Finite Group Databasebeta

← C127×#18519 #44582192

Subgroups — C127×#18519 #44582192

Order 32512.

914 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C127C211yesmaximal, characteristic
2C127×#3170C211yesmaximal, characteristic, complemented
3C127×#3104C211yesmaximal, characteristic, complemented
4C127×#3076C211yesmaximal, characteristic
5C127×#1649C211yesmaximal, characteristic, complemented
6C127×#1648C211yesmaximal, characteristic, complemented
7C127×#1645C211yesmaximal, characteristic, complemented
8C127×#1644C211yesmaximal, characteristic, complemented
9C127×#1637C211yesmaximal, characteristic, complemented
10C127×#1636C211yesmaximal, characteristic, complemented
11C127×#1633C211yesmaximal, characteristic, complemented
12C127×#1632C211yesmaximal, characteristic, complemented
13C127×#1542C211yesmaximal, characteristic, complemented
14C127×#1476C211yesmaximal, characteristic
15C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
16Q82×C127C2211yescharacteristic
17#557×C127—21no—
18#557×C127C2211yescharacteristic
19#554×C127—22no—
20#554×C127—21no—
21#554×C127—21no—
22#554×C127C2211yescharacteristic
23D4×Q8×C127—21no—
24D4×Q8×C127C2211yescharacteristic
25#533×C127—22no—
26#533×C127—21no—
27#533×C127—21no—
28#533×C127C2211yescharacteristic
29#533×C127C2211yescharacteristic
30C4×#41×C127—21no—
31C4×#41×C127C2211yescharacteristic
32C2×C4×Q8×C127—21no—
33C2×C4×Q8×C127C2211yescharacteristic
34#500×C127C2211yescharacteristic
35#494×C127C2211yescharacteristic
36#487×C127C2211yescharacteristic
37#487×C127C2211yescharacteristic
38#484×C127—21no—
39#479×C127—21no—
40#478×C127—21no—
41#477×C127C2211yescharacteristic
42#477×C127C2211yescharacteristic
43#477×C127C2211yescharacteristic
44#476×C127C2211yescharacteristic
45#475×C127C2211yescharacteristic
46#474×C127C2211yescharacteristic
47#467×C127—22no—
48#462×C127C2211yescharacteristic
49#462×C127C2211yescharacteristic
50#451×C127—21no—
51C4×Q16×C127—21no—
52C4×Q16×C127—21no—
53C4×Q16×C127—22no—
54#431×C127C2211yescharacteristic
55#427×C127—21no—
56C2×C4⋊C8×C127C2211yescharacteristic
57#416×C127—21no—
58C2×C4×C8×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic
60#333×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62#332×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65Q8⋊C8×C127C2211yescharacteristic
66Q8⋊C8×C127C2211yescharacteristic
67Q8⋊C8×C127C2211yescharacteristic
68Q8⋊C8×C127C2211yescharacteristic
69D4⋊C8×C127C2211yescharacteristic
70D4⋊C8×C127C2211yescharacteristic
71C2×#41×C127D411yescharacteristic
72C22×Q8×C127—21no—
73C22×Q8×C127D411yescharacteristic
74C2×Q16×C127—21no—
75C2×Q16×C127—21no—
76C2×Q16×C127—22no—
77C22×C8×C127—21no—
78C22×C8×C127—21no—
79C4⋊Q8×C127—22no—
80C4⋊Q8×C127—21no—
81C4⋊Q8×C127—22no—
82C4⋊Q8×C127—21no—
83C4⋊Q8×C127—21no—
84C4⋊Q8×C127—21no—
85C4⋊Q8×C127C2311yescharacteristic
86C4⋊Q8×C127C2311yescharacteristic
87C4⋊Q8×C127C2311yescharacteristic
88C4⋊Q8×C127C2311yescharacteristic
89#125×C127—22no—
90#125×C127—22no—
91#125×C127—22no—
92#125×C127—21no—
93#125×C127—21no—
94#125×C127—21no—
95#125×C127—21no—
96C22⋊Q8×C127—22no—
97C22⋊Q8×C127—22no—
98C22⋊Q8×C127—22no—
99C22⋊Q8×C127—22no—
100C22⋊Q8×C127—22no—
101C22⋊Q8×C127—21no—
102C22⋊Q8×C127—22no—
103C22⋊Q8×C127—21no—
104C22⋊Q8×C127—21no—
105C22⋊Q8×C127—22no—
106C22⋊Q8×C127—21no—
107C22⋊Q8×C127—21no—
108C22⋊Q8×C127D412yes—
109C4×Q8×C127—22no—
