Finite Group Databasebeta

← C127×#14015 #44577688

Subgroups — C127×#14015 #44577688

Order 32512.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C23×C4⋊C4×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C211yesmaximal, characteristic
4C2×#386×C127C211yesmaximal, characteristic
5C2×#385×C127C212yesmaximal, complemented
6C2×#385×C127C211yesmaximal, characteristic, complemented
7C127×#1444C212yesmaximal, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1436C212yesmaximal, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×C4×D4×C127—24no—
18C2×C4×D4×C127—24no—
19C2×C4×D4×C127—24no—
20C22×C4⋊C4×C127—24no—
21C22×C4⋊C4×C127—28no—
22C22×C4⋊C4×C127C2212yes—
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2212yes—
25C22×C4⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2212yes—
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2212yes—
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33#386×C127—24no—
34#386×C127C418yescomplemented
35#385×C127—28no—
36#385×C127—24no—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C2×#95×C127C2212yes—
44C25×C127C2311yescharacteristic
45C25×C127C2311yescharacteristic
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127C2×C414yes—
51C22×D4×C127D414yes—
52C22×D4×C127Q814yes—
53C23×C4×C127—22no—
54C23×C4×C127—22no—
55C23×C4×C127—24no—
56C23×C4×C127—24no—
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—24no—
62C23×C4×C127—24no—
63C23×C4×C127—22no—
64C23×C4×C127—22no—
65C23×C4×C127—22no—
66C23×C4×C127—22no—
67C23×C4×C127—24no—
68C23×C4×C127—42no—
69C23×C4×C127—42no—
70C23×C4×C127—42no—
71C23×C4×C127C2×C414yescomplemented
72C23×C4×C127D414yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2312yes—
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2312yes—
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2312yes—
81C23×C4×C127C2311yescharacteristic
82C4×D4×C127—232no—
83C2×C4⋊C4×C127—232no—
84C2×C4⋊C4×C127—24no—
85C2×C4⋊C4×C127—24no—
86C2×C4⋊C4×C127—24no—
87C2×C4⋊C4×C127—24no—
88C2×C4⋊C4×C127—24no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—22no—
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—24no—
93C2×C4⋊C4×C127—24no—
94C2×C4⋊C4×C127—42no—
95C2×C4⋊C4×C127D418yescomplemented
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—22no—
102C2×C22⋊C4×C127—22no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—24no—
105C2×C22⋊C4×C127—24no—
106C2×C22⋊C4×C127—22no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—24no—
110C2×C22⋊C4×C127—42no—
111C2×C22⋊C4×C127C2×C414yescomplemented
112C2×C22⋊C4×C127C2×C418yescomplemented
113C2×C22⋊C4×C127D414yes—
114C2×C42×C127—22no—
115C2×C42×C127—22no—
116C2×C42×C127—22no—
117#95×C127—24no—
118#95×C127—24no—
119#95×C127—24no—
120#95×C127—24no—
121#95×C127—24no—
122#95×C127—42no—
123#95×C127C2×C418yescomplemented
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—22no—
132C24×C127—21no—
133C24×C127—21no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127C22×C412yes—
137C24×C127C22×C412yes—
138C24×C127C2×D412yes—
139C24×C127C2×D412yes—
140C24×C127C2×D412yes—
141C24×C127C2×D412yes—
142C24×C127C2×Q812yes—
143C24×C127C2×Q812yes—
144C24×C127#4112yes—
145C24×C127#4112yes—
