Finite Group Databasebeta

← C2×C127×#1794 #44584292

Subgroups — C2×C127×#1794 #44584292

Order 32512.

3662 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#585×C127C211yesmaximal, characteristic
2C2×#421×C127C212yesmaximal, complemented
3C2×#416×C127C212yesmaximal, complemented
4C2×#410×C127C211yesmaximal, characteristic, complemented
5C2×#408×C127C211yesmaximal, characteristic, complemented
6C127×#1794C218yesmaximal, direct product factor
7#585×C127—24no—
8#585×C127—24no—
9#585×C127—22no—
10#585×C127—22no—
11#585×C127C414yescomplemented
12#585×C127C2214yes—
13C2×2−1+4×C127—22no—
14C2×2−1+4×C127C412yescomplemented
15C2×H(5,𝔽2)×C127—22no—
16C2×H(5,𝔽2)×C127—22no—
17C2×H(5,𝔽2)×C127C412yescomplemented
18C22×#41×C127—24no—
19C22×#41×C127—22no—
20C22×#41×C127C2212yes—
21C22×#41×C127C2211yescharacteristic
22C22×M16×C127C2211yescharacteristic, complemented
23C23×C8×C127C2211yescharacteristic, complemented
24C2×#117×C127C2212yescomplemented
25#421×C127—24no—
26#421×C127C2218yescomplemented
27C2×#104×C127—24no—
28#416×C127—24no—
29#416×C127C2218yescomplemented
30C2×#103×C127—22no—
31C2×#102×C127—22no—
32#410×C127—22no—
33#410×C127C2214yescomplemented
34C2×#99×C127—22no—
35#408×C127—22no—
36#408×C127C2214yescomplemented
37C2×C22⋊C8×C127—22no—
382−1+4×C127—28no—
392−1+4×C127—28no—
402−1+4×C127—28no—
412−1+4×C127—28no—
422−1+4×C127—24no—
432−1+4×C127—28no—
442−1+4×C127C2×C418yescomplemented
45H(5,𝔽2)×C127—28no—
46H(5,𝔽2)×C127—28no—
47H(5,𝔽2)×C127—216no—
48H(5,𝔽2)×C127—28no—
49H(5,𝔽2)×C127—28no—
50H(5,𝔽2)×C127—28no—
51H(5,𝔽2)×C127—24no—
52H(5,𝔽2)×C127—28no—
53H(5,𝔽2)×C127—28no—
54H(5,𝔽2)×C127C2×C418yescomplemented
55C2×#41×C127—24no—
56C2×#41×C127—28no—
57C2×#41×C127—24no—
58C2×#41×C127—216no—
59C2×#41×C127—216no—
60C2×#41×C127—28no—
61C2×#41×C127—28no—
62C2×#41×C127—216no—
63C2×#41×C127—216no—
64C2×#41×C127—24no—
65C2×#41×C127—24no—
66C2×#41×C127—24no—
67C2×#41×C127—28no—
68C2×#41×C127—22no—
69C2×#41×C127—22no—
70C2×#41×C127—28no—
71C2×#41×C127—22no—
72C2×#41×C127—22no—
73C2×#41×C127—22no—
74C2×#41×C127—22no—
75C2×#41×C127—22no—
76C2×#41×C127—22no—
77C2×#41×C127—22no—
78C2×#41×C127—22no—
79C2×#41×C127C2×C414yes—
80C2×#41×C127C2×C414yes—
81C2×#41×C127C2×C412yes—
82C2×#41×C127D414yes—
83C2×#41×C127D414yes—
84C2×#41×C127D414yes—
85C2×#41×C127D412yes—
86C2×#41×C127D412yes—
87C2×#41×C127C2314yes—
88C2×#41×C127C2312yes—
89C22×Q8×C127—22no—
90C22×Q8×C127—24no—
91C22×Q8×C127C2×C411yescharacteristic
92C22×Q8×C127D412yes—
93C22×D4×C127—28no—
94C22×D4×C127—22no—
95C22×D4×C127—24no—
96C22×D4×C127—22no—
97C22×D4×C127—24no—
98C22×D4×C127C2×C411yescharacteristic
99C22×D4×C127D412yes—
100C22×D4×C127D412yes—
101C23×C4×C127—24no—
102C23×C4×C127—22no—
103C23×C4×C127D412yes—
104C23×C4×C127C2311yescharacteristic
105C2×M16×C127—21no—
106C2×M16×C127—22no—
107C2×M16×C127—22no—
