Finite Group Databasebeta

← C127×#15316 #44578989

Subgroups — C127×#15316 #44578989

Order 32512.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C2×#396×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C211yesmaximal, characteristic, complemented
4C2×#394×C127C211yesmaximal, characteristic, complemented
5C2×#394×C127C211yesmaximal, characteristic, complemented
6C2×#390×C127C211yesmaximal, characteristic, complemented
7C2×#389×C127C211yesmaximal, characteristic, complemented
8C2×#385×C127C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1437C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C2×#121×C127—24no—
21C2×#121×C127—24no—
22C2×#121×C127—24no—
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C4⋊C4×C127C2211yescharacteristic
28C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
40C22×C22⋊C4×C127C2211yescharacteristic
41C22×C22⋊C4×C127C2211yescharacteristic
42C22×C22⋊C4×C127C2211yescharacteristic
43C22×C42×C127C2211yescharacteristic
44#396×C127—24no—
45#394×C127—24no—
46#394×C127—24no—
47#394×C127—24no—
48#390×C127—24no—
49#389×C127—24no—
50#385×C127—24no—
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C2×#95×C127C2211yescharacteristic
60C2×#95×C127C2211yescharacteristic
61C25×C127C2311yescharacteristic
62C25×C127C2311yescharacteristic
63C25×C127C2311yescharacteristic
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—22no—
72C22×D4×C127—22no—
73C22×D4×C127—22no—
74C22×D4×C127—22no—
75C22×D4×C127—22no—
76C22×D4×C127—22no—
77C22×D4×C127—22no—
78C22×D4×C127—41no—
79C22×D4×C127—41no—
80C22×D4×C127—41no—
81C22×D4×C127—41no—
82C22×D4×C127—41no—
83C22×D4×C127—41no—
84C22×D4×C127D414yes—
85C23×C4×C127—22no—
86C23×C4×C127—22no—
87C23×C4×C127—22no—
88C23×C4×C127—22no—
89C23×C4×C127—22no—
90C23×C4×C127—41no—
91C23×C4×C127—41no—
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2311yescharacteristic
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2311yescharacteristic
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2311yescharacteristic
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C23×C4×C127C2311yescharacteristic
102C23×C4×C127C2311yescharacteristic
103C23×C4×C127C2311yescharacteristic
104#121×C127—232no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127—22no—
107C2×C4⋊C4×C127—22no—
108C2×C4⋊C4×C127—22no—
109C2×C4⋊C4×C127—22no—
110C2×C4⋊C4×C127—22no—
111C2×C4⋊C4×C127—22no—
112C2×C4⋊C4×C127—22no—
113C2×C4⋊C4×C127—22no—
114C2×C4⋊C4×C127—22no—
115C2×C4⋊C4×C127—22no—
116C2×C4⋊C4×C127—22no—
117C2×C4⋊C4×C127—22no—
118C2×C4⋊C4×C127—41no—
119C2×C4⋊C4×C127—41no—
120C2×C4⋊C4×C127—41no—
121C2×C4⋊C4×C127D414yes—
122C2×C4⋊C4×C127D414yescomplemented
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—22no—
137C2×C22⋊C4×C127—22no—
138C2×C22⋊C4×C127—22no—
139C2×C22⋊C4×C127—22no—
140C2×C22⋊C4×C127—22no—
141C2×C22⋊C4×C127—22no—
142C2×C22⋊C4×C127—22no—
143C2×C22⋊C4×C127—22no—
144C2×C22⋊C4×C127—22no—
145C2×C22⋊C4×C127—22no—
146C2×C22⋊C4×C127—22no—
147C2×C22⋊C4×C127—22no—
148C2×C22⋊C4×C127—22no—
149C2×C22⋊C4×C127—22no—
150C2×C22⋊C4×C127—22no—
151C2×C22⋊C4×C127—22no—
152C2×C22⋊C4×C127—22no—
153C2×C22⋊C4×C127—41no—
154C2×C22⋊C4×C127—41no—
155C2×C22⋊C4×C127—41no—
156C2×C22⋊C4×C127—41no—
157C2×C22⋊C4×C127—41no—
158C2×C22⋊C4×C127—41no—
159C2×C22⋊C4×C127—41no—
