Finite Group Databasebeta

← C2×C127×#1795 #44584294

Subgroups — C2×C127×#1795 #44584294

Order 32512.

3946 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×H(5,𝔽2)×C127C211yesmaximal, characteristic
2C2×#421×C127C212yesmaximal, complemented
3C2×#418×C127C212yesmaximal, complemented
4C2×#413×C127C211yesmaximal, characteristic, complemented
5C2×#410×C127C211yesmaximal, characteristic, complemented
6C127×#1795C218yesmaximal, direct product factor
7C2×H(5,𝔽2)×C127—24no—
8C2×H(5,𝔽2)×C127—24no—
9C2×H(5,𝔽2)×C127—22no—
10C2×H(5,𝔽2)×C127—22no—
11C2×H(5,𝔽2)×C127—24no—
12C2×H(5,𝔽2)×C127—24no—
13C2×H(5,𝔽2)×C127C414yescomplemented
14C2×H(5,𝔽2)×C127C2214yes—
15C22×#41×C127—21no—
16C22×#41×C127C412yescomplemented
17C22×#41×C127C2211yescharacteristic
18C22×#41×C127C2211yescharacteristic
19C23×D4×C127—22no—
20C23×D4×C127—21no—
21C23×D4×C127C412yescomplemented
22C23×D4×C127C2211yescharacteristic
23C22×M16×C127C2212yescomplemented
24C2×#117×C127C2212yescomplemented
25#421×C127—24no—
26#421×C127C2218yescomplemented
27C2×#104×C127—24no—
28#418×C127—24no—
29#418×C127C2218yescomplemented
30C2×#102×C127—24no—
31#413×C127—22no—
32#413×C127C2214yescomplemented
33C2×#101×C127—21no—
34C2×#100×C127—21no—
35#410×C127—22no—
36#410×C127C2214yescomplemented
37C2×#99×C127—22no—
38C25×C127—22no—
39C25×C127—21no—
40H(5,𝔽2)×C127—216no—
41H(5,𝔽2)×C127—216no—
42H(5,𝔽2)×C127—216no—
43H(5,𝔽2)×C127—216no—
44H(5,𝔽2)×C127—216no—
45H(5,𝔽2)×C127—216no—
46H(5,𝔽2)×C127—216no—
47H(5,𝔽2)×C127—216no—
48C2×#41×C127—28no—
49C2×#41×C127—28no—
50C2×#41×C127—24no—
51C2×#41×C127—24no—
52C2×#41×C127—24no—
53C2×#41×C127—24no—
54C2×#41×C127—24no—
55C2×#41×C127—24no—
56C2×#41×C127—24no—
57C2×#41×C127—21no—
58C2×#41×C127—22no—
59C2×#41×C127—22no—
60C2×#41×C127—22no—
61C2×#41×C127—22no—
62C2×#41×C127—22no—
63C2×#41×C127—22no—
64C2×#41×C127—21no—
65C2×#41×C127C2×C412yes—
66C2×#41×C127C2×C412yes—
67C2×#41×C127C2×C418yescomplemented
68C2×#41×C127D414yes—
69C2×#41×C127D414yes—
70C2×#41×C127D412yes—
71C2×#41×C127D412yes—
72C2×#41×C127C2312yes—
73C2×#41×C127C2312yes—
74C22×Q8×C127C2×C411yescharacteristic
75C22×Q8×C127D411yescharacteristic
76C22×D4×C127—216no—
77C22×D4×C127—216no—
78C22×D4×C127—28no—
79C22×D4×C127—28no—
80C22×D4×C127—22no—
81C22×D4×C127—21no—
82C22×D4×C127—24no—
83C22×D4×C127—28no—
84C22×D4×C127—24no—
85C22×D4×C127—24no—
86C22×D4×C127—24no—
87C22×D4×C127—24no—
88C22×D4×C127—28no—
89C22×D4×C127—24no—
90C22×D4×C127—22no—
91C22×D4×C127—24no—
92C22×D4×C127—21no—
93C22×D4×C127—21no—
94C22×D4×C127—22no—
95C22×D4×C127—22no—
96C22×D4×C127—21no—
97C22×D4×C127C2×C411yescharacteristic
