Finite Group Databasebeta

← C127×#10565 #44574238

Subgroups — C127×#10565 #44574238

Order 32512.

532 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3187C211yesmaximal, characteristic
2C127×#1996C211yesmaximal, characteristic, complemented
3C127×#1964C211yesmaximal, characteristic
4C127×#1893C211yesmaximal, characteristic
5C127×#1892C211yesmaximal, characteristic, complemented
6C127×#1850C211yesmaximal, characteristic, complemented
7C127×#1289C211yesmaximal, characteristic, complemented
8C23×C8×C127C2211yescharacteristic
9C2×C22⋊Q8×C127C2211yescharacteristic
10C2×#121×C127C2211yescharacteristic
11#483×C127—21no—
12#481×C127—21no—
13#465×C127—21no—
14#465×C127—21no—
15#450×C127—21no—
16#448×C127—21no—
17C2×C4⋊C8×C127—21no—
18C2×#103×C127—21no—
19C2×#102×C127—21no—
20C2×#99×C127—21no—
21C2×#99×C127—21no—
22C2×C22⋊C8×C127C2211yescharacteristic
23#380×C127C2211yescharacteristic
24#380×C127C2211yescharacteristic
25C4×C22⋊C4×C127C2211yescharacteristic
26#342×C127—21no—
27#342×C127—21no—
28#340×C127—21no—
29#340×C127—21no—
30#336×C127—21no—
31C22×Q8×C127D411yescharacteristic
32C22×D4×C127—21no—
33C22×D4×C127D411yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C2×SD16×C127—21no—
36C2×SD16×C127—21no—
37C22×C8×C127—21no—
38C22×C8×C127—21no—
39C22×C8×C127—21no—
40C22×C8×C127—42no—
41C22×C8×C127D411yescharacteristic
42C22×C8×C127D411yescharacteristic
43C22⋊Q8×C127—21no—
44C22⋊Q8×C127—21no—
45C22⋊Q8×C127—21no—
46C22⋊Q8×C127—21no—
47#121×C127—21no—
48#121×C127—21no—
49#121×C127—21no—
50#121×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127D411yescharacteristic
55C2×C4⋊C4×C127D411yescharacteristic
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—21no—
60C2×C22⋊C4×C127D411yescharacteristic
61C2×C22⋊C4×C127D411yescharacteristic
62C2×C42×C127—21no—
63#106×C127—21no—
64#106×C127—21no—
65C4⋊C8×C127—42no—
66#103×C127—21no—
67#103×C127—21no—
68#103×C127—42no—
69#102×C127—21no—
70#102×C127—21no—
71#102×C127—42no—
72#99×C127—42no—
73#99×C127—42no—
74C22⋊C8×C127—21no—
75C22⋊C8×C127—21no—
76#95×C127—21no—
77#95×C127—21no—
78#95×C127—21no—
79C24×C127—21no—
80C24×C127C2×D411yescharacteristic
81C2×Q8×C127—21no—
82C2×Q8×C127—21no—
83C2×Q8×C127—41no—
84C2×Q8×C127—41no—
85C2×D4×C127—21no—
86C2×D4×C127—21no—
87C2×D4×C127—41no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127—41no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127—41no—
103C22×C4×C127—41no—
104C22×C4×C127C2×D411yescharacteristic
105C22×C4×C127C2×D411yescharacteristic
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127#4111yescharacteristic
108C22×C4×C127#4111yescharacteristic
109C22×C4×C127#4111yescharacteristic
110SD16×C127—81no—
111SD16×C127—81no—
112C2×C8×C127—22no—
113C2×C8×C127—22no—
114C2×C8×C127—22no—
115C2×C8×C127—21no—
116C2×C8×C127—21no—
117C2×C8×C127—41no—
118C2×C8×C127—41no—
119C2×C8×C127—41no—
120C2×C8×C127—41no—
121C2×C8×C127—41no—
122C2×C8×C127—41no—
123C4⋊C4×C127—21no—
124C4⋊C4×C127—21no—
125C4⋊C4×C127—21no—
126C4⋊C4×C127—21no—
127C4⋊C4×C127—41no—
128C4⋊C4×C127—41no—
129C4⋊C4×C127—41no—
130C4⋊C4×C127—41no—
131C4⋊C4×C127—41no—
132C4⋊C4×C127—41no—
133C22⋊C4×C127—21no—
134C22⋊C4×C127—21no—
135C22⋊C4×C127—21no—
136C22⋊C4×C127—41no—
