Finite Group Databasebeta

← C127×#21773 #44585446

Subgroups — C127×#21773 #44585446

Order 32512.

1622 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C127C211yesmaximal, characteristic
2C2×#407×C127C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
4C127×#1896C214yesmaximal, complemented
5C127×#1871C214yesmaximal, complemented
6C127×#1826C212yesmaximal, complemented
7C127×#1789C212yesmaximal, complemented
8C22×#41×C127C2211yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C22×M16×C127C2212yescomplemented
11#525×C127—21no—
12#525×C127—21no—
13#525×C127—21no—
14#525×C127—21no—
15#525×C127C412yescomplemented
16#525×C127C412yescomplemented
17#525×C127C2212yes—
18#525×C127C2212yes—
19C2×#123×C127—21no—
20C2×C22⋊Q8×C127C411yescharacteristic, complemented
21C2×C22⋊Q8×C127C411yescharacteristic, complemented
22C2×#121×C127C411yescharacteristic, complemented
23C2×#121×C127C411yescharacteristic, complemented
24C2×#120×C127—21no—
25C2×C4×D4×C127—21no—
26C2×C4×D4×C127—21no—
27C2×#117×C127C2211yescharacteristic
28C22×C22⋊C4×C127—21no—
29C22×C42×C127C2212yescomplemented
30C2×#104×C127C2218yescomplemented
31#407×C127—21no—
32#407×C127—21no—
33#407×C127C2212yes—
34#407×C127C2212yescomplemented
35C2×C22⋊C8×C127—21no—
36C2×C22⋊C8×C127—21no—
37C4×C22⋊C4×C127—21no—
38C4×C22⋊C4×C127—21no—
39C4×C22⋊C4×C127C2212yes—
40C4×C22⋊C4×C127C2212yescomplemented
41C2×#95×C127—21no—
42#339×C127C2218yescomplemented
43C25×C127D411yescharacteristic
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—44no—
47C2×#41×C127C2×C412yescomplemented
48C2×#41×C127C2312yes—
49C22×Q8×C127C2×C411yescharacteristic, complemented
50C22×D4×C127—21no—
51C22×D4×C127—21no—
52C22×D4×C127—21no—
53C22×D4×C127C2×C411yescharacteristic, complemented
54C23×C4×C127—22no—
55C23×C4×C127—21no—
56C23×C4×C127—44no—
57C23×C4×C127C2×C411yescharacteristic
58C23×C4×C127C2×C411yescharacteristic
59C23×C4×C127C2×C411yescharacteristic
60C23×C4×C127C2×C411yescharacteristic
61C23×C4×C127D411yescharacteristic
62C23×C4×C127D411yescharacteristic
63C23×C4×C127D411yescharacteristic
64C23×C4×C127D411yescharacteristic
65C23×C4×C127D411yescharacteristic
66C23×C4×C127D411yescharacteristic
67C23×C4×C127D411yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C2×M16×C127—22no—
72C2×M16×C127—44no—
73C2×M16×C127C2314yes—
74C22×C8×C127—22no—
75#123×C127—22no—
76#123×C127—22no—
77#123×C127—22no—
78#123×C127—22no—
79C22⋊Q8×C127—21no—
80C22⋊Q8×C127—21no—
81C22⋊Q8×C127—21no—
82C22⋊Q8×C127—21no—
83C22⋊Q8×C127C2×C412yes—
84C22⋊Q8×C127C2×C412yes—
85C22⋊Q8×C127C2×C412yescomplemented
86C22⋊Q8×C127C2×C412yescomplemented
87#121×C127—21no—
88#121×C127—21no—
89#121×C127—21no—
90#121×C127—21no—
91#121×C127C2×C412yes—
92#121×C127C2×C412yes—
93#121×C127C2×C412yescomplemented
94#121×C127C2×C412yescomplemented
95#120×C127—22no—
96#120×C127—22no—
97#120×C127—22no—
98#120×C127—22no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—22no—
104C4×D4×C127—22no—
105C4×D4×C127—22no—
106C4×D4×C127—22no—
107#117×C127—21no—
108#117×C127—21no—
109#117×C127C2×C412yescomplemented
110#117×C127C2312yes—
111C2×C4⋊C4×C127—21no—
112C2×C4⋊C4×C127—21no—
113C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
115C2×C22⋊C4×C127—28no—
116C2×C22⋊C4×C127—21no—
117C2×C22⋊C4×C127—21no—
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—21no—
121C2×C22⋊C4×C127—21no—
122C2×C22⋊C4×C127—21no—
123C2×C42×C127—21no—
124C2×C42×C127—22no—
