Finite Group Databasebeta

← C127×#14112 #44577785

Subgroups — C127×#14112 #44577785

Order 32512.

1846 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×#389×C127C211yesmaximal, characteristic, complemented
2C2×#388×C127C211yesmaximal, characteristic
3C2×#388×C127C211yesmaximal, characteristic
4C2×#385×C127C211yesmaximal, characteristic
5C2×#385×C127C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
8C127×#1444C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic
11C127×#1439C211yesmaximal, characteristic
12C127×#1436C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C4⋊#95C211yesmaximal, 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#389×C127—24no—
36#388×C127—24no—
37#388×C127C418yescomplemented
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—22no—
98C2×C4⋊C4×C127—41no—
99C2×C4⋊C4×C127—41no—
100C2×C4⋊C4×C127—41no—
101C2×C4⋊C4×C127—41no—
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—41no—
116C2×C22⋊C4×C127—41no—
117C2×C22⋊C4×C127C2×C414yes—
118C2×C22⋊C4×C127C2×C414yes—
119C2×C22⋊C4×C127C2×C414yes—
120C2×C22⋊C4×C127D414yes—
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—41no—
131C2×C42×C127—41no—
132C2×C42×C127—41no—
133C2×C42×C127C2×C414yescomplemented
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—22no—
146#95×C127—41no—
147#95×C127C2×C414yescomplemented
148#95×C127C2×C414yescomplemented
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×D412yes—
164C24×C127C2×Q812yes—
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×Q812yes—
264C22×C4×C127C2×Q812yes—
265C22×C4×C127#4112yes—
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—44no—
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—44no—
283C22⋊C4×C127—44no—
284C22⋊C4×C127C4⋊C4116yescomplemented
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×C127C2×C4⋊C414yes—
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×C127C2×C4⋊C414yes—
434C2×C4×C127C2×C4⋊C414yes—
435C2×C4×C127C4×D414yes—
436C2×C4×C127C4×D414yes—
437C2×C4×C127#12114yes—
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×C127C22×C4⋊C411yescharacteristic
454C22×C127C2×C4×D411yescharacteristic
455C22×C127C2×C4×D411yescharacteristic
456C22×C127C4×#4111yescharacteristic
457C22×C127C4×#4111yescharacteristic
458C22×C127#52011yescharacteristic
459C22×C127#52011yescharacteristic
460C22×C127C2×#12111yescharacteristic
461C22×C127#52511yescharacteristic
462C22×C127#52511yescharacteristic
463C22×C127#52511yescharacteristic
464C22×C127#52911yescharacteristic
465C22×C127#53211yescharacteristic
466C22×C127#53311yescharacteristic
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#54711yescharacteristic
479C22×C127#54811yescharacteristic
480C22×C127D4×Q811yescharacteristic
481C22×C127D4×Q811yescharacteristic
482C22×C127#55111yescharacteristic
483C22×C127#55211yescharacteristic
484C22×C127#55411yescharacteristic
485C22×C127#55411yescharacteristic
486C22×C127#55611yescharacteristic
487C22×C127#55911yescharacteristic
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#14112C12711yesmaximal, characteristic, direct product factor, Sylow
503C2×C127—44no—
504C2×C127#229611yescharacteristic
505C2×C127C4×#12111yescharacteristic
506C2×C127#233411yescharacteristic
507C2×C127D4×C4⋊C411yescharacteristic
508C2×C127D4×C4⋊C411yescharacteristic
509C2×C127#235911yescharacteristic
510C2×C127#236711yescharacteristic
511C2×C127#242411yescharacteristic
512C2×C127#242911yescharacteristic
513C2×C127#245511yescharacteristic
514C2×C127#246111yescharacteristic
515C2×C127#246511yescharacteristic
516C2×C127#247811yescharacteristic
517C2×C127#255611yescharacteristic
518C2×C127#258911yescharacteristic
519C2×#389C2×C12711yescharacteristic, complemented
520C2×#388C2×C12711yescharacteristic
521C2×#388C2×C12711yescharacteristic
522C2×#385C2×C12711yescharacteristic
523C2×#385C2×C12711yescharacteristic
524C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
525C2×C4×C22⋊C4C2×C12711yescharacteristic
526#1444C2×C12711yescharacteristic, complemented
527#1441C2×C12711yescharacteristic, complemented
528#1439C2×C12711yescharacteristic
529#1439C2×C12711yescharacteristic