146C24×C127C2411yescharacteristic
147C2×D4×C127—28no—
148C2×D4×C127—28no—
149C2×D4×C127—28no—
150C2×D4×C127—28no—
151C2×D4×C127—28no—
152C2×D4×C127—28no—
153C2×D4×C127C4⋊C4116yescomplemented
154C22×C4×C127—28no—
155C22×C4×C127—216no—
156C22×C4×C127—28no—
157C22×C4×C127—28no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—22no—
169C22×C4×C127—216no—
170C22×C4×C127—28no—
171C22×C4×C127—28no—
172C22×C4×C127—28no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—28no—
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—22no—
205C22×C4×C127—44no—
206C22×C4×C127—48no—
207C22×C4×C127—48no—
208C22×C4×C127—48no—
209C22×C4×C127—48no—
210C22×C4×C127—48no—
211C22×C4×C127—48no—
212C22×C4×C127—44no—
213C22×C4×C127—44no—
214C22×C4×C127—44no—
215C22×C4×C127—44no—
216C22×C4×C127C22×C414yes—
217C22×C4×C127C22×C412yes—
218C22×C4×C127C22×C414yes—
219C22×C4×C127C2×D412yes—
220C22×C4×C127C2×D412yes—
221C22×C4×C127C2×D414yes—
222C22×C4×C127C2×D412yes—
223C22×C4×C127C2×D412yes—
224C22×C4×C127C2×D414yes—
225C22×C4×C127C2×D414yes—
226C22×C4×C127C2×D412yes—
227C22×C4×C127C2×Q812yes—
228C22×C4×C127#4114yes—
229C4⋊C4×C127—216no—
230C4⋊C4×C127—28no—
231C4⋊C4×C127—216no—
232C4⋊C4×C127—48no—
233C22⋊C4×C127—28no—
234C22⋊C4×C127—28no—
235C22⋊C4×C127—28no—
236C22⋊C4×C127—216no—
237C22⋊C4×C127—48no—
238C22⋊C4×C127—44no—
239C42×C127—28no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—24no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—24no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—24no—
251C23×C127—24no—
252C23×C127—24no—
253C23×C127—24no—
254C23×C127—24no—
255C23×C127—24no—
256C23×C127—24no—
257C23×C127—22no—
258C23×C127—22no—
259C23×C127—24no—
260C23×C127—22no—
261C23×C127—22no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—24no—
265C23×C127—24no—
266C23×C127—24no—
267C23×C127—24no—
268C23×C127—41no—
269C23×C127—41no—
270C23×C127—42no—
271C23×C127—41no—
272C23×C127—41no—
273C23×C127—42no—
274C23×C127—42no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127—42no—
278C23×C127C2×C4⋊C414yes—
279C23×C127C2×C4⋊C414yescomplemented
280C23×C127C4×D414yes—
281C23×C127C4×D414yes—
282C23×C127#12014yes—
283C23×C127C22⋊Q814yes—
284C23×C127C22⋊Q814yes—
285C23×C127#12314yes—
286C23×C127C23×C411yescharacteristic
287C23×C127C22×D411yescharacteristic
288C23×C127C22×D411yescharacteristic
289C23×C127C22×D411yescharacteristic
290C23×C127C22×D412yes—
291C23×C127C22×Q811yescharacteristic
292C23×C127C2×#4111yescharacteristic
293C23×C127C2×#4111yescharacteristic
294C23×C127C2×#4112yes—
295C23×C127H(5,𝔽2)12yes—
296C23×C1272−1+412yes—
297D4×C127—232no—
298C2×C4×C127—232no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—22no—
302C2×C4×C127—22no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—24no—
306C2×C4×C127—22no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—22no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—24no—
316C2×C4×C127—24no—
317C2×C4×C127—24no—
318C2×C4×C127—22no—
319C2×C4×C127—22no—
320C2×C4×C127—22no—
321C2×C4×C127—22no—
322C2×C4×C127—24no—
323C2×C4×C127—22no—
324C2×C4×C127—24no—
325C2×C4×C127—24no—
326C2×C4×C127—24no—
327C2×C4×C127—24no—
328C2×C4×C127—416no—
329C2×C4×C127—416no—
330C2×C4×C127—416no—
