Finite Group Databasebeta

← C127×#14004 #44577677

Subgroups — C127×#14004 #44577677

Order 32512.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic, complemented
2C2×#385×C127C211yesmaximal, characteristic
3C2×#385×C127C211yesmaximal, characteristic
4C2×#385×C127C211yesmaximal, characteristic
5C2×#380×C127C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
7C22×#95×C127C211yesmaximal, characteristic
8C127×#1444C211yesmaximal, characteristic, complemented
9C127×#1442C211yesmaximal, characteristic, complemented
10C127×#1441C211yesmaximal, characteristic, complemented
11C127×#1441C211yesmaximal, characteristic, complemented
12C127×#1436C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×C4⋊#95C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C42×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33#389×C127—24no—
34#385×C127—24no—
35#385×C127—24no—
36#385×C127C418yescomplemented
37#380×C127—24no—
38C4×C22⋊C4×C127—24no—
39C2×#95×C127—24no—
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C25×C127C2311yescharacteristic
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—22no—
64C23×C4×C127—22no—
65C23×C4×C127—22no—
66C23×C4×C127—22no—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—22no—
71C23×C4×C127—22no—
72C23×C4×C127—41no—
73C23×C4×C127—41no—
74C23×C4×C127—41no—
75C23×C4×C127—41no—
76C23×C4×C127—41no—
77C23×C4×C127—41no—
78C23×C4×C127C2×C414yes—
79C23×C4×C127Q814yes—
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C23×C4×C127C2311yescharacteristic
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2311yescharacteristic
88C23×C4×C127C2311yescharacteristic
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C23×C4×C127C2311yescharacteristic
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—22no—
97C2×C4⋊C4×C127—22no—
98C2×C4⋊C4×C127—22no—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127—22no—
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127—22no—
107C2×C4⋊C4×C127—22no—
108C2×C4⋊C4×C127—41no—
109C2×C4⋊C4×C127—41no—
110C2×C4⋊C4×C127—41no—
111C2×C4⋊C4×C127—41no—
112C2×C4⋊C4×C127—41no—
113C2×C4⋊C4×C127—41no—
114C2×C4⋊C4×C127—41no—
115C2×C4⋊C4×C127—41no—
116C2×C4⋊C4×C127C2×C414yescomplemented
117C2×C4⋊C4×C127C2×C414yescomplemented
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C22⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—22no—
124C2×C22⋊C4×C127—22no—
125C2×C22⋊C4×C127C2×C414yes—
126C2×C22⋊C4×C127C2×C414yes—
127C2×C22⋊C4×C127D414yes—
128C2×C22⋊C4×C127D414yes—
129C2×C22⋊C4×C127Q814yes—
130C2×C42×C127—22no—
131C2×C42×C127—22no—
132C2×C42×C127—22no—
133C2×C42×C127—22no—
134C2×C42×C127—41no—
135C2×C42×C127—41no—
136#95×C127—22no—
137#95×C127—22no—
138#95×C127—22no—
139#95×C127—22no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—22no—
146#95×C127—22no—
147#95×C127—22no—
148#95×C127—22no—
149#95×C127—41no—
150#95×C127—41no—
151#95×C127C2×C414yescomplemented
152#95×C127C2×C414yescomplemented
153#95×C127D414yes—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127—21no—
157C24×C127—21no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127C22×C412yes—
163C24×C127C2×D412yes—
