Finite Group Databasebeta

← C127×#14204 #44577877

Subgroups — C127×#14204 #44577877

Order 32512.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C127C211yesmaximal, characteristic
2C2×#389×C127C211yesmaximal, characteristic, complemented
3C2×#389×C127C211yesmaximal, characteristic, complemented
4C2×#385×C127C211yesmaximal, characteristic
5C2×#385×C127C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
8C127×#1442C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic
11C127×#1437C211yesmaximal, characteristic
12C127×#1437C211yesmaximal, characteristic
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×#1436C211yesmaximal, characteristic, complemented
16C24×C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C42×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33C22×C42×C127C2211yescharacteristic
34C22×C42×C127C2211yescharacteristic
35#396×C127C418yescomplemented
36#389×C127—24no—
37#389×C127—24no—
38#385×C127—24no—
39#385×C127—24no—
40C4×C4⋊C4×C127—24no—
41C4×C22⋊C4×C127—24no—
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—41no—
65C23×C4×C127—41no—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127—22no—
86C2×C4⋊C4×C127—22no—
87C2×C4⋊C4×C127—22no—
88C2×C4⋊C4×C127—22no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—22no—
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—22no—
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—22no—
97C2×C4⋊C4×C127—41no—
98C2×C4⋊C4×C127—41no—
99C2×C4⋊C4×C127—41no—
100C2×C4⋊C4×C127C2×C414yescomplemented
101C2×C4⋊C4×C127C2×C414yescomplemented
102C2×C4⋊C4×C127C2×C414yescomplemented
103C2×C4⋊C4×C127D414yes—
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—41no—
117C2×C22⋊C4×C127—41no—
118C2×C22⋊C4×C127C2×C414yes—
119C2×C22⋊C4×C127C2×C414yes—
120C2×C22⋊C4×C127C2×C414yes—
121C2×C22⋊C4×C127Q814yes—
122C2×C42×C127—22no—
123C2×C42×C127—22no—
124C2×C42×C127—22no—
125C2×C42×C127—22no—
126C2×C42×C127—22no—
127C2×C42×C127—22no—
128C2×C42×C127—22no—
129C2×C42×C127—22no—
130C2×C42×C127—22no—
131C2×C42×C127—41no—
132C2×C42×C127—41no—
133C2×C42×C127—41no—
134#95×C127—22no—
135#95×C127—22no—
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—41no—
146#95×C127—41no—
147#95×C127C2×C414yescomplemented
148#95×C127D414yes—
149#95×C127D414yes—
150C24×C127—21no—
151C24×C127—21no—
152C24×C127—21no—
153C24×C127—21no—
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×Q812yes—
164C24×C127#4112yes—
165C24×C127C2411yescharacteristic
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
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—21no—
188C22×C4×C127—21no—
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—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—44no—
244C22×C4×C127—44no—
245C22×C4×C127—44no—
246C22×C4×C127—44no—
247C22×C4×C127—44no—
248C22×C4×C127—44no—
249C22×C4×C127C22×C412yes—
250C22×C4×C127C22×C412yes—
251C22×C4×C127C22×C412yes—
252C22×C4×C127C22×C412yes—
253C22×C4×C127C22×C412yes—
254C22×C4×C127C22×C412yes—
255C22×C4×C127C2×D412yes—
256C22×C4×C127C2×D412yes—
257C22×C4×C127C2×D412yes—
258C22×C4×C127C2×D412yes—
259C22×C4×C127C2×D412yes—
260C22×C4×C127C2×D412yes—
261C22×C4×C127C2×D412yes—
262C22×C4×C127C2×D412yes—
263C22×C4×C127C2×D412yes—
264C22×C4×C127C2×Q812yes—
265C22×C4×C127C2×Q812yes—
266C22×C4×C127#4112yes—