108C2×M16×C127C2312yescomplemented
109C22×C8×C127—21no—
110C22×C8×C127—21no—
111C22×C8×C127—22no—
112C22×C8×C127—22no—
113C22×C8×C127—21no—
114C22×C8×C127C2312yescomplemented
115#117×C127—22no—
116#117×C127—22no—
117#117×C127—22no—
118#117×C127C2314yescomplemented
119C2×C4⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C42×C127—22no—
122#104×C127—216no—
123#103×C127—28no—
124#102×C127—28no—
125#99×C127—28no—
126C22⋊C8×C127—28no—
127C24×C127—24no—
128C24×C127—22no—
129C24×C127C22⋊C412yes—
130C24×C127C2×D411yescharacteristic
131#41×C127—216no—
132#41×C127—216no—
133#41×C127—232no—
134#41×C127—232no—
135#41×C127—216no—
136#41×C127—216no—
137#41×C127—216no—
138#41×C127—216no—
139#41×C127—216no—
140#41×C127—216no—
141#41×C127—216no—
142#41×C127—24no—
143#41×C127—24no—
144#41×C127—216no—
145#41×C127—24no—
146#41×C127—24no—
147#41×C127—24no—
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×C127—24no—
163#41×C127C22⋊C418yes—
164#41×C127C22⋊C418yes—
165#41×C127C22×C418yes—
166#41×C127C2×D418yes—
167C2×Q8×C127—24no—
168C2×Q8×C127—28no—
169C2×Q8×C127—216no—
170C2×Q8×C127—28no—
171C2×Q8×C127—216no—
172C2×Q8×C127—22no—
173C2×Q8×C127—22no—
174C2×Q8×C127—22no—
175C2×Q8×C127—22no—
176C2×Q8×C127—22no—
177C2×Q8×C127C22⋊C414yes—
178C2×Q8×C127C22⋊C414yes—
179C2×Q8×C127C22⋊C412yes—
180C2×Q8×C127C22×C412yes—
181C2×Q8×C127C2×D414yes—
182C2×D4×C127—28no—
183C2×D4×C127—24no—
184C2×D4×C127—232no—
185C2×D4×C127—216no—
186C2×D4×C127—232no—
187C2×D4×C127—28no—
188C2×D4×C127—216no—
189C2×D4×C127—28no—
190C2×D4×C127—24no—
191C2×D4×C127—216no—
192C2×D4×C127—24no—
193C2×D4×C127—24no—
194C2×D4×C127—24no—
195C2×D4×C127—24no—
196C2×D4×C127—24no—
197C2×D4×C127—24no—
198C2×D4×C127—24no—
199C2×D4×C127—216no—
200C2×D4×C127—22no—
201C2×D4×C127—22no—
202C2×D4×C127—22no—
203C2×D4×C127—22no—
204C2×D4×C127—22no—
205C2×D4×C127C22⋊C412yes—
206C2×D4×C127C22⋊C414yes—
207C2×D4×C127C22⋊C414yes—
208C2×D4×C127C22⋊C414yes—
209C2×D4×C127C22×C412yes—
210C2×D4×C127C2×D414yes—
211C2×D4×C127C2×D414yes—
212C22×C4×C127—24no—
213C22×C4×C127—28no—
214C22×C4×C127—216no—
215C22×C4×C127—216no—
216C22×C4×C127—22no—
217C22×C4×C127—24no—
218C22×C4×C127—24no—
219C22×C4×C127—24no—
220C22×C4×C127—24no—
221C22×C4×C127—22no—
222C22×C4×C127—22no—
223C22×C4×C127—22no—
224C22×C4×C127—24no—
225C22×C4×C127—22no—
226C22×C4×C127—24no—
227C22×C4×C127—42no—
228C22×C4×C127C22⋊C412yes—
229C22×C4×C127C22⋊C414yes—
230C22×C4×C127C22×C411yescharacteristic
231C22×C4×C127C22×C411yescharacteristic
232C22×C4×C127C2×D414yes—
233C22×C4×C127C2×D411yescharacteristic
234C22×C4×C127C2×D412yes—
235C22×C4×C127C2×D412yes—
236C22×C4×C127C2×D412yes—
237C22×C4×C127C2×D412yes—
238C22×C4×C127C2×D411yescharacteristic
239C22×C4×C127C2×D411yescharacteristic
240C22×C4×C127C2411yescharacteristic
241M16×C127—24no—
242M16×C127—42no—
243C2×C8×C127—22no—
244C2×C8×C127—22no—