160C2×C22⋊C4×C127—41no—
161C2×C22⋊C4×C127—41no—
162C2×C22⋊C4×C127—41no—
163C2×C22⋊C4×C127D414yes—
164C2×C22⋊C4×C127D414yescomplemented
165C2×C42×C127—22no—
166C2×C42×C127—22no—
167C2×C42×C127—41no—
168#95×C127—22no—
169#95×C127—22no—
170#95×C127—22no—
171#95×C127—22no—
172#95×C127—22no—
173#95×C127—22no—
174#95×C127—22no—
175#95×C127—22no—
176#95×C127—41no—
177#95×C127—41no—
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×C127—21no—
208C24×C127—21no—
209C24×C127—21no—
210C24×C127—21no—
211C24×C127—21no—
212C24×C127—21no—
213C24×C127—21no—
214C24×C127—21no—
215C24×C127—21no—
216C24×C127—21no—
217C24×C127—21no—
218C24×C127C2×D412yes—
219C24×C127C2×D412yes—
220C24×C127C2×D412yes—
221C24×C127C2×D412yes—
222C24×C127#4112yes—
223C24×C127C2411yescharacteristic
224C2×D4×C127—28no—
225C2×D4×C127—28no—
226C2×D4×C127—28no—
227C2×D4×C127—28no—
228C2×D4×C127—44no—
229C2×D4×C127—44no—
230C2×D4×C127—44no—
231C2×D4×C127—44no—
232C2×D4×C127—44no—
233C2×D4×C127—44no—
234C2×D4×C127—44no—
235C2×D4×C127—44no—
236C2×D4×C127—44no—
237C2×D4×C127—44no—
238C2×D4×C127—44no—
239C2×D4×C127—44no—
240C2×D4×C127—44no—
241C2×D4×C127—44no—
242C2×D4×C127—44no—
243C2×D4×C127—44no—
244C2×D4×C127—44no—
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—28no—
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×C127—21no—
305C22×C4×C127—21no—
306C22×C4×C127—21no—
307C22×C4×C127—21no—
308C22×C4×C127—21no—
309C22×C4×C127—21no—
310C22×C4×C127—21no—
311C22×C4×C127—21no—
312C22×C4×C127—21no—
313C22×C4×C127—21no—
314C22×C4×C127—21no—
315C22×C4×C127—21no—
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×C127C2×D412yes—
323C22×C4×C127C2×D412yes—
324C22×C4×C127C2×D412yes—
325C22×C4×C127C2×D412yes—
326C22×C4×C127C2×D412yes—
327C22×C4×C127C2×D412yes—
328C22×C4×C127C2×D412yes—
329C22×C4×C127C2×D412yes—
330C22×C4×C127C2×D412yes—
331C22×C4×C127C2×D412yes—
332C22×C4×C127C2×D412yes—
333C22×C4×C127#4112yes—
334C22×C4×C127#4112yes—
335C22×C4×C127#4112yes—
336C4⋊C4×C127—28no—
337C4⋊C4×C127—28no—
338C4⋊C4×C127—44no—
339C4⋊C4×C127—44no—
340C4⋊C4×C127—44no—
341C4⋊C4×C127—44no—
342C22⋊C4×C127—28no—
343C22⋊C4×C127—28no—
344C22⋊C4×C127—28no—
345C22⋊C4×C127—44no—
346C22⋊C4×C127—44no—
347C22⋊C4×C127—44no—
348C22⋊C4×C127—44no—
349C22⋊C4×C127—44no—
350C22⋊C4×C127—44no—
351C22⋊C4×C127—44no—
352C22⋊C4×C127—44no—
353C22⋊C4×C127—44no—
354C22⋊C4×C127—44no—
355C22⋊C4×C127—44no—
356C42×C127—44no—
357C23×C127—22no—
358C23×C127—22no—
359C23×C127—22no—
360C23×C127—22no—
361C23×C127—22no—
362C23×C127—22no—
363C23×C127—22no—
364C23×C127—22no—
365C23×C127—22no—
366C23×C127—22no—
367C23×C127—22no—
368C23×C127—22no—
369C23×C127—22no—
370C23×C127—22no—
371C23×C127—22no—
372C23×C127—22no—
373C23×C127—22no—
374C23×C127—22no—
375C23×C127—22no—
376C23×C127—22no—
377C23×C127—22no—
378C23×C127—22no—
379C23×C127—22no—
380C23×C127—22no—
381C23×C127—22no—
382C23×C127—22no—
383C23×C127—22no—
384C23×C127—22no—
385C23×C127—22no—
386C23×C127—22no—
387C23×C127—22no—
388C23×C127—22no—
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×C127—41no—
442C23×C127—41no—
443C23×C127—41no—
444C23×C127—41no—
445C23×C127—41no—
446C23×C127—41no—
447C23×C127—41no—
448C23×C127—41no—
449C23×C127—41no—
450C23×C127—41no—
451C23×C127—41no—
452C23×C127—41no—
453C23×C127—41no—
