Finite Group Databasebeta

← C127×#14197 #44577870

Subgroups — C127×#14197 #44577870

Order 32512.

1578 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C211yesmaximal, characteristic
2C2×#388×C127C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
4C127×#1443C211yesmaximal, characteristic, complemented
5C127×#1443C211yesmaximal, characteristic, complemented
6C127×#1440C211yesmaximal, characteristic
7C127×#1437C211yesmaximal, characteristic
8C127×#1436C211yesmaximal, characteristic, complemented
9C127×#1436C211yesmaximal, characteristic, complemented
10C127×#1436C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C127×#1434C211yesmaximal, characteristic, complemented
13C127×C22⋊#95C211yesmaximal, characteristic
14C127×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C127C211yesmaximal, characteristic, complemented
16C24×C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C42×C127C2211yescharacteristic
26C22×C42×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28C22×C42×C127C2211yescharacteristic
29#397×C127C418yescomplemented
30#388×C127—24no—
31C4×C22⋊C4×C127—24no—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
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
54C25×C127C2311yescharacteristic
55C23×C4×C127—22no—
56C23×C4×C127—22no—
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—41no—
61C23×C4×C127—41no—
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—41no—
80C2×C4⋊C4×C127—41no—
81C2×C4⋊C4×C127C2×C414yescomplemented
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—41no—
93C2×C22⋊C4×C127—41no—
94C2×C22⋊C4×C127—41no—
95C2×C22⋊C4×C127—41no—
96C2×C22⋊C4×C127C2×C414yes—
97C2×C22⋊C4×C127C2×C414yes—
98C2×C22⋊C4×C127C2×C414yes—
99C2×C22⋊C4×C127D414yes—
100C2×C42×C127—22no—
101C2×C42×C127—22no—
102C2×C42×C127—22no—
103C2×C42×C127—22no—
104C2×C42×C127—22no—
105C2×C42×C127—22no—
106C2×C42×C127—22no—
107C2×C42×C127—41no—
108C2×C42×C127—41no—
109C2×C42×C127—41no—
110C2×C42×C127—41no—
111C2×C42×C127—41no—
112#95×C127—22no—
113#95×C127—22no—
114#95×C127—22no—
115#95×C127—22no—
116#95×C127—22no—
117#95×C127—22no—
118#95×C127—22no—
119#95×C127—22no—
120#95×C127—22no—
121#95×C127—22no—
122#95×C127—22no—
123#95×C127—22no—
124#95×C127—22no—
125#95×C127—22no—
126#95×C127—41no—
127#95×C127—41no—
128#95×C127—41no—
129#95×C127—41no—
130#95×C127—41no—
131#95×C127C2×C414yescomplemented
132#95×C127C2×C414yescomplemented
133#95×C127C2×C414yescomplemented
134C24×C127—21no—
135C24×C127—21no—
136C24×C127—21no—
137C24×C127—21no—
138C24×C127—21no—
139C24×C127—21no—
140C24×C127—21no—
141C24×C127—21no—
142C24×C127—21no—
143C24×C127—21no—
144C24×C127—21no—
145C24×C127—21no—
146C24×C127C22×C412yes—
147C24×C127C2×D412yes—
148C24×C127#4112yes—
149C24×C127C2411yescharacteristic
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—28no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
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—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—21no—
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—44no—
234C22×C4×C127—44no—
235C22×C4×C127—44no—
236C22×C4×C127—44no—
237C22×C4×C127—44no—
238C22×C4×C127—44no—
239C22×C4×C127C22×C412yes—
240C22×C4×C127C22×C412yes—
241C22×C4×C127C22×C412yes—
242C22×C4×C127C22×C412yes—
243C22×C4×C127C22×C412yes—
244C22×C4×C127C22×C412yes—
245C22×C4×C127C2×D412yes—
