Finite Group Databasebeta

← C127×#13813 #44577486

Subgroups — C127×#13813 #44577486

Order 32512.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#386×C127C212yesmaximal
3C2×C4×C22⋊C4×C127C212yesmaximal, complemented
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
5C22×#95×C127C211yesmaximal, characteristic, complemented
6C127×#1437C212yesmaximal, complemented
7C127×#1436C212yesmaximal, complemented
8C127×#1434C211yesmaximal, characteristic, complemented
9C127×C22⋊#95C211yesmaximal, characteristic, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C127C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C24×C4×C127C2212yes—
16C2×C4×D4×C127—28no—
17C2×C4×D4×C127C418yescomplemented
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C42×C127C2212yes—
25C22×C42×C127C2212yes—
26C22×C42×C127C2211yescharacteristic
27#386×C127C4116yescomplemented
28C4×C22⋊C4×C127—28no—
29C4×C22⋊C4×C127—24no—
30C2×#95×C127—24no—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2211yescharacteristic
41C25×C127C2311yescharacteristic
42C25×C127C2311yescharacteristic
43C22×D4×C127—24no—
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127C2×C414yes—
47C22×D4×C127C2×C418yes—
48C23×C4×C127—24no—
49C23×C4×C127—24no—
50C23×C4×C127—24no—
51C23×C4×C127—24no—
52C23×C4×C127—22no—
53C23×C4×C127—24no—
54C23×C4×C127—22no—
55C23×C4×C127—22no—
56C23×C4×C127—22no—
57C23×C4×C127—24no—
58C23×C4×C127—42no—
59C23×C4×C127—42no—
60C23×C4×C127—42no—
61C23×C4×C127—42no—
62C23×C4×C127C2×C414yes—
63C23×C4×C127C2×C414yescomplemented
64C23×C4×C127C2×C418yescomplemented
65C23×C4×C127C2312yes—
66C23×C4×C127C2312yes—
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2312yes—
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2312yes—
73C23×C4×C127C2311yescharacteristic
74C4×D4×C127—232no—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127C2×C414yescomplemented
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—42no—
83C2×C22⋊C4×C127—42no—
84C2×C22⋊C4×C127C2×C414yes—
85C2×C22⋊C4×C127C2×C414yescomplemented
86C2×C22⋊C4×C127C2×C418yescomplemented
87C2×C22⋊C4×C127C2×C418yescomplemented
88C2×C22⋊C4×C127C2×C418yescomplemented
89C2×C22⋊C4×C127D418yes—
90C2×C42×C127—24no—
91C2×C42×C127—24no—
92C2×C42×C127—24no—
93C2×C42×C127—24no—
94C2×C42×C127—24no—
95C2×C42×C127—42no—
96C2×C42×C127—42no—
97C2×C42×C127C2×C414yescomplemented
98#95×C127—22no—
99#95×C127—24no—
100#95×C127—24no—
101#95×C127—24no—
102#95×C127—22no—
103#95×C127—22no—
104#95×C127—42no—
105#95×C127C2×C418yescomplemented
106#95×C127C2×C418yescomplemented
107#95×C127D414yescomplemented
108C24×C127—21no—
109C24×C127—21no—
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—21no—
113C24×C127—21no—
114C24×C127—21no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—21no—
118C24×C127—21no—
119C24×C127—21no—
120C24×C127—21no—
121C24×C127—22no—
122C24×C127—21no—
123C24×C127C22×C414yes—
124C24×C127C22×C412yes—
125C24×C127C22×C412yes—
126C24×C127C22×C414yes—
127C24×C127C2×D414yes—
128C24×C127#4112yes—
129C24×C127#4112yes—
130C24×C127C2411yescharacteristic
131C2×D4×C127—28no—
132C2×D4×C127—28no—
133C2×D4×C127—216no—
134C2×D4×C127—216no—
135C2×D4×C127C42116yescomplemented
136C22×C4×C127—21no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—21no—
151C22×C4×C127—28no—
