Finite Group Databasebeta

← C127×#21425 #44585098

Subgroups — C127×#21425 #44585098

Order 32512.

1100 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic
3C2×C4×M16×C127C211yesmaximal, characteristic
4C127×#1997C212yesmaximal, complemented
5C127×#1966C212yesmaximal, complemented
6C127×#1901C214yesmaximal
7C4×#101×C127C214yesmaximal, complemented
8C22×M16×C127C2212yes—
9#533×C127—21no—
10#533×C127—21no—
11#533×C127—21no—
12#533×C127—21no—
13#533×C127—21no—
14#533×C127—21no—
15#533×C127—21no—
16#533×C127—21no—
17C2×C4⋊Q8×C127C2211yescharacteristic
18C2×C4⋊Q8×C127C2211yescharacteristic
19C2×#125×C127C412yes—
20C2×C22⋊Q8×C127C412yes—
21C2×C22⋊Q8×C127C2212yes—
22C2×C4×Q8×C127C412yes—
23C2×C4×Q8×C127C2212yes—
24C2×#117×C127C412yes—
25C22×C42×C127C2211yescharacteristic
26#432×C127—21no—
27#432×C127—21no—
28#431×C127—21no—
29#431×C127—21no—
30#423×C127C2212yes—
31C2×#101×C127C2218yes—
32#407×C127C2212yes—
33C4×M16×C127—21no—
34C4×M16×C127—21no—
35C4×M16×C127C2212yes—
36C4×M16×C127C2212yes—
37C4×M16×C127C2212yes—
38C2×#97×C127—21no—
39C2×C4×C8×C127—21no—
40#343×C127C2218yes—
41C22×Q8×C127C2×C412yes—
42C22×Q8×C127C2312yes—
43C23×C4×C127C2×C411yescharacteristic
44C23×C4×C127C2×C411yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C2×M16×C127—22no—
47C2×M16×C127—28no—
48C2×M16×C127C2314yes—
49C2×M16×C127C2314yes—
50C22×C8×C127—22no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59#125×C127—22no—
60#125×C127—22no—
61#125×C127—22no—
62#125×C127—22no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—22no—
66C22⋊Q8×C127—22no—
67C22⋊Q8×C127—22no—
68C22⋊Q8×C127—22no—
69C22⋊Q8×C127—22no—
70C22⋊Q8×C127—22no—
71C4×Q8×C127—22no—
72C4×Q8×C127—22no—
73C4×Q8×C127—22no—
74C4×Q8×C127—22no—
75C4×Q8×C127—22no—
76C4×Q8×C127—22no—
77C4×Q8×C127—22no—
78C4×Q8×C127—22no—
79#117×C127—22no—
80#117×C127—22no—
81#117×C127—22no—
82#117×C127—22no—
83C2×C4⋊C4×C127C2×C412yes—
84C2×C4⋊C4×C127C2×C412yes—
85C2×C4⋊C4×C127C2×C412yes—
86C2×C4⋊C4×C127C2×C414yes—
87C2×C4⋊C4×C127C2×C414yes—
88C2×C4⋊C4×C127C2312yes—
89C2×C22⋊C4×C127C2×C414yes—
90C2×C42×C127C2×C414yes—
91C2×C42×C127C2×C411yescharacteristic
92C2×C42×C127C2×C411yescharacteristic
93C2×C42×C127D411yescharacteristic
94C2×C42×C127D411yescharacteristic
95C2×C42×C127D411yescharacteristic
96C2×C42×C127D411yescharacteristic
97C2×C42×C127D411yescharacteristic
98C2×C42×C127D411yescharacteristic
99C2×C42×C127D411yescharacteristic
100C2×C42×C127D411yescharacteristic
101C2×C42×C127C2311yescharacteristic
102C2×C42×C127C2311yescharacteristic
103C4⋊C8×C127—22no—
104C4⋊C8×C127—22no—
105#101×C127—216no—
106C22⋊C8×C127—22no—
107C22⋊C8×C127—22no—
108#97×C127—22no—
109#97×C127—22no—
110#97×C127—22no—
111C4×C8×C127—22no—
112C4×C8×C127—22no—
113C4×C8×C127—22no—
114C24×C127C22×C411yescharacteristic
115C2×Q8×C127—22no—
116C2×Q8×C127—22no—
117C2×Q8×C127—22no—
118C2×Q8×C127—22no—
119C2×Q8×C127—28no—
120C2×Q8×C127—44no—
121C22×C4×C127—24no—
122C22×C4×C127—24no—
123C22×C4×C127—42no—
124C22×C4×C127C22⋊C411yescharacteristic
125C22×C4×C127C22⋊C411yescharacteristic
126C22×C4×C127C22⋊C411yescharacteristic
