Finite Group Databasebeta

← C127×#21381 #44585054

Subgroups — C127×#21381 #44585054

Order 32512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C127C211yesmaximal, characteristic
2C2×#433×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic, complemented
4C127×#1985C211yesmaximal, characteristic, complemented
5C127×#1984C211yesmaximal, characteristic, complemented
6C127×#1955C211yesmaximal, characteristic, complemented
7C127×#1954C211yesmaximal, characteristic, complemented
8C127×#1870C211yesmaximal, characteristic, complemented
9C127×#1870C211yesmaximal, characteristic, complemented
10C127×#1869C211yesmaximal, characteristic, complemented
11C127×#1869C211yesmaximal, characteristic, complemented
12C127×#1750C211yesmaximal, characteristic, complemented
13C127×#1750C211yesmaximal, characteristic, complemented
14C127×#1749C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C127C211yesmaximal, characteristic, complemented
16C22×M16×C127C2211yescharacteristic
17C23×C8×C127C2211yescharacteristic
18#529×C127—24no—
19#529×C127—24no—
20C2×#126×C127C411yescharacteristic
21C2×#126×C127C411yescharacteristic
22C2×#125×C127C411yescharacteristic
23C2×#124×C127C411yescharacteristic
24C2×#123×C127C411yescharacteristic
25C2×#123×C127C411yescharacteristic
26C2×C22⋊Q8×C127C411yescharacteristic
27C2×#121×C127C411yescharacteristic
28C2×C4×Q8×C127C2211yescharacteristic
29C2×C4×D4×C127C2211yescharacteristic
30C2×C4×D4×C127C2211yescharacteristic
31C2×C4×D4×C127C2211yescharacteristic
32C2×#117×C127C2211yescharacteristic
33C2×#117×C127C2211yescharacteristic
34C22×C42×C127C2211yescharacteristic
35#433×C127—24no—
36C2×C4⋊C8×C127C2211yescharacteristic
37C2×C4⋊C8×C127C2211yescharacteristic
38C2×C22⋊C8×C127C2211yescharacteristic
39C2×C22⋊C8×C127C2211yescharacteristic
40C2×C22⋊C8×C127C2211yescharacteristic
41C2×C22⋊C8×C127C2211yescharacteristic
42C2×C22⋊C8×C127C2211yescharacteristic
43C2×C22⋊C8×C127C2211yescharacteristic
44C2×C22⋊C8×C127C2211yescharacteristic
45C2×C22⋊C8×C127C2211yescharacteristic
46C2×C22⋊C8×C127C2211yescharacteristic
47C2×C22⋊C8×C127C2211yescharacteristic
48#405×C127—24no—
49C2×#97×C127C2211yescharacteristic
50C2×#97×C127C2211yescharacteristic
51C2×#97×C127C2211yescharacteristic
52C2×C4×C8×C127C2211yescharacteristic
53C2×C4×C8×C127C2211yescharacteristic
54C2×C4×C8×C127C2211yescharacteristic
55#336×C127C2211yescharacteristic
56#336×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62#336×C127C2211yescharacteristic
63C22×Q8×C127C2×C411yescharacteristic
64C22×D4×C127C2×C411yescharacteristic
65C22×D4×C127C2×C411yescharacteristic
66C22×D4×C127C2×C411yescharacteristic
67C23×C4×C127C2×C411yescharacteristic
68C23×C4×C127C2×C411yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C2×M16×C127—22no—
73C2×M16×C127—22no—
74C2×M16×C127—22no—
75C22×C8×C127—22no—
76C22×C8×C127—22no—
77C22×C8×C127—22no—
78C22×C8×C127C2311yescharacteristic
79C22×C8×C127C2311yescharacteristic
80C22×C8×C127C2311yescharacteristic
81C22×C8×C127C2311yescharacteristic
