Finite Group Databasebeta

← C127×#14442 #44578115

Subgroups — C127×#14442 #44578115

Order 32512.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 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
6C127×#1444C211yesmaximal, characteristic, complemented
7C127×#1442C211yesmaximal, characteristic, complemented
8C127×#1442C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic
11C127×#1439C211yesmaximal, characteristic
12C127×#1436C211yesmaximal, characteristic, complemented
13C127×C4⋊#95C211yesmaximal, characteristic, complemented
14C127×C4⋊#95C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic
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
33#389×C127—24no—
34#388×C127—24no—
35#388×C127C418yescomplemented
36#385×C127—24no—
37#385×C127—24no—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
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
56C25×C127C2311yescharacteristic
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—41no—
61C23×C4×C127—41no—
62C23×C4×C127—41no—
63C23×C4×C127—41no—
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
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
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
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—41no—
91C2×C4⋊C4×C127—41no—
92C2×C4⋊C4×C127—41no—
93C2×C4⋊C4×C127—41no—
94C2×C4⋊C4×C127—41no—
95C2×C4⋊C4×C127—41no—
96C2×C4⋊C4×C127—41no—
97C2×C4⋊C4×C127—41no—
98C2×C4⋊C4×C127—41no—
99C2×C4⋊C4×C127—41no—
100C2×C4⋊C4×C127C2×C414yescomplemented
101C2×C4⋊C4×C127D414yes—
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—41no—
110C2×C22⋊C4×C127—41no—
111C2×C22⋊C4×C127—41no—
112C2×C22⋊C4×C127—41no—
113C2×C22⋊C4×C127—41no—
114C2×C22⋊C4×C127—41no—
115C2×C22⋊C4×C127C2×C414yes—
116C2×C22⋊C4×C127C2×C414yes—
117C2×C22⋊C4×C127C2×C414yes—
118C2×C22⋊C4×C127D414yes—
119C2×C22⋊C4×C127Q814yes—
120C2×C42×C127—22no—
121C2×C42×C127—22no—
122C2×C42×C127—41no—
123C2×C42×C127—41no—
124C2×C42×C127—41no—
125C2×C42×C127C2×C414yescomplemented
126#95×C127—22no—
127#95×C127—22no—
128#95×C127—22no—
129#95×C127—22no—
130#95×C127—22no—
131#95×C127—22no—
132#95×C127—22no—
133#95×C127—22no—
134#95×C127—22no—
135#95×C127—41no—
136#95×C127—41no—
137#95×C127—41no—
138#95×C127—41no—
139#95×C127—41no—
140#95×C127—41no—
141#95×C127—41no—
142#95×C127C2×C414yescomplemented
143#95×C127C2×C414yescomplemented
144C24×C127—21no—
145C24×C127—21no—
146C24×C127—21no—
147C24×C127—21no—
148C24×C127—21no—
149C24×C127—21no—
150C24×C127—21no—
151C24×C127—21no—
152C24×C127—21no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127C22×C412yes—
157C24×C127C2×D412yes—
158C24×C127C2×Q812yes—
159C24×C127C2411yescharacteristic
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
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—21no—
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—44no—
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×Q812yes—
261C22×C4×C127C2×Q812yes—
262C22×C4×C127#4112yes—
263C22×C4×C127#4112yes—
264C22×C4×C127#4112yes—
265C4⋊C4×C127—28no—
266C4⋊C4×C127—44no—
267C4⋊C4×C127—44no—
268C4⋊C4×C127—44no—
269C4⋊C4×C127—44no—
270C4⋊C4×C127—44no—
271C4⋊C4×C127—44no—
272C4⋊C4×C127—44no—
273C22⋊C4×C127—28no—
274C22⋊C4×C127—44no—
275C22⋊C4×C127—44no—
276C22⋊C4×C127—44no—
277C22⋊C4×C127—44no—
278C22⋊C4×C127C4⋊C4116yescomplemented
279C42×C127—44no—
280C42×C127—44no—
281C23×C127—22no—
282C23×C127—22no—
283C23×C127—22no—
284C23×C127—22no—
285C23×C127—22no—
286C23×C127—22no—
287C23×C127—22no—
288C23×C127—22no—
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—41no—
300C23×C127—41no—
301C23×C127—41no—
302C23×C127—41no—
303C23×C127—41no—
304C23×C127—41no—
305C23×C127—41no—
306C23×C127—41no—
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×C127C2×C4⋊C414yes—
316C23×C127C23×C411yescharacteristic
