Finite Group Databasebeta

← C2×C127×#1796 #44584295

Subgroups — C2×C127×#1796 #44584295

Order 32512.

3602 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×2−1+4×C127C211yesmaximal, characteristic
2C2×#421×C127C212yesmaximal, complemented
3C2×#419×C127C212yesmaximal, complemented
4C2×#413×C127C211yesmaximal, characteristic, complemented
5C2×#410×C127C211yesmaximal, characteristic, complemented
6C127×#1796C218yesmaximal, direct product factor
7C2×2−1+4×C127—24no—
8C2×2−1+4×C127—24no—
9C2×2−1+4×C127—22no—
10C2×2−1+4×C127—22no—
11C2×2−1+4×C127—24no—
12C2×2−1+4×C127—24no—
13C2×2−1+4×C127C414yescomplemented
14C2×2−1+4×C127C2214yes—
15C22×#41×C127—21no—
16C22×#41×C127—22no—
17C22×#41×C127C412yescomplemented
18C22×#41×C127C2211yescharacteristic
19C22×#41×C127C2211yescharacteristic
20C23×Q8×C127—21no—
21C23×Q8×C127C412yescomplemented
22C23×Q8×C127C2211yescharacteristic
23C22×M16×C127C2212yes—
24C2×#117×C127C2212yes—
25#421×C127—24no—
26#421×C127C2218yescomplemented
27C2×#104×C127—24no—
28#419×C127—24no—
29#419×C127C2218yescomplemented
30C2×#103×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—
382−1+4×C127—216no—
392−1+4×C127—216no—
402−1+4×C127—216no—
412−1+4×C127—216no—
422−1+4×C127—216no—
432−1+4×C127—216no—
442−1+4×C127—216no—
452−1+4×C127—216no—
46C2×#41×C127—216no—
47C2×#41×C127—216no—
48C2×#41×C127—28no—
49C2×#41×C127—28no—
50C2×#41×C127—24no—
51C2×#41×C127—24no—
52C2×#41×C127—28no—
53C2×#41×C127—24no—
54C2×#41×C127—24no—
55C2×#41×C127—24no—
56C2×#41×C127—24no—
57C2×#41×C127—28no—
58C2×#41×C127—24no—
59C2×#41×C127—21no—
60C2×#41×C127—22no—
61C2×#41×C127—22no—
62C2×#41×C127—22no—
63C2×#41×C127—22no—
64C2×#41×C127—22no—
65C2×#41×C127—22no—
66C2×#41×C127—21no—
67C2×#41×C127C2×C412yes—
68C2×#41×C127C2×C412yes—
69C2×#41×C127C2×C418yescomplemented
70C2×#41×C127D414yes—
71C2×#41×C127D414yes—
72C2×#41×C127D412yes—
73C2×#41×C127D412yes—
74C2×#41×C127C2312yes—
75C2×#41×C127C2312yes—
76C22×Q8×C127—28no—
77C22×Q8×C127—28no—
78C22×Q8×C127—24no—
79C22×Q8×C127—24no—
80C22×Q8×C127—24no—
81C22×Q8×C127—24no—
82C22×Q8×C127—24no—
83C22×Q8×C127—24no—
84C22×Q8×C127—22no—
85C22×Q8×C127—24no—
86C22×Q8×C127—21no—
87C22×Q8×C127—21no—
88C22×Q8×C127—22no—
89C22×Q8×C127—22no—
90C22×Q8×C127—21no—
91C22×Q8×C127C2×C411yescharacteristic
92C22×Q8×C127C2×C412yes—
93C22×Q8×C127C2×C412yes—
94C22×Q8×C127C2×C418yescomplemented
95C22×Q8×C127D414yes—
96C22×Q8×C127D414yes—
97C22×Q8×C127D411yescharacteristic
98C22×Q8×C127C2312yes—
99C22×D4×C127—22no—
100C22×D4×C127—21no—
101C22×D4×C127C2×C411yescharacteristic
102C22×D4×C127D412yes—
103C22×D4×C127D411yescharacteristic
104C23×C4×C127—22no—
105C23×C4×C127—21no—
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×C127C2314yes—
116C22×C8×C127—22no—
