Finite Group Databasebeta

← C127×#14017 #44577690

Subgroups — C127×#14017 #44577690

Order 32512.

1810 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
1C22×C4×Q8×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
6C127×#1444C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1436C212yesmaximal
9C127×#1436C212yesmaximal
10C127×C4⋊#95C211yesmaximal, characteristic
11C127×C4⋊#95C211yesmaximal, characteristic
12C23×Q8×C127C2211yescharacteristic
13C2×C4×Q8×C127—24no—
14C2×C4×Q8×C127—24no—
15C2×C4×Q8×C127—24no—
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C42×C127C2212yes—
24C22×C42×C127C2211yescharacteristic
25C22×C42×C127C2211yescharacteristic
26C22×C42×C127C2211yescharacteristic
27#391×C127—24no—
28#391×C127C418yescomplemented
29#389×C127—24no—
30C4×C4⋊C4×C127—24no—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C22×Q8×C127—22no—
43C22×Q8×C127—22no—
44C22×Q8×C127—22no—
45C22×Q8×C127—22no—
46C22×Q8×C127C2×C414yes—
47C22×Q8×C127D414yes—
48C22×Q8×C127Q814yes—
49C23×C4×C127C2312yes—
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C4×Q8×C127—232no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—24no—
63C2×C4⋊C4×C127—24no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—42no—
79C2×C4⋊C4×C127C2×C414yes—
80C2×C4⋊C4×C127D414yes—
81C2×C4⋊C4×C127Q814yescomplemented
82C2×C42×C127—24no—
83C2×C42×C127—24no—
84C2×C42×C127—24no—
85C2×C42×C127—22no—
86C2×C42×C127—22no—
87C2×C42×C127—22no—
88C2×C42×C127—22no—
89C2×C42×C127—22no—
90C2×C42×C127—22no—
91C2×C42×C127—22no—
92C2×C42×C127C2×C414yes—
93C2×C42×C127D414yes—
94#95×C127—22no—
95#95×C127—22no—
96#95×C127—24no—
97#95×C127—24no—
98#95×C127—24no—
99#95×C127—24no—
100#95×C127—24no—
101#95×C127—42no—
102#95×C127—42no—
103#95×C127C2×C418yes—
104#95×C127C2×C418yes—
105C24×C127C2411yescharacteristic
106C2×Q8×C127—28no—
107C2×Q8×C127—28no—
108C2×Q8×C127—28no—
109C2×Q8×C127—28no—
110C2×Q8×C127—28no—
111C2×Q8×C127—28no—
112C2×Q8×C127C4⋊C4116yescomplemented
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—21no—
134C22×C4×C127—22no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—21no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—22no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—22no—
156C22×C4×C127—21no—
157C22×C4×C127—22no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127C22×C412yes—
169C22×C4×C127C22×C414yes—
170C22×C4×C127C22×C414yes—
171C22×C4×C127C22×C412yes—
172C22×C4×C127C22×C412yes—
173C22×C4×C127C2×D414yes—
174C22×C4×C127C2×D412yes—
175C22×C4×C127C2×D414yes—
176C22×C4×C127C2×D412yes—
177C22×C4×C127C2×D412yes—
178C22×C4×C127C2×D412yes—
179C22×C4×C127C2×D412yes—
180C22×C4×C127C2×Q812yes—
181C22×C4×C127C2×Q814yes—
182C22×C4×C127C2×Q812yes—
183C22×C4×C127C2×Q812yes—
184C22×C4×C127C2×Q812yes—
185C22×C4×C127#4112yes—
186C22×C4×C127#4112yes—
187C22×C4×C127#4112yes—
188C22×C4×C127#4112yes—
189C22×C4×C127#4112yes—
190C4⋊C4×C127—28no—
191C4⋊C4×C127—216no—
192C4⋊C4×C127—28no—
193C4⋊C4×C127—28no—
194C4⋊C4×C127—28no—
195C4⋊C4×C127—48no—
196C4⋊C4×C127—44no—
197C42×C127—216no—
198C42×C127—28no—
199C42×C127—28no—
200C42×C127—44no—
201C23×C127C23×C411yescharacteristic
202C23×C127C22×D411yescharacteristic
203C23×C127C22×D411yescharacteristic
204C23×C127C22×D411yescharacteristic
205C23×C127C22×Q811yescharacteristic
206C23×C127C22×Q811yescharacteristic
207C23×C127C2×#4111yescharacteristic
208C23×C127C2×#4111yescharacteristic