110C4×Q8×C127—22no—
111C4×Q8×C127—22no—
112C4×Q8×C127—21no—
113C4×Q8×C127—21no—
114C4×Q8×C127—21no—
115C4×Q8×C127—21no—
116C4×Q8×C127—21no—
117C4×Q8×C127—21no—
118C4×Q8×C127—21no—
119C4×Q8×C127—21no—
120C4×Q8×C127—21no—
121C4×Q8×C127D411yescharacteristic
122C4×Q8×C127D411yescharacteristic
123C4×Q8×C127D411yescharacteristic
124C4×Q8×C127D412yes—
125C4×Q8×C127C2311yescharacteristic
126C4×Q8×C127C2311yescharacteristic
127C4×Q8×C127C2311yescharacteristic
128C4×D4×C127—22no—
129C4×D4×C127—22no—
130C4×D4×C127—21no—
131C4×D4×C127—21no—
132C4×D4×C127—21no—
133C4×D4×C127—21no—
134C4×D4×C127D411yescharacteristic
135C4×D4×C127C2311yescharacteristic
136#117×C127—22no—
137#117×C127—21no—
138#117×C127—21no—
139#117×C127—21no—
140#117×C127D411yescharacteristic
141C2×C4⋊C4×C127—22no—
142C2×C4⋊C4×C127—21no—
143C2×C4⋊C4×C127—21no—
144C2×C4⋊C4×C127D411yescharacteristic
145C2×C42×C127—22no—
146C2×C42×C127—21no—
147C2×C42×C127—21no—
148C2×C42×C127C2311yescharacteristic
149#107×C127—22no—
150#107×C127—21no—
151#107×C127—21no—
152#107×C127—21no—
153#107×C127—21no—
154#106×C127—21no—
155#106×C127—21no—
156C4⋊C8×C127—21no—
157C4⋊C8×C127C2311yescharacteristic
158C4⋊C8×C127C2311yescharacteristic
159C4⋊C8×C127C2311yescharacteristic
160C4⋊C8×C127C2311yescharacteristic
161#103×C127—21no—
162#103×C127—21no—
163#103×C127—21no—
164#103×C127—21no—
165#103×C127—22no—
166#103×C127—21no—
167#103×C127—21no—
168#103×C127—22no—
169#102×C127—21no—
170#102×C127—21no—
171C22⋊C8×C127—21no—
172C4×C8×C127—21no—
173C4×C8×C127—21no—
174C4×C8×C127C2311yescharacteristic
175C4×C8×C127C2311yescharacteristic
176#41×C127—22no—
177#41×C127Q1614yescomplemented
178C2×Q8×C127—22no—
179C2×Q8×C127—22no—
180C2×Q8×C127—21no—
181C2×Q8×C127—21no—
182C2×Q8×C127—22no—
183C2×Q8×C127—21no—
184C2×Q8×C127—21no—
185C2×Q8×C127—41no—
186C2×Q8×C127—42no—
187C2×Q8×C127—42no—
188C2×Q8×C127C2×D411yescharacteristic
189C2×Q8×C127C2×D411yescharacteristic
190C2×Q8×C127C2×D411yescharacteristic
191C2×Q8×C127C2×D412yes—
192C2×D4×C127—21no—
193C2×D4×C127C2×D411yescharacteristic
194C22×C4×C127—21no—
195C22×C4×C127—22no—
196C22×C4×C127—21no—
197C22×C4×C127—22no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127C2×D411yescharacteristic
202C22×C4×C127C2×D411yescharacteristic
203C22×C4×C127C2×D411yescharacteristic
204Q16×C127—44no—
205Q16×C127—42no—
206Q16×C127—42no—
207C2×C8×C127—21no—
208C2×C8×C127—21no—
209C2×C8×C127—21no—
210C2×C8×C127—21no—
211C2×C8×C127—21no—
212C2×C8×C127—21no—
213C2×C8×C127—42no—
214C2×C8×C127—42no—
215C4⋊C4×C127—22no—
216C4⋊C4×C127—22no—
217C4⋊C4×C127—22no—
218C4⋊C4×C127—22no—
219C4⋊C4×C127—22no—
220C4⋊C4×C127—22no—
221C4⋊C4×C127—22no—
222C4⋊C4×C127—22no—
223C4⋊C4×C127—21no—
224C4⋊C4×C127—22no—
225C4⋊C4×C127—21no—
226C4⋊C4×C127—21no—
227C4⋊C4×C127—21no—
228C4⋊C4×C127—22no—
229C4⋊C4×C127—21no—
230C4⋊C4×C127—21no—
231C4⋊C4×C127—21no—
232C4⋊C4×C127—21no—
233C4⋊C4×C127—21no—
234C4⋊C4×C127—21no—
235C4⋊C4×C127—21no—
236C4⋊C4×C127—21no—
237C4⋊C4×C127—21no—
238C4⋊C4×C127—21no—
239C4⋊C4×C127—41no—
240C4⋊C4×C127—41no—
241C4⋊C4×C127C2×D411yescharacteristic
242C4⋊C4×C127C2×D411yescharacteristic
243C4⋊C4×C127C2×D412yes—
244C4⋊C4×C127C2×D411yescharacteristic
245C4⋊C4×C127C2×D411yescharacteristic
246C22⋊C4×C127—22no—
247C22⋊C4×C127—22no—
248C22⋊C4×C127—22no—
249C22⋊C4×C127—21no—
250C22⋊C4×C127—21no—
251C22⋊C4×C127—21no—
252C22⋊C4×C127—41no—
253C42×C127—22no—
254C42×C127—22no—