164C24×C127C2×D412yes—
165C24×C127C2×Q812yes—
166C24×C127C2×Q812yes—
167C24×C127#4112yes—
168C24×C127#4112yes—
169C24×C127C2411yescharacteristic
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—28no—
187C22×C4×C127—28no—
188C22×C4×C127—28no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
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—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—28no—
238C22×C4×C127—28no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—44no—
254C22×C4×C127—44no—
255C22×C4×C127—44no—
256C22×C4×C127—44no—
257C22×C4×C127—44no—
258C22×C4×C127—44no—
259C22×C4×C127—44no—
260C22×C4×C127—44no—
261C22×C4×C127—44no—
262C22×C4×C127—44no—
263C22×C4×C127—44no—
264C22×C4×C127—44no—
265C22×C4×C127—44no—
266C22×C4×C127—44no—
267C22×C4×C127—44no—
268C22×C4×C127—44no—
269C22×C4×C127C22×C412yes—
270C22×C4×C127C22×C412yes—
271C22×C4×C127C22×C412yes—
272C22×C4×C127C22×C412yes—
273C22×C4×C127C22×C412yes—
274C22×C4×C127C22×C412yes—
275C22×C4×C127C2×D412yes—
276C22×C4×C127C2×D412yes—
277C22×C4×C127C2×D412yes—
278C22×C4×C127C2×D412yes—
279C22×C4×C127C2×D412yes—
280C22×C4×C127C2×D412yes—
281C22×C4×C127C2×D412yes—
282C22×C4×C127C2×Q812yes—
283C22×C4×C127C2×Q812yes—
284C22×C4×C127C2×Q812yes—
285C22×C4×C127C2×Q812yes—
286C22×C4×C127#4112yes—
287C22×C4×C127#4112yes—
288C22×C4×C127#4112yes—
289C4⋊C4×C127—28no—
290C4⋊C4×C127—44no—
291C4⋊C4×C127—44no—
292C4⋊C4×C127—44no—
293C4⋊C4×C127—44no—
294C4⋊C4×C127—44no—
295C4⋊C4×C127—44no—
296C4⋊C4×C127—44no—
297C22⋊C4×C127—28no—
298C22⋊C4×C127—28no—
299C22⋊C4×C127—44no—
300C22⋊C4×C127C4⋊C4116yescomplemented
301C42×C127—44no—
302C42×C127—44no—
303C23×C127—22no—
304C23×C127—22no—
305C23×C127—22no—
306C23×C127—22no—
307C23×C127—22no—
308C23×C127—22no—
309C23×C127—22no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—22no—
313C23×C127—22no—
314C23×C127—22no—
315C23×C127—22no—
316C23×C127—22no—
317C23×C127—22no—
318C23×C127—22no—
319C23×C127—22no—
320C23×C127—22no—
321C23×C127—22no—
322C23×C127—22no—
323C23×C127—22no—
324C23×C127—22no—
325C23×C127—22no—
326C23×C127—22no—
327C23×C127—22no—
328C23×C127—22no—
329C23×C127—22no—
330C23×C127—22no—
331C23×C127C2×C4⋊C414yes—
332C23×C127C4×D414yes—
333C23×C127C4×Q814yes—
334C23×C127#12114yes—
335C23×C127C22⋊Q814yes—
336C23×C127#12514yes—
337C23×C127C4⋊Q814yes—
338C23×C127C23×C411yescharacteristic
339C23×C127C22×D411yescharacteristic
340C23×C127C22×D411yescharacteristic
341C23×C127C22×D411yescharacteristic
342C23×C127C22×Q811yescharacteristic
343C23×C127C22×Q811yescharacteristic
344C23×C127C2×#4111yescharacteristic
345C23×C127C2×#4111yescharacteristic
346C23×C127C2×#4111yescharacteristic
347C23×C127C2×#4111yescharacteristic
348C23×C127C2×#4111yescharacteristic
349C23×C127H(5,𝔽2)11yescharacteristic
350C23×C127H(5,𝔽2)11yescharacteristic
351C23×C127H(5,𝔽2)11yescharacteristic
352C23×C1272−1+411yescharacteristic
353C2×C4×C127—22no—
354C2×C4×C127—22no—
355C2×C4×C127—22no—
356C2×C4×C127—22no—
357C2×C4×C127—22no—
358C2×C4×C127—22no—
359C2×C4×C127—22no—
360C2×C4×C127—22no—
361C2×C4×C127—22no—
362C2×C4×C127—22no—
363C2×C4×C127—22no—
364C2×C4×C127—22no—
365C2×C4×C127—22no—
