Finite Group Databasebeta

← C2×C127×#1902 #44584666

Subgroups — C2×C127×#1902 #44584666

Order 32512.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C127C211yesmaximal, characteristic
2C2×#568×C127C211yesmaximal, characteristic
3C2×#421×C127C211yesmaximal, characteristic
4C2×#419×C127C211yesmaximal, characteristic, complemented
5C22×#101×C127C211yesmaximal, characteristic, complemented
6C127×#1902C218yesmaximal, direct product factor
7C2×#344×C127C211yesmaximal, characteristic, complemented
8C2×#338×C127C211yesmaximal, characteristic, complemented
9C22×#41×C127C2211yescharacteristic
10C23×Q8×C127C2211yescharacteristic
11C2×#137×C127—22no—
12C2×#137×C127—22no—
13C2×#137×C127—22no—
14C2×#137×C127—22no—
15C2×#137×C127C414yescomplemented
16C2×#137×C127C2214yes—
17C22×Q16×C127C412yescomplemented
18C22×SD16×C127C412yescomplemented
19#568×C127—22no—
20#568×C127—22no—
21#568×C127—22no—
22#568×C127C2214yes—
23C2×#131×C127—22no—
24C2×#131×C127—22no—
25C22×M16×C127—22no—
26C22×M16×C127C2211yescharacteristic
27C22×M16×C127C2211yescharacteristic
28C22×M16×C127C2211yescharacteristic
29C22×M16×C127C2211yescharacteristic
30C2×#117×C127C2211yescharacteristic
31#421×C127—22no—
32#421×C127C2214yes—
33C2×#104×C127—22no—
34#419×C127—22no—
35#419×C127C2214yescomplemented
36C2×#103×C127—22no—
37C2×#101×C127—22no—
38C2×#101×C127—22no—
39C2×#101×C127C2214yescomplemented
40#344×C127C2214yescomplemented
41#338×C127C2214yescomplemented
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—
50C2×#41×C127D412yes—
51C2×#41×C127D412yes—
52C2×#41×C127D412yes—
53C2×#41×C127C2312yes—
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×C127—21no—
62C22×Q8×C127—21no—
63C22×Q8×C127—21no—
64C22×Q8×C127—21no—
65C22×Q8×C127C2×C412yes—
66C22×Q8×C127C2×C412yes—
67C22×Q8×C127C2×C411yescharacteristic
68C22×Q8×C127C2312yes—
69C22×D4×C127—21no—
70C22×D4×C127C2×C411yescharacteristic
71C23×C4×C127—21no—
72C23×C4×C127—21no—
73C23×C4×C127C2311yescharacteristic
74#137×C127—28no—
75#137×C127—28no—
76#137×C127—28no—
77#137×C127—28no—
78C2×Q16×C127—24no—
79C2×Q16×C127—24no—
80C2×Q16×C127C2×C418yescomplemented
81C2×SD16×C127—24no—
82C2×SD16×C127—24no—
83C2×SD16×C127C2×C418yescomplemented
84#131×C127—28no—
85#131×C127—28no—
86#131×C127—28no—
87#131×C127—28no—
88C2×M16×C127—24no—
89C2×M16×C127—28no—
90C2×M16×C127—21no—
91C2×M16×C127—21no—
92C2×M16×C127—21no—
93C2×M16×C127—21no—
94C2×M16×C127—21no—
95C2×M16×C127—21no—
96C2×M16×C127—21no—
97C2×M16×C127—21no—
98C2×M16×C127—21no—
99C2×M16×C127—21no—
100C2×M16×C127—21no—
101C2×M16×C127—28no—
102C2×M16×C127—21no—
103C2×M16×C127—21no—
104C2×M16×C127—21no—
105C2×M16×C127—21no—
106C2×M16×C127—21no—
107C2×M16×C127C2×C412yes—
108C2×M16×C127D412yes—
109C2×M16×C127D412yes—
110C2×M16×C127D412yes—
111C2×M16×C127C2312yes—
112C2×M16×C127C2312yes—
113C2×M16×C127C2312yes—
114C2×M16×C127C2312yes—
115C22×C8×C127—24no—
116C22×C8×C127—21no—
117C22×C8×C127—21no—
118C22×C8×C127C2×C412yes—
119C22×C8×C127D412yes—
120#117×C127—21no—
121#117×C127—21no—
122#117×C127—21no—
123#117×C127C2312yes—
124C2×C4⋊C4×C127—21no—
125C2×C22⋊C4×C127—21no—
126C2×C42×C127—21no—
127#104×C127—28no—
128#103×C127—28no—
129#101×C127—28no—
130C24×C127—21no—
131C24×C127#4111yescharacteristic
132#41×C127—22no—
133#41×C127—22no—
134#41×C127—22no—