530#1436C2×C12711yescharacteristic, complemented
531#1436C2×C12711yescharacteristic, complemented
532#1436C2×C12711yescharacteristic, complemented
533C4⋊#95C2×C12711yescharacteristic, complemented
534C127#1411211yescharacteristic, 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#389—24no—
555#388—24no—
556#388C4×C12718yescomplemented
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—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
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—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4C2×C4×C12714yes—
637C2×C22⋊C4C2×C4×C12714yes—
638C2×C22⋊C4C2×C4×C12714yes—
639C2×C22⋊C4D4×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—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42C2×C4×C12714yescomplemented
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—22no—
665#95—41no—
666#95C2×C4×C12714yescomplemented
667#95C2×C4×C12714yescomplemented
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×D4×C12712yes—
683C24C2×Q8×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×Q8×C12712yes—
783C22×C4C2×Q8×C12712yes—
784C22×C4#41×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—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C4⋊C4×C127116yescomplemented
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—
842C23C2×C4⋊C4×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×C4C2×C4⋊C4×C12714yes—
953C2×C4C2×C4⋊C4×C12714yes—
954C2×C4C4×D4×C12714yes—
955C2×C4C4×D4×C12714yes—
956C2×C4#121×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—
972C22C22×C4⋊C4×C12711yescharacteristic
973C22C2×C4×D4×C12711yescharacteristic
974C22C2×C4×D4×C12711yescharacteristic
975C22C4×#41×C12711yescharacteristic
976C22C4×#41×C12711yescharacteristic
977C22#520×C12711yescharacteristic
978C22#520×C12711yescharacteristic
979C22C2×#121×C12711yescharacteristic
980C22#525×C12711yescharacteristic
981C22#525×C12711yescharacteristic
982C22#525×C12711yescharacteristic
983C22#529×C12711yescharacteristic
984C22#532×C12711yescharacteristic
985C22#533×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#547×C12711yescharacteristic
998C22#548×C12711yescharacteristic
999C22D4×Q8×C12711yescharacteristic
1000C22D4×Q8×C12711yescharacteristic
1001C22#551×C12711yescharacteristic
1002C22#552×C12711yescharacteristic
1003C22#554×C12711yescharacteristic
1004C22#554×C12711yescharacteristic
1005C22#556×C12711yescharacteristic
1006C22#559×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—
1022C2C127×#229611yescharacteristic
1023C2C4×#121×C12711yescharacteristic
1024C2C127×#233411yescharacteristic
1025C2D4×C4⋊C4×C12711yescharacteristic
1026C2D4×C4⋊C4×C12711yescharacteristic
1027C2C127×#235911yescharacteristic
1028C2C127×#236711yescharacteristic
1029C2C127×#242411yescharacteristic
1030C2C127×#242911yescharacteristic
1031C2C127×#245511yescharacteristic
1032C2C127×#246111yescharacteristic
1033C2C127×#246511yescharacteristic
1034C2C127×#247811yescharacteristic
1035C2C127×#255611yescharacteristic
1036C2C127×#258911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C127C2semidirect
6. C2×C4×C4⋊C4×C127C2semidirect
8. C127×#1444C2semidirect
9. C127×#1441C2semidirect
12. C127×#1436C2semidirect
13. C127×#1436C2semidirect
14. C127×#1436C2semidirect
15. C127×C4⋊#95C2semidirect
37. #388×C127C4semidirect
102. C2×C4⋊C4×C127C2×C4semidirect
133. C2×C42×C127C2×C4semidirect
147. #95×C127C2×C4semidirect
148. #95×C127C2×C4semidirect
284. C22⋊C4×C127C4⋊C4semidirect
502. #14112C127direct (N × H)
519. C2×#389C2×C127semidirect
524. C2×C4×C4⋊C4C2×C127semidirect
526. #1444C2×C127semidirect
527. #1441C2×C127semidirect
530. #1436C2×C127semidirect
531. #1436C2×C127semidirect
532. #1436C2×C127semidirect
533. C4⋊#95C2×C127semidirect
534. C127#14112direct (N × H)
556. #388C4×C127semidirect
621. C2×C4⋊C4C2×C4×C127semidirect
652. C2×C42C2×C4×C127semidirect
666. #95C2×C4×C127semidirect
667. #95C2×C4×C127semidirect
803. C22⋊C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#388×C1272
C2×#385×C1272
C2×C4×C4⋊C4×C1272
C2×C4×C22⋊C4×C1272
C127×#14442
C127×#14412
C127×#14392
C127×#14362
C127×C4⋊#952
#14112127