366C2×C4×C127—22no—
367C2×C4×C127—22no—
368C2×C4×C127—22no—
369C2×C4×C127—22no—
370C2×C4×C127—22no—
371C2×C4×C127—22no—
372C2×C4×C127—22no—
373C2×C4×C127—22no—
374C2×C4×C127—22no—
375C2×C4×C127—22no—
376C2×C4×C127—22no—
377C2×C4×C127—22no—
378C2×C4×C127—22no—
379C2×C4×C127—22no—
380C2×C4×C127—22no—
381C2×C4×C127—22no—
382C2×C4×C127—22no—
383C2×C4×C127—22no—
384C2×C4×C127—22no—
385C2×C4×C127—22no—
386C2×C4×C127—22no—
387C2×C4×C127—22no—
388C2×C4×C127—22no—
389C2×C4×C127—22no—
390C2×C4×C127—22no—
391C2×C4×C127—22no—
392C2×C4×C127—22no—
393C2×C4×C127—22no—
394C2×C4×C127—22no—
395C2×C4×C127—22no—
396C2×C4×C127—22no—
397C2×C4×C127—22no—
398C2×C4×C127—22no—
399C2×C4×C127—22no—
400C2×C4×C127—22no—
401C2×C4×C127—416no—
402C2×C4×C127—416no—
403C2×C4×C127—416no—
404C2×C4×C127—41no—
405C2×C4×C127—41no—
406C2×C4×C127—41no—
407C2×C4×C127—41no—
408C2×C4×C127—41no—
409C2×C4×C127—41no—
410C2×C4×C127—41no—
411C2×C4×C127—41no—
412C2×C4×C127—41no—
413C2×C4×C127—41no—
414C2×C4×C127—41no—
415C2×C4×C127—41no—
416C2×C4×C127—41no—
417C2×C4×C127—41no—
418C2×C4×C127—41no—
419C2×C4×C127—41no—
420C2×C4×C127—41no—
421C2×C4×C127—41no—
422C2×C4×C127—41no—
423C2×C4×C127—41no—
424C2×C4×C127—41no—
425C2×C4×C127—41no—
426C2×C4×C127—41no—
427C2×C4×C127—41no—
428C2×C4×C127—41no—
429C2×C4×C127—41no—
430C2×C4×C127—41no—
431C2×C4×C127—41no—
432C2×C4×C127—41no—
433C2×C4×C127—41no—
434C2×C4×C127—41no—
435C2×C4×C127—41no—
436C2×C4×C127—41no—
437C2×C4×C127—41no—
438C2×C4×C127—41no—
439C2×C4×C127—41no—
440C2×C4×C127—41no—
441C2×C4×C127—41no—
442C2×C4×C127—41no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127—41no—
449C2×C4×C127—41no—
450C2×C4×C127C2×C4⋊C414yes—
451C2×C4×C127C2×C4⋊C414yes—
452C2×C4×C127C4×D414yes—
453C2×C4×C127C22⋊Q814yes—
454C22×C127—24no—
455C22×C127—24no—
456C22×C127—24no—
457C22×C127—24no—
458C22×C127—24no—
459C22×C127—24no—
460C22×C127—24no—
461C22×C127—24no—
462C22×C127—24no—
463C22×C127—24no—
464C22×C127—24no—
465C22×C127—24no—
466C22×C127—24no—
467C22×C127—24no—
468C22×C127#38918yescomplemented
469C22×C127C22×C4⋊C411yescharacteristic
470C22×C127C2×C4×D411yescharacteristic
471C22×C127C2×C4×D411yescharacteristic
472C22×C127C2×C4×Q811yescharacteristic
473C22×C127C4×#4111yescharacteristic
474C22×C127#51811yescharacteristic
475C22×C127#52011yescharacteristic
476C22×C127C2×#12111yescharacteristic
477C22×C127C2×C22⋊Q811yescharacteristic
478C22×C127C2×C22⋊Q811yescharacteristic
479C22×C127#52511yescharacteristic
480C22×C127C2×#12511yescharacteristic
481C22×C127#52911yescharacteristic
482C22×C127C2×C4⋊Q811yescharacteristic
483C22×C127#53311yescharacteristic
484C22×C127#53811yescharacteristic
485C22×C127#53911yescharacteristic
486C22×C127#54311yescharacteristic
487C22×C127#54411yescharacteristic
488C22×C127D4211yescharacteristic
489C22×C127D4211yescharacteristic
490C22×C127#54611yescharacteristic
491C22×C127#54611yescharacteristic
492C22×C127#54611yescharacteristic
493C22×C127#54611yescharacteristic
494C22×C127#54611yescharacteristic
495C22×C127#54711yescharacteristic
496C22×C127#54711yescharacteristic
497C22×C127D4×Q811yescharacteristic
498C22×C127#55111yescharacteristic
