Finite Group Databasebeta

← C127×#18333 #44582006

Subgroups — C127×#18333 #44582006

Order 32512.

950 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3458C211yesmaximal, characteristic, complemented
2C127×#3215C212yesmaximal, complemented
3C127×#2610C211yesmaximal, characteristic
4C127×#1605C212yesmaximal, complemented
5C127×#1602C212yesmaximal, complemented
6C127×#1599C212yesmaximal, complemented
7C127×#1596C212yesmaximal
8C127×#1506C212yesmaximal, complemented
9C127×#1464C211yesmaximal, characteristic, complemented
10#544×C127—22no—
11#544×C127—22no—
12#544×C127—21no—
13#544×C127C2212yes—
14#543×C127—21no—
15#543×C127C2212yes—
16#533×C127—24no—
17#533×C127—21no—
18#533×C127C2212yes—
19C2×#124×C127C2211yescharacteristic
20C2×#117×C127—21no—
21C2×#117×C127C2211yescharacteristic
22#497×C127—22no—
23#489×C127—22no—
24#464×C127—24no—
25#451×C127C2214yes—
26#450×C127C2214yes—
27#432×C127C2212yes—
28#395×C127C2211yescharacteristic
29#394×C127C2211yescharacteristic
30#393×C127C2211yescharacteristic
31#392×C127C2211yescharacteristic
32#390×C127—21no—
33#388×C127—21no—
34#388×C127—21no—
35#386×C127—21no—
36#376×C127C2211yescharacteristic
37#328×C127C2214yes—
38#328×C127C2214yes—
39#324×C127C2212yes—
40#323×C127C2212yes—
41C22×Q8×C127C2311yescharacteristic
42C22×D4×C127—21no—
43C22×D4×C127C2311yescharacteristic
44C23×C4×C127D411yescharacteristic
45C2×Q16×C127—24no—
46C2×SD16×C127—24no—
47C4⋊Q8×C127—24no—
48C4⋊Q8×C127—21no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—24no—
51C4⋊Q8×C127D412yescomplemented
52C4⋊Q8×C127D412yescomplemented
53#125×C127—24no—
54#125×C127—22no—
55#125×C127—24no—
56#125×C127—22no—
57#124×C127—22no—
58#124×C127—22no—
59C22⋊Q8×C127—24no—
60C22⋊Q8×C127—24no—
61C22⋊Q8×C127—24no—
62C22⋊Q8×C127—22no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—24no—
66C22⋊Q8×C127C2314yes—
67C4×Q8×C127—22no—
68C4×Q8×C127—22no—
69C4×Q8×C127—22no—
70C4×Q8×C127D414yescomplemented
71#117×C127—22no—
72#117×C127—22no—
73#117×C127—22no—
74#117×C127—22no—
75#117×C127—22no—
76#117×C127—22no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127D411yescharacteristic
81C2×C4⋊C4×C127C2311yescharacteristic
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—21no—
84C2×C22⋊C4×C127—21no—
85C2×C22⋊C4×C127—21no—
86C2×C22⋊C4×C127—21no—
87C2×C22⋊C4×C127—21no—
88C2×C22⋊C4×C127—21no—
89C2×C22⋊C4×C127D411yescharacteristic
90C2×C22⋊C4×C127C2311yescharacteristic
91C2×C42×C127—22no—
92C2×C42×C127—21no—
93C2×C42×C127D411yescharacteristic
94C2×C42×C127C2311yescharacteristic
95C4⋊C8×C127—22no—
96#103×C127—24no—
97#102×C127—24no—
98C22⋊C8×C127C2314yes—
99#97×C127—22no—
100#95×C127—21no—
101#95×C127—21no—
102#95×C127—21no—
103#95×C127C2311yescharacteristic
104#95×C127C2311yescharacteristic
105C24×C127—21no—
106C24×C127C2×D411yescharacteristic
107C2×Q8×C127—22no—
108C2×Q8×C127—22no—
109C2×Q8×C127—22no—
110C2×Q8×C127—22no—
111C2×Q8×C127—81no—
112C2×Q8×C127C2×D414yes—
113C2×D4×C127—22no—
114C2×D4×C127—42no—
115C2×D4×C127—42no—
116C2×D4×C127—81no—
117C2×D4×C127—81no—
118C22×C4×C127—22no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—22no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127C2×D411yescharacteristic
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2411yescharacteristic
133Q16×C127—84no—
134SD16×C127—84no—
135C2×C8×C127—24no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—24no—
140C4⋊C4×C127—24no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—24no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—24no—
