Finite Group Databasebeta

← C127×#15614 #44579287

Subgroups — C127×#15614 #44579287

Order 32512.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic
2C2×#398×C127C211yesmaximal, characteristic, complemented
3C2×#396×C127C211yesmaximal, characteristic
4C2×#395×C127C211yesmaximal, characteristic, complemented
5C2×#389×C127C211yesmaximal, characteristic, complemented
6C2×#385×C127C211yesmaximal, characteristic
7C127×#1446C211yesmaximal, characteristic, complemented
8C127×#1444C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1441C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic
12C127×#1439C211yesmaximal, characteristic
13C127×#1437C211yesmaximal, characteristic
14C127×C4⋊#95C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C2×C22⋊Q8×C127—24no—
19C2×C22⋊Q8×C127—24no—
20C2×C22⋊Q8×C127—24no—
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C4⋊C4×C127C2211yescharacteristic
28C22×C4⋊C4×C127C2211yescharacteristic
29C22×C4⋊C4×C127C2211yescharacteristic
30C22×C4⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic
36C22×C22⋊C4×C127C2211yescharacteristic
37C22×C42×C127C2211yescharacteristic
38#398×C127—24no—
39#396×C127—24no—
40#395×C127—24no—
41#389×C127—24no—
42#385×C127—24no—
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C25×C127C2311yescharacteristic
60C22×Q8×C127—22no—
61C22×Q8×C127—22no—
62C22×Q8×C127—22no—
63C22×Q8×C127—22no—
64C22×Q8×C127—22no—
65C22×Q8×C127—41no—
66C22×Q8×C127—41no—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—22no—
71C23×C4×C127—22no—
72C23×C4×C127—41no—
73C23×C4×C127—41no—
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C23×C4×C127C2311yescharacteristic
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2311yescharacteristic
88C22⋊Q8×C127—232no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—22no—
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—22no—
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—22no—
97C2×C4⋊C4×C127—22no—
98C2×C4⋊C4×C127—22no—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127—22no—
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127—22no—
107C2×C4⋊C4×C127—22no—
108C2×C4⋊C4×C127—22no—
109C2×C4⋊C4×C127—22no—
110C2×C4⋊C4×C127—22no—
111C2×C4⋊C4×C127—41no—
112C2×C4⋊C4×C127—41no—
113C2×C4⋊C4×C127—41no—
114C2×C4⋊C4×C127—41no—
115C2×C4⋊C4×C127—41no—
116C2×C4⋊C4×C127D414yes—
117C2×C4⋊C4×C127D414yes—
118C2×C4⋊C4×C127D414yes—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C22⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—22no—
124C2×C22⋊C4×C127—22no—
125C2×C22⋊C4×C127—22no—
126C2×C22⋊C4×C127—22no—
127C2×C22⋊C4×C127—22no—
128C2×C22⋊C4×C127—22no—
129C2×C22⋊C4×C127—22no—
130C2×C22⋊C4×C127—41no—
131C2×C22⋊C4×C127—41no—
132C2×C22⋊C4×C127—41no—
133C2×C22⋊C4×C127—41no—
134C2×C22⋊C4×C127D414yes—
135C2×C22⋊C4×C127Q814yescomplemented
136C2×C22⋊C4×C127Q814yescomplemented
137C2×C42×C127—22no—
138C2×C42×C127—22no—
139C2×C42×C127—41no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—22no—
146#95×C127—22no—