499C22×C127#55111yescharacteristic
500C22×C127#55211yescharacteristic
501C22×C127#55411yescharacteristic
502C22×C127#55411yescharacteristic
503C22×C127#55411yescharacteristic
504C4×C127—24no—
505C4×C127—24no—
506C4×C127—24no—
507C4×C127—24no—
508C4×C127—42no—
509C4×C127—42no—
510C4×C127—42no—
511C4×C127—42no—
512C4×C127—42no—
513C4×C127—42no—
514C4×C127—42no—
515C4×C127—42no—
516C4×C127—81no—
517C4×C127—81no—
518#14004C12711yesmaximal, characteristic, direct product factor, Sylow
519C2×C127—28no—
520C2×C127C2×#38911yescharacteristic
521C2×C127C4×C22⋊Q811yescharacteristic
522C2×C127#232911yescharacteristic
523C2×C127D4×C4⋊C411yescharacteristic
524C2×C127#234911yescharacteristic
525C2×C127#235811yescharacteristic
526C2×C127#235911yescharacteristic
527C2×C127#242411yescharacteristic
528C2×C127#242511yescharacteristic
529C2×C127#243711yescharacteristic
530C2×C127#243811yescharacteristic
531C2×C127#244011yescharacteristic
532C2×C127#247311yescharacteristic
533C2×C127#250511yescharacteristic
534C2×C127#254911yescharacteristic
535C2×#389C2×C12711yescharacteristic, complemented
536C2×#385C2×C12711yescharacteristic
537C2×#385C2×C12711yescharacteristic
538C2×#385C2×C12711yescharacteristic
539C2×#380C2×C12711yescharacteristic
540C2×C4×C22⋊C4C2×C12711yescharacteristic
541C22×#95C2×C12711yescharacteristic
542#1444C2×C12711yescharacteristic, complemented
543#1442C2×C12711yescharacteristic, complemented
544#1441C2×C12711yescharacteristic, complemented
545#1441C2×C12711yescharacteristic, complemented
546#1436C2×C12711yescharacteristic, complemented
547#1436C2×C12711yescharacteristic, complemented
548C4⋊#95C2×C12711yescharacteristic, complemented
549C22⋊#95C2×C12711yescharacteristic
550C127#1400411yescharacteristic, direct product factor, Sylow
551C24×C4C22×C12711yescharacteristic
552C24×C4C22×C12711yescharacteristic
553C24×C4C22×C12711yescharacteristic
554C22×C4⋊C4C22×C12711yescharacteristic
555C22×C4⋊C4C22×C12711yescharacteristic
556C22×C4⋊C4C22×C12711yescharacteristic
557C22×C4⋊C4C22×C12711yescharacteristic
558C22×C4⋊C4C22×C12711yescharacteristic
559C22×C4⋊C4C22×C12711yescharacteristic
560C22×C4⋊C4C22×C12711yescharacteristic
561C22×C4⋊C4C22×C12711yescharacteristic
562C22×C22⋊C4C22×C12711yescharacteristic
563C22×C22⋊C4C22×C12711yescharacteristic
564C22×C22⋊C4C22×C12711yescharacteristic
565C22×C22⋊C4C22×C12711yescharacteristic
566C22×C42C22×C12711yescharacteristic
567C22×C42C22×C12711yescharacteristic
568#389—24no—
569#385—24no—
570#385—24no—
571#385C4×C12718yescomplemented
572#380—24no—
573C4×C22⋊C4—24no—
574C2×#95—24no—
575C2×#95C22×C12711yescharacteristic
576C2×#95C22×C12711yescharacteristic
577C2×#95C22×C12711yescharacteristic
578C2×#95C22×C12711yescharacteristic
579C2×#95C22×C12711yescharacteristic
580C2×#95C22×C12711yescharacteristic
581C2×#95C22×C12711yescharacteristic
582C2×#95C22×C12711yescharacteristic
583C2×#95C22×C12711yescharacteristic
584C2×#95C22×C12711yescharacteristic
585C2×#95C22×C12711yescharacteristic
586C2×#95C22×C12711yescharacteristic
587C2×#95C22×C12711yescharacteristic
588C2×#95C22×C12711yescharacteristic
589C2×#95C22×C12711yescharacteristic
