Finite Group Databasebeta

← C127×#18227 #44581900

Subgroups — C127×#18227 #44581900

Order 32512.

1130 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3535C211yesmaximal, characteristic
2C127×#3004C211yesmaximal, characteristic, complemented
3C2×#451×C127C211yesmaximal, characteristic, complemented
4C127×#2614C211yesmaximal, characteristic, complemented
5C127×#1606C212yesmaximal, complemented
6C127×#1605C212yesmaximal, complemented
7C127×#1603C212yesmaximal, complemented
8C127×#1602C212yesmaximal, complemented
9C127×#1516C211yesmaximal, characteristic, complemented
10C127×#1511C211yesmaximal, characteristic, complemented
11C127×#1468C211yesmaximal, characteristic, complemented
12C23×Q8×C127C2211yescharacteristic
13C2×#137×C127—21no—
14C22×Q16×C127—21no—
15#563×C127—21no—
16#562×C127—21no—
17#554×C127—21no—
18#552×C127—21no—
19#551×C127—21no—
20#551×C127—21no—
21#547×C127—21no—
22#546×C127—21no—
23#544×C127C2211yescharacteristic
24#543×C127C2211yescharacteristic
25#542×C127—21no—
26#539×C127—21no—
27#539×C127—21no—
28#539×C127C2211yescharacteristic
29#538×C127C2211yescharacteristic
30#536×C127—21no—
31#525×C127C2211yescharacteristic
32C2×#123×C127—21no—
33C2×#123×C127C2211yescharacteristic
34C2×C22⋊Q8×C127C2211yescharacteristic
35#451×C127—21no—
36#451×C127—21no—
37#451×C127—21no—
38#451×C127C2212yes—
39#451×C127C2212yes—
40#451×C127C2212yes—
41#448×C127—21no—
42#448×C127C2212yes—
43#419×C127—21no—
44C2×#103×C127—21no—
45#407×C127C2211yescharacteristic
46C2×C22⋊C8×C127C2211yescharacteristic
47#395×C127—21no—
48#395×C127C2212yes—
49#393×C127—21no—
50#393×C127C2212yes—
51#381×C127—21no—
52#381×C127C2211yescharacteristic
53#328×C127C2212yes—
54#328×C127C2212yes—
55#328×C127C2212yes—
56#327×C127C2212yes—
57#324×C127C2212yes—
58#323×C127C2212yes—
59C2×#41×C127—21no—
60C2×#41×C127D411yescharacteristic
61C22×Q8×C127—21no—
62C22×Q8×C127—21no—
63C22×Q8×C127—21no—
64C22×Q8×C127—21no—
65C22×Q8×C127—21no—
66C22×Q8×C127—44no—
67C22×Q8×C127D411yescharacteristic
68C22×Q8×C127C2312yes—
69C22×D4×C127D411yescharacteristic
70C23×C4×C127—21no—
71C23×C4×C127C2311yescharacteristic
72#137×C127—44no—
73C2×Q16×C127—22no—
74C2×Q16×C127—22no—
75C2×Q16×C127—22no—
76C2×Q16×C127—44no—
77C2×SD16×C127—22no—
78C2×M16×C127—21no—
79C22×C8×C127—21no—
80C4⋊Q8×C127—21no—
81C4⋊Q8×C127—21no—
82C4⋊Q8×C127—21no—
83#126×C127—21no—
84#126×C127—21no—
85#126×C127—21no—
86#126×C127—21no—
87#126×C127—21no—
88#126×C127—21no—
89#125×C127—21no—
90#125×C127—21no—
91#125×C127—21no—
92#125×C127—21no—
93#125×C127—21no—
94#124×C127—21no—
95#124×C127—21no—
96#124×C127—21no—
97#124×C127—21no—
98#123×C127—21no—
99#123×C127—21no—
100#123×C127—21no—
101#123×C127—21no—
102#123×C127—21no—
103#123×C127—21no—
104#123×C127—21no—
105#123×C127—21no—
106#123×C127—21no—
107#123×C127—21no—
108#123×C127—21no—
109#123×C127—21no—
110#123×C127—21no—
111#123×C127—21no—
112#123×C127—44no—
113C22⋊Q8×C127—21no—
114C22⋊Q8×C127—21no—
115C22⋊Q8×C127—21no—
116C22⋊Q8×C127—21no—
117C22⋊Q8×C127—21no—
118C22⋊Q8×C127—21no—
119C22⋊Q8×C127—21no—
120C22⋊Q8×C127—21no—
121C22⋊Q8×C127—21no—
122C22⋊Q8×C127—21no—
123C22⋊Q8×C127—21no—
124C22⋊Q8×C127—21no—
125C22⋊Q8×C127—21no—
126C22⋊Q8×C127—21no—
