Finite Group Databasebeta

← C127×#13998 #44577671

Subgroups — C127×#13998 #44577671

Order 32512.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic, complemented
3C2×#390×C127C212yesmaximal, complemented
4C2×#390×C127C211yesmaximal, characteristic, complemented
5C2×#389×C127C211yesmaximal, characteristic, complemented
6C2×#380×C127C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1438C212yesmaximal, complemented
11C127×#1437C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C24×C4×C127C2211yescharacteristic
15C2×#121×C127—24no—
16C2×#121×C127—24no—
17C2×#121×C127C418yescomplemented
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2212yes—
30C22×C42×C127C2211yescharacteristic
31C22×C42×C127C2212yes—
32C22×C42×C127C2211yescharacteristic
33#390×C127—24no—
34#390×C127—28no—
35#390×C127—24no—
36#389×C127—24no—
37#380×C127—24no—
38C4×C4⋊C4×C127—24no—
39C4×C22⋊C4×C127—24no—
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C2×#95×C127C2212yes—
44C2×#95×C127C2211yescharacteristic
45C25×C127C2312yes—
46C25×C127C2311yescharacteristic
47C22×D4×C127—24no—
48C22×D4×C127—24no—
49C22×D4×C127—24no—
50C22×D4×C127—24no—
51C22×D4×C127—22no—
52C22×D4×C127—22no—
53C22×D4×C127—22no—
54C22×D4×C127—22no—
55C22×D4×C127—22no—
56C22×D4×C127—22no—
57C22×D4×C127—42no—
58C22×D4×C127—42no—
59C22×D4×C127C2×C414yes—
60C22×D4×C127C2×C418yes—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—22no—
64C23×C4×C127—22no—
65C23×C4×C127—22no—
66C23×C4×C127—22no—
67C23×C4×C127C2×C414yes—
68C23×C4×C127C2312yes—
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2312yes—
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2312yes—
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77#121×C127—232no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—24no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—24no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127—42no—
86C2×C4⋊C4×C127C2×C414yes—
87C2×C4⋊C4×C127D414yes—
88C2×C4⋊C4×C127D414yes—
89C2×C4⋊C4×C127D414yescomplemented
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—24no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—24no—
105C2×C22⋊C4×C127—24no—
106C2×C22⋊C4×C127—24no—
107C2×C22⋊C4×C127—42no—
108C2×C22⋊C4×C127—42no—
109C2×C22⋊C4×C127—42no—
110C2×C22⋊C4×C127—42no—
111C2×C22⋊C4×C127—42no—
112C2×C22⋊C4×C127C2×C418yes—
113C2×C22⋊C4×C127D414yescomplemented
114C2×C42×C127—22no—
115C2×C42×C127—22no—
116C2×C42×C127—22no—
117C2×C42×C127—24no—
118C2×C42×C127—22no—
119C2×C42×C127—24no—
120C2×C42×C127—22no—
121C2×C42×C127—42no—
122C2×C42×C127D414yescomplemented
123#95×C127—22no—
124#95×C127—22no—
125#95×C127—24no—
126#95×C127—24no—
127#95×C127—24no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—21no—
132C24×C127—21no—
133C24×C127—21no—
134C24×C127—21no—
135C24×C127—21no—
136C24×C127—21no—
137C24×C127—21no—
138C24×C127—21no—
139C24×C127—21no—
140C24×C127—22no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—22no—
144C24×C127—22no—
145C24×C127—22no—
146C24×C127—22no—
147C24×C127—22no—
148C24×C127—22no—
149C24×C127—22no—
150C24×C127—22no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—22no—
