Finite Group Databasebeta

← C127×#14703 #44578376

Subgroups — C127×#14703 #44578376

Order 32512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic
5C2×C43×C127C211yesmaximal, characteristic
6C127×#1436C214yesmaximal
7C127×C4⋊#95C211yesmaximal, characteristic
8C127×C4⋊#95C211yesmaximal, characteristic
9C127×#1434C214yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2212yes—
16C22×C42×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2212yes—
20#391×C127—24no—
21#391×C127—24no—
22#391×C127C418yescomplemented
23#389×C127—24no—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2214yes—
28C2×#95×C127C2214yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
31C43×C127—24no—
32C22×Q8×C127—22no—
33C22×Q8×C127—22no—
34C22×Q8×C127—22no—
35C22×Q8×C127—22no—
36C22×Q8×C127—22no—
37C22×Q8×C127—22no—
38C22×Q8×C127C2×C414yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—28no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127C2×C414yes—
59C2×C42×C127—24no—
60C2×C42×C127—22no—
61C2×C42×C127—22no—
62C2×C42×C127—24no—
63C2×C42×C127—24no—
64C2×C42×C127—24no—
65C2×C42×C127—22no—
66C2×C42×C127—22no—
67C2×C42×C127—24no—
68C2×C42×C127—22no—
69C2×C42×C127—22no—
70C2×C42×C127C2×C414yes—
71C2×C42×C127D414yes—
72C2×C42×C127D414yes—
73C2×C42×C127Q818yescomplemented
74#95×C127—24no—
75#95×C127—28no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—28no—
79#95×C127—28no—
80#95×C127C2×C4116yes—
81C24×C127C2411yescharacteristic
82C2×Q8×C127—28no—
83C2×Q8×C127—28no—
84C2×Q8×C127—28no—
85C2×Q8×C127—44no—
86C2×Q8×C127—44no—
87C2×Q8×C127—44no—
88C2×Q8×C127—44no—
89C22×C4×C127—22no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
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—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—24no—
107C22×C4×C127—22no—
108C22×C4×C127—24no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—24no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—22no—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127C22×C414yes—
124C22×C4×C127C22×C414yes—
125C22×C4×C127C22×C414yes—
126C22×C4×C127C22×C412yes—
127C22×C4×C127C2×D414yes—
128C22×C4×C127C2×D412yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D412yes—
132C22×C4×C127C2×Q814yes—
133C22×C4×C127C2×Q814yes—
134C22×C4×C127C2×Q814yes—
135C22×C4×C127#4114yes—
136C22×C4×C127#4114yes—
137C22×C4×C127#4114yes—
138C22×C4×C127#4112yes—
139C22×C4×C127#4112yes—
140C22×C4×C127#4112yes—
141C22×C4×C127#4112yes—
142C4⋊C4×C127—28no—
143C4⋊C4×C127—44no—
144C4⋊C4×C127—48no—
145C4⋊C4×C127—44no—
146C42×C127—216no—
147C42×C127—28no—
148C42×C127—28no—
149C42×C127—216no—
150C42×C127—28no—
151C23×C127C23×C411yescharacteristic
152C23×C127C22×D411yescharacteristic
153C23×C127C22×D411yescharacteristic
154C23×C127C22×Q812yes—
155C23×C127C2×#4111yescharacteristic
156C23×C127C2×#4111yescharacteristic
157C23×C127C2×#4111yescharacteristic
158C23×C127C2×#4111yescharacteristic
159C23×C127C2×#4112yes—
160C23×C127C2×#4112yes—
161C23×C127C2×#4112yes—
162Q8×C127—416no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—28no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—44no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—44no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—44no—