454C23×C127—41no—
455C23×C127—41no—
456C23×C127—41no—
457C23×C127—41no—
458C23×C127—41no—
459C23×C127—41no—
460C23×C127—41no—
461C23×C127#12114yes—
462C23×C127C22×D411yescharacteristic
463C23×C127C22×D411yescharacteristic
464C23×C127C22×D411yescharacteristic
465C23×C127C22×D411yescharacteristic
466C23×C127C22×D411yescharacteristic
467C23×C127C2×#4111yescharacteristic
468C23×C127C2×#4111yescharacteristic
469C23×C127C2×#4111yescharacteristic
470C23×C127C2×#4111yescharacteristic
471C23×C127H(5,𝔽2)11yescharacteristic
472C23×C127H(5,𝔽2)11yescharacteristic
473C23×C127H(5,𝔽2)11yescharacteristic
474C23×C127H(5,𝔽2)11yescharacteristic
475C23×C1272−1+411yescharacteristic
476C23×C1272−1+411yescharacteristic
477D4×C127—416no—
478D4×C127—416no—
479D4×C127—416no—
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—22no—
493C2×C4×C127—22no—
494C2×C4×C127—22no—
495C2×C4×C127—22no—
496C2×C4×C127—22no—
497C2×C4×C127—22no—
498C2×C4×C127—22no—
499C2×C4×C127—22no—
500C2×C4×C127—22no—
501C2×C4×C127—22no—
502C2×C4×C127—22no—
503C2×C4×C127—22no—
504C2×C4×C127—22no—
505C2×C4×C127—22no—
506C2×C4×C127—22no—
507C2×C4×C127—22no—
508C2×C4×C127—22no—
509C2×C4×C127—22no—
510C2×C4×C127—22no—
511C2×C4×C127—22no—
512C2×C4×C127—22no—
513C2×C4×C127—416no—
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—41no—
543C2×C4×C127—41no—
544C2×C4×C127—41no—
545C2×C4×C127—41no—
546C2×C4×C127—41no—
547C2×C4×C127—41no—
548C2×C4×C127—41no—
549C2×C4×C127—41no—
550C2×C4×C127—41no—
551C2×C4×C127—41no—
552C2×C4×C127—41no—
553C2×C4×C127—41no—
554C2×C4×C127—41no—
555C2×C4×C127—41no—
556C2×C4×C127—41no—
557C2×C4×C127—41no—
558C2×C4×C127—41no—
559C2×C4×C127—41no—
560C2×C4×C127—41no—
561C2×C4×C127—41no—
562C2×C4×C127#12014yes—
563C2×C4×C127#12114yes—
564C2×C4×C127#12114yescomplemented
565C22×C127—24no—
566C22×C127—24no—
567C22×C127—24no—
568C22×C127—42no—
569C22×C127—42no—
570C22×C127—42no—
571C22×C127—42no—
572C22×C127—42no—
573C22×C127—42no—
574C22×C127—42no—
575C22×C127—42no—
576C22×C127—42no—
577C22×C127—42no—
578C22×C127—42no—
579C22×C127—42no—
580C22×C127—42no—
581C22×C127—42no—
582C22×C127—42no—
583C22×C127—42no—
584C22×C127—42no—
585C22×C127—42no—
586C22×C127—42no—
587C22×C127—42no—
588C22×C127—42no—
589C22×C127—42no—
590C22×C127—42no—
591C22×C127—42no—
592C22×C127—42no—
593C22×C127—42no—
594C22×C127—81no—
595C22×C127—81no—
596C22×C127—81no—
597C22×C127—81no—
598C22×C127—81no—
599C22×C127—81no—
600C22×C127—81no—
601C22×C127—81no—
602C22×C127—81no—
603C22×C127—81no—
604C22×C127—81no—
605C22×C127—81no—
606C22×C127—81no—
607C22×C127—81no—
608C22×C127—81no—
609C22×C127—81no—
610C22×C127C2×#12011yescharacteristic
611C22×C127C2×#12111yescharacteristic
612C22×C127C2×#12111yescharacteristic
613C22×C127C2×#12111yescharacteristic
614C22×C127#52911yescharacteristic
615C22×C127#53211yescharacteristic
616C22×C127#53411yescharacteristic
617C22×C127#53511yescharacteristic
618C22×C127#53611yescharacteristic
619C22×C127#53711yescharacteristic
620C22×C127#53711yescharacteristic
621C22×C127#53811yescharacteristic
622C22×C127#53911yescharacteristic
623C22×C127#54011yescharacteristic
624C22×C127#54211yescharacteristic
625C22×C127D4211yescharacteristic
626C22×C127D4211yescharacteristic
627C22×C127D4211yescharacteristic
628C22×C127D4211yescharacteristic
