Finite Group Databasebeta

← C127×#8376 #44572049

Subgroups — C127×#8376 #44572049

Order 32512.

1034 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C127C211yesmaximal, characteristic
2C127×#1823C212yesmaximal, complemented
3C127×#1799C211yesmaximal, characteristic, complemented
4C127×#1519C212yesmaximal, complemented
5C127×#1459C211yesmaximal, characteristic, complemented
6C22×#41×C127—21no—
7#547×C127—24no—
8#547×C127—24no—
9C2×C4⋊Q8×C127C411yescharacteristic, complemented
10C2×#123×C127—21no—
11C2×#123×C127—21no—
12C2×C22⋊Q8×C127—21no—
13C2×#121×C127C411yescharacteristic, complemented
14C2×#121×C127C2211yescharacteristic
15C2×C4×D4×C127C411yescharacteristic, complemented
16C2×C4×D4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C411yescharacteristic, complemented
18C22×C4⋊C4×C127C2211yescharacteristic
19C2×#99×C127—21no—
20C2×C22⋊C8×C127C2212yes—
21#380×C127C2212yes—
22#342×C127—21no—
23#340×C127—24no—
24#327×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C2×#41×C127—28no—
28C2×#41×C127—44no—
29C2×#41×C127—42no—
30C2×#41×C127—42no—
31C22×Q8×C127—21no—
32C22×D4×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127C2×C411yescharacteristic
35C22×D4×C127D411yescharacteristic
36C23×C4×C127—21no—
37C23×C4×C127—21no—
38C23×C4×C127—21no—
39C23×C4×C127C2×C411yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C22×C8×C127—22no—
42C4⋊Q8×C127—22no—
43C4⋊Q8×C127—22no—
44#123×C127—28no—
45#123×C127—28no—
46C22⋊Q8×C127—28no—
47#121×C127—22no—
48#121×C127—22no—
49#121×C127—22no—
50#121×C127D414yes—
51C4×D4×C127—22no—
52C4×D4×C127—22no—
53C4×D4×C127—22no—
54C4×D4×C127—22no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127—21no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127C2×C411yescharacteristic
63C2×C4⋊C4×C127C2×C411yescharacteristic
64C2×C4⋊C4×C127C2×C411yescharacteristic
65C2×C4⋊C4×C127D411yescharacteristic
66C2×C4⋊C4×C127D414yes—
67C2×C22⋊C4×C127—21no—
68C2×C22⋊C4×C127—21no—
69C2×C22⋊C4×C127—21no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127D411yescharacteristic
72C2×C22⋊C4×C127D411yescharacteristic
73C2×C42×C127C2×C411yescharacteristic
74#99×C127—42no—
75C22⋊C8×C127—22no—
76C22⋊C8×C127—22no—
77#95×C127—22no—
78C24×C127—21no—
79C24×C127C22⋊C411yescharacteristic
80C24×C127C2×D411yescharacteristic
81#41×C127—416no—
82#41×C127—416no—
83C2×Q8×C127—24no—
84C2×Q8×C127—42no—
85C2×Q8×C127—42no—
86C2×D4×C127—22no—
87C2×D4×C127—22no—
88C2×D4×C127—24no—
89C2×D4×C127—24no—
90C2×D4×C127—21no—
91C2×D4×C127—42no—
92C2×D4×C127—42no—
93C2×D4×C127—42no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—42no—
97C2×D4×C127C22⋊C412yes—
98C2×D4×C127D812yes—
99C2×D4×C127SD1612yes—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—24no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—42no—
109C22×C4×C127—42no—
110C22×C4×C127—42no—
111C22×C4×C127—42no—
112C22×C4×C127—42no—
113C22×C4×C127—41no—
114C22×C4×C127—41no—
115C22×C4×C127—42no—
116C22×C4×C127—42no—
117C22×C4×C127—42no—
118C22×C4×C127C22⋊C411yescharacteristic
119C22×C4×C127C22⋊C411yescharacteristic
120C22×C4×C127C22⋊C411yescharacteristic
121C22×C4×C127C22×C411yescharacteristic
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D411yescharacteristic
125C2×C8×C127—44no—
126C2×C8×C127—42no—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—24no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—21no—
132C4⋊C4×C127—24no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—44no—
