Finite Group Databasebeta

← C127×#18344 #44582017

Subgroups — C127×#18344 #44582017

Order 32512.

924 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×#3461C211yesmaximal, characteristic
2C127×#3238C212yesmaximal, complemented
3C127×#2546C211yesmaximal, characteristic, complemented
4C127×#1611C212yesmaximal, complemented
5C127×#1610C212yesmaximal
6C127×#1609C214yesmaximal, complemented
7C127×#1509C212yesmaximal, complemented
8C127×#1467C211yesmaximal, characteristic, complemented
9#544×C127C2211yescharacteristic
10#542×C127—22no—
11#541×C127—22no—
12#539×C127—21no—
13#539×C127C2212yes—
14#537×C127C2211yescharacteristic
15#536×C127—21no—
16#533×C127—22no—
17C2×C4⋊Q8×C127—21no—
18C2×C4⋊Q8×C127C2211yescharacteristic
19#529×C127—22no—
20#529×C127—21no—
21#529×C127C2212yes—
22C4×#41×C127—21no—
23C2×C4×Q8×C127C2211yescharacteristic
24#501×C127—22no—
25#489×C127—22no—
26#483×C127C2214yes—
27#480×C127C2214yes—
28#477×C127—22no—
29#476×C127—22no—
30#432×C127C2212yes—
31#398×C127C2212yes—
32#398×C127C2212yes—
33#391×C127—21no—
34#389×C127—21no—
35#389×C127—21no—
36C4×C4⋊C4×C127C2211yescharacteristic
37#328×C127C2214yes—
38#327×C127C2214yes—
39#324×C127C2212yes—
40#324×C127C2212yes—
41C2×#41×C127—21no—
42C22×Q8×C127—21no—
43C22×Q8×C127D411yescharacteristic
44C4⋊Q8×C127—22no—
45C4⋊Q8×C127—22no—
46C4⋊Q8×C127—22no—
47C4⋊Q8×C127—22no—
48C4⋊Q8×C127—44no—
49#126×C127—22no—
50#126×C127—22no—
51#126×C127—22no—
52#126×C127—22no—
53#125×C127—21no—
54#125×C127—22no—
55#125×C127—22no—
56#125×C127—22no—
57#125×C127D412yes—
58#124×C127—22no—
59#124×C127—21no—
60#124×C127D412yes—
61#123×C127—22no—
62#123×C127—22no—
63#123×C127—22no—
64#123×C127—22no—
65C22⋊Q8×C127—22no—
66C22⋊Q8×C127—22no—
67C22⋊Q8×C127—22no—
68C22⋊Q8×C127—22no—
69C22⋊Q8×C127—21no—
70C22⋊Q8×C127—22no—
71C22⋊Q8×C127C2312yes—
72#121×C127—22no—
73#121×C127—21no—
74#121×C127C2312yes—
75C4×Q8×C127—21no—
76C4×Q8×C127—21no—
77C4×Q8×C127—21no—
78C4×Q8×C127—22no—
79C4×Q8×C127—22no—
80C4×Q8×C127D412yes—
81C4×D4×C127—21no—
82C4×D4×C127—21no—
83C4×D4×C127—21no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127D412yes—
87#117×C127—22no—
88#117×C127—22no—
89#117×C127—21no—
90#117×C127—22no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—22no—
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—21no—
95C2×C4⋊C4×C127D411yescharacteristic
96C2×C4⋊C4×C127C2312yes—
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C42×C127—22no—
100C2×C42×C127—21no—
101C2×C42×C127D411yescharacteristic
102C2×C42×C127D411yescharacteristic
103C2×C42×C127C2311yescharacteristic
104#107×C127—24no—
105#106×C127—24no—
106C4⋊C8×C127—22no—
107#103×C127—24no—
108#102×C127—24no—
109C22⋊C8×C127C2314yes—
110#97×C127—22no—
111#95×C127—22no—
112#95×C127—22no—
113#95×C127C2312yes—
114#41×C127—42no—
115#41×C127—42no—
116C2×Q8×C127—21no—
117C2×Q8×C127—21no—
118C2×Q8×C127—22no—
119C2×Q8×C127—22no—
120C2×Q8×C127—41no—
121C2×Q8×C127—42no—
122C2×Q8×C127—42no—
123C2×Q8×C127—42no—
124C2×Q8×C127C2×D412yes—
125C2×D4×C127—21no—
126C2×D4×C127—22no—
127C2×D4×C127—21no—
128C2×D4×C127C2×D412yes—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127C2×D411yescharacteristic
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138C22×C4×C127C2×D411yescharacteristic
139C22×C4×C127C2×D411yescharacteristic
140C22×C4×C127C2411yescharacteristic
141C2×C8×C127—24no—
