Finite Group Databasebeta

← C2×C127×#1914 #44584688

Subgroups — C2×C127×#1914 #44584688

Order 32512.

1862 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C127C211yesmaximal, characteristic, complemented
2C2×#535×C127C211yesmaximal, characteristic
3C2×#413×C127C211yesmaximal, characteristic, complemented
4C22×#100×C127C212yesmaximal, complemented
5C127×#1914C218yesmaximal, direct product factor
6C2×#344×C127C212yesmaximal, complemented
7C22×#41×C127C2211yescharacteristic
8C23×D4×C127C2211yescharacteristic
9#568×C127—22no—
10#568×C127—24no—
11#568×C127C2214yescomplemented
12C2×#131×C127—24no—
13C22×M16×C127—22no—
14C22×M16×C127C2212yes—
15C22×M16×C127C2212yes—
16#535×C127—22no—
17#535×C127—22no—
18#535×C127C414yes—
19#535×C127C2214yes—
20C2×#127×C127—21no—
21C2×#124×C127—21no—
22C2×#121×C127—22no—
23C2×#120×C127C414yes—
24C2×#117×C127C2211yescharacteristic
25#413×C127—22no—
26#413×C127C2214yescomplemented
27C2×#101×C127—21no—
28C2×#100×C127—21no—
29C2×#100×C127—24no—
30C2×#100×C127—24no—
31C2×#100×C127C2218yescomplemented
32#344×C127C2218yescomplemented
33C25×C127C2×C412yes—
34C2×#41×C127—22no—
35C2×#41×C127—22no—
36C2×#41×C127—22no—
37C2×#41×C127—22no—
38C2×#41×C127C2×C412yes—
39C2×#41×C127D412yes—
40C2×#41×C127D412yes—
41C2×#41×C127C2312yes—
42C22×Q8×C127D411yescharacteristic
43C22×D4×C127—24no—
44C22×D4×C127—21no—
45C22×D4×C127—21no—
46C22×D4×C127—21no—
47C22×D4×C127—21no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127—22no—
51C22×D4×C127—22no—
52C22×D4×C127C2×C412yes—
53C22×D4×C127C2×C412yes—
54C22×D4×C127D411yescharacteristic
55C22×D4×C127C2312yes—
56C23×C4×C127D412yes—
57C23×C4×C127C2311yescharacteristic
58#131×C127—216no—
59#131×C127—216no—
60C2×M16×C127—24no—
61C2×M16×C127—28no—
62C2×M16×C127—22no—
63C2×M16×C127—28no—
64C2×M16×C127—22no—
65C2×M16×C127—22no—
66C2×M16×C127—22no—
67C2×M16×C127—22no—
68C2×M16×C127—22no—
69C2×M16×C127—22no—
70C2×M16×C127—22no—
71C2×M16×C127D414yescomplemented
72C2×M16×C127D414yescomplemented
73C2×M16×C127C2314yes—
74C2×M16×C127C2314yes—
75C22×C8×C127—24no—
76C22×C8×C127—22no—
77C22×C8×C127—22no—
78#127×C127—24no—
79#127×C127—24no—
80#124×C127—24no—
81#124×C127—24no—
82#121×C127—28no—
83#121×C127—28no—
84#120×C127—28no—
85#120×C127C2×C4116yes—
86#117×C127—21no—
87#117×C127—21no—
88#117×C127C2×C412yes—
89#117×C127C2312yes—
90C2×C4⋊C4×C127—21no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127C2×C412yes—
93C2×C42×C127—21no—
94#101×C127—24no—
95#100×C127—24no—
96#100×C127—216no—
97C24×C127—22no—
98C24×C127—22no—
99C24×C127—24no—
100C24×C127—24no—
101C24×C127—84no—
102C24×C127C22⋊C412yes—
103C24×C127C22×C414yes—
104C24×C127C22×C411yescharacteristic
105#41×C127—24no—
106#41×C127—24no—
107#41×C127—24no—
108#41×C127—24no—
109#41×C127—24no—
110#41×C127—24no—
111#41×C127—24no—
112#41×C127—24no—
113C2×Q8×C127—22no—
114C2×Q8×C127—22no—
115C2×Q8×C127C22⋊C412yes—
116C2×Q8×C127C2×D412yes—
117C2×D4×C127—24no—
118C2×D4×C127—24no—
119C2×D4×C127—216no—
120C2×D4×C127—22no—
121C2×D4×C127—22no—
122C2×D4×C127—24no—
123C2×D4×C127—24no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—24no—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—24no—
130C2×D4×C127—42no—
131C2×D4×C127—41no—
132C2×D4×C127—41no—
133C2×D4×C127—42no—
134C2×D4×C127—42no—
135C2×D4×C127—42no—
