Finite Group Databasebeta

← C127×#10323 #44573996

Subgroups — C127×#10323 #44573996

Order 32512.

664 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3187C211yesmaximal, characteristic
2C127×#2855C211yesmaximal, characteristic, complemented
3C127×#2854C211yesmaximal, characteristic
4C127×#1817C211yesmaximal, characteristic, complemented
5C127×#1520C211yesmaximal, characteristic, complemented
6C127×#1519C211yesmaximal, characteristic
7C127×#1289C211yesmaximal, characteristic, complemented
8C2×#123×C127—21no—
9C2×C22⋊Q8×C127C2211yescharacteristic
10C2×#121×C127C2211yescharacteristic
11C22×C42×C127C2211yescharacteristic
12#483×C127—21no—
13#481×C127—21no—
14#465×C127—22no—
15#450×C127—21no—
16#448×C127—21no—
17C2×C22⋊C8×C127C2211yescharacteristic
18C2×C22⋊C8×C127C2211yescharacteristic
19#391×C127—21no—
20#390×C127—21no—
21#389×C127—21no—
22#389×C127—21no—
23#388×C127—22no—
24#387×C127—22no—
25#386×C127—21no—
26#385×C127—21no—
27#381×C127—21no—
28#380×C127C2211yescharacteristic
29#380×C127C2211yescharacteristic
30#336×C127—22no—
31#328×C127—22no—
32#327×C127—22no—
33C22×Q8×C127D411yescharacteristic
34C22×D4×C127—21no—
35C22×D4×C127D411yescharacteristic
36C23×C4×C127D411yescharacteristic
37C23×C4×C127D411yescharacteristic
38C23×C4×C127C2311yescharacteristic
39C2×SD16×C127—22no—
40C22×C8×C127—21no—
41C22×C8×C127D412yes—
42#123×C127—42no—
43#123×C127—42no—
44C22⋊Q8×C127—21no—
45C22⋊Q8×C127—21no—
46C22⋊Q8×C127—21no—
47C22⋊Q8×C127—21no—
48#121×C127—21no—
49#121×C127—21no—
50#121×C127—21no—
51#121×C127—21no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127D411yescharacteristic
58C2×C4⋊C4×C127D411yescharacteristic
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—21no—
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—21no—
65C2×C42×C127—21no—
66C2×C42×C127—21no—
67C2×C42×C127—21no—
68C2×C42×C127—21no—
69C2×C42×C127—21no—
70C2×C42×C127—21no—
71#106×C127—22no—
72#103×C127—22no—
73#102×C127—22no—
74C22⋊C8×C127—21no—
75C22⋊C8×C127—21no—
76C22⋊C8×C127—21no—
77C22⋊C8×C127—21no—
78#95×C127—22no—
79#95×C127—22no—
80#95×C127—22no—
81#95×C127—22no—
82#95×C127D412yes—
83#95×C127D412yes—
84C24×C127—21no—
85C24×C127C2×D411yescharacteristic
86C2×Q8×C127—21no—
87C2×Q8×C127—21no—
88C2×Q8×C127—42no—
89C2×D4×C127—21no—
90C2×D4×C127—21no—
91C2×D4×C127—42no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C2×D4×C127—41no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—22no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—42no—
113C22×C4×C127—42no—
114C22×C4×C127SD1612yescomplemented
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127#4111yescharacteristic
121SD16×C127—82no—
122C2×C8×C127—22no—
123C2×C8×C127—42no—
124C2×C8×C127—42no—
125C2×C8×C127—41no—
126C4⋊C4×C127—21no—
127C4⋊C4×C127—21no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—42no—
131C4⋊C4×C127—42no—
132C4⋊C4×C127—44no—
133C4⋊C4×C127—44no—
134C4⋊C4×C127—41no—
135C4⋊C4×C127—41no—
136C22⋊C4×C127—44no—
137C22⋊C4×C127—44no—
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×C127—41no—
145C22⋊C4×C127—41no—
146C42×C127—41no—
147C42×C127—41no—
148C42×C127—41no—
149C42×C127—41no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—42no—
153C23×C127—42no—
154C23×C127—41no—
155C23×C127—41no—
156C23×C127—41no—
157C23×C127#12011yescharacteristic
158C23×C127#12011yescharacteristic
159C23×C127#12111yescharacteristic
160C23×C127C2×SD1611yescharacteristic
161C23×C127#13511yescharacteristic
162C23×C127AGL(1,ℤ/8)11yescharacteristic
163C23×C127#13711yescharacteristic
164Q8×C127—42no—
165Q8×C127—81no—
166D4×C127—42no—
167D4×C127—81no—
168D4×C127—81no—
169D4×C127—81no—
170D4×C127—81no—
171D4×C127—81no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
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—41no—
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—41no—
199C2×C4×C127—41no—
200C2×C4×C127—41no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—41no—
204C2×C4×C127—41no—
205C2×C4×C127#12011yescharacteristic
206C2×C4×C127#12111yescharacteristic
207C2×C4×C127#12111yescharacteristic
208C2×C4×C127#12711yescharacteristic
209C8×C127—42no—
210C8×C127—81no—
211C22×C127—21no—
212C22×C127—21no—
213C22×C127—21no—
214C22×C127—21no—
215C22×C127—21no—
216C22×C127—21no—
217C22×C127—41no—
218C22×C127—41no—
219C22×C127—41no—
220C22×C127—41no—
221C22×C127—82no—
222C22×C127—82no—
223C22×C127—81no—
224C22×C127—81no—
225C22×C127—81no—
226C22×C127#39211yescharacteristic