152C22×C4×C127—216no—
153C22×C4×C127—21no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—21no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
175C22×C4×C127—28no—
176C22×C4×C127—28no—
177C22×C4×C127—28no—
178C22×C4×C127—216no—
179C22×C4×C127—44no—
180C22×C4×C127—44no—
181C22×C4×C127—48no—
182C22×C4×C127—48no—
183C22×C4×C127—48no—
184C22×C4×C127—48no—
185C22×C4×C127—48no—
186C22×C4×C127—48no—
187C22×C4×C127—48no—
188C22×C4×C127—48no—
189C22×C4×C127—48no—
190C22×C4×C127C22×C414yes—
191C22×C4×C127C22×C414yes—
192C22×C4×C127C22×C414yes—
193C22×C4×C127C22×C412yes—
194C22×C4×C127C22×C414yes—
195C22×C4×C127C22×C412yes—
196C22×C4×C127C22×C412yes—
197C22×C4×C127C22×C412yes—
198C22×C4×C127C22×C412yes—
199C22×C4×C127C22×C414yes—
200C22×C4×C127C2×D414yes—
201C22×C4×C127C2×D414yes—
202C22×C4×C127C2×D412yes—
203C22×C4×C127C2×D414yes—
204C22×C4×C127#4112yes—
205C22×C4×C127#4114yes—
206C4⋊C4×C127—28no—
207C22⋊C4×C127—216no—
208C22⋊C4×C127—28no—
209C22⋊C4×C127—216no—
210C22⋊C4×C127—48no—
211C22⋊C4×C127C22⋊C4116yescomplemented
212C42×C127—28no—
213C42×C127—48no—
214C42×C127—48no—
215C23×C127—22no—
216C23×C127—24no—
217C23×C127—22no—
218C23×C127—24no—
219C23×C127—22no—
220C23×C127—24no—
221C23×C127—22no—
222C23×C127—24no—
223C23×C127—24no—
224C23×C127—22no—
225C23×C127—24no—
226C23×C127—24no—
227C23×C127—24no—
228C23×C127—22no—
229C23×C127—24no—
230C23×C127—22no—
231C23×C127—22no—
232C23×C127—24no—
233C23×C127—22no—
234C23×C127—22no—
235C23×C127—24no—
236C23×C127—22no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—22no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—24no—
245C23×C127—42no—
246C23×C127—42no—
247C23×C127—42no—
248C23×C127—41no—
249C23×C127—42no—
250C23×C127—41no—
251C23×C127—42no—
252C23×C127—41no—
253C23×C127—41no—
254C23×C127—42no—
255C23×C127C2×C4214yes—
256C23×C127C2×C4214yes—
257C23×C127C2×C22⋊C414yes—
258C23×C127#11714yes—
259C23×C127C4×D418yes—
260C23×C127C4×D418yes—
261C23×C127C23×C411yescharacteristic
262C23×C127C23×C412yes—
263C23×C127C22×D412yes—
264C23×C127C22×D411yescharacteristic
265C23×C127C2×#4111yescharacteristic
266C23×C127C2×#4111yescharacteristic
267C23×C127C2×#4111yescharacteristic
268C23×C127C2×#4112yes—
269C23×C127H(5,𝔽2)12yes—
270C23×C127H(5,𝔽2)11yescharacteristic
271C23×C1272−1+411yescharacteristic
272D4×C127—232no—
273C2×C4×C127—22no—
274C2×C4×C127—22no—
275C2×C4×C127—22no—
276C2×C4×C127—22no—
277C2×C4×C127—24no—
278C2×C4×C127—24no—
279C2×C4×C127—24no—
280C2×C4×C127—22no—
281C2×C4×C127—22no—
282C2×C4×C127—22no—
283C2×C4×C127—24no—
284C2×C4×C127—22no—
285C2×C4×C127—24no—
286C2×C4×C127—24no—
287C2×C4×C127—24no—
288C2×C4×C127—24no—
289C2×C4×C127—24no—
290C2×C4×C127—24no—
291C2×C4×C127—24no—
292C2×C4×C127—24no—
293C2×C4×C127—24no—
294C2×C4×C127—24no—
295C2×C4×C127—22no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—24no—
299C2×C4×C127—22no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—24no—
304C2×C4×C127—24no—
305C2×C4×C127—22no—
306C2×C4×C127—24no—
307C2×C4×C127—416no—
308C2×C4×C127—416no—
309C2×C4×C127—432no—
310C2×C4×C127—42no—
311C2×C4×C127—42no—
312C2×C4×C127—42no—
313C2×C4×C127—42no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127—42no—
318C2×C4×C127—42no—
319C2×C4×C127—42no—
320C2×C4×C127—42no—
321C2×C4×C127—42no—
322C2×C4×C127—42no—