629C22×C127#54611yescharacteristic
630C22×C127#54611yescharacteristic
631C22×C127#54611yescharacteristic
632C22×C127#54611yescharacteristic
633C22×C127#54611yescharacteristic
634C22×C127#54711yescharacteristic
635C22×C127#54711yescharacteristic
636C22×C127#54711yescharacteristic
637C22×C127#54811yescharacteristic
638C22×C127#54811yescharacteristic
639C22×C127#54811yescharacteristic
640C22×C127#55011yescharacteristic
641C22×C127#55311yescharacteristic
642C22×C127#55311yescharacteristic
643C22×C127#56211yescharacteristic
644C22×C127#56211yescharacteristic
645C4×C127—24no—
646C4×C127—24no—
647C4×C127—24no—
648C4×C127—42no—
649C4×C127—42no—
650C4×C127—42no—
651C4×C127—42no—
652C4×C127—42no—
653C4×C127—81no—
654C4×C127—81no—
655C4×C127—81no—
656C4×C127—81no—
657#15316C12711yesmaximal, characteristic, direct product factor, Sylow
658C2×C127—44no—
659C2×C127—82no—
660C2×C127—82no—
661C2×C127#240811yescharacteristic
662C2×C127#241011yescharacteristic
663C2×C127#241611yescharacteristic
664C2×C127#241611yescharacteristic
665C2×C127#242511yescharacteristic
666C2×C127#242611yescharacteristic
667C2×C127#242811yescharacteristic
668C2×C127#243211yescharacteristic
669C2×C127#255911yescharacteristic
670C2×C127#267211yescharacteristic
671C2×C127#267611yescharacteristic
672C2×C127#268111yescharacteristic
673C2×C127#268211yescharacteristic
674C2×C127#270111yescharacteristic
675C2×C127#271111yescharacteristic
676C22×#121C2×C12711yescharacteristic
677C2×#396C2×C12711yescharacteristic, complemented
678C2×#394C2×C12711yescharacteristic, complemented
679C2×#394C2×C12711yescharacteristic, complemented
680C2×#394C2×C12711yescharacteristic, complemented
681C2×#390C2×C12711yescharacteristic, complemented
682C2×#389C2×C12711yescharacteristic, complemented
683C2×#385C2×C12711yescharacteristic, complemented
684#1441C2×C12711yescharacteristic, complemented
685#1439C2×C12711yescharacteristic, complemented
686#1439C2×C12711yescharacteristic, complemented
687#1438C2×C12711yescharacteristic, complemented
688#1438C2×C12711yescharacteristic, complemented
689#1437C2×C12711yescharacteristic, complemented
690C22⋊#95C2×C12711yescharacteristic, complemented
691C127#1531611yescharacteristic, direct product factor, Sylow
692C23×D4C22×C12711yescharacteristic
693C23×D4C22×C12711yescharacteristic
694C23×D4C22×C12711yescharacteristic
695C24×C4C22×C12711yescharacteristic
696C2×#121—24no—
697C2×#121—24no—
698C2×#121—24no—
699C22×C4⋊C4C22×C12711yescharacteristic
700C22×C4⋊C4C22×C12711yescharacteristic
701C22×C4⋊C4C22×C12711yescharacteristic
702C22×C4⋊C4C22×C12711yescharacteristic
703C22×C4⋊C4C22×C12711yescharacteristic
704C22×C4⋊C4C22×C12711yescharacteristic
705C22×C22⋊C4C22×C12711yescharacteristic
706C22×C22⋊C4C22×C12711yescharacteristic
707C22×C22⋊C4C22×C12711yescharacteristic
708C22×C22⋊C4C22×C12711yescharacteristic
709C22×C22⋊C4C22×C12711yescharacteristic
710C22×C22⋊C4C22×C12711yescharacteristic
711C22×C22⋊C4C22×C12711yescharacteristic
712C22×C22⋊C4C22×C12711yescharacteristic
713C22×C22⋊C4C22×C12711yescharacteristic
714C22×C22⋊C4C22×C12711yescharacteristic
715C22×C22⋊C4C22×C12711yescharacteristic
716C22×C22⋊C4C22×C12711yescharacteristic
717C22×C22⋊C4C22×C12711yescharacteristic
718C22×C22⋊C4C22×C12711yescharacteristic
