Finite Group Databasebeta

← C127×#21632 #44585305

Subgroups — C127×#21632 #44585305

Order 32512.

884 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#446×C127C211yesmaximal, characteristic, complemented
2C2×#435×C127C211yesmaximal, characteristic
3C4×#124×C127C211yesmaximal, characteristic
4C127×#1985C211yesmaximal, characteristic, complemented
5C127×#1955C211yesmaximal, characteristic
6C127×#1924C211yesmaximal, characteristic, complemented
7C127×#1924C211yesmaximal, characteristic, complemented
8C127×#1923C211yesmaximal, characteristic, complemented
9C127×#1923C211yesmaximal, characteristic, complemented
10C127×#1831C211yesmaximal, characteristic, complemented
11C127×#1753C211yesmaximal, characteristic, complemented
12C127×#1753C211yesmaximal, characteristic, complemented
13C127×#1752C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C127C211yesmaximal, characteristic, complemented
15C4×#97×C127C211yesmaximal, characteristic, complemented
16C22×M16×C127C2211yescharacteristic
17C23×C8×C127C2211yescharacteristic
18C2×#124×C127C411yescharacteristic
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21#446×C127—24no—
22#435×C127—24no—
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×C4⋊C8×C127C2211yescharacteristic
26C2×C4⋊C8×C127C2211yescharacteristic
27C2×C22⋊C8×C127C2211yescharacteristic
28C2×C22⋊C8×C127C2211yescharacteristic
29C2×C22⋊C8×C127C2211yescharacteristic
30C2×C22⋊C8×C127C2211yescharacteristic
31C2×C22⋊C8×C127C2211yescharacteristic
32C2×C22⋊C8×C127C2211yescharacteristic
33C2×#97×C127C2211yescharacteristic
34C2×#97×C127C2211yescharacteristic
35C2×#97×C127C2211yescharacteristic
36C2×#97×C127C2211yescharacteristic
37C2×#97×C127C2211yescharacteristic
38C2×C4×C8×C127C2211yescharacteristic
39C2×C4×C8×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41#391×C127C411yescharacteristic
42#390×C127C411yescharacteristic
43#388×C127C411yescharacteristic
44#388×C127C411yescharacteristic
45#388×C127C411yescharacteristic
46#388×C127C411yescharacteristic
47#382×C127C411yescharacteristic
48C4×C22⋊C4×C127C2211yescharacteristic
49C4×C22⋊C4×C127C2211yescharacteristic
50C4×C22⋊C4×C127C2211yescharacteristic
51C4×C22⋊C4×C127C2211yescharacteristic
52C43×C127C2211yescharacteristic
53#336×C127C2211yescharacteristic
54#336×C127C2211yescharacteristic
55#336×C127C2211yescharacteristic
56#336×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61C22×Q8×C127C2×C411yescharacteristic
62C22×D4×C127C2×C411yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C2×M16×C127—22no—
66C2×M16×C127—22no—
67C2×M16×C127—22no—
68C22×C8×C127—22no—
69C22×C8×C127—22no—
70C22×C8×C127—22no—
71C22×C8×C127C2311yescharacteristic
72C22×C8×C127C2311yescharacteristic
73C22×C8×C127C2311yescharacteristic
74C22×C8×C127C2311yescharacteristic
75C22×C8×C127C2311yescharacteristic
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C22×C8×C127C2311yescharacteristic
79#124×C127—24no—
80C4×Q8×C127—22no—
81C4×Q8×C127—22no—
82C4×D4×C127—22no—
83C4×D4×C127—22no—
84C2×C4⋊C4×C127C2×C411yescharacteristic
85C2×C4⋊C4×C127C2×C411yescharacteristic
86C2×C4⋊C4×C127C2×C411yescharacteristic
87C2×C4⋊C4×C127C2×C411yescharacteristic
88C2×C22⋊C4×C127C2×C411yescharacteristic
89C2×C22⋊C4×C127C2×C411yescharacteristic
90C2×C22⋊C4×C127C2×C411yescharacteristic
91C2×C22⋊C4×C127C2×C411yescharacteristic
