Finite Group Databasebeta

← C127×#21489 #44585162

Subgroups — C127×#21489 #44585162

Order 32512.

1116 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C127C211yesmaximal, characteristic, complemented
2C2×#435×C127C211yesmaximal, characteristic, complemented
3C2×C8×D4×C127C211yesmaximal, characteristic, complemented
4C22×#97×C127C211yesmaximal, characteristic, complemented
5C4×#121×C127C211yesmaximal, characteristic
6C127×#1955C211yesmaximal, characteristic, complemented
7C127×#1940C211yesmaximal, characteristic, complemented
8C127×#1924C211yesmaximal, characteristic, complemented
9C127×#1924C211yesmaximal, characteristic, complemented
10C127×#1869C211yesmaximal, characteristic, complemented
11C127×#1869C211yesmaximal, characteristic, complemented
12C127×#1797C211yesmaximal, characteristic, complemented
13C127×#1771C211yesmaximal, characteristic, complemented
14C127×#1753C211yesmaximal, characteristic, complemented
15C127×#1752C211yesmaximal, characteristic, complemented
16C22×M16×C127C2211yescharacteristic
17C23×C8×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C23×C8×C127C2211yescharacteristic
20C2×#121×C127C411yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×C4×D4×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#435×C127—24no—
26#435×C127—24no—
27C8×D4×C127—24no—
28C2×C4⋊C8×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×C22⋊C8×C127C2211yescharacteristic
33C2×C22⋊C8×C127C2211yescharacteristic
34C2×C22⋊C8×C127C2211yescharacteristic
35C2×C22⋊C8×C127C2211yescharacteristic
36C2×C22⋊C8×C127C2211yescharacteristic
37C2×C22⋊C8×C127C2211yescharacteristic
38C2×C22⋊C8×C127C2211yescharacteristic
39C2×C22⋊C8×C127C2211yescharacteristic
40C2×#97×C127—24no—
41C2×#97×C127C2211yescharacteristic
42C2×#97×C127C2211yescharacteristic
43C2×#97×C127C2211yescharacteristic
44C2×#97×C127C2211yescharacteristic
45C2×#97×C127C2211yescharacteristic
46C2×C4×C8×C127C2211yescharacteristic
47#390×C127C411yescharacteristic
48#389×C127C411yescharacteristic
49#388×C127C411yescharacteristic
50#388×C127C411yescharacteristic
51#386×C127C411yescharacteristic
52#386×C127C411yescharacteristic
53#380×C127C411yescharacteristic
54C4×C4⋊C4×C127C2211yescharacteristic
55C4×C22⋊C4×C127C2211yescharacteristic
56C4×C22⋊C4×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62#336×C127C2211yescharacteristic
63C22×D4×C127C2×C411yescharacteristic
64C22×D4×C127C2×C411yescharacteristic
65C22×D4×C127C2×C411yescharacteristic
66C23×C4×C127C2×C411yescharacteristic
67C23×C4×C127C2×C411yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C2×M16×C127—22no—
72C2×M16×C127—22no—
73C2×M16×C127—22no—
74C22×C8×C127—22no—
75C22×C8×C127—22no—
76C22×C8×C127—22no—
77C22×C8×C127—22no—
78C22×C8×C127—22no—
79C22×C8×C127—22no—
80C22×C8×C127—22no—
81C22×C8×C127—22no—
82C22×C8×C127D414yescomplemented
83C22×C8×C127C2311yescharacteristic
84C22×C8×C127C2311yescharacteristic
85C22×C8×C127C2311yescharacteristic
86C22×C8×C127C2311yescharacteristic
87C22×C8×C127C2311yescharacteristic
88C22×C8×C127C2311yescharacteristic
89C22×C8×C127C2311yescharacteristic
90C22×C8×C127C2311yescharacteristic