719C22×C42C22×C12711yescharacteristic
720#396—24no—
721#394—24no—
722#394—24no—
723#394—24no—
724#390—24no—
725#389—24no—
726#385—24no—
727C2×#95C22×C12711yescharacteristic
728C2×#95C22×C12711yescharacteristic
729C2×#95C22×C12711yescharacteristic
730C2×#95C22×C12711yescharacteristic
731C2×#95C22×C12711yescharacteristic
732C2×#95C22×C12711yescharacteristic
733C2×#95C22×C12711yescharacteristic
734C2×#95C22×C12711yescharacteristic
735C2×#95C22×C12711yescharacteristic
736C2×#95C22×C12711yescharacteristic
737C25C23×C12711yescharacteristic
738C25C23×C12711yescharacteristic
739C25C23×C12711yescharacteristic
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4D4×C12714yes—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4C23×C12711yescharacteristic
769C23×C4C23×C12711yescharacteristic
770C23×C4C23×C12711yescharacteristic
771C23×C4C23×C12711yescharacteristic
772C23×C4C23×C12711yescharacteristic
773C23×C4C23×C12711yescharacteristic
774C23×C4C23×C12711yescharacteristic
775C23×C4C23×C12711yescharacteristic
776C23×C4C23×C12711yescharacteristic
777C23×C4C23×C12711yescharacteristic
778C23×C4C23×C12711yescharacteristic
779C23×C4C23×C12711yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—41no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4—41no—
797C2×C4⋊C4D4×C12714yes—
798C2×C4⋊C4D4×C12714yescomplemented
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4D4×C12714yes—
840C2×C22⋊C4D4×C12714yescomplemented
841C2×C42—22no—
842C2×C42—22no—
843C2×C42—41no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—41no—
853#95—41no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24C2×D4×C12712yes—
895C24C2×D4×C12712yes—
896C24C2×D4×C12712yes—
897C24C2×D4×C12712yes—
898C24#41×C12712yes—
899C24C24×C12711yescharacteristic
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
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—28no—
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×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C12712yes—
999C22×C4C2×D4×C12712yes—
1000C22×C4C2×D4×C12712yes—
1001C22×C4C2×D4×C12712yes—
1002C22×C4C2×D4×C12712yes—
1003C22×C4C2×D4×C12712yes—
1004C22×C4C2×D4×C12712yes—
1005C22×C4C2×D4×C12712yes—
1006C22×C4C2×D4×C12712yes—
1007C22×C4C2×D4×C12712yes—
1008C22×C4C2×D4×C12712yes—
1009C22×C4#41×C12712yes—
1010C22×C4#41×C12712yes—
1011C22×C4#41×C12712yes—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—44no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
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—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23#121×C12714yes—
1138C23C22×D4×C12711yescharacteristic
1139C23C22×D4×C12711yescharacteristic
1140C23C22×D4×C12711yescharacteristic
1141C23C22×D4×C12711yescharacteristic
1142C23C22×D4×C12711yescharacteristic
1143C23C2×#41×C12711yescharacteristic
1144C23C2×#41×C12711yescharacteristic
1145C23C2×#41×C12711yescharacteristic
1146C23C2×#41×C12711yescharacteristic
1147C23H(5,𝔽2)×C12711yescharacteristic
1148C23H(5,𝔽2)×C12711yescharacteristic
1149C23H(5,𝔽2)×C12711yescharacteristic
1150C23H(5,𝔽2)×C12711yescharacteristic
1151C232−1+4×C12711yescharacteristic
1152C232−1+4×C12711yescharacteristic
1153D4—416no—
1154D4—416no—
1155D4—416no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—416no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4#120×C12714yes—