127C22⋊Q8×C127D411yescharacteristic
128C22⋊Q8×C127D411yescharacteristic
129C22⋊Q8×C127D411yescharacteristic
130C22⋊Q8×C127C2311yescharacteristic
131C22⋊Q8×C127C2311yescharacteristic
132C22⋊Q8×C127C2311yescharacteristic
133#121×C127—21no—
134#121×C127—21no—
135#121×C127—21no—
136#121×C127—21no—
137#121×C127D411yescharacteristic
138#121×C127C2311yescharacteristic
139#120×C127—21no—
140#120×C127—21no—
141C4×Q8×C127—21no—
142C4×D4×C127—21no—
143C4×D4×C127—21no—
144C4×D4×C127—21no—
145C4×D4×C127—21no—
146C4×D4×C127—21no—
147C4×D4×C127—21no—
148C4×D4×C127—21no—
149#117×C127—21no—
150#117×C127—21no—
151#117×C127—21no—
152#117×C127D411yescharacteristic
153C2×C4⋊C4×C127—21no—
154C2×C4⋊C4×C127—21no—
155C2×C4⋊C4×C127—22no—
156C2×C4⋊C4×C127D411yescharacteristic
157C2×C4⋊C4×C127D411yescharacteristic
158C2×C4⋊C4×C127C2311yescharacteristic
159C2×C22⋊C4×C127—21no—
160C2×C22⋊C4×C127—21no—
161C2×C22⋊C4×C127—21no—
162C2×C22⋊C4×C127—22no—
163C2×C22⋊C4×C127D411yescharacteristic
164C2×C22⋊C4×C127D411yescharacteristic
165C2×C22⋊C4×C127C2311yescharacteristic
166#103×C127—22no—
167#103×C127—22no—
168#103×C127—22no—
169#103×C127—22no—
170C22⋊C8×C127—21no—
171C22⋊C8×C127—21no—
172C22⋊C8×C127C2312yes—
173C22⋊C8×C127C2312yes—
174#95×C127—22no—
175#95×C127—22no—
176#95×C127—21no—
177#95×C127C2312yes—
178C24×C127C2×D411yescharacteristic
179C24×C127C2×D411yescharacteristic
180#41×C127—42no—
181#41×C127—82no—
182C2×Q8×C127—21no—
183C2×Q8×C127—21no—
184C2×Q8×C127—21no—
185C2×Q8×C127—24no—
186C2×Q8×C127—24no—
187C2×Q8×C127—22no—
188C2×Q8×C127—22no—
189C2×Q8×C127—44no—
190C2×Q8×C127—42no—
191C2×Q8×C127—42no—
192C2×Q8×C127—44no—
193C2×Q8×C127—42no—
194C2×Q8×C127—44no—
195C2×Q8×C127—44no—
196C2×Q8×C127—41no—
197C2×Q8×C127—41no—
198C2×Q8×C127C2×D411yescharacteristic
199C2×Q8×C127C2×D411yescharacteristic
200C2×Q8×C127C2×D411yescharacteristic
201C2×D4×C127—21no—
202C2×D4×C127—21no—
203C2×D4×C127—21no—
204C2×D4×C127—21no—
205C2×D4×C127—21no—
206C2×D4×C127—21no—
207C2×D4×C127—21no—
208C2×D4×C127—42no—
209C2×D4×C127C2×D411yescharacteristic
210C22×C4×C127—24no—
211C22×C4×C127—21no—
212C22×C4×C127—22no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—22no—
220C22×C4×C127—42no—
221C22×C4×C127—42no—
222C22×C4×C127—41no—
223C22×C4×C127—41no—
224C22×C4×C127C2×D411yescharacteristic
225C22×C4×C127C2×D411yescharacteristic
226C22×C4×C127C2×D411yescharacteristic
227C22×C4×C127C2×D411yescharacteristic
228C22×C4×C127C2×D411yescharacteristic
229C22×C4×C127C2×D411yescharacteristic
230C22×C4×C127C2×D411yescharacteristic
231C22×C4×C127C2×D411yescharacteristic
232C22×C4×C127C2411yescharacteristic
233Q16×C127—44no—
234Q16×C127—44no—
235Q16×C127—44no—
236SD16×C127—44no—
237M16×C127—42no—
238C2×C8×C127—22no—
239C2×C8×C127—22no—
240C2×C8×C127—42no—
241C4⋊C4×C127—21no—
242C4⋊C4×C127—21no—
243C4⋊C4×C127—21no—
244C4⋊C4×C127—21no—
245C4⋊C4×C127—21no—
246C4⋊C4×C127—21no—
247C4⋊C4×C127—21no—
248C4⋊C4×C127—21no—
249C4⋊C4×C127—21no—
250C4⋊C4×C127—21no—
251C4⋊C4×C127—21no—
252C4⋊C4×C127—21no—
253C4⋊C4×C127—21no—
254C4⋊C4×C127—21no—
255C4⋊C4×C127—21no—
256C4⋊C4×C127—21no—
257C4⋊C4×C127—21no—
258C4⋊C4×C127—21no—
259C4⋊C4×C127—21no—
260C4⋊C4×C127—21no—
261C4⋊C4×C127—21no—
262C4⋊C4×C127—21no—
263C4⋊C4×C127—21no—