91#121×C127—24no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—22no—
95C4×D4×C127—22no—
96C4×D4×C127—22no—
97C4×D4×C127—22no—
98C2×C4⋊C4×C127C2×C411yescharacteristic
99C2×C4⋊C4×C127C2×C411yescharacteristic
100C2×C4⋊C4×C127C2×C411yescharacteristic
101C2×C4⋊C4×C127C2×C411yescharacteristic
102C2×C4⋊C4×C127C2×C411yescharacteristic
103C2×C22⋊C4×C127C2×C411yescharacteristic
104C2×C22⋊C4×C127C2×C411yescharacteristic
105C2×C22⋊C4×C127C2×C411yescharacteristic
106C2×C22⋊C4×C127C2×C411yescharacteristic
107C2×C22⋊C4×C127C2×C411yescharacteristic
108C2×C22⋊C4×C127C2×C411yescharacteristic
109C2×C22⋊C4×C127C2×C411yescharacteristic
110C2×C22⋊C4×C127C2×C411yescharacteristic
111C2×C22⋊C4×C127C2×C411yescharacteristic
112C2×C22⋊C4×C127C2×C411yescharacteristic
113C2×C42×C127—22no—
114C2×C42×C127—22no—
115C2×C42×C127C2×C411yescharacteristic
116C2×C42×C127C2×C411yescharacteristic
117C2×C42×C127C2311yescharacteristic
118C2×C42×C127C2311yescharacteristic
119C2×C42×C127C2311yescharacteristic
120C2×C42×C127C2311yescharacteristic
121C4⋊C8×C127—22no—
122C4⋊C8×C127—22no—
123C4⋊C8×C127—22no—
124C4⋊C8×C127—22no—
125C22⋊C8×C127—22no—
126C22⋊C8×C127—22no—
127C22⋊C8×C127—22no—
128C22⋊C8×C127—22no—
129C22⋊C8×C127—22no—
130C22⋊C8×C127—22no—
131C22⋊C8×C127—22no—
132C22⋊C8×C127—22no—
133#97×C127—22no—
134#97×C127—22no—
135#97×C127—22no—
136#97×C127—22no—
137#97×C127D414yescomplemented
138C4×C8×C127—22no—
139#95×C127C2×C411yescharacteristic
140#95×C127C2×C411yescharacteristic
141#95×C127C2×C411yescharacteristic
142#95×C127C2×C411yescharacteristic
143#95×C127C2×C411yescharacteristic
144#95×C127C2×C411yescharacteristic
145C24×C127C22×C411yescharacteristic
146C24×C127C22×C411yescharacteristic
147C24×C127C22×C411yescharacteristic
148C2×D4×C127—22no—
149C2×D4×C127—22no—
150C2×D4×C127—22no—
151C2×D4×C127—22no—
152C2×D4×C127—22no—
153C2×D4×C127—22no—
154C2×D4×C127—22no—
155C2×D4×C127—41no—
156C2×D4×C127M1614yescomplemented
157C22×C4×C127—21no—
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—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—41no—
178C22×C4×C127—41no—
179C22×C4×C127C22×C411yescharacteristic
180C22×C4×C127C22×C411yescharacteristic
181C22×C4×C127C22×C411yescharacteristic
182C22×C4×C127C22×C411yescharacteristic
183C22×C4×C127C22×C411yescharacteristic
184C22×C4×C127C22×C411yescharacteristic
185C22×C4×C127C22×C411yescharacteristic
186C22×C4×C127C22×C411yescharacteristic
187C22×C4×C127C22×C411yescharacteristic
188C22×C4×C127C22×C411yescharacteristic
189C22×C4×C127C22×C411yescharacteristic
190C22×C4×C127C2×D412yes—
191C22×C4×C127#4112yes—
192C22×C4×C127C2411yescharacteristic
193M16×C127—44no—
194C2×C8×C127—28no—
195C2×C8×C127—21no—
196C2×C8×C127—21no—
197C2×C8×C127—21no—
198C2×C8×C127—21no—
199C2×C8×C127—21no—
200C2×C8×C127—21no—
201C2×C8×C127—28no—
202C2×C8×C127—21no—
203C2×C8×C127—21no—
204C2×C8×C127—21no—
205C2×C8×C127—21no—
206C2×C8×C127—21no—
207C2×C8×C127—21no—
208C2×C8×C127—21no—
209C2×C8×C127—21no—
210C2×C8×C127—21no—
211C2×C8×C127—21no—
212C2×C8×C127—21no—
213C2×C8×C127—21no—
214C2×C8×C127—44no—
215C2×C8×C127C2×D412yes—
216C2×C8×C127C2×D412yes—