154C24×C127C22×C414yes—
155C24×C127C22×C412yes—
156C24×C127C2×D412yes—
157C24×C127#4112yes—
158C24×C127C2411yescharacteristic
159C2×D4×C127—216no—
160C2×D4×C127—216no—
161C2×D4×C127—28no—
162C2×D4×C127—28no—
163C2×D4×C127—28no—
164C2×D4×C127—48no—
165C2×D4×C127—48no—
166C2×D4×C127—48no—
167C2×D4×C127—48no—
168C2×D4×C127—48no—
169C2×D4×C127—44no—
170C2×D4×C127—44no—
171C2×D4×C127—44no—
172C2×D4×C127—44no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—21no—
176C22×C4×C127—22no—
177C22×C4×C127—21no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
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—22no—
188C22×C4×C127—21no—
189C22×C4×C127—22no—
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—22no—
200C22×C4×C127—22no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—22no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—22no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—28no—
212C22×C4×C127—28no—
213C22×C4×C127—28no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—22no—
220C22×C4×C127—22no—
221C22×C4×C127—44no—
222C22×C4×C127—44no—
223C22×C4×C127—44no—
224C22×C4×C127—44no—
225C22×C4×C127C22×C412yes—
226C22×C4×C127C22×C414yes—
227C22×C4×C127C22×C412yes—
228C22×C4×C127C2×D412yes—
229C22×C4×C127C2×D414yes—
230C22×C4×C127C2×D412yes—
231C22×C4×C127C2×D414yes—
232C22×C4×C127C2×D414yes—
233C22×C4×C127C2×D412yes—
234C22×C4×C127C2×D412yes—
235C22×C4×C127C2×D412yes—
236C22×C4×C127C2×D412yes—
237C22×C4×C127C2×D412yes—
238C22×C4×C127C2×D412yes—
239C22×C4×C127#4112yes—
240C22×C4×C127#4112yes—
241C22×C4×C127#4112yes—
242C22×C4×C127#4112yes—
243C4⋊C4×C127—28no—
244C4⋊C4×C127—48no—
245C4⋊C4×C127—44no—
246C4⋊C4×C127C22⋊C4116yescomplemented
247C22⋊C4×C127—28no—
248C22⋊C4×C127—216no—
249C22⋊C4×C127—28no—
250C22⋊C4×C127—48no—
251C22⋊C4×C127—48no—
252C22⋊C4×C127—48no—
253C22⋊C4×C127—48no—
254C22⋊C4×C127—48no—
255C42×C127—28no—
256C42×C127—48no—
257C42×C127—44no—
258C23×C127—22no—
259C23×C127—22no—
260C23×C127—22no—
261C23×C127—22no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—22no—
265C23×C127—22no—
266C23×C127—22no—
267C23×C127—22no—
268C23×C127—22no—
269C23×C127—22no—
270C23×C127—22no—
271C23×C127—22no—
272C23×C127—22no—
273C23×C127—22no—
274C23×C127—22no—
275C23×C127—22no—
276C23×C127—24no—
277C23×C127—24no—
278C23×C127—24no—
279C23×C127—24no—
280C23×C127—24no—
281C23×C127—24no—
282C23×C127—24no—
283C23×C127—41no—
284C23×C127—41no—
285C23×C127—41no—
286C23×C127—41no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—41no—
290C23×C127—41no—
291C23×C127—41no—
292C23×C127—41no—
293C23×C127—41no—
294C23×C127—41no—
295C23×C127—41no—
296C23×C127—41no—
297C23×C127—41no—
298C23×C127—41no—
299C23×C127—42no—
300C23×C127—42no—
301C23×C127—42no—
302C23×C127—42no—
303C23×C127—42no—
304C23×C127—42no—
305C23×C127—42no—
306C23×C127—42no—
307C23×C127—42no—
308C23×C127—42no—
309C23×C127—42no—
310C23×C127—42no—
311C23×C127—42no—
312C23×C127—42no—
313C23×C127—42no—
314C23×C127—42no—
315C23×C127—42no—
316C23×C127—42no—
317C23×C127—42no—
318C23×C127—42no—
319C23×C127—42no—
320C23×C127—42no—