331C2×C4×C127—42no—
332C2×C4×C127—41no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—42no—
336C2×C4×C127—41no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127—42no—
344C2×C4×C127—42no—
345C2×C4×C127—42no—
346C2×C4×C127—42no—
347C2×C4×C127—42no—
348C2×C4×C127—42no—
349C2×C4×C127—42no—
350C2×C4×C127—42no—
351C2×C4×C127—42no—
352C2×C4×C127—42no—
353C2×C4×C127—42no—
354C2×C4×C127C2×C4⋊C414yescomplemented
355C2×C4×C127C4×D418yescomplemented
356C2×C4×C127#12014yes—
357C22×C127—24no—
358C22×C127—24no—
359C22×C127—28no—
360C22×C127—28no—
361C22×C127—24no—
362C22×C127—24no—
363C22×C127—24no—
364C22×C127—28no—
365C22×C127—28no—
366C22×C127—24no—
367C22×C127—28no—
368C22×C127—24no—
369C22×C127—42no—
370C22×C127—42no—
371C22×C127—44no—
372C22×C127—42no—
373C22×C127—42no—
374C22×C127—42no—
375C22×C127—44no—
376C22×C127—44no—
377C22×C127—42no—
378C22×C127#38518yescomplemented
379C22×C127C22×C4⋊C411yescharacteristic
380C22×C127C2×C4×D411yescharacteristic
381C22×C127C2×C4×D412yes—
382C22×C127C2×C4×D411yescharacteristic
383C22×C127#52012yes—
384C22×C127C2×#12011yescharacteristic
385C22×C127C2×#12011yescharacteristic
386C22×C127C2×C22⋊Q811yescharacteristic
387C22×C127C2×C22⋊Q811yescharacteristic
388C22×C127C2×#12311yescharacteristic
389C22×C127#52511yescharacteristic
390C22×C127#52512yes—
391C22×C127#53411yescharacteristic
392C22×C127#53611yescharacteristic
393C22×C127#53912yes—
394C22×C127D4212yes—
395C22×C127D4212yes—
396C22×C127#54712yes—
397C22×C127#54712yes—
398C22×C127#54812yes—
399C22×C127D4×Q812yes—
400C22×C127#55312yes—
401C22×C127#55412yes—
402C4×C127—24no—
403C4×C127—24no—
404C4×C127—28no—
405C4×C127—44no—
406C4×C127—42no—
407C4×C127—42no—
408C4×C127—44no—
409C4×C127—42no—
410C4×C127—82no—
411#14015C12711yesmaximal, characteristic, direct product factor, Sylow
412C2×C127—28no—
413C2×C127—44no—
414C2×C127C2×#38511yescharacteristic
415C2×C127C4×#12011yescharacteristic
416C2×C127#232211yescharacteristic
417C2×C127D4×C4⋊C412yes—
418C2×C127#236112yes—
419C2×C127#240311yescharacteristic
420C2×C127#240611yescharacteristic
421C2×C127#240911yescharacteristic
422C2×C127#244312yes—
423C2×C127#244912yes—
424C2×C127#257911yescharacteristic
425C22×C4×D4C2×C12711yescharacteristic
426C23×C4⋊C4C2×C12711yescharacteristic, complemented
427C2×#386C2×C12711yescharacteristic
428C2×#386C2×C12711yescharacteristic
429C2×#385C2×C12712yescomplemented
430C2×#385C2×C12711yescharacteristic, complemented
431#1444C2×C12712yescomplemented
432#1439C2×C12712yescomplemented
433#1436C2×C12712yescomplemented
434C22⋊#95C2×C12711yescharacteristic, complemented
435C22⋊#95C2×C12711yescharacteristic, complemented
436C127#1401511yescharacteristic, direct product factor, Sylow
437C23×D4C22×C12711yescharacteristic
438C24×C4C22×C12711yescharacteristic
439C24×C4C22×C12711yescharacteristic
440C24×C4C22×C12711yescharacteristic
441C24×C4C22×C12711yescharacteristic
442C2×C4×D4—24no—
443C2×C4×D4—24no—
444C2×C4×D4—24no—
445C22×C4⋊C4—24no—
446C22×C4⋊C4—28no—
447C22×C4⋊C4C22×C12712yes—
448C22×C4⋊C4C22×C12711yescharacteristic
449C22×C4⋊C4C22×C12712yes—
450C22×C4⋊C4C22×C12712yes—
451C22×C22⋊C4C22×C12711yescharacteristic
452C22×C22⋊C4C22×C12711yescharacteristic