98C22×D4×C127C2×C412yes—
99C22×D4×C127C2×C412yes—
100C22×D4×C127C2×C418yescomplemented
101C22×D4×C127D412yes—
102C22×D4×C127D411yescharacteristic
103C22×D4×C127D414yes—
104C22×D4×C127D414yes—
105C22×D4×C127C2312yes—
106C23×C4×C127—22no—
107C23×C4×C127—21no—
108C23×C4×C127C2×C412yes—
109C23×C4×C127C2311yescharacteristic
110C2×M16×C127—22no—
111C2×M16×C127—22no—
112C2×M16×C127—22no—
113C2×M16×C127—22no—
114C2×M16×C127—22no—
115C2×M16×C127C2314yescomplemented
116C22×C8×C127—22no—
117#117×C127—22no—
118#117×C127—22no—
119#117×C127—22no—
120#117×C127C2314yescomplemented
121C2×C4⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C42×C127—22no—
124#104×C127—216no—
125#102×C127—216no—
126#101×C127—24no—
127#100×C127—24no—
128#99×C127—28no—
129C24×C127—28no—
130C24×C127—28no—
131C24×C127—22no—
132C24×C127—21no—
133C24×C127—22no—
134C24×C127—28no—
135C24×C127—24no—
136C24×C127—24no—
137C24×C127—22no—
138C24×C127—84no—
139C24×C127—88no—
140C24×C127C22⋊C412yes—
141C24×C127C2×D411yescharacteristic
142#41×C127—232no—
143#41×C127—232no—
144#41×C127—216no—
145#41×C127—216no—
146#41×C127—216no—
147#41×C127—216no—
148#41×C127—24no—
149#41×C127—24no—
150#41×C127—24no—
151#41×C127—24no—
152#41×C127—24no—
153#41×C127—24no—
154#41×C127—24no—
155#41×C127—24no—
156#41×C127—24no—
157#41×C127—24no—
158#41×C127—24no—
159#41×C127—24no—
160#41×C127—24no—
161#41×C127—24no—
162#41×C127C22⋊C418yes—
163#41×C127C2×D418yes—
164C2×Q8×C127—21no—
165C2×Q8×C127—21no—
166C2×Q8×C127—21no—
167C2×Q8×C127—22no—
168C2×Q8×C127—22no—
169C2×Q8×C127C22⋊C412yes—
170C2×Q8×C127C22⋊C412yes—
171C2×Q8×C127C22⋊C412yes—
172C2×Q8×C127C22×C412yes—
173C2×Q8×C127C2×D412yes—
174C2×D4×C127—28no—
175C2×D4×C127—28no—
176C2×D4×C127—28no—
177C2×D4×C127—28no—
178C2×D4×C127—264no—
179C2×D4×C127—264no—
180C2×D4×C127—232no—
181C2×D4×C127—232no—
182C2×D4×C127—216no—
183C2×D4×C127—216no—
184C2×D4×C127—22no—
185C2×D4×C127—28no—
186C2×D4×C127—24no—
187C2×D4×C127—24no—
188C2×D4×C127—24no—
189C2×D4×C127—24no—
190C2×D4×C127—22no—
191C2×D4×C127—216no—
192C2×D4×C127—216no—
193C2×D4×C127—22no—
194C2×D4×C127—21no—
195C2×D4×C127—22no—
196C2×D4×C127—21no—
197C2×D4×C127—22no—
198C2×D4×C127—21no—
199C2×D4×C127—22no—
200C2×D4×C127—28no—
201C2×D4×C127—24no—
202C2×D4×C127—22no—
203C2×D4×C127—24no—
204C2×D4×C127—22no—
205C2×D4×C127—24no—
206C2×D4×C127—24no—
207C2×D4×C127—24no—
208C2×D4×C127—24no—
209C2×D4×C127—24no—
210C2×D4×C127—22no—
211C2×D4×C127—24no—
212C2×D4×C127C22⋊C414yes—
213C2×D4×C127C22⋊C412yes—
214C2×D4×C127C22⋊C412yes—
215C2×D4×C127C22⋊C412yes—
216C2×D4×C127C22⋊C414yes—