317C23×C127C22×D411yescharacteristic
318C23×C127C22×D411yescharacteristic
319C23×C127C22×Q811yescharacteristic
320C23×C127C2×#4111yescharacteristic
321C23×C127C2×#4111yescharacteristic
322C23×C127C2×#4111yescharacteristic
323C23×C127H(5,𝔽2)11yescharacteristic
324C23×C127H(5,𝔽2)11yescharacteristic
325C23×C127H(5,𝔽2)11yescharacteristic
326C23×C127H(5,𝔽2)11yescharacteristic
327C23×C127H(5,𝔽2)11yescharacteristic
328C23×C1272−1+411yescharacteristic
329C23×C1272−1+411yescharacteristic
330C23×C1272−1+411yescharacteristic
331C2×C4×C127—22no—
332C2×C4×C127—22no—
333C2×C4×C127—22no—
334C2×C4×C127—22no—
335C2×C4×C127—22no—
336C2×C4×C127—22no—
337C2×C4×C127—22no—
338C2×C4×C127—22no—
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—416no—
371C2×C4×C127—41no—
372C2×C4×C127—41no—
373C2×C4×C127—41no—
374C2×C4×C127—41no—
375C2×C4×C127—41no—
376C2×C4×C127—41no—
377C2×C4×C127—41no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
380C2×C4×C127—41no—
381C2×C4×C127—41no—
382C2×C4×C127—41no—
383C2×C4×C127—41no—
384C2×C4×C127—41no—
385C2×C4×C127—41no—
386C2×C4×C127—41no—
387C2×C4×C127—41no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
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×C127C2×C4⋊C414yes—
428C2×C4×C127C2×C4⋊C414yes—
429C2×C4×C127C4×D414yes—
430C22×C127—24no—
431C22×C127—24no—
432C22×C127—24no—
433C22×C127—42no—
434C22×C127—42no—
435C22×C127—42no—
436C22×C127—42no—
437C22×C127—42no—
438C22×C127—42no—
439C22×C127—42no—
440C22×C127—42no—
441C22×C127—42no—
442C22×C127—42no—
443C22×C127—42no—
444C22×C127—42no—
445C22×C127C22×C4⋊C411yescharacteristic
446C22×C127C2×C4×D411yescharacteristic
447C22×C127C4×#4111yescharacteristic
448C22×C127#51811yescharacteristic
449C22×C127#52011yescharacteristic
450C22×C127#52011yescharacteristic
451C22×C127#52011yescharacteristic
452C22×C127#53411yescharacteristic
453C22×C127#53511yescharacteristic
454C22×C127#53611yescharacteristic
455C22×C127#53711yescharacteristic
456C22×C127#53811yescharacteristic
457C22×C127#53811yescharacteristic
458C22×C127#53911yescharacteristic
459C22×C127#53911yescharacteristic
460C22×C127#54111yescharacteristic
461C22×C127#54211yescharacteristic
462C22×C127#54411yescharacteristic
463C22×C127#54411yescharacteristic
464C22×C127D4211yescharacteristic
465C22×C127#54611yescharacteristic
466C22×C127#54611yescharacteristic
467C22×C127#54611yescharacteristic
468C22×C127#54711yescharacteristic
469C22×C127#54811yescharacteristic
470C22×C127D4×Q811yescharacteristic
471C22×C127#55411yescharacteristic
472C22×C127#55411yescharacteristic
473C22×C127#55411yescharacteristic
474C22×C127#55611yescharacteristic
475C22×C127#55911yescharacteristic
476C22×C127#56011yescharacteristic
477C22×C127#56211yescharacteristic
478C22×C127#56211yescharacteristic
479C22×C127#56311yescharacteristic
480C4×C127—24no—
481C4×C127—24no—
482C4×C127—24no—
483C4×C127—42no—
484C4×C127—42no—
485C4×C127—42no—
486C4×C127—42no—
487C4×C127—42no—
488C4×C127—42no—
489C4×C127—42no—
490C4×C127—81no—
491C4×C127—81no—
492C4×C127—81no—
493C4×C127—81no—
494#14442C12711yesmaximal, characteristic, direct product factor, Sylow
495C2×C127—44no—
496C2×C127#231711yescharacteristic
497C2×C127#232511yescharacteristic
498C2×C127#233411yescharacteristic
499C2×C127D4×C4⋊C411yescharacteristic
500C2×C127#234911yescharacteristic
501C2×C127#236711yescharacteristic
502C2×C127#237611yescharacteristic
503C2×C127#267811yescharacteristic
504C2×C127#268111yescharacteristic
505C2×C127#268911yescharacteristic
506C2×C127#270411yescharacteristic
507C2×C127#271011yescharacteristic
508C2×C127#272911yescharacteristic
509C2×C127#278811yescharacteristic
510C2×C127#280711yescharacteristic
511C2×#389C2×C12711yescharacteristic, complemented
512C2×#388C2×C12711yescharacteristic
