Finite Group Databasebeta

← C2×C127×#1793 #44584287

Subgroups — C2×C127×#1793 #44584287

Order 32512.

3682 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×2−1+4×C127C211yesmaximal, characteristic
2C22×#104×C127C212yesmaximal, complemented
3C2×#417×C127C212yesmaximal, complemented
4C22×#101×C127C211yesmaximal, characteristic, complemented
5C2×#391×C127C211yesmaximal, characteristic, complemented
6C127×#1793C218yesmaximal, direct product factor
7C2×2−1+4×C127—28no—
8C2×2−1+4×C127—24no—
9C2×2−1+4×C127—24no—
10C2×2−1+4×C127—22no—
11C2×2−1+4×C127C418yescomplemented
12C2×2−1+4×C127C2214yes—
13C22×#41×C127—22no—
14C22×#41×C127—22no—
15C22×#41×C127C2212yes—
16C23×Q8×C127—22no—
17C23×Q8×C127C2211yescharacteristic
18C22×M16×C127C2212yes—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C42×C127C2211yescharacteristic
21C2×#104×C127—28no—
22C2×#104×C127C2218yescomplemented
23#417×C127—24no—
24#417×C127C2218yescomplemented
25C2×#103×C127—22no—
26C2×#102×C127—22no—
27C2×#101×C127—24no—
28C2×#101×C127C2214yescomplemented
29#391×C127—22no—
30#391×C127C2214yescomplemented
31C2×#95×C127—22no—
322−1+4×C127—232no—
332−1+4×C127—216no—
342−1+4×C127—232no—
352−1+4×C127—216no—
362−1+4×C127—216no—
372−1+4×C127—28no—
382−1+4×C127C2×C4116yescomplemented
39C2×#41×C127—28no—
40C2×#41×C127—216no—
41C2×#41×C127—28no—
42C2×#41×C127—216no—
43C2×#41×C127—216no—
44C2×#41×C127—28no—
45C2×#41×C127—216no—
46C2×#41×C127—28no—
47C2×#41×C127—24no—
48C2×#41×C127—22no—
49C2×#41×C127—24no—
50C2×#41×C127—22no—
51C2×#41×C127C2×C418yes—
52C2×#41×C127D418yes—
53C2×#41×C127D414yes—
54C2×#41×C127C2314yes—
55C22×Q8×C127—22no—
56C22×Q8×C127—28no—
57C22×Q8×C127—216no—
58C22×Q8×C127—216no—
59C22×Q8×C127—28no—
60C22×Q8×C127—22no—
61C22×Q8×C127—24no—
62C22×Q8×C127—22no—
63C22×Q8×C127C2×C414yes—
64C22×Q8×C127D412yes—
65C22×Q8×C127D414yes—
66C22×Q8×C127D412yes—
67C22×Q8×C127C2312yes—
68C22×D4×C127—22no—
69C22×D4×C127—22no—
70C22×D4×C127D412yes—
71C23×C4×C127—24no—
72C23×C4×C127—22no—
73C23×C4×C127—21no—
74C23×C4×C127—21no—
75C23×C4×C127D412yes—
76C23×C4×C127C2311yescharacteristic
77C2×M16×C127—22no—
78C2×M16×C127—24no—
79C2×M16×C127—24no—
80C2×M16×C127C2314yes—
81C22×C8×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127C2312yes—
86C2×C42×C127—24no—
87C2×C42×C127—21no—
88C2×C42×C127C2312yes—
89#104×C127—216no—
90#103×C127—28no—
91#102×C127—28no—
92#101×C127—28no—
93#95×C127—28no—
94C24×C127—22no—
95C24×C127C2×D411yescharacteristic
96#41×C127—232no—
97#41×C127—264no—
98#41×C127—232no—
99#41×C127—264no—
100#41×C127—232no—
101#41×C127—232no—
102#41×C127—28no—
103#41×C127—28no—
104#41×C127—28no—
105#41×C127—28no—
106#41×C127—28no—
107#41×C127—24no—
108#41×C127—24no—
109#41×C127C22⋊C4116yes—
110#41×C127C22×C418yes—
111#41×C127C2×D418yes—
112C2×Q8×C127—28no—
113C2×Q8×C127—216no—
114C2×Q8×C127—232no—
115C2×Q8×C127—264no—
116C2×Q8×C127—232no—
117C2×Q8×C127—28no—
118C2×Q8×C127—28no—
119C2×Q8×C127—22no—
120C2×Q8×C127—24no—
121C2×Q8×C127—24no—
122C2×Q8×C127—28no—
123C2×Q8×C127—24no—
124C2×Q8×C127—28no—
125C2×Q8×C127—24no—
126C2×Q8×C127—24no—
127C2×Q8×C127C22⋊C418yes—
128C2×Q8×C127C22⋊C418yes—