246C22×C4×C127C2×D412yes—
247C22×C4×C127#4112yes—
248C22×C4×C127#4112yes—
249C22×C4×C127#4112yes—
250C22×C4×C127#4112yes—
251C22×C4×C127#4112yes—
252C22×C4×C127#4112yes—
253C22×C4×C127#4112yes—
254C22×C4×C127#4112yes—
255C4⋊C4×C127—44no—
256C4⋊C4×C127—44no—
257C22⋊C4×C127—28no—
258C22⋊C4×C127—28no—
259C22⋊C4×C127—28no—
260C22⋊C4×C127—44no—
261C22⋊C4×C127—44no—
262C22⋊C4×C127—44no—
263C42×C127—44no—
264C42×C127—44no—
265C42×C127—44no—
266C42×C127—44no—
267C23×C127—22no—
268C23×C127—22no—
269C23×C127—22no—
270C23×C127—22no—
271C23×C127—22no—
272C23×C127—22no—
273C23×C127—22no—
274C23×C127—22no—
275C23×C127—22no—
276C23×C127—22no—
277C23×C127—22no—
278C23×C127—22no—
279C23×C127—22no—
280C23×C127—22no—
281C23×C127—22no—
282C23×C127—22no—
283C23×C127—22no—
284C23×C127—22no—
285C23×C127—41no—
286C23×C127—41no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—41no—
290C23×C127—41no—
291C23×C127—41no—
292C23×C127—41no—
293C23×C127—41no—
294C23×C127—41no—
295C23×C127—41no—
296C23×C127—41no—
297C23×C127—41no—
298C23×C127—41no—
299C23×C127—41no—
300C23×C127—41no—
301C23×C127C4×D414yes—
302C23×C127C23×C411yescharacteristic
303C23×C127C22×D411yescharacteristic
304C23×C127C2×#4111yescharacteristic
305C23×C127C2×#4111yescharacteristic
306C23×C127C2×#4111yescharacteristic
307C23×C127C2×#4111yescharacteristic
308C23×C127C2×#4111yescharacteristic
309C23×C127C2×#4111yescharacteristic
310C23×C127C2×#4111yescharacteristic
311C23×C127C2×#4111yescharacteristic
312C23×C127C2×#4111yescharacteristic
313C23×C127H(5,𝔽2)11yescharacteristic
314C23×C127H(5,𝔽2)11yescharacteristic
315C23×C127H(5,𝔽2)11yescharacteristic
316C23×C1272−1+411yescharacteristic
317C2×C4×C127—22no—
318C2×C4×C127—22no—
319C2×C4×C127—22no—
320C2×C4×C127—22no—
321C2×C4×C127—22no—
322C2×C4×C127—22no—
323C2×C4×C127—22no—
324C2×C4×C127—22no—
325C2×C4×C127—22no—
326C2×C4×C127—22no—
327C2×C4×C127—22no—
328C2×C4×C127—22no—
329C2×C4×C127—22no—
330C2×C4×C127—22no—
331C2×C4×C127—22no—
332C2×C4×C127—22no—
333C2×C4×C127—22no—
334C2×C4×C127—22no—
335C2×C4×C127—22no—
336C2×C4×C127—22no—
337C2×C4×C127—22no—
338C2×C4×C127—22no—
339C2×C4×C127—22no—
340C2×C4×C127—22no—
341C2×C4×C127—22no—
342C2×C4×C127—22no—
343C2×C4×C127—22no—
344C2×C4×C127—22no—
345C2×C4×C127—22no—
346C2×C4×C127—22no—
347C2×C4×C127—22no—
348C2×C4×C127—22no—
349C2×C4×C127—22no—
350C2×C4×C127—22no—
351C2×C4×C127—22no—
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—416no—
360C2×C4×C127—41no—
361C2×C4×C127—41no—
362C2×C4×C127—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127—41no—
366C2×C4×C127—41no—
367C2×C4×C127—41no—
368C2×C4×C127—41no—
369C2×C4×C127—41no—
370C2×C4×C127—41no—
371C2×C4×C127—41no—
372C2×C4×C127—41no—
373C2×C4×C127—41no—
374C2×C4×C127—41no—
375C2×C4×C127—41no—
376C2×C4×C127—41no—
377C2×C4×C127—41no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
380C2×C4×C127—41no—
381C2×C4×C127—41no—
382C2×C4×C127—41no—
383C2×C4×C127—41no—
384C2×C4×C127—41no—
385C2×C4×C127—41no—
386C2×C4×C127—41no—
387C2×C4×C127—41no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
391C2×C4×C127—41no—
392C2×C4×C127—41no—
393C2×C4×C127—41no—
394C2×C4×C127—41no—
395C2×C4×C127—41no—
396C2×C4×C127—41no—
397C2×C4×C127—41no—
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#12314yes—
415C2×C4×C127#12614yes—
416C22×C127—24no—
417C22×C127—24no—
418C22×C127—24no—
419C22×C127—42no—