125C2×C42×C127—44no—
126C2×C42×C127C2314yes—
127#104×C127—48no—
128C22⋊C8×C127—22no—
129C22⋊C8×C127—22no—
130C22⋊C8×C127—22no—
131C22⋊C8×C127—22no—
132#95×C127—22no—
133#95×C127—22no—
134C24×C127—24no—
135C24×C127—21no—
136C24×C127—42no—
137C24×C127—42no—
138C24×C127C22⋊C411yescharacteristic
139C24×C127C22⋊C411yescharacteristic
140C24×C127C22⋊C411yescharacteristic
141C24×C127C22⋊C411yescharacteristic
142C24×C127C2×D411yescharacteristic
143C24×C127C2×D411yescharacteristic
144C24×C127C2×D411yescharacteristic
145#41×C127—28no—
146#41×C127—44no—
147#41×C127—44no—
148#41×C127—44no—
149C2×Q8×C127—21no—
150C2×Q8×C127—42no—
151C2×Q8×C127C22×C412yes—
152C2×D4×C127—22no—
153C2×D4×C127—22no—
154C2×D4×C127—22no—
155C2×D4×C127—22no—
156C2×D4×C127—22no—
157C2×D4×C127—22no—
158C2×D4×C127—21no—
159C2×D4×C127—42no—
160C2×D4×C127—44no—
161C2×D4×C127—44no—
162C2×D4×C127—44no—
163C2×D4×C127C22×C412yes—
164C22×C4×C127—24no—
165C22×C4×C127—24no—
166C22×C4×C127—24no—
167C22×C4×C127—28no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—24no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—42no—
175C22×C4×C127—42no—
176C22×C4×C127—42no—
177C22×C4×C127—42no—
178C22×C4×C127—42no—
179C22×C4×C127—42no—
180C22×C4×C127—42no—
181C22×C4×C127—42no—
182C22×C4×C127—42no—
183C22×C4×C127—42no—
184C22×C4×C127—42no—
185C22×C4×C127—44no—
186C22×C4×C127—44no—
187C22×C4×C127—44no—
188C22×C4×C127C22⋊C411yescharacteristic
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×C127C22×C411yescharacteristic
201C22×C4×C127C22×C411yescharacteristic
202C22×C4×C127C22×C411yescharacteristic
203C22×C4×C127C22×C411yescharacteristic
204C22×C4×C127C22×C411yescharacteristic
205C22×C4×C127C22×C411yescharacteristic
206C22×C4×C127C2×D411yescharacteristic
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2×D411yescharacteristic
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2411yescharacteristic
216M16×C127—28no—
217M16×C127—44no—
218C2×C8×C127—24no—
219C2×C8×C127—44no—
220C4⋊C4×C127—22no—
221C4⋊C4×C127—22no—
222C4⋊C4×C127—22no—
223C4⋊C4×C127—22no—
224C4⋊C4×C127—21no—
225C4⋊C4×C127—21no—
226C4⋊C4×C127C22×C412yes—
227C4⋊C4×C127C22×C412yes—
228C22⋊C4×C127—28no—
229C22⋊C4×C127—28no—
230C22⋊C4×C127—22no—
231C22⋊C4×C127—22no—
232C22⋊C4×C127—22no—
233C22⋊C4×C127—22no—
234C22⋊C4×C127—22no—
235C22⋊C4×C127—22no—
236C22⋊C4×C127—22no—
237C22⋊C4×C127—22no—
238C22⋊C4×C127—22no—
239C22⋊C4×C127—22no—
240C42×C127—22no—
241C42×C127—22no—
242C42×C127—28no—
243C42×C127—44no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—22no—
249C23×C127—22no—
250C23×C127—22no—
251C23×C127—22no—
252C23×C127—22no—
253C23×C127—22no—
254C23×C127—22no—
255C23×C127—22no—
256C23×C127—22no—
257C23×C127—41no—
258C23×C127—41no—
259C23×C127—41no—
260C23×C127—41no—
261C23×C127—41no—
262C23×C127—41no—
263C23×C127—41no—
264C23×C127—41no—
265C23×C127—416no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127#10414yescomplemented
270C23×C127C2×C22⋊C411yescharacteristic
271C23×C127C2×C22⋊C411yescharacteristic
272C23×C127C2×C22⋊C411yescharacteristic
273C23×C127C2×C22⋊C411yescharacteristic
274C23×C127C2×C22⋊C411yescharacteristic
275C23×C127C2×C22⋊C411yescharacteristic
276C23×C127C22×D411yescharacteristic
277Q8×C127—24no—
278Q8×C127—42no—
279D4×C127—24no—
280D4×C127—42no—
281D4×C127—44no—
282D4×C127—44no—
283D4×C127—44no—
284D4×C127—44no—
285D4×C127—44no—
286D4×C127—44no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—22no—