82C22×C8×C127C2311yescharacteristic
83C22×C8×C127C2311yescharacteristic
84C22×C8×C127C2311yescharacteristic
85C22×C8×C127C2311yescharacteristic
86#126×C127—24no—
87#126×C127—24no—
88#125×C127—24no—
89#124×C127—24no—
90#123×C127—24no—
91#123×C127—24no—
92C22⋊Q8×C127—24no—
93#121×C127—24no—
94C4×Q8×C127—22no—
95C4×Q8×C127—22no—
96C4×D4×C127—22no—
97C4×D4×C127—22no—
98C4×D4×C127—22no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102#117×C127—22no—
103#117×C127—22no—
104#117×C127D414yes—
105#117×C127D414yes—
106C2×C4⋊C4×C127C2×C411yescharacteristic
107C2×C4⋊C4×C127C2×C411yescharacteristic
108C2×C4⋊C4×C127C2×C411yescharacteristic
109C2×C4⋊C4×C127C2×C411yescharacteristic
110C2×C4⋊C4×C127C2×C411yescharacteristic
111C2×C4⋊C4×C127C2×C411yescharacteristic
112C2×C4⋊C4×C127C2×C411yescharacteristic
113C2×C4⋊C4×C127C2×C411yescharacteristic
114C2×C4⋊C4×C127C2×C411yescharacteristic
115C2×C4⋊C4×C127C2×C411yescharacteristic
116C2×C22⋊C4×C127C2×C411yescharacteristic
117C2×C22⋊C4×C127C2×C411yescharacteristic
118C2×C22⋊C4×C127C2×C411yescharacteristic
119C2×C22⋊C4×C127C2×C411yescharacteristic
120C2×C22⋊C4×C127C2×C411yescharacteristic
121C2×C22⋊C4×C127C2×C411yescharacteristic
122C2×C22⋊C4×C127C2×C411yescharacteristic
123C2×C22⋊C4×C127C2×C411yescharacteristic
124C2×C22⋊C4×C127C2×C411yescharacteristic
125C2×C22⋊C4×C127C2×C411yescharacteristic
126C2×C42×C127—22no—
127C2×C42×C127—22no—
128C2×C42×C127C2×C411yescharacteristic
129C2×C42×C127C2×C411yescharacteristic
130C2×C42×C127C2311yescharacteristic
131C2×C42×C127C2311yescharacteristic
132C2×C42×C127C2311yescharacteristic
133C2×C42×C127C2311yescharacteristic
134C4⋊C8×C127—22no—
135C4⋊C8×C127—22no—
136C22⋊C8×C127—22no—
137C22⋊C8×C127—22no—
138C22⋊C8×C127—22no—
139C22⋊C8×C127—22no—
140C22⋊C8×C127—22no—
141C22⋊C8×C127—22no—
142C22⋊C8×C127—22no—
143C22⋊C8×C127—22no—
144C22⋊C8×C127—22no—
145C22⋊C8×C127—22no—
146#97×C127—22no—
147#97×C127—22no—
148#97×C127—22no—
149C4×C8×C127—22no—
150C4×C8×C127—22no—
151C4×C8×C127—22no—
152C24×C127C22×C411yescharacteristic
153C24×C127C22×C411yescharacteristic
154C24×C127C22×C411yescharacteristic
155C2×Q8×C127—22no—
156C2×Q8×C127—22no—
157C2×Q8×C127—41no—
158C2×D4×C127—22no—
159C2×D4×C127—22no—
160C2×D4×C127—22no—
161C2×D4×C127—22no—
162C2×D4×C127—22no—
163C2×D4×C127—22no—
164C2×D4×C127—41no—
165C2×D4×C127—41no—
166C2×D4×C127—41no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
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—41no—
188C22×C4×C127—41no—
189C22×C4×C127C22×C411yescharacteristic
190C22×C4×C127C22×C411yescharacteristic
191C22×C4×C127C22×C411yescharacteristic
192C22×C4×C127C22×C411yescharacteristic
193C22×C4×C127C22×C411yescharacteristic
194C22×C4×C127C22×C411yescharacteristic
195C22×C4×C127C22×C411yescharacteristic
196C22×C4×C127C22×C411yescharacteristic
197C22×C4×C127C22×C411yescharacteristic
198C22×C4×C127C22×C411yescharacteristic
199C22×C4×C127C22×C411yescharacteristic
200C22×C4×C127C2×D412yes—
201C22×C4×C127C2×D412yes—
202C22×C4×C127C2411yescharacteristic