217C2×C8×C127C2×D412yes—
218C2×C8×C127C2×D412yes—
219C2×C8×C127#4112yes—
220C2×C8×C127#4112yes—
221C4⋊C4×C127—22no—
222C4⋊C4×C127—22no—
223C4⋊C4×C127—22no—
224C4⋊C4×C127—22no—
225C4⋊C4×C127—41no—
226C22⋊C4×C127—22no—
227C22⋊C4×C127—22no—
228C22⋊C4×C127—22no—
229C22⋊C4×C127—22no—
230C22⋊C4×C127—22no—
231C22⋊C4×C127—22no—
232C22⋊C4×C127—22no—
233C22⋊C4×C127—22no—
234C22⋊C4×C127—41no—
235C22⋊C4×C127—41no—
236C42×C127—22no—
237C42×C127—22no—
238C42×C127—21no—
239C42×C127—21no—
240C42×C127—21no—
241C42×C127—21no—
242C42×C127—21no—
243C42×C127—21no—
244C42×C127C2×D412yes—
245C42×C127#4112yes—
246C23×C127—21no—
247C23×C127—21no—
248C23×C127—21no—
249C23×C127—21no—
250C23×C127—21no—
251C23×C127—21no—
252C23×C127—21no—
253C23×C127—21no—
254C23×C127—21no—
255C23×C127—21no—
256C23×C127—21no—
257C23×C127—21no—
258C23×C127—21no—
259C23×C127—21no—
260C23×C127—21no—
261C23×C127—21no—
262C23×C127—21no—
263C23×C127C4×D412yes—
264C23×C127C2×M1612yes—
265C23×C127C2×M1612yes—
266C23×C127#13112yes—
267C23×C127C23×C411yescharacteristic
268D4×C127—28no—
269D4×C127—44no—
270D4×C127—44no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—21no—
274C2×C4×C127—21no—
275C2×C4×C127—21no—
276C2×C4×C127—21no—
277C2×C4×C127—21no—
278C2×C4×C127—21no—
279C2×C4×C127—22no—
280C2×C4×C127—22no—
281C2×C4×C127—22no—
282C2×C4×C127—22no—
283C2×C4×C127—21no—
284C2×C4×C127—21no—
285C2×C4×C127—21no—
286C2×C4×C127—21no—
287C2×C4×C127—21no—
288C2×C4×C127—21no—
289C2×C4×C127—21no—
290C2×C4×C127—21no—
291C2×C4×C127—21no—
292C2×C4×C127—21no—
293C2×C4×C127—21no—
294C2×C4×C127—21no—
295C2×C4×C127—21no—
296C2×C4×C127—21no—
297C2×C4×C127—21no—
298C2×C4×C127—21no—
299C2×C4×C127—21no—
300C2×C4×C127—21no—
301C2×C4×C127—21no—
302C2×C4×C127—21no—
303C2×C4×C127—21no—
304C2×C4×C127—44no—
305C2×C4×C127—44no—
306C2×C4×C127—41no—
307C2×C4×C127—41no—
308C2×C4×C127—41no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—41no—
313C2×C4×C127—41no—
314C2×C4×C127C4×D412yes—
315C2×C4×C127C4×D412yes—
316C2×C4×C127C4×D412yes—
317C2×C4×C127C2×M1612yes—
318C2×C4×C127C22×D411yescharacteristic
319C2×C4×C127C22×D411yescharacteristic
320C2×C4×C127C2×#4111yescharacteristic
321C2×C4×C127C2×#4111yescharacteristic
322C2×C4×C127C2×#4111yescharacteristic
323C2×C4×C127C2×#4111yescharacteristic
324C8×C127—22no—
325C8×C127—22no—
326C8×C127—22no—
327C8×C127—41no—
328C8×C127—41no—
329C8×C127—41no—
330C8×C127—41no—
331C8×C127#12114yescomplemented
332C22×C127—22no—
333C22×C127—22no—
334C22×C127—22no—
335C22×C127—22no—
336C22×C127—22no—
337C22×C127—22no—
338C22×C127—22no—
339C22×C127—22no—
340C22×C127—22no—
341C22×C127—41no—
342C22×C127—41no—
343C22×C127—41no—
344C22×C127—41no—
345C22×C127—41no—
346C22×C127—41no—
347C22×C127—41no—
348C22×C127—41no—
349C22×C127—41no—
350C22×C127—41no—
351C22×C127—41no—
352C22×C127#43514yescomplemented
353C22×C127C2×C4×D411yescharacteristic
354C22×C127C2×C4×D411yescharacteristic
355C22×C127C4×#4111yescharacteristic
356C22×C127C22×M1611yescharacteristic
357C22×C127C2×#13111yescharacteristic
358C22×C127#56811yescharacteristic
359C22×C127#56811yescharacteristic
360C4×C127—22no—
361C4×C127—22no—