135C4⋊C4×C127C22⋊C412yes—
136C4⋊C4×C127C22⋊C412yes—
137C4⋊C4×C127C22⋊C412yes—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—24no—
142C22⋊C4×C127—22no—
143C22⋊C4×C127—42no—
144C22⋊C4×C127—42no—
145C42×C127—21no—
146C42×C127—21no—
147C23×C127—21no—
148C23×C127—21no—
149C23×C127—22no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—41no—
153C23×C127—41no—
154C23×C127—42no—
155C23×C127—42no—
156C23×C127—41no—
157C23×C127—41no—
158C23×C127#10212yes—
159C23×C127C2×C22⋊C411yescharacteristic
160C23×C127#12012yes—
161C23×C127C2×D811yescharacteristic
162C23×C127C2×SD1611yescharacteristic
163C23×C127AGL(1,ℤ/8)12yes—
164Q8×C127—48no—
165D4×C127—24no—
166D4×C127—24no—
167D4×C127—42no—
168D4×C127—48no—
169D4×C127—44no—
170D4×C127—44no—
171D4×C127—42no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—24no—
175C2×C4×C127—22no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—41no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—48no—
185C2×C4×C127—48no—
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—44no—
193C2×C4×C127—44no—
194C2×C4×C127—42no—
195C2×C4×C127—41no—
196C2×C4×C127—41no—
197C2×C4×C127—82no—
198C2×C4×C127—82no—
199C2×C4×C127—82no—
200C2×C4×C127#10212yes—
201C2×C4×C127C2×C22⋊C411yescharacteristic
202C2×C4×C127C2×C22⋊C411yescharacteristic
203C2×C4×C127#12012yes—
204C8×C127—82no—
205C22×C127—21no—
206C22×C127—22no—
207C22×C127—21no—
208C22×C127—22no—
209C22×C127—22no—
210C22×C127—41no—
211C22×C127—41no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127—41no—
216C22×C127—41no—
217C22×C127—42no—
218C22×C127—42no—
219C22×C127—42no—
220C22×C127—82no—
221C22×C127—82no—
222C22×C127#37911yescharacteristic
223C22×C127C2×#10211yescharacteristic
224C22×C127#41811yescharacteristic
225C22×C127#44712yes—
226C22×C127#45012yes—
227C4×C127—22no—
228C4×C127—21no—
229C4×C127—22no—
230C4×C127—41no—
231C4×C127—41no—
232C4×C127—42no—
233C4×C127—42no—
234C4×C127—42no—
235C4×C127—162no—
236C4×C127#41012yes—
237#8376C12711yesmaximal, characteristic, direct product factor, Sylow
238C2×C127—22no—
239C2×C127—21no—
240C2×C127—21no—
241C2×C127—22no—
242C2×C127—42no—
243C2×C127—82no—
244C2×C127#178211yescharacteristic
245C2×C127#178611yescharacteristic
246C2×C127#179611yescharacteristic
247C2×#547C2×C12711yescharacteristic
248#1823C2×C12712yescomplemented
249#1799C2×C12711yescharacteristic, complemented
250#1519C2×C12712yescomplemented
251#1459C2×C12711yescharacteristic, complemented
252C127#837611yescharacteristic, direct product factor, Sylow
253C22×#41—21no—
254#547—24no—
255#547—24no—
256C2×C4⋊Q8C4×C12711yescharacteristic, complemented
257C2×#123—21no—
258C2×#123—21no—
259C2×C22⋊Q8—21no—
260C2×#121C4×C12711yescharacteristic, complemented
261C2×#121C22×C12711yescharacteristic
262C2×C4×D4C4×C12711yescharacteristic, complemented
263C2×C4×D4C22×C12711yescharacteristic
264C22×C4⋊C4C4×C12711yescharacteristic, complemented
265C22×C4⋊C4C22×C12711yescharacteristic
266C2×#99—21no—
267C2×C22⋊C8C22×C12712yes—
268#380C22×C12712yes—
269#342—21no—
270#340—24no—
271#327—24no—
272#324—21no—
273#323—21no—
274C2×#41—28no—
275C2×#41—44no—
276C2×#41—42no—
277C2×#41—42no—
278C22×Q8—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4C2×C4×C12711yescharacteristic
282C22×D4D4×C12711yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4C2×C4×C12711yescharacteristic
287C23×C4C23×C12711yescharacteristic
288C22×C8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291#123—28no—
