Finite Group Databasebeta

← C127×#21774 #44585447

Subgroups — C127×#21774 #44585447

Order 32512.

1486 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C127C211yesmaximal, characteristic
2C2×#407×C127C211yesmaximal, characteristic, complemented
3C127×#2280C211yesmaximal, characteristic, complemented
4C127×#1897C214yesmaximal, complemented
5C127×#1871C214yesmaximal, complemented
6C127×#1826C212yesmaximal, complemented
7C127×#1789C212yesmaximal, complemented
8C22×#41×C127C2211yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C22×M16×C127C2212yescomplemented
11#525×C127—21no—
12#525×C127—21no—
13#525×C127—21no—
14#525×C127—21no—
15#525×C127C412yescomplemented
16#525×C127C412yescomplemented
17#525×C127C2212yes—
18#525×C127C2212yes—
19C2×#123×C127—21no—
20C2×C22⋊Q8×C127C411yescharacteristic, complemented
21C2×C22⋊Q8×C127C411yescharacteristic, complemented
22C2×#121×C127C411yescharacteristic, complemented
23C2×#121×C127C411yescharacteristic, complemented
24C2×#120×C127—21no—
25C2×C4×D4×C127—21no—
26C2×C4×D4×C127—21no—
27C2×#117×C127C2211yescharacteristic
28C2×#117×C127C2212yescomplemented
29C2×#104×C127C2218yescomplemented
30#407×C127—21no—
31#407×C127—21no—
32#407×C127C2212yes—
33#407×C127C2212yescomplemented
34C2×C22⋊C8×C127—21no—
35C2×C22⋊C8×C127—21no—
36#381×C127—21no—
37#380×C127—21no—
38#380×C127—21no—
39#379×C127—21no—
40C4×C22⋊C4×C127C2212yes—
41C4×C22⋊C4×C127C2212yescomplemented
42#339×C127C2218yescomplemented
43C25×C127D411yescharacteristic
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—44no—
47C2×#41×C127C2×C412yes—
48C2×#41×C127C2312yes—
49C22×Q8×C127C2×C411yescharacteristic
50C22×D4×C127—21no—
51C22×D4×C127—21no—
52C22×D4×C127—21no—
53C22×D4×C127C2×C411yescharacteristic
54C23×C4×C127—21no—
55C23×C4×C127—44no—
56C23×C4×C127C2×C411yescharacteristic
57C23×C4×C127C2×C411yescharacteristic
58C23×C4×C127C2×C411yescharacteristic
59C23×C4×C127C2×C411yescharacteristic
60C23×C4×C127D411yescharacteristic
61C23×C4×C127D411yescharacteristic
62C23×C4×C127D411yescharacteristic
63C23×C4×C127D411yescharacteristic
64C23×C4×C127D411yescharacteristic
65C23×C4×C127D411yescharacteristic
66C23×C4×C127D411yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C2×M16×C127—22no—
71C2×M16×C127—44no—
72C2×M16×C127C2314yes—
73C22×C8×C127—22no—
74#123×C127—22no—
75#123×C127—22no—
76#123×C127—22no—
77#123×C127—22no—
78C22⋊Q8×C127—21no—
79C22⋊Q8×C127—21no—
80C22⋊Q8×C127—21no—
81C22⋊Q8×C127—21no—
82C22⋊Q8×C127C2×C412yes—
83C22⋊Q8×C127C2×C412yes—
84C22⋊Q8×C127C2×C412yes—
85C22⋊Q8×C127C2×C412yes—
86#121×C127—21no—
87#121×C127—21no—
88#121×C127—21no—
89#121×C127—21no—
90#121×C127C2×C412yes—
91#121×C127C2×C412yes—
92#121×C127C2×C412yes—
93#121×C127C2×C412yes—
94#120×C127—22no—
95#120×C127—22no—
96#120×C127—22no—
97#120×C127—22no—
98C4×D4×C127—22no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—22no—
104C4×D4×C127—22no—
105C4×D4×C127—22no—
106#117×C127—21no—
107#117×C127—21no—
108#117×C127—44no—
109#117×C127C2×C412yes—
110#117×C127C2312yes—
111C2×C4⋊C4×C127—21no—
112C2×C4⋊C4×C127—21no—
113C2×C4⋊C4×C127—22no—
114C2×C4⋊C4×C127C2×C411yescharacteristic
115C2×C4⋊C4×C127C2×C411yescharacteristic
116C2×C22⋊C4×C127—21no—
117C2×C22⋊C4×C127—21no—
118C2×C22⋊C4×C127—21no—
119C2×C22⋊C4×C127—21no—
120C2×C22⋊C4×C127—21no—