200C2×C4×C127—44no—
201C2×C4×C127—44no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127#11714yes—
206C2×C4×C127C4×D414yes—
207C2×C4×C127C4×D414yes—
208C2×C4×C127C4×Q818yes—
209C2×C4×C127#12114yes—
210C2×C4×C127C22⋊Q818yes—
211C2×C4×C127#12314yes—
212C2×C4×C127#12414yes—
213C2×C4×C127#12414yes—
214C2×C4×C127#12614yes—
215C2×C4×C127C4⋊Q814yes—
216C22×C127C2×#11711yescharacteristic
217C22×C127C2×C4×D411yescharacteristic
218C22×C127C2×C4×D411yescharacteristic
219C22×C127C2×C4×Q812yes—
220C22×C127C4×#4112yes—
221C22×C127C2×#12111yescharacteristic
222C22×C127C2×C22⋊Q812yes—
223C22×C127C2×#12311yescharacteristic
224C22×C127#52512yes—
225C22×C127C2×#12411yescharacteristic
226C22×C127C2×#12411yescharacteristic
227C22×C127C2×#12611yescharacteristic
228C22×C127#52912yes—
229C22×C127#52912yes—
230C22×C127#52912yes—
231C22×C127#52912yes—
232C22×C127C2×C4⋊Q811yescharacteristic
233C22×C127#53211yescharacteristic
234C22×C127#53211yescharacteristic
235C22×C127#53312yes—
236C22×C127#53312yes—
237C22×C127#53312yes—
238C22×C127#53312yes—
239C4×C127—24no—
240C4×C127—28no—
241C4×C127—24no—
242C4×C127—28no—
243C4×C127—44no—
244C4×C127—44no—
245C4×C127—82no—
246C4×C127—82no—
247C4×C127#38818yes—
248#14703C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127C2×#38811yescharacteristic
250C2×C127#229512yes—
251C2×C127C4×C22⋊Q812yes—
252C2×C127C4×#12411yescharacteristic
253C2×C127C4×C4⋊Q811yescharacteristic
254C2×C127#285011yescharacteristic
255C2×C127#285512yes—
256C2×C127#285711yescharacteristic
257C2×C127#286111yescharacteristic
258C2×C127#286211yescharacteristic
259C2×C127#286312yes—
260C2×#391C2×C12711yescharacteristic
261C2×#391C2×C12711yescharacteristic
262C2×#391C2×C12711yescharacteristic
263C2×#389C2×C12711yescharacteristic
264C2×C43C2×C12711yescharacteristic
265#1436C2×C12714yes—
266C4⋊#95C2×C12711yescharacteristic
267C4⋊#95C2×C12711yescharacteristic
268#1434C2×C12714yes—
269C127#1470311yescharacteristic, direct product factor, Sylow
270C23×Q8C22×C12711yescharacteristic
271C22×C4⋊C4C22×C12711yescharacteristic
272C22×C4⋊C4C22×C12711yescharacteristic
273C22×C4⋊C4C22×C12712yes—
274C22×C4⋊C4C22×C12711yescharacteristic
275C22×C42C22×C12712yes—
276C22×C42C22×C12711yescharacteristic
277C22×C42C22×C12711yescharacteristic
278C22×C42C22×C12711yescharacteristic
279C22×C42C22×C12712yes—
280#391—24no—
281#391—24no—
282#391C4×C12718yescomplemented
283#389—24no—
284C2×#95C22×C12712yes—
285C2×#95C22×C12712yes—
286C2×#95C22×C12714yes—
287C2×#95C22×C12714yes—
288C2×#95C22×C12714yes—
289C2×#95C22×C12712yes—
290C2×#95C22×C12714yes—
291C43—24no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8C2×C4×C12714yes—
299C23×C4C23×C12712yes—
300C23×C4C23×C12712yes—
301C23×C4C23×C12712yes—
302C23×C4C23×C12712yes—
303C23×C4C23×C12712yes—
304C23×C4C23×C12711yescharacteristic
305C23×C4C23×C12712yes—
306C23×C4C23×C12711yescharacteristic
307C23×C4C23×C12711yescharacteristic
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4C2×C4×C12714yes—
319C2×C42—24no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—24no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42C2×C4×C12714yes—
331C2×C42D4×C12714yes—
332C2×C42D4×C12714yes—
333C2×C42Q8×C12718yescomplemented
334#95—24no—
335#95—28no—
