Finite Group Databasebeta

← C127×#15280 #44578953

Subgroups — C127×#15280 #44578953

Order 32512.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
2C2×#396×C127C211yesmaximal, characteristic, complemented
3C2×#393×C127C211yesmaximal, characteristic, complemented
4C2×#391×C127C211yesmaximal, characteristic, complemented
5C2×#390×C127C211yesmaximal, characteristic
6C2×#386×C127C211yesmaximal, characteristic
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1441C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C2×C22⋊Q8×C127—24no—
20C2×C22⋊Q8×C127—24no—
21C2×C22⋊Q8×C127—24no—
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C4⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic
36C22×C22⋊C4×C127C2211yescharacteristic
37C22×C22⋊C4×C127C2211yescharacteristic
38C22×C22⋊C4×C127C2211yescharacteristic
39C22×C42×C127C2211yescharacteristic
40#396×C127—24no—
41#393×C127—24no—
42#391×C127—24no—
43#390×C127—24no—
44#386×C127—24no—
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
58C2×#95×C127C2211yescharacteristic
59C25×C127C2311yescharacteristic
60C25×C127C2311yescharacteristic
61C22×Q8×C127—22no—
62C22×Q8×C127—22no—
63C22×Q8×C127—22no—
64C22×Q8×C127—22no—
65C22×Q8×C127—41no—
66C22×Q8×C127—41no—
67C22×Q8×C127D414yescomplemented
68C22×D4×C127—22no—
69C22×D4×C127—22no—
70C22×D4×C127—22no—
71C22×D4×C127—22no—
72C22×D4×C127—41no—
73C22×D4×C127—41no—
74C22×D4×C127Q814yescomplemented
75C23×C4×C127—22no—
76C23×C4×C127—22no—
77C23×C4×C127—22no—
78C23×C4×C127—22no—
79C23×C4×C127—22no—
80C23×C4×C127—41no—
81C23×C4×C127—41no—
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
94C23×C4×C127C2311yescharacteristic
95C22⋊Q8×C127—232no—
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—22no—
109C2×C4⋊C4×C127—41no—
110C2×C4⋊C4×C127—41no—
111C2×C4⋊C4×C127—41no—
112C2×C4⋊C4×C127—41no—
113C2×C4⋊C4×C127D414yescomplemented
114C2×C22⋊C4×C127—22no—
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—22no—
117C2×C22⋊C4×C127—22no—
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×C127—22no—
126C2×C22⋊C4×C127—22no—
127C2×C22⋊C4×C127—22no—
128C2×C22⋊C4×C127—22no—
129C2×C22⋊C4×C127—22no—
130C2×C22⋊C4×C127—22no—
131C2×C22⋊C4×C127—22no—
132C2×C22⋊C4×C127—22no—
133C2×C22⋊C4×C127—22no—
134C2×C22⋊C4×C127—22no—
135C2×C22⋊C4×C127—22no—
136C2×C22⋊C4×C127—41no—
137C2×C22⋊C4×C127—41no—
138C2×C22⋊C4×C127—41no—
139C2×C22⋊C4×C127—41no—
140C2×C22⋊C4×C127—41no—
141C2×C22⋊C4×C127—41no—
142C2×C22⋊C4×C127—41no—
143C2×C22⋊C4×C127—41no—
144C2×C22⋊C4×C127—41no—
145C2×C22⋊C4×C127—41no—
146C2×C22⋊C4×C127D414yes—
147C2×C42×C127—22no—
148C2×C42×C127—22no—
149C2×C42×C127—41no—
150#95×C127—22no—
151#95×C127—22no—
152#95×C127—22no—
153#95×C127—22no—
154#95×C127—22no—
155#95×C127—22no—
156#95×C127—22no—
157#95×C127—22no—
158#95×C127—22no—
159#95×C127—22no—
160#95×C127—41no—
161#95×C127—41no—
162#95×C127—41no—
163#95×C127D414yes—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×C127—21no—
183C24×C127—21no—
184C24×C127—21no—
185C24×C127—21no—
186C24×C127—21no—
187C24×C127—21no—
188C24×C127—21no—
189C24×C127—21no—
190C24×C127C2×D412yes—
191C24×C127C2×Q812yes—
192C24×C127C2×Q812yes—
193C24×C127#4112yes—
194C24×C127C2411yescharacteristic