117#117×C127—22no—
118#117×C127—22no—
119#117×C127—22no—
120#117×C127C2314yes—
121C2×C4⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C42×C127—22no—
124#104×C127—216no—
125#103×C127—216no—
126#101×C127—24no—
127#100×C127—24no—
128#99×C127—28no—
129C24×C127—21no—
130C24×C127C22⋊C412yes—
131C24×C127C2×D411yescharacteristic
132#41×C127—264no—
133#41×C127—264no—
134#41×C127—232no—
135#41×C127—232no—
136#41×C127—216no—
137#41×C127—216no—
138#41×C127—216no—
139#41×C127—216no—
140#41×C127—24no—
141#41×C127—24no—
142#41×C127—24no—
143#41×C127—24no—
144#41×C127—24no—
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×C127C22⋊C418yes—
155#41×C127C2×D418yes—
156C2×Q8×C127—28no—
157C2×Q8×C127—28no—
158C2×Q8×C127—232no—
159C2×Q8×C127—232no—
160C2×Q8×C127—216no—
161C2×Q8×C127—216no—
162C2×Q8×C127—216no—
163C2×Q8×C127—216no—
164C2×Q8×C127—22no—
165C2×Q8×C127—21no—
166C2×Q8×C127—22no—
167C2×Q8×C127—21no—
168C2×Q8×C127—22no—
169C2×Q8×C127—21no—
170C2×Q8×C127—22no—
171C2×Q8×C127—28no—
172C2×Q8×C127—24no—
173C2×Q8×C127—24no—
174C2×Q8×C127—22no—
175C2×Q8×C127—24no—
176C2×Q8×C127—22no—
177C2×Q8×C127—24no—
178C2×Q8×C127—24no—
179C2×Q8×C127—24no—
180C2×Q8×C127—24no—
181C2×Q8×C127—22no—
182C2×Q8×C127—24no—
183C2×Q8×C127C22⋊C412yes—
184C2×Q8×C127C22⋊C412yes—
185C2×Q8×C127C22⋊C414yes—
186C2×Q8×C127C22⋊C414yes—
187C2×Q8×C127C22⋊C418yes—
188C2×Q8×C127C22⋊C412yes—
189C2×Q8×C127C22×C414yes—
190C2×Q8×C127C22×C412yes—
191C2×Q8×C127C2×D418yes—
192C2×Q8×C127C2×D412yes—
193C2×D4×C127—28no—
194C2×D4×C127—28no—
195C2×D4×C127—22no—
196C2×D4×C127—28no—
197C2×D4×C127—24no—
198C2×D4×C127—24no—
199C2×D4×C127—24no—
200C2×D4×C127—24no—
201C2×D4×C127—22no—
202C2×D4×C127—21no—
203C2×D4×C127—21no—
204C2×D4×C127—21no—
205C2×D4×C127—22no—
206C2×D4×C127—22no—
207C2×D4×C127C22⋊C414yes—
208C2×D4×C127C22⋊C412yes—
209C2×D4×C127C22⋊C412yes—
210C2×D4×C127C22⋊C412yes—
211C2×D4×C127C22×C412yes—
212C2×D4×C127C2×D414yes—
213C2×D4×C127C2×D412yes—
214C22×C4×C127—28no—
215C22×C4×C127—28no—
216C22×C4×C127—28no—
217C22×C4×C127—28no—
218C22×C4×C127—21no—
219C22×C4×C127—22no—
220C22×C4×C127—22no—
221C22×C4×C127—28no—
222C22×C4×C127—24no—
223C22×C4×C127—24no—
224C22×C4×C127—22no—
225C22×C4×C127—22no—
226C22×C4×C127—28no—
227C22×C4×C127—22no—
228C22×C4×C127—22no—
229C22×C4×C127—22no—
230C22×C4×C127—22no—
231C22×C4×C127—24no—
232C22×C4×C127—24no—
233C22×C4×C127—22no—
234C22×C4×C127—42no—
235C22×C4×C127C22⋊C412yes—
236C22×C4×C127C22⋊C414yes—
237C22×C4×C127C22×C414yes—
238C22×C4×C127C22×C411yescharacteristic
239C22×C4×C127C22×C411yescharacteristic
240C22×C4×C127C2×D411yescharacteristic
241C22×C4×C127C2×D412yes—
242C22×C4×C127C2×D412yes—
243C22×C4×C127C2×D412yes—
244C22×C4×C127C2×D412yes—
245C22×C4×C127C2×D411yescharacteristic