245C2×C8×C127—24no—
246C2×C8×C127—41no—
247C2×C8×C127—41no—
248C2×C8×C127—42no—
249C2×C8×C127—41no—
250C2×C8×C127—41no—
251C4⋊C4×C127—24no—
252C4⋊C4×C127—42no—
253C22⋊C4×C127—24no—
254C22⋊C4×C127—42no—
255C42×C127—24no—
256C42×C127—42no—
257C23×C127—216no—
258C23×C127—22no—
259C23×C127—24no—
260C23×C127—24no—
261C23×C127—22no—
262C23×C127—24no—
263C23×C127—42no—
264C23×C127—44no—
265C23×C127—84no—
266C23×C127—88no—
267C23×C127C2×C22⋊C411yescharacteristic
268C23×C127C2×C22⋊C414yes—
269C23×C127C2×C22⋊C411yescharacteristic
270C23×C127#12012yes—
271C23×C127#12012yes—
272C23×C127C22×D411yescharacteristic
273Q8×C127—216no—
274Q8×C127—24no—
275Q8×C127—24no—
276Q8×C127—24no—
277Q8×C127—24no—
278Q8×C127—24no—
279Q8×C127C2×C22⋊C418yes—
280D4×C127—232no—
281D4×C127—216no—
282D4×C127—28no—
283D4×C127—28no—
284D4×C127—28no—
285D4×C127—28no—
286D4×C127—28no—
287D4×C127—28no—
288D4×C127—24no—
289D4×C127—24no—
290D4×C127—24no—
291D4×C127—24no—
292D4×C127—24no—
293D4×C127C2×C22⋊C418yes—
294C2×C4×C127—216no—
295C2×C4×C127—232no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—22no—
299C2×C4×C127—24no—
300C2×C4×C127—22no—
301C2×C4×C127—28no—
302C2×C4×C127—28no—
303C2×C4×C127—24no—
304C2×C4×C127—24no—
305C2×C4×C127—28no—
306C2×C4×C127—24no—
307C2×C4×C127—28no—
308C2×C4×C127—24no—
309C2×C4×C127—44no—
310C2×C4×C127—84no—
311C2×C4×C127C2×C22⋊C414yes—
312C2×C4×C127C2×C22⋊C412yes—
313C2×C4×C127C2×C22⋊C412yes—
314C2×C4×C127C2×C22⋊C412yes—
315C2×C4×C127C2×C22⋊C412yes—
316C2×C4×C127C2×C22⋊C411yescharacteristic
317C2×C4×C127C2×C22⋊C411yescharacteristic
318C2×C4×C127#12011yescharacteristic
319C2×C4×C127#12011yescharacteristic
320C2×C4×C127#12011yescharacteristic
321C2×C4×C127#12012yes—
322C2×C4×C127#12012yes—
323C2×C4×C127#12012yes—
324C2×C4×C127#12012yes—
325C2×C4×C127#12011yescharacteristic
326C2×C4×C127C23×C411yescharacteristic
327C2×C4×C127C22×D412yes—
328C2×C4×C127C22×D412yes—
329C2×C4×C127C22×D411yescharacteristic
330C8×C127—42no—
331C8×C127—42no—
332C22×C127—24no—
333C22×C127—22no—
334C22×C127—24no—
335C22×C127—28no—
336C22×C127—41no—
337C22×C127—42no—
338C22×C127—41no—
339C22×C127—44no—
340C22×C127—44no—
341C22×C127—48no—
342C22×C127—82no—
343C22×C127—84no—
344C22×C127—84no—
345C22×C127—816no—
346C22×C127#37912yes—
347C22×C127#37911yescharacteristic
348C22×C127#37911yescharacteristic
349C22×C127C22×C22⋊C411yescharacteristic
350C22×C127C2×#12012yes—
351C4×C127—28no—
352C4×C127—24no—
353C4×C127—84no—
354C4×C127#37911yescharacteristic
355C4×C127#37912yes—
356C4×C127#37911yescharacteristic
357C4×C127C22×C22⋊C412yes—
358C4×C127C2×#12011yescharacteristic
359C4×C127C2×#12011yescharacteristic
360C2×#1794C12711yesmaximal, characteristic, direct product factor, Sylow
361C2×C127—22no—
362C2×C127—21no—
363C2×C127—22no—
364C2×C127—21no—
365C2×C127—44no—
366C2×C127—48no—
367C2×C127#179412yesdirect product factor