217C2×D4×C127C22⋊C414yes—
218C2×D4×C127C22⋊C418yes—
219C2×D4×C127C22×C414yes—
220C2×D4×C127C22×C412yes—
221C2×D4×C127C2×D414yes—
222C2×D4×C127C2×D412yes—
223C2×D4×C127C2×D418yes—
224C22×C4×C127—28no—
225C22×C4×C127—28no—
226C22×C4×C127—21no—
227C22×C4×C127—22no—
228C22×C4×C127—28no—
229C22×C4×C127—22no—
230C22×C4×C127—22no—
231C22×C4×C127—22no—
232C22×C4×C127—22no—
233C22×C4×C127—24no—
234C22×C4×C127—24no—
235C22×C4×C127—22no—
236C22×C4×C127—42no—
237C22×C4×C127C22⋊C412yes—
238C22×C4×C127C22⋊C414yes—
239C22×C4×C127C22×C414yes—
240C22×C4×C127C22×C411yescharacteristic
241C22×C4×C127C22×C411yescharacteristic
242C22×C4×C127C2×D411yescharacteristic
243C22×C4×C127C2×D412yes—
244C22×C4×C127C2×D412yes—
245C22×C4×C127C2×D412yes—
246C22×C4×C127C2×D412yes—
247C22×C4×C127C2×D411yescharacteristic
248C22×C4×C127C2×D411yescharacteristic
249C22×C4×C127C2411yescharacteristic
250M16×C127—24no—
251M16×C127—24no—
252M16×C127—42no—
253M16×C127—42no—
254C2×C8×C127—24no—
255C2×C8×C127—42no—
256C2×C8×C127—42no—
257C4⋊C4×C127—24no—
258C4⋊C4×C127—42no—
259C22⋊C4×C127—24no—
260C22⋊C4×C127—42no—
261C42×C127—24no—
262C42×C127—42no—
263C23×C127—232no—
264C23×C127—22no—
265C23×C127—24no—
266C23×C127—22no—
267C23×C127—24no—
268C23×C127—22no—
269C23×C127—22no—
270C23×C127—24no—
271C23×C127—22no—
272C23×C127—28no—
273C23×C127—28no—
274C23×C127—42no—
275C23×C127—44no—
276C23×C127—48no—
277C23×C127—44no—
278C23×C127—88no—
279C23×C127—84no—
280C23×C127—88no—
281C23×C127—84no—
282C23×C127—816no—
283C23×C127—816no—
284C23×C127—816no—
285C23×C127C2×C22⋊C411yescharacteristic
286C23×C127C2×C22⋊C414yes—
287C23×C127C2×C22⋊C411yescharacteristic
288C23×C127#12012yes—
289C23×C127#12012yes—
290C23×C127C22×D411yescharacteristic
291Q8×C127—22no—
292Q8×C127—24no—
293Q8×C127—22no—
294Q8×C127—22no—
295Q8×C127—24no—
296Q8×C127C2×C22⋊C414yes—
297D4×C127—232no—
298D4×C127—232no—
299D4×C127—28no—
300D4×C127—28no—
301D4×C127—28no—
302D4×C127—28no—
303D4×C127—24no—
304D4×C127—22no—
305D4×C127—24no—
306D4×C127—28no—
307D4×C127—24no—
308D4×C127—22no—
309D4×C127—22no—
310D4×C127—24no—
311D4×C127—24no—
312D4×C127—28no—
313D4×C127C2×C22⋊C414yes—
314D4×C127C2×C22⋊C418yes—
315C2×C4×C127—232no—
316C2×C4×C127—22no—
317C2×C4×C127—22no—
318C2×C4×C127—22no—
319C2×C4×C127—22no—
320C2×C4×C127—22no—
321C2×C4×C127—24no—
322C2×C4×C127—24no—
323C2×C4×C127—28no—
324C2×C4×C127—28no—
325C2×C4×C127—24no—
326C2×C4×C127—24no—
327C2×C4×C127—44no—
328C2×C4×C127—84no—
329C2×C4×C127C2×C22⋊C414yes—
330C2×C4×C127C2×C22⋊C411yescharacteristic
331C2×C4×C127C2×C22⋊C411yescharacteristic
332C2×C4×C127C2×C22⋊C412yes—
