Finite Group Databasebeta

← C127×#15423 #44579096

Subgroups — C127×#15423 #44579096

Order 32512.

2054 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C127C211yesmaximal, characteristic, complemented
2C2×#392×C127C211yesmaximal, characteristic
3C2×#390×C127C211yesmaximal, characteristic, complemented
4C2×#388×C127C211yesmaximal, characteristic, complemented
5C2×#388×C127C211yesmaximal, characteristic, complemented
6C2×#388×C127C211yesmaximal, characteristic, complemented
7C127×#1441C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1437C211yesmaximal, characteristic, complemented
15C127×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊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×C42×C127C2211yescharacteristic
38C22×C42×C127C2211yescharacteristic
39#394×C127—24no—
40#392×C127—24no—
41#390×C127—24no—
42#388×C127—24no—
43#388×C127—24no—
44#388×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
57C25×C127C2311yescharacteristic
58C25×C127C2311yescharacteristic
59C25×C127C2311yescharacteristic
60C22×D4×C127—22no—
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—22no—
69C22×D4×C127—22no—
70C22×D4×C127—22no—
71C22×D4×C127—41no—
72C22×D4×C127—41no—
73C22×D4×C127—41no—
74C22×D4×C127—41no—
75C22×D4×C127—41no—
76C22×D4×C127—41no—
77C22×D4×C127—41no—
78C22×D4×C127—41no—
79C22×D4×C127—41no—
80C22×D4×C127—41no—
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
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—41no—
97C2×C4⋊C4×C127—41no—
98C2×C4⋊C4×C127—41no—
99C2×C4⋊C4×C127—41no—
100C2×C4⋊C4×C127—41no—
101C2×C4⋊C4×C127D414yescomplemented
102C2×C22⋊C4×C127—22no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
106C2×C22⋊C4×C127—22no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127—22no—
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—41no—
131C2×C22⋊C4×C127—41no—
132C2×C22⋊C4×C127—41no—
133C2×C22⋊C4×C127—41no—
134C2×C22⋊C4×C127—41no—
135C2×C22⋊C4×C127—41no—
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—22no—
150C2×C42×C127—22no—
151C2×C42×C127—22no—
152C2×C42×C127—41no—
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×C127—41no—
164#95×C127D414yescomplemented
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×C127—21no—
191C24×C127—21no—
192C24×C127—21no—
193C24×C127—21no—
194C24×C127—21no—
195C24×C127—21no—
196C24×C127—21no—
197C24×C127—21no—
198C24×C127—21no—
199C24×C127—21no—
200C24×C127—21no—
201C24×C127—21no—
202C24×C127—21no—
203C24×C127—21no—
204C24×C127—21no—
205C24×C127—21no—
206C24×C127—21no—
207C24×C127C2×D412yes—
208C24×C127#4112yes—
209C24×C127#4112yes—
210C24×C127C2411yescharacteristic
211C2×D4×C127—28no—
212C2×D4×C127—44no—
213C2×D4×C127—44no—
214C2×D4×C127—44no—
215C2×D4×C127—44no—
216C2×D4×C127—44no—
217C2×D4×C127—44no—
218C2×D4×C127—44no—
219C2×D4×C127—44no—
220C2×D4×C127—44no—
221C2×D4×C127—44no—
222C2×D4×C127—44no—
223C2×D4×C127—44no—
224C2×D4×C127—44no—
225C2×D4×C127—44no—
226C2×D4×C127—44no—