149C4⋊C4×C127—81no—
150C4⋊C4×C127C2×D414yes—
151C22⋊C4×C127—24no—
152C22⋊C4×C127—24no—
153C22⋊C4×C127—22no—
154C22⋊C4×C127—22no—
155C22⋊C4×C127—42no—
156C22⋊C4×C127—41no—
157C22⋊C4×C127—41no—
158C22⋊C4×C127—42no—
159C22⋊C4×C127—42no—
160C22⋊C4×C127—81no—
161C22⋊C4×C127—81no—
162C42×C127—24no—
163C42×C127—24no—
164C42×C127—21no—
165C42×C127—21no—
166C42×C127—42no—
167C42×C127C2×D412yes—
168C42×C127C2×D412yes—
169C23×C127—21no—
170C23×C127—21no—
171C23×C127—41no—
172C23×C127—41no—
173C23×C127—41no—
174C23×C127—41no—
175C23×C127—41no—
176C23×C127—41no—
177C23×C127—41no—
178C23×C127—41no—
179C23×C127—41no—
180C23×C127#13712yes—
181C23×C127C22×D411yescharacteristic
182Q8×C127—44no—
183Q8×C127—44no—
184Q8×C127—82no—
185Q8×C127—82no—
186Q8×C127—82no—
187D4×C127—44no—
188D4×C127—84no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—22no—
196C2×C4×C127—24no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—24no—
200C2×C4×C127—41no—
201C2×C4×C127—41no—
202C2×C4×C127—41no—
203C2×C4×C127—41no—
204C2×C4×C127—41no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—41no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—82no—
213C2×C4×C127—82no—
214C2×C4×C127#12011yescharacteristic
215C2×C4×C127#12011yescharacteristic
216C2×C4×C127#12012yes—
217C2×C4×C127#13712yes—
218C2×C4×C127C22×D412yes—
219C8×C127—44no—
220C22×C127—21no—
221C22×C127—21no—
222C22×C127—22no—
223C22×C127—42no—
224C22×C127—41no—
225C22×C127—41no—
226C22×C127—81no—
227C22×C127—81no—
228C22×C127—81no—
229C22×C127—81no—
230C22×C127—81no—
231C22×C127—81no—
232C22×C127—81no—
233C22×C127—81no—
234C22×C127C2×#12011yescharacteristic
235C22×C127C2×#13711yescharacteristic
236C22×C127C2×#13711yescharacteristic
237C4×C127—21no—
238C4×C127—21no—
239C4×C127—22no—
240C4×C127—22no—
241C4×C127—22no—
242C4×C127—42no—
243C4×C127—41no—
244C4×C127—44no—
245C4×C127—41no—
246C4×C127—44no—
247C4×C127—81no—
248C4×C127—81no—
249#18333C12711yesmaximal, characteristic, direct product factor, Sylow
250C2×C127—21no—
251C2×C127—21no—
252C2×C127—42no—
253C2×C127—161no—
254C2×C127#300411yescharacteristic
255C2×C127#301811yescharacteristic
256C2×C127#302711yescharacteristic
257#3458C2×C12711yescharacteristic, complemented
258#3215C2×C12712yescomplemented
259#2610C2×C12711yescharacteristic
260#1605C2×C12712yescomplemented
261#1602C2×C12712yescomplemented
262#1599C2×C12712yescomplemented
263#1596C2×C12712yes—
264#1506C2×C12712yescomplemented
265#1464C2×C12711yescharacteristic, complemented
266C127#1833311yescharacteristic, direct product factor, Sylow
267#544—22no—
268#544—22no—
269#544—21no—
270#544C22×C12712yes—
271#543—21no—
272#543C22×C12712yes—
273#533—24no—
274#533—21no—
275#533C22×C12712yes—
276C2×#124C22×C12711yescharacteristic
277C2×#117—21no—
278C2×#117C22×C12711yescharacteristic
279#497—22no—
280#489—22no—
281#464—24no—
282#451C22×C12714yes—
283#450C22×C12714yes—
284#432C22×C12712yes—
285#395C22×C12711yescharacteristic
286#394C22×C12711yescharacteristic
287#393C22×C12711yescharacteristic
288#392C22×C12711yescharacteristic
289#390—21no—
290#388—21no—
291#388—21no—
292#386—21no—
293#376C22×C12711yescharacteristic
294#328C22×C12714yes—
295#328C22×C12714yes—
296#324C22×C12712yes—
297#323C22×C12712yes—
298C22×Q8C23×C12711yescharacteristic
299C22×D4—21no—
300C22×D4C23×C12711yescharacteristic
301C23×C4D4×C12711yescharacteristic
302C2×Q16—24no—
303C2×SD16—24no—
304C4⋊Q8—24no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—24no—