302C2×C4×C127—28no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
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×C127—41no—
315C2×C4×C127—41no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—44no—
319C2×C4×C127—416no—
320C2×C4×C127—44no—
321C2×C4×C127—42no—
322C2×C4×C127—42no—
323C2×C4×C127—44no—
324C2×C4×C127—42no—
325C2×C4×C127—44no—
326C2×C4×C127C2×C22⋊C411yescharacteristic
327C2×C4×C127C2×C22⋊C411yescharacteristic
328C2×C4×C127C2×C22⋊C411yescharacteristic
329C2×C4×C127C2×C22⋊C411yescharacteristic
330C2×C4×C127C2×C22⋊C411yescharacteristic
331C2×C4×C127C2×C22⋊C411yescharacteristic
332C2×C4×C127C23×C411yescharacteristic
333C2×C4×C127C22×D411yescharacteristic
334C2×C4×C127H(5,𝔽2)14yes—
335C8×C127—44no—
336C22×C127—28no—
337C22×C127—21no—
338C22×C127—21no—
339C22×C127—21no—
340C22×C127—21no—
341C22×C127—21no—
342C22×C127—21no—
343C22×C127—21no—
344C22×C127—21no—
345C22×C127—21no—
346C22×C127—21no—
347C22×C127—21no—
348C22×C127—21no—
349C22×C127—21no—
350C22×C127—21no—
351C22×C127—21no—
352C22×C127—21no—
353C22×C127—44no—
354C22×C127—44no—
355C22×C127—44no—
356C22×C127—44no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—42no—
360C22×C127—42no—
361C22×C127—42no—
362C22×C127—84no—
363C22×C127C2×#10412yes—
364C22×C127C2×#10412yes—
365C22×C127C2×#10412yes—
366C22×C127#42112yes—
367C22×C127C22×C22⋊C411yescharacteristic
368C22×C127#53412yes—
369C4×C127—21no—
370C4×C127—21no—
371C4×C127—21no—
372C4×C127—21no—
373C4×C127—21no—
374C4×C127—21no—
375C4×C127—48no—
376C4×C127—42no—
377C4×C127—42no—
378C4×C127—42no—
379C4×C127#51812yes—
380C4×C127#53412yes—
381#21773C12711yesmaximal, characteristic, direct product factor, Sylow
382C2×C127—22no—
383C2×C127—22no—
384C2×C127—22no—
385C2×C127—22no—
386C2×C127—22no—
387C2×C127—41no—
388C2×C127—41no—
389C2×C127—82no—
390C2×C127#230811yescharacteristic
391C2×C127C22×#10411yescharacteristic
392C2×C127C2×#42111yescharacteristic
393C2×#525C2×C12711yescharacteristic
394C2×#407C2×C12711yescharacteristic, complemented
395C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
396#1896C2×C12714yescomplemented
397#1871C2×C12714yescomplemented
398#1826C2×C12712yescomplemented
399#1789C2×C12712yescomplemented
400C127#2177311yescharacteristic, direct product factor, Sylow
401C22×#41C22×C12711yescharacteristic
402C24×C4C22×C12711yescharacteristic
403C22×M16C22×C12712yescomplemented
404#525—21no—
405#525—21no—
406#525—21no—
407#525—21no—
408#525C4×C12712yescomplemented
409#525C4×C12712yescomplemented
410#525C22×C12712yes—
411#525C22×C12712yes—
412C2×#123—21no—
413C2×C22⋊Q8C4×C12711yescharacteristic, complemented
414C2×C22⋊Q8C4×C12711yescharacteristic, complemented
415C2×#121C4×C12711yescharacteristic, complemented
416C2×#121C4×C12711yescharacteristic, complemented
417C2×#120—21no—
418C2×C4×D4—21no—
419C2×C4×D4—21no—
420C2×#117C22×C12711yescharacteristic
421C22×C22⋊C4—21no—
422C22×C42C22×C12712yescomplemented
423C2×#104C22×C12718yescomplemented
424#407—21no—
425#407—21no—
426#407C22×C12712yes—
427#407C22×C12712yescomplemented
428C2×C22⋊C8—21no—
429C2×C22⋊C8—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4C22×C12712yes—
433C4×C22⋊C4C22×C12712yescomplemented
434C2×#95—21no—
435#339C22×C12718yescomplemented
436C25D4×C12711yescharacteristic
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—44no—
440C2×#41C2×C4×C12712yescomplemented
441C2×#41C23×C12712yes—