203M16×C127—28no—
204C2×C8×C127—28no—
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—21no—
215C2×C8×C127—21no—
216C2×C8×C127—21no—
217C2×C8×C127—21no—
218C2×C8×C127—21no—
219C2×C8×C127—21no—
220C2×C8×C127—21no—
221C2×C8×C127—21no—
222C2×C8×C127—21no—
223C2×C8×C127—21no—
224C2×C8×C127—21no—
225C2×C8×C127#4112yes—
226C2×C8×C127#4112yes—
227C2×C8×C127#4112yes—
228C2×C8×C127#4112yes—
229C4⋊C4×C127—22no—
230C4⋊C4×C127—22no—
231C4⋊C4×C127—22no—
232C4⋊C4×C127—22no—
233C4⋊C4×C127—22no—
234C4⋊C4×C127—22no—
235C4⋊C4×C127—22no—
236C4⋊C4×C127—22no—
237C4⋊C4×C127C22⋊C414yes—
238C4⋊C4×C127C22⋊C414yes—
239C22⋊C4×C127—22no—
240C22⋊C4×C127—22no—
241C22⋊C4×C127—22no—
242C22⋊C4×C127—22no—
243C22⋊C4×C127—22no—
244C22⋊C4×C127—22no—
245C22⋊C4×C127—22no—
246C22⋊C4×C127—22no—
247C22⋊C4×C127C22⋊C414yes—
248C22⋊C4×C127C22⋊C414yes—
249C42×C127—22no—
250C42×C127—22no—
251C42×C127—21no—
252C42×C127—21no—
253C42×C127—21no—
254C42×C127—21no—
255C42×C127C2×D412yes—
256C42×C127C2×D412yes—
257C42×C127C2×D412yes—
258C42×C127C2×D412yes—
259C23×C127—21no—
260C23×C127—21no—
261C23×C127—21no—
262C23×C127—21no—
263C23×C127—21no—
264C23×C127—21no—
265C23×C127—21no—
266C23×C127—21no—
267C23×C127—21no—
268C23×C127—21no—
269C23×C127—21no—
270C23×C127—21no—
271C23×C127—21no—
272C23×C127—21no—
273C23×C127—21no—
274C23×C127—21no—
275C23×C127—21no—
276C23×C127—21no—
277C23×C127—21no—
278C23×C127C2×C22⋊C412yes—
279C23×C127#13112yes—
280C23×C127C23×C411yescharacteristic
281Q8×C127—44no—
282D4×C127—44no—
283D4×C127—44no—
284D4×C127—44no—
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—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—21no—
302C2×C4×C127—21no—
303C2×C4×C127—21no—
304C2×C4×C127—21no—
305C2×C4×C127—21no—
306C2×C4×C127—21no—
307C2×C4×C127—21no—
308C2×C4×C127—21no—
309C2×C4×C127—21no—
310C2×C4×C127—21no—
311C2×C4×C127—21no—
312C2×C4×C127—21no—
313C2×C4×C127—21no—
314C2×C4×C127—21no—
315C2×C4×C127—21no—
316C2×C4×C127—44no—
317C2×C4×C127—44no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127C2×C22⋊C412yes—
327C2×C4×C127C2×C22⋊C412yes—
328C2×C4×C127C2×C22⋊C412yes—
329C2×C4×C127C2×C22⋊C412yes—
330C2×C4×C127C2×C22⋊C412yes—
331C2×C4×C127#13112yes—
332C2×C4×C127C22×D411yescharacteristic
333C2×C4×C127C22×D411yescharacteristic
334C2×C4×C127C2×#4111yescharacteristic
335C2×C4×C127C2×#4111yescharacteristic
336C2×C4×C127C2×#4111yescharacteristic
337C2×C4×C127C2×#4111yescharacteristic
338C8×C127—22no—
339C8×C127—22no—
340C8×C127—22no—
341C8×C127—22no—
342C8×C127—41no—
343C8×C127—41no—
344C8×C127—41no—
345C8×C127—41no—
346C22×C127—22no—
347C22×C127—22no—
348C22×C127—22no—
349C22×C127—22no—
350C22×C127—22no—
351C22×C127—22no—
352C22×C127—41no—
353C22×C127—41no—
354C22×C127—41no—
355C22×C127—41no—
356C22×C127—41no—
357C22×C127—41no—
358C22×C127—41no—
359C22×C127—41no—
360C22×C127—41no—
361C22×C127—41no—
362C22×C127—41no—
363C22×C127—41no—
364C22×C127—41no—
365C22×C127—41no—
366C22×C127—41no—
367C22×C127C22×C22⋊C411yescharacteristic
368C22×C127C4×#4111yescharacteristic