264C4⋊C4×C127—44no—
265C4⋊C4×C127C2×D411yescharacteristic
266C4⋊C4×C127C2×D411yescharacteristic
267C4⋊C4×C127C2×D411yescharacteristic
268C4⋊C4×C127C2×D411yescharacteristic
269C22⋊C4×C127—21no—
270C22⋊C4×C127—21no—
271C22⋊C4×C127—21no—
272C22⋊C4×C127—21no—
273C22⋊C4×C127—21no—
274C22⋊C4×C127—21no—
275C22⋊C4×C127—21no—
276C22⋊C4×C127—21no—
277C22⋊C4×C127—21no—
278C22⋊C4×C127—21no—
279C22⋊C4×C127—21no—
280C22⋊C4×C127—21no—
281C22⋊C4×C127—21no—
282C22⋊C4×C127—21no—
283C22⋊C4×C127—21no—
284C22⋊C4×C127—21no—
285C22⋊C4×C127—21no—
286C22⋊C4×C127—21no—
287C22⋊C4×C127—21no—
288C22⋊C4×C127—21no—
289C22⋊C4×C127—21no—
290C22⋊C4×C127—21no—
291C22⋊C4×C127—21no—
292C22⋊C4×C127—44no—
293C22⋊C4×C127—42no—
294C42×C127—21no—
295C42×C127—21no—
296C42×C127—21no—
297C42×C127—21no—
298C42×C127—21no—
299C23×C127—22no—
300C23×C127—22no—
301C23×C127—21no—
302C23×C127—21no—
303C23×C127—22no—
304C23×C127—41no—
305C23×C127—41no—
306C23×C127—41no—
307C23×C127#12011yescharacteristic
308C23×C127#12011yescharacteristic
309C23×C127C22×D411yescharacteristic
310Q8×C127—24no—
311Q8×C127—24no—
312Q8×C127—41no—
313Q8×C127—41no—
314Q8×C127—41no—
315Q8×C127—42no—
316Q8×C127—42no—
317Q8×C127—44no—
318Q8×C127—44no—
319Q8×C127—81no—
320Q8×C127—81no—
321Q8×C127—81no—
322D4×C127—41no—
323D4×C127—42no—
324D4×C127—42no—
325D4×C127—42no—
326D4×C127—81no—
327D4×C127—81no—
328D4×C127—81no—
329D4×C127—81no—
330C2×C4×C127—22no—
331C2×C4×C127—22no—
332C2×C4×C127—24no—
333C2×C4×C127—21no—
334C2×C4×C127—21no—
335C2×C4×C127—21no—
336C2×C4×C127—21no—
337C2×C4×C127—21no—
338C2×C4×C127—21no—
339C2×C4×C127—21no—
340C2×C4×C127—21no—
341C2×C4×C127—21no—
342C2×C4×C127—21no—
343C2×C4×C127—22no—
344C2×C4×C127—41no—
345C2×C4×C127—41no—
346C2×C4×C127—41no—
347C2×C4×C127—41no—
348C2×C4×C127—42no—
349C2×C4×C127—44no—
350C2×C4×C127—42no—
351C2×C4×C127—44no—
352C2×C4×C127—42no—
353C2×C4×C127—41no—
354C2×C4×C127—41no—
355C2×C4×C127—42no—
356C2×C4×C127—42no—
357C2×C4×C127—42no—
358C2×C4×C127—81no—
359C2×C4×C127—81no—
360C2×C4×C127—81no—
361C2×C4×C127—81no—
362C2×C4×C127—81no—
363C2×C4×C127—81no—
364C2×C4×C127#12011yescharacteristic
365C2×C4×C127#12011yescharacteristic
366C2×C4×C127C22×D411yescharacteristic
367C2×C4×C127C22×D411yescharacteristic
368C8×C127—42no—
369C8×C127—42no—
370C22×C127—21no—
371C22×C127—21no—
372C22×C127—21no—
373C22×C127—21no—
374C22×C127—21no—
375C22×C127—21no—
376C22×C127—21no—
377C22×C127—44no—
378C22×C127—41no—
379C22×C127—41no—
380C22×C127—41no—
381C22×C127—41no—
382C22×C127—41no—
383C22×C127—41no—
384C22×C127—82no—
385C22×C127B(4,𝔽2)12yes—
386C22×C127C2×#12011yescharacteristic
387C22×C127#57812yes—
388C4×C127—21no—
389C4×C127—21no—
390C4×C127—21no—
391C4×C127—21no—
392C4×C127—41no—
393C4×C127—41no—
394C4×C127—41no—
395C4×C127—41no—
396C4×C127—41no—
397C4×C127—41no—
398C4×C127—44no—
399C4×C127—41no—
400C4×C127—41no—
401C4×C127—41no—
402C4×C127—41no—
403C4×C127—82no—
404#18227C12711yesmaximal, characteristic, direct product factor, Sylow
405C2×C127—22no—
406C2×C127—22no—
407C2×C127—41no—
408C2×C127—81no—
409C2×C127—81no—
410C2×C127#301111yescharacteristic
411C2×C127#302211yescharacteristic
412C2×C127C2×B(4,𝔽2)11yescharacteristic
413#3535C2×C12711yescharacteristic