147#95×C127—22no—
148#95×C127—22no—
149#95×C127—22no—
150#95×C127—22no—
151#95×C127—22no—
152#95×C127—41no—
153#95×C127—41no—
154#95×C127—41no—
155#95×C127—41no—
156C24×C127—21no—
157C24×C127—21no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127C2×D412yes—
169C24×C127C2×Q812yes—
170C24×C127C2×Q812yes—
171C24×C127C2411yescharacteristic
172C2×Q8×C127—28no—
173C2×Q8×C127—44no—
174C2×Q8×C127—44no—
175C2×Q8×C127—44no—
176C2×Q8×C127—44no—
177C2×Q8×C127—44no—
178C2×Q8×C127—44no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—28no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—44no—
261C22×C4×C127—44no—
262C22×C4×C127—44no—
263C22×C4×C127—44no—
264C22×C4×C127—44no—
265C22×C4×C127—44no—
266C22×C4×C127C2×D412yes—
267C22×C4×C127C2×D412yes—
268C22×C4×C127C2×D412yes—
269C22×C4×C127C2×D412yes—
270C22×C4×C127C2×D412yes—
271C22×C4×C127C2×D412yes—
272C22×C4×C127C2×D412yes—
273C22×C4×C127C2×D412yes—
274C22×C4×C127C2×D412yes—
275C22×C4×C127C2×D412yes—
276C22×C4×C127C2×D412yes—
277C22×C4×C127C2×Q812yes—
278C22×C4×C127C2×Q812yes—
279C22×C4×C127C2×Q812yes—
280C22×C4×C127C2×Q812yes—
281C22×C4×C127#4112yes—
282C22×C4×C127#4112yes—
283C22×C4×C127#4112yes—
284C4⋊C4×C127—28no—
285C4⋊C4×C127—28no—
286C4⋊C4×C127—28no—
287C4⋊C4×C127—28no—
288C4⋊C4×C127—44no—
289C4⋊C4×C127—44no—
290C4⋊C4×C127—44no—
291C4⋊C4×C127—44no—
292C4⋊C4×C127—44no—
293C4⋊C4×C127—44no—
294C22⋊C4×C127—28no—
295C22⋊C4×C127—28no—
296C22⋊C4×C127—28no—
297C22⋊C4×C127—44no—
298C22⋊C4×C127—44no—
299C22⋊C4×C127—44no—
300C42×C127—44no—
301C23×C127—22no—
302C23×C127—22no—
303C23×C127—22no—
304C23×C127—22no—
305C23×C127—22no—
306C23×C127—22no—
307C23×C127—22no—
308C23×C127—22no—
309C23×C127—22no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—22no—
313C23×C127—22no—
314C23×C127—22no—
315C23×C127—22no—
316C23×C127—22no—
317C23×C127—22no—
318C23×C127—22no—
319C23×C127—41no—
320C23×C127—41no—
321C23×C127—41no—
322C23×C127—41no—
323C23×C127—41no—
324C23×C127—41no—
325C23×C127—41no—
326C23×C127—41no—
327C23×C127—41no—
328C23×C127—41no—
329C23×C127—41no—
330C23×C127—41no—
331C23×C127—41no—
332C23×C127—41no—
333C23×C127—41no—
334C23×C127—41no—
335C23×C127C4⋊Q814yes—
336C23×C127C22×D411yescharacteristic
337C23×C127C22×D411yescharacteristic
338C23×C127C22×D411yescharacteristic
339C23×C127C22×D411yescharacteristic
340C23×C127C22×Q811yescharacteristic
341C23×C127C22×Q811yescharacteristic
342C23×C127C2×#4111yescharacteristic
343C23×C127C2×#4111yescharacteristic
344C23×C127C2×#4111yescharacteristic
345C23×C127H(5,𝔽2)11yescharacteristic
346C23×C127H(5,𝔽2)11yescharacteristic
347C23×C127H(5,𝔽2)11yescharacteristic
348C23×C1272−1+411yescharacteristic
349C23×C1272−1+411yescharacteristic
350C23×C1272−1+411yescharacteristic
351Q8×C127—416no—
352C2×C4×C127—22no—
353C2×C4×C127—22no—
354C2×C4×C127—22no—
355C2×C4×C127—22no—
356C2×C4×C127—22no—
357C2×C4×C127—22no—
358C2×C4×C127—22no—
359C2×C4×C127—22no—
360C2×C4×C127—22no—
361C2×C4×C127—22no—
362C2×C4×C127—22no—
363C2×C4×C127—22no—
364C2×C4×C127—22no—