368C2×C127C2×#37911yescharacteristic
369C2×#585C2×C12711yescharacteristic
370C2×#421C2×C12712yescomplemented
371C2×#416C2×C12712yescomplemented
372C2×#410C2×C12711yescharacteristic, complemented
373C2×#408C2×C12711yescharacteristic, complemented
374#1794C2×C12718yesdirect product factor
375C127C2×#179411yescharacteristic, direct product factor, Sylow
376#585—24no—
377#585—24no—
378#585—22no—
379#585—22no—
380#585C4×C12714yescomplemented
381#585C22×C12714yes—
382C2×2−1+4—22no—
383C2×2−1+4C4×C12712yescomplemented
384C2×H(5,𝔽2)—22no—
385C2×H(5,𝔽2)—22no—
386C2×H(5,𝔽2)C4×C12712yescomplemented
387C22×#41—24no—
388C22×#41—22no—
389C22×#41C22×C12712yes—
390C22×#41C22×C12711yescharacteristic
391C22×M16C22×C12711yescharacteristic, complemented
392C23×C8C22×C12711yescharacteristic, complemented
393C2×#117C22×C12712yescomplemented
394#421—24no—
395#421C22×C12718yescomplemented
396C2×#104—24no—
397#416—24no—
398#416C22×C12718yescomplemented
399C2×#103—22no—
400C2×#102—22no—
401#410—22no—
402#410C22×C12714yescomplemented
403C2×#99—22no—
404#408—22no—
405#408C22×C12714yescomplemented
406C2×C22⋊C8—22no—
4072−1+4—28no—
4082−1+4—28no—
4092−1+4—28no—
4102−1+4—28no—
4112−1+4—24no—
4122−1+4—28no—
4132−1+4C2×C4×C12718yescomplemented
414H(5,𝔽2)—28no—
415H(5,𝔽2)—28no—
416H(5,𝔽2)—216no—
417H(5,𝔽2)—28no—
418H(5,𝔽2)—28no—
419H(5,𝔽2)—28no—
420H(5,𝔽2)—24no—
421H(5,𝔽2)—28no—
422H(5,𝔽2)—28no—
423H(5,𝔽2)C2×C4×C12718yescomplemented
424C2×#41—24no—
425C2×#41—28no—
426C2×#41—24no—
427C2×#41—216no—
428C2×#41—216no—
429C2×#41—28no—
430C2×#41—28no—
431C2×#41—216no—
432C2×#41—216no—
433C2×#41—24no—
434C2×#41—24no—
435C2×#41—24no—
436C2×#41—28no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—28no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41C2×C4×C12714yes—
449C2×#41C2×C4×C12714yes—
450C2×#41C2×C4×C12712yes—
451C2×#41D4×C12714yes—
452C2×#41D4×C12714yes—
453C2×#41D4×C12714yes—
454C2×#41D4×C12712yes—
455C2×#41D4×C12712yes—
456C2×#41C23×C12714yes—
457C2×#41C23×C12712yes—
458C22×Q8—22no—
459C22×Q8—24no—
460C22×Q8C2×C4×C12711yescharacteristic
461C22×Q8D4×C12712yes—
462C22×D4—28no—
463C22×D4—22no—
464C22×D4—24no—
465C22×D4—22no—
466C22×D4—24no—
467C22×D4C2×C4×C12711yescharacteristic
468C22×D4D4×C12712yes—
469C22×D4D4×C12712yes—
470C23×C4—24no—
471C23×C4—22no—
472C23×C4D4×C12712yes—
473C23×C4C23×C12711yescharacteristic
474C2×M16—21no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16C23×C12712yescomplemented
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—21no—
483C22×C8C23×C12712yescomplemented
484#117—22no—
485#117—22no—
486#117—22no—
487#117C23×C12714yescomplemented
488C2×C4⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C42—22no—
491#104—216no—
492#103—28no—
493#102—28no—
494#99—28no—
495C22⋊C8—28no—
496C24—24no—
497C24—22no—
498C24C22⋊C4×C12712yes—
