Finite Group Databasebeta

← C127×#13978 #44577651

Subgroups — C127×#13978 #44577651

Order 32512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic
5C2×#382×C127C211yesmaximal, characteristic
6C127×#1442C214yesmaximal
7C127×#1436C214yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C4×#95×C127C211yesmaximal, characteristic
10C23×Q8×C127C2211yescharacteristic
11C2×C4×Q8×C127—24no—
12C2×C4×Q8×C127—24no—
13C2×C4×Q8×C127—24no—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C42×C127C2212yes—
20C22×C42×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23#391×C127—24no—
24#391×C127C418yescomplemented
25#389×C127—24no—
26#382×C127—24no—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2214yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2214yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2214yes—
34C22×Q8×C127—22no—
35C22×Q8×C127—22no—
36C22×Q8×C127—22no—
37C22×Q8×C127—22no—
38C22×Q8×C127C2×C414yes—
39C22×Q8×C127D414yes—
40C22×Q8×C127Q814yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C4×Q8×C127—232no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—24no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—28no—
63C2×C4⋊C4×C127C2×C414yes—
64C2×C4⋊C4×C127D414yes—
65C2×C42×C127—24no—
66C2×C42×C127—24no—
67C2×C42×C127—24no—
68C2×C42×C127—22no—
69C2×C42×C127—22no—
70C2×C42×C127—22no—
71C2×C42×C127—22no—
72C2×C42×C127—22no—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127C2×C414yes—
76C2×C42×C127D414yes—
77#95×C127—28no—
78#95×C127—24no—
79#95×C127—28no—
80#95×C127—24no—
81#95×C127—28no—
82#95×C127—24no—
83#95×C127C2×C4116yes—
84C24×C127C2411yescharacteristic
85C2×Q8×C127—28no—
86C2×Q8×C127—28no—
87C2×Q8×C127—28no—
88C2×Q8×C127—28no—
89C2×Q8×C127—28no—
90C2×Q8×C127—28no—
91C2×Q8×C127C4⋊C4116yescomplemented
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—22no—
105C22×C4×C127—21no—
106C22×C4×C127—24no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—24no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—24no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—24no—
127C22×C4×C127—24no—
128C22×C4×C127C22×C414yes—
129C22×C4×C127C22×C414yes—
130C22×C4×C127C22×C414yes—
131C22×C4×C127C22×C412yes—
132C22×C4×C127C2×D414yes—
133C22×C4×C127C2×D412yes—
134C22×C4×C127C2×D414yes—
135C22×C4×C127C2×D412yes—
136C22×C4×C127C2×D412yes—
137C22×C4×C127C2×D412yes—
138C22×C4×C127C2×D412yes—
139C22×C4×C127C2×Q814yes—
140C22×C4×C127C2×Q812yes—
141C22×C4×C127#4114yes—
142C22×C4×C127#4114yes—
143C22×C4×C127#4112yes—
144C22×C4×C127#4112yes—
145C4⋊C4×C127—216no—
146C4⋊C4×C127—28no—
147C4⋊C4×C127—28no—
148C4⋊C4×C127—44no—
149C4⋊C4×C127—48no—
150C42×C127—216no—
151C42×C127—28no—
152C42×C127—28no—
153C42×C127—44no—
154C23×C127C23×C411yescharacteristic
155C23×C127C22×D411yescharacteristic
156C23×C127C22×D411yescharacteristic
157C23×C127C22×D411yescharacteristic
158C23×C127C22×Q811yescharacteristic
159C23×C127C2×#4111yescharacteristic
160C23×C127C2×#4111yescharacteristic
161C23×C127C2×#4112yes—
162C23×C127C2×#4112yes—
163C23×C1272−1+412yes—
164C23×C1272−1+412yes—