590C2×#95C22×C12711yescharacteristic
591C2×#95C22×C12711yescharacteristic
592C2×#95C22×C12711yescharacteristic
593C25C23×C12711yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4C2×C4×C12714yes—
614C23×C4Q8×C12714yes—
615C23×C4C23×C12711yescharacteristic
616C23×C4C23×C12711yescharacteristic
617C23×C4C23×C12711yescharacteristic
618C23×C4C23×C12711yescharacteristic
619C23×C4C23×C12711yescharacteristic
620C23×C4C23×C12711yescharacteristic
621C23×C4C23×C12711yescharacteristic
622C23×C4C23×C12711yescharacteristic
623C23×C4C23×C12711yescharacteristic
624C23×C4C23×C12711yescharacteristic
625C23×C4C23×C12711yescharacteristic
626C23×C4C23×C12711yescharacteristic
627C23×C4C23×C12711yescharacteristic
628C23×C4C23×C12711yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4C2×C4×C12714yescomplemented
652C2×C4⋊C4C2×C4×C12714yescomplemented
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4C2×C4×C12714yes—
661C2×C22⋊C4C2×C4×C12714yes—
662C2×C22⋊C4D4×C12714yes—
663C2×C22⋊C4D4×C12714yes—
664C2×C22⋊C4Q8×C12714yes—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—41no—
670C2×C42—41no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—41no—
685#95—41no—
686#95C2×C4×C12714yescomplemented
687#95C2×C4×C12714yescomplemented
688#95D4×C12714yes—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C22×C4×C12712yes—
698C24C2×D4×C12712yes—
699C24C2×D4×C12712yes—
700C24C2×Q8×C12712yes—
701C24C2×Q8×C12712yes—
702C24#41×C12712yes—
703C24#41×C12712yes—
704C24C24×C12711yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4C22×C4×C12712yes—
805C22×C4C22×C4×C12712yes—
806C22×C4C22×C4×C12712yes—
807C22×C4C22×C4×C12712yes—
808C22×C4C22×C4×C12712yes—
809C22×C4C22×C4×C12712yes—
810C22×C4C2×D4×C12712yes—
811C22×C4C2×D4×C12712yes—
812C22×C4C2×D4×C12712yes—
813C22×C4C2×D4×C12712yes—
814C22×C4C2×D4×C12712yes—
815C22×C4C2×D4×C12712yes—
816C22×C4C2×D4×C12712yes—
817C22×C4C2×Q8×C12712yes—
818C22×C4C2×Q8×C12712yes—
819C22×C4C2×Q8×C12712yes—
820C22×C4C2×Q8×C12712yes—
821C22×C4#41×C12712yes—
822C22×C4#41×C12712yes—
823C22×C4#41×C12712yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4C4⋊C4×C127116yescomplemented
836C42—44no—
837C42—44no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊C4×C12714yes—
867C23C4×D4×C12714yes—
868C23C4×Q8×C12714yes—
869C23#121×C12714yes—
870C23C22⋊Q8×C12714yes—
871C23#125×C12714yes—
872C23C4⋊Q8×C12714yes—
873C23C23×C4×C12711yescharacteristic
874C23C22×D4×C12711yescharacteristic
875C23C22×D4×C12711yescharacteristic
876C23C22×D4×C12711yescharacteristic
877C23C22×Q8×C12711yescharacteristic
878C23C22×Q8×C12711yescharacteristic
879C23C2×#41×C12711yescharacteristic
880C23C2×#41×C12711yescharacteristic
881C23C2×#41×C12711yescharacteristic
882C23C2×#41×C12711yescharacteristic
883C23C2×#41×C12711yescharacteristic
884C23H(5,𝔽2)×C12711yescharacteristic
885C23H(5,𝔽2)×C12711yescharacteristic
886C23H(5,𝔽2)×C12711yescharacteristic
887C232−1+4×C12711yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—416no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4C2×C4⋊C4×C12714yes—
986C2×C4C2×C4⋊C4×C12714yes—
987C2×C4C4×D4×C12714yes—
