Finite Group Databasebeta

← C2×C127×#1395 #44576261

Subgroups — C2×C127×#1395 #44576261

Order 32512.

766 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#413×C127C211yesmaximal, characteristic
2C2×#410×C127C211yesmaximal, characteristic
3C2×#408×C127C211yesmaximal, characteristic
4C127×#1395C214yesmaximal, direct product factor
5C22×#41×C127C2211yescharacteristic
6C22×M16×C127—21no—
7C22×M16×C127C411yescharacteristic, complemented
8C23×C8×C127C411yescharacteristic, complemented
9C2×#117×C127—21no—
10#413×C127—21no—
11#413×C127—21no—
12#413×C127C412yescomplemented
13#413×C127C2212yes—
14C2×#101×C127C412yescomplemented
15C2×#100×C127—21no—
16#410×C127—21no—
17#410×C127—21no—
18#410×C127C412yes—
19#410×C127C2212yes—
20C2×#99×C127—21no—
21C2×#99×C127C412yes—
22#408×C127—21no—
23#408×C127—21no—
24#408×C127C412yescomplemented
25#408×C127C2212yes—
26C2×C22⋊C8×C127—21no—
27C2×C22⋊C8×C127—21no—
28C2×#41×C127—41no—
29C2×#41×C127—41no—
30C2×#41×C127—41no—
31C2×#41×C127—41no—
32C2×#41×C127C2×C411yescharacteristic
33C2×#41×C127C2×C411yescharacteristic
34C2×#41×C127C2×C411yescharacteristic
35C2×#41×C127D411yescharacteristic
36C2×#41×C127D411yescharacteristic
37C2×#41×C127D411yescharacteristic
38C2×#41×C127Q811yescharacteristic
39C2×#41×C127C2311yescharacteristic
40C22×Q8×C127C2×C411yescharacteristic
41C22×D4×C127C2×C411yescharacteristic
42C22×D4×C127D411yescharacteristic
43C22×D4×C127Q811yescharacteristic
44C23×C4×C127C2×C411yescharacteristic
45C23×C4×C127D411yescharacteristic
46C23×C4×C127D411yescharacteristic
47C2×M16×C127—21no—
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C2×M16×C127—22no—
51C2×M16×C127—41no—
52C2×M16×C127—41no—
53C2×M16×C127—41no—
54C2×M16×C127—41no—
55C2×M16×C127—41no—
56C2×M16×C127C2×C412yescomplemented
57C22×C8×C127—21no—
58C22×C8×C127—21no—
59C22×C8×C127—21no—
60C22×C8×C127—41no—
61C22×C8×C127—41no—
62C22×C8×C127—41no—
63C22×C8×C127C2×C412yescomplemented
64#117×C127—22no—
65#117×C127—22no—
66#117×C127—41no—
67#117×C127—41no—
68C2×C4⋊C4×C127—41no—
69C2×C22⋊C4×C127—22no—
70C2×C42×C127—41no—
71#101×C127—22no—
72#101×C127C2×C414yescomplemented
73#100×C127—22no—
74#100×C127—22no—
75#99×C127—22no—
76#99×C127—22no—
77#99×C127—22no—
78#99×C127C2×C414yes—
79C22⋊C8×C127—22no—
80C22⋊C8×C127—22no—
81C22⋊C8×C127—22no—
82C22⋊C8×C127—22no—
83C24×C127C22⋊C411yescharacteristic
84C24×C127C4⋊C411yescharacteristic
85C24×C127C4⋊C411yescharacteristic
86#41×C127—41no—
87#41×C127—41no—
88#41×C127—41no—
89#41×C127—41no—
90#41×C127—41no—
91#41×C127—41no—
92#41×C127—41no—
93#41×C127—41no—
94#41×C127—41no—
95#41×C127—41no—
96#41×C127—41no—
97#41×C127—41no—
98#41×C127—41no—
99#41×C127—41no—
100#41×C127—41no—
101#41×C127—41no—
102C2×Q8×C127—41no—
103C2×Q8×C127—41no—
104C2×Q8×C127C4211yescharacteristic
105C2×Q8×C127C22⋊C411yescharacteristic
106C2×Q8×C127C4⋊C411yescharacteristic
107C2×Q8×C127C22×C411yescharacteristic
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127—41no—
111C2×D4×C127—41no—
112C2×D4×C127—41no—
113C2×D4×C127—41no—
114C2×D4×C127C4211yescharacteristic
115C2×D4×C127C22⋊C411yescharacteristic
116C2×D4×C127C22⋊C411yescharacteristic
117C2×D4×C127C22⋊C411yescharacteristic
118C2×D4×C127C4⋊C411yescharacteristic
119C2×D4×C127C4⋊C411yescharacteristic
120C2×D4×C127C4⋊C411yescharacteristic
121C2×D4×C127C4⋊C411yescharacteristic
122C2×D4×C127C4⋊C411yescharacteristic