227C22×C127#44811yescharacteristic
228C22×C127#44911yescharacteristic
229C22×C127#45011yescharacteristic
230C22×C127#45211yescharacteristic
231C22×C127#46511yescharacteristic
232C22×C127#46811yescharacteristic
233C4×C127—21no—
234C4×C127—21no—
235C4×C127—21no—
236C4×C127—42no—
237C4×C127—42no—
238C4×C127—82no—
239C4×C127—82no—
240C4×C127—81no—
241C4×C127—81no—
242C4×C127—81no—
243C4×C127#45812yes—
244#10323C12711yesmaximal, characteristic, direct product factor, Sylow
245C2×C127—21no—
246C2×C127—21no—
247C2×C127—21no—
248C2×C127—21no—
249C2×C127—21no—
250C2×C127—21no—
251C2×C127—161no—
252C2×C127#200011yescharacteristic
253C2×C127#201011yescharacteristic
254C2×C127#202211yescharacteristic
255#3187C2×C12711yescharacteristic
256#2855C2×C12711yescharacteristic, complemented
257#2854C2×C12711yescharacteristic
258#1817C2×C12711yescharacteristic, complemented
259#1520C2×C12711yescharacteristic, complemented
260#1519C2×C12711yescharacteristic
261#1289C2×C12711yescharacteristic, complemented
262C127#1032311yescharacteristic, direct product factor, Sylow
263C2×#123—21no—
264C2×C22⋊Q8C22×C12711yescharacteristic
265C2×#121C22×C12711yescharacteristic
266C22×C42C22×C12711yescharacteristic
267#483—21no—
268#481—21no—
269#465—22no—
270#450—21no—
271#448—21no—
272C2×C22⋊C8C22×C12711yescharacteristic
273C2×C22⋊C8C22×C12711yescharacteristic
274#391—21no—
275#390—21no—
276#389—21no—
277#389—21no—
278#388—22no—
279#387—22no—
280#386—21no—
281#385—21no—
282#381—21no—
283#380C22×C12711yescharacteristic
284#380C22×C12711yescharacteristic
285#336—22no—
286#328—22no—
287#327—22no—
288C22×Q8D4×C12711yescharacteristic
289C22×D4—21no—
290C22×D4D4×C12711yescharacteristic
291C23×C4D4×C12711yescharacteristic
292C23×C4D4×C12711yescharacteristic
293C23×C4C23×C12711yescharacteristic
294C2×SD16—22no—
295C22×C8—21no—
296C22×C8D4×C12712yes—
297#123—42no—
298#123—42no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4D4×C12711yescharacteristic
313C2×C4⋊C4D4×C12711yescharacteristic
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326#106—22no—
327#103—22no—
328#102—22no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95D4×C12712yes—
338#95D4×C12712yes—
339C24—21no—
340C24C2×D4×C12711yescharacteristic
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—42no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4SD16×C12712yescomplemented
370C22×C4C2×D4×C12711yescharacteristic
371C22×C4C2×D4×C12711yescharacteristic
372C22×C4C2×D4×C12711yescharacteristic
373C22×C4C2×D4×C12711yescharacteristic
374C22×C4C2×D4×C12711yescharacteristic
375C22×C4#41×C12711yescharacteristic
376SD16—82no—
377C2×C8—22no—
378C2×C8—42no—
379C2×C8—42no—
380C2×C8—41no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C42—41no—
402C42—41no—
403C42—41no—
404C42—41no—
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23#120×C12711yescharacteristic
413C23#120×C12711yescharacteristic
414C23#121×C12711yescharacteristic
415C23C2×SD16×C12711yescharacteristic
416C23#135×C12711yescharacteristic
417C23AGL(1,ℤ/8)×C12711yescharacteristic
418C23#137×C12711yescharacteristic
419Q8—42no—
420Q8—81no—
421D4—42no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4#120×C12711yescharacteristic
461C2×C4#121×C12711yescharacteristic
462C2×C4#121×C12711yescharacteristic
463C2×C4#127×C12711yescharacteristic
464C8—42no—
465C8—81no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22#392×C12711yescharacteristic
482C22#448×C12711yescharacteristic
483C22#449×C12711yescharacteristic
484C22#450×C12711yescharacteristic
485C22#452×C12711yescharacteristic
486C22#465×C12711yescharacteristic
487C22#468×C12711yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—82no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4#458×C12712yes—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—161no—
506C2C127×#200011yescharacteristic
507C2C127×#201011yescharacteristic
508C2C127×#202211yescharacteristic
subgroupG/H
center, socleC22×C127#392
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×#2855C2semidirect
4. C127×#1817C2semidirect
5. C127×#1520C2semidirect
7. C127×#1289C2semidirect
114. C22×C4×C127SD16semidirect
244. #10323C127direct (N × H)
256. #2855C2×C127semidirect
258. #1817C2×C127semidirect
259. #1520C2×C127semidirect
261. #1289C2×C127semidirect
262. C127#10323direct (N × H)
369. 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×#28552
C127×#28542
C127×#18172
C127×#15202
C127×#15192
C127×#12892
#10323127