323C2×C4×C127—42no—
324C2×C4×C127C2×C4214yes—
325C2×C4×C127C2×C22⋊C414yes—
326C2×C4×C127C2×C22⋊C414yes—
327C2×C4×C127C4×D414yes—
328C2×C4×C127C4×D418yescomplemented
329C22×C127—24no—
330C22×C127—24no—
331C22×C127—24no—
332C22×C127—24no—
333C22×C127—28no—
334C22×C127—28no—
335C22×C127—28no—
336C22×C127—28no—
337C22×C127—24no—
338C22×C127—24no—
339C22×C127—24no—
340C22×C127—24no—
341C22×C127—24no—
342C22×C127—42no—
343C22×C127—42no—
344C22×C127—42no—
345C22×C127—42no—
346C22×C127—44no—
347C22×C127—44no—
348C22×C127—44no—
349C22×C127—44no—
350C22×C127C4×C22⋊C418yescomplemented
351C22×C127C22×C4211yescharacteristic
352C22×C127C22×C22⋊C411yescharacteristic
353C22×C127C2×#11711yescharacteristic
354C22×C127C2×C4×D411yescharacteristic
355C22×C127C2×C4×D412yes—
356C22×C127C2×C4×D412yes—
357C22×C127C2×C4×D412yes—
358C22×C127C4×#4111yescharacteristic
359C22×C127C4×#4112yes—
360C22×C127#51811yescharacteristic
361C22×C127#51812yes—
362C22×C127#52011yescharacteristic
363C22×C127#52012yes—
364C22×C127D4212yes—
365C22×C127#54612yes—
366C22×C127#54612yes—
367C22×C127#54611yescharacteristic
368C22×C127#54712yes—
369C22×C127#54811yescharacteristic
370C22×C127#55112yes—
371C22×C127#55211yescharacteristic
372C22×C127#55311yescharacteristic
373C22×C127#55312yes—
374C4×C127—24no—
375C4×C127—24no—
376C4×C127—24no—
377C4×C127—28no—
378C4×C127—24no—
379C4×C127—42no—
380C4×C127—44no—
381C4×C127—44no—
382C4×C127—44no—
383#13813C12711yesmaximal, characteristic, direct product factor, Sylow
384C2×C127—28no—
385C2×C127—44no—
386C2×C127C2×C4×C22⋊C411yescharacteristic
387C2×C127C42×D411yescharacteristic
388C2×C127#227511yescharacteristic
389C2×C127D4×C22⋊C411yescharacteristic
390C2×C127#233911yescharacteristic
391C2×C127#235211yescharacteristic
392C2×C127#235311yescharacteristic
393C2×C127#235812yes—
394C2×C127#235912yes—
395C2×C127#236112yes—
396C2×C127#236412yes—
397C22×C4×D4C2×C12711yescharacteristic
398C2×#386C2×C12712yes—
399C2×C4×C22⋊C4C2×C12712yescomplemented
400C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
401C22×#95C2×C12711yescharacteristic, complemented
402#1437C2×C12712yescomplemented
403#1436C2×C12712yescomplemented
404#1434C2×C12711yescharacteristic, complemented
405C22⋊#95C2×C12711yescharacteristic, complemented
406C22⋊#95C2×C12711yescharacteristic, complemented
407C4×#95C2×C12711yescharacteristic, complemented
408C127#1381311yescharacteristic, direct product factor, Sylow
409C23×D4C22×C12711yescharacteristic
410C24×C4C22×C12711yescharacteristic
411C24×C4C22×C12711yescharacteristic
412C24×C4C22×C12712yes—
413C2×C4×D4—28no—
414C2×C4×D4C4×C12718yescomplemented
415C22×C4⋊C4C22×C12711yescharacteristic
416C22×C22⋊C4C22×C12711yescharacteristic
417C22×C22⋊C4C22×C12712yes—
418C22×C22⋊C4C22×C12712yes—
419C22×C22⋊C4C22×C12712yes—
420C22×C22⋊C4C22×C12711yescharacteristic
421C22×C42C22×C12712yes—
422C22×C42C22×C12712yes—
423C22×C42C22×C12711yescharacteristic
424#386C4×C127116yescomplemented
425C4×C22⋊C4—28no—
426C4×C22⋊C4—24no—
427C2×#95—24no—
428C2×#95C22×C12711yescharacteristic
429C2×#95C22×C12711yescharacteristic
430C2×#95C22×C12711yescharacteristic
431C2×#95C22×C12712yes—
432C2×#95C22×C12712yes—
433C2×#95C22×C12712yes—
434C2×#95C22×C12712yes—
435C2×#95C22×C12712yes—
436C2×#95C22×C12712yes—
437C2×#95C22×C12711yescharacteristic