123C2×D4×C127C22×C411yescharacteristic
124C2×D4×C127C2×D411yescharacteristic
125C2×D4×C127C2×Q811yescharacteristic
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—21no—
132C22×C4×C127—21no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—42no—
139C22×C4×C127C4211yescharacteristic
140C22×C4×C127C4211yescharacteristic
141C22×C4×C127C22⋊C411yescharacteristic
142C22×C4×C127C22⋊C411yescharacteristic
143C22×C4×C127C22⋊C411yescharacteristic
144C22×C4×C127C22⋊C411yescharacteristic
145C22×C4×C127C22⋊C411yescharacteristic
146C22×C4×C127C22⋊C411yescharacteristic
147C22×C4×C127C22⋊C411yescharacteristic
148C22×C4×C127C4⋊C411yescharacteristic
149C22×C4×C127C4⋊C411yescharacteristic
150C22×C4×C127C4⋊C411yescharacteristic
151C22×C4×C127C4⋊C411yescharacteristic
152C22×C4×C127C22×C411yescharacteristic
153C22×C4×C127C2×D411yescharacteristic
154C22×C4×C127C2×D411yescharacteristic
155M16×C127—24no—
156M16×C127—42no—
157M16×C127—42no—
158M16×C127—42no—
159M16×C127—42no—
160M16×C127—42no—
161C2×C8×C127—22no—
162C2×C8×C127—22no—
163C2×C8×C127—42no—
164C2×C8×C127—42no—
165C2×C8×C127—42no—
166C2×C8×C127—42no—
167C2×C8×C127—41no—
168C2×C8×C127—41no—
169C2×C8×C127—41no—
170C2×C8×C127—41no—
171C2×C8×C127—42no—
172C4⋊C4×C127—42no—
173C4⋊C4×C127—42no—
174C22⋊C4×C127—24no—
175C22⋊C4×C127—42no—
176C42×C127—42no—
177C42×C127—42no—
178C23×C127—21no—
179C23×C127—21no—
180C23×C127—21no—
181C23×C127—21no—
182C23×C127—21no—
183C23×C127—21no—
184C23×C127—42no—
185C23×C127—42no—
186C23×C127—42no—
187C23×C127#9511yescharacteristic
188C23×C127#9511yescharacteristic
189C23×C127#9511yescharacteristic
190C23×C127#9511yescharacteristic
191C23×C127C2×C22⋊C411yescharacteristic
192C23×C127C2×C4⋊C411yescharacteristic
193C23×C127C2×C4⋊C411yescharacteristic
194Q8×C127—41no—
195Q8×C127—41no—
196Q8×C127—41no—
197Q8×C127—41no—
198D4×C127—41no—
199D4×C127—41no—
200D4×C127—41no—
201D4×C127—41no—
202D4×C127—41no—
203D4×C127—41no—
204D4×C127—41no—
205D4×C127—41no—
206D4×C127—41no—
207D4×C127—41no—
208D4×C127—41no—
209D4×C127—41no—
210C2×C4×C127—21no—
211C2×C4×C127—21no—
212C2×C4×C127—21no—
213C2×C4×C127—21no—
214C2×C4×C127—21no—
215C2×C4×C127—21no—
216C2×C4×C127—21no—
217C2×C4×C127—21no—
218C2×C4×C127—21no—
219C2×C4×C127—21no—
220C2×C4×C127—21no—
221C2×C4×C127—21no—
222C2×C4×C127—21no—
223C2×C4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
230C2×C4×C127—21no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—44no—
241C2×C4×C127—84no—
242C2×C4×C127#9511yescharacteristic
243C2×C4×C127#9511yescharacteristic
244C2×C4×C127#9511yescharacteristic
245C2×C4×C127#9511yescharacteristic
246C2×C4×C127#9911yescharacteristic
247C2×C4×C127#9911yescharacteristic
248C2×C4×C127#9911yescharacteristic
249C2×C4×C127#9911yescharacteristic
250C2×C4×C127C2×C4211yescharacteristic
251C2×C4×C127C2×C22⋊C411yescharacteristic
252C2×C4×C127C2×C22⋊C411yescharacteristic
253C2×C4×C127C2×C4⋊C411yescharacteristic
254C8×C127—44no—
255C8×C127—42no—
256C8×C127—42no—
257C22×C127—22no—
258C22×C127—21no—
259C22×C127—21no—
260C22×C127—21no—
261C22×C127—21no—
262C22×C127—21no—
263C22×C127—21no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—41no—
267C22×C127—41no—
268C22×C127—41no—
269C22×C127—41no—
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—42no—
274C22×C127—81no—
275C22×C127—81no—
276C22×C127#34211yescharacteristic
277C22×C127#34211yescharacteristic