333C2×C4×C127C2×C22⋊C412yes—
334C2×C4×C127C2×C22⋊C411yescharacteristic
335C2×C4×C127C2×C22⋊C411yescharacteristic
336C2×C4×C127C2×C22⋊C411yescharacteristic
337C2×C4×C127C2×C22⋊C411yescharacteristic
338C2×C4×C127#12012yes—
339C2×C4×C127#12012yes—
340C2×C4×C127#12012yes—
341C2×C4×C127#12012yes—
342C2×C4×C127#12012yes—
343C2×C4×C127#12012yes—
344C2×C4×C127C23×C411yescharacteristic
345C2×C4×C127C22×D412yes—
346C2×C4×C127C22×D412yes—
347C2×C4×C127C22×D411yescharacteristic
348C8×C127—44no—
349C22×C127—24no—
350C22×C127—22no—
351C22×C127—24no—
352C22×C127—28no—
353C22×C127—24no—
354C22×C127—41no—
355C22×C127—42no—
356C22×C127—41no—
357C22×C127—44no—
358C22×C127—48no—
359C22×C127—44no—
360C22×C127—48no—
361C22×C127—44no—
362C22×C127—44no—
363C22×C127—48no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—88no—
367C22×C127—88no—
368C22×C127—832no—
369C22×C127#37911yescharacteristic
370C22×C127#37912yes—
371C22×C127#37911yescharacteristic
372C22×C127C22×C22⋊C411yescharacteristic
373C22×C127C2×#12012yes—
374C4×C127—24no—
375C4×C127—24no—
376C4×C127—84no—
377C4×C127#37912yes—
378C4×C127#37911yescharacteristic
379C4×C127#37911yescharacteristic
380C4×C127C22×C22⋊C411yescharacteristic
381C4×C127C22×C22⋊C411yescharacteristic
382C4×C127C2×#12012yes—
383C2×#1795C12711yesmaximal, characteristic, direct product factor, Sylow
384C2×C127—22no—
385C2×C127—21no—
386C2×C127—21no—
387C2×C127—22no—
388C2×C127—48no—
389C2×C127—44no—
390C2×C127—44no—
391C2×C127#179512yesdirect product factor
392C2×C127C2×#37911yescharacteristic
393C22×H(5,𝔽2)C2×C12711yescharacteristic
394C2×#421C2×C12712yescomplemented
395C2×#418C2×C12712yescomplemented
396C2×#413C2×C12711yescharacteristic, complemented
397C2×#410C2×C12711yescharacteristic, complemented
398#1795C2×C12718yesdirect product factor
399C127C2×#179511yescharacteristic, direct product factor, Sylow
400C2×H(5,𝔽2)—24no—
401C2×H(5,𝔽2)—24no—
402C2×H(5,𝔽2)—22no—
403C2×H(5,𝔽2)—22no—
404C2×H(5,𝔽2)—24no—
405C2×H(5,𝔽2)—24no—
406C2×H(5,𝔽2)C4×C12714yescomplemented
407C2×H(5,𝔽2)C22×C12714yes—
408C22×#41—21no—
409C22×#41C4×C12712yescomplemented
410C22×#41C22×C12711yescharacteristic
411C22×#41C22×C12711yescharacteristic
412C23×D4—22no—
413C23×D4—21no—
414C23×D4C4×C12712yescomplemented
415C23×D4C22×C12711yescharacteristic
416C22×M16C22×C12712yescomplemented
417C2×#117C22×C12712yescomplemented
418#421—24no—
419#421C22×C12718yescomplemented
420C2×#104—24no—
421#418—24no—
422#418C22×C12718yescomplemented
423C2×#102—24no—
424#413—22no—
425#413C22×C12714yescomplemented
426C2×#101—21no—
427C2×#100—21no—
428#410—22no—