513C2×#388C2×C12711yescharacteristic
514C2×#385C2×C12711yescharacteristic
515C2×#385C2×C12711yescharacteristic
516#1444C2×C12711yescharacteristic, complemented
517#1442C2×C12711yescharacteristic, complemented
518#1442C2×C12711yescharacteristic, complemented
519#1441C2×C12711yescharacteristic, complemented
520#1439C2×C12711yescharacteristic
521#1439C2×C12711yescharacteristic
522#1436C2×C12711yescharacteristic, complemented
523C4⋊#95C2×C12711yescharacteristic, complemented
524C4⋊#95C2×C12711yescharacteristic, complemented
525C22⋊#95C2×C12711yescharacteristic
526C127#1444211yescharacteristic, direct product factor, Sylow
527C24×C4C22×C12711yescharacteristic
528C22×C4⋊C4C22×C12711yescharacteristic
529C22×C4⋊C4C22×C12711yescharacteristic
530C22×C4⋊C4C22×C12711yescharacteristic
531C22×C4⋊C4C22×C12711yescharacteristic
532C22×C4⋊C4C22×C12711yescharacteristic
533C22×C4⋊C4C22×C12711yescharacteristic
534C22×C4⋊C4C22×C12711yescharacteristic
535C22×C4⋊C4C22×C12711yescharacteristic
536C22×C22⋊C4C22×C12711yescharacteristic
537C22×C22⋊C4C22×C12711yescharacteristic
538C22×C22⋊C4C22×C12711yescharacteristic
539C22×C22⋊C4C22×C12711yescharacteristic
540C22×C22⋊C4C22×C12711yescharacteristic
541C22×C22⋊C4C22×C12711yescharacteristic
542C22×C42C22×C12711yescharacteristic
543C22×C42C22×C12711yescharacteristic
544#389—24no—
545#388—24no—
546#388C4×C12718yescomplemented
547#385—24no—
548#385—24no—
549C2×#95C22×C12711yescharacteristic
550C2×#95C22×C12711yescharacteristic
551C2×#95C22×C12711yescharacteristic
552C2×#95C22×C12711yescharacteristic
553C2×#95C22×C12711yescharacteristic
554C2×#95C22×C12711yescharacteristic
555C2×#95C22×C12711yescharacteristic
556C2×#95C22×C12711yescharacteristic
557C2×#95C22×C12711yescharacteristic
558C2×#95C22×C12711yescharacteristic
559C2×#95C22×C12711yescharacteristic
560C2×#95C22×C12711yescharacteristic
561C2×#95C22×C12711yescharacteristic
562C2×#95C22×C12711yescharacteristic
563C2×#95C22×C12711yescharacteristic
564C2×#95C22×C12711yescharacteristic
565C2×#95C22×C12711yescharacteristic
566C2×#95C22×C12711yescharacteristic
567C25C23×C12711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C12711yescharacteristic
576C23×C4C23×C12711yescharacteristic
577C23×C4C23×C12711yescharacteristic
578C23×C4C23×C12711yescharacteristic
579C23×C4C23×C12711yescharacteristic
580C23×C4C23×C12711yescharacteristic
581C23×C4C23×C12711yescharacteristic
582C23×C4C23×C12711yescharacteristic
583C23×C4C23×C12711yescharacteristic
584C23×C4C23×C12711yescharacteristic
585C23×C4C23×C12711yescharacteristic
586C23×C4C23×C12711yescharacteristic
587C23×C4C23×C12711yescharacteristic
588C23×C4C23×C12711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×C4×C12714yescomplemented
612C2×C4⋊C4D4×C12714yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C12714yes—
627C2×C22⋊C4C2×C4×C12714yes—
628C2×C22⋊C4C2×C4×C12714yes—
629C2×C22⋊C4D4×C12714yes—
630C2×C22⋊C4Q8×C12714yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C12714yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C12714yescomplemented
654#95C2×C4×C12714yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C12712yes—
668C24C2×D4×C12712yes—
669C24C2×Q8×C12712yes—
670C24C24×C12711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
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—21no—
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—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C12712yes—
761C22×C4C22×C4×C12712yes—
762C22×C4C22×C4×C12712yes—
763C22×C4C22×C4×C12712yes—
764C22×C4C22×C4×C12712yes—
765C22×C4C22×C4×C12712yes—
766C22×C4C2×D4×C12712yes—
767C22×C4C2×D4×C12712yes—
768C22×C4C2×D4×C12712yes—
769C22×C4C2×D4×C12712yes—
770C22×C4C2×D4×C12712yes—
771C22×C4C2×Q8×C12712yes—
772C22×C4C2×Q8×C12712yes—
773C22×C4#41×C12712yes—