321C23×C127—42no—
322C23×C127—42no—
323C23×C127—42no—
324C23×C127—42no—
325C23×C127—42no—
326C23×C127—42no—
327C23×C127C4×D414yes—
328C23×C127C23×C411yescharacteristic
329C23×C127C22×D411yescharacteristic
330C23×C127C22×D411yescharacteristic
331C23×C127C22×D411yescharacteristic
332C23×C127C22×D411yescharacteristic
333C23×C127C22×D411yescharacteristic
334C23×C127C2×#4111yescharacteristic
335C23×C127C2×#4111yescharacteristic
336C23×C127C2×#4111yescharacteristic
337C23×C127C2×#4111yescharacteristic
338C23×C127C2×#4111yescharacteristic
339C23×C127H(5,𝔽2)11yescharacteristic
340C23×C127H(5,𝔽2)11yescharacteristic
341C23×C127H(5,𝔽2)11yescharacteristic
342C23×C1272−1+411yescharacteristic
343D4×C127—432no—
344D4×C127—416no—
345C2×C4×C127—24no—
346C2×C4×C127—24no—
347C2×C4×C127—22no—
348C2×C4×C127—22no—
349C2×C4×C127—22no—
350C2×C4×C127—24no—
351C2×C4×C127—24no—
352C2×C4×C127—24no—
353C2×C4×C127—24no—
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—24no—
363C2×C4×C127—22no—
364C2×C4×C127—22no—
365C2×C4×C127—22no—
366C2×C4×C127—24no—
367C2×C4×C127—22no—
368C2×C4×C127—22no—
369C2×C4×C127—22no—
370C2×C4×C127—24no—
371C2×C4×C127—22no—
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—42no—
379C2×C4×C127—41no—
380C2×C4×C127—41no—
381C2×C4×C127—42no—
382C2×C4×C127—42no—
383C2×C4×C127—41no—
384C2×C4×C127—41no—
385C2×C4×C127—41no—
386C2×C4×C127—41no—
387C2×C4×C127—42no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
391C2×C4×C127—41no—
392C2×C4×C127—416no—
393C2×C4×C127—42no—
394C2×C4×C127—42no—
395C2×C4×C127—42no—
396C2×C4×C127—42no—
397C2×C4×C127—42no—
398C2×C4×C127—42no—
399C2×C4×C127—42no—
400C2×C4×C127C2×C22⋊C418yes—
401C2×C4×C127C2×C22⋊C414yes—
402C2×C4×C127C4×D414yes—
403C2×C4×C127C4×D414yes—
404C2×C4×C127#12114yes—
405C2×C4×C127#12114yes—
406C2×C4×C127#12114yescomplemented
407C2×C4×C127#12414yes—
408C2×C4×C127#12714yes—
409C22×C127—24no—
410C22×C127—24no—
411C22×C127—24no—
412C22×C127—42no—
413C22×C127—42no—
414C22×C127—42no—
415C22×C127—42no—
416C22×C127—42no—
417C22×C127—42no—
418C22×C127—42no—
419C22×C127—42no—
420C22×C127—42no—
421C22×C127—42no—
422C22×C127—42no—
423C22×C127—42no—
424C22×C127—44no—
425C22×C127—44no—
426C22×C127—44no—
427C22×C127—44no—
428C22×C127—44no—
429C22×C127—44no—
430C22×C127—44no—
431C22×C127—82no—
432C22×C127—82no—
433C22×C127—82no—
434C22×C127—82no—
435C22×C127—82no—
436C22×C127—82no—
437C22×C127—82no—
438C22×C127—82no—
439C22×C127C22×C22⋊C411yescharacteristic
440C22×C127C2×C4×D411yescharacteristic
441C22×C127C2×C4×D411yescharacteristic
442C22×C127C2×C4×D411yescharacteristic
443C22×C127C4×#4111yescharacteristic
444C22×C127#51811yescharacteristic
445C22×C127#52011yescharacteristic
446C22×C127C2×#12111yescharacteristic
447C22×C127C2×#12111yescharacteristic
448C22×C127C2×#12111yescharacteristic
449C22×C127#52511yescharacteristic
450C22×C127C2×#12411yescharacteristic
451C22×C127#52911yescharacteristic
452C22×C127C2×#12711yescharacteristic
453C22×C127#53211yescharacteristic
454C22×C127#53511yescharacteristic
455C22×C127#53711yescharacteristic
456C22×C127#54011yescharacteristic