135#41×C127—22no—
136#41×C127—22no—
137#41×C127—22no—
138#41×C127—22no—
139#41×C127—22no—
140#41×C127—22no—
141#41×C127—22no—
142#41×C127—22no—
143#41×C127—22no—
144#41×C127C22⋊C414yes—
145#41×C127C22⋊C414yes—
146#41×C127C2×D414yes—
147#41×C127C2×D414yes—
148C2×Q8×C127—21no—
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—22no—
156C2×Q8×C127—22no—
157C2×Q8×C127—22no—
158C2×Q8×C127—22no—
159C2×Q8×C127—22no—
160C2×Q8×C127—22no—
161C2×Q8×C127—22no—
162C2×Q8×C127—22no—
163C2×Q8×C127—22no—
164C2×Q8×C127—22no—
165C2×Q8×C127—22no—
166C2×Q8×C127—41no—
167C2×Q8×C127—41no—
168C2×Q8×C127—41no—
169C2×Q8×C127—41no—
170C2×Q8×C127—41no—
171C2×Q8×C127—41no—
172C2×Q8×C127—41no—
173C2×Q8×C127—41no—
174C2×Q8×C127—41no—
175C2×Q8×C127—41no—
176C2×Q8×C127—41no—
177C2×Q8×C127—41no—
178C2×Q8×C127C22⋊C412yes—
179C2×Q8×C127C22⋊C412yes—
180C2×Q8×C127C22×C414yes—
181C2×Q8×C127C22×C412yes—
182C2×D4×C127—22no—
183C2×D4×C127—22no—
184C2×D4×C127—22no—
185C2×D4×C127—22no—
186C2×D4×C127—22no—
187C2×D4×C127—22no—
188C2×D4×C127—21no—
189C2×D4×C127—21no—
190C2×D4×C127—21no—
191C2×D4×C127C22⋊C412yes—
192C2×D4×C127C22⋊C412yes—
193C2×D4×C127C22×C412yes—
194C22×C4×C127—21no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—22no—
198C22×C4×C127—22no—
199C22×C4×C127—22no—
200C22×C4×C127—22no—
201C22×C4×C127—22no—
202C22×C4×C127—22no—
203C22×C4×C127—22no—
204C22×C4×C127—41no—
205C22×C4×C127—41no—
206C22×C4×C127—41no—
207C22×C4×C127—41no—
208C22×C4×C127—41no—
209C22×C4×C127C22×C411yescharacteristic
210C22×C4×C127C22×C411yescharacteristic
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×C127C2×D411yescharacteristic
219C22×C4×C127#4111yescharacteristic
220C22×C4×C127#4111yescharacteristic
221C22×C4×C127#4111yescharacteristic
222C22×C4×C127C2411yescharacteristic
223Q16×C127—216no—
224SD16×C127—216no—
225M16×C127—216no—
226M16×C127—22no—
227M16×C127—22no—
228M16×C127—22no—
229M16×C127—22no—
230M16×C127—22no—
231M16×C127—22no—
232M16×C127—22no—
233M16×C127—22no—
234M16×C127—22no—
235M16×C127—22no—
236M16×C127—22no—
237M16×C127—22no—
238M16×C127—22no—
239M16×C127—41no—
240M16×C127—41no—
241M16×C127C2×D414yes—
242C2×C8×C127—216no—
243C2×C8×C127—22no—
244C2×C8×C127—22no—
245C2×C8×C127—22no—
246C2×C8×C127—22no—
247C2×C8×C127—22no—
248C2×C8×C127—22no—
249C2×C8×C127—22no—
250C2×C8×C127—22no—
251C2×C8×C127—41no—
252C2×C8×C127—41no—
253C2×C8×C127C22×C414yes—
254C2×C8×C127C2×D414yes—
255C4⋊C4×C127—22no—
256C4⋊C4×C127—41no—
257C22⋊C4×C127—22no—
258C22⋊C4×C127—41no—
259C42×C127—22no—
260C42×C127—41no—
261C23×C127—22no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—42no—
265C23×C127—82no—
266C23×C127C4×D411yescharacteristic
267C23×C127C4×D411yescharacteristic
268C23×C127#12111yescharacteristic
269C23×C127#12111yescharacteristic
270C23×C127#12311yescharacteristic
271C23×C127#12311yescharacteristic
272C23×C127C2×#4111yescharacteristic
273Q8×C127—22no—
274Q8×C127—22no—
275Q8×C127—22no—
276Q8×C127—24no—
277Q8×C127—24no—
278Q8×C127—42no—
279Q8×C127—42no—
280Q8×C127—42no—
281Q8×C127—42no—
282Q8×C127—42no—
283Q8×C127—42no—
284Q8×C127C2×C22⋊C414yes—
285D4×C127—24no—
286D4×C127—24no—
287D4×C127—24no—
288D4×C127—24no—
289D4×C127—22no—
290D4×C127—22no—
291D4×C127—22no—