429#410C22×C12714yescomplemented
430C2×#99—22no—
431C25—22no—
432C25—21no—
433H(5,𝔽2)—216no—
434H(5,𝔽2)—216no—
435H(5,𝔽2)—216no—
436H(5,𝔽2)—216no—
437H(5,𝔽2)—216no—
438H(5,𝔽2)—216no—
439H(5,𝔽2)—216no—
440H(5,𝔽2)—216no—
441C2×#41—28no—
442C2×#41—28no—
443C2×#41—24no—
444C2×#41—24no—
445C2×#41—24no—
446C2×#41—24no—
447C2×#41—24no—
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—21no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—21no—
458C2×#41C2×C4×C12712yes—
459C2×#41C2×C4×C12712yes—
460C2×#41C2×C4×C12718yescomplemented
461C2×#41D4×C12714yes—
462C2×#41D4×C12714yes—
463C2×#41D4×C12712yes—
464C2×#41D4×C12712yes—
465C2×#41C23×C12712yes—
466C2×#41C23×C12712yes—
467C22×Q8C2×C4×C12711yescharacteristic
468C22×Q8D4×C12711yescharacteristic
469C22×D4—216no—
470C22×D4—216no—
471C22×D4—28no—
472C22×D4—28no—
473C22×D4—22no—
474C22×D4—21no—
475C22×D4—24no—
476C22×D4—28no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4—24no—
481C22×D4—28no—
482C22×D4—24no—
483C22×D4—22no—
484C22×D4—24no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—22no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4C2×C4×C12711yescharacteristic
491C22×D4C2×C4×C12712yes—
492C22×D4C2×C4×C12712yes—
493C22×D4C2×C4×C12718yescomplemented
494C22×D4D4×C12712yes—
495C22×D4D4×C12711yescharacteristic
496C22×D4D4×C12714yes—
497C22×D4D4×C12714yes—
498C22×D4C23×C12712yes—
499C23×C4—22no—
500C23×C4—21no—
501C23×C4C2×C4×C12712yes—
502C23×C4C23×C12711yescharacteristic
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16C23×C12714yescomplemented
509C22×C8—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117C23×C12714yescomplemented
514C2×C4⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C42—22no—
517#104—216no—
518#102—216no—
519#101—24no—
520#100—24no—
521#99—28no—
522C24—28no—
523C24—28no—
524C24—22no—
525C24—21no—
526C24—22no—
527C24—28no—
528C24—24no—
529C24—24no—
530C24—22no—
531C24—84no—
532C24—88no—
533C24C22⋊C4×C12712yes—
534C24C2×D4×C12711yescharacteristic
535#41—232no—
536#41—232no—
537#41—216no—
538#41—216no—
539#41—216no—
540#41—216no—
541#41—24no—
542#41—24no—
543#41—24no—
544#41—24no—
545#41—24no—
546#41—24no—
547#41—24no—
548#41—24no—
549#41—24no—
550#41—24no—
551#41—24no—
552#41—24no—
553#41—24no—
554#41—24no—
555#41C22⋊C4×C12718yes—
556#41C2×D4×C12718yes—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8C22⋊C4×C12712yes—
563C2×Q8C22⋊C4×C12712yes—
564C2×Q8C22⋊C4×C12712yes—
565C2×Q8C22×C4×C12712yes—
566C2×Q8C2×D4×C12712yes—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—264no—
572C2×D4—264no—
573C2×D4—232no—