137C22⋊C4×C127—41no—
138C22⋊C4×C127—41no—
139C22⋊C4×C127—41no—
140C22⋊C4×C127—41no—
141C22⋊C4×C127—41no—
142C22⋊C4×C127—41no—
143C22⋊C4×C127—41no—
144C22⋊C4×C127SD1612yescomplemented
145C42×C127—41no—
146C42×C127—41no—
147C23×C127—41no—
148C23×C127—41no—
149C23×C127—41no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—81no—
153C23×C127—81no—
154C23×C127#12111yescharacteristic
155C23×C127#12111yescharacteristic
156C23×C127#12111yescharacteristic
157C23×C127C2×SD1611yescharacteristic
158C23×C127#13511yescharacteristic
159C23×C127AGL(1,ℤ/8)11yescharacteristic
160C23×C127#13711yescharacteristic
161Q8×C127—42no—
162Q8×C127—41no—
163Q8×C127—41no—
164D4×C127—42no—
165D4×C127—41no—
166D4×C127—41no—
167D4×C127—81no—
168D4×C127—81no—
169D4×C127—81no—
170D4×C127—81no—
171C2×C4×C127—21no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—21no—
175C2×C4×C127—21no—
176C2×C4×C127—21no—
177C2×C4×C127—22no—
178C2×C4×C127—41no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—41no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—41no—
191C2×C4×C127—81no—
192C2×C4×C127—81no—
193C2×C4×C127—81no—
194C2×C4×C127—81no—
195C2×C4×C127—81no—
196C2×C4×C127—81no—
197C2×C4×C127—81no—
198C2×C4×C127—81no—
199C2×C4×C127#12011yescharacteristic
200C2×C4×C127#12311yescharacteristic
201C2×C4×C127#12311yescharacteristic
202C2×C4×C127#12411yescharacteristic
203C8×C127—42no—
204C8×C127—41no—
205C8×C127—41no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—21no—
210C22×C127—21no—
211C22×C127—21no—
212C22×C127—41no—
213C22×C127—41no—
214C22×C127—41no—
215C22×C127—41no—
216C22×C127—81no—
217C22×C127—81no—
218C22×C127—81no—
219C22×C127—161no—
220C22×C127—161no—
221C22×C127#39411yescharacteristic
222C22×C127#46011yescharacteristic
223C22×C127#46111yescharacteristic
224C22×C127#46311yescharacteristic
225C22×C127#46411yescharacteristic
226C22×C127#46511yescharacteristic
227C22×C127#46811yescharacteristic
228C4×C127—21no—
229C4×C127—21no—
230C4×C127—21no—
231C4×C127—42no—
232C4×C127—81no—
233C4×C127—81no—
234C4×C127—81no—
235C4×C127—81no—
236C4×C127—161no—
237C4×C127—161no—
238C4×C127B(4,𝔽2)11yescharacteristic
239C4×C127#45811yescharacteristic
240#10565C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127—21no—
242C2×C127—21no—
243C2×C127—21no—
244C2×C127—21no—
245C2×C127—21no—
246C2×C127—21no—
247C2×C127—161no—
248C2×C127#204411yescharacteristic
249C2×C127#205311yescharacteristic
250C2×C127#205511yescharacteristic
251#3187C2×C12711yescharacteristic
252#1996C2×C12711yescharacteristic, complemented
253#1964C2×C12711yescharacteristic
254#1893C2×C12711yescharacteristic
255#1892C2×C12711yescharacteristic, complemented
256#1850C2×C12711yescharacteristic, complemented
257#1289C2×C12711yescharacteristic, complemented
258C127#1056511yescharacteristic, direct product factor, Sylow
259C23×C8C22×C12711yescharacteristic
260C2×C22⋊Q8C22×C12711yescharacteristic
261C2×#121C22×C12711yescharacteristic
262#483—21no—
263#481—21no—
264#465—21no—
265#465—21no—
266#450—21no—
267#448—21no—
268C2×C4⋊C8—21no—
269C2×#103—21no—
270C2×#102—21no—
271C2×#99—21no—
272C2×#99—21no—
273C2×C22⋊C8C22×C12711yescharacteristic
274#380C22×C12711yescharacteristic
