Finite Group Databasebeta

← C127×#21465 #44585138

Subgroups — C127×#21465 #44585138

Order 32512.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C127C211yesmaximal, characteristic
2C2×#452×C127C211yesmaximal, characteristic
3C2×#440×C127C211yesmaximal, characteristic, complemented
4C2×C4×Q16×C127C211yesmaximal, characteristic, complemented
5C127×#2323C211yesmaximal, characteristic, complemented
6C127×#1878C211yesmaximal, characteristic, complemented
7C127×#1877C211yesmaximal, characteristic, complemented
8C127×#1872C211yesmaximal, characteristic, complemented
9C127×#1863C211yesmaximal, characteristic, complemented
10C127×#1862C211yesmaximal, characteristic, complemented
11C127×#1852C211yesmaximal, characteristic, complemented
12C127×#1788C211yesmaximal, characteristic
13C127×#1763C211yesmaximal, characteristic, complemented
14C4×#102×C127C211yesmaximal, characteristic, complemented
15C127×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C127C2211yescharacteristic
17C22×Q16×C127C2211yescharacteristic
18C22×SD16×C127C2211yescharacteristic
19C2×C22⋊Q8×C127C2211yescharacteristic
20#520×C127—24no—
21#520×C127—24no—
22C2×C4×Q8×C127C2211yescharacteristic
23C2×C4×Q8×C127C2211yescharacteristic
24C2×C4×Q8×C127C2211yescharacteristic
25C2×C4×D4×C127—21no—
26C2×C4×D4×C127—21no—
27C2×C4×D4×C127C2211yescharacteristic
28C2×C4×D4×C127C2211yescharacteristic
29C2×#117×C127—21no—
30C2×#117×C127C2211yescharacteristic
31C22×C4⋊C4×C127—21no—
32C22×C4⋊C4×C127C2211yescharacteristic
33#452×C127C418yescomplemented
34#440×C127—24no—
35C4×Q16×C127—24no—
36C2×#107×C127C2211yescharacteristic
37C2×#107×C127C2211yescharacteristic
38C2×#103×C127C2211yescharacteristic
39C2×#103×C127C2211yescharacteristic
40C2×#103×C127C2211yescharacteristic
41C2×#103×C127C2211yescharacteristic
42C2×#103×C127C2211yescharacteristic
43C2×#102×C127C2211yescharacteristic
44C2×#102×C127C2211yescharacteristic
45C2×#102×C127C2211yescharacteristic
46C2×C22⋊C8×C127C2211yescharacteristic
47C2×C22⋊C8×C127C2211yescharacteristic
48C2×#97×C127C2211yescharacteristic
49C2×C4×C8×C127C2211yescharacteristic
50#391×C127C2211yescharacteristic
51#389×C127—21no—
52#389×C127C2211yescharacteristic
53#388×C127—21no—
54#388×C127—21no—
55#387×C127—21no—
56#380×C127C2211yescharacteristic
57C4×C4⋊C4×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#340×C127C2211yescharacteristic
61#340×C127C2211yescharacteristic
62#336×C127C2211yescharacteristic
63#336×C127C2211yescharacteristic
64C2×#41×C127—22no—
65C2×#41×C127—22no—
66C2×#41×C127—22no—
67C2×#41×C127—22no—
68C2×#41×C127—22no—
69C2×#41×C127C2×C414yes—
70C22×Q8×C127C2311yescharacteristic
71C22×Q8×C127C2311yescharacteristic
72C22×D4×C127—21no—
73C22×D4×C127C2311yescharacteristic
74C23×C4×C127—21no—
75C23×C4×C127—21no—
76C23×C4×C127—21no—
77C23×C4×C127—21no—
78C23×C4×C127C2311yescharacteristic
79C2×Q16×C127—22no—
80C2×Q16×C127—22no—
81C2×Q16×C127C2×C414yescomplemented
82C2×SD16×C127—22no—
83C2×SD16×C127—22no—
84C2×SD16×C127C2×C414yescomplemented
85C22×C8×C127C2311yescharacteristic
86C22×C8×C127C2311yescharacteristic
87C22×C8×C127C2311yescharacteristic
88C22×C8×C127C2311yescharacteristic
89C22⋊Q8×C127—22no—
90C22⋊Q8×C127C2×C414yescomplemented
91C4×Q8×C127—22no—
92C4×Q8×C127—22no—
93C4×Q8×C127—22no—
94C4×Q8×C127—22no—
95C4×Q8×C127—22no—
96C4×Q8×C127D414yes—
97C4×D4×C127—28no—
98C4×D4×C127—28no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127D414yes—
103#117×C127—28no—
104#117×C127—22no—
105#117×C127—22no—