453C22×C22⋊C4C22×C12712yes—
454C22×C22⋊C4C22×C12711yescharacteristic
455C22×C22⋊C4C22×C12712yes—
456C22×C22⋊C4C22×C12711yescharacteristic
457C22×C42C22×C12711yescharacteristic
458#386—24no—
459#386C4×C12718yescomplemented
460#385—28no—
461#385—24no—
462C2×#95C22×C12712yes—
463C2×#95C22×C12712yes—
464C2×#95C22×C12712yes—
465C2×#95C22×C12712yes—
466C2×#95C22×C12712yes—
467C2×#95C22×C12712yes—
468C2×#95C22×C12712yes—
469C25C23×C12711yescharacteristic
470C25C23×C12711yescharacteristic
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4C2×C4×C12714yes—
476C22×D4D4×C12714yes—
477C22×D4Q8×C12714yes—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—24no—
487C23×C4—24no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—24no—
493C23×C4—42no—
494C23×C4—42no—
495C23×C4—42no—
496C23×C4C2×C4×C12714yescomplemented
497C23×C4D4×C12714yes—
498C23×C4C23×C12712yes—
499C23×C4C23×C12712yes—
500C23×C4C23×C12711yescharacteristic
501C23×C4C23×C12712yes—
502C23×C4C23×C12711yescharacteristic
503C23×C4C23×C12711yescharacteristic
504C23×C4C23×C12711yescharacteristic
505C23×C4C23×C12712yes—
506C23×C4C23×C12711yescharacteristic
507C4×D4—232no—
508C2×C4⋊C4—232no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4D4×C12718yescomplemented
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4C2×C4×C12714yescomplemented
537C2×C22⋊C4C2×C4×C12718yescomplemented
538C2×C22⋊C4D4×C12714yes—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542#95—24no—
543#95—24no—
544#95—24no—
545#95—24no—
546#95—24no—
547#95—42no—
548#95C2×C4×C12718yescomplemented
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—21no—
555C24—21no—
556C24—22no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24C22×C4×C12712yes—
562C24C22×C4×C12712yes—
563C24C2×D4×C12712yes—
564C24C2×D4×C12712yes—
565C24C2×D4×C12712yes—
566C24C2×D4×C12712yes—
567C24C2×Q8×C12712yes—
568C24C2×Q8×C12712yes—
569C24#41×C12712yes—
570C24#41×C12712yes—
571C24C24×C12711yescharacteristic
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4C4⋊C4×C127116yescomplemented
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—216no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—28no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—44no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4C22×C4×C12714yes—
642C22×C4C22×C4×C12712yes—
643C22×C4C22×C4×C12714yes—
644C22×C4C2×D4×C12712yes—
645C22×C4C2×D4×C12712yes—
646C22×C4C2×D4×C12714yes—
647C22×C4C2×D4×C12712yes—
648C22×C4C2×D4×C12712yes—
649C22×C4C2×D4×C12714yes—
650C22×C4C2×D4×C12714yes—
651C22×C4C2×D4×C12712yes—
652C22×C4C2×Q8×C12712yes—
653C22×C4#41×C12714yes—
654C4⋊C4—216no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—48no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—216no—
662C22⋊C4—48no—
663C22⋊C4—44no—
664C42—28no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—41no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23C2×C4⋊C4×C12714yes—
704C23C2×C4⋊C4×C12714yescomplemented
705C23C4×D4×C12714yes—
706C23C4×D4×C12714yes—
707C23#120×C12714yes—
708C23C22⋊Q8×C12714yes—
709C23C22⋊Q8×C12714yes—
710C23#123×C12714yes—
711C23C23×C4×C12711yescharacteristic
712C23C22×D4×C12711yescharacteristic