420C22×C127—42no—
421C22×C127—42no—
422C22×C127—42no—
423C22×C127—42no—
424C22×C127—42no—
425C22×C127—42no—
426C22×C127—42no—
427C22×C127—42no—
428C22×C127—42no—
429C22×C127—42no—
430C22×C127—42no—
431C22×C127C2×C4×D411yescharacteristic
432C22×C127C4×#4111yescharacteristic
433C22×C127C4×#4111yescharacteristic
434C22×C127C4×#4111yescharacteristic
435C22×C127C4×#4111yescharacteristic
436C22×C127#51811yescharacteristic
437C22×C127#52011yescharacteristic
438C22×C127C2×#12311yescharacteristic
439C22×C127#52511yescharacteristic
440C22×C127C2×#12611yescharacteristic
441C22×C127#52911yescharacteristic
442C22×C127#52911yescharacteristic
443C22×C127#52911yescharacteristic
444C22×C127#52911yescharacteristic
445C22×C127#52911yescharacteristic
446C22×C127#53811yescharacteristic
447C22×C127#53811yescharacteristic
448C22×C127#54211yescharacteristic
449C22×C127#54211yescharacteristic
450C22×C127#54611yescharacteristic
451C22×C127#54611yescharacteristic
452C22×C127#54611yescharacteristic
453C22×C127#54711yescharacteristic
454C22×C127#55111yescharacteristic
455C22×C127#55111yescharacteristic
456C22×C127#55111yescharacteristic
457C22×C127#55211yescharacteristic
458C22×C127#55211yescharacteristic
459C22×C127#55311yescharacteristic
460C22×C127#55311yescharacteristic
461C22×C127#55311yescharacteristic
462C22×C127#55311yescharacteristic
463C22×C127#55311yescharacteristic
464C22×C127#55611yescharacteristic
465C22×C127#55911yescharacteristic
466C4×C127—24no—
467C4×C127—24no—
468C4×C127—42no—
469C4×C127—42no—
470C4×C127—42no—
471C4×C127—42no—
472C4×C127—42no—
473C4×C127—42no—
474C4×C127—42no—
475C4×C127—42no—
476C4×C127—42no—
477C4×C127—42no—
478C4×C127—81no—
479C4×C127—81no—
480#14197C12711yesmaximal, characteristic, direct product factor, Sylow
481C2×C127—44no—
482C2×C127C4×#12311yescharacteristic
483C2×C127C4×#12611yescharacteristic
484C2×C127#233711yescharacteristic
485C2×C127#235911yescharacteristic
486C2×C127#236411yescharacteristic
487C2×C127#237311yescharacteristic
488C2×C127#237411yescharacteristic
489C2×C127#244411yescharacteristic
490C2×C127#244711yescharacteristic
491C2×C127#247011yescharacteristic
492C2×C127#248011yescharacteristic
493C2×C127#249411yescharacteristic
494C2×C127#253011yescharacteristic
495C2×C127#257811yescharacteristic
496C2×C127#259511yescharacteristic
497C2×#397C2×C12711yescharacteristic
498C2×#388C2×C12711yescharacteristic
499C2×C4×C22⋊C4C2×C12711yescharacteristic
500#1443C2×C12711yescharacteristic, complemented
501#1443C2×C12711yescharacteristic, complemented
502#1440C2×C12711yescharacteristic
503#1437C2×C12711yescharacteristic
504#1436C2×C12711yescharacteristic, complemented
505#1436C2×C12711yescharacteristic, complemented
506#1436C2×C12711yescharacteristic, complemented
507#1436C2×C12711yescharacteristic, complemented
508#1434C2×C12711yescharacteristic, complemented
509C22⋊#95C2×C12711yescharacteristic
510C22⋊#95C2×C12711yescharacteristic
511C4×#95C2×C12711yescharacteristic, complemented
512C127#1419711yescharacteristic, direct product factor, Sylow
513C24×C4C22×C12711yescharacteristic
514C22×C4⋊C4C22×C12711yescharacteristic
515C22×C4⋊C4C22×C12711yescharacteristic
516C22×C22⋊C4C22×C12711yescharacteristic
517C22×C22⋊C4C22×C12711yescharacteristic
518C22×C22⋊C4C22×C12711yescharacteristic
519C22×C22⋊C4C22×C12711yescharacteristic
520C22×C22⋊C4C22×C12711yescharacteristic