209C23×C127C2×#4111yescharacteristic
210C23×C127C2×#4111yescharacteristic
211C23×C127C2×#4111yescharacteristic
212C23×C127H(5,𝔽2)11yescharacteristic
213C23×C1272−1+411yescharacteristic
214C23×C1272−1+411yescharacteristic
215C23×C1272−1+411yescharacteristic
216Q8×C127—232no—
217C2×C4×C127—22no—
218C2×C4×C127—24no—
219C2×C4×C127—24no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—24no—
223C2×C4×C127—22no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—22no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—22no—
236C2×C4×C127—24no—
237C2×C4×C127—24no—
238C2×C4×C127—22no—
239C2×C4×C127—22no—
240C2×C4×C127—24no—
241C2×C4×C127—24no—
242C2×C4×C127—22no—
243C2×C4×C127—22no—
244C2×C4×C127—22no—
245C2×C4×C127—22no—
246C2×C4×C127—22no—
247C2×C4×C127—22no—
248C2×C4×C127—24no—
249C2×C4×C127—24no—
250C2×C4×C127—22no—
251C2×C4×C127—22no—
252C2×C4×C127—22no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—42no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—42no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—42no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127—41no—
267C2×C4×C127—42no—
268C2×C4×C127—41no—
269C2×C4×C127—42no—
270C2×C4×C127—41no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127—42no—
274C2×C4×C127—41no—
275C2×C4×C127—42no—
276C2×C4×C127—42no—
277C2×C4×C127—42no—
278C2×C4×C127—42no—
279C2×C4×C127—42no—
280C2×C4×C127—42no—
281C2×C4×C127—42no—
282C2×C4×C127—42no—
283C2×C4×C127—42no—
284C2×C4×C127C2×C4⋊C418yes—
285C2×C4×C127C2×C4⋊C414yes—
286C2×C4×C127C4×D414yes—
287C2×C4×C127C4×D414yes—
288C2×C4×C127C4×Q814yescomplemented
289C2×C4×C127#12014yes—
290C2×C4×C127C22⋊Q814yes—
291C2×C4×C127C22⋊Q814yes—
292C2×C4×C127C22⋊Q814yes—
293C2×C4×C127#12314yes—
294C22×C127C22×C4⋊C411yescharacteristic
295C22×C127C2×C4×D411yescharacteristic
296C22×C127C2×C4×D411yescharacteristic
297C22×C127C2×C4×Q811yescharacteristic
298C22×C127C4×#4111yescharacteristic
299C22×C127#51911yescharacteristic
300C22×C127#52011yescharacteristic
301C22×C127C2×#12011yescharacteristic
302C22×C127C2×C22⋊Q811yescharacteristic
303C22×C127C2×C22⋊Q811yescharacteristic
304C22×C127C2×C22⋊Q811yescharacteristic
305C22×C127C2×#12311yescharacteristic
306C22×C127#52511yescharacteristic
307C22×C127#52911yescharacteristic
308C22×C127#53311yescharacteristic
309C22×C127#53611yescharacteristic
310C22×C127#53711yescharacteristic
311C22×C127#54111yescharacteristic
312C22×C127#54211yescharacteristic
313C22×C127#54611yescharacteristic
314C22×C127#54711yescharacteristic
315C22×C127#54811yescharacteristic
316C22×C127#54811yescharacteristic
317C22×C127#54811yescharacteristic
318C22×C127D4×Q811yescharacteristic
319C22×C127D4×Q811yescharacteristic
320C22×C127#55011yescharacteristic
321C22×C127#55611yescharacteristic
322C22×C127#55611yescharacteristic
323C22×C127#55711yescharacteristic
324C22×C127#55711yescharacteristic
325C22×C127#55711yescharacteristic
326C22×C127#55711yescharacteristic
327C22×C127Q8211yescharacteristic
328C22×C127#55911yescharacteristic
329C4×C127—24no—
330C4×C127—28no—
331C4×C127—24no—
332C4×C127—42no—
333C4×C127—44no—
334C4×C127—42no—
335C4×C127—44no—
336C4×C127—42no—
337C4×C127—42no—
338C4×C127—82no—
339C4×C127#38518yes—
340#14017C12711yesmaximal, characteristic, direct product factor, Sylow
341C2×C127C2×#38511yescharacteristic
342C2×C127C4×C22⋊Q811yescharacteristic
343C2×C127#232311yescharacteristic