127C22×C4×C127C22⋊C411yescharacteristic
128C22×C4×C127C22⋊C411yescharacteristic
129C22×C4×C127C22⋊C411yescharacteristic
130C22×C4×C127C22⋊C411yescharacteristic
131C22×C4×C127C22⋊C411yescharacteristic
132C22×C4×C127C22×C414yes—
133C22×C4×C127C22×C411yescharacteristic
134C22×C4×C127C22×C411yescharacteristic
135C22×C4×C127C22×C411yescharacteristic
136C22×C4×C127C22×C411yescharacteristic
137C22×C4×C127C22×C414yes—
138C22×C4×C127C22×C411yescharacteristic
139C22×C4×C127C2×D411yescharacteristic
140C22×C4×C127C2×D411yescharacteristic
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D411yescharacteristic
143C22×C4×C127C2411yescharacteristic
144M16×C127—28no—
145M16×C127—24no—
146M16×C127—28no—
147M16×C127#4118yes—
148C2×C8×C127—28no—
149C2×C8×C127—24no—
150C2×C8×C127—24no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—24no—
156C4⋊C4×C127—24no—
157C4⋊C4×C127—24no—
158C4⋊C4×C127—24no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127—22no—
161C4⋊C4×C127—22no—
162C4⋊C4×C127—22no—
163C22⋊C4×C127—24no—
164C22⋊C4×C127—24no—
165C42×C127—24no—
166C42×C127—24no—
167C42×C127C22⋊C411yescharacteristic
168C42×C127C22⋊C411yescharacteristic
169C42×C127C22⋊C411yescharacteristic
170C42×C127C22⋊C411yescharacteristic
171C42×C127C22⋊C411yescharacteristic
172C42×C127C22⋊C411yescharacteristic
173C42×C127C22⋊C411yescharacteristic
174C42×C127C22⋊C411yescharacteristic
175C42×C127C2×D411yescharacteristic
176C42×C127C2×D411yescharacteristic
177C42×C127C2×D411yescharacteristic
178C42×C127C2×D411yescharacteristic
179C42×C127C2×D411yescharacteristic
180C42×C127C2×D411yescharacteristic
181C42×C127C2×D411yescharacteristic
182C42×C127C2×D411yescharacteristic
183C23×C127—22no—
184C23×C127—22no—
185C23×C127—41no—
186C23×C127C2×C22⋊C411yescharacteristic
187C23×C127C2×C22⋊C411yescharacteristic
188C23×C127C23×C411yescharacteristic
189Q8×C127—44no—
190Q8×C127—44no—
191Q8×C127—44no—
192Q8×C127—44no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—22no—
206C2×C4×C127—24no—
207C2×C4×C127—24no—
208C2×C4×C127—28no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—44no—
213C2×C4×C127#10114yescomplemented
214C2×C4×C127C2×C22⋊C411yescharacteristic
215C2×C4×C127C2×C22⋊C411yescharacteristic
216C2×C4×C127C2×C22⋊C411yescharacteristic
217C2×C4×C127C2×C22⋊C411yescharacteristic
218C2×C4×C127C2×C22⋊C411yescharacteristic
219C2×C4×C127C2×C22⋊C411yescharacteristic
220C2×C4×C127C2×C22⋊C411yescharacteristic
221C2×C4×C127C2×C22⋊C411yescharacteristic
222C2×C4×C127C2×C22⋊C411yescharacteristic
223C2×C4×C127C2×C22⋊C411yescharacteristic
224C2×C4×C127C22×D411yescharacteristic
225C2×C4×C127C22×D411yescharacteristic
226C2×C4×C127C2×#4114yes—
227C8×C127—28no—
228C8×C127—44no—
229C22×C127—21no—
230C22×C127—21no—
231C22×C127—21no—
232C22×C127—21no—
233C22×C127—21no—
234C22×C127—21no—
235C22×C127—21no—
236C22×C127—44no—
237C22×C127C2×#10112yes—
238C22×C127C22×C22⋊C411yescharacteristic
239C22×C127C4×#4112yes—
240C4×C127—21no—
241C4×C127—21no—
242C4×C127—21no—
243C4×C127—21no—
244C4×C127—21no—
245C4×C127—21no—
246C4×C127—21no—
247C4×C127—44no—
248C4×C127—44no—
249C4×C127C2×#10112yes—