414#3004C2×C12711yescharacteristic, complemented
415C2×#451C2×C12711yescharacteristic, complemented
416#2614C2×C12711yescharacteristic, complemented
417#1606C2×C12712yescomplemented
418#1605C2×C12712yescomplemented
419#1603C2×C12712yescomplemented
420#1602C2×C12712yescomplemented
421#1516C2×C12711yescharacteristic, complemented
422#1511C2×C12711yescharacteristic, complemented
423#1468C2×C12711yescharacteristic, complemented
424C127#1822711yescharacteristic, direct product factor, Sylow
425C23×Q8C22×C12711yescharacteristic
426C2×#137—21no—
427C22×Q16—21no—
428#563—21no—
429#562—21no—
430#554—21no—
431#552—21no—
432#551—21no—
433#551—21no—
434#547—21no—
435#546—21no—
436#544C22×C12711yescharacteristic
437#543C22×C12711yescharacteristic
438#542—21no—
439#539—21no—
440#539—21no—
441#539C22×C12711yescharacteristic
442#538C22×C12711yescharacteristic
443#536—21no—
444#525C22×C12711yescharacteristic
445C2×#123—21no—
446C2×#123C22×C12711yescharacteristic
447C2×C22⋊Q8C22×C12711yescharacteristic
448#451—21no—
449#451—21no—
450#451—21no—
451#451C22×C12712yes—
452#451C22×C12712yes—
453#451C22×C12712yes—
454#448—21no—
455#448C22×C12712yes—
456#419—21no—
457C2×#103—21no—
458#407C22×C12711yescharacteristic
459C2×C22⋊C8C22×C12711yescharacteristic
460#395—21no—
461#395C22×C12712yes—
462#393—21no—
463#393C22×C12712yes—
464#381—21no—
465#381C22×C12711yescharacteristic
466#328C22×C12712yes—
467#328C22×C12712yes—
468#328C22×C12712yes—
469#327C22×C12712yes—
470#324C22×C12712yes—
471#323C22×C12712yes—
472C2×#41—21no—
473C2×#41D4×C12711yescharacteristic
474C22×Q8—21no—
475C22×Q8—21no—
476C22×Q8—21no—
477C22×Q8—21no—
478C22×Q8—21no—
479C22×Q8—44no—
480C22×Q8D4×C12711yescharacteristic
481C22×Q8C23×C12712yes—
482C22×D4D4×C12711yescharacteristic
483C23×C4—21no—
484C23×C4C23×C12711yescharacteristic
485#137—44no—
486C2×Q16—22no—
487C2×Q16—22no—
488C2×Q16—22no—
489C2×Q16—44no—
490C2×SD16—22no—
491C2×M16—21no—
492C22×C8—21no—
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#125—21no—
503#125—21no—
504#125—21no—
505#125—21no—
506#125—21no—
507#124—21no—
508#124—21no—
509#124—21no—
510#124—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523#123—21no—
524#123—21no—
525#123—44no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8D4×C12711yescharacteristic
541C22⋊Q8D4×C12711yescharacteristic
542C22⋊Q8D4×C12711yescharacteristic
543C22⋊Q8C23×C12711yescharacteristic
544C22⋊Q8C23×C12711yescharacteristic
545C22⋊Q8C23×C12711yescharacteristic
546#121—21no—
547#121—21no—
548#121—21no—
549#121—21no—
550#121D4×C12711yescharacteristic
551#121C23×C12711yescharacteristic
552#120—21no—
553#120—21no—
554C4×Q8—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562#117—21no—
563#117—21no—
564#117—21no—
565#117D4×C12711yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4D4×C12711yescharacteristic
570C2×C4⋊C4D4×C12711yescharacteristic
571C2×C4⋊C4C23×C12711yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4D4×C12711yescharacteristic
577C2×C22⋊C4D4×C12711yescharacteristic
578C2×C22⋊C4C23×C12711yescharacteristic
579#103—22no—
580#103—22no—
581#103—22no—
582#103—22no—
583C22⋊C8—21no—
584C22⋊C8—21no—
585C22⋊C8C23×C12712yes—
586C22⋊C8C23×C12712yes—
587#95—22no—
588#95—22no—
