Finite Group Databasebeta

← C127×#10993 #44574666

Subgroups — C127×#10993 #44574666

Order 32512.

1458 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C127C211yesmaximal, characteristic
2C2×#413×C127C211yesmaximal, characteristic, complemented
3C127×#2879C211yesmaximal, characteristic, complemented
4C2×#407×C127C212yesmaximal, complemented
5C2×#344×C127C212yesmaximal, complemented
6C22×#41×C127C2211yescharacteristic
7C24×C4×C127C2211yescharacteristic
8C22×M16×C127C2212yes—
9C22×M16×C127C2212yes—
10#525×C127—24no—
11#525×C127—24no—
12C2×#123×C127C412yes—
13C2×C22⋊Q8×C127—21no—
14C2×#121×C127—21no—
15C2×#120×C127C412yes—
16C2×C4×D4×C127—22no—
17C2×#117×C127C2211yescharacteristic
18#413×C127—24no—
19C2×#101×C127—21no—
20C2×#100×C127—21no—
21#408×C127—24no—
22#407×C127—24no—
23#407×C127—22no—
24#407×C127—24no—
25C2×C22⋊C8×C127—24no—
26#344×C127—24no—
27C25×C127C2×C411yescharacteristic
28C2×#41×C127—22no—
29C2×#41×C127—22no—
30C2×#41×C127—22no—
31C2×#41×C127—22no—
32C2×#41×C127—22no—
33C2×#41×C127—22no—
34C22×Q8×C127D411yescharacteristic
35C22×D4×C127—22no—
36C22×D4×C127C2×C412yes—
37C22×D4×C127D411yescharacteristic
38C23×C4×C127—21no—
39C23×C4×C127—21no—
40C23×C4×C127—22no—
41C23×C4×C127—22no—
42C23×C4×C127—22no—
43C23×C4×C127—22no—
44C23×C4×C127—22no—
45C23×C4×C127C2×C411yescharacteristic
46C23×C4×C127D412yes—
47C23×C4×C127D414yes—
48C23×C4×C127C2311yescharacteristic
49C2×M16×C127—22no—
50C2×M16×C127—22no—
51C2×M16×C127—22no—
52C2×M16×C127—22no—
53C2×M16×C127—22no—
54C2×M16×C127—22no—
55C2×M16×C127—22no—
56C2×M16×C127—22no—
57C2×M16×C127—22no—
58C2×M16×C127—22no—
59C2×M16×C127—22no—
60C2×M16×C127D414yescomplemented
61C22×C8×C127—22no—
62C22×C8×C127D414yescomplemented
63#123×C127—24no—
64#123×C127—24no—
65C22⋊Q8×C127—28no—
66#121×C127—28no—
67#120×C127—24no—
68#120×C127—24no—
69C4×D4×C127—216no—
70#117×C127—22no—
71#117×C127D414yes—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—21no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127C2×C412yes—
77C2×C42×C127—21no—
78#101×C127—24no—
79#100×C127—24no—
80C22⋊C8×C127—216no—
81C22⋊C8×C127—28no—
82C24×C127—21no—
83C24×C127—22no—
84C24×C127—21no—
85C24×C127—22no—
86C24×C127—44no—
87C24×C127C22⋊C412yes—
88C24×C127C22⋊C412yes—
89C24×C127C22×C411yescharacteristic
90#41×C127—42no—
91#41×C127—42no—
92#41×C127—42no—
93#41×C127—42no—
94#41×C127—42no—
95#41×C127—42no—
96#41×C127—42no—
97#41×C127—42no—
98C2×Q8×C127—21no—
99C2×Q8×C127—22no—
100C2×Q8×C127—22no—
101C2×Q8×C127—21no—
102C2×D4×C127—28no—
103C2×D4×C127—22no—
104C2×D4×C127—22no—
105C2×D4×C127—24no—
106C2×D4×C127—24no—
107C2×D4×C127—21no—
108C2×D4×C127—22no—
109C2×D4×C127—22no—
110C2×D4×C127—21no—
111C2×D4×C127—48no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—24no—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127—24no—
123C22×C4×C127—24no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—22no—
127C22×C4×C127—41no—
128C22×C4×C127—41no—
129C22×C4×C127—42no—
130C22×C4×C127—42no—
131C22×C4×C127—42no—
132C22×C4×C127—42no—
133C22×C4×C127—41no—
134C22×C4×C127—41no—
135C22×C4×C127—42no—
136C22×C4×C127—42no—
137C22×C4×C127C22⋊C412yes—
138C22×C4×C127C22⋊C412yes—
139C22×C4×C127C2×D411yescharacteristic
140C22×C4×C127C2×D412yes—
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D412yes—
143C22×C4×C127C2×D412yes—
144C22×C4×C127C2×D412yes—
145C22×C4×C127#4112yes—
146C22×C4×C127#4112yes—
147M16×C127—24no—
148M16×C127—24no—
149M16×C127—42no—
150M16×C127—42no—
151M16×C127—42no—
152M16×C127—42no—
153M16×C127—42no—
154M16×C127—42no—
155C2×C8×C127—24no—
156C2×C8×C127—24no—
157C2×C8×C127—24no—
158C2×C8×C127—24no—