365C2×C4×C127—22no—
366C2×C4×C127—22no—
367C2×C4×C127—22no—
368C2×C4×C127—22no—
369C2×C4×C127—22no—
370C2×C4×C127—22no—
371C2×C4×C127—22no—
372C2×C4×C127—22no—
373C2×C4×C127—22no—
374C2×C4×C127—22no—
375C2×C4×C127—22no—
376C2×C4×C127—22no—
377C2×C4×C127—22no—
378C2×C4×C127—22no—
379C2×C4×C127—22no—
380C2×C4×C127—22no—
381C2×C4×C127—22no—
382C2×C4×C127—22no—
383C2×C4×C127—22no—
384C2×C4×C127—22no—
385C2×C4×C127—22no—
386C2×C4×C127—22no—
387C2×C4×C127—22no—
388C2×C4×C127—22no—
389C2×C4×C127—22no—
390C2×C4×C127—22no—
391C2×C4×C127—22no—
392C2×C4×C127—22no—
393C2×C4×C127—22no—
394C2×C4×C127—22no—
395C2×C4×C127—22no—
396C2×C4×C127—22no—
397C2×C4×C127—416no—
398C2×C4×C127—41no—
399C2×C4×C127—41no—
400C2×C4×C127—41no—
401C2×C4×C127—41no—
402C2×C4×C127—41no—
403C2×C4×C127—41no—
404C2×C4×C127—41no—
405C2×C4×C127—41no—
406C2×C4×C127—41no—
407C2×C4×C127—41no—
408C2×C4×C127—41no—
409C2×C4×C127—41no—
410C2×C4×C127—41no—
411C2×C4×C127—41no—
412C2×C4×C127—41no—
413C2×C4×C127—41no—
414C2×C4×C127—41no—
415C2×C4×C127—41no—
416C2×C4×C127—41no—
417C2×C4×C127—41no—
418C2×C4×C127—41no—
419C2×C4×C127—41no—
420C2×C4×C127—41no—
421C2×C4×C127—41no—
422C2×C4×C127—41no—
423C2×C4×C127—41no—
424C2×C4×C127—41no—
425C2×C4×C127—41no—
426C2×C4×C127—41no—
427C2×C4×C127—41no—
428C2×C4×C127—41no—
429C2×C4×C127—41no—
430C2×C4×C127—41no—
431C2×C4×C127—41no—
432C2×C4×C127—41no—
433C2×C4×C127—41no—
434C2×C4×C127—41no—
435C2×C4×C127—41no—
436C2×C4×C127—41no—
437C2×C4×C127—41no—
438C2×C4×C127—41no—
439C2×C4×C127—41no—
440C2×C4×C127—41no—
441C2×C4×C127—41no—
442C2×C4×C127—41no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127#12014yes—
449C2×C4×C127#12114yes—
450C2×C4×C127C22⋊Q814yescomplemented
451C22×C127—24no—
452C22×C127—24no—
453C22×C127—24no—
454C22×C127—42no—
455C22×C127—42no—
456C22×C127—42no—
457C22×C127—42no—
458C22×C127—42no—
459C22×C127—42no—
460C22×C127—42no—
461C22×C127—42no—
462C22×C127—42no—
463C22×C127—42no—
464C22×C127—42no—
465C22×C127—42no—
466C22×C127C2×#12011yescharacteristic
467C22×C127C2×#12111yescharacteristic
468C22×C127C2×C22⋊Q811yescharacteristic
469C22×C127C2×C4⋊Q811yescharacteristic
470C22×C127#53211yescharacteristic
471C22×C127#53311yescharacteristic
472C22×C127#53511yescharacteristic
473C22×C127#53611yescharacteristic
474C22×C127#53711yescharacteristic
475C22×C127#53711yescharacteristic
476C22×C127#53911yescharacteristic
477C22×C127#54111yescharacteristic
478C22×C127#54211yescharacteristic
479C22×C127#54311yescharacteristic
480C22×C127#54411yescharacteristic
481C22×C127D4211yescharacteristic
482C22×C127D4211yescharacteristic
483C22×C127#54611yescharacteristic
484C22×C127#54611yescharacteristic
485C22×C127#54611yescharacteristic
486C22×C127#54611yescharacteristic
487C22×C127#54711yescharacteristic
488C22×C127#54711yescharacteristic
489C22×C127#54811yescharacteristic
490C22×C127D4×Q811yescharacteristic
491C22×C127D4×Q811yescharacteristic
492C22×C127D4×Q811yescharacteristic
493C22×C127D4×Q811yescharacteristic