106C2×C4⋊C4×C127—28no—
107C2×C4⋊C4×C127—21no—
108C2×C4⋊C4×C127—21no—
109C2×C4⋊C4×C127—21no—
110C2×C4⋊C4×C127—21no—
111C2×C4⋊C4×C127—22no—
112C2×C4⋊C4×C127—22no—
113C2×C4⋊C4×C127—21no—
114C2×C4⋊C4×C127—21no—
115C2×C4⋊C4×C127D411yescharacteristic
116C2×C4⋊C4×C127D411yescharacteristic
117C2×C4⋊C4×C127C2311yescharacteristic
118C2×C4⋊C4×C127C2311yescharacteristic
119C2×C4⋊C4×C127C2311yescharacteristic
120C2×C4⋊C4×C127C2311yescharacteristic
121C2×C4⋊C4×C127C2311yescharacteristic
122C2×C22⋊C4×C127—21no—
123C2×C22⋊C4×C127—21no—
124C2×C22⋊C4×C127—21no—
125C2×C22⋊C4×C127—21no—
126C2×C22⋊C4×C127D411yescharacteristic
127C2×C22⋊C4×C127D411yescharacteristic
128C2×C42×C127—21no—
129C2×C42×C127—21no—
130C2×C42×C127—21no—
131C2×C42×C127—21no—
132C2×C42×C127C2311yescharacteristic
133C2×C42×C127C2311yescharacteristic
134#107×C127—22no—
135#107×C127—22no—
136#103×C127—22no—
137#103×C127—22no—
138#103×C127—22no—
139#103×C127—22no—
140#103×C127C2×C414yescomplemented
141#102×C127—22no—
142#102×C127—22no—
143#102×C127C2×C414yescomplemented
144C22⋊C8×C127—22no—
145C22⋊C8×C127C2×C414yescomplemented
146#97×C127—22no—
147C4×C8×C127—22no—
148#95×C127—21no—
149#95×C127—21no—
150#95×C127—21no—
151#95×C127—21no—
152#95×C127—21no—
153C24×C127—21no—
154C24×C127C2×D411yescharacteristic
155#41×C127—28no—
156#41×C127—28no—
157#41×C127—28no—
158#41×C127—28no—
159C2×Q8×C127—21no—
160C2×Q8×C127—21no—
161C2×Q8×C127—21no—
162C2×Q8×C127—21no—
163C2×Q8×C127—21no—
164C2×Q8×C127—21no—
165C2×Q8×C127—21no—
166C2×Q8×C127—21no—
167C2×Q8×C127C22×C412yes—
168C2×Q8×C127C22×C412yes—
169C2×Q8×C127C2×D412yes—
170C2×Q8×C127#4112yes—
171C2×D4×C127—24no—
172C2×D4×C127—24no—
173C2×D4×C127—24no—
174C2×D4×C127—21no—
175C2×D4×C127—21no—
176C2×D4×C127—21no—
177C2×D4×C127C22×C412yes—
178C2×D4×C127C2×D412yes—
179C2×D4×C127#4112yes—
180C22×C4×C127—24no—
181C22×C4×C127—24no—
182C22×C4×C127—21no—
183C22×C4×C127—24no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—24no—
193C22×C4×C127—24no—
194C22×C4×C127—24no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—81no—
198C22×C4×C127—81no—
199C22×C4×C127—81no—
200C22×C4×C127—81no—
201C22×C4×C127—81no—
202C22×C4×C127—81no—
203C22×C4×C127C22×C412yes—
204C22×C4×C127C2×D411yescharacteristic
205C22×C4×C127C2×D411yescharacteristic
206C22×C4×C127C2×D411yescharacteristic
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127#4112yes—
210C22×C4×C127C2411yescharacteristic
211Q16×C127—28no—
212SD16×C127—28no—
213C2×C8×C127—21no—
214C2×C8×C127—21no—
215C2×C8×C127—21no—
216C2×C8×C127—21no—
217C2×C8×C127—21no—
218C2×C8×C127—21no—
219C2×C8×C127—21no—
220C2×C8×C127—21no—
221C2×C8×C127—21no—
222C2×C8×C127—21no—
223C2×C8×C127C22×C412yes—
224C2×C8×C127C22×C412yes—
225C4⋊C4×C127—24no—
226C4⋊C4×C127—24no—
227C4⋊C4×C127—24no—
228C4⋊C4×C127—22no—
229C4⋊C4×C127—24no—
230C4⋊C4×C127—22no—
231C4⋊C4×C127—21no—
232C4⋊C4×C127—21no—
233C4⋊C4×C127—21no—
234C4⋊C4×C127—21no—
235C4⋊C4×C127—21no—
236C4⋊C4×C127—21no—
237C4⋊C4×C127—21no—
238C4⋊C4×C127—42no—
239C4⋊C4×C127—81no—
240C4⋊C4×C127C22×C412yes—
241C4⋊C4×C127C2×D412yes—
242C4⋊C4×C127C2×D412yes—
243C22⋊C4×C127—24no—
244C22⋊C4×C127—24no—
245C22⋊C4×C127—24no—
246C22⋊C4×C127—22no—
247C22⋊C4×C127—22no—
248C22⋊C4×C127—81no—
249C42×C127—24no—
250C42×C127—24no—
251C42×C127—21no—
252C42×C127—21no—
253C42×C127—42no—
254C42×C127—81no—
255C42×C127C2×D412yes—
256C42×C127C2×D412yes—
257C23×C127—22no—
258C23×C127—21no—
259C23×C127—22no—
260C23×C127—21no—
261C23×C127—22no—
262C23×C127—21no—
263C23×C127—21no—