92C2×C22⋊C4×C127C2×C411yescharacteristic
93C2×C22⋊C4×C127C2×C411yescharacteristic
94C2×C22⋊C4×C127C2×C411yescharacteristic
95C2×C22⋊C4×C127C2×C411yescharacteristic
96C2×C22⋊C4×C127C2×C411yescharacteristic
97C2×C22⋊C4×C127C2×C411yescharacteristic
98C2×C42×C127C2×C411yescharacteristic
99C2×C42×C127C2×C411yescharacteristic
100C2×C42×C127C2×C411yescharacteristic
101C2×C42×C127C2×C411yescharacteristic
102C2×C42×C127C2311yescharacteristic
103C2×C42×C127C2311yescharacteristic
104C2×C42×C127C2311yescharacteristic
105C2×C42×C127C2311yescharacteristic
106C2×C42×C127C2311yescharacteristic
107C4⋊C8×C127—22no—
108C4⋊C8×C127—22no—
109C4⋊C8×C127—22no—
110C4⋊C8×C127—22no—
111C22⋊C8×C127—22no—
112C22⋊C8×C127—22no—
113C22⋊C8×C127—22no—
114C22⋊C8×C127—22no—
115C22⋊C8×C127—22no—
116C22⋊C8×C127—22no—
117#97×C127—22no—
118#97×C127—22no—
119#97×C127—22no—
120#97×C127—22no—
121#97×C127D414yes—
122C4×C8×C127—22no—
123C4×C8×C127—22no—
124C4×C8×C127—22no—
125#95×C127C2×C411yescharacteristic
126#95×C127C2×C411yescharacteristic
127#95×C127C2×C411yescharacteristic
128#95×C127C2×C411yescharacteristic
129#95×C127C2×C411yescharacteristic
130#95×C127C2×C411yescharacteristic
131#95×C127C2×C411yescharacteristic
132#95×C127C2×C411yescharacteristic
133C24×C127C22×C411yescharacteristic
134C24×C127C22×C411yescharacteristic
135C2×Q8×C127—22no—
136C2×Q8×C127—22no—
137C2×Q8×C127—41no—
138C2×D4×C127—22no—
139C2×D4×C127—22no—
140C2×D4×C127—41no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127C22×C411yescharacteristic
154C22×C4×C127C22×C411yescharacteristic
155C22×C4×C127C22×C411yescharacteristic
156C22×C4×C127C22×C411yescharacteristic
157C22×C4×C127C22×C411yescharacteristic
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C22×C411yescharacteristic
160C22×C4×C127C22×C411yescharacteristic
161C22×C4×C127C22×C411yescharacteristic
162C22×C4×C127C22×C411yescharacteristic
163C22×C4×C127C22×C411yescharacteristic
164C22×C4×C127C22×C411yescharacteristic
165C22×C4×C127C2411yescharacteristic
166M16×C127—44no—
167C2×C8×C127—21no—
168C2×C8×C127—21no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127—44no—
186C2×C8×C127C2×D412yes—
187C2×C8×C127C2×D412yes—
188C2×C8×C127#4112yes—
189C2×C8×C127#4112yes—
190C2×C8×C127#4112yes—
191C2×C8×C127#4112yes—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—22no—
194C4⋊C4×C127—22no—
195C4⋊C4×C127—22no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—22no—
200C22⋊C4×C127—22no—
201C22⋊C4×C127—22no—
202C22⋊C4×C127—22no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127M1614yescomplemented
206C42×C127—22no—
207C42×C127—22no—
208C42×C127—21no—
209C42×C127—21no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127—21no—
213C42×C127—21no—
214C42×C127—21no—
215C42×C127—21no—
216C42×C127—41no—
217C42×C127—41no—
218C42×C127C2×D412yes—
219C42×C127#4112yes—
220C23×C127—21no—
221C23×C127—21no—
222C23×C127—21no—
223C23×C127—21no—
224C23×C127—21no—
225C23×C127—21no—
226C23×C127—21no—
227C23×C127—21no—
228C23×C127—21no—
229C23×C127—21no—
230C23×C127—21no—
231C23×C127—21no—
232C23×C127—21no—
233C23×C127C2×M1612yes—
234C23×C127C23×C411yescharacteristic
235Q8×C127—44no—
236D4×C127—44no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—21no—
262C2×C4×C127—21no—
263C2×C4×C127—21no—
264C2×C4×C127—21no—
265C2×C4×C127—21no—
266C2×C4×C127—21no—
267C2×C4×C127—21no—
