Finite Group Databasebeta

← C127×#19066 #44582739

Subgroups — C127×#19066 #44582739

Order 32512.

852 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3550C211yesmaximal, characteristic
2C127×#3237C211yesmaximal, characteristic, complemented
3C127×#3216C211yesmaximal, characteristic
4C127×#3162C211yesmaximal, characteristic, complemented
5C127×#1664C214yesmaximal, complemented
6C127×#1660C214yesmaximal, complemented
7C127×#1537C211yesmaximal, characteristic, complemented
8C127×#1531C211yesmaximal, characteristic, complemented
9C127×#1530C211yesmaximal, characteristic
10#563×C127C2214yes—
11#559×C127—21no—
12Q82×C127—21no—
13#556×C127—21no—
14#556×C127—21no—
15D4×Q8×C127—21no—
16D4×Q8×C127—21no—
17#542×C127—22no—
18#542×C127—22no—
19#536×C127—22no—
20#533×C127C2211yescharacteristic
21#533×C127C2211yescharacteristic
22#533×C127C2211yescharacteristic
23#532×C127C2211yescharacteristic
24#501×C127—21no—
25#501×C127—21no—
26#501×C127C2212yes—
27#501×C127C2212yes—
28#501×C127C2212yes—
29#497×C127C2212yes—
30#491×C127C2212yes—
31#489×C127C2212yes—
32#485×C127—22no—
33#477×C127—21no—
34#475×C127—21no—
35#462×C127—21no—
36#460×C127—21no—
37#452×C127—22no—
38#432×C127C2211yescharacteristic
39#432×C127C2211yescharacteristic
40#427×C127—22no—
41C2×#97×C127C2211yescharacteristic
42#330×C127C2214yes—
43#330×C127C2214yes—
44#329×C127C2214yes—
45C2×#41×C127D412yes—
46C22×Q8×C127—22no—
47C2×Q16×C127—22no—
48C2×SD16×C127—22no—
49C22×C8×C127—21no—
50C4⋊Q8×C127—22no—
51C4⋊Q8×C127—22no—
52C4⋊Q8×C127—24no—
53C4⋊Q8×C127D411yescharacteristic
54C4⋊Q8×C127D411yescharacteristic
55C4⋊Q8×C127D411yescharacteristic
56C4⋊Q8×C127D411yescharacteristic
57C4⋊Q8×C127D411yescharacteristic
58C4⋊Q8×C127C2311yescharacteristic
59C4⋊Q8×C127C2311yescharacteristic
60#127×C127D411yescharacteristic
61#126×C127—24no—
62#126×C127—24no—
63#125×C127—21no—
64#125×C127C2312yes—
65#125×C127C2312yes—
66#124×C127—24no—
67#124×C127—22no—
68#124×C127—22no—
69#124×C127C2312yes—
70#123×C127—24no—
71#123×C127—24no—
72C22⋊Q8×C127—22no—
73C22⋊Q8×C127—22no—
74C22⋊Q8×C127—21no—
75C22⋊Q8×C127—21no—
76C22⋊Q8×C127—21no—
77C22⋊Q8×C127—21no—
78C22⋊Q8×C127—24no—
79C22⋊Q8×C127—24no—
80C22⋊Q8×C127—21no—
81C22⋊Q8×C127—21no—
82#121×C127—21no—
83#121×C127—21no—
84C4×Q8×C127—22no—
85C4×Q8×C127—22no—
86C4×Q8×C127—21no—
87C4×Q8×C127—21no—
88C4×Q8×C127—21no—
89C4×Q8×C127—21no—
90C4×Q8×C127—21no—
91C4×Q8×C127—21no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—21no—
95C4×D4×C127—21no—
96#117×C127—22no—
97#117×C127—21no—
98#117×C127D412yes—
99#117×C127D412yes—
100C2×C42×C127C2311yescharacteristic
101#107×C127—22no—
102#107×C127—22no—
103#107×C127—22no—
104#106×C127—22no—
105#106×C127—22no—
106#106×C127—22no—
107C4⋊C8×C127—21no—
108C4⋊C8×C127—21no—
109#103×C127—22no—
110#103×C127—22no—
111#103×C127—22no—
112#102×C127—22no—
113C22⋊C8×C127—21no—
114C22⋊C8×C127—21no—
115#97×C127—21no—
116#97×C127C2312yes—
117#97×C127C2312yes—
118#97×C127C2312yes—
119#41×C127—82no—
120C2×Q8×C127—24no—
121C2×Q8×C127—21no—
122C2×Q8×C127—21no—
123C2×Q8×C127—21no—
124C2×Q8×C127—21no—
125C2×Q8×C127—21no—
126C2×Q8×C127—21no—
127C2×Q8×C127—84no—
128C2×Q8×C127C2×D412yes—
129C2×D4×C127—22no—
130C2×D4×C127—21no—
131C2×D4×C127—21no—
132C2×D4×C127C2×D412yes—
133C22×C4×C127—24no—
134C22×C4×C127—22no—
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138Q16×C127—82no—