121C2×C22⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—22no—
124C2×C42×C127—21no—
125C2×C42×C127C2314yes—
126#104×C127—48no—
127C22⋊C8×C127—22no—
128C22⋊C8×C127—22no—
129C22⋊C8×C127—22no—
130C22⋊C8×C127—22no—
131#95×C127—22no—
132#95×C127—22no—
133C24×C127—21no—
134C24×C127—42no—
135C24×C127—42no—
136C24×C127—42no—
137C24×C127C22⋊C411yescharacteristic
138C24×C127C22⋊C411yescharacteristic
139C24×C127C22⋊C411yescharacteristic
140C24×C127C22⋊C411yescharacteristic
141C24×C127C2×D411yescharacteristic
142C24×C127C2×D411yescharacteristic
143C24×C127C2×D411yescharacteristic
144#41×C127—28no—
145#41×C127—44no—
146#41×C127—44no—
147#41×C127—44no—
148C2×Q8×C127—21no—
149C2×Q8×C127—42no—
150C2×Q8×C127C22×C412yes—
151C2×D4×C127—22no—
152C2×D4×C127—22no—
153C2×D4×C127—22no—
154C2×D4×C127—22no—
155C2×D4×C127—22no—
156C2×D4×C127—22no—
157C2×D4×C127—21no—
158C2×D4×C127—42no—
159C2×D4×C127—44no—
160C2×D4×C127—44no—
161C2×D4×C127—44no—
162C2×D4×C127C22×C412yes—
163C22×C4×C127—24no—
164C22×C4×C127—24no—
165C22×C4×C127—24no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—24no—
172C22×C4×C127—42no—
173C22×C4×C127—42no—
174C22×C4×C127—42no—
175C22×C4×C127—42no—
176C22×C4×C127—42no—
177C22×C4×C127—42no—
178C22×C4×C127—42no—
179C22×C4×C127—42no—
180C22×C4×C127—42no—
181C22×C4×C127—42no—
182C22×C4×C127—42no—
183C22×C4×C127—44no—
184C22×C4×C127C22⋊C411yescharacteristic
185C22×C4×C127C22⋊C411yescharacteristic
186C22×C4×C127C22⋊C411yescharacteristic
187C22×C4×C127C22⋊C411yescharacteristic
188C22×C4×C127C22⋊C411yescharacteristic
189C22×C4×C127C22⋊C411yescharacteristic
190C22×C4×C127C22⋊C411yescharacteristic
191C22×C4×C127C22⋊C411yescharacteristic
192C22×C4×C127C22⋊C411yescharacteristic
193C22×C4×C127C22⋊C411yescharacteristic
194C22×C4×C127C22⋊C411yescharacteristic
195C22×C4×C127C22⋊C411yescharacteristic
196C22×C4×C127C22×C411yescharacteristic
197C22×C4×C127C22×C411yescharacteristic
198C22×C4×C127C22×C411yescharacteristic
199C22×C4×C127C22×C411yescharacteristic
200C22×C4×C127C22×C411yescharacteristic
201C22×C4×C127C22×C411yescharacteristic
202C22×C4×C127C2×D411yescharacteristic
203C22×C4×C127C2×D411yescharacteristic
204C22×C4×C127C2×D411yescharacteristic
205C22×C4×C127C2×D411yescharacteristic
206C22×C4×C127C2×D411yescharacteristic
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2×D411yescharacteristic
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2411yescharacteristic
212M16×C127—28no—
213M16×C127—44no—
214C2×C8×C127—24no—
215C2×C8×C127—44no—
216C4⋊C4×C127—22no—
217C4⋊C4×C127—22no—
218C4⋊C4×C127—22no—
219C4⋊C4×C127—22no—
220C4⋊C4×C127—21no—
221C4⋊C4×C127—21no—
222C4⋊C4×C127—44no—
223C4⋊C4×C127C22×C412yes—
224C4⋊C4×C127C22×C412yes—
225C22⋊C4×C127—22no—
226C22⋊C4×C127—22no—
227C22⋊C4×C127—22no—
228C22⋊C4×C127—22no—
229C22⋊C4×C127—22no—
230C22⋊C4×C127—22no—
231C22⋊C4×C127—22no—
232C22⋊C4×C127—22no—
233C22⋊C4×C127—22no—
234C22⋊C4×C127—22no—
235C22⋊C4×C127—44no—
236C22⋊C4×C127—44no—
237C22⋊C4×C127—44no—
238C42×C127—22no—
239C42×C127—22no—
240C42×C127—28no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—22no—
249C23×C127—22no—
250C23×C127—22no—
251C23×C127—41no—
252C23×C127—41no—
253C23×C127—41no—
254C23×C127—41no—
255C23×C127—41no—
256C23×C127—41no—
257C23×C127—41no—
258C23×C127—41no—
259C23×C127—41no—
260C23×C127—41no—
261C23×C127—41no—
262C23×C127—41no—
263C23×C127—42no—