774C22×C4#41×C12712yes—
775C22×C4#41×C12712yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C127116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C12714yes—
827C23C23×C4×C12711yescharacteristic
828C23C22×D4×C12711yescharacteristic
829C23C22×D4×C12711yescharacteristic
830C23C22×Q8×C12711yescharacteristic
831C23C2×#41×C12711yescharacteristic
832C23C2×#41×C12711yescharacteristic
833C23C2×#41×C12711yescharacteristic
834C23H(5,𝔽2)×C12711yescharacteristic
835C23H(5,𝔽2)×C12711yescharacteristic
836C23H(5,𝔽2)×C12711yescharacteristic
837C23H(5,𝔽2)×C12711yescharacteristic
838C23H(5,𝔽2)×C12711yescharacteristic
839C232−1+4×C12711yescharacteristic
840C232−1+4×C12711yescharacteristic
841C232−1+4×C12711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
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×C4C2×C4⋊C4×C12714yes—
939C2×C4C2×C4⋊C4×C12714yes—
940C2×C4C4×D4×C12714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C12711yescharacteristic
957C22C2×C4×D4×C12711yescharacteristic
958C22C4×#41×C12711yescharacteristic
959C22#518×C12711yescharacteristic
960C22#520×C12711yescharacteristic
961C22#520×C12711yescharacteristic
962C22#520×C12711yescharacteristic
963C22#534×C12711yescharacteristic
964C22#535×C12711yescharacteristic
965C22#536×C12711yescharacteristic
966C22#537×C12711yescharacteristic
967C22#538×C12711yescharacteristic
968C22#538×C12711yescharacteristic
969C22#539×C12711yescharacteristic
970C22#539×C12711yescharacteristic
971C22#541×C12711yescharacteristic
972C22#542×C12711yescharacteristic
973C22#544×C12711yescharacteristic
974C22#544×C12711yescharacteristic
975C22D42×C12711yescharacteristic
976C22#546×C12711yescharacteristic
977C22#546×C12711yescharacteristic
978C22#546×C12711yescharacteristic
979C22#547×C12711yescharacteristic
980C22#548×C12711yescharacteristic
981C22D4×Q8×C12711yescharacteristic
982C22#554×C12711yescharacteristic
983C22#554×C12711yescharacteristic
984C22#554×C12711yescharacteristic
985C22#556×C12711yescharacteristic
986C22#559×C12711yescharacteristic
987C22#560×C12711yescharacteristic
988C22#562×C12711yescharacteristic
989C22#562×C12711yescharacteristic
990C22#563×C12711yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C127×#231711yescharacteristic
1007C2C127×#232511yescharacteristic
1008C2C127×#233411yescharacteristic
1009C2D4×C4⋊C4×C12711yescharacteristic
1010C2C127×#234911yescharacteristic
1011C2C127×#236711yescharacteristic
1012C2C127×#237611yescharacteristic
1013C2C127×#267811yescharacteristic
1014C2C127×#268111yescharacteristic
1015C2C127×#268911yescharacteristic
1016C2C127×#270411yescharacteristic
1017C2C127×#271011yescharacteristic
1018C2C127×#272911yescharacteristic
1019C2C127×#278811yescharacteristic
1020C2C127×#280711yescharacteristic
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. C127×#1444C2semidirect
7. C127×#1442C2semidirect
8. C127×#1442C2semidirect
9. C127×#1441C2semidirect
12. C127×#1436C2semidirect
13. C127×C4⋊#95C2semidirect
14. C127×C4⋊#95C2semidirect
35. #388×C127C4semidirect
100. C2×C4⋊C4×C127C2×C4semidirect
125. C2×C42×C127C2×C4semidirect
142. #95×C127C2×C4semidirect
143. #95×C127C2×C4semidirect
278. C22⋊C4×C127C4⋊C4semidirect
494. #14442C127direct (N × H)
511. C2×#389C2×C127semidirect
516. #1444C2×C127semidirect
517. #1442C2×C127semidirect
518. #1442C2×C127semidirect
519. #1441C2×C127semidirect
522. #1436C2×C127semidirect
523. C4⋊#95C2×C127semidirect
524. C4⋊#95C2×C127semidirect
526. C127#14442direct (N × H)
546. #388C4×C127semidirect
611. C2×C4⋊C4C2×C4×C127semidirect
636. C2×C42C2×C4×C127semidirect
653. #95C2×C4×C127semidirect
654. #95C2×C4×C127semidirect
789. 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
C127×#14442
C127×#14422
C127×#14412
C127×#14392
C127×#14362
C127×C4⋊#952
C127×C22⋊#952
#14442127