278C22×C127C2×#9511yescharacteristic
279C4×C127—21no—
280C4×C127—21no—
281C4×C127—21no—
282C4×C127—21no—
283C4×C127—21no—
284C4×C127—21no—
285C4×C127—84no—
286C4×C127#34211yescharacteristic
287C4×C127#34211yescharacteristic
288C4×C127C2×#9911yescharacteristic
289C4×C127C2×#9911yescharacteristic
290C2×#1395C12711yesmaximal, characteristic, direct product factor, Sylow
291C2×C127—21no—
292C2×C127—21no—
293C2×C127—41no—
294C2×C127—41no—
295C2×C127—41no—
296C2×C127—41no—
297C2×C127—41no—
298C2×C127—41no—
299C2×C127#139512yesdirect product factor
300C2×C127C2×#34211yescharacteristic
301C2×#413C2×C12711yescharacteristic
302C2×#410C2×C12711yescharacteristic
303C2×#408C2×C12711yescharacteristic
304#1395C2×C12714yesdirect product factor
305C127C2×#139511yescharacteristic, direct product factor, Sylow
306C22×#41C22×C12711yescharacteristic
307C22×M16—21no—
308C22×M16C4×C12711yescharacteristic, complemented
309C23×C8C4×C12711yescharacteristic, complemented
310C2×#117—21no—
311#413—21no—
312#413—21no—
313#413C4×C12712yescomplemented
314#413C22×C12712yes—
315C2×#101C4×C12712yescomplemented
316C2×#100—21no—
317#410—21no—
318#410—21no—
319#410C4×C12712yes—
320#410C22×C12712yes—
321C2×#99—21no—
322C2×#99C4×C12712yes—
323#408—21no—
324#408—21no—
325#408C4×C12712yescomplemented
326#408C22×C12712yes—
327C2×C22⋊C8—21no—
328C2×C22⋊C8—21no—
329C2×#41—41no—
330C2×#41—41no—
331C2×#41—41no—
332C2×#41—41no—
333C2×#41C2×C4×C12711yescharacteristic
334C2×#41C2×C4×C12711yescharacteristic
335C2×#41C2×C4×C12711yescharacteristic
336C2×#41D4×C12711yescharacteristic
337C2×#41D4×C12711yescharacteristic
338C2×#41D4×C12711yescharacteristic
339C2×#41Q8×C12711yescharacteristic
340C2×#41C23×C12711yescharacteristic
341C22×Q8C2×C4×C12711yescharacteristic
342C22×D4C2×C4×C12711yescharacteristic
343C22×D4D4×C12711yescharacteristic
344C22×D4Q8×C12711yescharacteristic
345C23×C4C2×C4×C12711yescharacteristic
346C23×C4D4×C12711yescharacteristic
347C23×C4D4×C12711yescharacteristic
348C2×M16—21no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—41no—
353C2×M16—41no—
354C2×M16—41no—
355C2×M16—41no—
356C2×M16—41no—
357C2×M16C2×C4×C12712yescomplemented
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—41no—
362C22×C8—41no—
363C22×C8—41no—
364C22×C8C2×C4×C12712yescomplemented
365#117—22no—
366#117—22no—
367#117—41no—
368#117—41no—
369C2×C4⋊C4—41no—
370C2×C22⋊C4—22no—
371C2×C42—41no—
372#101—22no—
373#101C2×C4×C12714yescomplemented
374#100—22no—
375#100—22no—
376#99—22no—
377#99—22no—
378#99—22no—
379#99C2×C4×C12714yes—
380C22⋊C8—22no—
381C22⋊C8—22no—
382C22⋊C8—22no—
383C22⋊C8—22no—
384C24C22⋊C4×C12711yescharacteristic
385C24C4⋊C4×C12711yescharacteristic
386C24C4⋊C4×C12711yescharacteristic
387#41—41no—
388#41—41no—
389#41—41no—
390#41—41no—
391#41—41no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8C42×C12711yescharacteristic
406C2×Q8C22⋊C4×C12711yescharacteristic
407C2×Q8C4⋊C4×C12711yescharacteristic
408C2×Q8C22×C4×C12711yescharacteristic
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4C42×C12711yescharacteristic
416C2×D4C22⋊C4×C12711yescharacteristic
417C2×D4C22⋊C4×C12711yescharacteristic
418C2×D4C22⋊C4×C12711yescharacteristic
419C2×D4C4⋊C4×C12711yescharacteristic
420C2×D4C4⋊C4×C12711yescharacteristic
421C2×D4C4⋊C4×C12711yescharacteristic
422C2×D4C4⋊C4×C12711yescharacteristic