227C2×D4×C127—44no—
228C2×D4×C127—44no—
229C2×D4×C127—44no—
230C2×D4×C127—44no—
231C2×D4×C127—44no—
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—21no—
287C22×C4×C127—21no—
288C22×C4×C127—21no—
289C22×C4×C127—21no—
290C22×C4×C127—21no—
291C22×C4×C127—21no—
292C22×C4×C127—21no—
293C22×C4×C127—21no—
294C22×C4×C127—21no—
295C22×C4×C127—21no—
296C22×C4×C127—21no—
297C22×C4×C127—21no—
298C22×C4×C127—21no—
299C22×C4×C127—21no—
300C22×C4×C127—21no—
301C22×C4×C127—21no—
302C22×C4×C127—21no—
303C22×C4×C127—21no—
304C22×C4×C127C2×D412yes—
305C22×C4×C127C2×D412yes—
306C22×C4×C127C2×D412yes—
307C22×C4×C127C2×D412yes—
308C22×C4×C127C2×D412yes—
309C22×C4×C127C2×D412yes—
310C22×C4×C127C2×D412yes—
311C22×C4×C127C2×D412yes—
312C22×C4×C127#4112yes—
313C22×C4×C127#4112yes—
314C22×C4×C127#4112yes—
315C22×C4×C127#4112yes—
316C4⋊C4×C127—44no—
317C4⋊C4×C127—44no—
318C4⋊C4×C127—44no—
319C22⋊C4×C127—28no—
320C22⋊C4×C127—28no—
321C22⋊C4×C127—28no—
322C22⋊C4×C127—44no—
323C22⋊C4×C127—44no—
324C22⋊C4×C127—44no—
325C22⋊C4×C127—44no—
326C22⋊C4×C127—44no—
327C22⋊C4×C127—44no—
328C22⋊C4×C127—44no—
329C22⋊C4×C127—44no—
330C22⋊C4×C127—44no—
331C22⋊C4×C127—44no—
332C22⋊C4×C127—44no—
333C22⋊C4×C127—44no—
334C42×C127—44no—
335C42×C127—44no—
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—22no—
351C23×C127—22no—
352C23×C127—22no—
353C23×C127—22no—
354C23×C127—22no—
355C23×C127—22no—
356C23×C127—22no—
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×C127—41no—
395C23×C127—41no—
396C23×C127—41no—
397C23×C127—41no—
398C23×C127—41no—
399C23×C127—41no—
400C23×C127—41no—
401C23×C127—41no—
402C23×C127—41no—
403C23×C127—41no—
404C23×C127—41no—
405C23×C127—41no—
406C23×C127—41no—
407C23×C127—41no—
408C23×C127—41no—
409C23×C127—41no—
410C23×C127—41no—
411C23×C127—41no—
412C23×C127—41no—
413C23×C127—41no—
414C23×C127—41no—
415C23×C127—41no—
416C23×C127—41no—
417C23×C127—41no—
418C23×C127—41no—
419C23×C127—41no—
420C23×C127—41no—
421C23×C127—41no—
422C23×C127—41no—
423C23×C127—41no—
424C23×C127—41no—
425C23×C127—41no—
426C23×C127—41no—
427C23×C127—41no—
428C23×C127—41no—
429C23×C127—41no—
430C23×C127—41no—
431C23×C127—41no—
432C23×C127—41no—
433C23×C127—41no—
434C23×C127—41no—
435C23×C127—41no—
436C23×C127—41no—
437C23×C127—41no—
438C23×C127—41no—
439C23×C127—41no—
440C23×C127—41no—
441C23×C127C22×D411yescharacteristic
442C23×C127C22×D411yescharacteristic
443C23×C127C22×D411yescharacteristic
444C23×C127C2×#4111yescharacteristic
445C23×C127C2×#4111yescharacteristic
446C23×C127C2×#4111yescharacteristic
447C23×C127C2×#4111yescharacteristic
448C23×C127C2×#4111yescharacteristic
449C23×C127C2×#4111yescharacteristic
450C23×C127H(5,𝔽2)11yescharacteristic
451C23×C127H(5,𝔽2)11yescharacteristic
452C23×C127H(5,𝔽2)11yescharacteristic
453C23×C127H(5,𝔽2)11yescharacteristic
454C23×C127H(5,𝔽2)11yescharacteristic
455C23×C127H(5,𝔽2)11yescharacteristic
456D4×C127—416no—
457D4×C127—416no—
458D4×C127—416no—