494C22×C127D4×Q811yescharacteristic
495C22×C127#55211yescharacteristic
496C22×C127#55411yescharacteristic
497C22×C127#55411yescharacteristic
498C22×C127#55411yescharacteristic
499C22×C127#56211yescharacteristic
500C22×C127#56311yescharacteristic
501C4×C127—24no—
502C4×C127—24no—
503C4×C127—24no—
504C4×C127—42no—
505C4×C127—42no—
506C4×C127—42no—
507C4×C127—42no—
508C4×C127—42no—
509C4×C127—42no—
510C4×C127—42no—
511C4×C127—42no—
512C4×C127—42no—
513C4×C127—81no—
514C4×C127—81no—
515#15614C12711yesmaximal, characteristic, direct product factor, Sylow
516C2×C127—44no—
517C2×C127#240811yescharacteristic
518C2×C127#241711yescharacteristic
519C2×C127#242911yescharacteristic
520C2×C127#243011yescharacteristic
521C2×C127#243411yescharacteristic
522C2×C127#244011yescharacteristic
523C2×C127#245211yescharacteristic
524C2×C127#254911yescharacteristic
525C2×C127#255611yescharacteristic
526C2×C127#268111yescharacteristic
527C2×C127#268311yescharacteristic
528C2×C127#269211yescharacteristic
529C2×C127#269811yescharacteristic
530C2×C127#270411yescharacteristic
531C2×C127#272011yescharacteristic
532C22×C22⋊Q8C2×C12711yescharacteristic
533C2×#398C2×C12711yescharacteristic, complemented
534C2×#396C2×C12711yescharacteristic
535C2×#395C2×C12711yescharacteristic, complemented
536C2×#389C2×C12711yescharacteristic, complemented
537C2×#385C2×C12711yescharacteristic
538#1446C2×C12711yescharacteristic, complemented
539#1444C2×C12711yescharacteristic, complemented
540#1441C2×C12711yescharacteristic, complemented
541#1441C2×C12711yescharacteristic, complemented
542#1439C2×C12711yescharacteristic
543#1439C2×C12711yescharacteristic
544#1437C2×C12711yescharacteristic
545C4⋊#95C2×C12711yescharacteristic, complemented
546C22⋊#95C2×C12711yescharacteristic
547C127#1561411yescharacteristic, direct product factor, Sylow
548C23×Q8C22×C12711yescharacteristic
549C24×C4C22×C12711yescharacteristic
550C2×C22⋊Q8—24no—
551C2×C22⋊Q8—24no—
552C2×C22⋊Q8—24no—
553C22×C4⋊C4C22×C12711yescharacteristic
554C22×C4⋊C4C22×C12711yescharacteristic
555C22×C4⋊C4C22×C12711yescharacteristic
556C22×C4⋊C4C22×C12711yescharacteristic
557C22×C4⋊C4C22×C12711yescharacteristic
558C22×C4⋊C4C22×C12711yescharacteristic
559C22×C4⋊C4C22×C12711yescharacteristic
560C22×C4⋊C4C22×C12711yescharacteristic
561C22×C4⋊C4C22×C12711yescharacteristic
562C22×C4⋊C4C22×C12711yescharacteristic
563C22×C22⋊C4C22×C12711yescharacteristic
564C22×C22⋊C4C22×C12711yescharacteristic
565C22×C22⋊C4C22×C12711yescharacteristic
566C22×C22⋊C4C22×C12711yescharacteristic
567C22×C22⋊C4C22×C12711yescharacteristic
568C22×C22⋊C4C22×C12711yescharacteristic
569C22×C42C22×C12711yescharacteristic
570#398—24no—
571#396—24no—
572#395—24no—
573#389—24no—
574#385—24no—
575C2×#95C22×C12711yescharacteristic
576C2×#95C22×C12711yescharacteristic
577C2×#95C22×C12711yescharacteristic
578C2×#95C22×C12711yescharacteristic
579C2×#95C22×C12711yescharacteristic
580C2×#95C22×C12711yescharacteristic
581C2×#95C22×C12711yescharacteristic
582C2×#95C22×C12711yescharacteristic