267C22×C4×C127#4112yes—
268C22×C4×C127#4112yes—
269C22×C4×C127#4112yes—
270C22×C4×C127#4112yes—
271C4⋊C4×C127—28no—
272C4⋊C4×C127—28no—
273C4⋊C4×C127—28no—
274C4⋊C4×C127—28no—
275C4⋊C4×C127—44no—
276C4⋊C4×C127—44no—
277C4⋊C4×C127—44no—
278C4⋊C4×C127—44no—
279C22⋊C4×C127—28no—
280C22⋊C4×C127—28no—
281C22⋊C4×C127—28no—
282C22⋊C4×C127—28no—
283C22⋊C4×C127—44no—
284C22⋊C4×C127—44no—
285C42×C127—28no—
286C42×C127—44no—
287C42×C127—44no—
288C42×C127—44no—
289C23×C127—22no—
290C23×C127—22no—
291C23×C127—22no—
292C23×C127—22no—
293C23×C127—22no—
294C23×C127—22no—
295C23×C127—22no—
296C23×C127—22no—
297C23×C127—22no—
298C23×C127—22no—
299C23×C127—22no—
300C23×C127—22no—
301C23×C127—22no—
302C23×C127—22no—
303C23×C127—22no—
304C23×C127—22no—
305C23×C127—22no—
306C23×C127—22no—
307C23×C127—41no—
308C23×C127—41no—
309C23×C127—41no—
310C23×C127—41no—
311C23×C127—41no—
312C23×C127—41no—
313C23×C127—41no—
314C23×C127—41no—
315C23×C127—41no—
316C23×C127—41no—
317C23×C127—41no—
318C23×C127—41no—
319C23×C127—41no—
320C23×C127—41no—
321C23×C127—41no—
322C23×C127—41no—
323C23×C127C4×Q814yes—
324C23×C127C23×C411yescharacteristic
325C23×C127C22×D411yescharacteristic
326C23×C127C22×D411yescharacteristic
327C23×C127C22×D411yescharacteristic
328C23×C127C22×Q811yescharacteristic
329C23×C127C2×#4111yescharacteristic
330C23×C127C2×#4111yescharacteristic
331C23×C127C2×#4111yescharacteristic
332C23×C127C2×#4111yescharacteristic
333C23×C127C2×#4111yescharacteristic
334C23×C127C2×#4111yescharacteristic
335C23×C127H(5,𝔽2)11yescharacteristic
336C23×C127H(5,𝔽2)11yescharacteristic
337C23×C1272−1+411yescharacteristic
338C23×C1272−1+411yescharacteristic
339C2×C4×C127—22no—
340C2×C4×C127—22no—
341C2×C4×C127—22no—
342C2×C4×C127—22no—
343C2×C4×C127—22no—
344C2×C4×C127—22no—
345C2×C4×C127—22no—
346C2×C4×C127—22no—
347C2×C4×C127—22no—
348C2×C4×C127—22no—
349C2×C4×C127—22no—
350C2×C4×C127—22no—
351C2×C4×C127—22no—
352C2×C4×C127—22no—
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—416no—
391C2×C4×C127—41no—
392C2×C4×C127—41no—
393C2×C4×C127—41no—
394C2×C4×C127—41no—
395C2×C4×C127—41no—
396C2×C4×C127—41no—
397C2×C4×C127—41no—
398C2×C4×C127—41no—
399C2×C4×C127—41no—
400C2×C4×C127—41no—
401C2×C4×C127—41no—
402C2×C4×C127—41no—
403C2×C4×C127—41no—
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×C127C4×D414yes—
434C2×C4×C127C4×D414yes—
435C2×C4×C127C4×D414yes—
436C2×C4×C127#12114yes—
437C2×C4×C127C22⋊Q814yes—
438C22×C127—24no—
439C22×C127—24no—
440C22×C127—24no—
441C22×C127—42no—
442C22×C127—42no—
443C22×C127—42no—
444C22×C127—42no—
445C22×C127—42no—
446C22×C127—42no—
447C22×C127—42no—
448C22×C127—42no—
449C22×C127—42no—
450C22×C127—42no—
451C22×C127—42no—
452C22×C127—42no—
453C22×C127C2×C4×D411yescharacteristic
454C22×C127C2×C4×D411yescharacteristic
455C22×C127C2×C4×D411yescharacteristic
456C22×C127C2×C4×Q811yescharacteristic
457C22×C127C4×#4111yescharacteristic
458C22×C127#52011yescharacteristic
459C22×C127#52011yescharacteristic
460C22×C127C2×#12111yescharacteristic
461C22×C127C2×C22⋊Q811yescharacteristic
462C22×C127#52511yescharacteristic
463C22×C127#52511yescharacteristic
464C22×C127#52911yescharacteristic
465C22×C127#52911yescharacteristic
466C22×C127#53211yescharacteristic
467C22×C127#53311yescharacteristic