459C2×C4×C127—22no—
460C2×C4×C127—22no—
461C2×C4×C127—22no—
462C2×C4×C127—22no—
463C2×C4×C127—22no—
464C2×C4×C127—22no—
465C2×C4×C127—22no—
466C2×C4×C127—22no—
467C2×C4×C127—22no—
468C2×C4×C127—22no—
469C2×C4×C127—22no—
470C2×C4×C127—22no—
471C2×C4×C127—22no—
472C2×C4×C127—22no—
473C2×C4×C127—22no—
474C2×C4×C127—22no—
475C2×C4×C127—22no—
476C2×C4×C127—22no—
477C2×C4×C127—22no—
478C2×C4×C127—22no—
479C2×C4×C127—22no—
480C2×C4×C127—22no—
481C2×C4×C127—22no—
482C2×C4×C127—22no—
483C2×C4×C127—22no—
484C2×C4×C127—22no—
485C2×C4×C127—22no—
486C2×C4×C127—22no—
487C2×C4×C127—22no—
488C2×C4×C127—22no—
489C2×C4×C127—22no—
490C2×C4×C127—22no—
491C2×C4×C127—22no—
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—41no—
502C2×C4×C127—41no—
503C2×C4×C127—41no—
504C2×C4×C127—41no—
505C2×C4×C127—41no—
506C2×C4×C127—41no—
507C2×C4×C127—41no—
508C2×C4×C127—41no—
509C2×C4×C127—41no—
510C2×C4×C127—41no—
511C2×C4×C127—41no—
512C2×C4×C127—41no—
513C2×C4×C127—41no—
514C2×C4×C127—41no—
515C2×C4×C127—41no—
516C2×C4×C127—41no—
517C2×C4×C127—41no—
518C2×C4×C127—41no—
519C2×C4×C127—41no—
520C2×C4×C127—41no—
521C2×C4×C127—41no—
522C2×C4×C127—41no—
523C2×C4×C127—41no—
524C2×C4×C127—41no—
525C2×C4×C127—41no—
526C2×C4×C127—41no—
527C2×C4×C127—41no—
528C2×C4×C127—41no—
529C2×C4×C127—41no—
530C2×C4×C127—41no—
531C2×C4×C127—41no—
532C2×C4×C127—41no—
533C2×C4×C127—41no—
534C2×C4×C127—41no—
535C2×C4×C127—41no—
536C2×C4×C127—41no—
537C2×C4×C127—41no—
538C2×C4×C127—41no—
539C2×C4×C127—41no—
540C2×C4×C127—41no—
541C2×C4×C127—41no—
542C2×C4×C127#12114yes—
543C22×C127—42no—
544C22×C127—42no—
545C22×C127—42no—
546C22×C127—42no—
547C22×C127—42no—
548C22×C127—42no—
549C22×C127—42no—
550C22×C127—42no—
551C22×C127—42no—
552C22×C127—42no—
553C22×C127—42no—
554C22×C127—42no—
555C22×C127—42no—
556C22×C127—42no—
557C22×C127—42no—
558C22×C127—42no—
559C22×C127—42no—
560C22×C127—42no—
561C22×C127—42no—
562C22×C127—42no—
563C22×C127—42no—
564C22×C127—81no—
565C22×C127—81no—
566C22×C127—81no—
567C22×C127—81no—
568C22×C127—81no—
569C22×C127—81no—
570C22×C127—81no—
571C22×C127—81no—
572C22×C127—81no—
573C22×C127—81no—
574C22×C127—81no—
575C22×C127—81no—
576C22×C127—81no—
577C22×C127—81no—
578C22×C127—81no—
579C22×C127—81no—
580C22×C127—81no—
581C22×C127—81no—
582C22×C127—81no—
583C22×C127—81no—
584C22×C127—81no—
585C22×C127—81no—
586C22×C127—81no—
587C22×C127—81no—
588C22×C127C2×#12111yescharacteristic
589C22×C127#52511yescharacteristic
590C22×C127#52511yescharacteristic
591C22×C127#52511yescharacteristic
592C22×C127#52911yescharacteristic
593C22×C127#53211yescharacteristic
594C22×C127#53411yescharacteristic
595C22×C127#53511yescharacteristic
596C22×C127#53511yescharacteristic
597C22×C127#53811yescharacteristic
598C22×C127#53811yescharacteristic
599C22×C127#53811yescharacteristic
600C22×C127#53811yescharacteristic
601C22×C127#54011yescharacteristic
602C22×C127#54011yescharacteristic
603C22×C127D4211yescharacteristic