142C4⋊C4×C127—24no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—24no—
159C4⋊C4×C127—44no—
160C4⋊C4×C127—41no—
161C4⋊C4×C127—41no—
162C4⋊C4×C127—44no—
163C4⋊C4×C127C2×D412yes—
164C4⋊C4×C127C2×D412yes—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—22no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—22no—
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—22no—
173C22⋊C4×C127—22no—
174C42×C127—22no—
175C42×C127—22no—
176C42×C127—21no—
177C42×C127—22no—
178C42×C127—21no—
179C42×C127—21no—
180C42×C127—21no—
181C42×C127—42no—
182C42×C127C2×D412yes—
183C42×C127C2×D412yes—
184C23×C127—22no—
185C23×C127C22×D411yescharacteristic
186Q8×C127—44no—
187Q8×C127—42no—
188Q8×C127—42no—
189Q8×C127—84no—
190Q8×C127—81no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—42no—
194D4×C127—42no—
195D4×C127—81no—
196C2×C4×C127—21no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—21no—
200C2×C4×C127—22no—
201C2×C4×C127—24no—
202C2×C4×C127—21no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—21no—
206C2×C4×C127—21no—
207C2×C4×C127—22no—
208C2×C4×C127—21no—
209C2×C4×C127—21no—
210C2×C4×C127—41no—
211C2×C4×C127—44no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—44no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—82no—
221C2×C4×C127#12011yescharacteristic
222C2×C4×C127#12012yes—
223C2×C4×C127#12011yescharacteristic
224C2×C4×C127AGL(1,ℤ/8)12yes—
225C2×C4×C127C22×D412yes—
226C8×C127—44no—
227C22×C127—21no—
228C22×C127—21no—
229C22×C127—42no—
230C22×C127—42no—
231C22×C127—42no—
232C22×C127C2×#12011yescharacteristic
233C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
234C22×C127#57511yescharacteristic
235C4×C127—22no—
236C4×C127—22no—
237C4×C127—21no—
238C4×C127—22no—
239C4×C127—44no—
240C4×C127—41no—
241C4×C127—42no—
242C4×C127—42no—
243C4×C127—41no—
244C4×C127—41no—
245C4×C127—42no—
246C4×C127—82no—
247C4×C127#45612yes—
248#18344C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—21no—
250C2×C127—21no—
251C2×C127—82no—
252C2×C127#300611yescharacteristic
253C2×C127C2×#45611yescharacteristic
254C2×C127#302811yescharacteristic
255#3461C2×C12711yescharacteristic
256#3238C2×C12712yescomplemented
257#2546C2×C12711yescharacteristic, complemented
258#1611C2×C12712yescomplemented
259#1610C2×C12712yes—
260#1609C2×C12714yescomplemented
261#1509C2×C12712yescomplemented
262#1467C2×C12711yescharacteristic, complemented
263C127#1834411yescharacteristic, direct product factor, Sylow
264#544C22×C12711yescharacteristic
265#542—22no—
266#541—22no—
267#539—21no—
268#539C22×C12712yes—
269#537C22×C12711yescharacteristic
270#536—21no—
271#533—22no—
272C2×C4⋊Q8—21no—
273C2×C4⋊Q8C22×C12711yescharacteristic
274#529—22no—
275#529—21no—
276#529C22×C12712yes—
277C4×#41—21no—
278C2×C4×Q8C22×C12711yescharacteristic
279#501—22no—
280#489—22no—
281#483C22×C12714yes—
282#480C22×C12714yes—
283#477—22no—
284#476—22no—
285#432C22×C12712yes—
286#398C22×C12712yes—
287#398C22×C12712yes—
288#391—21no—
289#389—21no—
290#389—21no—
291C4×C4⋊C4C22×C12711yescharacteristic
292#328C22×C12714yes—
293#327C22×C12714yes—
294#324C22×C12712yes—
295#324C22×C12712yes—
296C2×#41—21no—
297C22×Q8—21no—
298C22×Q8D4×C12711yescharacteristic
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—44no—
304#126—22no—
305#126—22no—
306#126—22no—
307#126—22no—
308#125—21no—
309#125—22no—