468C22×C127#53811yescharacteristic
469C22×C127#53911yescharacteristic
470C22×C127#54111yescharacteristic
471C22×C127#54211yescharacteristic
472C22×C127D4211yescharacteristic
473C22×C127D4211yescharacteristic
474C22×C127#54611yescharacteristic
475C22×C127#54611yescharacteristic
476C22×C127#54711yescharacteristic
477C22×C127#54711yescharacteristic
478C22×C127#54811yescharacteristic
479C22×C127#54811yescharacteristic
480C22×C127D4×Q811yescharacteristic
481C22×C127D4×Q811yescharacteristic
482C22×C127#55211yescharacteristic
483C22×C127#55211yescharacteristic
484C22×C127#55311yescharacteristic
485C22×C127#55311yescharacteristic
486C22×C127#55411yescharacteristic
487C22×C127#55411yescharacteristic
488C4×C127—24no—
489C4×C127—24no—
490C4×C127—24no—
491C4×C127—24no—
492C4×C127—24no—
493C4×C127—42no—
494C4×C127—42no—
495C4×C127—42no—
496C4×C127—42no—
497C4×C127—42no—
498C4×C127—42no—
499C4×C127—42no—
500C4×C127—81no—
501C4×C127—81no—
502#14204C12711yesmaximal, characteristic, direct product factor, Sylow
503C2×C127—44no—
504C2×C127C4×#12111yescharacteristic
505C2×C127C4×C22⋊Q811yescharacteristic
506C2×C127#233411yescharacteristic
507C2×C127#236011yescharacteristic
508C2×C127#236011yescharacteristic
509C2×C127#236111yescharacteristic
510C2×C127#236111yescharacteristic
511C2×C127#242411yescharacteristic
512C2×C127#242911yescharacteristic
513C2×C127#244911yescharacteristic
514C2×C127#245211yescharacteristic
515C2×C127#247011yescharacteristic
516C2×C127#247511yescharacteristic
517C2×C127#255811yescharacteristic
518C2×C127#258711yescharacteristic
519C2×#396C2×C12711yescharacteristic
520C2×#389C2×C12711yescharacteristic, complemented
521C2×#389C2×C12711yescharacteristic, complemented
522C2×#385C2×C12711yescharacteristic
523C2×#385C2×C12711yescharacteristic
524C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
525C2×C4×C22⋊C4C2×C12711yescharacteristic
526#1442C2×C12711yescharacteristic, complemented
527#1441C2×C12711yescharacteristic, complemented
528#1439C2×C12711yescharacteristic
529#1437C2×C12711yescharacteristic
530#1437C2×C12711yescharacteristic
531#1436C2×C12711yescharacteristic, complemented
532#1436C2×C12711yescharacteristic, complemented
533#1436C2×C12711yescharacteristic, complemented
534C127#1420411yescharacteristic, direct product factor, Sylow
535C24×C4C22×C12711yescharacteristic
536C22×C4⋊C4C22×C12711yescharacteristic
537C22×C4⋊C4C22×C12711yescharacteristic
538C22×C4⋊C4C22×C12711yescharacteristic
539C22×C4⋊C4C22×C12711yescharacteristic
540C22×C4⋊C4C22×C12711yescharacteristic
541C22×C4⋊C4C22×C12711yescharacteristic
542C22×C4⋊C4C22×C12711yescharacteristic
543C22×C4⋊C4C22×C12711yescharacteristic
544C22×C22⋊C4C22×C12711yescharacteristic
545C22×C22⋊C4C22×C12711yescharacteristic
546C22×C22⋊C4C22×C12711yescharacteristic
547C22×C22⋊C4C22×C12711yescharacteristic
548C22×C22⋊C4C22×C12711yescharacteristic
549C22×C22⋊C4C22×C12711yescharacteristic
550C22×C42C22×C12711yescharacteristic
551C22×C42C22×C12711yescharacteristic
552C22×C42C22×C12711yescharacteristic
553C22×C42C22×C12711yescharacteristic
554#396C4×C12718yescomplemented
555#389—24no—
556#389—24no—
557#385—24no—
558#385—24no—
559C4×C4⋊C4—24no—
560C4×C22⋊C4—24no—
561C2×#95C22×C12711yescharacteristic
562C2×#95C22×C12711yescharacteristic
563C2×#95C22×C12711yescharacteristic