250C4×C127C2×#10112yes—
251C4×C127#41312yes—
252C4×C127#52512yes—
253C4×C127#53212yes—
254#21425C12711yesmaximal, characteristic, direct product factor, Sylow
255C2×C127—22no—
256C2×C127—22no—
257C2×C127—41no—
258C2×C127#229711yescharacteristic
259C2×C127C22×#10111yescharacteristic
260C2×C127C2×#41311yescharacteristic
261C2×#533C2×C12711yescharacteristic
262#2920C2×C12711yescharacteristic
263C2×C4×M16C2×C12711yescharacteristic
264#1997C2×C12712yescomplemented
265#1966C2×C12712yescomplemented
266#1901C2×C12714yes—
267C4×#101C2×C12714yescomplemented
268C127#2142511yescharacteristic, direct product factor, Sylow
269C22×M16C22×C12712yes—
270#533—21no—
271#533—21no—
272#533—21no—
273#533—21no—
274#533—21no—
275#533—21no—
276#533—21no—
277#533—21no—
278C2×C4⋊Q8C22×C12711yescharacteristic
279C2×C4⋊Q8C22×C12711yescharacteristic
280C2×#125C4×C12712yes—
281C2×C22⋊Q8C4×C12712yes—
282C2×C22⋊Q8C22×C12712yes—
283C2×C4×Q8C4×C12712yes—
284C2×C4×Q8C22×C12712yes—
285C2×#117C4×C12712yes—
286C22×C42C22×C12711yescharacteristic
287#432—21no—
288#432—21no—
289#431—21no—
290#431—21no—
291#423C22×C12712yes—
292C2×#101C22×C12718yes—
293#407C22×C12712yes—
294C4×M16—21no—
295C4×M16—21no—
296C4×M16C22×C12712yes—
297C4×M16C22×C12712yes—
298C4×M16C22×C12712yes—
299C2×#97—21no—
300C2×C4×C8—21no—
301#343C22×C12718yes—
302C22×Q8C2×C4×C12712yes—
303C22×Q8C23×C12712yes—
304C23×C4C2×C4×C12711yescharacteristic
305C23×C4C2×C4×C12711yescharacteristic
306C23×C4C23×C12711yescharacteristic
307C2×M16—22no—
308C2×M16—28no—
309C2×M16C23×C12714yes—
310C2×M16C23×C12714yes—
311C22×C8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320#125—22no—
321#125—22no—
322#125—22no—
323#125—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344C2×C4⋊C4C2×C4×C12712yes—
345C2×C4⋊C4C2×C4×C12712yes—
346C2×C4⋊C4C2×C4×C12712yes—
347C2×C4⋊C4C2×C4×C12714yes—
348C2×C4⋊C4C2×C4×C12714yes—
349C2×C4⋊C4C23×C12712yes—
350C2×C22⋊C4C2×C4×C12714yes—
351C2×C42C2×C4×C12714yes—
352C2×C42C2×C4×C12711yescharacteristic
353C2×C42C2×C4×C12711yescharacteristic
354C2×C42D4×C12711yescharacteristic
355C2×C42D4×C12711yescharacteristic
356C2×C42D4×C12711yescharacteristic
357C2×C42D4×C12711yescharacteristic
358C2×C42D4×C12711yescharacteristic
359C2×C42D4×C12711yescharacteristic
360C2×C42D4×C12711yescharacteristic
361C2×C42D4×C12711yescharacteristic
362C2×C42C23×C12711yescharacteristic
363C2×C42C23×C12711yescharacteristic
364C4⋊C8—22no—
365C4⋊C8—22no—
366#101—216no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369#97—22no—
370#97—22no—
371#97—22no—
372C4×C8—22no—
373C4×C8—22no—
374C4×C8—22no—
375C24C22×C4×C12711yescharacteristic
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—28no—
381C2×Q8—44no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—42no—
385C22×C4C22⋊C4×C12711yescharacteristic
386C22×C4C22⋊C4×C12711yescharacteristic
387C22×C4C22⋊C4×C12711yescharacteristic
388C22×C4C22⋊C4×C12711yescharacteristic
389C22×C4C22⋊C4×C12711yescharacteristic
390C22×C4C22⋊C4×C12711yescharacteristic
391C22×C4C22⋊C4×C12711yescharacteristic
392C22×C4C22⋊C4×C12711yescharacteristic