292D4×C127C2×C22⋊C414yes—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—24no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—42no—
302C2×C4×C127—42no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—42no—
307C2×C4×C127—42no—
308C2×C4×C127—82no—
309C2×C4×C127C2×C22⋊C411yescharacteristic
310C2×C4×C127C2×C22⋊C411yescharacteristic
311C2×C4×C127C2×C22⋊C411yescharacteristic
312C2×C4×C127C2×C22⋊C411yescharacteristic
313C2×C4×C127C4×D411yescharacteristic
314C2×C4×C127C4×D411yescharacteristic
315C2×C4×C127C4×D411yescharacteristic
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#12111yescharacteristic
324C2×C4×C127#12111yescharacteristic
325C2×C4×C127#12111yescharacteristic
326C2×C4×C127#12111yescharacteristic
327C2×C4×C127#12111yescharacteristic
328C2×C4×C127#12111yescharacteristic
329C2×C4×C127#12311yescharacteristic
330C2×C4×C127#12311yescharacteristic
331C2×C4×C127C23×C411yescharacteristic
332C2×C4×C127C22×D411yescharacteristic
333C2×C4×C127C22×D411yescharacteristic
334C2×C4×C127C22×D411yescharacteristic
335C2×C4×C127C22×D411yescharacteristic
336C2×C4×C127C2×#4111yescharacteristic
337C8×C127—24no—
338C8×C127—24no—
339C8×C127—24no—
340C8×C127—42no—
341C22×C127—22no—
342C22×C127—22no—
343C22×C127—22no—
344C22×C127—24no—
345C22×C127—41no—
346C22×C127—41no—
347C22×C127—41no—
348C22×C127—41no—
349C22×C127—44no—
350C22×C127—82no—
351C22×C127—82no—
352C22×C127#38611yescharacteristic
353C22×C127#38611yescharacteristic
354C22×C127#38611yescharacteristic
355C22×C127#38611yescharacteristic
356C22×C127C2×C4×D411yescharacteristic
357C22×C127C2×#12111yescharacteristic
358C22×C127C2×#12311yescharacteristic
359C4×C127—24no—
360C4×C127—44no—
361C4×C127—82no—
362C4×C127#38611yescharacteristic
363C4×C127#38611yescharacteristic
364C4×C127#38611yescharacteristic
365C4×C127#38611yescharacteristic
366C4×C127C22×C22⋊C411yescharacteristic
367C4×C127C2×C4×D411yescharacteristic
368C4×C127C2×#12011yescharacteristic
369C4×C127C2×#12111yescharacteristic
370C2×#1902C12711yesmaximal, characteristic, direct product factor, Sylow
371C2×C127—21no—
372C2×C127—21no—
373C2×C127—21no—
374C2×C127—21no—
375C2×C127—21no—
376C2×C127—21no—
377C2×C127—44no—
378C2×C127#190212yesdirect product factor
379C2×C127C2×#38611yescharacteristic
380C22×#137C2×C12711yescharacteristic
381C2×#568C2×C12711yescharacteristic
382C2×#421C2×C12711yescharacteristic
383C2×#419C2×C12711yescharacteristic, complemented
384C22×#101C2×C12711yescharacteristic, complemented
385#1902C2×C12718yesdirect product factor
386C2×#344C2×C12711yescharacteristic, complemented
387C2×#338C2×C12711yescharacteristic, complemented
388C127C2×#190211yescharacteristic, direct product factor, Sylow
389C22×#41C22×C12711yescharacteristic
390C23×Q8C22×C12711yescharacteristic
391C2×#137—22no—
392C2×#137—22no—
393C2×#137—22no—
394C2×#137—22no—
395C2×#137C4×C12714yescomplemented
396C2×#137C22×C12714yes—
397C22×Q16C4×C12712yescomplemented
398C22×SD16C4×C12712yescomplemented
399#568—22no—
400#568—22no—
401#568—22no—
402#568C22×C12714yes—
403C2×#131—22no—
404C2×#131—22no—
405C22×M16—22no—
406C22×M16C22×C12711yescharacteristic
407C22×M16C22×C12711yescharacteristic
408C22×M16C22×C12711yescharacteristic
409C22×M16C22×C12711yescharacteristic
410C2×#117C22×C12711yescharacteristic
411#421—22no—
412#421C22×C12714yes—
413C2×#104—22no—