423C2×D4C4⋊C4×C12711yescharacteristic
424C2×D4C22×C4×C12711yescharacteristic
425C2×D4C2×D4×C12711yescharacteristic
426C2×D4C2×Q8×C12711yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4C42×C12711yescharacteristic
441C22×C4C42×C12711yescharacteristic
442C22×C4C22⋊C4×C12711yescharacteristic
443C22×C4C22⋊C4×C12711yescharacteristic
444C22×C4C22⋊C4×C12711yescharacteristic
445C22×C4C22⋊C4×C12711yescharacteristic
446C22×C4C22⋊C4×C12711yescharacteristic
447C22×C4C22⋊C4×C12711yescharacteristic
448C22×C4C22⋊C4×C12711yescharacteristic
449C22×C4C4⋊C4×C12711yescharacteristic
450C22×C4C4⋊C4×C12711yescharacteristic
451C22×C4C4⋊C4×C12711yescharacteristic
452C22×C4C4⋊C4×C12711yescharacteristic
453C22×C4C22×C4×C12711yescharacteristic
454C22×C4C2×D4×C12711yescharacteristic
455C22×C4C2×D4×C12711yescharacteristic
456M16—24no—
457M16—42no—
458M16—42no—
459M16—42no—
460M16—42no—
461M16—42no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—42no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8—42no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C22⋊C4—24no—
476C22⋊C4—42no—
477C42—42no—
478C42—42no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23#95×C12711yescharacteristic
489C23#95×C12711yescharacteristic
490C23#95×C12711yescharacteristic
491C23#95×C12711yescharacteristic
492C23C2×C22⋊C4×C12711yescharacteristic
493C23C2×C4⋊C4×C12711yescharacteristic
494C23C2×C4⋊C4×C12711yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—44no—
542C2×C4—84no—
543C2×C4#95×C12711yescharacteristic
544C2×C4#95×C12711yescharacteristic
545C2×C4#95×C12711yescharacteristic
546C2×C4#95×C12711yescharacteristic
547C2×C4#99×C12711yescharacteristic
548C2×C4#99×C12711yescharacteristic
549C2×C4#99×C12711yescharacteristic
550C2×C4#99×C12711yescharacteristic
551C2×C4C2×C42×C12711yescharacteristic
552C2×C4C2×C22⋊C4×C12711yescharacteristic
553C2×C4C2×C22⋊C4×C12711yescharacteristic
554C2×C4C2×C4⋊C4×C12711yescharacteristic
555C8—44no—
556C8—42no—
557C8—42no—
558C22—22no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22#342×C12711yescharacteristic
578C22#342×C12711yescharacteristic
579C22C2×#95×C12711yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—84no—
587C4#342×C12711yescharacteristic
588C4#342×C12711yescharacteristic
589C4C2×#99×C12711yescharacteristic
590C4C2×#99×C12711yescharacteristic
591C2—21no—
592C2—21no—
593C2—41no—
594C2—41no—
595C2—41no—
596C2—41no—
597C2—41no—
598C2—41no—
599C2C127×#139512yesdirect product factor
600C2C2×#342×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC2×#41C23×C127
socleC22×C127#342
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1395C2direct (N × H)
7. C22×M16×C127C4semidirect
8. C23×C8×C127C4semidirect
12. #413×C127C4semidirect
14. C2×#101×C127C4semidirect
24. #408×C127C4semidirect
56. C2×M16×C127C2×C4semidirect
63. C22×C8×C127C2×C4semidirect
72. #101×C127C2×C4semidirect
290. C2×#1395C127direct (N × H)
299. C2×C127#1395direct (N × H)
304. #1395C2×C127direct (N × H)
305. C127C2×#1395direct (N × H)
308. C22×M16C4×C127semidirect
309. C23×C8C4×C127semidirect
313. #413C4×C127semidirect
315. C2×#101C4×C127semidirect
325. #408C4×C127semidirect
357. C2×M16C2×C4×C127semidirect
364. C22×C8C2×C4×C127semidirect
373. #101C2×C4×C127semidirect
599. C2C127×#1395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#413×C1272
C2×#410×C1272
C2×#408×C1272
C127×#13952
C2×#1395127