129C2×Q8×C127C22×C414yes—
130C2×Q8×C127C2×D414yes—
131C2×Q8×C127C2×D414yes—
132C2×D4×C127—28no—
133C2×D4×C127—216no—
134C2×D4×C127—28no—
135C2×D4×C127—24no—
136C2×D4×C127—28no—
137C2×D4×C127—24no—
138C2×D4×C127—24no—
139C2×D4×C127—22no—
140C2×D4×C127C22⋊C418yes—
141C2×D4×C127C2×D414yes—
142C22×C4×C127—216no—
143C22×C4×C127—232no—
144C22×C4×C127—22no—
145C22×C4×C127—24no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—28no—
149C22×C4×C127—24no—
150C22×C4×C127—28no—
151C22×C4×C127—24no—
152C22×C4×C127—24no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—42no—
156C22×C4×C127—42no—
157C22×C4×C127—44no—
158C22×C4×C127—41no—
159C22×C4×C127—41no—
160C22×C4×C127C22⋊C418yes—
161C22×C4×C127C22×C412yes—
162C22×C4×C127C2×D414yes—
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127C2×D414yes—
165C22×C4×C127C2×D412yes—
166C22×C4×C127C2×D412yes—
167C22×C4×C127C2×D412yes—
168C22×C4×C127C2411yescharacteristic
169M16×C127—24no—
170M16×C127—24no—
171M16×C127—44no—
172C2×C8×C127—24no—
173C2×C8×C127—44no—
174C4⋊C4×C127—24no—
175C4⋊C4×C127—42no—
176C42×C127—24no—
177C42×C127—42no—
178C23×C127—22no—
179C23×C127—22no—
180C23×C127—24no—
181C23×C127—28no—
182C23×C127—44no—
183C23×C127—44no—
184C23×C127C2×C22⋊C412yes—
185C23×C127#12012yes—
186C23×C127#12011yescharacteristic
187C23×C127#12011yescharacteristic
188C23×C127C22×D411yescharacteristic
189Q8×C127—232no—
190Q8×C127—28no—
191Q8×C127—24no—
192Q8×C127—28no—
193Q8×C127—28no—
194Q8×C127—216no—
195Q8×C127C2×C22⋊C418yes—
196D4×C127—232no—
197D4×C127—28no—
198D4×C127—28no—
199D4×C127—216no—
200D4×C127—24no—
201D4×C127—28no—
202D4×C127C2×C22⋊C418yes—
203C2×C4×C127—264no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—28no—
208C2×C4×C127—28no—
209C2×C4×C127—28no—
210C2×C4×C127—28no—
211C2×C4×C127—28no—
212C2×C4×C127—216no—
213C2×C4×C127—24no—
214C2×C4×C127—48no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—44no—
218C2×C4×C127—42no—
219C2×C4×C127—82no—
220C2×C4×C127—82no—
221C2×C4×C127C2×C22⋊C418yes—
222C2×C4×C127C2×C22⋊C414yes—
223C2×C4×C127C2×C22⋊C414yes—
224C2×C4×C127C2×C22⋊C412yes—
225C2×C4×C127#12014yes—
226C2×C4×C127#12014yes—
227C2×C4×C127#12012yes—
228C2×C4×C127#12012yes—
229C2×C4×C127C23×C411yescharacteristic
230C2×C4×C127C22×D412yes—
231C2×C4×C127C22×D412yes—
232C2×C4×C127C22×D411yescharacteristic
233C8×C127—44no—
234C22×C127—24no—
235C22×C127—24no—
236C22×C127—21no—
237C22×C127—21no—
238C22×C127—21no—
239C22×C127—21no—
240C22×C127—28no—
241C22×C127—416no—
242C22×C127—44no—
243C22×C127—44no—
244C22×C127#37912yes—
245C22×C127#37912yes—
246C22×C127#45412yes—
247C22×C127#45612yes—
248C22×C127C22×C22⋊C411yescharacteristic
249C22×C127C2×#12011yescharacteristic
250C22×C127C2×#12011yescharacteristic
251C4×C127—28no—
252C4×C127—28no—
253C4×C127—44no—
254C4×C127—82no—
255C4×C127#37914yes—
256C4×C127C22×C22⋊C412yes—
257C4×C127C2×#12012yes—
258C2×#1793C12711yesmaximal, characteristic, direct product factor, Sylow
259C2×C127—21no—
260C2×C127—21no—
261C2×C127—22no—
262C2×C127—48no—
263C2×C127#179314yesdirect product factor
264C2×C127C2×#37911yescharacteristic
265C2×C127C2×#45411yescharacteristic
266C2×C127C2×#45611yescharacteristic