264C23×C127—42no—
265C23×C127—416no—
266C23×C127—42no—
267C23×C127C2×C22⋊C411yescharacteristic
268C23×C127C2×C22⋊C411yescharacteristic
269C23×C127C2×C22⋊C411yescharacteristic
270C23×C127C2×C22⋊C411yescharacteristic
271C23×C127C2×C22⋊C411yescharacteristic
272C23×C127C2×C22⋊C411yescharacteristic
273C23×C127C22×D411yescharacteristic
274Q8×C127—24no—
275Q8×C127—42no—
276D4×C127—24no—
277D4×C127—42no—
278D4×C127—44no—
279D4×C127—44no—
280D4×C127—44no—
281D4×C127—44no—
282D4×C127—44no—
283D4×C127—44no—
284C2×C4×C127—22no—
285C2×C4×C127—22no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—22no—
302C2×C4×C127—41no—
303C2×C4×C127—41no—
304C2×C4×C127—41no—
305C2×C4×C127—41no—
306C2×C4×C127—41no—
307C2×C4×C127—41no—
308C2×C4×C127—41no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—41no—
313C2×C4×C127—41no—
314C2×C4×C127—44no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127—42no—
318C2×C4×C127—44no—
319C2×C4×C127—44no—
320C2×C4×C127—44no—
321C2×C4×C127—44no—
322C2×C4×C127C2×C22⋊C411yescharacteristic
323C2×C4×C127C2×C22⋊C411yescharacteristic
324C2×C4×C127C2×C22⋊C411yescharacteristic
325C2×C4×C127C2×C22⋊C411yescharacteristic
326C2×C4×C127C2×C22⋊C411yescharacteristic
327C2×C4×C127C2×C22⋊C411yescharacteristic
328C2×C4×C127C23×C411yescharacteristic
329C2×C4×C127C22×D411yescharacteristic
330C2×C4×C127H(5,𝔽2)14yes—
331C8×C127—44no—
332C22×C127—21no—
333C22×C127—21no—
334C22×C127—21no—
335C22×C127—21no—
336C22×C127—21no—
337C22×C127—21no—
338C22×C127—21no—
339C22×C127—21no—
340C22×C127—21no—
341C22×C127—21no—
342C22×C127—21no—
343C22×C127—21no—
344C22×C127—21no—
345C22×C127—21no—
346C22×C127—21no—
347C22×C127—21no—
348C22×C127—21no—
349C22×C127—21no—
350C22×C127—44no—
351C22×C127—44no—
352C22×C127—44no—
353C22×C127—44no—
354C22×C127—44no—
355C22×C127—44no—
356C22×C127—44no—
357C22×C127—42no—
358C22×C127—42no—
359C22×C127—42no—
360C22×C127—84no—
361C22×C127#42112yes—
362C22×C127#42112yes—
363C22×C127C22×C22⋊C411yescharacteristic
364C22×C127#53412yes—
365C4×C127—21no—
366C4×C127—21no—
367C4×C127—21no—
368C4×C127—21no—
369C4×C127—21no—
370C4×C127—21no—
371C4×C127—42no—
372C4×C127—42no—
373C4×C127—42no—
374C4×C127—84no—
375C4×C127#51812yes—
376C4×C127#53412yes—
377#21774C12711yesmaximal, characteristic, direct product factor, Sylow
378C2×C127—22no—
379C2×C127—22no—
380C2×C127—22no—
381C2×C127—41no—
382C2×C127—41no—
383C2×C127—41no—
384C2×C127—41no—
385C2×C127—82no—
386C2×C127#230811yescharacteristic
387C2×C127C2×#42111yescharacteristic
388C2×C127C2×#42111yescharacteristic
389C2×#525C2×C12711yescharacteristic
390C2×#407C2×C12711yescharacteristic, complemented
391#2280C2×C12711yescharacteristic, complemented
392#1897C2×C12714yescomplemented
393#1871C2×C12714yescomplemented
394#1826C2×C12712yescomplemented
395#1789C2×C12712yescomplemented
396C127#2177411yescharacteristic, direct product factor, Sylow
397C22×#41C22×C12711yescharacteristic
398C24×C4C22×C12711yescharacteristic
399C22×M16C22×C12712yescomplemented
400#525—21no—
401#525—21no—
402#525—21no—
403#525—21no—
404#525C4×C12712yescomplemented
405#525C4×C12712yescomplemented
406#525C22×C12712yes—
407#525C22×C12712yes—
408C2×#123—21no—
409C2×C22⋊Q8C4×C12711yescharacteristic, complemented
410C2×C22⋊Q8C4×C12711yescharacteristic, complemented
411C2×#121C4×C12711yescharacteristic, complemented