362C4×C127—22no—
363C4×C127—22no—
364C4×C127—41no—
365C4×C127—41no—
366C4×C127—41no—
367C4×C127—41no—
368C4×C127—41no—
369C4×C127—41no—
370C4×C127—41no—
371C4×C127C2×#12111yescharacteristic
372C4×C127#52511yescharacteristic
373C4×C127#52911yescharacteristic
374C4×C127#53211yescharacteristic
375#21489C12711yesmaximal, characteristic, direct product factor, Sylow
376C2×C127—24no—
377C2×C127—42no—
378C2×C127—81no—
379C2×C127C4×#12111yescharacteristic
380C2×C127C2×#43511yescharacteristic
381C2×C127#293211yescharacteristic
382C2×C127#293311yescharacteristic
383C2×C127D4×M1611yescharacteristic
384C2×C127#296811yescharacteristic
385C2×C127#297011yescharacteristic
386C2×#435C2×C12711yescharacteristic, complemented
387C2×#435C2×C12711yescharacteristic, complemented
388C2×C8×D4C2×C12711yescharacteristic, complemented
389C22×#97C2×C12711yescharacteristic, complemented
390C4×#121C2×C12711yescharacteristic
391#1955C2×C12711yescharacteristic, complemented
392#1940C2×C12711yescharacteristic, complemented
393#1924C2×C12711yescharacteristic, complemented
394#1924C2×C12711yescharacteristic, complemented
395#1869C2×C12711yescharacteristic, complemented
396#1869C2×C12711yescharacteristic, complemented
397#1797C2×C12711yescharacteristic, complemented
398#1771C2×C12711yescharacteristic, complemented
399#1753C2×C12711yescharacteristic, complemented
400#1752C2×C12711yescharacteristic, complemented
401C127#2148911yescharacteristic, direct product factor, Sylow
402C22×M16C22×C12711yescharacteristic
403C23×C8C22×C12711yescharacteristic
404C23×C8C22×C12711yescharacteristic
405C23×C8C22×C12711yescharacteristic
406C2×#121C4×C12711yescharacteristic
407C2×C4×D4C22×C12711yescharacteristic
408C2×C4×D4C22×C12711yescharacteristic
409C2×C4×D4C22×C12711yescharacteristic
410C22×C42C22×C12711yescharacteristic
411#435—24no—
412#435—24no—
413C8×D4—24no—
414C2×C4⋊C8C22×C12711yescharacteristic
415C2×C4⋊C8C22×C12711yescharacteristic
416C2×C4⋊C8C22×C12711yescharacteristic
417C2×C4⋊C8C22×C12711yescharacteristic
418C2×C22⋊C8C22×C12711yescharacteristic
419C2×C22⋊C8C22×C12711yescharacteristic
420C2×C22⋊C8C22×C12711yescharacteristic
421C2×C22⋊C8C22×C12711yescharacteristic
422C2×C22⋊C8C22×C12711yescharacteristic
423C2×C22⋊C8C22×C12711yescharacteristic
424C2×C22⋊C8C22×C12711yescharacteristic
425C2×C22⋊C8C22×C12711yescharacteristic
426C2×#97—24no—
427C2×#97C22×C12711yescharacteristic
428C2×#97C22×C12711yescharacteristic
429C2×#97C22×C12711yescharacteristic
430C2×#97C22×C12711yescharacteristic
431C2×#97C22×C12711yescharacteristic
432C2×C4×C8C22×C12711yescharacteristic
433#390C4×C12711yescharacteristic
434#389C4×C12711yescharacteristic
435#388C4×C12711yescharacteristic
436#388C4×C12711yescharacteristic
437#386C4×C12711yescharacteristic
438#386C4×C12711yescharacteristic
439#380C4×C12711yescharacteristic
440C4×C4⋊C4C22×C12711yescharacteristic
441C4×C22⋊C4C22×C12711yescharacteristic
442C4×C22⋊C4C22×C12711yescharacteristic
443#336C22×C12711yescharacteristic
444#336C22×C12711yescharacteristic
445#336C22×C12711yescharacteristic
446#336C22×C12711yescharacteristic
447#336C22×C12711yescharacteristic