308C4⋊Q8D4×C12712yescomplemented
309C4⋊Q8D4×C12712yescomplemented
310#125—24no—
311#125—22no—
312#125—24no—
313#125—22no—
314#124—22no—
315#124—22no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8C23×C12714yes—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8D4×C12714yescomplemented
328#117—22no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117—22no—
333#117—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4D4×C12711yescharacteristic
338C2×C4⋊C4C23×C12711yescharacteristic
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4D4×C12711yescharacteristic
347C2×C22⋊C4C23×C12711yescharacteristic
348C2×C42—22no—
349C2×C42—21no—
350C2×C42D4×C12711yescharacteristic
351C2×C42C23×C12711yescharacteristic
352C4⋊C8—22no—
353#103—24no—
354#102—24no—
355C22⋊C8C23×C12714yes—
356#97—22no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95C23×C12711yescharacteristic
361#95C23×C12711yescharacteristic
362C24—21no—
363C24C2×D4×C12711yescharacteristic
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—81no—
369C2×Q8C2×D4×C12714yes—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—81no—
374C2×D4—81no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4C2×D4×C12711yescharacteristic
385C22×C4C2×D4×C12711yescharacteristic
386C22×C4C2×D4×C12711yescharacteristic
387C22×C4C2×D4×C12711yescharacteristic
388C22×C4C2×D4×C12711yescharacteristic
389C22×C4C24×C12711yescharacteristic
390Q16—84no—
391SD16—84no—
392C2×C8—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—81no—
407C4⋊C4C2×D4×C12714yes—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—42no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C42—24no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42—42no—
424C42C2×D4×C12712yes—
425C42C2×D4×C12712yes—
426C23—21no—
427C23—21no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23#137×C12712yes—
438C23C22×D4×C12711yescharacteristic
439Q8—44no—
440Q8—44no—
441Q8—82no—
442Q8—82no—
443Q8—82no—
444D4—44no—
445D4—84no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4#120×C12711yescharacteristic
472C2×C4#120×C12711yescharacteristic
473C2×C4#120×C12712yes—
474C2×C4#137×C12712yes—
475C2×C4C22×D4×C12712yes—
476C8—44no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×#120×C12711yescharacteristic
492C22C2×#137×C12711yescharacteristic
493C22C2×#137×C12711yescharacteristic
494C4—21no—
495C4—21no—
496C4—22no—
497C4—22no—
498C4—22no—
499C4—42no—
500C4—41no—
501C4—44no—
502C4—41no—
503C4—44no—
504C4—81no—
505C4—81no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—161no—
510C2C127×#300411yescharacteristic
511C2C127×#301811yescharacteristic
512C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radical#392×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
1. C127×#3458C2semidirect
2. C127×#3215C2semidirect
4. C127×#1605C2semidirect
5. C127×#1602C2semidirect
6. C127×#1599C2semidirect
8. C127×#1506C2semidirect
9. C127×#1464C2semidirect
51. C4⋊Q8×C127D4semidirect
52. C4⋊Q8×C127D4semidirect
70. C4×Q8×C127D4semidirect
249. #18333C127direct (N × H)
257. #3458C2×C127semidirect
258. #3215C2×C127semidirect
260. #1605C2×C127semidirect
261. #1602C2×C127semidirect
262. #1599C2×C127semidirect
264. #1506C2×C127semidirect
265. #1464C2×C127semidirect
266. C127#18333direct (N × H)
308. C4⋊Q8D4×C127semidirect
309. C4⋊Q8D4×C127semidirect
327. C4×Q8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34582
C127×#32152
C127×#26102
C127×#16052
C127×#16022
C127×#15992
C127×#15962
C127×#15062
C127×#14642
#18333127