369C22×C127C4×#4111yescharacteristic
370C22×C127C2×#13111yescharacteristic
371C22×C127C2×#13111yescharacteristic
372C22×C127#56811yescharacteristic
373C22×C127#56811yescharacteristic
374C4×C127—22no—
375C4×C127—22no—
376C4×C127—22no—
377C4×C127—22no—
378C4×C127—22no—
379C4×C127—22no—
380C4×C127—41no—
381C4×C127—41no—
382C4×C127—41no—
383C4×C127—41no—
384C4×C127—41no—
385C4×C127#52511yescharacteristic
386C4×C127#52511yescharacteristic
387C4×C127#53211yescharacteristic
388C4×C127#53211yescharacteristic
389#21381C12711yesmaximal, characteristic, direct product factor, Sylow
390C2×C127—42no—
391C2×C127—42no—
392C2×C127—81no—
393C2×C127#229711yescharacteristic
394C2×C127#288011yescharacteristic
395C2×C127#288011yescharacteristic
396C2×C127#296611yescharacteristic
397C2×C127#296711yescharacteristic
398C2×C127#296811yescharacteristic
399C2×C127#296911yescharacteristic
400C2×#529C2×C12711yescharacteristic
401C2×#433C2×C12711yescharacteristic, complemented
402C2×#405C2×C12711yescharacteristic, complemented
403#1985C2×C12711yescharacteristic, complemented
404#1984C2×C12711yescharacteristic, complemented
405#1955C2×C12711yescharacteristic, complemented
406#1954C2×C12711yescharacteristic, complemented
407#1870C2×C12711yescharacteristic, complemented
408#1870C2×C12711yescharacteristic, complemented
409#1869C2×C12711yescharacteristic, complemented
410#1869C2×C12711yescharacteristic, complemented
411#1750C2×C12711yescharacteristic, complemented
412#1750C2×C12711yescharacteristic, complemented
413#1749C2×C12711yescharacteristic, complemented
414C4×C22⋊C8C2×C12711yescharacteristic, complemented
415C127#2138111yescharacteristic, direct product factor, Sylow
416C22×M16C22×C12711yescharacteristic
417C23×C8C22×C12711yescharacteristic
418#529—24no—
419#529—24no—
420C2×#126C4×C12711yescharacteristic
421C2×#126C4×C12711yescharacteristic
422C2×#125C4×C12711yescharacteristic
423C2×#124C4×C12711yescharacteristic
424C2×#123C4×C12711yescharacteristic
425C2×#123C4×C12711yescharacteristic
426C2×C22⋊Q8C4×C12711yescharacteristic
427C2×#121C4×C12711yescharacteristic
428C2×C4×Q8C22×C12711yescharacteristic
429C2×C4×D4C22×C12711yescharacteristic
430C2×C4×D4C22×C12711yescharacteristic
431C2×C4×D4C22×C12711yescharacteristic
432C2×#117C22×C12711yescharacteristic
433C2×#117C22×C12711yescharacteristic
434C22×C42C22×C12711yescharacteristic
435#433—24no—
436C2×C4⋊C8C22×C12711yescharacteristic
437C2×C4⋊C8C22×C12711yescharacteristic
438C2×C22⋊C8C22×C12711yescharacteristic
439C2×C22⋊C8C22×C12711yescharacteristic
440C2×C22⋊C8C22×C12711yescharacteristic
441C2×C22⋊C8C22×C12711yescharacteristic
442C2×C22⋊C8C22×C12711yescharacteristic
443C2×C22⋊C8C22×C12711yescharacteristic
444C2×C22⋊C8C22×C12711yescharacteristic
445C2×C22⋊C8C22×C12711yescharacteristic
446C2×C22⋊C8C22×C12711yescharacteristic
447C2×C22⋊C8C22×C12711yescharacteristic
448#405—24no—
449C2×#97C22×C12711yescharacteristic
450C2×#97C22×C12711yescharacteristic
451C2×#97C22×C12711yescharacteristic
452C2×C4×C8C22×C12711yescharacteristic