195C2×Q8×C127—28no—
196C2×Q8×C127—28no—
197C2×Q8×C127—44no—
198C2×Q8×C127—44no—
199C2×Q8×C127—44no—
200C2×Q8×C127—44no—
201C2×Q8×C127—44no—
202C2×D4×C127—28no—
203C2×D4×C127—28no—
204C2×D4×C127—44no—
205C2×D4×C127—44no—
206C2×D4×C127—44no—
207C2×D4×C127—44no—
208C2×D4×C127—44no—
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—28no—
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—21no—
238C22×C4×C127—21no—
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—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127—21no—
267C22×C4×C127—21no—
268C22×C4×C127—21no—
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—44no—
287C22×C4×C127—44no—
288C22×C4×C127—44no—
289C22×C4×C127—44no—
290C22×C4×C127—44no—
291C22×C4×C127—44no—
292C22×C4×C127C2×D412yes—
293C22×C4×C127C2×D412yes—
294C22×C4×C127C2×D412yes—
295C22×C4×C127C2×D412yes—
296C22×C4×C127C2×D412yes—
297C22×C4×C127C2×D412yes—
298C22×C4×C127C2×D412yes—
299C22×C4×C127C2×D412yes—
300C22×C4×C127C2×D412yes—
301C22×C4×C127C2×D412yes—
302C22×C4×C127C2×D412yes—
303C22×C4×C127C2×Q812yes—
304C22×C4×C127#4112yes—
305C22×C4×C127#4112yes—
306C22×C4×C127#4112yes—
307C4⋊C4×C127—28no—
308C4⋊C4×C127—28no—
309C4⋊C4×C127—28no—
310C4⋊C4×C127—44no—
311C4⋊C4×C127—44no—
312C4⋊C4×C127—44no—
313C22⋊C4×C127—28no—
314C22⋊C4×C127—28no—
315C22⋊C4×C127—44no—
316C22⋊C4×C127—44no—
317C22⋊C4×C127—44no—
318C22⋊C4×C127—44no—
319C22⋊C4×C127—44no—
320C22⋊C4×C127—44no—
321C22⋊C4×C127—44no—
322C22⋊C4×C127—44no—
323C22⋊C4×C127—44no—
324C42×C127—44no—
325C23×C127—22no—
326C23×C127—22no—
327C23×C127—22no—
328C23×C127—22no—
329C23×C127—22no—
330C23×C127—22no—
331C23×C127—22no—
332C23×C127—22no—
333C23×C127—22no—
334C23×C127—22no—
335C23×C127—22no—
336C23×C127—22no—
337C23×C127—22no—
338C23×C127—22no—
339C23×C127—22no—
340C23×C127—22no—
341C23×C127—22no—
342C23×C127—22no—
343C23×C127—22no—
344C23×C127—22no—
345C23×C127—22no—
346C23×C127—22no—
347C23×C127—22no—
348C23×C127—22no—
349C23×C127—22no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—41no—
353C23×C127—41no—
354C23×C127—41no—
355C23×C127—41no—
356C23×C127—41no—
357C23×C127—41no—
358C23×C127—41no—
359C23×C127—41no—
360C23×C127—41no—
361C23×C127—41no—
362C23×C127—41no—
363C23×C127—41no—
364C23×C127—41no—
365C23×C127—41no—
366C23×C127—41no—
367C23×C127—41no—
368C23×C127—41no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127—41no—
372C23×C127—41no—
373C23×C127—41no—
374C23×C127—41no—
375C23×C127—41no—
376C23×C127—41no—
377C23×C127—41no—
378C23×C127—41no—
379C23×C127—41no—
380C23×C127—41no—
381C23×C127—41no—
382C23×C127—41no—
383C23×C127—41no—
384C23×C127—41no—
385C23×C127—41no—
386C23×C127—41no—
387C23×C127—41no—
388C23×C127—41no—
389C23×C127—41no—
390C23×C127—41no—
391C23×C127—41no—
392C23×C127—41no—
393C23×C127—41no—
394C23×C127C22⋊Q814yes—
395C23×C127C22×D411yescharacteristic
396C23×C127C22×D411yescharacteristic
397C23×C127C22×D411yescharacteristic
398C23×C127C22×D411yescharacteristic
399C23×C127C22×Q811yescharacteristic
400C23×C127C2×#4111yescharacteristic
401C23×C127C2×#4111yescharacteristic
402C23×C127C2×#4111yescharacteristic
403C23×C127C2×#4111yescharacteristic
404C23×C127H(5,𝔽2)11yescharacteristic
405C23×C127H(5,𝔽2)11yescharacteristic