246C22×C4×C127C2×D411yescharacteristic
247C22×C4×C127C2411yescharacteristic
248M16×C127—24no—
249M16×C127—24no—
250M16×C127—42no—
251M16×C127—42no—
252C2×C8×C127—24no—
253C2×C8×C127—42no—
254C2×C8×C127—42no—
255C4⋊C4×C127—24no—
256C4⋊C4×C127—42no—
257C22⋊C4×C127—24no—
258C22⋊C4×C127—42no—
259C42×C127—24no—
260C42×C127—42no—
261C23×C127—22no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—22no—
265C23×C127—22no—
266C23×C127—42no—
267C23×C127—44no—
268C23×C127—44no—
269C23×C127C2×C22⋊C411yescharacteristic
270C23×C127C2×C22⋊C414yes—
271C23×C127C2×C22⋊C411yescharacteristic
272C23×C127#12012yes—
273C23×C127#12012yes—
274C23×C127C22×D411yescharacteristic
275Q8×C127—232no—
276Q8×C127—22no—
277Q8×C127—24no—
278Q8×C127—28no—
279Q8×C127—24no—
280Q8×C127—22no—
281Q8×C127—22no—
282Q8×C127—24no—
283Q8×C127—24no—
284Q8×C127—28no—
285Q8×C127—24no—
286Q8×C127C2×C22⋊C414yes—
287Q8×C127C2×C22⋊C418yes—
288D4×C127—232no—
289D4×C127—28no—
290D4×C127—28no—
291D4×C127—28no—
292D4×C127—28no—
293D4×C127—22no—
294D4×C127—24no—
295D4×C127—24no—
296D4×C127—22no—
297D4×C127—22no—
298D4×C127C2×C22⋊C414yes—
299C2×C4×C127—232no—
300C2×C4×C127—232no—
301C2×C4×C127—24no—
302C2×C4×C127—22no—
303C2×C4×C127—28no—
304C2×C4×C127—24no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—28no—
308C2×C4×C127—24no—
309C2×C4×C127—22no—
310C2×C4×C127—22no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—28no—
314C2×C4×C127—28no—
315C2×C4×C127—24no—
316C2×C4×C127—24no—
317C2×C4×C127—44no—
318C2×C4×C127—84no—
319C2×C4×C127C2×C22⋊C414yes—
320C2×C4×C127C2×C22⋊C411yescharacteristic
321C2×C4×C127C2×C22⋊C411yescharacteristic
322C2×C4×C127C2×C22⋊C412yes—
323C2×C4×C127C2×C22⋊C412yes—
324C2×C4×C127C2×C22⋊C411yescharacteristic
325C2×C4×C127C2×C22⋊C411yescharacteristic
326C2×C4×C127C2×C22⋊C411yescharacteristic
327C2×C4×C127C2×C22⋊C411yescharacteristic
328C2×C4×C127#12012yes—
329C2×C4×C127#12012yes—
330C2×C4×C127#12012yes—
331C2×C4×C127#12012yes—
332C2×C4×C127#12012yes—
333C2×C4×C127#12012yes—
334C2×C4×C127C23×C411yescharacteristic
335C2×C4×C127C22×D412yes—
336C2×C4×C127C22×D412yes—
337C2×C4×C127C22×D411yescharacteristic
338C8×C127—44no—
339C22×C127—24no—
340C22×C127—22no—
341C22×C127—24no—
342C22×C127—24no—
343C22×C127—41no—
344C22×C127—42no—
345C22×C127—41no—
346C22×C127—44no—
347C22×C127—44no—
348C22×C127—44no—
349C22×C127—44no—
350C22×C127—44no—
351C22×C127—44no—
352C22×C127#37911yescharacteristic
353C22×C127#37912yes—
354C22×C127#37911yescharacteristic
355C22×C127C22×C22⋊C411yescharacteristic
356C22×C127C2×#12012yes—
357C4×C127—28no—
358C4×C127—24no—
359C4×C127—24no—
360C4×C127—84no—
361C4×C127#37912yes—
362C4×C127#37911yescharacteristic
363C4×C127#37911yescharacteristic
364C4×C127C22×C22⋊C411yescharacteristic