267C22×2−1+4C2×C12711yescharacteristic
268C22×#104C2×C12712yescomplemented
269C2×#417C2×C12712yescomplemented
270C22×#101C2×C12711yescharacteristic, complemented
271C2×#391C2×C12711yescharacteristic, complemented
272#1793C2×C12718yesdirect product factor
273C127C2×#179311yescharacteristic, direct product factor, Sylow
274C2×2−1+4—28no—
275C2×2−1+4—24no—
276C2×2−1+4—24no—
277C2×2−1+4—22no—
278C2×2−1+4C4×C12718yescomplemented
279C2×2−1+4C22×C12714yes—
280C22×#41—22no—
281C22×#41—22no—
282C22×#41C22×C12712yes—
283C23×Q8—22no—
284C23×Q8C22×C12711yescharacteristic
285C22×M16C22×C12712yes—
286C22×C4⋊C4C22×C12711yescharacteristic
287C22×C42C22×C12711yescharacteristic
288C2×#104—28no—
289C2×#104C22×C12718yescomplemented
290#417—24no—
291#417C22×C12718yescomplemented
292C2×#103—22no—
293C2×#102—22no—
294C2×#101—24no—
295C2×#101C22×C12714yescomplemented
296#391—22no—
297#391C22×C12714yescomplemented
298C2×#95—22no—
2992−1+4—232no—
3002−1+4—216no—
3012−1+4—232no—
3022−1+4—216no—
3032−1+4—216no—
3042−1+4—28no—
3052−1+4C2×C4×C127116yescomplemented
306C2×#41—28no—
307C2×#41—216no—
308C2×#41—28no—
309C2×#41—216no—
310C2×#41—216no—
311C2×#41—28no—
312C2×#41—216no—
313C2×#41—28no—
314C2×#41—24no—
315C2×#41—22no—
316C2×#41—24no—
317C2×#41—22no—
318C2×#41C2×C4×C12718yes—
319C2×#41D4×C12718yes—
320C2×#41D4×C12714yes—
321C2×#41C23×C12714yes—
322C22×Q8—22no—
323C22×Q8—28no—
324C22×Q8—216no—
325C22×Q8—216no—
326C22×Q8—28no—
327C22×Q8—22no—
328C22×Q8—24no—
329C22×Q8—22no—
330C22×Q8C2×C4×C12714yes—
331C22×Q8D4×C12712yes—
332C22×Q8D4×C12714yes—
333C22×Q8D4×C12712yes—
334C22×Q8C23×C12712yes—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4D4×C12712yes—
338C23×C4—24no—
339C23×C4—22no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4D4×C12712yes—
343C23×C4C23×C12711yescharacteristic
344C2×M16—22no—
345C2×M16—24no—
346C2×M16—24no—
347C2×M16C23×C12714yes—
348C22×C8—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C23×C12712yes—
353C2×C42—24no—
354C2×C42—21no—
355C2×C42C23×C12712yes—
356#104—216no—
357#103—28no—
358#102—28no—
359#101—28no—
360#95—28no—
361C24—22no—
362C24C2×D4×C12711yescharacteristic
363#41—232no—
364#41—264no—
365#41—232no—
366#41—264no—
367#41—232no—
368#41—232no—
369#41—28no—
370#41—28no—
371#41—28no—
372#41—28no—
373#41—28no—
374#41—24no—
375#41—24no—
376#41C22⋊C4×C127116yes—
377#41C22×C4×C12718yes—
378#41C2×D4×C12718yes—
379C2×Q8—28no—
380C2×Q8—216no—
381C2×Q8—232no—
382C2×Q8—264no—
383C2×Q8—232no—
384C2×Q8—28no—
385C2×Q8—28no—
386C2×Q8—22no—
387C2×Q8—24no—
388C2×Q8—24no—
389C2×Q8—28no—
390C2×Q8—24no—
391C2×Q8—28no—
392C2×Q8—24no—
393C2×Q8—24no—
394C2×Q8C22⋊C4×C12718yes—
395C2×Q8C22⋊C4×C12718yes—
396C2×Q8C22×C4×C12714yes—
397C2×Q8C2×D4×C12714yes—
398C2×Q8C2×D4×C12714yes—
399C2×D4—28no—
400C2×D4—216no—
401C2×D4—28no—
402C2×D4—24no—
403C2×D4—28no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4C22⋊C4×C12718yes—
408C2×D4C2×D4×C12714yes—
409C22×C4—216no—
410C22×C4—232no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—28no—
416C22×C4—24no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—44no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4C22⋊C4×C12718yes—