604C22×C127D4211yescharacteristic
605C22×C127#54611yescharacteristic
606C22×C127#54611yescharacteristic
607C22×C127#54611yescharacteristic
608C22×C127#54611yescharacteristic
609C22×C127#54611yescharacteristic
610C22×C127#55011yescharacteristic
611C22×C127#55011yescharacteristic
612C22×C127#55011yescharacteristic
613C22×C127#55111yescharacteristic
614C22×C127#55111yescharacteristic
615C22×C127#55111yescharacteristic
616C22×C127#55311yescharacteristic
617C22×C127#55311yescharacteristic
618C22×C127#55311yescharacteristic
619C22×C127#55511yescharacteristic
620C22×C127#55511yescharacteristic
621C22×C127#56011yescharacteristic
622C22×C127H(3,𝔽4)11yescharacteristic
623C4×C127—24no—
624C4×C127—42no—
625C4×C127—42no—
626C4×C127—42no—
627C4×C127—42no—
628C4×C127—42no—
629C4×C127—42no—
630C4×C127—42no—
631C4×C127—42no—
632C4×C127—42no—
633C4×C127—81no—
634C4×C127—81no—
635#15423C12711yesmaximal, characteristic, direct product factor, Sylow
636C2×C127—82no—
637C2×C127—82no—
638C2×C127—82no—
639C2×C127#241411yescharacteristic
640C2×C127#242811yescharacteristic
641C2×C127#245611yescharacteristic
642C2×C127#245611yescharacteristic
643C2×C127#246711yescharacteristic
644C2×C127#247611yescharacteristic
645C2×C127#253411yescharacteristic
646C2×C127#255411yescharacteristic
647C2×C127#261011yescharacteristic
648C2×C127#267011yescharacteristic
649C2×C127#267311yescharacteristic
650C2×C127#268511yescharacteristic
651C2×C127#273311yescharacteristic
652C2×C127#275311yescharacteristic
653C2×C127#275611yescharacteristic
654C2×#394C2×C12711yescharacteristic, complemented
655C2×#392C2×C12711yescharacteristic
656C2×#390C2×C12711yescharacteristic, complemented
657C2×#388C2×C12711yescharacteristic, complemented
658C2×#388C2×C12711yescharacteristic, complemented
659C2×#388C2×C12711yescharacteristic, complemented
660#1441C2×C12711yescharacteristic, complemented
661#1439C2×C12711yescharacteristic, complemented
662#1439C2×C12711yescharacteristic, complemented
663#1438C2×C12711yescharacteristic, complemented
664#1438C2×C12711yescharacteristic, complemented
665#1438C2×C12711yescharacteristic, complemented
666#1438C2×C12711yescharacteristic, complemented
667#1437C2×C12711yescharacteristic, complemented
668#1434C2×C12711yescharacteristic, complemented
669C127#1542311yescharacteristic, direct product factor, Sylow
670C23×D4C22×C12711yescharacteristic
671C23×D4C22×C12711yescharacteristic
672C23×D4C22×C12711yescharacteristic
673C22×C4⋊C4C22×C12711yescharacteristic
674C22×C4⋊C4C22×C12711yescharacteristic
675C22×C4⋊C4C22×C12711yescharacteristic
676C22×C22⋊C4C22×C12711yescharacteristic
677C22×C22⋊C4C22×C12711yescharacteristic
678C22×C22⋊C4C22×C12711yescharacteristic
679C22×C22⋊C4C22×C12711yescharacteristic
680C22×C22⋊C4C22×C12711yescharacteristic
681C22×C22⋊C4C22×C12711yescharacteristic
682C22×C22⋊C4C22×C12711yescharacteristic
683C22×C22⋊C4C22×C12711yescharacteristic
684C22×C22⋊C4C22×C12711yescharacteristic