292#123—28no—
293C22⋊Q8—28no—
294#121—22no—
295#121—22no—
296#121—22no—
297#121D4×C12714yes—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C2×C4×C12711yescharacteristic
310C2×C4⋊C4C2×C4×C12711yescharacteristic
311C2×C4⋊C4C2×C4×C12711yescharacteristic
312C2×C4⋊C4D4×C12711yescharacteristic
313C2×C4⋊C4D4×C12714yes—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4D4×C12711yescharacteristic
319C2×C22⋊C4D4×C12711yescharacteristic
320C2×C42C2×C4×C12711yescharacteristic
321#99—42no—
322C22⋊C8—22no—
323C22⋊C8—22no—
324#95—22no—
325C24—21no—
326C24C22⋊C4×C12711yescharacteristic
327C24C2×D4×C12711yescharacteristic
328#41—416no—
329#41—416no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—21no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—42no—
344C2×D4C22⋊C4×C12712yes—
345C2×D4D8×C12712yes—
346C2×D4SD16×C12712yes—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C22⋊C4×C12711yescharacteristic
366C22×C4C22⋊C4×C12711yescharacteristic
367C22×C4C22⋊C4×C12711yescharacteristic
368C22×C4C22×C4×C12711yescharacteristic
369C22×C4C2×D4×C12712yes—
370C22×C4C2×D4×C12712yes—
371C22×C4C2×D4×C12711yescharacteristic
372C2×C8—44no—
373C2×C8—42no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—44no—
382C4⋊C4C22⋊C4×C12712yes—
383C4⋊C4C22⋊C4×C12712yes—
384C4⋊C4C22⋊C4×C12712yes—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—24no—
389C22⋊C4—22no—
390C22⋊C4—42no—
391C22⋊C4—42no—
392C42—21no—
393C42—21no—
394C23—21no—
395C23—21no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—42no—
402C23—42no—
403C23—41no—
404C23—41no—
405C23#102×C12712yes—
406C23C2×C22⋊C4×C12711yescharacteristic
407C23#120×C12712yes—
408C23C2×D8×C12711yescharacteristic
409C23C2×SD16×C12711yescharacteristic
410C23AGL(1,ℤ/8)×C12712yes—
411Q8—48no—
412D4—24no—
413D4—24no—
414D4—42no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—42no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—48no—
431C2×C4—42no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4#102×C12712yes—
448C2×C4C2×C22⋊C4×C12711yescharacteristic
449C2×C4C2×C22⋊C4×C12711yescharacteristic
450C2×C4#120×C12712yes—
451C8—82no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—41no—
463C22—41no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22#379×C12711yescharacteristic
470C22C2×#102×C12711yescharacteristic
471C22#418×C12711yescharacteristic
472C22#447×C12712yes—
473C22#450×C12712yes—
474C4—22no—
475C4—21no—
476C4—22no—
477C4—41no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—41no—
482C4—162no—
483C4#410×C12712yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—42no—
489C2—82no—
490C2C127×#178211yescharacteristic
491C2C127×#178611yescharacteristic
492C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#547×C127C2
LCSG ▷ C22×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×#1823C2semidirect
3. C127×#1799C2semidirect
4. C127×#1519C2semidirect
5. C127×#1459C2semidirect
9. C2×C4⋊Q8×C127C4semidirect
13. C2×#121×C127C4semidirect
15. C2×C4×D4×C127C4semidirect
17. C22×C4⋊C4×C127C4semidirect
237. #8376C127direct (N × H)
248. #1823C2×C127semidirect
249. #1799C2×C127semidirect
250. #1519C2×C127semidirect
251. #1459C2×C127semidirect
252. C127#8376direct (N × H)
256. C2×C4⋊Q8C4×C127semidirect
260. C2×#121C4×C127semidirect
262. C2×C4×D4C4×C127semidirect
264. C22×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1272
C127×#18232
C127×#17992
C127×#15192
C127×#14592
#8376127