478C22—82no—
479C22—816no—
480C22—82no—
481C22—82no—
482C22#388×C12714yes—
483C22#440×C12714yes—
484C22#442×C12714yes—
485C22#468×C12714yes—
486C22#469×C12714yes—
487C22#489×C12714yes—
488C22#490×C12714yes—
489C22C2×C4×D4×C12711yescharacteristic
490C22C2×#121×C12711yescharacteristic
491C22C2×#124×C12711yescharacteristic
492C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
493C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
494C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
495C22C2×#137×C12711yescharacteristic
496C4—44no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4—82no—
501C4#388×C12714yes—
502C4C2×#117×C12711yescharacteristic
503C4C2×C4×D4×C12711yescharacteristic
504C4C2×#123×C12711yescharacteristic
505C4C2×#126×C12711yescharacteristic
506C2—84no—
507C2C127×#193618yesdirect product factor
508C2C2×#388×C12711yescharacteristic
509C2C2×#440×C12711yescharacteristic
510C2C2×#442×C12711yescharacteristic
511C2C2×#468×C12711yescharacteristic
512C2C2×#469×C12711yescharacteristic
513C2C2×#489×C12711yescharacteristic
514C2C2×#490×C12711yescharacteristic
subgroupG/H
center, socleC24×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×#97×C127C2semidirect
5. C2×#389×C127C2semidirect
6. C127×#1936C2direct (N × H)
7. C2×#340×C127C2semidirect
8. C2×#340×C127C2semidirect
20. C2×#102×C127C4semidirect
24. C2×#97×C127C22semidirect
28. #389×C127C22semidirect
30. #340×C127C22semidirect
31. #340×C127C22semidirect
78. #102×C127C2×C4semidirect
248. C2×#1936C127direct (N × H)
250. C2×C127#1936direct (N × H)
260. C22×#97C2×C127semidirect
262. C2×#389C2×C127semidirect
263. #1936C2×C127direct (N × H)
264. C2×#340C2×C127semidirect
265. C2×#340C2×C127semidirect
266. C127C2×#1936direct (N × H)
278. C2×#102C4×C127semidirect
282. C2×#97C22×C127semidirect
286. #389C22×C127semidirect
288. #340C22×C127semidirect
289. #340C22×C127semidirect
336. #102C2×C4×C127semidirect
507. C2C127×#1936direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#102×C1272
C22×#97×C1272
C2×#390×C1272
C2×#389×C1272
C127×#19362
C2×#340×C1272
C2×#1936127