583C2×#95C22×C12711yescharacteristic
584C2×#95C22×C12711yescharacteristic
585C2×#95C22×C12711yescharacteristic
586C2×#95C22×C12711yescharacteristic
587C2×#95C22×C12711yescharacteristic
588C2×#95C22×C12711yescharacteristic
589C2×#95C22×C12711yescharacteristic
590C2×#95C22×C12711yescharacteristic
591C25C23×C12711yescharacteristic
592C22×Q8—22no—
593C22×Q8—22no—
594C22×Q8—22no—
595C22×Q8—22no—
596C22×Q8—22no—
597C22×Q8—41no—
598C22×Q8—41no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—41no—
605C23×C4—41no—
606C23×C4C23×C12711yescharacteristic
607C23×C4C23×C12711yescharacteristic
608C23×C4C23×C12711yescharacteristic
609C23×C4C23×C12711yescharacteristic
610C23×C4C23×C12711yescharacteristic
611C23×C4C23×C12711yescharacteristic
612C23×C4C23×C12711yescharacteristic
613C23×C4C23×C12711yescharacteristic
614C23×C4C23×C12711yescharacteristic
615C23×C4C23×C12711yescharacteristic
616C23×C4C23×C12711yescharacteristic
617C23×C4C23×C12711yescharacteristic
618C23×C4C23×C12711yescharacteristic
619C23×C4C23×C12711yescharacteristic
620C22⋊Q8—232no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4D4×C12714yes—
649C2×C4⋊C4D4×C12714yes—
650C2×C4⋊C4D4×C12714yes—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4D4×C12714yes—
667C2×C22⋊C4Q8×C12714yescomplemented
668C2×C22⋊C4Q8×C12714yescomplemented
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—41no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24C2×D4×C12712yes—
701C24C2×Q8×C12712yes—
702C24C2×Q8×C12712yes—
703C24C24×C12711yescharacteristic
704C2×Q8—28no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—28no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4C2×D4×C12712yes—
799C22×C4C2×D4×C12712yes—
800C22×C4C2×D4×C12712yes—
801C22×C4C2×D4×C12712yes—
802C22×C4C2×D4×C12712yes—
803C22×C4C2×D4×C12712yes—
804C22×C4C2×D4×C12712yes—
805C22×C4C2×D4×C12712yes—
806C22×C4C2×D4×C12712yes—
807C22×C4C2×D4×C12712yes—
808C22×C4C2×D4×C12712yes—
809C22×C4C2×Q8×C12712yes—
810C22×C4C2×Q8×C12712yes—
811C22×C4C2×Q8×C12712yes—
812C22×C4C2×Q8×C12712yes—
813C22×C4#41×C12712yes—
814C22×C4#41×C12712yes—
815C22×C4#41×C12712yes—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C42—44no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23C4⋊Q8×C12714yes—
868C23C22×D4×C12711yescharacteristic
869C23C22×D4×C12711yescharacteristic
870C23C22×D4×C12711yescharacteristic
871C23C22×D4×C12711yescharacteristic
872C23C22×Q8×C12711yescharacteristic
873C23C22×Q8×C12711yescharacteristic
874C23C2×#41×C12711yescharacteristic
875C23C2×#41×C12711yescharacteristic
876C23C2×#41×C12711yescharacteristic
877C23H(5,𝔽2)×C12711yescharacteristic
878C23H(5,𝔽2)×C12711yescharacteristic
879C23H(5,𝔽2)×C12711yescharacteristic
880C232−1+4×C12711yescharacteristic
881C232−1+4×C12711yescharacteristic
882C232−1+4×C12711yescharacteristic
883Q8—416no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—416no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4#120×C12714yes—
981C2×C4#121×C12714yes—