344C2×C127Q8×C4⋊C411yescharacteristic
345C2×C127#235111yescharacteristic
346C2×C127#236511yescharacteristic
347C2×C127#236711yescharacteristic
348C2×C127#240711yescharacteristic
349C2×C127#240911yescharacteristic
350C2×C127#244611yescharacteristic
351C2×C127#244811yescharacteristic
352C2×C127#245111yescharacteristic
353C2×C127#245311yescharacteristic
354C2×C127#258111yescharacteristic
355C2×C127#258211yescharacteristic
356C22×C4×Q8C2×C12711yescharacteristic
357C2×#391C2×C12711yescharacteristic
358C2×#391C2×C12711yescharacteristic
359C2×#389C2×C12711yescharacteristic
360C2×C4×C4⋊C4C2×C12711yescharacteristic
361#1444C2×C12712yes—
362#1442C2×C12712yes—
363#1436C2×C12712yes—
364#1436C2×C12712yes—
365C4⋊#95C2×C12711yescharacteristic
366C4⋊#95C2×C12711yescharacteristic
367C127#1401711yescharacteristic, direct product factor, Sylow
368C23×Q8C22×C12711yescharacteristic
369C2×C4×Q8—24no—
370C2×C4×Q8—24no—
371C2×C4×Q8—24no—
372C22×C4⋊C4C22×C12712yes—
373C22×C4⋊C4C22×C12711yescharacteristic
374C22×C4⋊C4C22×C12711yescharacteristic
375C22×C4⋊C4C22×C12712yes—
376C22×C4⋊C4C22×C12711yescharacteristic
377C22×C4⋊C4C22×C12711yescharacteristic
378C22×C4⋊C4C22×C12711yescharacteristic
379C22×C42C22×C12712yes—
380C22×C42C22×C12711yescharacteristic
381C22×C42C22×C12711yescharacteristic
382C22×C42C22×C12711yescharacteristic
383#391—24no—
384#391C4×C12718yescomplemented
385#389—24no—
386C4×C4⋊C4—24no—
387C2×#95C22×C12712yes—
388C2×#95C22×C12712yes—
389C2×#95C22×C12711yescharacteristic
390C2×#95C22×C12712yes—
391C2×#95C22×C12712yes—
392C2×#95C22×C12712yes—
393C2×#95C22×C12711yescharacteristic
394C2×#95C22×C12712yes—
395C2×#95C22×C12712yes—
396C2×#95C22×C12712yes—
397C2×#95C22×C12712yes—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8C2×C4×C12714yes—
403C22×Q8D4×C12714yes—
404C22×Q8Q8×C12714yes—
405C23×C4C23×C12712yes—
406C23×C4C23×C12712yes—
407C23×C4C23×C12711yescharacteristic
408C23×C4C23×C12712yes—
409C23×C4C23×C12711yescharacteristic
410C23×C4C23×C12711yescharacteristic
411C23×C4C23×C12711yescharacteristic
412C23×C4C23×C12712yes—
413C23×C4C23×C12711yescharacteristic
414C23×C4C23×C12711yescharacteristic
415C23×C4C23×C12711yescharacteristic
416C4×Q8—232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4C2×C4×C12714yes—
436C2×C4⋊C4D4×C12714yes—
437C2×C4⋊C4Q8×C12714yescomplemented
438C2×C42—24no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42C2×C4×C12714yes—
449C2×C42D4×C12714yes—
450#95—22no—
451#95—22no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—42no—
458#95—42no—
459#95C2×C4×C12718yes—
460#95C2×C4×C12718yes—
461C24C24×C12711yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8C4⋊C4×C127116yescomplemented
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4C22×C4×C12712yes—
525C22×C4C22×C4×C12714yes—
526C22×C4C22×C4×C12714yes—
527C22×C4C22×C4×C12712yes—
528C22×C4C22×C4×C12712yes—
529C22×C4C2×D4×C12714yes—
530C22×C4C2×D4×C12712yes—
531C22×C4C2×D4×C12714yes—
532C22×C4C2×D4×C12712yes—
533C22×C4C2×D4×C12712yes—
534C22×C4C2×D4×C12712yes—
535C22×C4C2×D4×C12712yes—
536C22×C4C2×Q8×C12712yes—
537C22×C4C2×Q8×C12714yes—
538C22×C4C2×Q8×C12712yes—
539C22×C4C2×Q8×C12712yes—
540C22×C4C2×Q8×C12712yes—
541C22×C4#41×C12712yes—
542C22×C4#41×C12712yes—
543C22×C4#41×C12712yes—
544C22×C4#41×C12712yes—
545C22×C4#41×C12712yes—
546C4⋊C4—28no—
547C4⋊C4—216no—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—48no—