574C2×D4—232no—
575C2×D4—216no—
576C2×D4—216no—
577C2×D4—22no—
578C2×D4—28no—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—216no—
585C2×D4—216no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—28no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—24no—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—22no—
604C2×D4—24no—
605C2×D4C22⋊C4×C12714yes—
606C2×D4C22⋊C4×C12712yes—
607C2×D4C22⋊C4×C12712yes—
608C2×D4C22⋊C4×C12712yes—
609C2×D4C22⋊C4×C12714yes—
610C2×D4C22⋊C4×C12714yes—
611C2×D4C22⋊C4×C12718yes—
612C2×D4C22×C4×C12714yes—
613C2×D4C22×C4×C12712yes—
614C2×D4C2×D4×C12714yes—
615C2×D4C2×D4×C12712yes—
616C2×D4C2×D4×C12718yes—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—28no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—22no—
629C22×C4—42no—
630C22×C4C22⋊C4×C12712yes—
631C22×C4C22⋊C4×C12714yes—
632C22×C4C22×C4×C12714yes—
633C22×C4C22×C4×C12711yescharacteristic
634C22×C4C22×C4×C12711yescharacteristic
635C22×C4C2×D4×C12711yescharacteristic
636C22×C4C2×D4×C12712yes—
637C22×C4C2×D4×C12712yes—
638C22×C4C2×D4×C12712yes—
639C22×C4C2×D4×C12712yes—
640C22×C4C2×D4×C12711yescharacteristic
641C22×C4C2×D4×C12711yescharacteristic
642C22×C4C24×C12711yescharacteristic
643M16—24no—
644M16—24no—
645M16—42no—
646M16—42no—
647C2×C8—24no—
648C2×C8—42no—
649C2×C8—42no—
650C4⋊C4—24no—
651C4⋊C4—42no—
652C22⋊C4—24no—
653C22⋊C4—42no—
654C42—24no—
655C42—42no—
656C23—232no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—28no—
666C23—28no—
667C23—42no—
668C23—44no—
669C23—48no—
670C23—44no—
671C23—88no—
672C23—84no—
673C23—88no—
674C23—84no—
675C23—816no—
676C23—816no—
677C23—816no—
678C23C2×C22⋊C4×C12711yescharacteristic
679C23C2×C22⋊C4×C12714yes—
680C23C2×C22⋊C4×C12711yescharacteristic
681C23#120×C12712yes—
682C23#120×C12712yes—
683C23C22×D4×C12711yescharacteristic
684Q8—22no—
685Q8—24no—
686Q8—22no—
687Q8—22no—
688Q8—24no—
689Q8C2×C22⋊C4×C12714yes—
690D4—232no—
691D4—232no—
692D4—28no—
693D4—28no—
694D4—28no—
695D4—28no—
696D4—24no—
697D4—22no—
698D4—24no—
699D4—28no—
700D4—24no—
701D4—22no—
702D4—22no—
703D4—24no—
704D4—24no—
705D4—28no—
706D4C2×C22⋊C4×C12714yes—
707D4C2×C22⋊C4×C12718yes—
708C2×C4—232no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—44no—
721C2×C4—84no—
722C2×C4C2×C22⋊C4×C12714yes—
723C2×C4C2×C22⋊C4×C12711yescharacteristic
724C2×C4C2×C22⋊C4×C12711yescharacteristic
725C2×C4C2×C22⋊C4×C12711yescharacteristic
726C2×C4C2×C22⋊C4×C12711yescharacteristic
727C2×C4C2×C22⋊C4×C12712yes—
728C2×C4C2×C22⋊C4×C12712yes—
729C2×C4C2×C22⋊C4×C12711yescharacteristic
730C2×C4C2×C22⋊C4×C12711yescharacteristic