406C23×C127H(5,𝔽2)11yescharacteristic
407C23×C127H(5,𝔽2)11yescharacteristic
408C23×C1272−1+411yescharacteristic
409C23×C1272−1+411yescharacteristic
410Q8×C127—416no—
411D4×C127—416no—
412C2×C4×C127—22no—
413C2×C4×C127—22no—
414C2×C4×C127—22no—
415C2×C4×C127—22no—
416C2×C4×C127—22no—
417C2×C4×C127—22no—
418C2×C4×C127—22no—
419C2×C4×C127—22no—
420C2×C4×C127—22no—
421C2×C4×C127—22no—
422C2×C4×C127—22no—
423C2×C4×C127—22no—
424C2×C4×C127—22no—
425C2×C4×C127—22no—
426C2×C4×C127—22no—
427C2×C4×C127—22no—
428C2×C4×C127—22no—
429C2×C4×C127—22no—
430C2×C4×C127—22no—
431C2×C4×C127—22no—
432C2×C4×C127—22no—
433C2×C4×C127—22no—
434C2×C4×C127—22no—
435C2×C4×C127—22no—
436C2×C4×C127—22no—
437C2×C4×C127—22no—
438C2×C4×C127—22no—
439C2×C4×C127—22no—
440C2×C4×C127—22no—
441C2×C4×C127—22no—
442C2×C4×C127—22no—
443C2×C4×C127—22no—
444C2×C4×C127—22no—
445C2×C4×C127—22no—
446C2×C4×C127—22no—
447C2×C4×C127—22no—
448C2×C4×C127—416no—
449C2×C4×C127—41no—
450C2×C4×C127—41no—
451C2×C4×C127—41no—
452C2×C4×C127—41no—
453C2×C4×C127—41no—
454C2×C4×C127—41no—
455C2×C4×C127—41no—
456C2×C4×C127—41no—
457C2×C4×C127—41no—
458C2×C4×C127—41no—
459C2×C4×C127—41no—
460C2×C4×C127—41no—
461C2×C4×C127—41no—
462C2×C4×C127—41no—
463C2×C4×C127—41no—
464C2×C4×C127—41no—
465C2×C4×C127—41no—
466C2×C4×C127—41no—
467C2×C4×C127—41no—
468C2×C4×C127—41no—
469C2×C4×C127—41no—
470C2×C4×C127—41no—
471C2×C4×C127—41no—
472C2×C4×C127—41no—
473C2×C4×C127—41no—
474C2×C4×C127—41no—
475C2×C4×C127—41no—
476C2×C4×C127—41no—
477C2×C4×C127—41no—
478C2×C4×C127—41no—
479C2×C4×C127—41no—
480C2×C4×C127—41no—
481C2×C4×C127—41no—
482C2×C4×C127—41no—
483C2×C4×C127—41no—
484C2×C4×C127—41no—
485C2×C4×C127—41no—
486C2×C4×C127—41no—
487C2×C4×C127—41no—
488C2×C4×C127—41no—
489C2×C4×C127—41no—
490C2×C4×C127—41no—
491C2×C4×C127—41no—
492C2×C4×C127—41no—
493C2×C4×C127—41no—
494C2×C4×C127—41no—
495C2×C4×C127—41no—
496C2×C4×C127—41no—
497C2×C4×C127—41no—
498C2×C4×C127—41no—
499C2×C4×C127—41no—
500C2×C4×C127—41no—
501C2×C4×C127#12014yes—
502C2×C4×C127#12114yes—
503C2×C4×C127C22⋊Q814yescomplemented
504C22×C127—24no—
505C22×C127—24no—
506C22×C127—24no—
507C22×C127—42no—
508C22×C127—42no—
509C22×C127—42no—
510C22×C127—42no—
511C22×C127—42no—
512C22×C127—42no—
513C22×C127—42no—
514C22×C127—42no—
515C22×C127—42no—
516C22×C127—42no—
517C22×C127—42no—
518C22×C127—42no—
519C22×C127—42no—
520C22×C127—42no—
521C22×C127—42no—
522C22×C127—42no—
523C22×C127—42no—
524C22×C127—42no—
525C22×C127—42no—
526C22×C127—81no—
527C22×C127—81no—
528C22×C127—81no—
529C22×C127—81no—
530C22×C127—81no—
531C22×C127—81no—
532C22×C127—81no—
533C22×C127—81no—
534C22×C127C2×#12011yescharacteristic
535C22×C127C2×#12111yescharacteristic
536C22×C127C2×C22⋊Q811yescharacteristic
537C22×C127C2×C22⋊Q811yescharacteristic
538C22×C127#52911yescharacteristic
539C22×C127#53211yescharacteristic
540C22×C127#53411yescharacteristic
541C22×C127#53511yescharacteristic
542C22×C127#53611yescharacteristic
543C22×C127#53711yescharacteristic
544C22×C127#53811yescharacteristic
545C22×C127#53911yescharacteristic
546C22×C127#54211yescharacteristic
547C22×C127#54211yescharacteristic
548C22×C127#54311yescharacteristic
549C22×C127D4211yescharacteristic