442C22×Q8C2×C4×C12711yescharacteristic, complemented
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C2×C4×C12711yescharacteristic, complemented
447C23×C4—22no—
448C23×C4—21no—
449C23×C4—44no—
450C23×C4C2×C4×C12711yescharacteristic
451C23×C4C2×C4×C12711yescharacteristic
452C23×C4C2×C4×C12711yescharacteristic
453C23×C4C2×C4×C12711yescharacteristic
454C23×C4D4×C12711yescharacteristic
455C23×C4D4×C12711yescharacteristic
456C23×C4D4×C12711yescharacteristic
457C23×C4D4×C12711yescharacteristic
458C23×C4D4×C12711yescharacteristic
459C23×C4D4×C12711yescharacteristic
460C23×C4D4×C12711yescharacteristic
461C23×C4C23×C12711yescharacteristic
462C23×C4C23×C12711yescharacteristic
463C23×C4C23×C12711yescharacteristic
464C2×M16—22no—
465C2×M16—44no—
466C2×M16C23×C12714yes—
467C22×C8—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8C2×C4×C12712yes—
477C22⋊Q8C2×C4×C12712yes—
478C22⋊Q8C2×C4×C12712yescomplemented
479C22⋊Q8C2×C4×C12712yescomplemented
480#121—21no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121C2×C4×C12712yes—
485#121C2×C4×C12712yes—
486#121C2×C4×C12712yescomplemented
487#121C2×C4×C12712yescomplemented
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500#117—21no—
501#117—21no—
502#117C2×C4×C12712yescomplemented
503#117C23×C12712yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
507C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
508C2×C22⋊C4—28no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C42—21no—
517C2×C42—22no—
518C2×C42—44no—
519C2×C42C23×C12714yes—
520#104—48no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525#95—22no—
526#95—22no—
527C24—24no—
528C24—21no—
529C24—42no—
530C24—42no—
531C24C22⋊C4×C12711yescharacteristic
532C24C22⋊C4×C12711yescharacteristic
533C24C22⋊C4×C12711yescharacteristic
534C24C22⋊C4×C12711yescharacteristic
535C24C2×D4×C12711yescharacteristic
536C24C2×D4×C12711yescharacteristic
537C24C2×D4×C12711yescharacteristic
538#41—28no—
539#41—44no—
540#41—44no—
541#41—44no—
542C2×Q8—21no—
543C2×Q8—42no—
544C2×Q8C22×C4×C12712yes—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4C22×C4×C12712yes—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—28no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4C22⋊C4×C12711yescharacteristic
582C22×C4C22⋊C4×C12711yescharacteristic
583C22×C4C22⋊C4×C12711yescharacteristic
584C22×C4C22⋊C4×C12711yescharacteristic
585C22×C4C22⋊C4×C12711yescharacteristic
586C22×C4C22⋊C4×C12711yescharacteristic
587C22×C4C22⋊C4×C12711yescharacteristic
588C22×C4C22⋊C4×C12711yescharacteristic
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×C4C2×D4×C12711yescharacteristic
600C22×C4C2×D4×C12711yescharacteristic
601C22×C4C2×D4×C12711yescharacteristic
602C22×C4C2×D4×C12711yescharacteristic
603C22×C4C2×D4×C12711yescharacteristic
604C22×C4C2×D4×C12711yescharacteristic
605C22×C4C2×D4×C12711yescharacteristic
606C22×C4C2×D4×C12711yescharacteristic
607C22×C4C2×D4×C12711yescharacteristic
608C22×C4C24×C12711yescharacteristic
609M16—28no—
610M16—44no—
611C2×C8—24no—
612C2×C8—44no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4C22×C4×C12712yes—
620C4⋊C4C22×C4×C12712yes—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C42—22no—
634C42—22no—
635C42—28no—
636C42—44no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—416no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23#104×C12714yescomplemented
663C23C2×C22⋊C4×C12711yescharacteristic