139SD16×C127—82no—
140C2×C8×C127—24no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127—22no—
144C4⋊C4×C127—24no—
145C4⋊C4×C127—24no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—21no—
157C4⋊C4×C127—21no—
158C4⋊C4×C127—21no—
159C4⋊C4×C127—21no—
160C4⋊C4×C127—41no—
161C4⋊C4×C127—41no—
162C4⋊C4×C127C2×D412yes—
163C4⋊C4×C127C2×D412yes—
164C4⋊C4×C127C2×D412yes—
165C4⋊C4×C127C2×D412yes—
166C22⋊C4×C127—24no—
167C22⋊C4×C127—24no—
168C22⋊C4×C127—24no—
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—22no—
173C22⋊C4×C127—41no—
174C42×C127—24no—
175C42×C127—22no—
176C42×C127—22no—
177C42×C127—41no—
178C42×C127C2×D411yescharacteristic
179C42×C127C2×D411yescharacteristic
180C42×C127C2×D411yescharacteristic
181C42×C127C2411yescharacteristic
182C23×C127—22no—
183C23×C127#12011yescharacteristic
184Q8×C127—42no—
185Q8×C127—42no—
186Q8×C127—42no—
187Q8×C127—42no—
188Q8×C127—41no—
189Q8×C127—41no—
190Q8×C127—42no—
191Q8×C127—42no—
192Q8×C127—84no—
193D4×C127—42no—
194D4×C127—42no—
195D4×C127—42no—
196D4×C127—82no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—41no—
204C2×C4×C127—41no—
205C2×C4×C127—44no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—84no—
209C2×C4×C127#12011yescharacteristic
210C2×C4×C127#12011yescharacteristic
211C2×C4×C127#12011yescharacteristic
212C2×C4×C127C22×D411yescharacteristic
213C2×C4×C127C22×D411yescharacteristic
214C2×C4×C127C22×D411yescharacteristic
215C8×C127—24no—
216C8×C127—42no—
217C8×C127—42no—
218C22×C127—21no—
219C22×C127—21no—
220C22×C127—21no—
221C22×C127—42no—
222C22×C127—42no—
223C22×C127—42no—
224C22×C127C2×#12011yescharacteristic
225C4×C127—21no—
226C4×C127—21no—
227C4×C127—21no—
228C4×C127—21no—
229C4×C127—21no—
230C4×C127—42no—
231C4×C127—42no—
232C4×C127—42no—
233C4×C127—42no—
234C4×C127—42no—
235C4×C127—81no—
236C4×C127—81no—
237C4×C127#45612yes—
238#19066C12711yesmaximal, characteristic, direct product factor, Sylow
239C2×C127—41no—
240C2×C127—82no—
241C2×C127C2×#45611yescharacteristic
242C2×C127#301911yescharacteristic
243C2×C127#302011yescharacteristic
244#3550C2×C12711yescharacteristic
245#3237C2×C12711yescharacteristic, complemented
246#3216C2×C12711yescharacteristic
247#3162C2×C12711yescharacteristic, complemented
248#1664C2×C12714yescomplemented
249#1660C2×C12714yescomplemented
250#1537C2×C12711yescharacteristic, complemented
251#1531C2×C12711yescharacteristic, complemented
252#1530C2×C12711yescharacteristic
253C127#1906611yescharacteristic, direct product factor, Sylow
254#563C22×C12714yes—
255#559—21no—
256Q82—21no—
257#556—21no—
258#556—21no—
259D4×Q8—21no—
260D4×Q8—21no—
261#542—22no—
262#542—22no—
263#536—22no—
264#533C22×C12711yescharacteristic
265#533C22×C12711yescharacteristic
266#533C22×C12711yescharacteristic
267#532C22×C12711yescharacteristic
268#501—21no—
269#501—21no—
270#501C22×C12712yes—
271#501C22×C12712yes—
272#501C22×C12712yes—
273#497C22×C12712yes—
274#491C22×C12712yes—
275#489C22×C12712yes—
276#485—22no—
277#477—21no—
278#475—21no—
279#462—21no—
280#460—21no—
281#452—22no—
282#432C22×C12711yescharacteristic
283#432C22×C12711yescharacteristic
284#427—22no—
285C2×#97C22×C12711yescharacteristic
286#330C22×C12714yes—
287#330C22×C12714yes—
288#329C22×C12714yes—
289C2×#41D4×C12712yes—
290C22×Q8—22no—
291C2×Q16—22no—
292C2×SD16—22no—
