Finite Group Databasebeta

← C127×#11017 #44574690

Subgroups — C127×#11017 #44574690

Order 32512.

1358 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
1C22×#137×C127C211yesmaximal, characteristic
2C22×#104×C127C211yesmaximal, characteristic
3C2×#419×C127C211yesmaximal, characteristic, complemented
4C127×#2311C211yesmaximal, characteristic
5C2×#391×C127C211yesmaximal, characteristic, complemented
6C2×#343×C127C211yesmaximal, characteristic, complemented
7C2×#339×C127C211yesmaximal, characteristic, complemented
8C22×#41×C127C2211yescharacteristic
9C23×Q8×C127C2211yescharacteristic
10C2×#137×C127—22no—
11C2×#137×C127—22no—
12C2×#137×C127—22no—
13C2×#137×C127—22no—
14C2×#137×C127—22no—
15C2×#137×C127C414yescomplemented
16C22×Q16×C127—21no—
17C22×SD16×C127—21no—
18C22×M16×C127C2211yescharacteristic
19C22×M16×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23C2×#104×C127—22no—
24C2×#104×C127—22no—
25C2×#104×C127—22no—
26#419×C127—22no—
27#419×C127—22no—
28C2×#103×C127—22no—
29#391×C127—22no—
30#391×C127—21no—
31#391×C127—22no—
32#390×C127—21no—
33#386×C127—22no—
34#380×C127—22no—
35C2×#95×C127—22no—
36#343×C127—22no—
37#339×C127—22no—
38C2×#41×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C2×#41×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C2×#41×C127—21no—
48C2×#41×C127C2×C412yes—
49C2×#41×C127D412yes—
50C22×Q8×C127—21no—
51C22×Q8×C127—21no—
52C22×Q8×C127—21no—
53C22×Q8×C127—21no—
54C22×Q8×C127—21no—
55C22×Q8×C127—21no—
56C22×Q8×C127—21no—
57C22×Q8×C127—21no—
58C22×Q8×C127—21no—
59C22×Q8×C127—21no—
60C22×Q8×C127—21no—
61C22×Q8×C127C2×C412yes—
62C22×Q8×C127D411yescharacteristic
63C22×Q8×C127D412yes—
64C22×Q8×C127D412yes—
65C22×D4×C127—21no—
66C22×D4×C127D411yescharacteristic
67C23×C4×C127—21no—
68C23×C4×C127—21no—
69C23×C4×C127—21no—
70C23×C4×C127D412yes—
71C23×C4×C127C2311yescharacteristic
72#137×C127—28no—
73#137×C127—28no—
74#137×C127—28no—
75#137×C127—28no—
76C2×Q16×C127—24no—
77C2×Q16×C127—24no—
78C2×Q16×C127—24no—
79C2×SD16×C127—24no—
80C2×SD16×C127—24no—
81C2×SD16×C127—24no—
82C2×M16×C127—21no—
83C2×M16×C127—21no—
84C2×M16×C127—21no—
85C2×M16×C127—21no—
86C2×M16×C127—21no—
87C2×M16×C127—21no—
88C2×M16×C127—21no—
89C2×M16×C127—21no—
90C2×M16×C127C2×C412yes—
91C2×M16×C127D412yes—
92C2×M16×C127D412yes—
93C2×M16×C127D412yes—
94C22×C8×C127—21no—
95C22×C8×C127—21no—
96#117×C127—21no—
97#117×C127—21no—
98#117×C127—21no—
99#117×C127—21no—
100C2×C4⋊C4×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C4⋊C4×C127—21no—
103C2×C4⋊C4×C127—21no—
104C2×C4⋊C4×C127—21no—
105C2×C4⋊C4×C127—21no—
106C2×C4⋊C4×C127D412yes—
107C2×C22⋊C4×C127—21no—
108C2×C22⋊C4×C127—24no—
109C2×C42×C127—21no—
110C2×C42×C127—21no—
111C2×C42×C127—21no—
112C2×C42×C127—21no—
113C2×C42×C127—21no—
114C2×C42×C127—21no—
115C2×C42×C127D412yes—
116#104×C127—28no—
117#103×C127—28no—
118#95×C127—28no—
119#95×C127—24no—
120C24×C127—21no—
121C24×C127C2×D411yescharacteristic
122#41×C127—22no—
123#41×C127—22no—
124#41×C127—22no—
125#41×C127—22no—
126#41×C127—22no—
127#41×C127—22no—
128#41×C127—22no—
129#41×C127—22no—
130#41×C127—41no—