268C2×C4×C127—41no—
269C2×C4×C127—41no—
270C2×C4×C127—41no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—41no—
276C2×C4×C127C4×D412yes—
277C2×C4×C127C4×D412yes—
278C2×C4×C127C2×M1612yes—
279C2×C4×C127C2×M1612yes—
280C2×C4×C127#13112yes—
281C2×C4×C127C22×D411yescharacteristic
282C2×C4×C127C2×#4111yescharacteristic
283C2×C4×C127C2×#4111yescharacteristic
284C2×C4×C127C2×#4111yescharacteristic
285C2×C4×C127C2×#4111yescharacteristic
286C2×C4×C127C2×#4111yescharacteristic
287C8×C127—22no—
288C8×C127—22no—
289C8×C127—22no—
290C8×C127—41no—
291C8×C127—41no—
292C8×C127—41no—
293C8×C127—41no—
294C8×C127#12414yescomplemented
295C22×C127—22no—
296C22×C127—22no—
297C22×C127—22no—
298C22×C127—41no—
299C22×C127—41no—
300C22×C127—41no—
301C22×C127—41no—
302C22×C127—41no—
303C22×C127—41no—
304C22×C127—41no—
305C22×C127—41no—
306C22×C127—41no—
307C22×C127—41no—
308C22×C127—41no—
309C22×C127C2×C4×D411yescharacteristic
310C22×C127C4×#4111yescharacteristic
311C22×C127C4×#4111yescharacteristic
312C22×C127C22×M1611yescharacteristic
313C22×C127C2×#13111yescharacteristic
314C22×C127#56811yescharacteristic
315C22×C127#56811yescharacteristic
316C4×C127—22no—
317C4×C127—22no—
318C4×C127—22no—
319C4×C127—22no—
320C4×C127—22no—
321C4×C127—41no—
322C4×C127—41no—
323C4×C127—41no—
324C4×C127—41no—
325C4×C127—41no—
326C4×C127—41no—
327C4×C127—41no—
328C4×C127C2×#12411yescharacteristic
329C4×C127#52911yescharacteristic
330C4×C127#52911yescharacteristic
331C4×C127#53211yescharacteristic
332#21632C12711yesmaximal, characteristic, direct product factor, Sylow
333C2×C127—42no—
334C2×C127—81no—
335C2×C127C4×#12411yescharacteristic
336C2×C127D4×M1611yescharacteristic
337C2×C127#293511yescharacteristic
338C2×C127#296511yescharacteristic
339C2×C127#296711yescharacteristic
340C2×C127#296811yescharacteristic
341C2×C127#297011yescharacteristic
342C2×#446C2×C12711yescharacteristic, complemented
343C2×#435C2×C12711yescharacteristic
344C4×#124C2×C12711yescharacteristic
345#1985C2×C12711yescharacteristic, complemented
346#1955C2×C12711yescharacteristic
347#1924C2×C12711yescharacteristic, complemented
348#1924C2×C12711yescharacteristic, complemented
349#1923C2×C12711yescharacteristic, complemented
350#1923C2×C12711yescharacteristic, complemented
351#1831C2×C12711yescharacteristic, complemented
352#1753C2×C12711yescharacteristic, complemented
353#1753C2×C12711yescharacteristic, complemented
354#1752C2×C12711yescharacteristic, complemented
355C8×C22⋊C4C2×C12711yescharacteristic, complemented
356C4×#97C2×C12711yescharacteristic, complemented
357C127#2163211yescharacteristic, direct product factor, Sylow
358C22×M16C22×C12711yescharacteristic
359C23×C8C22×C12711yescharacteristic
360C2×#124C4×C12711yescharacteristic
361C2×C4×Q8C22×C12711yescharacteristic
362C2×C4×D4C22×C12711yescharacteristic
363#446—24no—
364#435—24no—
365C2×C4⋊C8C22×C12711yescharacteristic
366C2×C4⋊C8C22×C12711yescharacteristic
367C2×C4⋊C8C22×C12711yescharacteristic
368C2×C4⋊C8C22×C12711yescharacteristic
369C2×C22⋊C8C22×C12711yescharacteristic
370C2×C22⋊C8C22×C12711yescharacteristic
371C2×C22⋊C8C22×C12711yescharacteristic
372C2×C22⋊C8C22×C12711yescharacteristic
373C2×C22⋊C8C22×C12711yescharacteristic
374C2×C22⋊C8C22×C12711yescharacteristic
375C2×#97C22×C12711yescharacteristic
376C2×#97C22×C12711yescharacteristic