365C4×C127C22×C22⋊C411yescharacteristic
366C4×C127C2×#12012yes—
367C2×#1796C12711yesmaximal, characteristic, direct product factor, Sylow
368C2×C127—22no—
369C2×C127—21no—
370C2×C127—21no—
371C2×C127—22no—
372C2×C127—44no—
373C2×C127—44no—
374C2×C127#179612yesdirect product factor
375C2×C127C2×#37911yescharacteristic
376C22×2−1+4C2×C12711yescharacteristic
377C2×#421C2×C12712yescomplemented
378C2×#419C2×C12712yescomplemented
379C2×#413C2×C12711yescharacteristic, complemented
380C2×#410C2×C12711yescharacteristic, complemented
381#1796C2×C12718yesdirect product factor
382C127C2×#179611yescharacteristic, direct product factor, Sylow
383C2×2−1+4—24no—
384C2×2−1+4—24no—
385C2×2−1+4—22no—
386C2×2−1+4—22no—
387C2×2−1+4—24no—
388C2×2−1+4—24no—
389C2×2−1+4C4×C12714yescomplemented
390C2×2−1+4C22×C12714yes—
391C22×#41—21no—
392C22×#41—22no—
393C22×#41C4×C12712yescomplemented
394C22×#41C22×C12711yescharacteristic
395C22×#41C22×C12711yescharacteristic
396C23×Q8—21no—
397C23×Q8C4×C12712yescomplemented
398C23×Q8C22×C12711yescharacteristic
399C22×M16C22×C12712yes—
400C2×#117C22×C12712yes—
401#421—24no—
402#421C22×C12718yescomplemented
403C2×#104—24no—
404#419—24no—
405#419C22×C12718yescomplemented
406C2×#103—24no—
407#413—22no—
408#413C22×C12714yescomplemented
409C2×#101—21no—
410C2×#100—21no—
411#410—22no—
412#410C22×C12714yescomplemented
413C2×#99—22no—
4142−1+4—216no—
4152−1+4—216no—
4162−1+4—216no—
4172−1+4—216no—
4182−1+4—216no—
4192−1+4—216no—
4202−1+4—216no—
4212−1+4—216no—
422C2×#41—216no—
423C2×#41—216no—
424C2×#41—28no—
425C2×#41—28no—
426C2×#41—24no—
427C2×#41—24no—
428C2×#41—28no—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—24no—
435C2×#41—21no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—21no—
443C2×#41C2×C4×C12712yes—
444C2×#41C2×C4×C12712yes—
445C2×#41C2×C4×C12718yescomplemented
446C2×#41D4×C12714yes—
447C2×#41D4×C12714yes—
448C2×#41D4×C12712yes—
449C2×#41D4×C12712yes—
450C2×#41C23×C12712yes—
451C2×#41C23×C12712yes—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—24no—
455C22×Q8—24no—
456C22×Q8—24no—
457C22×Q8—24no—
458C22×Q8—24no—
459C22×Q8—24no—
460C22×Q8—22no—
461C22×Q8—24no—
462C22×Q8—21no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—21no—
467C22×Q8C2×C4×C12711yescharacteristic
468C22×Q8C2×C4×C12712yes—
469C22×Q8C2×C4×C12712yes—
470C22×Q8C2×C4×C12718yescomplemented
471C22×Q8D4×C12714yes—
472C22×Q8D4×C12714yes—
473C22×Q8D4×C12711yescharacteristic
474C22×Q8C23×C12712yes—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4C2×C4×C12711yescharacteristic
478C22×D4D4×C12712yes—
479C22×D4D4×C12711yescharacteristic
480C23×C4—22no—
481C23×C4—21no—
482C23×C4—22no—
483C23×C4—21no—
484C23×C4C2×C4×C12712yes—