131#41×C127—41no—
132#41×C127—41no—
133#41×C127—41no—
134#41×C127—41no—
135#41×C127—41no—
136#41×C127—41no—
137#41×C127—41no—
138C2×Q8×C127—22no—
139C2×Q8×C127—22no—
140C2×Q8×C127—22no—
141C2×Q8×C127—21no—
142C2×Q8×C127—22no—
143C2×Q8×C127—22no—
144C2×Q8×C127—22no—
145C2×Q8×C127—22no—
146C2×Q8×C127—22no—
147C2×Q8×C127—22no—
148C2×Q8×C127—22no—
149C2×Q8×C127—21no—
150C2×Q8×C127—21no—
151C2×Q8×C127—22no—
152C2×Q8×C127—22no—
153C2×Q8×C127—22no—
154C2×Q8×C127—22no—
155C2×Q8×C127—21no—
156C2×Q8×C127—21no—
157C2×Q8×C127—22no—
158C2×Q8×C127—41no—
159C2×Q8×C127—41no—
160C2×Q8×C127—41no—
161C2×Q8×C127—41no—
162C2×Q8×C127—41no—
163C2×Q8×C127—41no—
164C2×Q8×C127—41no—
165C2×Q8×C127—41no—
166C2×Q8×C127—41no—
167C2×Q8×C127—41no—
168C2×Q8×C127—41no—
169C2×Q8×C127—41no—
170C2×Q8×C127C22⋊C412yes—
171C2×Q8×C127C22⋊C414yescomplemented
172C2×D4×C127—22no—
173C2×D4×C127—22no—
174C2×D4×C127—21no—
175C2×D4×C127—21no—
176C2×D4×C127—21no—
177C2×D4×C127—21no—
178C2×D4×C127—21no—
179C2×D4×C127—41no—
180C2×D4×C127—41no—
181C2×D4×C127—41no—
182C2×D4×C127—41no—
183C2×D4×C127C22⋊C412yes—
184C22×C4×C127—24no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—21no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—42no—
197C22×C4×C127—41no—
198C22×C4×C127—41no—
199C22×C4×C127—41no—
200C22×C4×C127—41no—
201C22×C4×C127—41no—
202C22×C4×C127—41no—
203C22×C4×C127—41no—
204C22×C4×C127—41no—
205C22×C4×C127—41no—
206C22×C4×C127—41no—
207C22×C4×C127—44no—
208C22×C4×C127C22×C411yescharacteristic
209C22×C4×C127C2×D411yescharacteristic
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2×D411yescharacteristic
216C22×C4×C127C2×D411yescharacteristic
217C22×C4×C127C2×D411yescharacteristic
218C22×C4×C127#4111yescharacteristic
219C22×C4×C127#4111yescharacteristic
220C22×C4×C127#4111yescharacteristic
221C22×C4×C127#4111yescharacteristic
222Q16×C127—216no—
223SD16×C127—216no—
224M16×C127—22no—
225M16×C127—22no—
226M16×C127—22no—
227M16×C127—22no—
228M16×C127—22no—
229M16×C127—41no—
230M16×C127—41no—
231M16×C127C22⋊C414yescomplemented
232C2×C8×C127—22no—
233C2×C8×C127—22no—
234C2×C8×C127—22no—
235C2×C8×C127—22no—
236C2×C8×C127—41no—
237C2×C8×C127—41no—
238C4⋊C4×C127—22no—
239C4⋊C4×C127—22no—
240C4⋊C4×C127—41no—
241C4⋊C4×C127—41no—
242C4⋊C4×C127—41no—
243C4⋊C4×C127—41no—
244C22⋊C4×C127—41no—
245C22⋊C4×C127—41no—
246C22⋊C4×C127—84no—
247C42×C127—22no—
248C42×C127—22no—
249C42×C127—41no—
250C42×C127—41no—
251C42×C127—41no—
252C42×C127—41no—
253C23×C127—22no—
254C23×C127—22no—
255C23×C127—22no—
256C23×C127—41no—
257C23×C127—41no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127C4×D411yescharacteristic
261C23×C127#12011yescharacteristic
262C23×C127#12011yescharacteristic
263C23×C127#12111yescharacteristic
264C23×C127#12111yescharacteristic
265C23×C127#12111yescharacteristic
266C23×C127#12711yescharacteristic
267Q8×C127—24no—
268Q8×C127—22no—
269Q8×C127—24no—
270Q8×C127—22no—
271Q8×C127—42no—
272Q8×C127—42no—
273Q8×C127—42no—
274Q8×C127—42no—
275Q8×C127—42no—
276Q8×C127—42no—
277Q8×C127—41no—
278Q8×C127—41no—
279D4×C127—22no—
280D4×C127—22no—
281D4×C127—42no—
282D4×C127—42no—