499C24C2×D4×C12711yescharacteristic
500#41—216no—
501#41—216no—
502#41—232no—
503#41—232no—
504#41—216no—
505#41—216no—
506#41—216no—
507#41—216no—
508#41—216no—
509#41—216no—
510#41—216no—
511#41—24no—
512#41—24no—
513#41—216no—
514#41—24no—
515#41—24no—
516#41—24no—
517#41—24no—
518#41—24no—
519#41—24no—
520#41—24no—
521#41—24no—
522#41—24no—
523#41—24no—
524#41—24no—
525#41—24no—
526#41—24no—
527#41—24no—
528#41—24no—
529#41—24no—
530#41—24no—
531#41—24no—
532#41C22⋊C4×C12718yes—
533#41C22⋊C4×C12718yes—
534#41C22×C4×C12718yes—
535#41C2×D4×C12718yes—
536C2×Q8—24no—
537C2×Q8—28no—
538C2×Q8—216no—
539C2×Q8—28no—
540C2×Q8—216no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8C22⋊C4×C12714yes—
547C2×Q8C22⋊C4×C12714yes—
548C2×Q8C22⋊C4×C12712yes—
549C2×Q8C22×C4×C12712yes—
550C2×Q8C2×D4×C12714yes—
551C2×D4—28no—
552C2×D4—24no—
553C2×D4—232no—
554C2×D4—216no—
555C2×D4—232no—
556C2×D4—28no—
557C2×D4—216no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—216no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—216no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4C22⋊C4×C12712yes—
575C2×D4C22⋊C4×C12714yes—
576C2×D4C22⋊C4×C12714yes—
577C2×D4C22⋊C4×C12714yes—
578C2×D4C22×C4×C12712yes—
579C2×D4C2×D4×C12714yes—
580C2×D4C2×D4×C12714yes—
581C22×C4—24no—
582C22×C4—28no—
583C22×C4—216no—
584C22×C4—216no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—42no—
597C22×C4C22⋊C4×C12712yes—
598C22×C4C22⋊C4×C12714yes—
599C22×C4C22×C4×C12711yescharacteristic
600C22×C4C22×C4×C12711yescharacteristic
601C22×C4C2×D4×C12714yes—
602C22×C4C2×D4×C12711yescharacteristic
603C22×C4C2×D4×C12712yes—
604C22×C4C2×D4×C12712yes—
605C22×C4C2×D4×C12712yes—
606C22×C4C2×D4×C12712yes—
607C22×C4C2×D4×C12711yescharacteristic
608C22×C4C2×D4×C12711yescharacteristic
609C22×C4C24×C12711yescharacteristic
610M16—24no—
611M16—42no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—24no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—42no—
618C2×C8—41no—
619C2×C8—41no—
620C4⋊C4—24no—
621C4⋊C4—42no—
622C22⋊C4—24no—
623C22⋊C4—42no—
624C42—24no—
625C42—42no—
626C23—216no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—44no—
634C23—84no—
635C23—88no—
636C23C2×C22⋊C4×C12711yescharacteristic
637C23C2×C22⋊C4×C12714yes—
638C23C2×C22⋊C4×C12711yescharacteristic
639C23#120×C12712yes—
640C23#120×C12712yes—
641C23C22×D4×C12711yescharacteristic
642Q8—216no—
643Q8—24no—
644Q8—24no—
645Q8—24no—
646Q8—24no—
647Q8—24no—
648Q8C2×C22⋊C4×C12718yes—
649D4—232no—
650D4—216no—
651D4—28no—
652D4—28no—
653D4—28no—
654D4—28no—
655D4—28no—
656D4—28no—
657D4—24no—
658D4—24no—
659D4—24no—
660D4—24no—
661D4—24no—
662D4C2×C22⋊C4×C12718yes—
663C2×C4—216no—
664C2×C4—232no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—84no—
680C2×C4C2×C22⋊C4×C12714yes—
681C2×C4C2×C22⋊C4×C12712yes—
682C2×C4C2×C22⋊C4×C12712yes—