159C2×C8×C127—42no—
160C2×C8×C127—42no—
161C4⋊C4×C127—28no—
162C4⋊C4×C127—24no—
163C22⋊C4×C127—28no—
164C22⋊C4×C127—28no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127C22⋊C414yes—
167C42×C127—24no—
168C23×C127—24no—
169C23×C127—28no—
170C23×C127—22no—
171C23×C127—24no—
172C23×C127—22no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—44no—
176C23×C127—42no—
177C23×C127—42no—
178C23×C127—44no—
179C23×C127—44no—
180C23×C127—48no—
181C23×C127—44no—
182C23×C127—41no—
183C23×C127—41no—
184C23×C127—42no—
185C23×C127C2×C22⋊C411yescharacteristic
186C23×C127C2×C22⋊C411yescharacteristic
187C23×C127C2×C22⋊C411yescharacteristic
188C23×C127C4×D412yes—
189C23×C127C4×D412yes—
190Q8×C127—42no—
191Q8×C127—42no—
192D4×C127—416no—
193D4×C127—44no—
194D4×C127—44no—
195D4×C127—42no—
196D4×C127—42no—
197C2×C4×C127—24no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—24no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—44no—
204C2×C4×C127—41no—
205C2×C4×C127—41no—
206C2×C4×C127—42no—
207C2×C4×C127—44no—
208C2×C4×C127—44no—
209C2×C4×C127—44no—
210C2×C4×C127—44no—
211C2×C4×C127—44no—
212C2×C4×C127—44no—
213C2×C4×C127#12012yes—
214C2×C4×C127#12011yescharacteristic
215C2×C4×C127#12012yes—
216C2×C4×C127#12012yes—
217C2×C4×C127#12011yescharacteristic
218C2×C4×C127#12112yes—
219C2×C4×C127#12112yes—
220C2×C4×C127#12112yes—
221C2×C4×C127#12112yes—
222C2×C4×C127#12112yes—
223C2×C4×C127#12112yes—
224C2×C4×C127#12311yescharacteristic
225C2×C4×C127#12312yes—
226C2×C4×C127#12311yescharacteristic
227C2×C4×C127#12412yes—
228C2×C4×C127#12712yes—
229C8×C127—44no—
230C8×C127—44no—
231C22×C127—22no—
232C22×C127—24no—
233C22×C127—24no—
234C22×C127—28no—
235C22×C127—41no—
236C22×C127—41no—
237C22×C127—42no—
238C22×C127—42no—
239C22×C127—44no—
240C22×C127—44no—
241C22×C127—48no—
242C22×C127—44no—
243C22×C127—44no—
244C22×C127—42no—
245C22×C127—44no—
246C22×C127—42no—
247C22×C127—82no—
248C22×C127#37911yescharacteristic
249C22×C127#38611yescharacteristic
250C22×C127#38612yes—
251C22×C127#38611yescharacteristic
252C22×C127#39012yes—
253C4×C127—44no—
254C4×C127—42no—
255C4×C127—42no—
256C4×C127#39212yes—
257C4×C127#39212yes—
258C4×C127#39412yes—
259C4×C127#39412yes—
260#10993C12711yesmaximal, characteristic, direct product factor, Sylow
261C2×C127—21no—
262C2×C127—22no—
263C2×C127—21no—
264C2×C127—22no—
265C2×C127—44no—
266C2×C127—82no—
267C2×C127#143811yescharacteristic
268C2×C127#189112yes—
269C2×#525C2×C12711yescharacteristic
270C2×#413C2×C12711yescharacteristic, complemented
271#2879C2×C12711yescharacteristic, complemented
272C2×#407C2×C12712yescomplemented
273C2×#344C2×C12712yescomplemented
274C127#1099311yescharacteristic, direct product factor, Sylow
275C22×#41C22×C12711yescharacteristic
276C24×C4C22×C12711yescharacteristic
277C22×M16C22×C12712yes—
278C22×M16C22×C12712yes—
279#525—24no—
280#525—24no—
281C2×#123C4×C12712yes—
282C2×C22⋊Q8—21no—
283C2×#121—21no—
284C2×#120C4×C12712yes—
285C2×C4×D4—22no—
286C2×#117C22×C12711yescharacteristic
287#413—24no—
288C2×#101—21no—
289C2×#100—21no—
290#408—24no—
291#407—24no—
292#407—22no—
293#407—24no—
294C2×C22⋊C8—24no—
295#344—24no—
296C25C2×C4×C12711yescharacteristic
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C22×Q8D4×C12711yescharacteristic
304C22×D4—22no—
305C22×D4C2×C4×C12712yes—
306C22×D4D4×C12711yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4C2×C4×C12711yescharacteristic
315C23×C4D4×C12712yes—
316C23×C4D4×C12714yes—
317C23×C4C23×C12711yescharacteristic
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16D4×C12714yescomplemented
330C22×C8—22no—
331C22×C8D4×C12714yescomplemented