453C2×C4×C8C22×C12711yescharacteristic
454C2×C4×C8C22×C12711yescharacteristic
455#336C22×C12711yescharacteristic
456#336C22×C12711yescharacteristic
457#336C22×C12711yescharacteristic
458#336C22×C12711yescharacteristic
459#336C22×C12711yescharacteristic
460#336C22×C12711yescharacteristic
461#336C22×C12711yescharacteristic
462#336C22×C12711yescharacteristic
463C22×Q8C2×C4×C12711yescharacteristic
464C22×D4C2×C4×C12711yescharacteristic
465C22×D4C2×C4×C12711yescharacteristic
466C22×D4C2×C4×C12711yescharacteristic
467C23×C4C2×C4×C12711yescharacteristic
468C23×C4C2×C4×C12711yescharacteristic
469C23×C4C23×C12711yescharacteristic
470C23×C4C23×C12711yescharacteristic
471C23×C4C23×C12711yescharacteristic
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C22×C8—22no—
476C22×C8—22no—
477C22×C8—22no—
478C22×C8C23×C12711yescharacteristic
479C22×C8C23×C12711yescharacteristic
480C22×C8C23×C12711yescharacteristic
481C22×C8C23×C12711yescharacteristic
482C22×C8C23×C12711yescharacteristic
483C22×C8C23×C12711yescharacteristic
484C22×C8C23×C12711yescharacteristic
485C22×C8C23×C12711yescharacteristic
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117D4×C12714yes—
505#117D4×C12714yes—
506C2×C4⋊C4C2×C4×C12711yescharacteristic
507C2×C4⋊C4C2×C4×C12711yescharacteristic
508C2×C4⋊C4C2×C4×C12711yescharacteristic
509C2×C4⋊C4C2×C4×C12711yescharacteristic
510C2×C4⋊C4C2×C4×C12711yescharacteristic
511C2×C4⋊C4C2×C4×C12711yescharacteristic
512C2×C4⋊C4C2×C4×C12711yescharacteristic
513C2×C4⋊C4C2×C4×C12711yescharacteristic
514C2×C4⋊C4C2×C4×C12711yescharacteristic
515C2×C4⋊C4C2×C4×C12711yescharacteristic
516C2×C22⋊C4C2×C4×C12711yescharacteristic
517C2×C22⋊C4C2×C4×C12711yescharacteristic
518C2×C22⋊C4C2×C4×C12711yescharacteristic
519C2×C22⋊C4C2×C4×C12711yescharacteristic
520C2×C22⋊C4C2×C4×C12711yescharacteristic
521C2×C22⋊C4C2×C4×C12711yescharacteristic
522C2×C22⋊C4C2×C4×C12711yescharacteristic
523C2×C22⋊C4C2×C4×C12711yescharacteristic
524C2×C22⋊C4C2×C4×C12711yescharacteristic
525C2×C22⋊C4C2×C4×C12711yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×C4×C12711yescharacteristic
529C2×C42C2×C4×C12711yescharacteristic
530C2×C42C23×C12711yescharacteristic
531C2×C42C23×C12711yescharacteristic
532C2×C42C23×C12711yescharacteristic
533C2×C42C23×C12711yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546#97—22no—
547#97—22no—
548#97—22no—
549C4×C8—22no—
550C4×C8—22no—
551C4×C8—22no—
552C24C22×C4×C12711yescharacteristic
553C24C22×C4×C12711yescharacteristic
554C24C22×C4×C12711yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×C4×C12711yescharacteristic
590C22×C4C22×C4×C12711yescharacteristic
591C22×C4C22×C4×C12711yescharacteristic
592C22×C4C22×C4×C12711yescharacteristic
593C22×C4C22×C4×C12711yescharacteristic
594C22×C4C22×C4×C12711yescharacteristic
595C22×C4C22×C4×C12711yescharacteristic
596C22×C4C22×C4×C12711yescharacteristic
597C22×C4C22×C4×C12711yescharacteristic
598C22×C4C22×C4×C12711yescharacteristic
599C22×C4C22×C4×C12711yescharacteristic