336#95—24no—
337#95—24no—
338#95—28no—
339#95—28no—
340#95C2×C4×C127116yes—
341C24C24×C12711yescharacteristic
342C2×Q8—28no—
343C2×Q8—28no—
344C2×Q8—28no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—44no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
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—24no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4C22×C4×C12714yes—
384C22×C4C22×C4×C12714yes—
385C22×C4C22×C4×C12714yes—
386C22×C4C22×C4×C12712yes—
387C22×C4C2×D4×C12714yes—
388C22×C4C2×D4×C12712yes—
389C22×C4C2×D4×C12712yes—
390C22×C4C2×D4×C12712yes—
391C22×C4C2×D4×C12712yes—
392C22×C4C2×Q8×C12714yes—
393C22×C4C2×Q8×C12714yes—
394C22×C4C2×Q8×C12714yes—
395C22×C4#41×C12714yes—
396C22×C4#41×C12714yes—
397C22×C4#41×C12714yes—
398C22×C4#41×C12712yes—
399C22×C4#41×C12712yes—
400C22×C4#41×C12712yes—
401C22×C4#41×C12712yes—
402C4⋊C4—28no—
403C4⋊C4—44no—
404C4⋊C4—48no—
405C4⋊C4—44no—
406C42—216no—
407C42—28no—
408C42—28no—
409C42—216no—
410C42—28no—
411C23C23×C4×C12711yescharacteristic
412C23C22×D4×C12711yescharacteristic
413C23C22×D4×C12711yescharacteristic
414C23C22×Q8×C12712yes—
415C23C2×#41×C12711yescharacteristic
416C23C2×#41×C12711yescharacteristic
417C23C2×#41×C12711yescharacteristic
418C23C2×#41×C12711yescharacteristic
419C23C2×#41×C12712yes—
420C23C2×#41×C12712yes—
421C23C2×#41×C12712yes—
422Q8—416no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—28no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4#117×C12714yes—
466C2×C4C4×D4×C12714yes—
467C2×C4C4×D4×C12714yes—
468C2×C4C4×Q8×C12718yes—
469C2×C4#121×C12714yes—
470C2×C4C22⋊Q8×C12718yes—
471C2×C4#123×C12714yes—
472C2×C4#124×C12714yes—
473C2×C4#124×C12714yes—
474C2×C4#126×C12714yes—
475C2×C4C4⋊Q8×C12714yes—
476C22C2×#117×C12711yescharacteristic
477C22C2×C4×D4×C12711yescharacteristic
478C22C2×C4×D4×C12711yescharacteristic
479C22C2×C4×Q8×C12712yes—
480C22C4×#41×C12712yes—
481C22C2×#121×C12711yescharacteristic
482C22C2×C22⋊Q8×C12712yes—
483C22C2×#123×C12711yescharacteristic
484C22#525×C12712yes—
485C22C2×#124×C12711yescharacteristic
486C22C2×#124×C12711yescharacteristic
487C22C2×#126×C12711yescharacteristic
488C22#529×C12712yes—
489C22#529×C12712yes—
490C22#529×C12712yes—
491C22#529×C12712yes—
492C22C2×C4⋊Q8×C12711yescharacteristic
493C22#532×C12711yescharacteristic
494C22#532×C12711yescharacteristic
495C22#533×C12712yes—
496C22#533×C12712yes—
497C22#533×C12712yes—
498C22#533×C12712yes—
499C4—24no—
500C4—28no—
501C4—24no—
502C4—28no—
503C4—44no—
504C4—44no—
505C4—82no—
506C4—82no—
507C4#388×C12718yes—
508C2C2×#388×C12711yescharacteristic
509C2C127×#229512yes—
510C2C4×C22⋊Q8×C12712yes—
511C2C4×#124×C12711yescharacteristic
512C2C4×C4⋊Q8×C12711yescharacteristic
513C2C127×#285011yescharacteristic
514C2C127×#285512yes—
515C2C127×#285711yescharacteristic
516C2C127×#286111yescharacteristic
517C2C127×#286211yescharacteristic
518C2C127×#286312yes—
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
22. #391×C127C4semidirect
73. C2×C42×C127Q8semidirect
248. #14703C127direct (N × H)
269. C127#14703direct (N × H)
282. #391C4×C127semidirect
333. C2×C42Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C2×#389×C1272
C2×C43×C1272
C127×#14362
C127×C4⋊#952
C127×#14342
#14703127