521C22×C22⋊C4C22×C12711yescharacteristic
522C22×C42C22×C12711yescharacteristic
523C22×C42C22×C12711yescharacteristic
524C22×C42C22×C12711yescharacteristic
525C22×C42C22×C12711yescharacteristic
526#397C4×C12718yescomplemented
527#388—24no—
528C4×C22⋊C4—24no—
529C2×#95C22×C12711yescharacteristic
530C2×#95C22×C12711yescharacteristic
531C2×#95C22×C12711yescharacteristic
532C2×#95C22×C12711yescharacteristic
533C2×#95C22×C12711yescharacteristic
534C2×#95C22×C12711yescharacteristic
535C2×#95C22×C12711yescharacteristic
536C2×#95C22×C12711yescharacteristic
537C2×#95C22×C12711yescharacteristic
538C2×#95C22×C12711yescharacteristic
539C2×#95C22×C12711yescharacteristic
540C2×#95C22×C12711yescharacteristic
541C2×#95C22×C12711yescharacteristic
542C2×#95C22×C12711yescharacteristic
543C2×#95C22×C12711yescharacteristic
544C2×#95C22×C12711yescharacteristic
545C2×#95C22×C12711yescharacteristic
546C2×#95C22×C12711yescharacteristic
547C2×#95C22×C12711yescharacteristic
548C2×#95C22×C12711yescharacteristic
549C2×#95C22×C12711yescharacteristic
550C2×#95C22×C12711yescharacteristic
551C25C23×C12711yescharacteristic
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—41no—
558C23×C4—41no—
559C23×C4C23×C12711yescharacteristic
560C23×C4C23×C12711yescharacteristic
561C23×C4C23×C12711yescharacteristic
562C23×C4C23×C12711yescharacteristic
563C23×C4C23×C12711yescharacteristic
564C23×C4C23×C12711yescharacteristic
565C23×C4C23×C12711yescharacteristic
566C23×C4C23×C12711yescharacteristic
567C23×C4C23×C12711yescharacteristic
568C23×C4C23×C12711yescharacteristic
569C23×C4C23×C12711yescharacteristic
570C23×C4C23×C12711yescharacteristic
571C23×C4C23×C12711yescharacteristic
572C23×C4C23×C12711yescharacteristic
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4C2×C4×C12714yescomplemented
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4C2×C4×C12714yes—
594C2×C22⋊C4C2×C4×C12714yes—
595C2×C22⋊C4C2×C4×C12714yes—
596C2×C22⋊C4D4×C12714yes—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42—41no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95C2×C4×C12714yescomplemented
629#95C2×C4×C12714yescomplemented
630#95C2×C4×C12714yescomplemented
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C22×C4×C12712yes—
644C24C2×D4×C12712yes—
645C24#41×C12712yes—
646C24C24×C12711yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—28no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
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—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4C22×C4×C12712yes—
737C22×C4C22×C4×C12712yes—
738C22×C4C22×C4×C12712yes—
739C22×C4C22×C4×C12712yes—
740C22×C4C22×C4×C12712yes—
741C22×C4C22×C4×C12712yes—
742C22×C4C2×D4×C12712yes—
743C22×C4C2×D4×C12712yes—
744C22×C4#41×C12712yes—
745C22×C4#41×C12712yes—
746C22×C4#41×C12712yes—
747C22×C4#41×C12712yes—
748C22×C4#41×C12712yes—
749C22×C4#41×C12712yes—
750C22×C4#41×C12712yes—
751C22×C4#41×C12712yes—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C42—44no—
761C42—44no—
762C42—44no—
763C42—44no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23C4×D4×C12714yes—
799C23C23×C4×C12711yescharacteristic
800C23C22×D4×C12711yescharacteristic
801C23C2×#41×C12711yescharacteristic
802C23C2×#41×C12711yescharacteristic
803C23C2×#41×C12711yescharacteristic
804C23C2×#41×C12711yescharacteristic
805C23C2×#41×C12711yescharacteristic