589#95—21no—
590#95C23×C12712yes—
591C24C2×D4×C12711yescharacteristic
592C24C2×D4×C12711yescharacteristic
593#41—42no—
594#41—82no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—24no—
599C2×Q8—24no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—44no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—41no—
610C2×Q8—41no—
611C2×Q8C2×D4×C12711yescharacteristic
612C2×Q8C2×D4×C12711yescharacteristic
613C2×Q8C2×D4×C12711yescharacteristic
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—42no—
622C2×D4C2×D4×C12711yescharacteristic
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4C2×D4×C12711yescharacteristic
638C22×C4C2×D4×C12711yescharacteristic
639C22×C4C2×D4×C12711yescharacteristic
640C22×C4C2×D4×C12711yescharacteristic
641C22×C4C2×D4×C12711yescharacteristic
642C22×C4C2×D4×C12711yescharacteristic
643C22×C4C2×D4×C12711yescharacteristic
644C22×C4C2×D4×C12711yescharacteristic
645C22×C4C24×C12711yescharacteristic
646Q16—44no—
647Q16—44no—
648Q16—44no—
649SD16—44no—
650M16—42no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—42no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—44no—
678C4⋊C4C2×D4×C12711yescharacteristic
679C4⋊C4C2×D4×C12711yescharacteristic
680C4⋊C4C2×D4×C12711yescharacteristic
681C4⋊C4C2×D4×C12711yescharacteristic
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—44no—
706C22⋊C4—42no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23#120×C12711yescharacteristic
721C23#120×C12711yescharacteristic
722C23C22×D4×C12711yescharacteristic
723Q8—24no—
724Q8—24no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—42no—
729Q8—42no—
730Q8—44no—
731Q8—44no—
732Q8—81no—
733Q8—81no—
734Q8—81no—
735D4—41no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4#120×C12711yescharacteristic
778C2×C4#120×C12711yescharacteristic
779C2×C4C22×D4×C12711yescharacteristic
780C2×C4C22×D4×C12711yescharacteristic
781C8—42no—
782C8—42no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—44no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—82no—
798C22B(4,𝔽2)×C12712yes—
799C22C2×#120×C12711yescharacteristic
800C22#578×C12712yes—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—44no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C2—22no—
818C2—22no—
819C2—41no—
820C2—81no—
821C2—81no—
822C2C127×#301111yescharacteristic
823C2C127×#302211yescharacteristic
824C2C2×B(4,𝔽2)×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3004C2semidirect
3. C2×#451×C127C2semidirect
4. C127×#2614C2semidirect
5. C127×#1606C2semidirect
6. C127×#1605C2semidirect
7. C127×#1603C2semidirect
8. C127×#1602C2semidirect
9. C127×#1516C2semidirect
10. C127×#1511C2semidirect
11. C127×#1468C2semidirect
404. #18227C127direct (N × H)
414. #3004C2×C127semidirect
415. C2×#451C2×C127semidirect
416. #2614C2×C127semidirect
417. #1606C2×C127semidirect
418. #1605C2×C127semidirect
419. #1603C2×C127semidirect
420. #1602C2×C127semidirect
421. #1516C2×C127semidirect
422. #1511C2×C127semidirect
423. #1468C2×C127semidirect
424. C127#18227direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35352
C127×#30042
C2×#451×C1272
C127×#26142
C127×#16062
C127×#16052
C127×#16032
C127×#16022
C127×#15162
C127×#15112
C127×#14682
#18227127