600C22×C4C2×D4×C12712yes—
601C22×C4C2×D4×C12712yes—
602C22×C4C24×C12711yescharacteristic
603M16—28no—
604C2×C8—28no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8#41×C12712yes—
626C2×C8#41×C12712yes—
627C2×C8#41×C12712yes—
628C2×C8#41×C12712yes—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊C4×C12714yes—
638C4⋊C4C22⋊C4×C12714yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊C4×C12714yes—
648C22⋊C4C22⋊C4×C12714yes—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42C2×D4×C12712yes—
656C42C2×D4×C12712yes—
657C42C2×D4×C12712yes—
658C42C2×D4×C12712yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊C4×C12712yes—
679C23#131×C12712yes—
680C23C23×C4×C12711yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊C4×C12712yes—
727C2×C4C2×C22⋊C4×C12712yes—
728C2×C4C2×C22⋊C4×C12712yes—
729C2×C4C2×C22⋊C4×C12712yes—
730C2×C4C2×C22⋊C4×C12712yes—
731C2×C4#131×C12712yes—
732C2×C4C22×D4×C12711yescharacteristic
733C2×C4C22×D4×C12711yescharacteristic
734C2×C4C2×#41×C12711yescharacteristic
735C2×C4C2×#41×C12711yescharacteristic
736C2×C4C2×#41×C12711yescharacteristic
737C2×C4C2×#41×C12711yescharacteristic
738C8—22no—
739C8—22no—
740C8—22no—
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊C4×C12711yescharacteristic
768C22C4×#41×C12711yescharacteristic
769C22C4×#41×C12711yescharacteristic
770C22C2×#131×C12711yescharacteristic
771C22C2×#131×C12711yescharacteristic
772C22#568×C12711yescharacteristic
773C22#568×C12711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#525×C12711yescharacteristic
786C4#525×C12711yescharacteristic
787C4#532×C12711yescharacteristic
788C4#532×C12711yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2C127×#229711yescharacteristic
793C2C127×#288011yescharacteristic
794C2C127×#288011yescharacteristic
795C2C127×#296611yescharacteristic
796C2C127×#296711yescharacteristic
797C2C127×#296811yescharacteristic
798C2C127×#296911yescharacteristic
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
2. C2×#433×C127C2semidirect
3. C2×#405×C127C2semidirect
4. C127×#1985C2semidirect
5. C127×#1984C2semidirect
6. C127×#1955C2semidirect
7. C127×#1954C2semidirect
8. C127×#1870C2semidirect
9. C127×#1870C2semidirect
10. C127×#1869C2semidirect
11. C127×#1869C2semidirect
12. C127×#1750C2semidirect
13. C127×#1750C2semidirect
14. C127×#1749C2semidirect
15. C4×C22⋊C8×C127C2semidirect
389. #21381C127direct (N × H)
401. C2×#433C2×C127semidirect
402. C2×#405C2×C127semidirect
403. #1985C2×C127semidirect
404. #1984C2×C127semidirect
405. #1955C2×C127semidirect
406. #1954C2×C127semidirect
407. #1870C2×C127semidirect
408. #1870C2×C127semidirect
409. #1869C2×C127semidirect
410. #1869C2×C127semidirect
411. #1750C2×C127semidirect
412. #1750C2×C127semidirect
413. #1749C2×C127semidirect
414. C4×C22⋊C8C2×C127semidirect
415. C127#21381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#529×C1272
C2×#433×C1272
C2×#405×C1272
C127×#19852
C127×#19842
C127×#19552
C127×#19542
C127×#18702
C127×#18692
C127×#17502
C127×#17492
C4×C22⋊C8×C1272
#21381127