982C2×C4C22⋊Q8×C12714yescomplemented
983C22—24no—
984C22—24no—
985C22—24no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22C2×#120×C12711yescharacteristic
999C22C2×#121×C12711yescharacteristic
1000C22C2×C22⋊Q8×C12711yescharacteristic
1001C22C2×C4⋊Q8×C12711yescharacteristic
1002C22#532×C12711yescharacteristic
1003C22#533×C12711yescharacteristic
1004C22#535×C12711yescharacteristic
1005C22#536×C12711yescharacteristic
1006C22#537×C12711yescharacteristic
1007C22#537×C12711yescharacteristic
1008C22#539×C12711yescharacteristic
1009C22#541×C12711yescharacteristic
1010C22#542×C12711yescharacteristic
1011C22#543×C12711yescharacteristic
1012C22#544×C12711yescharacteristic
1013C22D42×C12711yescharacteristic
1014C22D42×C12711yescharacteristic
1015C22#546×C12711yescharacteristic
1016C22#546×C12711yescharacteristic
1017C22#546×C12711yescharacteristic
1018C22#546×C12711yescharacteristic
1019C22#547×C12711yescharacteristic
1020C22#547×C12711yescharacteristic
1021C22#548×C12711yescharacteristic
1022C22D4×Q8×C12711yescharacteristic
1023C22D4×Q8×C12711yescharacteristic
1024C22D4×Q8×C12711yescharacteristic
1025C22D4×Q8×C12711yescharacteristic
1026C22D4×Q8×C12711yescharacteristic
1027C22#552×C12711yescharacteristic
1028C22#554×C12711yescharacteristic
1029C22#554×C12711yescharacteristic
1030C22#554×C12711yescharacteristic
1031C22#562×C12711yescharacteristic
1032C22#563×C12711yescharacteristic
1033C4—24no—
1034C4—24no—
1035C4—24no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—81no—
1047C2—44no—
1048C2C127×#240811yescharacteristic
1049C2C127×#241711yescharacteristic
1050C2C127×#242911yescharacteristic
1051C2C127×#243011yescharacteristic
1052C2C127×#243411yescharacteristic
1053C2C127×#244011yescharacteristic
1054C2C127×#245211yescharacteristic
1055C2C127×#254911yescharacteristic
1056C2C127×#255611yescharacteristic
1057C2C127×#268111yescharacteristic
1058C2C127×#268311yescharacteristic
1059C2C127×#269211yescharacteristic
1060C2C127×#269811yescharacteristic
1061C2C127×#270411yescharacteristic
1062C2C127×#272011yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#398×C127C2semidirect
4. C2×#395×C127C2semidirect
5. C2×#389×C127C2semidirect
7. C127×#1446C2semidirect
8. C127×#1444C2semidirect
9. C127×#1441C2semidirect
10. C127×#1441C2semidirect
14. C127×C4⋊#95C2semidirect
135. C2×C22⋊C4×C127Q8semidirect
136. C2×C22⋊C4×C127Q8semidirect
450. C2×C4×C127C22⋊Q8semidirect
515. #15614C127direct (N × H)
533. C2×#398C2×C127semidirect
535. C2×#395C2×C127semidirect
536. C2×#389C2×C127semidirect
538. #1446C2×C127semidirect
539. #1444C2×C127semidirect
540. #1441C2×C127semidirect
541. #1441C2×C127semidirect
545. C4⋊#95C2×C127semidirect
547. C127#15614direct (N × H)
667. C2×C22⋊C4Q8×C127semidirect
668. C2×C22⋊C4Q8×C127semidirect
982. C2×C4C22⋊Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C2×#398×C1272
C2×#396×C1272
C2×#395×C1272
C2×#389×C1272
C2×#385×C1272
C127×#14462
C127×#14442
C127×#14412
C127×#14392
C127×#14372
C127×C4⋊#952
C127×C22⋊#952
#15614127