412C2×#121C4×C12711yescharacteristic, complemented
413C2×#120—21no—
414C2×C4×D4—21no—
415C2×C4×D4—21no—
416C2×#117C22×C12711yescharacteristic
417C2×#117C22×C12712yescomplemented
418C2×#104C22×C12718yescomplemented
419#407—21no—
420#407—21no—
421#407C22×C12712yes—
422#407C22×C12712yescomplemented
423C2×C22⋊C8—21no—
424C2×C22⋊C8—21no—
425#381—21no—
426#380—21no—
427#380—21no—
428#379—21no—
429C4×C22⋊C4C22×C12712yes—
430C4×C22⋊C4C22×C12712yescomplemented
431#339C22×C12718yescomplemented
432C25D4×C12711yescharacteristic
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—44no—
436C2×#41C2×C4×C12712yes—
437C2×#41C23×C12712yes—
438C22×Q8C2×C4×C12711yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C2×C4×C12711yescharacteristic
443C23×C4—21no—
444C23×C4—44no—
445C23×C4C2×C4×C12711yescharacteristic
446C23×C4C2×C4×C12711yescharacteristic
447C23×C4C2×C4×C12711yescharacteristic
448C23×C4C2×C4×C12711yescharacteristic
449C23×C4D4×C12711yescharacteristic
450C23×C4D4×C12711yescharacteristic
451C23×C4D4×C12711yescharacteristic
452C23×C4D4×C12711yescharacteristic
453C23×C4D4×C12711yescharacteristic
454C23×C4D4×C12711yescharacteristic
455C23×C4D4×C12711yescharacteristic
456C23×C4C23×C12711yescharacteristic
457C23×C4C23×C12711yescharacteristic
458C23×C4C23×C12711yescharacteristic
459C2×M16—22no—
460C2×M16—44no—
461C2×M16C23×C12714yes—
462C22×C8—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471C22⋊Q8C2×C4×C12712yes—
472C22⋊Q8C2×C4×C12712yes—
473C22⋊Q8C2×C4×C12712yes—
474C22⋊Q8C2×C4×C12712yes—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121C2×C4×C12712yes—
480#121C2×C4×C12712yes—
481#121C2×C4×C12712yes—
482#121C2×C4×C12712yes—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495#117—21no—
496#117—21no—
497#117—44no—
498#117C2×C4×C12712yes—
499#117C23×C12712yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4C2×C4×C12711yescharacteristic
504C2×C4⋊C4C2×C4×C12711yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C42—21no—
514C2×C42C23×C12714yes—
515#104—48no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#95—22no—
521#95—22no—
522C24—21no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24C22⋊C4×C12711yescharacteristic
527C24C22⋊C4×C12711yescharacteristic
528C24C22⋊C4×C12711yescharacteristic
529C24C22⋊C4×C12711yescharacteristic
530C24C2×D4×C12711yescharacteristic
531C24C2×D4×C12711yescharacteristic
532C24C2×D4×C12711yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—42no—
539C2×Q8C22×C4×C12712yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4C22×C4×C12712yes—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—44no—
573C22×C4C22⋊C4×C12711yescharacteristic
574C22×C4C22⋊C4×C12711yescharacteristic
575C22×C4C22⋊C4×C12711yescharacteristic
576C22×C4C22⋊C4×C12711yescharacteristic
577C22×C4C22⋊C4×C12711yescharacteristic
578C22×C4C22⋊C4×C12711yescharacteristic
579C22×C4C22⋊C4×C12711yescharacteristic
580C22×C4C22⋊C4×C12711yescharacteristic
581C22×C4C22⋊C4×C12711yescharacteristic
582C22×C4C22⋊C4×C12711yescharacteristic
583C22×C4C22⋊C4×C12711yescharacteristic
584C22×C4C22⋊C4×C12711yescharacteristic
585C22×C4C22×C4×C12711yescharacteristic
586C22×C4C22×C4×C12711yescharacteristic
587C22×C4C22×C4×C12711yescharacteristic
588C22×C4C22×C4×C12711yescharacteristic
589C22×C4C22×C4×C12711yescharacteristic