264C23×C127—21no—
265C23×C127—21no—
266C23×C127—41no—
267C23×C127—41no—
268C23×C127—41no—
269C23×C127—41no—
270C23×C127C4×D412yes—
271C23×C127C22×D411yescharacteristic
272Q8×C127—22no—
273Q8×C127—22no—
274Q8×C127—22no—
275Q8×C127—22no—
276Q8×C127—22no—
277Q8×C127—41no—
278Q8×C127—41no—
279Q8×C127C4×D414yes—
280D4×C127—216no—
281D4×C127—22no—
282D4×C127—22no—
283D4×C127—22no—
284D4×C127C4×D414yes—
285C2×C4×C127—216no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—21no—
289C2×C4×C127—21no—
290C2×C4×C127—22no—
291C2×C4×C127—21no—
292C2×C4×C127—21no—
293C2×C4×C127—21no—
294C2×C4×C127—21no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—21no—
302C2×C4×C127—21no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—21no—
306C2×C4×C127—21no—
307C2×C4×C127—21no—
308C2×C4×C127—21no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—41no—
313C2×C4×C127—41no—
314C2×C4×C127—41no—
315C2×C4×C127—41no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—84no—
324C2×C4×C127—84no—
325C2×C4×C127—84no—
326C2×C4×C127C4×D412yes—
327C2×C4×C127#12012yes—
328C2×C4×C127#12012yes—
329C2×C4×C127C23×C411yescharacteristic
330C2×C4×C127C22×D411yescharacteristic
331C2×C4×C127C22×D411yescharacteristic
332C2×C4×C127C2×#4111yescharacteristic
333C2×C4×C127C2×#4111yescharacteristic
334C2×C4×C127C2×#4111yescharacteristic
335C8×C127—22no—
336C8×C127—22no—
337C8×C127—41no—
338C8×C127—41no—
339C22×C127—22no—
340C22×C127—22no—
341C22×C127—22no—
342C22×C127—24no—
343C22×C127—41no—
344C22×C127—42no—
345C22×C127—41no—
346C22×C127—42no—
347C22×C127—42no—
348C22×C127—42no—
349C22×C127—41no—
350C22×C127—42no—
351C22×C127—41no—
352C22×C127—42no—
353C22×C127C2×C4×D411yescharacteristic
354C22×C127C2×#12011yescharacteristic
355C22×C127#52511yescharacteristic
356C22×C127#57611yescharacteristic
357C22×C127#57711yescharacteristic
358C22×C127#57811yescharacteristic
359C22×C127#57811yescharacteristic
360C4×C127—22no—
361C4×C127—22no—
362C4×C127—22no—
363C4×C127—24no—
364C4×C127—42no—
365C4×C127—41no—
366C4×C127—41no—
367C4×C127—42no—
368C4×C127—42no—
369C4×C127—42no—
370C4×C127—81no—
371C4×C127—81no—
372C4×C127C2×C4×D411yescharacteristic
373C4×C127C2×C4×D411yescharacteristic
374C4×C127#52511yescharacteristic
375C4×C127#52511yescharacteristic
376#21465C12711yesmaximal, characteristic, direct product factor, Sylow
377C2×C127—42no—
378C2×C127—44no—
379C2×C127C4×#12011yescharacteristic
380C2×C127#294711yescharacteristic
381C2×C127#295111yescharacteristic
382C2×C127#301111yescharacteristic
383C2×C127#301211yescharacteristic
384C2×C127#312011yescharacteristic
385C2×C127#312411yescharacteristic
386C2×#520C2×C12711yescharacteristic
387C2×#452C2×C12711yescharacteristic
388C2×#440C2×C12711yescharacteristic, complemented
389C2×C4×Q16C2×C12711yescharacteristic, complemented
390#2323C2×C12711yescharacteristic, complemented
391#1878C2×C12711yescharacteristic, complemented
392#1877C2×C12711yescharacteristic, complemented
393#1872C2×C12711yescharacteristic, complemented
394#1863C2×C12711yescharacteristic, complemented
395#1862C2×C12711yescharacteristic, complemented
396#1852C2×C12711yescharacteristic, complemented
397#1788C2×C12711yescharacteristic
398#1763C2×C12711yescharacteristic, complemented
399C4×#102C2×C12711yescharacteristic, complemented
400#1750C2×C12711yescharacteristic, complemented
401C127#2146511yescharacteristic, direct product factor, Sylow
402C22×#41C22×C12711yescharacteristic
403C22×Q16C22×C12711yescharacteristic
404C22×SD16C22×C12711yescharacteristic