550C22×C127D4211yescharacteristic
551C22×C127#54611yescharacteristic
552C22×C127#54611yescharacteristic
553C22×C127#54611yescharacteristic
554C22×C127#54611yescharacteristic
555C22×C127#54611yescharacteristic
556C22×C127#54811yescharacteristic
557C22×C127#54811yescharacteristic
558C22×C127#54811yescharacteristic
559C22×C127D4×Q811yescharacteristic
560C22×C127D4×Q811yescharacteristic
561C22×C127#55011yescharacteristic
562C22×C127#55011yescharacteristic
563C22×C127#55111yescharacteristic
564C22×C127#55411yescharacteristic
565C22×C127#55411yescharacteristic
566C22×C127#55611yescharacteristic
567C22×C127#56211yescharacteristic
568C22×C127#56211yescharacteristic
569C4×C127—24no—
570C4×C127—24no—
571C4×C127—24no—
572C4×C127—42no—
573C4×C127—42no—
574C4×C127—42no—
575C4×C127—42no—
576C4×C127—42no—
577C4×C127—42no—
578C4×C127—81no—
579C4×C127—81no—
580C4×C127—81no—
581C4×C127—81no—
582#15280C12711yesmaximal, characteristic, direct product factor, Sylow
583C2×C127—44no—
584C2×C127—82no—
585C2×C127#240911yescharacteristic
586C2×C127#241011yescharacteristic
587C2×C127#242611yescharacteristic
588C2×C127#243111yescharacteristic
589C2×C127#243711yescharacteristic
590C2×C127#245011yescharacteristic
591C2×C127#245211yescharacteristic
592C2×C127#253811yescharacteristic
593C2×C127#256011yescharacteristic
594C2×C127#267611yescharacteristic
595C2×C127#268111yescharacteristic
596C2×C127#269211yescharacteristic
597C2×C127#270011yescharacteristic
598C2×C127#273011yescharacteristic
599C2×C127#273211yescharacteristic
600C22×C22⋊Q8C2×C12711yescharacteristic, complemented
601C2×#396C2×C12711yescharacteristic, complemented
602C2×#393C2×C12711yescharacteristic, complemented
603C2×#391C2×C12711yescharacteristic, complemented
604C2×#390C2×C12711yescharacteristic
605C2×#386C2×C12711yescharacteristic
606#1444C2×C12711yescharacteristic, complemented
607#1441C2×C12711yescharacteristic, complemented
608#1439C2×C12711yescharacteristic, complemented
609#1439C2×C12711yescharacteristic, complemented
610#1439C2×C12711yescharacteristic, complemented
611#1439C2×C12711yescharacteristic, complemented
612#1438C2×C12711yescharacteristic
613#1436C2×C12711yescharacteristic, complemented
614C22⋊#95C2×C12711yescharacteristic, complemented
615C127#1528011yescharacteristic, direct product factor, Sylow
616C23×Q8C22×C12711yescharacteristic
617C23×D4C22×C12711yescharacteristic
618C24×C4C22×C12711yescharacteristic
619C2×C22⋊Q8—24no—
620C2×C22⋊Q8—24no—
621C2×C22⋊Q8—24no—
622C22×C4⋊C4C22×C12711yescharacteristic
623C22×C4⋊C4C22×C12711yescharacteristic
624C22×C4⋊C4C22×C12711yescharacteristic
625C22×C4⋊C4C22×C12711yescharacteristic
626C22×C4⋊C4C22×C12711yescharacteristic
627C22×C4⋊C4C22×C12711yescharacteristic
628C22×C22⋊C4C22×C12711yescharacteristic
629C22×C22⋊C4C22×C12711yescharacteristic
630C22×C22⋊C4C22×C12711yescharacteristic
631C22×C22⋊C4C22×C12711yescharacteristic
632C22×C22⋊C4C22×C12711yescharacteristic
633C22×C22⋊C4C22×C12711yescharacteristic
634C22×C22⋊C4C22×C12711yescharacteristic
635C22×C22⋊C4C22×C12711yescharacteristic
636C22×C22⋊C4C22×C12711yescharacteristic
637C22×C22⋊C4C22×C12711yescharacteristic
638C22×C22⋊C4C22×C12711yescharacteristic
639C22×C42C22×C12711yescharacteristic