255C42×C127—21no—
256C42×C127—21no—
257C42×C127—22no—
258C42×C127—21no—
259C42×C127—21no—
260C42×C127—21no—
261C42×C127—21no—
262C42×C127—21no—
263C42×C127—41no—
264C42×C127C2×D411yescharacteristic
265C42×C127C2×D411yescharacteristic
266C42×C127C2×D411yescharacteristic
267C42×C127C2411yescharacteristic
268C23×C127—21no—
269C23×C127#12011yescharacteristic
270Q8×C127—21no—
271Q8×C127—21no—
272Q8×C127—21no—
273Q8×C127—21no—
274Q8×C127—42no—
275Q8×C127—42no—
276Q8×C127—44no—
277Q8×C127—42no—
278Q8×C127—41no—
279Q8×C127—41no—
280Q8×C127—41no—
281Q8×C127—41no—
282Q8×C127—82no—
283Q8×C127C2×Q1612yes—
284Q8×C127#13512yes—
285D4×C127—24no—
286D4×C127—21no—
287D4×C127C2×Q1612yes—
288C2×C4×C127—21no—
289C2×C4×C127—21no—
290C2×C4×C127—21no—
291C2×C4×C127—21no—
292C2×C4×C127—24no—
293C2×C4×C127—21no—
294C2×C4×C127—21no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—21no—
298C2×C4×C127—21no—
299C2×C4×C127—21no—
300C2×C4×C127—41no—
301C2×C4×C127—42no—
302C2×C4×C127—44no—
303C2×C4×C127—41no—
304C2×C4×C127—41no—
305C2×C4×C127—41no—
306C2×C4×C127—41no—
307C2×C4×C127—81no—
308C2×C4×C127—81no—
309C2×C4×C127—82no—
310C2×C4×C127#12011yescharacteristic
311C2×C4×C127#12011yescharacteristic
312C2×C4×C127#12011yescharacteristic
313C2×C4×C127C2×Q1612yes—
314C2×C4×C127#13712yes—
315C2×C4×C127C22×D411yescharacteristic
316C2×C4×C127C22×D411yescharacteristic
317C2×C4×C127C22×D411yescharacteristic
318C8×C127—22no—
319C8×C127—41no—
320C8×C127—41no—
321C8×C127—41no—
322C8×C127—41no—
323C8×C127—41no—
324C22×C127—21no—
325C22×C127—21no—
326C22×C127—22no—
327C22×C127—41no—
328C22×C127—41no—
329C22×C127#45112yes—
330C22×C127C2×#12011yescharacteristic
331C4×C127—22no—
332C4×C127—21no—
333C4×C127—22no—
334C4×C127—21no—
335C4×C127—21no—
336C4×C127—41no—
337C4×C127—42no—
338C4×C127—41no—
339C4×C127—41no—
340C4×C127—42no—
341C4×C127—41no—
342C4×C127—41no—
343C4×C127—81no—
344C4×C127—81no—
345C4×C127#45112yes—
346C4×C127C22×Q1611yescharacteristic
347C4×C127C2×#13511yescharacteristic
348C4×C127C2×#13711yescharacteristic
349C4×C127#57511yescharacteristic
350#18519C12711yesmaximal, characteristic, direct product factor, Sylow
351C2×C127—22no—
352C2×C127—42no—
353C2×C127C2×#45111yescharacteristic
354C2×C127#300211yescharacteristic
355C2×C127#301811yescharacteristic
356Q8×#41C2×C12711yescharacteristic
357#3170C2×C12711yescharacteristic, complemented
358#3104C2×C12711yescharacteristic, complemented
359#3076C2×C12711yescharacteristic
360#1649C2×C12711yescharacteristic, complemented
361#1648C2×C12711yescharacteristic, complemented
362#1645C2×C12711yescharacteristic, complemented
363#1644C2×C12711yescharacteristic, complemented
364#1637C2×C12711yescharacteristic, complemented
365#1636C2×C12711yescharacteristic, complemented
366#1633C2×C12711yescharacteristic, complemented
367#1632C2×C12711yescharacteristic, complemented
368#1542C2×C12711yescharacteristic, complemented
369#1476C2×C12711yescharacteristic
370C2×Q8⋊C8C2×C12711yescharacteristic, complemented
371C127#1851911yescharacteristic, direct product factor, Sylow
372Q82C22×C12711yescharacteristic
373#557—21no—
374#557C22×C12711yescharacteristic
375#554—22no—
376#554—21no—
377#554—21no—
378#554C22×C12711yescharacteristic
379D4×Q8—21no—
380D4×Q8C22×C12711yescharacteristic
381#533—22no—
382#533—21no—
383#533—21no—
384#533C22×C12711yescharacteristic
385#533C22×C12711yescharacteristic