485C23×C4C23×C12711yescharacteristic
486C2×M16—22no—
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16C23×C12714yes—
492C22×C8—22no—
493#117—22no—
494#117—22no—
495#117—22no—
496#117C23×C12714yes—
497C2×C4⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C42—22no—
500#104—216no—
501#103—216no—
502#101—24no—
503#100—24no—
504#99—28no—
505C24—21no—
506C24C22⋊C4×C12712yes—
507C24C2×D4×C12711yescharacteristic
508#41—264no—
509#41—264no—
510#41—232no—
511#41—232no—
512#41—216no—
513#41—216no—
514#41—216no—
515#41—216no—
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#41C22⋊C4×C12718yes—
531#41C2×D4×C12718yes—
532C2×Q8—28no—
533C2×Q8—28no—
534C2×Q8—232no—
535C2×Q8—232no—
536C2×Q8—216no—
537C2×Q8—216no—
538C2×Q8—216no—
539C2×Q8—216no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—28no—
548C2×Q8—24no—
549C2×Q8—24no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—24no—
554C2×Q8—24no—
555C2×Q8—24no—
556C2×Q8—24no—
557C2×Q8—22no—
558C2×Q8—24no—
559C2×Q8C22⋊C4×C12712yes—
560C2×Q8C22⋊C4×C12712yes—
561C2×Q8C22⋊C4×C12714yes—
562C2×Q8C22⋊C4×C12714yes—
563C2×Q8C22⋊C4×C12718yes—
564C2×Q8C22⋊C4×C12712yes—
565C2×Q8C22×C4×C12714yes—
566C2×Q8C22×C4×C12712yes—
567C2×Q8C2×D4×C12718yes—
568C2×Q8C2×D4×C12712yes—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—22no—
572C2×D4—28no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4C22⋊C4×C12714yes—
584C2×D4C22⋊C4×C12712yes—
585C2×D4C22⋊C4×C12712yes—
586C2×D4C22⋊C4×C12712yes—
587C2×D4C22×C4×C12712yes—
588C2×D4C2×D4×C12714yes—
589C2×D4C2×D4×C12712yes—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—28no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—42no—
611C22×C4C22⋊C4×C12712yes—
612C22×C4C22⋊C4×C12714yes—
613C22×C4C22×C4×C12714yes—
614C22×C4C22×C4×C12711yescharacteristic
615C22×C4C22×C4×C12711yescharacteristic
616C22×C4C2×D4×C12711yescharacteristic
617C22×C4C2×D4×C12712yes—
618C22×C4C2×D4×C12712yes—
619C22×C4C2×D4×C12712yes—
620C22×C4C2×D4×C12712yes—
621C22×C4C2×D4×C12711yescharacteristic
622C22×C4C2×D4×C12711yescharacteristic
623C22×C4C24×C12711yescharacteristic
624M16—24no—
625M16—24no—
626M16—42no—
627M16—42no—
628C2×C8—24no—
629C2×C8—42no—
630C2×C8—42no—
631C4⋊C4—24no—
632C4⋊C4—42no—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C42—24no—
636C42—42no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—42no—
643C23—44no—
644C23—44no—
645C23C2×C22⋊C4×C12711yescharacteristic
646C23C2×C22⋊C4×C12714yes—
647C23C2×C22⋊C4×C12711yescharacteristic
648C23#120×C12712yes—
649C23#120×C12712yes—
650C23C22×D4×C12711yescharacteristic
651Q8—232no—
652Q8—22no—
653Q8—24no—
654Q8—28no—
655Q8—24no—
656Q8—22no—
657Q8—22no—
658Q8—24no—
659Q8—24no—
660Q8—28no—
661Q8—24no—
662Q8C2×C22⋊C4×C12714yes—
663Q8C2×C22⋊C4×C12718yes—