414#419—22no—
415#419C22×C12714yescomplemented
416C2×#103—22no—
417C2×#101—22no—
418C2×#101—22no—
419C2×#101C22×C12714yescomplemented
420#344C22×C12714yescomplemented
421#338C22×C12714yescomplemented
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41C2×C4×C12712yes—
429C2×#41D4×C12712yes—
430C2×#41D4×C12712yes—
431C2×#41D4×C12712yes—
432C2×#41D4×C12712yes—
433C2×#41C23×C12712yes—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8C2×C4×C12712yes—
446C22×Q8C2×C4×C12712yes—
447C22×Q8C2×C4×C12711yescharacteristic
448C22×Q8C23×C12712yes—
449C22×D4—21no—
450C22×D4C2×C4×C12711yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4C23×C12711yescharacteristic
454#137—28no—
455#137—28no—
456#137—28no—
457#137—28no—
458C2×Q16—24no—
459C2×Q16—24no—
460C2×Q16C2×C4×C12718yescomplemented
461C2×SD16—24no—
462C2×SD16—24no—
463C2×SD16C2×C4×C12718yescomplemented
464#131—28no—
465#131—28no—
466#131—28no—
467#131—28no—
468C2×M16—24no—
469C2×M16—28no—
470C2×M16—21no—
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×M16—21no—
480C2×M16—21no—
481C2×M16—28no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16C2×C4×C12712yes—
488C2×M16D4×C12712yes—
489C2×M16D4×C12712yes—
490C2×M16D4×C12712yes—
491C2×M16C23×C12712yes—
492C2×M16C23×C12712yes—
493C2×M16C23×C12712yes—
494C2×M16C23×C12712yes—
495C22×C8—24no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8C2×C4×C12712yes—
499C22×C8D4×C12712yes—
500#117—21no—
501#117—21no—
502#117—21no—
503#117C23×C12712yes—
504C2×C4⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C42—21no—
507#104—28no—
508#103—28no—
509#101—28no—
510C24—21no—
511C24#41×C12711yescharacteristic
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41C22⋊C4×C12714yes—
525#41C22⋊C4×C12714yes—
526#41C2×D4×C12714yes—
527#41C2×D4×C12714yes—
528C2×Q8—21no—
529C2×Q8—21no—
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—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—41no—
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×Q8C22⋊C4×C12712yes—
559C2×Q8C22⋊C4×C12712yes—
560C2×Q8C22×C4×C12714yes—
561C2×Q8C22×C4×C12712yes—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4C22⋊C4×C12712yes—
572C2×D4C22⋊C4×C12712yes—
573C2×D4C22×C4×C12712yes—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
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×C4#41×C12711yescharacteristic
600C22×C4#41×C12711yescharacteristic
601C22×C4#41×C12711yescharacteristic
602C22×C4C24×C12711yescharacteristic
603Q16—216no—
604SD16—216no—
605M16—216no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—22no—
618M16—22no—
619M16—41no—
620M16—41no—
621M16C2×D4×C12714yes—
622C2×C8—216no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8C22×C4×C12714yes—
634C2×C8C2×D4×C12714yes—
635C4⋊C4—22no—
636C4⋊C4—41no—
637C22⋊C4—22no—
638C22⋊C4—41no—
639C42—22no—
640C42—41no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—82no—
646C23C4×D4×C12711yescharacteristic
647C23C4×D4×C12711yescharacteristic
648C23#121×C12711yescharacteristic
649C23#121×C12711yescharacteristic
650C23#123×C12711yescharacteristic
651C23#123×C12711yescharacteristic
652C23C2×#41×C12711yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—24no—