332#123—24no—
333#123—24no—
334C22⋊Q8—28no—
335#121—28no—
336#120—24no—
337#120—24no—
338C4×D4—216no—
339#117—22no—
340#117D4×C12714yes—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4C2×C4×C12712yes—
346C2×C42—21no—
347#101—24no—
348#100—24no—
349C22⋊C8—216no—
350C22⋊C8—28no—
351C24—21no—
352C24—22no—
353C24—21no—
354C24—22no—
355C24—44no—
356C24C22⋊C4×C12712yes—
357C24C22⋊C4×C12712yes—
358C24C22×C4×C12711yescharacteristic
359#41—42no—
360#41—42no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×D4—28no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—21no—
380C2×D4—48no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4C22⋊C4×C12712yes—
407C22×C4C22⋊C4×C12712yes—
408C22×C4C2×D4×C12711yescharacteristic
409C22×C4C2×D4×C12711yescharacteristic
410C22×C4C2×D4×C12712yes—
411C22×C4C2×D4×C12712yes—
412C22×C4C2×D4×C12712yes—
413C22×C4C2×D4×C12712yes—
414C22×C4#41×C12712yes—
415C22×C4#41×C12712yes—
416M16—24no—
417M16—24no—
418M16—42no—
419M16—42no—
420M16—42no—
421M16—42no—
422M16—42no—
423M16—42no—
424C2×C8—24no—
425C2×C8—24no—
426C2×C8—24no—
427C2×C8—24no—
428C2×C8—42no—
429C2×C8—42no—
430C4⋊C4—28no—
431C4⋊C4—24no—
432C22⋊C4—28no—
433C22⋊C4—28no—
434C22⋊C4—22no—
435C22⋊C4C22⋊C4×C12714yes—
436C42—24no—
437C23—24no—
438C23—28no—
439C23—22no—
440C23—24no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—44no—
445C23—42no—
446C23—42no—
447C23—44no—
448C23—44no—
449C23—48no—
450C23—44no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23C2×C22⋊C4×C12711yescharacteristic
455C23C2×C22⋊C4×C12711yescharacteristic
456C23C2×C22⋊C4×C12711yescharacteristic
457C23C4×D4×C12712yes—
458C23C4×D4×C12712yes—
459Q8—42no—
460Q8—42no—
461D4—416no—
462D4—44no—
463D4—44no—
464D4—42no—
465D4—42no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—44no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4#120×C12711yescharacteristic
483C2×C4#120×C12712yes—
484C2×C4#120×C12711yescharacteristic
485C2×C4#120×C12712yes—
486C2×C4#120×C12712yes—
487C2×C4#121×C12712yes—
488C2×C4#121×C12712yes—
489C2×C4#121×C12712yes—
490C2×C4#121×C12712yes—
491C2×C4#121×C12712yes—
492C2×C4#121×C12712yes—
493C2×C4#123×C12711yescharacteristic
494C2×C4#123×C12712yes—
495C2×C4#123×C12711yescharacteristic
496C2×C4#124×C12712yes—
497C2×C4#127×C12712yes—
498C8—44no—
499C8—44no—
500C22—22no—
501C22—24no—
502C22—24no—
503C22—28no—
504C22—41no—
505C22—41no—
506C22—42no—
507C22—42no—
508C22—44no—
509C22—44no—
510C22—48no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—44no—
515C22—42no—
516C22—82no—
517C22#379×C12711yescharacteristic
518C22#386×C12711yescharacteristic
519C22#386×C12712yes—
520C22#386×C12711yescharacteristic
521C22#390×C12712yes—
522C4—44no—
523C4—42no—
524C4—42no—
525C4#392×C12712yes—
526C4#392×C12712yes—
527C4#394×C12712yes—
528C4#394×C12712yes—
529C2—21no—
530C2—22no—
531C2—21no—
532C2—22no—
533C2—44no—
534C2—82no—
535C2C127×#143811yescharacteristic
536C2C127×#189112yes—
subgroupG/H
centerC2×C4×C127#120
commutatorC24C22×C4×C127
Frattini, cosocleC23×C4C23×C127
socleC22×C127#386
prime radicalC2×#525×C127C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C127C2semidirect
3. C127×#2879C2semidirect
4. C2×#407×C127C2semidirect
5. C2×#344×C127C2semidirect
60. C2×M16×C127D4semidirect
62. C22×C8×C127D4semidirect
260. #10993C127direct (N × H)
270. C2×#413C2×C127semidirect
271. #2879C2×C127semidirect
272. C2×#407C2×C127semidirect
273. C2×#344C2×C127semidirect
274. C127#10993direct (N × H)
329. C2×M16D4×C127semidirect
331. C22×C8D4×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×#413×C1272
C127×#28792
C2×#407×C1272
C2×#344×C1272
#10993127