165Q8×C127—232no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—22no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—22no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—28no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—28no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—44no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—44no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—44no—
209C2×C4×C127—44no—
210C2×C4×C127C2×C4⋊C418yes—
211C2×C4×C127C2×C4⋊C414yes—
212C2×C4×C127C4×D414yes—
213C2×C4×C127C4×D414yes—
214C2×C4×C127#12014yes—
215C2×C4×C127C22⋊Q814yes—
216C2×C4×C127C22⋊Q814yes—
217C2×C4×C127#12314yes—
218C2×C4×C127#12414yes—
219C22×C127C22×C4⋊C411yescharacteristic
220C22×C127C2×C4×D411yescharacteristic
221C22×C127C2×C4×D411yescharacteristic
222C22×C127C4×#4112yes—
223C22×C127#51912yes—
224C22×C127C2×#12011yescharacteristic
225C22×C127C2×C22⋊Q811yescharacteristic
226C22×C127C2×C22⋊Q811yescharacteristic
227C22×C127C2×#12311yescharacteristic
228C22×C127C2×#12411yescharacteristic
229C22×C127#52912yes—
230C22×C127#53211yescharacteristic
231C22×C127#53611yescharacteristic
232C22×C127#53611yescharacteristic
233C22×C127#54112yes—
234C22×C127#54712yes—
235C22×C127#54812yes—
236C22×C127#54812yes—
237C22×C127#54812yes—
238C22×C127#55212yes—
239C22×C127#55612yes—
240C22×C127#55712yes—
241C22×C127#55712yes—
242C4×C127—24no—
243C4×C127—28no—
244C4×C127—44no—
245C4×C127—44no—
246C4×C127—42no—
247C4×C127—44no—
248C4×C127—44no—
249C4×C127—82no—
250C4×C127#38518yes—
251#13978C12711yesmaximal, characteristic, direct product factor, Sylow
252C2×C127C2×#38511yescharacteristic
253C2×C127C4×#12411yescharacteristic
254C2×C127#232711yescharacteristic
255C2×C127#235112yes—
256C2×C127#236212yes—
257C2×C127#242112yes—
258C2×C127#243211yescharacteristic
259C2×C127#243611yescharacteristic
260C2×C127#245312yes—
261C2×C127#256511yescharacteristic
262C2×C127#256811yescharacteristic
263C22×C4×Q8C2×C12711yescharacteristic
264C2×#391C2×C12711yescharacteristic
265C2×#391C2×C12711yescharacteristic
266C2×#389C2×C12711yescharacteristic
267C2×#382C2×C12711yescharacteristic
268#1442C2×C12714yes—
269#1436C2×C12714yes—
270C4⋊#95C2×C12711yescharacteristic
271C4×#95C2×C12711yescharacteristic
272C127#1397811yescharacteristic, direct product factor, Sylow
273C23×Q8C22×C12711yescharacteristic
274C2×C4×Q8—24no—
275C2×C4×Q8—24no—
276C2×C4×Q8—24no—
277C22×C4⋊C4C22×C12712yes—
278C22×C4⋊C4C22×C12712yes—
279C22×C4⋊C4C22×C12711yescharacteristic
280C22×C4⋊C4C22×C12711yescharacteristic
281C22×C4⋊C4C22×C12711yescharacteristic
282C22×C42C22×C12712yes—
283C22×C42C22×C12711yescharacteristic
284C22×C42C22×C12711yescharacteristic
285C22×C42C22×C12711yescharacteristic
286#391—24no—
287#391C4×C12718yescomplemented
288#389—24no—
289#382—24no—
290C2×#95C22×C12712yes—
291C2×#95C22×C12712yes—
292C2×#95C22×C12714yes—
293C2×#95C22×C12714yes—
294C2×#95C22×C12714yes—
295C2×#95C22×C12712yes—
296C2×#95C22×C12714yes—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8C2×C4×C12714yes—
302C22×Q8D4×C12714yes—
303C22×Q8Q8×C12714yes—
304C23×C4C23×C12712yes—
305C23×C4C23×C12712yes—
306C23×C4C23×C12712yes—
307C23×C4C23×C12712yes—
308C23×C4C23×C12711yescharacteristic
309C23×C4C23×C12712yes—
310C23×C4C23×C12712yes—
311C23×C4C23×C12711yescharacteristic
312C23×C4C23×C12711yescharacteristic
313C4×Q8—232no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4C2×C4×C12714yes—