136C2×D4×C127—42no—
137C2×D4×C127—41no—
138C2×D4×C127—42no—
139C2×D4×C127—41no—
140C2×D4×C127—88no—
141C2×D4×C127C22⋊C414yes—
142C2×D4×C127C22⋊C412yes—
143C2×D4×C127C22×C414yes—
144C2×D4×C127C2×D412yes—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127C22⋊C412yes—
151C22×C4×C127C22⋊C414yes—
152C22×C4×C127C22×C411yescharacteristic
153C22×C4×C127C2×D414yes—
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D412yes—
160C22×C4×C127#4112yes—
161C22×C4×C127#4112yes—
162C22×C4×C127C2411yescharacteristic
163M16×C127—216no—
164M16×C127—24no—
165M16×C127—24no—
166M16×C127—24no—
167M16×C127—24no—
168M16×C127—24no—
169M16×C127—42no—
170M16×C127—42no—
171M16×C127C2×D418yescomplemented
172C2×C8×C127—216no—
173C2×C8×C127—24no—
174C2×C8×C127—24no—
175C2×C8×C127—24no—
176C2×C8×C127—24no—
177C2×C8×C127—42no—
178C2×C8×C127—42no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127—22no—
181C22⋊C4×C127—22no—
182C22⋊C4×C127—216no—
183C22⋊C4×C127C22×C414yes—
184C42×C127—22no—
185C42×C127—22no—
186C23×C127—22no—
187C23×C127—22no—
188C23×C127—24no—
189C23×C127—28no—
190C23×C127—42no—
191C23×C127—44no—
192C23×C127—48no—
193C23×C127—42no—
194C23×C127—44no—
195C23×C127—42no—
196C23×C127—88no—
197C23×C127—84no—
198C23×C127—84no—
199C23×C127—88no—
200C23×C127C2×C22⋊C411yescharacteristic
201C23×C127C2×C22⋊C414yes—
202C23×C127C2×C22⋊C411yescharacteristic
203C23×C127C4×D412yes—
204C23×C127C4×D412yes—
205C23×C127C23×C411yescharacteristic
206Q8×C127—24no—
207Q8×C127—24no—
208D4×C127—28no—
209D4×C127—28no—
210D4×C127—24no—
211D4×C127—24no—
212D4×C127—42no—
213D4×C127—44no—
214D4×C127—42no—
215D4×C127—42no—
216D4×C127—42no—
217D4×C127—44no—
218D4×C127—816no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—24no—
222C2×C4×C127—24no—
223C2×C4×C127—24no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—44no—
227C2×C4×C127C2×C22⋊C414yes—
228C2×C4×C127C2×C22⋊C411yescharacteristic
229C2×C4×C127C2×C22⋊C411yescharacteristic
230C2×C4×C127C4×D412yes—
231C2×C4×C127C4×D412yes—
232C2×C4×C127#12012yes—
233C2×C4×C127#12011yescharacteristic
234C2×C4×C127#12011yescharacteristic
235C2×C4×C127#12112yes—
236C2×C4×C127#12112yes—
237C2×C4×C127#12112yes—
238C2×C4×C127#12112yes—
239C2×C4×C127#12311yescharacteristic
240C2×C4×C127#12312yes—
241C2×C4×C127#12311yescharacteristic
242C2×C4×C127C22×D412yes—
243C2×C4×C127C22×D411yescharacteristic
244C2×C4×C127C22×D411yescharacteristic
245C2×C4×C127C2×#4112yes—
246C8×C127—28no—
247C8×C127—44no—
248C22×C127—22no—
249C22×C127—24no—
250C22×C127—24no—
251C22×C127—41no—
252C22×C127—42no—
253C22×C127—41no—
254C22×C127—44no—
255C22×C127—48no—
256C22×C127—44no—
257C22×C127—44no—
258C22×C127—82no—
259C22×C127—88no—
260C22×C127—84no—
261C22×C127—88no—
262C22×C127—84no—
263C22×C127#38611yescharacteristic
264C22×C127#38612yes—
265C22×C127#38611yescharacteristic
266C22×C127C22×C22⋊C411yescharacteristic
267C22×C127C2×C4×D412yes—
268C4×C127—24no—
269C4×C127—44no—
270C4×C127#38611yescharacteristic
271C4×C127#38611yescharacteristic
272C4×C127#38612yes—
273C4×C127C2×#12011yescharacteristic
274C4×C127C2×#12112yes—
275C4×C127C2×#12311yescharacteristic
276C2×#1914C12711yesmaximal, characteristic, direct product factor, Sylow
277C2×C127—21no—
278C2×C127—21no—
279C2×C127—22no—
280C2×C127—22no—
281C2×C127—44no—