393C22×C4C22×C4×C12714yes—
394C22×C4C22×C4×C12711yescharacteristic
395C22×C4C22×C4×C12711yescharacteristic
396C22×C4C22×C4×C12711yescharacteristic
397C22×C4C22×C4×C12711yescharacteristic
398C22×C4C22×C4×C12714yes—
399C22×C4C22×C4×C12711yescharacteristic
400C22×C4C2×D4×C12711yescharacteristic
401C22×C4C2×D4×C12711yescharacteristic
402C22×C4C2×D4×C12711yescharacteristic
403C22×C4C2×D4×C12711yescharacteristic
404C22×C4C24×C12711yescharacteristic
405M16—28no—
406M16—24no—
407M16—28no—
408M16#41×C12718yes—
409C2×C8—28no—
410C2×C8—24no—
411C2×C8—24no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C42—24no—
427C42—24no—
428C42C22⋊C4×C12711yescharacteristic
429C42C22⋊C4×C12711yescharacteristic
430C42C22⋊C4×C12711yescharacteristic
431C42C22⋊C4×C12711yescharacteristic
432C42C22⋊C4×C12711yescharacteristic
433C42C22⋊C4×C12711yescharacteristic
434C42C22⋊C4×C12711yescharacteristic
435C42C22⋊C4×C12711yescharacteristic
436C42C2×D4×C12711yescharacteristic
437C42C2×D4×C12711yescharacteristic
438C42C2×D4×C12711yescharacteristic
439C42C2×D4×C12711yescharacteristic
440C42C2×D4×C12711yescharacteristic
441C42C2×D4×C12711yescharacteristic
442C42C2×D4×C12711yescharacteristic
443C42C2×D4×C12711yescharacteristic
444C23—22no—
445C23—22no—
446C23—41no—
447C23C2×C22⋊C4×C12711yescharacteristic
448C23C2×C22⋊C4×C12711yescharacteristic
449C23C23×C4×C12711yescharacteristic
450Q8—44no—
451Q8—44no—
452Q8—44no—
453Q8—44no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—28no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4#101×C12714yescomplemented
475C2×C4C2×C22⋊C4×C12711yescharacteristic
476C2×C4C2×C22⋊C4×C12711yescharacteristic
477C2×C4C2×C22⋊C4×C12711yescharacteristic
478C2×C4C2×C22⋊C4×C12711yescharacteristic
479C2×C4C2×C22⋊C4×C12711yescharacteristic
480C2×C4C2×C22⋊C4×C12711yescharacteristic
481C2×C4C2×C22⋊C4×C12711yescharacteristic
482C2×C4C2×C22⋊C4×C12711yescharacteristic
483C2×C4C2×C22⋊C4×C12711yescharacteristic
484C2×C4C2×C22⋊C4×C12711yescharacteristic
485C2×C4C22×D4×C12711yescharacteristic
486C2×C4C22×D4×C12711yescharacteristic
487C2×C4C2×#41×C12714yes—
488C8—28no—
489C8—44no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—44no—
498C22C2×#101×C12712yes—
499C22C22×C22⋊C4×C12711yescharacteristic
500C22C4×#41×C12712yes—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—44no—
509C4—44no—
510C4C2×#101×C12712yes—
511C4C2×#101×C12712yes—
512C4#413×C12712yes—
513C4#525×C12712yes—
514C4#532×C12712yes—
515C2—22no—
516C2—22no—
517C2—41no—
518C2C127×#229711yescharacteristic
519C2C22×#101×C12711yescharacteristic
520C2C2×#413×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC24×C127C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1997C2semidirect
5. C127×#1966C2semidirect
7. C4×#101×C127C2semidirect
213. C2×C4×C127#101semidirect
254. #21425C127direct (N × H)
264. #1997C2×C127semidirect
265. #1966C2×C127semidirect
267. C4×#101C2×C127semidirect
268. C127#21425direct (N × H)
474. C2×C4#101×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1272
C127×#29202
C2×C4×M16×C1272
C127×#19972
C127×#19662
C127×#19012
C4×#101×C1272
#21425127