386C4×#41—21no—
387C4×#41C22×C12711yescharacteristic
388C2×C4×Q8—21no—
389C2×C4×Q8C22×C12711yescharacteristic
390#500C22×C12711yescharacteristic
391#494C22×C12711yescharacteristic
392#487C22×C12711yescharacteristic
393#487C22×C12711yescharacteristic
394#484—21no—
395#479—21no—
396#478—21no—
397#477C22×C12711yescharacteristic
398#477C22×C12711yescharacteristic
399#477C22×C12711yescharacteristic
400#476C22×C12711yescharacteristic
401#475C22×C12711yescharacteristic
402#474C22×C12711yescharacteristic
403#467—22no—
404#462C22×C12711yescharacteristic
405#462C22×C12711yescharacteristic
406#451—21no—
407C4×Q16—21no—
408C4×Q16—21no—
409C4×Q16—22no—
410#431C22×C12711yescharacteristic
411#427—21no—
412C2×C4⋊C8C22×C12711yescharacteristic
413#416—21no—
414C2×C4×C8C22×C12711yescharacteristic
415#333C22×C12711yescharacteristic
416#333C22×C12711yescharacteristic
417#332C22×C12711yescharacteristic
418#332C22×C12711yescharacteristic
419Q8⋊C8C22×C12711yescharacteristic
420Q8⋊C8C22×C12711yescharacteristic
421Q8⋊C8C22×C12711yescharacteristic
422Q8⋊C8C22×C12711yescharacteristic
423Q8⋊C8C22×C12711yescharacteristic
424Q8⋊C8C22×C12711yescharacteristic
425D4⋊C8C22×C12711yescharacteristic
426D4⋊C8C22×C12711yescharacteristic
427C2×#41D4×C12711yescharacteristic
428C22×Q8—21no—
429C22×Q8D4×C12711yescharacteristic
430C2×Q16—21no—
431C2×Q16—21no—
432C2×Q16—22no—
433C22×C8—21no—
434C22×C8—21no—
435C4⋊Q8—22no—
436C4⋊Q8—21no—
437C4⋊Q8—22no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8—21no—
441C4⋊Q8C23×C12711yescharacteristic
442C4⋊Q8C23×C12711yescharacteristic
443C4⋊Q8C23×C12711yescharacteristic
444C4⋊Q8C23×C12711yescharacteristic
445#125—22no—
446#125—22no—
447#125—22no—
448#125—21no—
449#125—21no—
450#125—21no—
451#125—21no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—21no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8D4×C12712yes—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—21no—
469C4×Q8—21no—
470C4×Q8—21no—
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8D4×C12711yescharacteristic
478C4×Q8D4×C12711yescharacteristic
479C4×Q8D4×C12711yescharacteristic
480C4×Q8D4×C12712yes—
481C4×Q8C23×C12711yescharacteristic
482C4×Q8C23×C12711yescharacteristic
483C4×Q8C23×C12711yescharacteristic
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4D4×C12711yescharacteristic
491C4×D4C23×C12711yescharacteristic
492#117—22no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117D4×C12711yescharacteristic
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4D4×C12711yescharacteristic
501C2×C42—22no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42C23×C12711yescharacteristic
505#107—21no—
506#107—21no—
507#107—22no—
508#107—21no—
509#107—21no—
510#106—21no—
511#106—21no—
512C4⋊C8—21no—
513C4⋊C8C23×C12711yescharacteristic
514C4⋊C8C23×C12711yescharacteristic
515C4⋊C8C23×C12711yescharacteristic
516C4⋊C8C23×C12711yescharacteristic
517#103—21no—
518#103—21no—
519#103—21no—
520#103—21no—
521#103—22no—
522#103—21no—
523#103—21no—
524#103—22no—
525#102—21no—
526#102—21no—
527C22⋊C8—21no—
528C4×C8—21no—
529C4×C8—21no—
530C4×C8C23×C12711yescharacteristic
531C4×C8C23×C12711yescharacteristic
532#41—22no—
533#41Q16×C12714yescomplemented
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—41no—
542C2×Q8—42no—
543C2×Q8—42no—
544C2×Q8C2×D4×C12711yescharacteristic
545C2×Q8C2×D4×C12711yescharacteristic