275#380C22×C12711yescharacteristic
276C4×C22⋊C4C22×C12711yescharacteristic
277#342—21no—
278#342—21no—
279#340—21no—
280#340—21no—
281#336—21no—
282C22×Q8D4×C12711yescharacteristic
283C22×D4—21no—
284C22×D4D4×C12711yescharacteristic
285C23×C4C23×C12711yescharacteristic
286C2×SD16—21no—
287C2×SD16—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—42no—
292C22×C8D4×C12711yescharacteristic
293C22×C8D4×C12711yescharacteristic
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4D4×C12711yescharacteristic
306C2×C4⋊C4D4×C12711yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4D4×C12711yescharacteristic
312C2×C22⋊C4D4×C12711yescharacteristic
313C2×C42—21no—
314#106—21no—
315#106—21no—
316C4⋊C8—42no—
317#103—21no—
318#103—21no—
319#103—42no—
320#102—21no—
321#102—21no—
322#102—42no—
323#99—42no—
324#99—42no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327#95—21no—
328#95—21no—
329#95—21no—
330C24—21no—
331C24C2×D4×C12711yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4C2×D4×C12711yescharacteristic
356C22×C4C2×D4×C12711yescharacteristic
357C22×C4C2×D4×C12711yescharacteristic
358C22×C4#41×C12711yescharacteristic
359C22×C4#41×C12711yescharacteristic
360C22×C4#41×C12711yescharacteristic
361SD16—81no—
362SD16—81no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—41no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4SD16×C12712yescomplemented
396C42—41no—
397C42—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23#121×C12711yescharacteristic
406C23#121×C12711yescharacteristic
407C23#121×C12711yescharacteristic
408C23C2×SD16×C12711yescharacteristic
409C23#135×C12711yescharacteristic
410C23AGL(1,ℤ/8)×C12711yescharacteristic
411C23#137×C12711yescharacteristic
412Q8—42no—
413Q8—41no—
414Q8—41no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—81no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4#120×C12711yescharacteristic
451C2×C4#123×C12711yescharacteristic
452C2×C4#123×C12711yescharacteristic
453C2×C4#124×C12711yescharacteristic
454C8—42no—
455C8—41no—
456C8—41no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—161no—
471C22—161no—
472C22#394×C12711yescharacteristic
473C22#460×C12711yescharacteristic
474C22#461×C12711yescharacteristic
475C22#463×C12711yescharacteristic
476C22#464×C12711yescharacteristic
477C22#465×C12711yescharacteristic
478C22#468×C12711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—81no—
487C4—161no—
488C4—161no—
489C4B(4,𝔽2)×C12711yescharacteristic
490C4#458×C12711yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—161no—
498C2C127×#204411yescharacteristic
499C2C127×#205311yescharacteristic
500C2C127×#205511yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC2×#121×C127C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1996C2semidirect
5. C127×#1892C2semidirect
6. C127×#1850C2semidirect
7. C127×#1289C2semidirect
144. C22⋊C4×C127SD16semidirect
240. #10565C127direct (N × H)
252. #1996C2×C127semidirect
255. #1892C2×C127semidirect
256. #1850C2×C127semidirect
257. #1289C2×C127semidirect
258. C127#10565direct (N × H)
395. C22⋊C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31872
C127×#19962
C127×#19642
C127×#18932
C127×#18922
C127×#18502
C127×#12892
#10565127