552C4⋊C4—44no—
553C42—216no—
554C42—28no—
555C42—28no—
556C42—44no—
557C23C23×C4×C12711yescharacteristic
558C23C22×D4×C12711yescharacteristic
559C23C22×D4×C12711yescharacteristic
560C23C22×D4×C12711yescharacteristic
561C23C22×Q8×C12711yescharacteristic
562C23C22×Q8×C12711yescharacteristic
563C23C2×#41×C12711yescharacteristic
564C23C2×#41×C12711yescharacteristic
565C23C2×#41×C12711yescharacteristic
566C23C2×#41×C12711yescharacteristic
567C23C2×#41×C12711yescharacteristic
568C23H(5,𝔽2)×C12711yescharacteristic
569C232−1+4×C12711yescharacteristic
570C232−1+4×C12711yescharacteristic
571C232−1+4×C12711yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4C2×C4⋊C4×C12718yes—
641C2×C4C2×C4⋊C4×C12714yes—
642C2×C4C4×D4×C12714yes—
643C2×C4C4×D4×C12714yes—
644C2×C4C4×Q8×C12714yescomplemented
645C2×C4#120×C12714yes—
646C2×C4C22⋊Q8×C12714yes—
647C2×C4C22⋊Q8×C12714yes—
648C2×C4C22⋊Q8×C12714yes—
649C2×C4#123×C12714yes—
650C22C22×C4⋊C4×C12711yescharacteristic
651C22C2×C4×D4×C12711yescharacteristic
652C22C2×C4×D4×C12711yescharacteristic
653C22C2×C4×Q8×C12711yescharacteristic
654C22C4×#41×C12711yescharacteristic
655C22#519×C12711yescharacteristic
656C22#520×C12711yescharacteristic
657C22C2×#120×C12711yescharacteristic
658C22C2×C22⋊Q8×C12711yescharacteristic
659C22C2×C22⋊Q8×C12711yescharacteristic
660C22C2×C22⋊Q8×C12711yescharacteristic
661C22C2×#123×C12711yescharacteristic
662C22#525×C12711yescharacteristic
663C22#529×C12711yescharacteristic
664C22#533×C12711yescharacteristic
665C22#536×C12711yescharacteristic
666C22#537×C12711yescharacteristic
667C22#541×C12711yescharacteristic
668C22#542×C12711yescharacteristic
669C22#546×C12711yescharacteristic
670C22#547×C12711yescharacteristic
671C22#548×C12711yescharacteristic
672C22#548×C12711yescharacteristic
673C22#548×C12711yescharacteristic
674C22D4×Q8×C12711yescharacteristic
675C22D4×Q8×C12711yescharacteristic
676C22#550×C12711yescharacteristic
677C22#556×C12711yescharacteristic
678C22#556×C12711yescharacteristic
679C22#557×C12711yescharacteristic
680C22#557×C12711yescharacteristic
681C22#557×C12711yescharacteristic
682C22#557×C12711yescharacteristic
683C22Q82×C12711yescharacteristic
684C22#559×C12711yescharacteristic
685C4—24no—
686C4—28no—
687C4—24no—
688C4—42no—
689C4—44no—
690C4—42no—
691C4—44no—
692C4—42no—
693C4—42no—
694C4—82no—
695C4#385×C12718yes—
696C2C2×#385×C12711yescharacteristic
697C2C4×C22⋊Q8×C12711yescharacteristic
698C2C127×#232311yescharacteristic
699C2Q8×C4⋊C4×C12711yescharacteristic
700C2C127×#235111yescharacteristic
701C2C127×#236511yescharacteristic
702C2C127×#236711yescharacteristic
703C2C127×#240711yescharacteristic
704C2C127×#240911yescharacteristic
705C2C127×#244611yescharacteristic
706C2C127×#244811yescharacteristic
707C2C127×#245111yescharacteristic
708C2C127×#245311yescharacteristic
709C2C127×#258111yescharacteristic
710C2C127×#258211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
28. #391×C127C4semidirect
81. C2×C4⋊C4×C127Q8semidirect
112. C2×Q8×C127C4⋊C4semidirect
288. C2×C4×C127C4×Q8semidirect
340. #14017C127direct (N × H)
367. C127#14017direct (N × H)
384. #391C4×C127semidirect
437. C2×C4⋊C4Q8×C127semidirect
468. C2×Q8C4⋊C4×C127semidirect
644. C2×C4C4×Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1272
C2×#391×C1272
C2×#389×C1272
C2×C4×C4⋊C4×C1272
C127×#14442
C127×#14422
C127×#14362
C127×C4⋊#952
#14017127