590C22×C4C22×C4×C12711yescharacteristic
591C22×C4C2×D4×C12711yescharacteristic
592C22×C4C2×D4×C12711yescharacteristic
593C22×C4C2×D4×C12711yescharacteristic
594C22×C4C2×D4×C12711yescharacteristic
595C22×C4C2×D4×C12711yescharacteristic
596C22×C4C2×D4×C12711yescharacteristic
597C22×C4C2×D4×C12711yescharacteristic
598C22×C4C2×D4×C12711yescharacteristic
599C22×C4C2×D4×C12711yescharacteristic
600C22×C4C24×C12711yescharacteristic
601M16—28no—
602M16—44no—
603C2×C8—24no—
604C2×C8—44no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—44no—
612C4⋊C4C22×C4×C12712yes—
613C4⋊C4C22×C4×C12712yes—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C42—22no—
628C42—22no—
629C42—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—416no—
655C23—42no—
656C23C2×C22⋊C4×C12711yescharacteristic
657C23C2×C22⋊C4×C12711yescharacteristic
658C23C2×C22⋊C4×C12711yescharacteristic
659C23C2×C22⋊C4×C12711yescharacteristic
660C23C2×C22⋊C4×C12711yescharacteristic
661C23C2×C22⋊C4×C12711yescharacteristic
662C23C22×D4×C12711yescharacteristic
663Q8—24no—
664Q8—42no—
665D4—24no—
666D4—42no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671D4—44no—
672D4—44no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4C2×C22⋊C4×C12711yescharacteristic
712C2×C4C2×C22⋊C4×C12711yescharacteristic
713C2×C4C2×C22⋊C4×C12711yescharacteristic
714C2×C4C2×C22⋊C4×C12711yescharacteristic
715C2×C4C2×C22⋊C4×C12711yescharacteristic
716C2×C4C2×C22⋊C4×C12711yescharacteristic
717C2×C4C23×C4×C12711yescharacteristic
718C2×C4C22×D4×C12711yescharacteristic
719C2×C4H(5,𝔽2)×C12714yes—
720C8—44no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22#421×C12712yes—
751C22#421×C12712yes—
752C22C22×C22⋊C4×C12711yescharacteristic
753C22#534×C12712yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—84no—
764C4#518×C12712yes—
765C4#534×C12712yes—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—41no—
772C2—41no—
773C2—82no—
774C2C127×#230811yescharacteristic
775C2C2×#421×C12711yescharacteristic
776C2C2×#421×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC2×#525×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C127C2semidirect
3. C127×#2280C2semidirect
4. C127×#1897C2semidirect
5. C127×#1871C2semidirect
6. C127×#1826C2semidirect
7. C127×#1789C2semidirect
10. C22×M16×C127C22semidirect
15. #525×C127C4semidirect
16. #525×C127C4semidirect
20. C2×C22⋊Q8×C127C4semidirect
21. C2×C22⋊Q8×C127C4semidirect
22. C2×#121×C127C4semidirect
23. C2×#121×C127C4semidirect
28. C2×#117×C127C22semidirect
29. C2×#104×C127C22semidirect
33. #407×C127C22semidirect
41. C4×C22⋊C4×C127C22semidirect
42. #339×C127C22semidirect
377. #21774C127direct (N × H)
390. C2×#407C2×C127semidirect
391. #2280C2×C127semidirect
392. #1897C2×C127semidirect
393. #1871C2×C127semidirect
394. #1826C2×C127semidirect
395. #1789C2×C127semidirect
396. C127#21774direct (N × H)
399. C22×M16C22×C127semidirect
404. #525C4×C127semidirect
405. #525C4×C127semidirect
409. C2×C22⋊Q8C4×C127semidirect
410. C2×C22⋊Q8C4×C127semidirect
411. C2×#121C4×C127semidirect
412. C2×#121C4×C127semidirect
417. C2×#117C22×C127semidirect
418. C2×#104C22×C127semidirect
422. #407C22×C127semidirect
430. C4×C22⋊C4C22×C127semidirect
431. #339C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1272
C2×#407×C1272
C127×#22802
C127×#18972
C127×#18712
C127×#18262
C127×#17892
#21774127