293C22×C8—21no—
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C4⋊Q8—24no—
297C4⋊Q8D4×C12711yescharacteristic
298C4⋊Q8D4×C12711yescharacteristic
299C4⋊Q8D4×C12711yescharacteristic
300C4⋊Q8D4×C12711yescharacteristic
301C4⋊Q8D4×C12711yescharacteristic
302C4⋊Q8C23×C12711yescharacteristic
303C4⋊Q8C23×C12711yescharacteristic
304#127D4×C12711yescharacteristic
305#126—24no—
306#126—24no—
307#125—21no—
308#125C23×C12712yes—
309#125C23×C12712yes—
310#124—24no—
311#124—22no—
312#124—22no—
313#124C23×C12712yes—
314#123—24no—
315#123—24no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326#121—21no—
327#121—21no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—21no—
340#117—22no—
341#117—21no—
342#117D4×C12712yes—
343#117D4×C12712yes—
344C2×C42C23×C12711yescharacteristic
345#107—22no—
346#107—22no—
347#107—22no—
348#106—22no—
349#106—22no—
350#106—22no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353#103—22no—
354#103—22no—
355#103—22no—
356#102—22no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359#97—21no—
360#97C23×C12712yes—
361#97C23×C12712yes—
362#97C23×C12712yes—
363#41—82no—
364C2×Q8—24no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—84no—
372C2×Q8C2×D4×C12712yes—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4C2×D4×C12712yes—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4C2×D4×C12711yescharacteristic
380C22×C4C2×D4×C12711yescharacteristic
381C22×C4C2×D4×C12711yescharacteristic
382Q16—82no—
383SD16—82no—
384C2×C8—24no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C12712yes—
407C4⋊C4C2×D4×C12712yes—
408C4⋊C4C2×D4×C12712yes—
409C4⋊C4C2×D4×C12712yes—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—41no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—41no—
422C42C2×D4×C12711yescharacteristic
423C42C2×D4×C12711yescharacteristic
424C42C2×D4×C12711yescharacteristic
425C42C24×C12711yescharacteristic
426C23—22no—
427C23#120×C12711yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—41no—
433Q8—41no—
434Q8—42no—
435Q8—42no—
436Q8—84no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—82no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—84no—
453C2×C4#120×C12711yescharacteristic
454C2×C4#120×C12711yescharacteristic
455C2×C4#120×C12711yescharacteristic
456C2×C4C22×D4×C12711yescharacteristic
457C2×C4C22×D4×C12711yescharacteristic
458C2×C4C22×D4×C12711yescharacteristic
459C8—24no—
460C8—42no—
461C8—42no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22C2×#120×C12711yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—81no—
481C4#456×C12712yes—
482C2—41no—
483C2—82no—
484C2C2×#456×C12711yescharacteristic
485C2C127×#301911yescharacteristic
486C2C127×#302011yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ 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×#3237C2semidirect
4. C127×#3162C2semidirect
5. C127×#1664C2semidirect
6. C127×#1660C2semidirect
7. C127×#1537C2semidirect
8. C127×#1531C2semidirect
238. #19066C127direct (N × H)
245. #3237C2×C127semidirect
247. #3162C2×C127semidirect
248. #1664C2×C127semidirect
249. #1660C2×C127semidirect
250. #1537C2×C127semidirect
251. #1531C2×C127semidirect
253. C127#19066direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35502
C127×#32372
C127×#32162
C127×#31622
C127×#16642
C127×#16602
C127×#15372
C127×#15312
C127×#15302
#19066127