283D4×C127—42no—
284D4×C127—42no—
285D4×C127—41no—
286D4×C127—41no—
287C2×C4×C127—24no—
288C2×C4×C127—22no—
289C2×C4×C127—24no—
290C2×C4×C127—44no—
291C2×C4×C127—42no—
292C2×C4×C127—44no—
293C2×C4×C127—42no—
294C2×C4×C127—42no—
295C2×C4×C127—42no—
296C2×C4×C127—41no—
297C2×C4×C127—41no—
298C2×C4×C127—42no—
299C2×C4×C127—42no—
300C2×C4×C127—42no—
301C2×C4×C127—42no—
302C2×C4×C127—42no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—44no—
307C2×C4×C127—42no—
308C2×C4×C127—42no—
309C2×C4×C127—42no—
310C2×C4×C127—44no—
311C2×C4×C127—42no—
312C2×C4×C127—82no—
313C2×C4×C127C2×C22⋊C411yescharacteristic
314C2×C4×C127C2×C22⋊C411yescharacteristic
315C2×C4×C127C2×C22⋊C411yescharacteristic
316C2×C4×C127C4×D411yescharacteristic
317C2×C4×C127C4×D411yescharacteristic
318C2×C4×C127C4×D411yescharacteristic
319C2×C4×C127#12011yescharacteristic
320C2×C4×C127#12011yescharacteristic
321C2×C4×C127#12011yescharacteristic
322C2×C4×C127#12011yescharacteristic
323C2×C4×C127#12011yescharacteristic
324C2×C4×C127#12011yescharacteristic
325C2×C4×C127#12111yescharacteristic
326C2×C4×C127#12111yescharacteristic
327C2×C4×C127#12111yescharacteristic
328C2×C4×C127#12111yescharacteristic
329C2×C4×C127#12111yescharacteristic
330C2×C4×C127#12111yescharacteristic
331C2×C4×C127#12111yescharacteristic
332C2×C4×C127#12111yescharacteristic
333C2×C4×C127#12111yescharacteristic
334C2×C4×C127#12311yescharacteristic
335C2×C4×C127#12311yescharacteristic
336C2×C4×C127#12311yescharacteristic
337C2×C4×C127#12311yescharacteristic
338C2×C4×C127#12411yescharacteristic
339C2×C4×C127#12411yescharacteristic
340C2×C4×C127#12711yescharacteristic
341C8×C127—24no—
342C8×C127—42no—
343C22×C127—22no—
344C22×C127—22no—
345C22×C127—21no—
346C22×C127—21no—
347C22×C127—21no—
348C22×C127—21no—
349C22×C127—22no—
350C22×C127—22no—
351C22×C127—44no—
352C22×C127—42no—
353C22×C127—81no—
354C22×C127—81no—
355C22×C127—82no—
356C22×C127#38611yescharacteristic
357C22×C127#38611yescharacteristic
358C22×C127#39011yescharacteristic
359C22×C127#39211yescharacteristic
360C22×C127#39211yescharacteristic
361C22×C127#39211yescharacteristic
362C22×C127#39411yescharacteristic
363C22×C127#45512yes—
364C22×C127#45612yes—
365C4×C127—44no—
366C4×C127—42no—
367C4×C127—44no—
368C4×C127—82no—
369C4×C127—82no—
370C4×C127#37911yescharacteristic
371C4×C127#38611yescharacteristic
372C4×C127#38611yescharacteristic
373C4×C127#39011yescharacteristic
374C4×C127#39211yescharacteristic
375C4×C127#39411yescharacteristic
376C4×C127#39411yescharacteristic
377C4×C127#39411yescharacteristic
378#11017C12711yesmaximal, characteristic, direct product factor, Sylow
379C2×C127—21no—
380C2×C127—21no—
381C2×C127—21no—
382C2×C127—21no—
383C2×C127—82no—
384C2×C127#143811yescharacteristic
385C2×C127#188212yes—
386C2×C127#200411yescharacteristic
387C2×C127#200511yescharacteristic
388C2×C127#200712yes—
389C22×#137C2×C12711yescharacteristic
390C22×#104C2×C12711yescharacteristic
391C2×#419C2×C12711yescharacteristic, complemented
392#2311C2×C12711yescharacteristic
393C2×#391C2×C12711yescharacteristic, complemented