657Q8—24no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8C2×C22⋊C4×C12714yes—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4C2×C22⋊C4×C12714yes—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—82no—
689C2×C4C2×C22⋊C4×C12711yescharacteristic
690C2×C4C2×C22⋊C4×C12711yescharacteristic
691C2×C4C2×C22⋊C4×C12711yescharacteristic
692C2×C4C2×C22⋊C4×C12711yescharacteristic
693C2×C4C4×D4×C12711yescharacteristic
694C2×C4C4×D4×C12711yescharacteristic
695C2×C4C4×D4×C12711yescharacteristic
696C2×C4C4×D4×C12711yescharacteristic
697C2×C4C4×D4×C12711yescharacteristic
698C2×C4C4×D4×C12711yescharacteristic
699C2×C4#120×C12711yescharacteristic
700C2×C4#120×C12711yescharacteristic
701C2×C4#120×C12711yescharacteristic
702C2×C4#120×C12711yescharacteristic
703C2×C4#121×C12711yescharacteristic
704C2×C4#121×C12711yescharacteristic
705C2×C4#121×C12711yescharacteristic
706C2×C4#121×C12711yescharacteristic
707C2×C4#121×C12711yescharacteristic
708C2×C4#121×C12711yescharacteristic
709C2×C4#123×C12711yescharacteristic
710C2×C4#123×C12711yescharacteristic
711C2×C4C23×C4×C12711yescharacteristic
712C2×C4C22×D4×C12711yescharacteristic
713C2×C4C22×D4×C12711yescharacteristic
714C2×C4C22×D4×C12711yescharacteristic
715C2×C4C22×D4×C12711yescharacteristic
716C2×C4C2×#41×C12711yescharacteristic
717C8—24no—
718C8—24no—
719C8—24no—
720C8—42no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—44no—
730C22—82no—
731C22—82no—
732C22#386×C12711yescharacteristic
733C22#386×C12711yescharacteristic
734C22#386×C12711yescharacteristic
735C22#386×C12711yescharacteristic
736C22C2×C4×D4×C12711yescharacteristic
737C22C2×#121×C12711yescharacteristic
738C22C2×#123×C12711yescharacteristic
739C4—24no—
740C4—44no—
741C4—82no—
742C4#386×C12711yescharacteristic
743C4#386×C12711yescharacteristic
744C4#386×C12711yescharacteristic
745C4#386×C12711yescharacteristic
746C4C22×C22⋊C4×C12711yescharacteristic
747C4C2×C4×D4×C12711yescharacteristic
748C4C2×#120×C12711yescharacteristic
749C4C2×#121×C12711yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—44no—
757C2C127×#190212yesdirect product factor
758C2C2×#386×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×#41×C127C22
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
4. C2×#419×C127C2semidirect
5. C22×#101×C127C2semidirect
6. C127×#1902C2direct (N × H)
7. C2×#344×C127C2semidirect
8. C2×#338×C127C2semidirect
15. C2×#137×C127C4semidirect
17. C22×Q16×C127C4semidirect
18. C22×SD16×C127C4semidirect
35. #419×C127C22semidirect
39. C2×#101×C127C22semidirect
40. #344×C127C22semidirect
41. #338×C127C22semidirect
80. C2×Q16×C127C2×C4semidirect
83. C2×SD16×C127C2×C4semidirect
370. C2×#1902C127direct (N × H)
378. C2×C127#1902direct (N × H)
383. C2×#419C2×C127semidirect
384. C22×#101C2×C127semidirect
385. #1902C2×C127direct (N × H)
386. C2×#344C2×C127semidirect
387. C2×#338C2×C127semidirect
388. C127C2×#1902direct (N × H)
395. C2×#137C4×C127semidirect
397. C22×Q16C4×C127semidirect
398. C22×SD16C4×C127semidirect
415. #419C22×C127semidirect
419. C2×#101C22×C127semidirect
420. #344C22×C127semidirect
421. #338C22×C127semidirect
460. C2×Q16C2×C4×C127semidirect
463. C2×SD16C2×C4×C127semidirect
757. C2C127×#1902direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#137×C1272
C2×#568×C1272
C2×#421×C1272
C2×#419×C1272
C22×#101×C1272
C127×#19022
C2×#344×C1272
C2×#338×C1272
C2×#1902127