405C2×C22⋊Q8C22×C12711yescharacteristic
406#520—24no—
407#520—24no—
408C2×C4×Q8C22×C12711yescharacteristic
409C2×C4×Q8C22×C12711yescharacteristic
410C2×C4×Q8C22×C12711yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4—21no—
413C2×C4×D4C22×C12711yescharacteristic
414C2×C4×D4C22×C12711yescharacteristic
415C2×#117—21no—
416C2×#117C22×C12711yescharacteristic
417C22×C4⋊C4—21no—
418C22×C4⋊C4C22×C12711yescharacteristic
419#452C4×C12718yescomplemented
420#440—24no—
421C4×Q16—24no—
422C2×#107C22×C12711yescharacteristic
423C2×#107C22×C12711yescharacteristic
424C2×#103C22×C12711yescharacteristic
425C2×#103C22×C12711yescharacteristic
426C2×#103C22×C12711yescharacteristic
427C2×#103C22×C12711yescharacteristic
428C2×#103C22×C12711yescharacteristic
429C2×#102C22×C12711yescharacteristic
430C2×#102C22×C12711yescharacteristic
431C2×#102C22×C12711yescharacteristic
432C2×C22⋊C8C22×C12711yescharacteristic
433C2×C22⋊C8C22×C12711yescharacteristic
434C2×#97C22×C12711yescharacteristic
435C2×C4×C8C22×C12711yescharacteristic
436#391C22×C12711yescharacteristic
437#389—21no—
438#389C22×C12711yescharacteristic
439#388—21no—
440#388—21no—
441#387—21no—
442#380C22×C12711yescharacteristic
443C4×C4⋊C4C22×C12711yescharacteristic
444#340C22×C12711yescharacteristic
445#340C22×C12711yescharacteristic
446#340C22×C12711yescharacteristic
447#340C22×C12711yescharacteristic
448#336C22×C12711yescharacteristic
449#336C22×C12711yescharacteristic
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C2×C4×C12714yes—
456C22×Q8C23×C12711yescharacteristic
457C22×Q8C23×C12711yescharacteristic
458C22×D4—21no—
459C22×D4C23×C12711yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C12711yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16C2×C4×C12714yescomplemented
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16C2×C4×C12714yescomplemented
471C22×C8C23×C12711yescharacteristic
472C22×C8C23×C12711yescharacteristic
473C22×C8C23×C12711yescharacteristic
474C22×C8C23×C12711yescharacteristic
475C22⋊Q8—22no—
476C22⋊Q8C2×C4×C12714yescomplemented
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8D4×C12714yes—
483C4×D4—28no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4D4×C12714yes—
489#117—28no—
490#117—22no—
491#117—22no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C12711yescharacteristic
502C2×C4⋊C4D4×C12711yescharacteristic
503C2×C4⋊C4C23×C12711yescharacteristic
504C2×C4⋊C4C23×C12711yescharacteristic
505C2×C4⋊C4C23×C12711yescharacteristic
506C2×C4⋊C4C23×C12711yescharacteristic
507C2×C4⋊C4C23×C12711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4D4×C12711yescharacteristic
513C2×C22⋊C4D4×C12711yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42C23×C12711yescharacteristic
519C2×C42C23×C12711yescharacteristic
520#107—22no—
521#107—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#103—22no—
526#103C2×C4×C12714yescomplemented
527#102—22no—
528#102—22no—
529#102C2×C4×C12714yescomplemented
530C22⋊C8—22no—
531C22⋊C8C2×C4×C12714yescomplemented
532#97—22no—
533C4×C8—22no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24C2×D4×C12711yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C22×C4×C12712yes—
554C2×Q8C22×C4×C12712yes—
555C2×Q8C2×D4×C12712yes—
556C2×Q8#41×C12712yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×C4×C12712yes—
564C2×D4C2×D4×C12712yes—
565C2×D4#41×C12712yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C22×C4×C12712yes—
590C22×C4C2×D4×C12711yescharacteristic
591C22×C4C2×D4×C12711yescharacteristic