394C2×#343C2×C12711yescharacteristic, complemented
395C2×#339C2×C12711yescharacteristic, complemented
396C127#1101711yescharacteristic, direct product factor, Sylow
397C22×#41C22×C12711yescharacteristic
398C23×Q8C22×C12711yescharacteristic
399C2×#137—22no—
400C2×#137—22no—
401C2×#137—22no—
402C2×#137—22no—
403C2×#137—22no—
404C2×#137C4×C12714yescomplemented
405C22×Q16—21no—
406C22×SD16—21no—
407C22×M16C22×C12711yescharacteristic
408C22×M16C22×C12711yescharacteristic
409C2×#117C22×C12711yescharacteristic
410C22×C4⋊C4C22×C12711yescharacteristic
411C22×C42C22×C12711yescharacteristic
412C2×#104—22no—
413C2×#104—22no—
414C2×#104—22no—
415#419—22no—
416#419—22no—
417C2×#103—22no—
418#391—21no—
419#391—22no—
420#391—22no—
421#390—21no—
422#386—22no—
423#380—22no—
424C2×#95—22no—
425#343—22no—
426#339—22no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41C2×C4×C12712yes—
438C2×#41D4×C12712yes—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8C2×C4×C12712yes—
451C22×Q8D4×C12711yescharacteristic
452C22×Q8D4×C12712yes—
453C22×Q8D4×C12712yes—
454C22×D4—21no—
455C22×D4D4×C12711yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4D4×C12712yes—
460C23×C4C23×C12711yescharacteristic
461#137—28no—
462#137—28no—
463#137—28no—
464#137—28no—
465C2×Q16—24no—
466C2×Q16—24no—
467C2×Q16—24no—
468C2×SD16—24no—
469C2×SD16—24no—
470C2×SD16—24no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16C2×C4×C12712yes—
480C2×M16D4×C12712yes—
481C2×M16D4×C12712yes—
482C2×M16D4×C12712yes—
483C22×C8—21no—
484C22×C8—21no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C12712yes—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—24no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42D4×C12712yes—
505#104—28no—
506#103—28no—
507#95—28no—
508#95—24no—
509C24—21no—
510C24C2×D4×C12711yescharacteristic
511#41—22no—
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8C22⋊C4×C12712yes—
560C2×Q8C22⋊C4×C12714yescomplemented
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4C22⋊C4×C12712yes—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—44no—
597C22×C4C22×C4×C12711yescharacteristic
598C22×C4C2×D4×C12711yescharacteristic
599C22×C4C2×D4×C12711yescharacteristic
600C22×C4C2×D4×C12711yescharacteristic
601C22×C4C2×D4×C12711yescharacteristic
602C22×C4C2×D4×C12711yescharacteristic
603C22×C4C2×D4×C12711yescharacteristic
604C22×C4C2×D4×C12711yescharacteristic
605C22×C4C2×D4×C12711yescharacteristic
606C22×C4C2×D4×C12711yescharacteristic
607C22×C4#41×C12711yescharacteristic
608C22×C4#41×C12711yescharacteristic
609C22×C4#41×C12711yescharacteristic
610C22×C4#41×C12711yescharacteristic
611Q16—216no—
612SD16—216no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—22no—
618M16—41no—
619M16—41no—
620M16C22⋊C4×C12714yescomplemented
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—41no—
626C2×C8—41no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—84no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23C4×D4×C12711yescharacteristic
650C23#120×C12711yescharacteristic
651C23#120×C12711yescharacteristic
652C23#121×C12711yescharacteristic
653C23#121×C12711yescharacteristic