731C2×C4#120×C12712yes—
732C2×C4#120×C12712yes—
733C2×C4#120×C12712yes—
734C2×C4#120×C12712yes—
735C2×C4#120×C12712yes—
736C2×C4#120×C12712yes—
737C2×C4C23×C4×C12711yescharacteristic
738C2×C4C22×D4×C12712yes—
739C2×C4C22×D4×C12712yes—
740C2×C4C22×D4×C12711yescharacteristic
741C8—44no—
742C22—24no—
743C22—22no—
744C22—24no—
745C22—28no—
746C22—24no—
747C22—41no—
748C22—42no—
749C22—41no—
750C22—44no—
751C22—48no—
752C22—44no—
753C22—48no—
754C22—44no—
755C22—44no—
756C22—48no—
757C22—44no—
758C22—44no—
759C22—88no—
760C22—88no—
761C22—832no—
762C22#379×C12711yescharacteristic
763C22#379×C12712yes—
764C22#379×C12711yescharacteristic
765C22C22×C22⋊C4×C12711yescharacteristic
766C22C2×#120×C12712yes—
767C4—24no—
768C4—24no—
769C4—84no—
770C4#379×C12712yes—
771C4#379×C12711yescharacteristic
772C4#379×C12711yescharacteristic
773C4C22×C22⋊C4×C12711yescharacteristic
774C4C22×C22⋊C4×C12711yescharacteristic
775C4C2×#120×C12712yes—
776C2—22no—
777C2—21no—
778C2—21no—
779C2—22no—
780C2—48no—
781C2—44no—
782C2—44no—
783C2C127×#179512yesdirect product factor
784C2C2×#379×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×H(5,𝔽2)×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#421×C127C2semidirect
3. C2×#418×C127C2semidirect
4. C2×#413×C127C2semidirect
5. C2×#410×C127C2semidirect
6. C127×#1795C2direct (N × H)
13. C2×H(5,𝔽2)×C127C4semidirect
16. C22×#41×C127C4semidirect
21. C23×D4×C127C4semidirect
23. C22×M16×C127C22semidirect
24. C2×#117×C127C22semidirect
26. #421×C127C22semidirect
29. #418×C127C22semidirect
32. #413×C127C22semidirect
36. #410×C127C22semidirect
67. C2×#41×C127C2×C4semidirect
100. C22×D4×C127C2×C4semidirect
115. C2×M16×C127C23semidirect
120. #117×C127C23semidirect
383. C2×#1795C127direct (N × H)
391. C2×C127#1795direct (N × H)
394. C2×#421C2×C127semidirect
395. C2×#418C2×C127semidirect
396. C2×#413C2×C127semidirect
397. C2×#410C2×C127semidirect
398. #1795C2×C127direct (N × H)
399. C127C2×#1795direct (N × H)
406. C2×H(5,𝔽2)C4×C127semidirect
409. C22×#41C4×C127semidirect
414. C23×D4C4×C127semidirect
416. C22×M16C22×C127semidirect
417. C2×#117C22×C127semidirect
419. #421C22×C127semidirect
422. #418C22×C127semidirect
425. #413C22×C127semidirect
429. #410C22×C127semidirect
460. C2×#41C2×C4×C127semidirect
493. C22×D4C2×C4×C127semidirect
508. C2×M16C23×C127semidirect
513. #117C23×C127semidirect
783. C2C127×#1795direct (N × H)

Maximal subgroups

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

subgroupindex
C22×H(5,𝔽2)×C1272
C2×#421×C1272
C2×#418×C1272
C2×#413×C1272
C2×#410×C1272
C127×#17952
C2×#1795127