546C2×Q8C2×D4×C12711yescharacteristic
547C2×Q8C2×D4×C12712yes—
548C2×D4—21no—
549C2×D4C2×D4×C12711yescharacteristic
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4C2×D4×C12711yescharacteristic
558C22×C4C2×D4×C12711yescharacteristic
559C22×C4C2×D4×C12711yescharacteristic
560Q16—44no—
561Q16—42no—
562Q16—42no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—42no—
570C2×C8—42no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4C2×D4×C12711yescharacteristic
598C4⋊C4C2×D4×C12711yescharacteristic
599C4⋊C4C2×D4×C12712yes—
600C4⋊C4C2×D4×C12711yescharacteristic
601C4⋊C4C2×D4×C12711yescharacteristic
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—41no—
609C42—22no—
610C42—22no—
611C42—21no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—41no—
620C42C2×D4×C12711yescharacteristic
621C42C2×D4×C12711yescharacteristic
622C42C2×D4×C12711yescharacteristic
623C42C24×C12711yescharacteristic
624C23—21no—
625C23#120×C12711yescharacteristic
626Q8—21no—
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—42no—
631Q8—42no—
632Q8—44no—
633Q8—42no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—82no—
639Q8C2×Q16×C12712yes—
640Q8#135×C12712yes—
641D4—24no—
642D4—21no—
643D4C2×Q16×C12712yes—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—24no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—82no—
666C2×C4#120×C12711yescharacteristic
667C2×C4#120×C12711yescharacteristic
668C2×C4#120×C12711yescharacteristic
669C2×C4C2×Q16×C12712yes—
670C2×C4#137×C12712yes—
671C2×C4C22×D4×C12711yescharacteristic
672C2×C4C22×D4×C12711yescharacteristic
673C2×C4C22×D4×C12711yescharacteristic
674C8—22no—
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C22—21no—
681C22—21no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22#451×C12712yes—
686C22C2×#120×C12711yescharacteristic
687C4—22no—
688C4—21no—
689C4—22no—
690C4—21no—
691C4—21no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4#451×C12712yes—
702C4C22×Q16×C12711yescharacteristic
703C4C2×#135×C12711yescharacteristic
704C4C2×#137×C12711yescharacteristic
705C4#575×C12711yescharacteristic
706C2—22no—
707C2—42no—
708C2C2×#451×C12711yescharacteristic
709C2C127×#300211yescharacteristic
710C2C127×#301811yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
prime radicalC2×#41×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3170C2semidirect
3. C127×#3104C2semidirect
5. C127×#1649C2semidirect
6. C127×#1648C2semidirect
7. C127×#1645C2semidirect
8. C127×#1644C2semidirect
9. C127×#1637C2semidirect
10. C127×#1636C2semidirect
11. C127×#1633C2semidirect
12. C127×#1632C2semidirect
13. C127×#1542C2semidirect
15. C2×Q8⋊C8×C127C2semidirect
177. #41×C127Q16semidirect
350. #18519C127direct (N × H)
357. #3170C2×C127semidirect
358. #3104C2×C127semidirect
360. #1649C2×C127semidirect
361. #1648C2×C127semidirect
362. #1645C2×C127semidirect
363. #1644C2×C127semidirect
364. #1637C2×C127semidirect
365. #1636C2×C127semidirect
366. #1633C2×C127semidirect
367. #1632C2×C127semidirect
368. #1542C2×C127semidirect
370. C2×Q8⋊C8C2×C127semidirect
371. C127#18519direct (N × H)
533. #41Q16×C127semidirect

Maximal subgroups

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

subgroupindex
Q8×#41×C1272
C127×#31702
C127×#31042
C127×#30762
C127×#16492
C127×#16482
C127×#16452
C127×#16442
C127×#16372
C127×#16362
C127×#16332
C127×#16322
C127×#15422
C127×#14762
C2×Q8⋊C8×C1272
#18519127