327C2×C4⋊C4D4×C12714yes—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42C2×C4×C12714yes—
339C2×C42D4×C12714yes—
340#95—28no—
341#95—24no—
342#95—28no—
343#95—24no—
344#95—28no—
345#95—24no—
346#95C2×C4×C127116yes—
347C24C24×C12711yescharacteristic
348C2×Q8—28no—
349C2×Q8—28no—
350C2×Q8—28no—
351C2×Q8—28no—
352C2×Q8—28no—
353C2×Q8—28no—
354C2×Q8C4⋊C4×C127116yescomplemented
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4C22×C4×C12714yes—
392C22×C4C22×C4×C12714yes—
393C22×C4C22×C4×C12714yes—
394C22×C4C22×C4×C12712yes—
395C22×C4C2×D4×C12714yes—
396C22×C4C2×D4×C12712yes—
397C22×C4C2×D4×C12714yes—
398C22×C4C2×D4×C12712yes—
399C22×C4C2×D4×C12712yes—
400C22×C4C2×D4×C12712yes—
401C22×C4C2×D4×C12712yes—
402C22×C4C2×Q8×C12714yes—
403C22×C4C2×Q8×C12712yes—
404C22×C4#41×C12714yes—
405C22×C4#41×C12714yes—
406C22×C4#41×C12712yes—
407C22×C4#41×C12712yes—
408C4⋊C4—216no—
409C4⋊C4—28no—
410C4⋊C4—28no—
411C4⋊C4—44no—
412C4⋊C4—48no—
413C42—216no—
414C42—28no—
415C42—28no—
416C42—44no—
417C23C23×C4×C12711yescharacteristic
418C23C22×D4×C12711yescharacteristic
419C23C22×D4×C12711yescharacteristic
420C23C22×D4×C12711yescharacteristic
421C23C22×Q8×C12711yescharacteristic
422C23C2×#41×C12711yescharacteristic
423C23C2×#41×C12711yescharacteristic
424C23C2×#41×C12712yes—
425C23C2×#41×C12712yes—
426C232−1+4×C12712yes—
427C232−1+4×C12712yes—
428Q8—232no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—28no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4C2×C4⋊C4×C12718yes—
474C2×C4C2×C4⋊C4×C12714yes—
475C2×C4C4×D4×C12714yes—
476C2×C4C4×D4×C12714yes—
477C2×C4#120×C12714yes—
478C2×C4C22⋊Q8×C12714yes—
479C2×C4C22⋊Q8×C12714yes—
480C2×C4#123×C12714yes—
481C2×C4#124×C12714yes—
482C22C22×C4⋊C4×C12711yescharacteristic
483C22C2×C4×D4×C12711yescharacteristic
484C22C2×C4×D4×C12711yescharacteristic
485C22C4×#41×C12712yes—
486C22#519×C12712yes—
487C22C2×#120×C12711yescharacteristic
488C22C2×C22⋊Q8×C12711yescharacteristic
489C22C2×C22⋊Q8×C12711yescharacteristic
490C22C2×#123×C12711yescharacteristic
491C22C2×#124×C12711yescharacteristic
492C22#529×C12712yes—
493C22#532×C12711yescharacteristic
494C22#536×C12711yescharacteristic
495C22#536×C12711yescharacteristic
496C22#541×C12712yes—
497C22#547×C12712yes—
498C22#548×C12712yes—
499C22#548×C12712yes—
500C22#548×C12712yes—
501C22#552×C12712yes—
502C22#556×C12712yes—
503C22#557×C12712yes—
504C22#557×C12712yes—
505C4—24no—
506C4—28no—
507C4—44no—
508C4—44no—
509C4—42no—
510C4—44no—
511C4—44no—
512C4—82no—
513C4#385×C12718yes—
514C2C2×#385×C12711yescharacteristic
515C2C4×#124×C12711yescharacteristic
516C2C127×#232711yescharacteristic
517C2C127×#235112yes—
518C2C127×#236212yes—
519C2C127×#242112yes—
520C2C127×#243211yescharacteristic
521C2C127×#243611yescharacteristic
522C2C127×#245312yes—
523C2C127×#256511yescharacteristic
524C2C127×#256811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
24. #391×C127C4semidirect
91. C2×Q8×C127C4⋊C4semidirect
251. #13978C127direct (N × H)
272. C127#13978direct (N × H)
287. #391C4×C127semidirect
354. C2×Q8C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1272
C2×#391×C1272
C2×#389×C1272
C2×#382×C1272
C127×#14422
C127×#14362
C127×C4⋊#952
C4×#95×C1272
#13978127