457C22×C127#54211yescharacteristic
458C22×C127D4211yescharacteristic
459C22×C127D4211yescharacteristic
460C22×C127D4211yescharacteristic
461C22×C127#54611yescharacteristic
462C22×C127#54611yescharacteristic
463C22×C127#54611yescharacteristic
464C22×C127#54711yescharacteristic
465C22×C127#54811yescharacteristic
466C22×C127#54811yescharacteristic
467C22×C127#54811yescharacteristic
468C22×C127#55011yescharacteristic
469C22×C127#55011yescharacteristic
470C22×C127#55011yescharacteristic
471C22×C127#55311yescharacteristic
472C22×C127#55311yescharacteristic
473C22×C127#55511yescharacteristic
474C4×C127—28no—
475C4×C127—24no—
476C4×C127—42no—
477C4×C127—44no—
478C4×C127—42no—
479C4×C127—42no—
480C4×C127—42no—
481C4×C127—82no—
482C4×C127#39018yescomplemented
483#13998C12711yesmaximal, characteristic, direct product factor, Sylow
484C2×C127—44no—
485C2×C127—84no—
486C2×C127C2×#39011yescharacteristic
487C2×C127C4×#12111yescharacteristic
488C2×C127#232411yescharacteristic
489C2×C127D4×C22⋊C411yescharacteristic
490C2×C127#234111yescharacteristic
491C2×C127#236111yescharacteristic
492C2×C127#236311yescharacteristic
493C2×C127#241411yescharacteristic
494C2×C127#241611yescharacteristic
495C2×C127#242611yescharacteristic
496C2×C127#242811yescharacteristic
497C2×C127#249011yescharacteristic
498C2×C127#249111yescharacteristic
499C2×C127#254011yescharacteristic
500C2×C127#254111yescharacteristic
501C22×#121C2×C12711yescharacteristic
502C2×#390C2×C12711yescharacteristic, complemented
503C2×#390C2×C12712yescomplemented
504C2×#390C2×C12711yescharacteristic, complemented
505C2×#389C2×C12711yescharacteristic, complemented
506C2×#380C2×C12711yescharacteristic, complemented
507C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
508C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
509#1439C2×C12712yescomplemented
510#1438C2×C12712yescomplemented
511#1437C2×C12712yescomplemented
512C127#1399811yescharacteristic, direct product factor, Sylow
513C23×D4C22×C12711yescharacteristic
514C23×D4C22×C12712yes—
515C24×C4C22×C12711yescharacteristic
516C2×#121—24no—
517C2×#121—24no—
518C2×#121C4×C12718yescomplemented
519C22×C4⋊C4C22×C12711yescharacteristic
520C22×C4⋊C4C22×C12712yes—
521C22×C4⋊C4C22×C12711yescharacteristic
522C22×C4⋊C4C22×C12711yescharacteristic
523C22×C22⋊C4C22×C12712yes—
524C22×C22⋊C4C22×C12711yescharacteristic
525C22×C22⋊C4C22×C12712yes—
526C22×C22⋊C4C22×C12712yes—
527C22×C22⋊C4C22×C12712yes—
528C22×C22⋊C4C22×C12712yes—
529C22×C22⋊C4C22×C12711yescharacteristic
530C22×C22⋊C4C22×C12712yes—
531C22×C42C22×C12711yescharacteristic
532C22×C42C22×C12712yes—
533C22×C42C22×C12711yescharacteristic
534#390—24no—
535#390—28no—
536#390—24no—
537#389—24no—
538#380—24no—
539C4×C4⋊C4—24no—
540C4×C22⋊C4—24no—
541C2×#95C22×C12711yescharacteristic
542C2×#95C22×C12712yes—
543C2×#95C22×C12712yes—
544C2×#95C22×C12712yes—
545C2×#95C22×C12711yescharacteristic
546C25C23×C12712yes—
547C25C23×C12711yescharacteristic
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—42no—
559C22×D4—42no—
560C22×D4C2×C4×C12714yes—
561C22×D4C2×C4×C12718yes—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4C2×C4×C12714yes—