685C22×C22⋊C4C22×C12711yescharacteristic
686C22×C22⋊C4C22×C12711yescharacteristic
687C22×C22⋊C4C22×C12711yescharacteristic
688C22×C22⋊C4C22×C12711yescharacteristic
689C22×C22⋊C4C22×C12711yescharacteristic
690C22×C22⋊C4C22×C12711yescharacteristic
691C22×C42C22×C12711yescharacteristic
692C22×C42C22×C12711yescharacteristic
693#394—24no—
694#392—24no—
695#390—24no—
696#388—24no—
697#388—24no—
698#388—24no—
699C2×#95C22×C12711yescharacteristic
700C2×#95C22×C12711yescharacteristic
701C2×#95C22×C12711yescharacteristic
702C2×#95C22×C12711yescharacteristic
703C2×#95C22×C12711yescharacteristic
704C2×#95C22×C12711yescharacteristic
705C2×#95C22×C12711yescharacteristic
706C2×#95C22×C12711yescharacteristic
707C2×#95C22×C12711yescharacteristic
708C2×#95C22×C12711yescharacteristic
709C2×#95C22×C12711yescharacteristic
710C2×#95C22×C12711yescharacteristic
711C25C23×C12711yescharacteristic
712C25C23×C12711yescharacteristic
713C25C23×C12711yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C23×C4C23×C12711yescharacteristic
736C23×C4C23×C12711yescharacteristic
737C23×C4C23×C12711yescharacteristic
738C23×C4C23×C12711yescharacteristic
739C23×C4C23×C12711yescharacteristic
740C23×C4C23×C12711yescharacteristic
741C23×C4C23×C12711yescharacteristic
742C23×C4C23×C12711yescharacteristic
743C23×C4C23×C12711yescharacteristic
744C23×C4C23×C12711yescharacteristic
745C23×C4C23×C12711yescharacteristic
746C23×C4C23×C12711yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C4⋊C4—41no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4D4×C12714yescomplemented
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4D4×C12714yes—
801C2×C42—22no—
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—22no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C12714yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C12712yes—
862C24#41×C12712yes—
863C24#41×C12712yes—
864C24C24×C12711yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4C2×D4×C12712yes—
959C22×C4C2×D4×C12712yes—
960C22×C4C2×D4×C12712yes—
961C22×C4C2×D4×C12712yes—
962C22×C4C2×D4×C12712yes—
963C22×C4C2×D4×C12712yes—
964C22×C4C2×D4×C12712yes—
965C22×C4C2×D4×C12712yes—
966C22×C4#41×C12712yes—
967C22×C4#41×C12712yes—
968C22×C4#41×C12712yes—
969C22×C4#41×C12712yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C42—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C12711yescharacteristic
1096C23C22×D4×C12711yescharacteristic
1097C23C22×D4×C12711yescharacteristic
1098C23C2×#41×C12711yescharacteristic
1099C23C2×#41×C12711yescharacteristic
1100C23C2×#41×C12711yescharacteristic
1101C23C2×#41×C12711yescharacteristic
1102C23C2×#41×C12711yescharacteristic
1103C23C2×#41×C12711yescharacteristic
1104C23H(5,𝔽2)×C12711yescharacteristic
1105C23H(5,𝔽2)×C12711yescharacteristic
1106C23H(5,𝔽2)×C12711yescharacteristic
1107C23H(5,𝔽2)×C12711yescharacteristic
1108C23H(5,𝔽2)×C12711yescharacteristic