282C2×C127—84no—
283C2×C127#191412yesdirect product factor
284C2×C127C2×#38611yescharacteristic
285C2×#568C2×C12711yescharacteristic, complemented
286C2×#535C2×C12711yescharacteristic
287C2×#413C2×C12711yescharacteristic, complemented
288C22×#100C2×C12712yescomplemented
289#1914C2×C12718yesdirect product factor
290C2×#344C2×C12712yescomplemented
291C127C2×#191411yescharacteristic, direct product factor, Sylow
292C22×#41C22×C12711yescharacteristic
293C23×D4C22×C12711yescharacteristic
294#568—22no—
295#568—24no—
296#568C22×C12714yescomplemented
297C2×#131—24no—
298C22×M16—22no—
299C22×M16C22×C12712yes—
300C22×M16C22×C12712yes—
301#535—22no—
302#535—22no—
303#535C4×C12714yes—
304#535C22×C12714yes—
305C2×#127—21no—
306C2×#124—21no—
307C2×#121—22no—
308C2×#120C4×C12714yes—
309C2×#117C22×C12711yescharacteristic
310#413—22no—
311#413C22×C12714yescomplemented
312C2×#101—21no—
313C2×#100—21no—
314C2×#100—24no—
315C2×#100—24no—
316C2×#100C22×C12718yescomplemented
317#344C22×C12718yescomplemented
318C25C2×C4×C12712yes—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41C2×C4×C12712yes—
324C2×#41D4×C12712yes—
325C2×#41D4×C12712yes—
326C2×#41C23×C12712yes—
327C22×Q8D4×C12711yescharacteristic
328C22×D4—24no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4C2×C4×C12712yes—
338C22×D4C2×C4×C12712yes—
339C22×D4D4×C12711yescharacteristic
340C22×D4C23×C12712yes—
341C23×C4D4×C12712yes—
342C23×C4C23×C12711yescharacteristic
343#131—216no—
344#131—216no—
345C2×M16—24no—
346C2×M16—28no—
347C2×M16—22no—
348C2×M16—28no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16D4×C12714yescomplemented
357C2×M16D4×C12714yescomplemented
358C2×M16C23×C12714yes—
359C2×M16C23×C12714yes—
360C22×C8—24no—
361C22×C8—22no—
362C22×C8—22no—
363#127—24no—
364#127—24no—
365#124—24no—
366#124—24no—
367#121—28no—
368#121—28no—
369#120—28no—
370#120C2×C4×C127116yes—
371#117—21no—
372#117—21no—
373#117C2×C4×C12712yes—
374#117C23×C12712yes—
375C2×C4⋊C4—21no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4C2×C4×C12712yes—
378C2×C42—21no—
379#101—24no—
380#100—24no—
381#100—216no—
382C24—22no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—84no—
387C24C22⋊C4×C12712yes—
388C24C22×C4×C12714yes—
389C24C22×C4×C12711yescharacteristic
390#41—24no—
391#41—24no—
392#41—24no—
393#41—24no—
394#41—24no—
395#41—24no—
396#41—24no—
397#41—24no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8C22⋊C4×C12712yes—
401C2×Q8C2×D4×C12712yes—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—216no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—24no—
415C2×D4—41no—
416C2×D4—42no—
417C2×D4—41no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—88no—
426C2×D4C22⋊C4×C12714yes—
427C2×D4C22⋊C4×C12712yes—
428C2×D4C22×C4×C12714yes—
429C2×D4C2×D4×C12712yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4C22⋊C4×C12712yes—
436C22×C4C22⋊C4×C12714yes—
437C22×C4C22×C4×C12711yescharacteristic
438C22×C4C2×D4×C12714yes—
439C22×C4C2×D4×C12711yescharacteristic
440C22×C4C2×D4×C12711yescharacteristic
441C22×C4C2×D4×C12711yescharacteristic
442C22×C4C2×D4×C12711yescharacteristic
443C22×C4C2×D4×C12712yes—
444C22×C4C2×D4×C12712yes—
445C22×C4#41×C12712yes—
446C22×C4#41×C12712yes—
447C22×C4C24×C12711yescharacteristic
448M16—216no—
449M16—24no—
450M16—24no—
451M16—24no—