640#396—24no—
641#393—24no—
642#391—24no—
643#390—24no—
644#386—24no—
645C2×#95C22×C12711yescharacteristic
646C2×#95C22×C12711yescharacteristic
647C2×#95C22×C12711yescharacteristic
648C2×#95C22×C12711yescharacteristic
649C2×#95C22×C12711yescharacteristic
650C2×#95C22×C12711yescharacteristic
651C2×#95C22×C12711yescharacteristic
652C2×#95C22×C12711yescharacteristic
653C2×#95C22×C12711yescharacteristic
654C2×#95C22×C12711yescharacteristic
655C2×#95C22×C12711yescharacteristic
656C2×#95C22×C12711yescharacteristic
657C2×#95C22×C12711yescharacteristic
658C2×#95C22×C12711yescharacteristic
659C25C23×C12711yescharacteristic
660C25C23×C12711yescharacteristic
661C22×Q8—22no—
662C22×Q8—22no—
663C22×Q8—22no—
664C22×Q8—22no—
665C22×Q8—41no—
666C22×Q8—41no—
667C22×Q8D4×C12714yescomplemented
668C22×D4—22no—
669C22×D4—22no—
670C22×D4—22no—
671C22×D4—22no—
672C22×D4—41no—
673C22×D4—41no—
674C22×D4Q8×C12714yescomplemented
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4C23×C12711yescharacteristic
683C23×C4C23×C12711yescharacteristic
684C23×C4C23×C12711yescharacteristic
685C23×C4C23×C12711yescharacteristic
686C23×C4C23×C12711yescharacteristic
687C23×C4C23×C12711yescharacteristic
688C23×C4C23×C12711yescharacteristic
689C23×C4C23×C12711yescharacteristic
690C23×C4C23×C12711yescharacteristic
691C23×C4C23×C12711yescharacteristic
692C23×C4C23×C12711yescharacteristic
693C23×C4C23×C12711yescharacteristic
694C23×C4C23×C12711yescharacteristic
695C22⋊Q8—232no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4D4×C12714yescomplemented
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4D4×C12714yes—
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—41no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—41no—
761#95—41no—
762#95—41no—
763#95D4×C12714yes—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24C2×D4×C12712yes—
791C24C2×Q8×C12712yes—
792C24C2×Q8×C12712yes—
793C24#41×C12712yes—
794C24C24×C12711yescharacteristic
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4C2×D4×C12712yes—
893C22×C4C2×D4×C12712yes—
894C22×C4C2×D4×C12712yes—
895C22×C4C2×D4×C12712yes—
896C22×C4C2×D4×C12712yes—
897C22×C4C2×D4×C12712yes—
898C22×C4C2×D4×C12712yes—
899C22×C4C2×D4×C12712yes—
900C22×C4C2×D4×C12712yes—
901C22×C4C2×D4×C12712yes—
902C22×C4C2×D4×C12712yes—
903C22×C4C2×Q8×C12712yes—
904C22×C4#41×C12712yes—
905C22×C4#41×C12712yes—
906C22×C4#41×C12712yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—44no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C22⋊Q8×C12714yes—
995C23C22×D4×C12711yescharacteristic
996C23C22×D4×C12711yescharacteristic
997C23C22×D4×C12711yescharacteristic
998C23C22×D4×C12711yescharacteristic
999C23C22×Q8×C12711yescharacteristic
1000C23C2×#41×C12711yescharacteristic
1001C23C2×#41×C12711yescharacteristic
1002C23C2×#41×C12711yescharacteristic
1003C23C2×#41×C12711yescharacteristic
1004C23H(5,𝔽2)×C12711yescharacteristic
1005C23H(5,𝔽2)×C12711yescharacteristic
1006C23H(5,𝔽2)×C12711yescharacteristic
1007C23H(5,𝔽2)×C12711yescharacteristic
1008C232−1+4×C12711yescharacteristic
1009C232−1+4×C12711yescharacteristic
1010Q8—416no—
1011D4—416no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—416no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4#120×C12714yes—