569C23×C4C23×C12712yes—
570C23×C4C23×C12711yescharacteristic
571C23×C4C23×C12711yescharacteristic
572C23×C4C23×C12712yes—
573C23×C4C23×C12711yescharacteristic
574C23×C4C23×C12711yescharacteristic
575C23×C4C23×C12712yes—
576C23×C4C23×C12711yescharacteristic
577C23×C4C23×C12711yescharacteristic
578#121—232no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—42no—
587C2×C4⋊C4C2×C4×C12714yes—
588C2×C4⋊C4D4×C12714yes—
589C2×C4⋊C4D4×C12714yes—
590C2×C4⋊C4D4×C12714yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4C2×C4×C12718yes—
614C2×C22⋊C4D4×C12714yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—24no—
619C2×C42—22no—
620C2×C42—24no—
621C2×C42—22no—
622C2×C42—42no—
623C2×C42D4×C12714yescomplemented
624#95—22no—
625#95—22no—
626#95—24no—
627#95—24no—
628#95—24no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24C22×C4×C12714yes—
656C24C22×C4×C12712yes—
657C24C2×D4×C12712yes—
658C24#41×C12712yes—
659C24C24×C12711yescharacteristic
660C2×D4—216no—
661C2×D4—216no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
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—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4C22×C4×C12712yes—
727C22×C4C22×C4×C12714yes—
728C22×C4C22×C4×C12712yes—
729C22×C4C2×D4×C12712yes—
730C22×C4C2×D4×C12714yes—
731C22×C4C2×D4×C12712yes—
732C22×C4C2×D4×C12714yes—
733C22×C4C2×D4×C12714yes—
734C22×C4C2×D4×C12712yes—
735C22×C4C2×D4×C12712yes—
736C22×C4C2×D4×C12712yes—
737C22×C4C2×D4×C12712yes—
738C22×C4C2×D4×C12712yes—
739C22×C4C2×D4×C12712yes—
740C22×C4#41×C12712yes—
741C22×C4#41×C12712yes—
742C22×C4#41×C12712yes—
743C22×C4#41×C12712yes—
744C4⋊C4—28no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4C22⋊C4×C127116yescomplemented
748C22⋊C4—28no—
749C22⋊C4—216no—
750C22⋊C4—28no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C42—48no—
758C42—44no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23C4×D4×C12714yes—
829C23C23×C4×C12711yescharacteristic
830C23C22×D4×C12711yescharacteristic
831C23C22×D4×C12711yescharacteristic
832C23C22×D4×C12711yescharacteristic
833C23C22×D4×C12711yescharacteristic
834C23C22×D4×C12711yescharacteristic
835C23C2×#41×C12711yescharacteristic
836C23C2×#41×C12711yescharacteristic
837C23C2×#41×C12711yescharacteristic
838C23C2×#41×C12711yescharacteristic
839C23C2×#41×C12711yescharacteristic
840C23H(5,𝔽2)×C12711yescharacteristic
841C23H(5,𝔽2)×C12711yescharacteristic
842C23H(5,𝔽2)×C12711yescharacteristic
843C232−1+4×C12711yescharacteristic
844D4—432no—
845D4—416no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
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—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—416no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4C2×C22⋊C4×C12718yes—
902C2×C4C2×C22⋊C4×C12714yes—
903C2×C4C4×D4×C12714yes—
904C2×C4C4×D4×C12714yes—
905C2×C4#121×C12714yes—
906C2×C4#121×C12714yes—
907C2×C4#121×C12714yescomplemented
908C2×C4#124×C12714yes—
909C2×C4#127×C12714yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C22×C22⋊C4×C12711yescharacteristic
941C22C2×C4×D4×C12711yescharacteristic