1109C23H(5,𝔽2)×C12711yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4#121×C12714yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#121×C12711yescharacteristic
1243C22#525×C12711yescharacteristic
1244C22#525×C12711yescharacteristic
1245C22#525×C12711yescharacteristic
1246C22#529×C12711yescharacteristic
1247C22#532×C12711yescharacteristic
1248C22#534×C12711yescharacteristic
1249C22#535×C12711yescharacteristic
1250C22#535×C12711yescharacteristic
1251C22#538×C12711yescharacteristic
1252C22#538×C12711yescharacteristic
1253C22#538×C12711yescharacteristic
1254C22#538×C12711yescharacteristic
1255C22#540×C12711yescharacteristic
1256C22#540×C12711yescharacteristic
1257C22D42×C12711yescharacteristic
1258C22D42×C12711yescharacteristic
1259C22#546×C12711yescharacteristic
1260C22#546×C12711yescharacteristic
1261C22#546×C12711yescharacteristic
1262C22#546×C12711yescharacteristic
1263C22#546×C12711yescharacteristic
1264C22#550×C12711yescharacteristic
1265C22#550×C12711yescharacteristic
1266C22#550×C12711yescharacteristic
1267C22#551×C12711yescharacteristic
1268C22#551×C12711yescharacteristic
1269C22#551×C12711yescharacteristic
1270C22#553×C12711yescharacteristic
1271C22#553×C12711yescharacteristic
1272C22#553×C12711yescharacteristic
1273C22#555×C12711yescharacteristic
1274C22#555×C12711yescharacteristic
1275C22#560×C12711yescharacteristic
1276C22H(3,𝔽4)×C12711yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C127×#241411yescharacteristic
1293C2C127×#242811yescharacteristic
1294C2C127×#245611yescharacteristic
1295C2C127×#245611yescharacteristic
1296C2C127×#246711yescharacteristic
1297C2C127×#247611yescharacteristic
1298C2C127×#253411yescharacteristic
1299C2C127×#255411yescharacteristic
1300C2C127×#261011yescharacteristic
1301C2C127×#267011yescharacteristic
1302C2C127×#267311yescharacteristic
1303C2C127×#268511yescharacteristic
1304C2C127×#273311yescharacteristic
1305C2C127×#275311yescharacteristic
1306C2C127×#275611yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#394×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#388×C127C2semidirect
5. C2×#388×C127C2semidirect
6. C2×#388×C127C2semidirect
7. C127×#1441C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1438C2semidirect
14. C127×#1437C2semidirect
15. C127×#1434C2semidirect
101. C2×C4⋊C4×C127D4semidirect
164. #95×C127D4semidirect
635. #15423C127direct (N × H)
654. C2×#394C2×C127semidirect
656. C2×#390C2×C127semidirect
657. C2×#388C2×C127semidirect
658. C2×#388C2×C127semidirect
659. C2×#388C2×C127semidirect
660. #1441C2×C127semidirect
661. #1439C2×C127semidirect
662. #1439C2×C127semidirect
663. #1438C2×C127semidirect
664. #1438C2×C127semidirect
665. #1438C2×C127semidirect
666. #1438C2×C127semidirect
667. #1437C2×C127semidirect
668. #1434C2×C127semidirect
669. C127#15423direct (N × H)
755. C2×C4⋊C4D4×C127semidirect
818. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C2×#388×C1272
C127×#14412
C127×#14392
C127×#14382
C127×#14372
C127×#14342
#15423127