448#336C22×C12711yescharacteristic
449C22×D4C2×C4×C12711yescharacteristic
450C22×D4C2×C4×C12711yescharacteristic
451C22×D4C2×C4×C12711yescharacteristic
452C23×C4C2×C4×C12711yescharacteristic
453C23×C4C2×C4×C12711yescharacteristic
454C23×C4C23×C12711yescharacteristic
455C23×C4C23×C12711yescharacteristic
456C23×C4C23×C12711yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C22×C8—22no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8D4×C12714yescomplemented
469C22×C8C23×C12711yescharacteristic
470C22×C8C23×C12711yescharacteristic
471C22×C8C23×C12711yescharacteristic
472C22×C8C23×C12711yescharacteristic
473C22×C8C23×C12711yescharacteristic
474C22×C8C23×C12711yescharacteristic
475C22×C8C23×C12711yescharacteristic
476C22×C8C23×C12711yescharacteristic
477#121—24no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C2×C4⋊C4C2×C4×C12711yescharacteristic
485C2×C4⋊C4C2×C4×C12711yescharacteristic
486C2×C4⋊C4C2×C4×C12711yescharacteristic
487C2×C4⋊C4C2×C4×C12711yescharacteristic
488C2×C4⋊C4C2×C4×C12711yescharacteristic
489C2×C22⋊C4C2×C4×C12711yescharacteristic
490C2×C22⋊C4C2×C4×C12711yescharacteristic
491C2×C22⋊C4C2×C4×C12711yescharacteristic
492C2×C22⋊C4C2×C4×C12711yescharacteristic
493C2×C22⋊C4C2×C4×C12711yescharacteristic
494C2×C22⋊C4C2×C4×C12711yescharacteristic
495C2×C22⋊C4C2×C4×C12711yescharacteristic
496C2×C22⋊C4C2×C4×C12711yescharacteristic
497C2×C22⋊C4C2×C4×C12711yescharacteristic
498C2×C22⋊C4C2×C4×C12711yescharacteristic
499C2×C42—22no—
500C2×C42—22no—
501C2×C42C2×C4×C12711yescharacteristic
502C2×C42C2×C4×C12711yescharacteristic
503C2×C42C23×C12711yescharacteristic
504C2×C42C23×C12711yescharacteristic
505C2×C42C23×C12711yescharacteristic
506C2×C42C23×C12711yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519#97—22no—
520#97—22no—
521#97—22no—
522#97—22no—
523#97D4×C12714yescomplemented
524C4×C8—22no—
525#95C2×C4×C12711yescharacteristic
526#95C2×C4×C12711yescharacteristic
527#95C2×C4×C12711yescharacteristic
528#95C2×C4×C12711yescharacteristic
529#95C2×C4×C12711yescharacteristic
530#95C2×C4×C12711yescharacteristic
531C24C22×C4×C12711yescharacteristic
532C24C22×C4×C12711yescharacteristic
533C24C22×C4×C12711yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—41no—
542C2×D4M16×C12714yescomplemented
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4C22×C4×C12711yescharacteristic
566C22×C4C22×C4×C12711yescharacteristic
567C22×C4C22×C4×C12711yescharacteristic
568C22×C4C22×C4×C12711yescharacteristic
569C22×C4C22×C4×C12711yescharacteristic
570C22×C4C22×C4×C12711yescharacteristic
571C22×C4C22×C4×C12711yescharacteristic
572C22×C4C22×C4×C12711yescharacteristic
573C22×C4C22×C4×C12711yescharacteristic
574C22×C4C22×C4×C12711yescharacteristic
575C22×C4C22×C4×C12711yescharacteristic
576C22×C4C2×D4×C12712yes—
577C22×C4#41×C12712yes—
578C22×C4C24×C12711yescharacteristic
579M16—44no—
580C2×C8—28no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—28no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—44no—
601C2×C8C2×D4×C12712yes—
602C2×C8C2×D4×C12712yes—
603C2×C8C2×D4×C12712yes—
604C2×C8C2×D4×C12712yes—
605C2×C8#41×C12712yes—