664D4—232no—
665D4—28no—
666D4—28no—
667D4—28no—
668D4—28no—
669D4—22no—
670D4—24no—
671D4—24no—
672D4—22no—
673D4—22no—
674D4C2×C22⋊C4×C12714yes—
675C2×C4—232no—
676C2×C4—232no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—44no—
694C2×C4—84no—
695C2×C4C2×C22⋊C4×C12714yes—
696C2×C4C2×C22⋊C4×C12711yescharacteristic
697C2×C4C2×C22⋊C4×C12711yescharacteristic
698C2×C4C2×C22⋊C4×C12711yescharacteristic
699C2×C4C2×C22⋊C4×C12711yescharacteristic
700C2×C4C2×C22⋊C4×C12712yes—
701C2×C4C2×C22⋊C4×C12712yes—
702C2×C4C2×C22⋊C4×C12711yescharacteristic
703C2×C4C2×C22⋊C4×C12711yescharacteristic
704C2×C4#120×C12712yes—
705C2×C4#120×C12712yes—
706C2×C4#120×C12712yes—
707C2×C4#120×C12712yes—
708C2×C4#120×C12712yes—
709C2×C4#120×C12712yes—
710C2×C4C23×C4×C12711yescharacteristic
711C2×C4C22×D4×C12712yes—
712C2×C4C22×D4×C12712yes—
713C2×C4C22×D4×C12711yescharacteristic
714C8—44no—
715C22—24no—
716C22—22no—
717C22—24no—
718C22—24no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22#379×C12711yescharacteristic
729C22#379×C12712yes—
730C22#379×C12711yescharacteristic
731C22C22×C22⋊C4×C12711yescharacteristic
732C22C2×#120×C12712yes—
733C4—28no—
734C4—24no—
735C4—24no—
736C4—84no—
737C4#379×C12712yes—
738C4#379×C12711yescharacteristic
739C4#379×C12711yescharacteristic
740C4C22×C22⋊C4×C12711yescharacteristic
741C4C22×C22⋊C4×C12711yescharacteristic
742C4C2×#120×C12712yes—
743C2—22no—
744C2—21no—
745C2—21no—
746C2—22no—
747C2—44no—
748C2—44no—
749C2C127×#179612yesdirect product factor
750C2C2×#379×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×2−1+4×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×#419×C127C2semidirect
4. C2×#413×C127C2semidirect
5. C2×#410×C127C2semidirect
6. C127×#1796C2direct (N × H)
13. C2×2−1+4×C127C4semidirect
17. C22×#41×C127C4semidirect
21. C23×Q8×C127C4semidirect
26. #421×C127C22semidirect
29. #419×C127C22semidirect
32. #413×C127C22semidirect
36. #410×C127C22semidirect
69. C2×#41×C127C2×C4semidirect
94. C22×Q8×C127C2×C4semidirect
367. C2×#1796C127direct (N × H)
374. C2×C127#1796direct (N × H)
377. C2×#421C2×C127semidirect
378. C2×#419C2×C127semidirect
379. C2×#413C2×C127semidirect
380. C2×#410C2×C127semidirect
381. #1796C2×C127direct (N × H)
382. C127C2×#1796direct (N × H)
389. C2×2−1+4C4×C127semidirect
393. C22×#41C4×C127semidirect
397. C23×Q8C4×C127semidirect
402. #421C22×C127semidirect
405. #419C22×C127semidirect
408. #413C22×C127semidirect
412. #410C22×C127semidirect
445. C2×#41C2×C4×C127semidirect
470. C22×Q8C2×C4×C127semidirect
749. C2C127×#1796direct (N × H)

Maximal subgroups

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

subgroupindex
C22×2−1+4×C1272
C2×#421×C1272
C2×#419×C1272
C2×#413×C1272
C2×#410×C1272
C127×#17962
C2×#1796127