377C2×#97C22×C12711yescharacteristic
378C2×#97C22×C12711yescharacteristic
379C2×#97C22×C12711yescharacteristic
380C2×C4×C8C22×C12711yescharacteristic
381C2×C4×C8C22×C12711yescharacteristic
382C2×C4×C8C22×C12711yescharacteristic
383#391C4×C12711yescharacteristic
384#390C4×C12711yescharacteristic
385#388C4×C12711yescharacteristic
386#388C4×C12711yescharacteristic
387#388C4×C12711yescharacteristic
388#388C4×C12711yescharacteristic
389#382C4×C12711yescharacteristic
390C4×C22⋊C4C22×C12711yescharacteristic
391C4×C22⋊C4C22×C12711yescharacteristic
392C4×C22⋊C4C22×C12711yescharacteristic
393C4×C22⋊C4C22×C12711yescharacteristic
394C43C22×C12711yescharacteristic
395#336C22×C12711yescharacteristic
396#336C22×C12711yescharacteristic
397#336C22×C12711yescharacteristic
398#336C22×C12711yescharacteristic
399#336C22×C12711yescharacteristic
400#336C22×C12711yescharacteristic
401#336C22×C12711yescharacteristic
402#336C22×C12711yescharacteristic
403C22×Q8C2×C4×C12711yescharacteristic
404C22×D4C2×C4×C12711yescharacteristic
405C23×C4C23×C12711yescharacteristic
406C23×C4C23×C12711yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8C23×C12711yescharacteristic
414C22×C8C23×C12711yescharacteristic
415C22×C8C23×C12711yescharacteristic
416C22×C8C23×C12711yescharacteristic
417C22×C8C23×C12711yescharacteristic
418C22×C8C23×C12711yescharacteristic
419C22×C8C23×C12711yescharacteristic
420C22×C8C23×C12711yescharacteristic
421#124—24no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×D4—22no—
425C4×D4—22no—
426C2×C4⋊C4C2×C4×C12711yescharacteristic
427C2×C4⋊C4C2×C4×C12711yescharacteristic
428C2×C4⋊C4C2×C4×C12711yescharacteristic
429C2×C4⋊C4C2×C4×C12711yescharacteristic
430C2×C22⋊C4C2×C4×C12711yescharacteristic
431C2×C22⋊C4C2×C4×C12711yescharacteristic
432C2×C22⋊C4C2×C4×C12711yescharacteristic
433C2×C22⋊C4C2×C4×C12711yescharacteristic
434C2×C22⋊C4C2×C4×C12711yescharacteristic
435C2×C22⋊C4C2×C4×C12711yescharacteristic
436C2×C22⋊C4C2×C4×C12711yescharacteristic
437C2×C22⋊C4C2×C4×C12711yescharacteristic
438C2×C22⋊C4C2×C4×C12711yescharacteristic
439C2×C22⋊C4C2×C4×C12711yescharacteristic
440C2×C42C2×C4×C12711yescharacteristic
441C2×C42C2×C4×C12711yescharacteristic
442C2×C42C2×C4×C12711yescharacteristic
443C2×C42C2×C4×C12711yescharacteristic
444C2×C42C23×C12711yescharacteristic
445C2×C42C23×C12711yescharacteristic
446C2×C42C23×C12711yescharacteristic
447C2×C42C23×C12711yescharacteristic
448C2×C42C23×C12711yescharacteristic
449C4⋊C8—22no—
450C4⋊C8—22no—
451C4⋊C8—22no—
452C4⋊C8—22no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459#97—22no—
460#97—22no—
461#97—22no—
462#97—22no—
463#97D4×C12714yes—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467#95C2×C4×C12711yescharacteristic
468#95C2×C4×C12711yescharacteristic
469#95C2×C4×C12711yescharacteristic
470#95C2×C4×C12711yescharacteristic
471#95C2×C4×C12711yescharacteristic
472#95C2×C4×C12711yescharacteristic
473#95C2×C4×C12711yescharacteristic
474#95C2×C4×C12711yescharacteristic
475C24C22×C4×C12711yescharacteristic
476C24C22×C4×C12711yescharacteristic
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—41no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4C22×C4×C12711yescharacteristic
496C22×C4C22×C4×C12711yescharacteristic
497C22×C4C22×C4×C12711yescharacteristic
498C22×C4C22×C4×C12711yescharacteristic