452M16—24no—
453M16—24no—
454M16—42no—
455M16—42no—
456M16C2×D4×C12718yescomplemented
457C2×C8—216no—
458C2×C8—24no—
459C2×C8—24no—
460C2×C8—24no—
461C2×C8—24no—
462C2×C8—42no—
463C2×C8—42no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—216no—
468C22⋊C4C22×C4×C12714yes—
469C42—22no—
470C42—22no—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—28no—
475C23—42no—
476C23—44no—
477C23—48no—
478C23—42no—
479C23—44no—
480C23—42no—
481C23—88no—
482C23—84no—
483C23—84no—
484C23—88no—
485C23C2×C22⋊C4×C12711yescharacteristic
486C23C2×C22⋊C4×C12714yes—
487C23C2×C22⋊C4×C12711yescharacteristic
488C23C4×D4×C12712yes—
489C23C4×D4×C12712yes—
490C23C23×C4×C12711yescharacteristic
491Q8—24no—
492Q8—24no—
493D4—28no—
494D4—28no—
495D4—24no—
496D4—24no—
497D4—42no—
498D4—44no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—44no—
503D4—816no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4C2×C22⋊C4×C12714yes—
513C2×C4C2×C22⋊C4×C12711yescharacteristic
514C2×C4C2×C22⋊C4×C12711yescharacteristic
515C2×C4C4×D4×C12712yes—
516C2×C4C4×D4×C12712yes—
517C2×C4#120×C12711yescharacteristic
518C2×C4#120×C12712yes—
519C2×C4#120×C12711yescharacteristic
520C2×C4#121×C12712yes—
521C2×C4#121×C12712yes—
522C2×C4#121×C12712yes—
523C2×C4#121×C12712yes—
524C2×C4#123×C12711yescharacteristic
525C2×C4#123×C12711yescharacteristic
526C2×C4#123×C12712yes—
527C2×C4C22×D4×C12712yes—
528C2×C4C22×D4×C12711yescharacteristic
529C2×C4C22×D4×C12711yescharacteristic
530C2×C4C2×#41×C12712yes—
531C8—28no—
532C8—44no—
533C22—22no—
534C22—24no—
535C22—24no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—44no—
540C22—48no—
541C22—44no—
542C22—44no—
543C22—82no—
544C22—88no—
545C22—84no—
546C22—88no—
547C22—84no—
548C22#386×C12711yescharacteristic
549C22#386×C12712yes—
550C22#386×C12711yescharacteristic
551C22C22×C22⋊C4×C12711yescharacteristic
552C22C2×C4×D4×C12712yes—
553C4—24no—
554C4—44no—
555C4#386×C12711yescharacteristic
556C4#386×C12711yescharacteristic
557C4#386×C12712yes—
558C4C2×#120×C12711yescharacteristic
559C4C2×#121×C12712yes—
560C4C2×#123×C12711yescharacteristic
561C2—21no—
562C2—21no—
563C2—22no—
564C2—22no—
565C2—44no—
566C2—84no—
567C2C127×#191412yesdirect product factor
568C2C2×#386×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#535×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#568×C127C2semidirect
3. C2×#413×C127C2semidirect
4. C22×#100×C127C2semidirect
5. C127×#1914C2direct (N × H)
6. C2×#344×C127C2semidirect
11. #568×C127C22semidirect
26. #413×C127C22semidirect
31. C2×#100×C127C22semidirect
32. #344×C127C22semidirect
71. C2×M16×C127D4semidirect
72. C2×M16×C127D4semidirect
171. M16×C127C2×D4semidirect
276. C2×#1914C127direct (N × H)
283. C2×C127#1914direct (N × H)
285. C2×#568C2×C127semidirect
287. C2×#413C2×C127semidirect
288. C22×#100C2×C127semidirect
289. #1914C2×C127direct (N × H)
290. C2×#344C2×C127semidirect
291. C127C2×#1914direct (N × H)
296. #568C22×C127semidirect
311. #413C22×C127semidirect
316. C2×#100C22×C127semidirect
317. #344C22×C127semidirect
356. C2×M16D4×C127semidirect
357. C2×M16D4×C127semidirect
456. M16C2×D4×C127semidirect
567. C2C127×#1914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#568×C1272
C2×#535×C1272
C2×#413×C1272
C22×#100×C1272
C127×#19142
C2×#344×C1272
C2×#1914127