564C2×#95C22×C12711yescharacteristic
565C2×#95C22×C12711yescharacteristic
566C2×#95C22×C12711yescharacteristic
567C2×#95C22×C12711yescharacteristic
568C2×#95C22×C12711yescharacteristic
569C2×#95C22×C12711yescharacteristic
570C2×#95C22×C12711yescharacteristic
571C2×#95C22×C12711yescharacteristic
572C2×#95C22×C12711yescharacteristic
573C2×#95C22×C12711yescharacteristic
574C2×#95C22×C12711yescharacteristic
575C2×#95C22×C12711yescharacteristic
576C2×#95C22×C12711yescharacteristic
577C25C23×C12711yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C12711yescharacteristic
586C23×C4C23×C12711yescharacteristic
587C23×C4C23×C12711yescharacteristic
588C23×C4C23×C12711yescharacteristic
589C23×C4C23×C12711yescharacteristic
590C23×C4C23×C12711yescharacteristic
591C23×C4C23×C12711yescharacteristic
592C23×C4C23×C12711yescharacteristic
593C23×C4C23×C12711yescharacteristic
594C23×C4C23×C12711yescharacteristic
595C23×C4C23×C12711yescharacteristic
596C23×C4C23×C12711yescharacteristic
597C23×C4C23×C12711yescharacteristic
598C23×C4C23×C12711yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4C2×C4×C12714yescomplemented
620C2×C4⋊C4C2×C4×C12714yescomplemented
621C2×C4⋊C4C2×C4×C12714yescomplemented
622C2×C4⋊C4D4×C12714yes—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4—41no—
637C2×C22⋊C4C2×C4×C12714yes—
638C2×C22⋊C4C2×C4×C12714yes—
639C2×C22⋊C4C2×C4×C12714yes—
640C2×C22⋊C4Q8×C12714yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42—41no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—41no—
665#95—41no—
666#95C2×C4×C12714yescomplemented
667#95D4×C12714yes—
668#95D4×C12714yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C12712yes—
682C24C2×Q8×C12712yes—
683C24#41×C12712yes—
684C24C24×C12711yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—28no—
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—21no—
722C22×C4—21no—
723C22×C4—21no—
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—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C12712yes—
769C22×C4C22×C4×C12712yes—
770C22×C4C22×C4×C12712yes—
771C22×C4C22×C4×C12712yes—
772C22×C4C22×C4×C12712yes—
773C22×C4C22×C4×C12712yes—
774C22×C4C2×D4×C12712yes—
775C22×C4C2×D4×C12712yes—
776C22×C4C2×D4×C12712yes—
777C22×C4C2×D4×C12712yes—
778C22×C4C2×D4×C12712yes—
779C22×C4C2×D4×C12712yes—
780C22×C4C2×D4×C12712yes—
781C22×C4C2×D4×C12712yes—
782C22×C4C2×D4×C12712yes—
783C22×C4C2×Q8×C12712yes—
784C22×C4C2×Q8×C12712yes—
785C22×C4#41×C12712yes—
786C22×C4#41×C12712yes—
787C22×C4#41×C12712yes—
788C22×C4#41×C12712yes—
789C22×C4#41×C12712yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C42—28no—
805C42—44no—
806C42—44no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C4×Q8×C12714yes—
843C23C23×C4×C12711yescharacteristic
844C23C22×D4×C12711yescharacteristic
845C23C22×D4×C12711yescharacteristic
846C23C22×D4×C12711yescharacteristic
847C23C22×Q8×C12711yescharacteristic
848C23C2×#41×C12711yescharacteristic
849C23C2×#41×C12711yescharacteristic
850C23C2×#41×C12711yescharacteristic
851C23C2×#41×C12711yescharacteristic
852C23C2×#41×C12711yescharacteristic
853C23C2×#41×C12711yescharacteristic
854C23H(5,𝔽2)×C12711yescharacteristic
855C23H(5,𝔽2)×C12711yescharacteristic
856C232−1+4×C12711yescharacteristic