499C22×C4C22×C4×C12711yescharacteristic
500C22×C4C22×C4×C12711yescharacteristic
501C22×C4C22×C4×C12711yescharacteristic
502C22×C4C22×C4×C12711yescharacteristic
503C22×C4C22×C4×C12711yescharacteristic
504C22×C4C22×C4×C12711yescharacteristic
505C22×C4C22×C4×C12711yescharacteristic
506C22×C4C22×C4×C12711yescharacteristic
507C22×C4C24×C12711yescharacteristic
508M16—44no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—44no—
528C2×C8C2×D4×C12712yes—
529C2×C8C2×D4×C12712yes—
530C2×C8#41×C12712yes—
531C2×C8#41×C12712yes—
532C2×C8#41×C12712yes—
533C2×C8#41×C12712yes—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4M16×C12714yescomplemented
548C42—22no—
549C42—22no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—41no—
559C42—41no—
560C42C2×D4×C12712yes—
561C42#41×C12712yes—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C2×M16×C12712yes—
576C23C23×C4×C12711yescharacteristic
577Q8—44no—
578D4—44no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4C4×D4×C12712yes—
619C2×C4C4×D4×C12712yes—
620C2×C4C2×M16×C12712yes—
621C2×C4C2×M16×C12712yes—
622C2×C4#131×C12712yes—
623C2×C4C22×D4×C12711yescharacteristic
624C2×C4C2×#41×C12711yescharacteristic
625C2×C4C2×#41×C12711yescharacteristic
626C2×C4C2×#41×C12711yescharacteristic
627C2×C4C2×#41×C12711yescharacteristic
628C2×C4C2×#41×C12711yescharacteristic
629C8—22no—
630C8—22no—
631C8—22no—
632C8—41no—
633C8—41no—
634C8—41no—
635C8—41no—
636C8#124×C12714yescomplemented
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×C4×D4×C12711yescharacteristic
652C22C4×#41×C12711yescharacteristic
653C22C4×#41×C12711yescharacteristic
654C22C22×M16×C12711yescharacteristic
655C22C2×#131×C12711yescharacteristic
656C22#568×C12711yescharacteristic
657C22#568×C12711yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4C2×#124×C12711yescharacteristic
671C4#529×C12711yescharacteristic
672C4#529×C12711yescharacteristic
673C4#532×C12711yescharacteristic
674C2—42no—
675C2—81no—
676C2C4×#124×C12711yescharacteristic
677C2D4×M16×C12711yescharacteristic
678C2C127×#293511yescharacteristic
679C2C127×#296511yescharacteristic
680C2C127×#296711yescharacteristic
681C2C127×#296811yescharacteristic
682C2C127×#297011yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC22×D4×C127C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#446×C127C2semidirect
4. C127×#1985C2semidirect
6. C127×#1924C2semidirect
7. C127×#1924C2semidirect
8. C127×#1923C2semidirect
9. C127×#1923C2semidirect
10. C127×#1831C2semidirect
11. C127×#1753C2semidirect
12. C127×#1753C2semidirect
13. C127×#1752C2semidirect
14. C8×C22⋊C4×C127C2semidirect
15. C4×#97×C127C2semidirect
205. C22⋊C4×C127M16semidirect
294. C8×C127#124semidirect
332. #21632C127direct (N × H)
342. C2×#446C2×C127semidirect
345. #1985C2×C127semidirect
347. #1924C2×C127semidirect
348. #1924C2×C127semidirect
349. #1923C2×C127semidirect
350. #1923C2×C127semidirect
351. #1831C2×C127semidirect
352. #1753C2×C127semidirect
353. #1753C2×C127semidirect
354. #1752C2×C127semidirect
355. C8×C22⋊C4C2×C127semidirect
356. C4×#97C2×C127semidirect
357. C127#21632direct (N × H)
547. C22⋊C4M16×C127semidirect
636. C8#124×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#446×C1272
C2×#435×C1272
C4×#124×C1272
C127×#19852
C127×#19552
C127×#19242
C127×#19232
C127×#18312
C127×#17532
C127×#17522
C8×C22⋊C4×C1272
C4×#97×C1272
#21632127