683C2×C4C2×C22⋊C4×C12712yes—
684C2×C4C2×C22⋊C4×C12712yes—
685C2×C4C2×C22⋊C4×C12711yescharacteristic
686C2×C4C2×C22⋊C4×C12711yescharacteristic
687C2×C4#120×C12711yescharacteristic
688C2×C4#120×C12711yescharacteristic
689C2×C4#120×C12711yescharacteristic
690C2×C4#120×C12711yescharacteristic
691C2×C4#120×C12712yes—
692C2×C4#120×C12712yes—
693C2×C4#120×C12712yes—
694C2×C4#120×C12712yes—
695C2×C4C23×C4×C12711yescharacteristic
696C2×C4C22×D4×C12712yes—
697C2×C4C22×D4×C12712yes—
698C2×C4C22×D4×C12711yescharacteristic
699C8—42no—
700C8—42no—
701C22—24no—
702C22—22no—
703C22—24no—
704C22—28no—
705C22—41no—
706C22—42no—
707C22—41no—
708C22—44no—
709C22—44no—
710C22—48no—
711C22—82no—
712C22—84no—
713C22—84no—
714C22—816no—
715C22#379×C12712yes—
716C22#379×C12711yescharacteristic
717C22#379×C12711yescharacteristic
718C22C22×C22⋊C4×C12711yescharacteristic
719C22C2×#120×C12712yes—
720C4—28no—
721C4—24no—
722C4—84no—
723C4#379×C12711yescharacteristic
724C4#379×C12712yes—
725C4#379×C12711yescharacteristic
726C4C22×C22⋊C4×C12712yes—
727C4C2×#120×C12711yescharacteristic
728C4C2×#120×C12711yescharacteristic
729C2—22no—
730C2—21no—
731C2—22no—
732C2—21no—
733C2—44no—
734C2—48no—
735C2C127×#179412yesdirect product factor
736C2C2×#379×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127#379
prime radicalC2×#585×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×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×#416×C127C2semidirect
4. C2×#410×C127C2semidirect
5. C2×#408×C127C2semidirect
6. C127×#1794C2direct (N × H)
11. #585×C127C4semidirect
14. C2×2−1+4×C127C4semidirect
17. C2×H(5,𝔽2)×C127C4semidirect
22. C22×M16×C127C22semidirect
23. C23×C8×C127C22semidirect
24. C2×#117×C127C22semidirect
26. #421×C127C22semidirect
29. #416×C127C22semidirect
33. #410×C127C22semidirect
36. #408×C127C22semidirect
44. 2−1+4×C127C2×C4semidirect
54. H(5,𝔽2)×C127C2×C4semidirect
108. C2×M16×C127C23semidirect
114. C22×C8×C127C23semidirect
118. #117×C127C23semidirect
360. C2×#1794C127direct (N × H)
367. C2×C127#1794direct (N × H)
370. C2×#421C2×C127semidirect
371. C2×#416C2×C127semidirect
372. C2×#410C2×C127semidirect
373. C2×#408C2×C127semidirect
374. #1794C2×C127direct (N × H)
375. C127C2×#1794direct (N × H)
380. #585C4×C127semidirect
383. C2×2−1+4C4×C127semidirect
386. C2×H(5,𝔽2)C4×C127semidirect
391. C22×M16C22×C127semidirect
392. C23×C8C22×C127semidirect
393. C2×#117C22×C127semidirect
395. #421C22×C127semidirect
398. #416C22×C127semidirect
402. #410C22×C127semidirect
405. #408C22×C127semidirect
413. 2−1+4C2×C4×C127semidirect
423. H(5,𝔽2)C2×C4×C127semidirect
477. C2×M16C23×C127semidirect
483. C22×C8C23×C127semidirect
487. #117C23×C127semidirect
735. C2C127×#1794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#585×C1272
C2×#421×C1272
C2×#416×C1272
C2×#410×C1272
C2×#408×C1272
C127×#17942
C2×#1794127