654C23#121×C12711yescharacteristic
655C23#127×C12711yescharacteristic
656Q8—24no—
657Q8—22no—
658Q8—24no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—41no—
667Q8—41no—
668D4—22no—
669D4—22no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—41no—
675D4—41no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—82no—
702C2×C4C2×C22⋊C4×C12711yescharacteristic
703C2×C4C2×C22⋊C4×C12711yescharacteristic
704C2×C4C2×C22⋊C4×C12711yescharacteristic
705C2×C4C4×D4×C12711yescharacteristic
706C2×C4C4×D4×C12711yescharacteristic
707C2×C4C4×D4×C12711yescharacteristic
708C2×C4#120×C12711yescharacteristic
709C2×C4#120×C12711yescharacteristic
710C2×C4#120×C12711yescharacteristic
711C2×C4#120×C12711yescharacteristic
712C2×C4#120×C12711yescharacteristic
713C2×C4#120×C12711yescharacteristic
714C2×C4#121×C12711yescharacteristic
715C2×C4#121×C12711yescharacteristic
716C2×C4#121×C12711yescharacteristic
717C2×C4#121×C12711yescharacteristic
718C2×C4#121×C12711yescharacteristic
719C2×C4#121×C12711yescharacteristic
720C2×C4#121×C12711yescharacteristic
721C2×C4#121×C12711yescharacteristic
722C2×C4#121×C12711yescharacteristic
723C2×C4#123×C12711yescharacteristic
724C2×C4#123×C12711yescharacteristic
725C2×C4#123×C12711yescharacteristic
726C2×C4#123×C12711yescharacteristic
727C2×C4#124×C12711yescharacteristic
728C2×C4#124×C12711yescharacteristic
729C2×C4#127×C12711yescharacteristic
730C8—24no—
731C8—42no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—22no—
740C22—44no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—82no—
745C22#386×C12711yescharacteristic
746C22#386×C12711yescharacteristic
747C22#390×C12711yescharacteristic
748C22#392×C12711yescharacteristic
749C22#392×C12711yescharacteristic
750C22#392×C12711yescharacteristic
751C22#394×C12711yescharacteristic
752C22#455×C12712yes—
753C22#456×C12712yes—
754C4—44no—
755C4—42no—
756C4—44no—
757C4—82no—
758C4—82no—
759C4#379×C12711yescharacteristic
760C4#386×C12711yescharacteristic
761C4#386×C12711yescharacteristic
762C4#390×C12711yescharacteristic
763C4#392×C12711yescharacteristic
764C4#394×C12711yescharacteristic
765C4#394×C12711yescharacteristic
766C4#394×C12711yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—82no—
772C2C127×#143811yescharacteristic
773C2C127×#188212yes—
774C2C127×#200411yescharacteristic
775C2C127×#200511yescharacteristic
776C2C127×#200712yes—
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×#41×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#419×C127C2semidirect
5. C2×#391×C127C2semidirect
6. C2×#343×C127C2semidirect
7. C2×#339×C127C2semidirect
15. C2×#137×C127C4semidirect
171. C2×Q8×C127C22⋊C4semidirect
231. M16×C127C22⋊C4semidirect
378. #11017C127direct (N × H)
391. C2×#419C2×C127semidirect
393. C2×#391C2×C127semidirect
394. C2×#343C2×C127semidirect
395. C2×#339C2×C127semidirect
396. C127#11017direct (N × H)
404. C2×#137C4×C127semidirect
560. C2×Q8C22⋊C4×C127semidirect
620. M16C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1272
C22×#104×C1272
C2×#419×C1272
C127×#23112
C2×#391×C1272
C2×#343×C1272
C2×#339×C1272
#11017127