664C23C2×C22⋊C4×C12711yescharacteristic
665C23C2×C22⋊C4×C12711yescharacteristic
666C23C2×C22⋊C4×C12711yescharacteristic
667C23C2×C22⋊C4×C12711yescharacteristic
668C23C2×C22⋊C4×C12711yescharacteristic
669C23C22×D4×C12711yescharacteristic
670Q8—24no—
671Q8—42no—
672D4—24no—
673D4—42no—
674D4—44no—
675D4—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—44no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4C2×C22⋊C4×C12711yescharacteristic
720C2×C4C2×C22⋊C4×C12711yescharacteristic
721C2×C4C2×C22⋊C4×C12711yescharacteristic
722C2×C4C2×C22⋊C4×C12711yescharacteristic
723C2×C4C2×C22⋊C4×C12711yescharacteristic
724C2×C4C2×C22⋊C4×C12711yescharacteristic
725C2×C4C23×C4×C12711yescharacteristic
726C2×C4C22×D4×C12711yescharacteristic
727C2×C4H(5,𝔽2)×C12714yes—
728C8—44no—
729C22—28no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22C2×#104×C12712yes—
757C22C2×#104×C12712yes—
758C22C2×#104×C12712yes—
759C22#421×C12712yes—
760C22C22×C22⋊C4×C12711yescharacteristic
761C22#534×C12712yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—48no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4#518×C12712yes—
773C4#534×C12712yes—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—22no—
778C2—22no—
779C2—41no—
780C2—41no—
781C2—82no—
782C2C127×#230811yescharacteristic
783C2C22×#104×C12711yescharacteristic
784C2C2×#421×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC2×#525×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C127C2semidirect
3. C2×C4×C22⋊C4×C127C2semidirect
4. C127×#1896C2semidirect
5. C127×#1871C2semidirect
6. C127×#1826C2semidirect
7. C127×#1789C2semidirect
10. C22×M16×C127C22semidirect
15. #525×C127C4semidirect
16. #525×C127C4semidirect
20. C2×C22⋊Q8×C127C4semidirect
21. C2×C22⋊Q8×C127C4semidirect
22. C2×#121×C127C4semidirect
23. C2×#121×C127C4semidirect
29. C22×C42×C127C22semidirect
30. C2×#104×C127C22semidirect
34. #407×C127C22semidirect
40. C4×C22⋊C4×C127C22semidirect
42. #339×C127C22semidirect
47. C2×#41×C127C2×C4semidirect
49. C22×Q8×C127C2×C4semidirect
53. C22×D4×C127C2×C4semidirect
85. C22⋊Q8×C127C2×C4semidirect
86. C22⋊Q8×C127C2×C4semidirect
93. #121×C127C2×C4semidirect
94. #121×C127C2×C4semidirect
109. #117×C127C2×C4semidirect
113. C2×C4⋊C4×C127C2×C4semidirect
114. C2×C4⋊C4×C127C2×C4semidirect
269. C23×C127#104semidirect
381. #21773C127direct (N × H)
394. C2×#407C2×C127semidirect
395. C2×C4×C22⋊C4C2×C127semidirect
396. #1896C2×C127semidirect
397. #1871C2×C127semidirect
398. #1826C2×C127semidirect
399. #1789C2×C127semidirect
400. C127#21773direct (N × H)
403. C22×M16C22×C127semidirect
408. #525C4×C127semidirect
409. #525C4×C127semidirect
413. C2×C22⋊Q8C4×C127semidirect
414. C2×C22⋊Q8C4×C127semidirect
415. C2×#121C4×C127semidirect
416. C2×#121C4×C127semidirect
422. C22×C42C22×C127semidirect
423. C2×#104C22×C127semidirect
427. #407C22×C127semidirect
433. C4×C22⋊C4C22×C127semidirect
435. #339C22×C127semidirect
440. C2×#41C2×C4×C127semidirect
442. C22×Q8C2×C4×C127semidirect
446. C22×D4C2×C4×C127semidirect
478. C22⋊Q8C2×C4×C127semidirect
479. C22⋊Q8C2×C4×C127semidirect
486. #121C2×C4×C127semidirect
487. #121C2×C4×C127semidirect
502. #117C2×C4×C127semidirect
506. C2×C4⋊C4C2×C4×C127semidirect
507. C2×C4⋊C4C2×C4×C127semidirect
662. C23#104×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1272
C2×#407×C1272
C2×C4×C22⋊C4×C1272
C127×#18962
C127×#18712
C127×#18262
C127×#17892
#21773127