988C2×C4C22⋊Q8×C12714yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#389×C12718yescomplemented
1004C22C22×C4⋊C4×C12711yescharacteristic
1005C22C2×C4×D4×C12711yescharacteristic
1006C22C2×C4×D4×C12711yescharacteristic
1007C22C2×C4×Q8×C12711yescharacteristic
1008C22C4×#41×C12711yescharacteristic
1009C22#518×C12711yescharacteristic
1010C22#520×C12711yescharacteristic
1011C22C2×#121×C12711yescharacteristic
1012C22C2×C22⋊Q8×C12711yescharacteristic
1013C22C2×C22⋊Q8×C12711yescharacteristic
1014C22#525×C12711yescharacteristic
1015C22C2×#125×C12711yescharacteristic
1016C22#529×C12711yescharacteristic
1017C22C2×C4⋊Q8×C12711yescharacteristic
1018C22#533×C12711yescharacteristic
1019C22#538×C12711yescharacteristic
1020C22#539×C12711yescharacteristic
1021C22#543×C12711yescharacteristic
1022C22#544×C12711yescharacteristic
1023C22D42×C12711yescharacteristic
1024C22D42×C12711yescharacteristic
1025C22#546×C12711yescharacteristic
1026C22#546×C12711yescharacteristic
1027C22#546×C12711yescharacteristic
1028C22#546×C12711yescharacteristic
1029C22#546×C12711yescharacteristic
1030C22#547×C12711yescharacteristic
1031C22#547×C12711yescharacteristic
1032C22D4×Q8×C12711yescharacteristic
1033C22#551×C12711yescharacteristic
1034C22#551×C12711yescharacteristic
1035C22#552×C12711yescharacteristic
1036C22#554×C12711yescharacteristic
1037C22#554×C12711yescharacteristic
1038C22#554×C12711yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×#389×C12711yescharacteristic
1055C2C4×C22⋊Q8×C12711yescharacteristic
1056C2C127×#232911yescharacteristic
1057C2D4×C4⋊C4×C12711yescharacteristic
1058C2C127×#234911yescharacteristic
1059C2C127×#235811yescharacteristic
1060C2C127×#235911yescharacteristic
1061C2C127×#242411yescharacteristic
1062C2C127×#242511yescharacteristic
1063C2C127×#243711yescharacteristic
1064C2C127×#243811yescharacteristic
1065C2C127×#244011yescharacteristic
1066C2C127×#247311yescharacteristic
1067C2C127×#250511yescharacteristic
1068C2C127×#254911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C127C2semidirect
8. C127×#1444C2semidirect
9. C127×#1442C2semidirect
10. C127×#1441C2semidirect
11. C127×#1441C2semidirect
12. C127×#1436C2semidirect
13. C127×#1436C2semidirect
14. C127×C4⋊#95C2semidirect
36. #385×C127C4semidirect
116. C2×C4⋊C4×C127C2×C4semidirect
117. C2×C4⋊C4×C127C2×C4semidirect
151. #95×C127C2×C4semidirect
152. #95×C127C2×C4semidirect
300. C22⋊C4×C127C4⋊C4semidirect
468. C22×C127#389semidirect
518. #14004C127direct (N × H)
535. C2×#389C2×C127semidirect
542. #1444C2×C127semidirect
543. #1442C2×C127semidirect
544. #1441C2×C127semidirect
545. #1441C2×C127semidirect
546. #1436C2×C127semidirect
547. #1436C2×C127semidirect
548. C4⋊#95C2×C127semidirect
550. C127#14004direct (N × H)
571. #385C4×C127semidirect
651. C2×C4⋊C4C2×C4×C127semidirect
652. C2×C4⋊C4C2×C4×C127semidirect
686. #95C2×C4×C127semidirect
687. #95C2×C4×C127semidirect
835. C22⋊C4C4⋊C4×C127semidirect
1003. C22#389×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#385×C1272
C2×#380×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14442
C127×#14422
C127×#14412
C127×#14362
C127×C4⋊#952
C127×C22⋊#952
#14004127