1102C2×C4#121×C12714yes—
1103C2×C4C22⋊Q8×C12714yescomplemented
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22C2×#120×C12711yescharacteristic
1135C22C2×#121×C12711yescharacteristic
1136C22C2×C22⋊Q8×C12711yescharacteristic
1137C22C2×C22⋊Q8×C12711yescharacteristic
1138C22#529×C12711yescharacteristic
1139C22#532×C12711yescharacteristic
1140C22#534×C12711yescharacteristic
1141C22#535×C12711yescharacteristic
1142C22#536×C12711yescharacteristic
1143C22#537×C12711yescharacteristic
1144C22#538×C12711yescharacteristic
1145C22#539×C12711yescharacteristic
1146C22#542×C12711yescharacteristic
1147C22#542×C12711yescharacteristic
1148C22#543×C12711yescharacteristic
1149C22D42×C12711yescharacteristic
1150C22D42×C12711yescharacteristic
1151C22#546×C12711yescharacteristic
1152C22#546×C12711yescharacteristic
1153C22#546×C12711yescharacteristic
1154C22#546×C12711yescharacteristic
1155C22#546×C12711yescharacteristic
1156C22#548×C12711yescharacteristic
1157C22#548×C12711yescharacteristic
1158C22#548×C12711yescharacteristic
1159C22D4×Q8×C12711yescharacteristic
1160C22D4×Q8×C12711yescharacteristic
1161C22#550×C12711yescharacteristic
1162C22#550×C12711yescharacteristic
1163C22#551×C12711yescharacteristic
1164C22#554×C12711yescharacteristic
1165C22#554×C12711yescharacteristic
1166C22#556×C12711yescharacteristic
1167C22#562×C12711yescharacteristic
1168C22#562×C12711yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—82no—
1184C2C127×#240911yescharacteristic
1185C2C127×#241011yescharacteristic
1186C2C127×#242611yescharacteristic
1187C2C127×#243111yescharacteristic
1188C2C127×#243711yescharacteristic
1189C2C127×#245011yescharacteristic
1190C2C127×#245211yescharacteristic
1191C2C127×#253811yescharacteristic
1192C2C127×#256011yescharacteristic
1193C2C127×#267611yescharacteristic
1194C2C127×#268111yescharacteristic
1195C2C127×#269211yescharacteristic
1196C2C127×#270011yescharacteristic
1197C2C127×#273011yescharacteristic
1198C2C127×#273211yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C127C2semidirect
2. C2×#396×C127C2semidirect
3. C2×#393×C127C2semidirect
4. C2×#391×C127C2semidirect
7. C127×#1444C2semidirect
8. C127×#1441C2semidirect
9. C127×#1439C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
14. C127×#1436C2semidirect
15. C127×C22⋊#95C2semidirect
67. C22×Q8×C127D4semidirect
74. C22×D4×C127Q8semidirect
113. C2×C4⋊C4×C127D4semidirect
503. C2×C4×C127C22⋊Q8semidirect
582. #15280C127direct (N × H)
600. C22×C22⋊Q8C2×C127semidirect
601. C2×#396C2×C127semidirect
602. C2×#393C2×C127semidirect
603. C2×#391C2×C127semidirect
606. #1444C2×C127semidirect
607. #1441C2×C127semidirect
608. #1439C2×C127semidirect
609. #1439C2×C127semidirect
610. #1439C2×C127semidirect
611. #1439C2×C127semidirect
613. #1436C2×C127semidirect
614. C22⋊#95C2×C127semidirect
615. C127#15280direct (N × H)
667. C22×Q8D4×C127semidirect
674. C22×D4Q8×C127semidirect
713. C2×C4⋊C4D4×C127semidirect
1103. C2×C4C22⋊Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C2×#396×C1272
C2×#393×C1272
C2×#391×C1272
C2×#390×C1272
C2×#386×C1272
C127×#14442
C127×#14412
C127×#14392
C127×#14382
C127×#14362
C127×C22⋊#952
#15280127