438C25C23×C12711yescharacteristic
439C25C23×C12711yescharacteristic
440C22×D4—24no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4C2×C4×C12714yes—
444C22×D4C2×C4×C12718yes—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—22no—
450C23×C4—24no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—24no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4C2×C4×C12714yes—
460C23×C4C2×C4×C12714yescomplemented
461C23×C4C2×C4×C12718yescomplemented
462C23×C4C23×C12712yes—
463C23×C4C23×C12712yes—
464C23×C4C23×C12711yescharacteristic
465C23×C4C23×C12712yes—
466C23×C4C23×C12711yescharacteristic
467C23×C4C23×C12711yescharacteristic
468C23×C4C23×C12711yescharacteristic
469C23×C4C23×C12712yes—
470C23×C4C23×C12711yescharacteristic
471C4×D4—232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4C2×C4×C12714yescomplemented
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4C2×C4×C12714yes—
482C2×C22⋊C4C2×C4×C12714yescomplemented
483C2×C22⋊C4C2×C4×C12718yescomplemented
484C2×C22⋊C4C2×C4×C12718yescomplemented
485C2×C22⋊C4C2×C4×C12718yescomplemented
486C2×C22⋊C4D4×C12718yes—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—24no—
490C2×C42—24no—
491C2×C42—24no—
492C2×C42—42no—
493C2×C42—42no—
494C2×C42C2×C4×C12714yescomplemented
495#95—22no—
496#95—24no—
497#95—24no—
498#95—24no—
499#95—22no—
500#95—22no—
501#95—42no—
502#95C2×C4×C12718yescomplemented
503#95C2×C4×C12718yescomplemented
504#95D4×C12714yescomplemented
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—22no—
519C24—21no—
520C24C22×C4×C12714yes—
521C24C22×C4×C12712yes—
522C24C22×C4×C12712yes—
523C24C22×C4×C12714yes—
524C24C2×D4×C12714yes—
525C24#41×C12712yes—
526C24#41×C12712yes—
527C24C24×C12711yescharacteristic
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4C42×C127116yescomplemented
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—28no—
549C22×C4—216no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—216no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4C22×C4×C12714yes—
588C22×C4C22×C4×C12714yes—
589C22×C4C22×C4×C12714yes—
590C22×C4C22×C4×C12712yes—
591C22×C4C22×C4×C12714yes—
592C22×C4C22×C4×C12712yes—
593C22×C4C22×C4×C12712yes—
594C22×C4C22×C4×C12712yes—
595C22×C4C22×C4×C12712yes—
596C22×C4C22×C4×C12714yes—
597C22×C4C2×D4×C12714yes—
598C22×C4C2×D4×C12714yes—
599C22×C4C2×D4×C12712yes—
600C22×C4C2×D4×C12714yes—
601C22×C4#41×C12712yes—
602C22×C4#41×C12714yes—
603C4⋊C4—28no—
604C22⋊C4—216no—
605C22⋊C4—28no—
606C22⋊C4—216no—
607C22⋊C4—48no—
608C22⋊C4C22⋊C4×C127116yescomplemented
609C42—28no—
610C42—48no—
611C42—48no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23C2×C42×C12714yes—
653C23C2×C42×C12714yes—
654C23C2×C22⋊C4×C12714yes—
655C23#117×C12714yes—
656C23C4×D4×C12718yes—
657C23C4×D4×C12718yes—
658C23C23×C4×C12711yescharacteristic
659C23C23×C4×C12712yes—
660C23C22×D4×C12712yes—
661C23C22×D4×C12711yescharacteristic
662C23C2×#41×C12711yescharacteristic
663C23C2×#41×C12711yescharacteristic
664C23C2×#41×C12711yescharacteristic
665C23C2×#41×C12712yes—
666C23H(5,𝔽2)×C12712yes—
667C23H(5,𝔽2)×C12711yescharacteristic
668C232−1+4×C12711yescharacteristic
669D4—232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—416no—
705C2×C4—416no—
706C2×C4—432no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4C2×C42×C12714yes—