1239C2×C4#121×C12714yes—
1240C2×C4#121×C12714yescomplemented
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22C2×#120×C12711yescharacteristic
1287C22C2×#121×C12711yescharacteristic
1288C22C2×#121×C12711yescharacteristic
1289C22C2×#121×C12711yescharacteristic
1290C22#529×C12711yescharacteristic
1291C22#532×C12711yescharacteristic
1292C22#534×C12711yescharacteristic
1293C22#535×C12711yescharacteristic
1294C22#536×C12711yescharacteristic
1295C22#537×C12711yescharacteristic
1296C22#537×C12711yescharacteristic
1297C22#538×C12711yescharacteristic
1298C22#539×C12711yescharacteristic
1299C22#540×C12711yescharacteristic
1300C22#542×C12711yescharacteristic
1301C22D42×C12711yescharacteristic
1302C22D42×C12711yescharacteristic
1303C22D42×C12711yescharacteristic
1304C22D42×C12711yescharacteristic
1305C22#546×C12711yescharacteristic
1306C22#546×C12711yescharacteristic
1307C22#546×C12711yescharacteristic
1308C22#546×C12711yescharacteristic
1309C22#546×C12711yescharacteristic
1310C22#547×C12711yescharacteristic
1311C22#547×C12711yescharacteristic
1312C22#547×C12711yescharacteristic
1313C22#548×C12711yescharacteristic
1314C22#548×C12711yescharacteristic
1315C22#548×C12711yescharacteristic
1316C22#550×C12711yescharacteristic
1317C22#553×C12711yescharacteristic
1318C22#553×C12711yescharacteristic
1319C22#562×C12711yescharacteristic
1320C22#562×C12711yescharacteristic
1321C4—24no—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2C127×#240811yescharacteristic
1337C2C127×#241011yescharacteristic
1338C2C127×#241611yescharacteristic
1339C2C127×#241611yescharacteristic
1340C2C127×#242511yescharacteristic
1341C2C127×#242611yescharacteristic
1342C2C127×#242811yescharacteristic
1343C2C127×#243211yescharacteristic
1344C2C127×#255911yescharacteristic
1345C2C127×#267211yescharacteristic
1346C2C127×#267611yescharacteristic
1347C2C127×#268111yescharacteristic
1348C2C127×#268211yescharacteristic
1349C2C127×#270111yescharacteristic
1350C2C127×#271111yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#396×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#394×C127C2semidirect
5. C2×#394×C127C2semidirect
6. C2×#390×C127C2semidirect
7. C2×#389×C127C2semidirect
8. C2×#385×C127C2semidirect
9. C127×#1441C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1438C2semidirect
13. C127×#1438C2semidirect
14. C127×#1437C2semidirect
15. C127×C22⋊#95C2semidirect
122. C2×C4⋊C4×C127D4semidirect
164. C2×C22⋊C4×C127D4semidirect
564. C2×C4×C127#121semidirect
657. #15316C127direct (N × H)
677. C2×#396C2×C127semidirect
678. C2×#394C2×C127semidirect
679. C2×#394C2×C127semidirect
680. C2×#394C2×C127semidirect
681. C2×#390C2×C127semidirect
682. C2×#389C2×C127semidirect
683. C2×#385C2×C127semidirect
684. #1441C2×C127semidirect
685. #1439C2×C127semidirect
686. #1439C2×C127semidirect
687. #1438C2×C127semidirect
688. #1438C2×C127semidirect
689. #1437C2×C127semidirect
690. C22⋊#95C2×C127semidirect
691. C127#15316direct (N × H)
798. C2×C4⋊C4D4×C127semidirect
840. C2×C22⋊C4D4×C127semidirect
1240. C2×C4#121×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C2×#396×C1272
C2×#394×C1272
C2×#390×C1272
C2×#389×C1272
C2×#385×C1272
C127×#14412
C127×#14392
C127×#14382
C127×#14372
C127×C22⋊#952
#15316127