606C2×C8#41×C12712yes—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—41no—
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—41no—
621C22⋊C4—41no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42C2×D4×C12712yes—
631C42#41×C12712yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23C4×D4×C12712yes—
650C23C2×M16×C12712yes—
651C23C2×M16×C12712yes—
652C23#131×C12712yes—
653C23C23×C4×C12711yescharacteristic
654D4—28no—
655D4—44no—
656D4—44no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4C4×D4×C12712yes—
701C2×C4C4×D4×C12712yes—
702C2×C4C4×D4×C12712yes—
703C2×C4C2×M16×C12712yes—
704C2×C4C22×D4×C12711yescharacteristic
705C2×C4C22×D4×C12711yescharacteristic
706C2×C4C2×#41×C12711yescharacteristic
707C2×C4C2×#41×C12711yescharacteristic
708C2×C4C2×#41×C12711yescharacteristic
709C2×C4C2×#41×C12711yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8#121×C12714yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22#435×C12714yescomplemented
739C22C2×C4×D4×C12711yescharacteristic
740C22C2×C4×D4×C12711yescharacteristic
741C22C4×#41×C12711yescharacteristic
742C22C22×M16×C12711yescharacteristic
743C22C2×#131×C12711yescharacteristic
744C22#568×C12711yescharacteristic
745C22#568×C12711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4C2×#121×C12711yescharacteristic
758C4#525×C12711yescharacteristic
759C4#529×C12711yescharacteristic
760C4#532×C12711yescharacteristic
761C2—24no—
762C2—42no—
763C2—81no—
764C2C4×#121×C12711yescharacteristic
765C2C2×#435×C12711yescharacteristic
766C2C127×#293211yescharacteristic
767C2C127×#293311yescharacteristic
768C2D4×M16×C12711yescharacteristic
769C2C127×#296811yescharacteristic
770C2C127×#297011yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC2×#121×C127C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C127C2semidirect
2. C2×#435×C127C2semidirect
3. C2×C8×D4×C127C2semidirect
4. C22×#97×C127C2semidirect
6. C127×#1955C2semidirect
7. C127×#1940C2semidirect
8. C127×#1924C2semidirect
9. C127×#1924C2semidirect
10. C127×#1869C2semidirect
11. C127×#1869C2semidirect
12. C127×#1797C2semidirect
13. C127×#1771C2semidirect
14. C127×#1753C2semidirect
15. C127×#1752C2semidirect
82. C22×C8×C127D4semidirect
137. #97×C127D4semidirect
156. C2×D4×C127M16semidirect
331. C8×C127#121semidirect
352. C22×C127#435semidirect
375. #21489C127direct (N × H)
386. C2×#435C2×C127semidirect
387. C2×#435C2×C127semidirect
388. C2×C8×D4C2×C127semidirect
389. C22×#97C2×C127semidirect
391. #1955C2×C127semidirect
392. #1940C2×C127semidirect
393. #1924C2×C127semidirect
394. #1924C2×C127semidirect
395. #1869C2×C127semidirect
396. #1869C2×C127semidirect
397. #1797C2×C127semidirect
398. #1771C2×C127semidirect
399. #1753C2×C127semidirect
400. #1752C2×C127semidirect
401. C127#21489direct (N × H)
468. C22×C8D4×C127semidirect
523. #97D4×C127semidirect
542. C2×D4M16×C127semidirect
717. C8#121×C127semidirect
738. C22#435×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1272
C2×C8×D4×C1272
C22×#97×C1272
C4×#121×C1272
C127×#19552
C127×#19402
C127×#19242
C127×#18692
C127×#17972
C127×#17712
C127×#17532
C127×#17522
#21489127