713C23C22×D4×C12711yescharacteristic
714C23C22×D4×C12711yescharacteristic
715C23C22×D4×C12712yes—
716C23C22×Q8×C12711yescharacteristic
717C23C2×#41×C12711yescharacteristic
718C23C2×#41×C12711yescharacteristic
719C23C2×#41×C12712yes—
720C23H(5,𝔽2)×C12712yes—
721C232−1+4×C12712yes—
722D4—232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4C2×C4⋊C4×C12714yescomplemented
780C2×C4C4×D4×C12718yescomplemented
781C2×C4#120×C12714yes—
782C22—24no—
783C22—24no—
784C22—28no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—28no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22#385×C12718yescomplemented
804C22C22×C4⋊C4×C12711yescharacteristic
805C22C2×C4×D4×C12711yescharacteristic
806C22C2×C4×D4×C12712yes—
807C22C2×C4×D4×C12711yescharacteristic
808C22#520×C12712yes—
809C22C2×#120×C12711yescharacteristic
810C22C2×#120×C12711yescharacteristic
811C22C2×C22⋊Q8×C12711yescharacteristic
812C22C2×C22⋊Q8×C12711yescharacteristic
813C22C2×#123×C12711yescharacteristic
814C22#525×C12711yescharacteristic
815C22#525×C12712yes—
816C22#534×C12711yescharacteristic
817C22#536×C12711yescharacteristic
818C22#539×C12712yes—
819C22D42×C12712yes—
820C22D42×C12712yes—
821C22#547×C12712yes—
822C22#547×C12712yes—
823C22#548×C12712yes—
824C22D4×Q8×C12712yes—
825C22#553×C12712yes—
826C22#554×C12712yes—
827C4—24no—
828C4—24no—
829C4—28no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—42no—
835C4—82no—
836C2—28no—
837C2—44no—
838C2C2×#385×C12711yescharacteristic
839C2C4×#120×C12711yescharacteristic
840C2C127×#232211yescharacteristic
841C2D4×C4⋊C4×C12712yes—
842C2C127×#236112yes—
843C2C127×#240311yescharacteristic
844C2C127×#240611yescharacteristic
845C2C127×#240911yescharacteristic
846C2C127×#244312yes—
847C2C127×#244912yes—
848C2C127×#257911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊C4×C127C2semidirect
5. C2×#385×C127C2semidirect
6. C2×#385×C127C2semidirect
7. C127×#1444C2semidirect
8. C127×#1439C2semidirect
9. C127×#1436C2semidirect
10. C127×C22⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
34. #386×C127C4semidirect
71. C23×C4×C127C2×C4semidirect
95. C2×C4⋊C4×C127D4semidirect
111. C2×C22⋊C4×C127C2×C4semidirect
112. C2×C22⋊C4×C127C2×C4semidirect
123. #95×C127C2×C4semidirect
153. C2×D4×C127C4⋊C4semidirect
279. C23×C127C2×C4⋊C4semidirect
354. C2×C4×C127C2×C4⋊C4semidirect
355. C2×C4×C127C4×D4semidirect
378. C22×C127#385semidirect
411. #14015C127direct (N × H)
426. C23×C4⋊C4C2×C127semidirect
429. C2×#385C2×C127semidirect
430. C2×#385C2×C127semidirect
431. #1444C2×C127semidirect
432. #1439C2×C127semidirect
433. #1436C2×C127semidirect
434. C22⋊#95C2×C127semidirect
435. C22⋊#95C2×C127semidirect
436. C127#14015direct (N × H)
459. #386C4×C127semidirect
496. C23×C4C2×C4×C127semidirect
520. C2×C4⋊C4D4×C127semidirect
536. C2×C22⋊C4C2×C4×C127semidirect
537. C2×C22⋊C4C2×C4×C127semidirect
548. #95C2×C4×C127semidirect
578. C2×D4C4⋊C4×C127semidirect
704. C23C2×C4⋊C4×C127semidirect
779. C2×C4C2×C4⋊C4×C127semidirect
780. C2×C4C4×D4×C127semidirect
803. C22#385×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
C23×C4⋊C4×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14442
C127×#14392
C127×#14362
C127×C22⋊#952
#14015127