428C22×C4C22×C4×C12712yes—
429C22×C4C2×D4×C12714yes—
430C22×C4C2×D4×C12711yescharacteristic
431C22×C4C2×D4×C12714yes—
432C22×C4C2×D4×C12712yes—
433C22×C4C2×D4×C12712yes—
434C22×C4C2×D4×C12712yes—
435C22×C4C24×C12711yescharacteristic
436M16—24no—
437M16—24no—
438M16—44no—
439C2×C8—24no—
440C2×C8—44no—
441C4⋊C4—24no—
442C4⋊C4—42no—
443C42—24no—
444C42—42no—
445C23—22no—
446C23—22no—
447C23—24no—
448C23—28no—
449C23—44no—
450C23—44no—
451C23C2×C22⋊C4×C12712yes—
452C23#120×C12711yescharacteristic
453C23#120×C12712yes—
454C23#120×C12711yescharacteristic
455C23C22×D4×C12711yescharacteristic
456Q8—232no—
457Q8—28no—
458Q8—24no—
459Q8—28no—
460Q8—28no—
461Q8—216no—
462Q8C2×C22⋊C4×C12718yes—
463D4—232no—
464D4—28no—
465D4—28no—
466D4—216no—
467D4—24no—
468D4—28no—
469D4C2×C22⋊C4×C12718yes—
470C2×C4—264no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—28no—
475C2×C4—28no—
476C2×C4—28no—
477C2×C4—28no—
478C2×C4—28no—
479C2×C4—216no—
480C2×C4—24no—
481C2×C4—42no—
482C2×C4—48no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4C2×C22⋊C4×C12718yes—
489C2×C4C2×C22⋊C4×C12714yes—
490C2×C4C2×C22⋊C4×C12714yes—
491C2×C4C2×C22⋊C4×C12712yes—
492C2×C4#120×C12714yes—
493C2×C4#120×C12714yes—
494C2×C4#120×C12712yes—
495C2×C4#120×C12712yes—
496C2×C4C23×C4×C12711yescharacteristic
497C2×C4C22×D4×C12712yes—
498C2×C4C22×D4×C12712yes—
499C2×C4C22×D4×C12711yescharacteristic
500C8—44no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—24no—
506C22—24no—
507C22—28no—
508C22—44no—
509C22—44no—
510C22—416no—
511C22#379×C12712yes—
512C22#379×C12712yes—
513C22#454×C12712yes—
514C22#456×C12712yes—
515C22C22×C22⋊C4×C12711yescharacteristic
516C22C2×#120×C12711yescharacteristic
517C22C2×#120×C12711yescharacteristic
518C4—28no—
519C4—28no—
520C4—44no—
521C4—82no—
522C4#379×C12714yes—
523C4C22×C22⋊C4×C12712yes—
524C4C2×#120×C12712yes—
525C2—21no—
526C2—21no—
527C2—22no—
528C2—48no—
529C2C127×#179314yesdirect product factor
530C2C2×#379×C12711yescharacteristic
531C2C2×#454×C12711yescharacteristic
532C2C2×#456×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×2−1+4×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#104×C127C2semidirect
3. C2×#417×C127C2semidirect
4. C22×#101×C127C2semidirect
5. C2×#391×C127C2semidirect
6. C127×#1793C2direct (N × H)
11. C2×2−1+4×C127C4semidirect
22. C2×#104×C127C22semidirect
24. #417×C127C22semidirect
28. C2×#101×C127C22semidirect
30. #391×C127C22semidirect
38. 2−1+4×C127C2×C4semidirect
258. C2×#1793C127direct (N × H)
263. C2×C127#1793direct (N × H)
268. C22×#104C2×C127semidirect
269. C2×#417C2×C127semidirect
270. C22×#101C2×C127semidirect
271. C2×#391C2×C127semidirect
272. #1793C2×C127direct (N × H)
273. C127C2×#1793direct (N × H)
278. C2×2−1+4C4×C127semidirect
289. C2×#104C22×C127semidirect
291. #417C22×C127semidirect
295. C2×#101C22×C127semidirect
297. #391C22×C127semidirect
305. 2−1+4C2×C4×C127semidirect
529. C2C127×#1793direct (N × H)

Maximal subgroups

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

subgroupindex
C22×2−1+4×C1272
C22×#104×C1272
C2×#417×C1272
C22×#101×C1272
C2×#391×C1272
C127×#17932
C2×#1793127