942C22C2×C4×D4×C12711yescharacteristic
943C22C2×C4×D4×C12711yescharacteristic
944C22C4×#41×C12711yescharacteristic
945C22#518×C12711yescharacteristic
946C22#520×C12711yescharacteristic
947C22C2×#121×C12711yescharacteristic
948C22C2×#121×C12711yescharacteristic
949C22C2×#121×C12711yescharacteristic
950C22#525×C12711yescharacteristic
951C22C2×#124×C12711yescharacteristic
952C22#529×C12711yescharacteristic
953C22C2×#127×C12711yescharacteristic
954C22#532×C12711yescharacteristic
955C22#535×C12711yescharacteristic
956C22#537×C12711yescharacteristic
957C22#540×C12711yescharacteristic
958C22#542×C12711yescharacteristic
959C22D42×C12711yescharacteristic
960C22D42×C12711yescharacteristic
961C22D42×C12711yescharacteristic
962C22#546×C12711yescharacteristic
963C22#546×C12711yescharacteristic
964C22#546×C12711yescharacteristic
965C22#547×C12711yescharacteristic
966C22#548×C12711yescharacteristic
967C22#548×C12711yescharacteristic
968C22#548×C12711yescharacteristic
969C22#550×C12711yescharacteristic
970C22#550×C12711yescharacteristic
971C22#550×C12711yescharacteristic
972C22#553×C12711yescharacteristic
973C22#553×C12711yescharacteristic
974C22#555×C12711yescharacteristic
975C4—28no—
976C4—24no—
977C4—42no—
978C4—44no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—82no—
983C4#390×C12718yescomplemented
984C2—44no—
985C2—84no—
986C2C2×#390×C12711yescharacteristic
987C2C4×#121×C12711yescharacteristic
988C2C127×#232411yescharacteristic
989C2D4×C22⋊C4×C12711yescharacteristic
990C2C127×#234111yescharacteristic
991C2C127×#236111yescharacteristic
992C2C127×#236311yescharacteristic
993C2C127×#241411yescharacteristic
994C2C127×#241611yescharacteristic
995C2C127×#242611yescharacteristic
996C2C127×#242811yescharacteristic
997C2C127×#249011yescharacteristic
998C2C127×#249111yescharacteristic
999C2C127×#254011yescharacteristic
1000C2C127×#254111yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#390×C127C2semidirect
5. C2×#389×C127C2semidirect
6. C2×#380×C127C2semidirect
7. C2×C4×C4⋊C4×C127C2semidirect
8. C2×C4×C22⋊C4×C127C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×#1437C2semidirect
17. C2×#121×C127C4semidirect
89. C2×C4⋊C4×C127D4semidirect
113. C2×C22⋊C4×C127D4semidirect
122. C2×C42×C127D4semidirect
246. C4⋊C4×C127C22⋊C4semidirect
406. C2×C4×C127#121semidirect
482. C4×C127#390semidirect
483. #13998C127direct (N × H)
502. C2×#390C2×C127semidirect
503. C2×#390C2×C127semidirect
504. C2×#390C2×C127semidirect
505. C2×#389C2×C127semidirect
506. C2×#380C2×C127semidirect
507. C2×C4×C4⋊C4C2×C127semidirect
508. C2×C4×C22⋊C4C2×C127semidirect
509. #1439C2×C127semidirect
510. #1438C2×C127semidirect
511. #1437C2×C127semidirect
512. C127#13998direct (N × H)
518. C2×#121C4×C127semidirect
590. C2×C4⋊C4D4×C127semidirect
614. C2×C22⋊C4D4×C127semidirect
623. C2×C42D4×C127semidirect
747. C4⋊C4C22⋊C4×C127semidirect
907. C2×C4#121×C127semidirect
983. C4#390×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×#390×C1272
C2×#389×C1272
C2×#380×C1272
C2×C4×C4⋊C4×C1272
C2×C4×C22⋊C4×C1272
C127×#14392
C127×#14382
C127×#14372
#13998127