857C232−1+4×C12711yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
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—416no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
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×C4C4×D4×C12714yes—
953C2×C4C4×D4×C12714yes—
954C2×C4C4×D4×C12714yes—
955C2×C4#121×C12714yes—
956C2×C4C22⋊Q8×C12714yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C4×D4×C12711yescharacteristic
973C22C2×C4×D4×C12711yescharacteristic
974C22C2×C4×D4×C12711yescharacteristic
975C22C2×C4×Q8×C12711yescharacteristic
976C22C4×#41×C12711yescharacteristic
977C22#520×C12711yescharacteristic
978C22#520×C12711yescharacteristic
979C22C2×#121×C12711yescharacteristic
980C22C2×C22⋊Q8×C12711yescharacteristic
981C22#525×C12711yescharacteristic
982C22#525×C12711yescharacteristic
983C22#529×C12711yescharacteristic
984C22#529×C12711yescharacteristic
985C22#532×C12711yescharacteristic
986C22#533×C12711yescharacteristic
987C22#538×C12711yescharacteristic
988C22#539×C12711yescharacteristic
989C22#541×C12711yescharacteristic
990C22#542×C12711yescharacteristic
991C22D42×C12711yescharacteristic
992C22D42×C12711yescharacteristic
993C22#546×C12711yescharacteristic
994C22#546×C12711yescharacteristic
995C22#547×C12711yescharacteristic
996C22#547×C12711yescharacteristic
997C22#548×C12711yescharacteristic
998C22#548×C12711yescharacteristic
999C22D4×Q8×C12711yescharacteristic
1000C22D4×Q8×C12711yescharacteristic
1001C22#552×C12711yescharacteristic
1002C22#552×C12711yescharacteristic
1003C22#553×C12711yescharacteristic
1004C22#553×C12711yescharacteristic
1005C22#554×C12711yescharacteristic
1006C22#554×C12711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C4×#121×C12711yescharacteristic
1023C2C4×C22⋊Q8×C12711yescharacteristic
1024C2C127×#233411yescharacteristic
1025C2C127×#236011yescharacteristic
1026C2C127×#236011yescharacteristic
1027C2C127×#236111yescharacteristic
1028C2C127×#236111yescharacteristic
1029C2C127×#242411yescharacteristic
1030C2C127×#242911yescharacteristic
1031C2C127×#244911yescharacteristic
1032C2C127×#245211yescharacteristic
1033C2C127×#247011yescharacteristic
1034C2C127×#247511yescharacteristic
1035C2C127×#255811yescharacteristic
1036C2C127×#258711yescharacteristic
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
2. C2×#389×C127C2semidirect
3. C2×#389×C127C2semidirect
6. C2×C4×C4⋊C4×C127C2semidirect
8. C127×#1442C2semidirect
9. C127×#1441C2semidirect
13. C127×#1436C2semidirect
14. C127×#1436C2semidirect
15. C127×#1436C2semidirect
35. #396×C127C4semidirect
100. C2×C4⋊C4×C127C2×C4semidirect
101. C2×C4⋊C4×C127C2×C4semidirect
102. C2×C4⋊C4×C127C2×C4semidirect
147. #95×C127C2×C4semidirect
502. #14204C127direct (N × H)
520. C2×#389C2×C127semidirect
521. C2×#389C2×C127semidirect
524. C2×C4×C4⋊C4C2×C127semidirect
526. #1442C2×C127semidirect
527. #1441C2×C127semidirect
531. #1436C2×C127semidirect
532. #1436C2×C127semidirect
533. #1436C2×C127semidirect
534. C127#14204direct (N × H)
554. #396C4×C127semidirect
619. C2×C4⋊C4C2×C4×C127semidirect
620. C2×C4⋊C4C2×C4×C127semidirect
621. C2×C4⋊C4C2×C4×C127semidirect
666. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1272
C2×#389×C1272
C2×#385×C1272
C2×C4×C4⋊C4×C1272
C2×C4×C22⋊C4×C1272
C127×#14422
C127×#14412
C127×#14392
C127×#14372
C127×#14362
#14204127