806C23C2×#41×C12711yescharacteristic
807C23C2×#41×C12711yescharacteristic
808C23C2×#41×C12711yescharacteristic
809C23C2×#41×C12711yescharacteristic
810C23H(5,𝔽2)×C12711yescharacteristic
811C23H(5,𝔽2)×C12711yescharacteristic
812C23H(5,𝔽2)×C12711yescharacteristic
813C232−1+4×C12711yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—416no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4#123×C12714yes—
912C2×C4#126×C12714yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×C4×D4×C12711yescharacteristic
929C22C4×#41×C12711yescharacteristic
930C22C4×#41×C12711yescharacteristic
931C22C4×#41×C12711yescharacteristic
932C22C4×#41×C12711yescharacteristic
933C22#518×C12711yescharacteristic
934C22#520×C12711yescharacteristic
935C22C2×#123×C12711yescharacteristic
936C22#525×C12711yescharacteristic
937C22C2×#126×C12711yescharacteristic
938C22#529×C12711yescharacteristic
939C22#529×C12711yescharacteristic
940C22#529×C12711yescharacteristic
941C22#529×C12711yescharacteristic
942C22#529×C12711yescharacteristic
943C22#538×C12711yescharacteristic
944C22#538×C12711yescharacteristic
945C22#542×C12711yescharacteristic
946C22#542×C12711yescharacteristic
947C22#546×C12711yescharacteristic
948C22#546×C12711yescharacteristic
949C22#546×C12711yescharacteristic
950C22#547×C12711yescharacteristic
951C22#551×C12711yescharacteristic
952C22#551×C12711yescharacteristic
953C22#551×C12711yescharacteristic
954C22#552×C12711yescharacteristic
955C22#552×C12711yescharacteristic
956C22#553×C12711yescharacteristic
957C22#553×C12711yescharacteristic
958C22#553×C12711yescharacteristic
959C22#553×C12711yescharacteristic
960C22#553×C12711yescharacteristic
961C22#556×C12711yescharacteristic
962C22#559×C12711yescharacteristic
963C4—24no—
964C4—24no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—81no—
977C2—44no—
978C2C4×#123×C12711yescharacteristic
979C2C4×#126×C12711yescharacteristic
980C2C127×#233711yescharacteristic
981C2C127×#235911yescharacteristic
982C2C127×#236411yescharacteristic
983C2C127×#237311yescharacteristic
984C2C127×#237411yescharacteristic
985C2C127×#244411yescharacteristic
986C2C127×#244711yescharacteristic
987C2C127×#247011yescharacteristic
988C2C127×#248011yescharacteristic
989C2C127×#249411yescharacteristic
990C2C127×#253011yescharacteristic
991C2C127×#257811yescharacteristic
992C2C127×#259511yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1443C2semidirect
5. C127×#1443C2semidirect
8. C127×#1436C2semidirect
9. C127×#1436C2semidirect
10. C127×#1436C2semidirect
11. C127×#1436C2semidirect
12. C127×#1434C2semidirect
15. C4×#95×C127C2semidirect
29. #397×C127C4semidirect
81. C2×C4⋊C4×C127C2×C4semidirect
131. #95×C127C2×C4semidirect
132. #95×C127C2×C4semidirect
133. #95×C127C2×C4semidirect
480. #14197C127direct (N × H)
500. #1443C2×C127semidirect
501. #1443C2×C127semidirect
504. #1436C2×C127semidirect
505. #1436C2×C127semidirect
506. #1436C2×C127semidirect
507. #1436C2×C127semidirect
508. #1434C2×C127semidirect
511. C4×#95C2×C127semidirect
512. C127#14197direct (N × H)
526. #397C4×C127semidirect
578. C2×C4⋊C4C2×C4×C127semidirect
628. #95C2×C4×C127semidirect
629. #95C2×C4×C127semidirect
630. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1272
C2×#388×C1272
C2×C4×C22⋊C4×C1272
C127×#14432
C127×#14402
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
C4×#95×C1272
#14197127