310#125—22no—
311#125—22no—
312#125D4×C12712yes—
313#124—22no—
314#124—21no—
315#124D4×C12712yes—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8C23×C12712yes—
327#121—22no—
328#121—21no—
329#121C23×C12712yes—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8D4×C12712yes—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C12712yes—
342#117—22no—
343#117—22no—
344#117—21no—
345#117—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4D4×C12711yescharacteristic
351C2×C4⋊C4C23×C12712yes—
352C2×C4⋊C4C23×C12711yescharacteristic
353C2×C4⋊C4C23×C12711yescharacteristic
354C2×C42—22no—
355C2×C42—21no—
356C2×C42D4×C12711yescharacteristic
357C2×C42D4×C12711yescharacteristic
358C2×C42C23×C12711yescharacteristic
359#107—24no—
360#106—24no—
361C4⋊C8—22no—
362#103—24no—
363#102—24no—
364C22⋊C8C23×C12714yes—
365#97—22no—
366#95—22no—
367#95—22no—
368#95C23×C12712yes—
369#41—42no—
370#41—42no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—41no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×Q8C2×D4×C12712yes—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4C2×D4×C12712yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4C2×D4×C12711yescharacteristic
390C22×C4C2×D4×C12711yescharacteristic
391C22×C4C2×D4×C12711yescharacteristic
392C22×C4C2×D4×C12711yescharacteristic
393C22×C4C2×D4×C12711yescharacteristic
394C22×C4C2×D4×C12711yescharacteristic
395C22×C4C24×C12711yescharacteristic
396C2×C8—24no—
397C4⋊C4—24no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—24no—
414C4⋊C4—44no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—44no—
418C4⋊C4C2×D4×C12712yes—
419C4⋊C4C2×D4×C12712yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C42—22no—
430C42—22no—
431C42—21no—
432C42—22no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42—42no—
437C42C2×D4×C12712yes—
438C42C2×D4×C12712yes—
439C23—22no—
440C23C22×D4×C12711yescharacteristic
441Q8—44no—
442Q8—42no—
443Q8—42no—
444Q8—84no—
445Q8—81no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—81no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4#120×C12711yescharacteristic
477C2×C4#120×C12712yes—
478C2×C4#120×C12711yescharacteristic
479C2×C4AGL(1,ℤ/8)×C12712yes—
480C2×C4C22×D4×C12712yes—
481C8—44no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22C2×#120×C12711yescharacteristic
488C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
489C22#575×C12711yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—22no—
494C4—44no—
495C4—41no—
496C4—42no—
497C4—42no—
498C4—41no—
499C4—41no—
500C4—42no—
501C4—82no—
502C4#456×C12712yes—
503C2—21no—
504C2—21no—
505C2—82no—
506C2C127×#300611yescharacteristic
507C2C2×#456×C12711yescharacteristic
508C2C127×#302811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radical#537×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3238C2semidirect
3. C127×#2546C2semidirect
4. C127×#1611C2semidirect
6. C127×#1609C2semidirect
7. C127×#1509C2semidirect
8. C127×#1467C2semidirect
248. #18344C127direct (N × H)
256. #3238C2×C127semidirect
257. #2546C2×C127semidirect
258. #1611C2×C127semidirect
260. #1609C2×C127semidirect
261. #1509C2×C127semidirect
262. #1467C2×C127semidirect
263. C127#18344direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34612
C127×#32382
C127×#25462
C127×#16112
C127×#16102
C127×#16092
C127×#15092
C127×#14672
#18344127