592C22×C4C2×D4×C12711yescharacteristic
593C22×C4C2×D4×C12711yescharacteristic
594C22×C4C2×D4×C12711yescharacteristic
595C22×C4#41×C12712yes—
596C22×C4C24×C12711yescharacteristic
597Q16—28no—
598SD16—28no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C22×C4×C12712yes—
610C2×C8C22×C4×C12712yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C22×C4×C12712yes—
627C4⋊C4C2×D4×C12712yes—
628C4⋊C4C2×D4×C12712yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—81no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—42no—
640C42—81no—
641C42C2×D4×C12712yes—
642C42C2×D4×C12712yes—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C4×D4×C12712yes—
657C23C22×D4×C12711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8C4×D4×C12714yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4C4×D4×C12714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4C4×D4×C12712yes—
713C2×C4#120×C12712yes—
714C2×C4#120×C12712yes—
715C2×C4C23×C4×C12711yescharacteristic
716C2×C4C22×D4×C12711yescharacteristic
717C2×C4C22×D4×C12711yescharacteristic
718C2×C4C2×#41×C12711yescharacteristic
719C2×C4C2×#41×C12711yescharacteristic
720C2×C4C2×#41×C12711yescharacteristic
721C8—22no—
722C8—22no—
723C8—41no—
724C8—41no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×C4×D4×C12711yescharacteristic
740C22C2×#120×C12711yescharacteristic
741C22#525×C12711yescharacteristic
742C22#576×C12711yescharacteristic
743C22#577×C12711yescharacteristic
744C22#578×C12711yescharacteristic
745C22#578×C12711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—24no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—81no—
757C4—81no—
758C4C2×C4×D4×C12711yescharacteristic
759C4C2×C4×D4×C12711yescharacteristic
760C4#525×C12711yescharacteristic
761C4#525×C12711yescharacteristic
762C2—42no—
763C2—44no—
764C2C4×#120×C12711yescharacteristic
765C2C127×#294711yescharacteristic
766C2C127×#295111yescharacteristic
767C2C127×#301111yescharacteristic
768C2C127×#301211yescharacteristic
769C2C127×#312011yescharacteristic
770C2C127×#312411yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#440×C127C2semidirect
4. C2×C4×Q16×C127C2semidirect
5. C127×#2323C2semidirect
6. C127×#1878C2semidirect
7. C127×#1877C2semidirect
8. C127×#1872C2semidirect
9. C127×#1863C2semidirect
10. C127×#1862C2semidirect
11. C127×#1852C2semidirect
13. C127×#1763C2semidirect
14. C4×#102×C127C2semidirect
15. C127×#1750C2semidirect
33. #452×C127C4semidirect
81. C2×Q16×C127C2×C4semidirect
84. C2×SD16×C127C2×C4semidirect
90. C22⋊Q8×C127C2×C4semidirect
140. #103×C127C2×C4semidirect
143. #102×C127C2×C4semidirect
145. C22⋊C8×C127C2×C4semidirect
376. #21465C127direct (N × H)
388. C2×#440C2×C127semidirect
389. C2×C4×Q16C2×C127semidirect
390. #2323C2×C127semidirect
391. #1878C2×C127semidirect
392. #1877C2×C127semidirect
393. #1872C2×C127semidirect
394. #1863C2×C127semidirect
395. #1862C2×C127semidirect
396. #1852C2×C127semidirect
398. #1763C2×C127semidirect
399. C4×#102C2×C127semidirect
400. #1750C2×C127semidirect
401. C127#21465direct (N × H)
419. #452C4×C127semidirect
467. C2×Q16C2×C4×C127semidirect
470. C2×SD16C2×C4×C127semidirect
476. C22⋊Q8C2×C4×C127semidirect
526. #103C2×C4×C127semidirect
529. #102C2×C4×C127semidirect
531. C22⋊C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1272
C2×#452×C1272
C2×#440×C1272
C2×C4×Q16×C1272
C127×#23232
C127×#18782
C127×#18772
C127×#18722
C127×#18632
C127×#18622
C127×#18522
C127×#17882
C127×#17632
C4×#102×C1272
C127×#17502
#21465127