722C2×C4C2×C22⋊C4×C12714yes—
723C2×C4C2×C22⋊C4×C12714yes—
724C2×C4C4×D4×C12714yes—
725C2×C4C4×D4×C12718yescomplemented
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—28no—
731C22—28no—
732C22—28no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22C4×C22⋊C4×C12718yescomplemented
748C22C22×C42×C12711yescharacteristic
749C22C22×C22⋊C4×C12711yescharacteristic
750C22C2×#117×C12711yescharacteristic
751C22C2×C4×D4×C12711yescharacteristic
752C22C2×C4×D4×C12712yes—
753C22C2×C4×D4×C12712yes—
754C22C2×C4×D4×C12712yes—
755C22C4×#41×C12711yescharacteristic
756C22C4×#41×C12712yes—
757C22#518×C12711yescharacteristic
758C22#518×C12712yes—
759C22#520×C12711yescharacteristic
760C22#520×C12712yes—
761C22D42×C12712yes—
762C22#546×C12712yes—
763C22#546×C12712yes—
764C22#546×C12711yescharacteristic
765C22#547×C12712yes—
766C22#548×C12711yescharacteristic
767C22#551×C12712yes—
768C22#552×C12711yescharacteristic
769C22#553×C12711yescharacteristic
770C22#553×C12712yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—28no—
775C4—24no—
776C4—42no—
777C4—44no—
778C4—44no—
779C4—44no—
780C2—28no—
781C2—44no—
782C2C2×C4×C22⋊C4×C12711yescharacteristic
783C2C42×D4×C12711yescharacteristic
784C2C127×#227511yescharacteristic
785C2D4×C22⋊C4×C12711yescharacteristic
786C2C127×#233911yescharacteristic
787C2C127×#235211yescharacteristic
788C2C127×#235311yescharacteristic
789C2C127×#235812yes—
790C2C127×#235912yes—
791C2C127×#236112yes—
792C2C127×#236412yes—
subgroupG/H
center, socleC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C127C2semidirect
4. C2×C4×C22⋊C4×C127C2semidirect
5. C22×#95×C127C2semidirect
6. C127×#1437C2semidirect
7. C127×#1436C2semidirect
8. C127×#1434C2semidirect
9. C127×C22⋊#95C2semidirect
10. C127×C22⋊#95C2semidirect
11. C4×#95×C127C2semidirect
17. C2×C4×D4×C127C4semidirect
27. #386×C127C4semidirect
63. C23×C4×C127C2×C4semidirect
64. C23×C4×C127C2×C4semidirect
76. C2×C4⋊C4×C127C2×C4semidirect
85. C2×C22⋊C4×C127C2×C4semidirect
86. C2×C22⋊C4×C127C2×C4semidirect
87. C2×C22⋊C4×C127C2×C4semidirect
88. C2×C22⋊C4×C127C2×C4semidirect
97. C2×C42×C127C2×C4semidirect
105. #95×C127C2×C4semidirect
106. #95×C127C2×C4semidirect
107. #95×C127D4semidirect
135. C2×D4×C127C42semidirect
211. C22⋊C4×C127C22⋊C4semidirect
328. C2×C4×C127C4×D4semidirect
350. C22×C127C4×C22⋊C4semidirect
383. #13813C127direct (N × H)
399. C2×C4×C22⋊C4C2×C127semidirect
400. C2×C4×C22⋊C4C2×C127semidirect
401. C22×#95C2×C127semidirect
402. #1437C2×C127semidirect
403. #1436C2×C127semidirect
404. #1434C2×C127semidirect
405. C22⋊#95C2×C127semidirect
406. C22⋊#95C2×C127semidirect
407. C4×#95C2×C127semidirect
408. C127#13813direct (N × H)
414. C2×C4×D4C4×C127semidirect
424. #386C4×C127semidirect
460. C23×C4C2×C4×C127semidirect
461. C23×C4C2×C4×C127semidirect
473. C2×C4⋊C4C2×C4×C127semidirect
482. C2×C22⋊C4C2×C4×C127semidirect
483. C2×C22⋊C4C2×C4×C127semidirect
484. C2×C22⋊C4C2×C4×C127semidirect
485. C2×C22⋊C4C2×C4×C127semidirect
494. C2×C42C2×C4×C127semidirect
502. #95C2×C4×C127semidirect
503. #95C2×C4×C127semidirect
504. #95D4×C127semidirect
532. C2×D4C42×C127semidirect
608. C22⋊C4C22⋊C4×C127semidirect
725. C2×C4C4×D4×C127semidirect
747. C22C4×C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
C4×#95×C1272
#13813127